i
EFFECTS OF VERTICAL GROUND MOTION INTENSITY
ON HYBRID RETAINING WALLS
by
Otgontulga Suidiimanan
B.S., Mongolian Technical University, 1993
M.S., Mongolian Technical University, 1995
f
A thesis submitted to the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Civil Engineering
2002
r
This thesis for the Master of Science
degree by
Otgontulga Suidiimanan
has been approved
by
*2
Date
Otgontulga Suidiimanan (M.S., Civil Engineering)
Effects of Vertical Ground Motion Intensity on Hybrid Retaining Walls
Thesis directed by Professor NienYin Chang
ABSTRACT
During last five years a hybrid retaining wall system has been investigated
by Professor NienYin Chang and Dr. ShingChun Trever Wang at the Center for
Geotechnical Engineering Science (CGES), University of the Colorado at Denver.
A hybrid wall adopts the features of continuous rigid facing from conventional
retaining wall and reinforcement in the backfill from MSE retaining wall. It is a
remarkable innovation of the retaining wall system.
This thesis study was a continuation of previous research and focused on
effects of vertical ground motion, real time history analysis, wall height and wall
geogrid connection conditions for a 10 and 20m hybrid retaining walls. Numerical
analysis of hybrid retaining wall system was performed using the NDCE3D finite
element method computer program. Imperial Valley earthquake in both horizontal
and vertical motion were selected as seismic loads. Real time history analyses
were examined on 10m wall under ah=0.687g and ah=0.687g; av=0.408g motion
using the GRIZ postprocessor, where ah and av are horizontal and vertical peak
ground acceleration.
m
Analysis results responded coefficient of vertical acceleration is one of the
essential factors for the seismic resistant retaining wall. However, conventional
externally stabilized wall and in the MononobeOkabe method were not assumed
reinforcement in the backfill, neglecting vertical ground motion effect for the
calculation of the seismic resultant force and their results could be wrong. This
thesis study could consequently initiate first analysis of vertical acceleration effect
on hybrid retaining wall.
This abstract accurately represents the content of the candidates thesis. I
recommend its publication.
Signed
IV
ACKNOWLEDGEMENT
This thesis was performed under the supervision of Professor NienYin
Chang and Dr. ShingChun Trever Wang. I am grateful for their guidance, support
and encouragement throughout my study at the University of Colorado at Denver.
I also would like to thank Professor John R. Mays for serving on the final
examination committee.
Dr. NienYin Chang, Director of Center for Geotechnical Engineering
Science (CGES) has established a collaborative agreement with Dr. Mike Puso at
the Lawrence Livermore National Laboratory (LLNL), which allows the access to
the NTKE3D source code for further development and its use in the nonlinear
analysis of difficult soilstructure interaction problems. I would like to express my
great appreciation for the permission to use the NIKE3D program. Gratitude is
also extended to our NIKE/SSI group members for sharing knowledge and
information, particularly Dr. Fatih Oncul and Mr. Kevin ZehZon Lee.
The financial support from the Government of Mongolia and Department
of Civil Engineering at the University of Colorado at Denver in the forms of
tuition scholarship and research assistantship through various CDOT research
projects is also greatly appreciated.
Finally, I would like to thank to my father Suidiimanan Sodov, mother
Orolmaa Sanjmyatav, wife Narantuya Amarbayar son Hashkhuu and Mitchell for
their unfaltering understanding and support while I was working on my thesis.
CONTENTS
Figures...............................................................xii
Tables................................................................xvi
Chapter
1. Introduction.........................................................1
1.1 Problem Statement...................................................1
1.2 Objective...........................................................2
1.3 Research Approach...................................................2
1.4 Engineering Significance............................................4
2. Literature Reviews...................................................5
2.1 Introduction........................................................5
2.2 MononobeOkabe Method..............................................5
2.2.1 Revision to MononobeOkabe Method.................................9
2.3 Seismic Analysis of MSE Segmental Retaining Walls.................11
2.3.1 Potential Failure Modes..........................................12
2.3.2 Seismic Performance of MSE Walls
with Full Eleight Rigid Facing...................................14
vii
2.4 Summary of Seismic Pressure Evaluation Method by
Victor Elias, Barry R. Christopher and Ryan B. Berg (2001)..........16
3. Theoretical Background of NIKE3D Program............................24
3.1 Implementation of NIKE3D Program....................................24
3.2 Interface Formulation..............................................25
3.3 Material Models of NIKE3D..........................................26
3.3.1 RambergOsgood Nonlinear Model....................................27
3.4 Eigenvalue Analysis and Rayleigh Damping...........................28
4. Analysis Program and Input Parameters...............................29
4.1 Purpose...........................................................29
4.2 Input Parameters...................................................30
4.2.1 Applied Loading...................................................30
4.2.2 Wall Geometries...................................................32
4.2.3 Boundary Conditions............................................. 33
4.2.4 Sliding Interfaces................................................38
4.2.5 Material Models and Parameters....................................40
5. Presentation and Interpretations of Analysis Results................45
5.1 Introduction...................................................... 45
5.2 Time Histories of Resultant Earth Pressure,
Resultant OTM and Moment Arm........................................47
viii
5.3 Time Histories of Resultant Bearing Pressure,
OTM and Moment Arm................................................50
5.4 Time Histories of Wall Forward Displacement......................52
5.5 Time Histories of Resultant Inclusion Stress
and Overturning Moment............................................54
5.6 Maximum Stresses, Resultants, Shear and Moment
Imparted on Concrete Wall Section.................................56
5.7 Maximum Bearing Pressure.........................................60
5.8 Maximum Wall Deformation.........................................64
5.9 Maximum Inclusion Stress.........................................66
6. Discussion of Results.............................................69
6.1 Introduction......................................................69
6.2 Transient Performance of 10m wall under ah=0.687g Motion........69
6.2.1 Earth Pressure..................................................70
6.2.2 Bearing Pressure................................................73
6.2.3 Wall Deformation................................................75
6.2.4 Inclusion Stress................................................76
6.2.5 Summary.........................................................79
6.3 Transient Performance of 10m wall
under ah=0.687g and av=0.408g Motion..............................80
6.3.1 Earth Pressure..................................................80
ix
6.3.2 Bearing Pressure................................................81
6.3.3 Wall Deformation......:.........................................81
6.3.4 Inclusion Stress.................................................81
6.3.5 Summary..........................................................87
6.4 Effect of Wall Height............................................88
6.4.1 Earth Pressure...................................................88
6.4.2 Bearing Pressure.................................................91
6.4.3 Wall Deformation.................................................93
6.4.4 Inclusion Connection Stress......................................95
6.5 Effect of Ground Motion Intensity.................................99
6.5.1 Earth Pressure...................................................99
6.5.2 Bearing Pressure................................................100
6.5.3 Wall Deformation................................................101
6.5.4 Maximum Connection Stress.......................................101
6.6 Effect of Inclusion Connection Condition.........................102
6.6.1 Earth Pressure..................................................102
6.6.2 Bearing Pressure................................................104
6.6.3 Wall Deformation................................................106
6.6.4 Inclusion Stress................................................108
6.7 Comparison FEM Results with Conventional
Method and Current Design Specification 2001......................Ill
x
6.7.1 Comparison Results of M0 Method with NIKE3D...................Ill
6.7.2 Comparison Results of NIKE3D
with Current Design Guideline 2001...........................112
7. Summary, Conclusions and Recommendation for Future Study..........120
7.1 Summary........................................................120
7.2 Conclusions....................................................121
7.3 Recommendation for Future Studies..............................124
Appendix
A1. Transient Analysis of 10m wall under 1,5H Motion................126
A2. Transient Analysis of 10m wall under 1.5H+3V Motion.............141
B. Lateral Earth Pressure Distribution Behind Concrete Wall Section.155
C. Bearing Pressure Distribution Beneath the Wall Footing.........160
D. Wall Face Deformation..........................................165
El. Inclusion Stress Distribution for 10m Wall....................170
E2. Inclusion Stress Distribution for 20m Wall....................213
F. Coulomb and MononobeOkabe Active Thrust
Calculation Spreadsheet.........................................326
References.........................................................329
xi
FIGURES
Figure
2.1 Forces acting on active wedge in MononobeOkabe analysis.........6
2.2 Forces acting on passive wedge in MononobeOkabe analysis........6
2.3 Total earth pressure distribution due to soilweight............10
2.4 Typical geosynthetic reinforced retaining wall
with segmental facing...........................................13
2.5 Potential failure modes of MSE segmental retaining wall.........13
2.6 Staged construction procedure for FHR facing retaining wall.....15
2.7 Typical MSE retaining wall with FHR facing......................15
2.8 Seismic externally stability of a MSE wall......................17
2.9 Contour map of horizontal acceleration coefficient..............18
2.10 Seismic internal stability of a MSE wall........................23
4.1 Loading curves adopted in NIKE3D analysis.......................31
4.2. a 10m wall dimensions and materials .............................34
4.2. b 10m wall finite element mesh ..................................35
4.3. a 20m wall dimensions and materials .............................36
4.3. b 20m wall finite element mesh ..................................37
4.4 Boundary conditions used in analysis............................38
5.1 Selected nodal points for analysis result presentation .........47
xii
5.2 Time history of lateral earth pressure net thrust..................49
5.3 Time history of lateral earth pressure net OTM ....................49
5.4 Time history of moment arm of earth pressure.......................49
5.5 Time history of bearing pressure net thrust N......................51
5.6 Time history of bearing pressure net OTM ..........................51
5.7 Time history of bearing pressure net moment arm....................51
5.8. a Time history of wall forward displacement (at bottom).............53
5.8. b Time history of wall forward displacement (at top)................54
5.9 Time history of inclusion net thrust...............................56
5.10 Time history of inclusion net OTM...................................56
5.11 Static and dynamic earth pressure distribution
imparted on 20m wall under ah=0.458g Motion.......................59
5.12 Net thrusts imparted on 20m wall under ah=0.458g Motion...........61
5.13 Shear and moment diagram for 20m wall.............................62
5.14 Example of resultant static and dynamic thrusts
and their point applications for 20m wall.........................63
5.15 Example of bearing pressure distributions for 20m wall............63
5.16 Static and dynamic resultant bearing pressures
and resultant overturning moments for 20m wall....................64
5.17 Wall displacement for 20m wall under ah=0.458g Motion.............65
5.18a Maximum dynamic inclusion stresses for 10m wall...................67
xiii
5.18b Maximum dynamic inclusion stresses for 20m wall
68
6.1 Synchronization of maximum earth pressure
with horizontal peak ground acceleration .........................72
6.2 Synchronization of maximum bearing pressure
with horizontal peak ground acceleration..........................73
6.3 Synchronization of maximum deformation
with horizontal peak ground acceleration..........................75
6.4 Synchronization of maximum inclusion stress
with horizontal peak ground acceleration..........................77
6.5 Synchronization of maximum earth pressure
with horizontal peak ground acceleration..........................82
6.6 Time histories of bearing pressure.................................84
6.7 Synchronization of maximum wall deformation
with horizontal peak ground acceleration..........................85
6.8 Synchronization of maximum inclusion stress
with horizontal peak ground acceleration..........................86
6.9 Earth pressure distribution for 10 and 20m walls..................89
6.10 Bearing pressure distribution for 10m wall........................92
6.11 Bearing pressure distribution for 20m wall attached case..........92
6.12 Wall forward displacement for 10 and 20m walls....................94
6.13 Inclusion connection stress for 10m wall..........................96
xiv
6.14 Inclusion connection stress for 20m wall attached case............96
6.15 Seismic induced earth pressure.....................................99
6.16 Seismic induced bearing pressure..................................100
6.17 Seismic induced forward displacement............................. 101
6.18 Seismic induced maximum connection stress.........................101
6.19 Earth pressure distribution for 20m wall (attached & detached)...103
6.20 Bearing pressure distribution for 20m wall attached case.........105
6.21 Bearing pressure distribution for 20m wall detached case.........105
6.22 Forward displacement for 20m wall (attached & detached)..........107
6.23 Dynamic inclusion stress (att) 20m wall under horizontal motion ..109
6.24 Dynamic inclusion stress (det) 20m wall under horizontal motion... 110
6.25 MO maximum earth pressure........................................117
6.26 AASFITO maximum earth pressure....................................117
6.27 NIKE3D maximum earth pressure.....................................117
6.28 Resultant OTM at wall base for 10m wall..........................118
6.29 Resultant thrust imparted on wall for 10m wall...................118
6.30 Point application from wall base for 10m wall....................118
6.31 Resultant OTM at wall base for 20m wall..........................119
6.32 Resultant thrust imparted on wall for 20m wall...................119
6.33 Point application from wall base for 20m wall....................119
xv
TABLES
Table
4.1 All analysis table..............................................30
4.2 Results of RAMBO program for average sand of 125 psf............42
4.3 Mechanical properties of commercially available geogrid.........43
4.4 Input material parameters for the thesis study..................44
6.1 Resultant earth pressure for 10 and 20m walls..................90
6.2 Resultant bearing pressure for 10 and 20m walls................93
6.3 Resultant displacement for 10 and 20m walls....................95
6.4 Inclusion connection stress for 10m wall.......................97
6.5 Inclusion connection stress for 20m wall ......................97
6.6 Resultant earth pressure for attached and detached case........103
6.7 Resultant bearing pressures for attached and detached case.....106
6.8 Deformation and tilts for attached and detached case...........108
6.9 Results of MononobeOkabe method...............................113
6.10 Results of NIKE3D analysis.....................................114
6.11 Results of current design guideline 2001.......................115
xvi
1. Introduction
1.1 Problem Statement
Retaining wall serves principally to support or resist lateral earth and water
pressure. It can be found almost everywhere in civil related work, highway
retaining walls, bridge abutments, building basement walls, earth dams, and
waterfront bulkhead. Conventionally retaining walls are divided into two major
groups, externally and internally stabilized walls. The externally stabilized walls
include gravity and semigravity wall, cantilever wall, and sheet pile wall. The
internally stabilized walls include wrapped around walls, mechanically stabilized
earth (MSE) segmental walls, geosynthetic reinforced soil (GRS) walls. Typically
advantages of internally stabilized MSE and GRS walls are low material cost,
short construction period, and ease of construction. Externally stabilized
conventional retaining walls require less excavation, however they are usually cost
more.
The Center for Geotechnical Engineering Science at University of
Colorado at Denver has devoted the last four years of its research effort on a
hybrid retaining wall system that combined advantage of externally and internally
stabilized walls subjected to seismic loading. This study continues the previous
research and focuses more on the effect of horizontal and vertical acceleration
intensities, wall heights and wallgeogrid connection conditions.
1
1.2 Objective
The objectives of this thesis study are to numerically examine the seismic
responses of 10 and 20m hybrid retaining walls and further to formulate the
guidelines for the design. The study is focused on the effect of the combination of
horizontal and vertical ground motion, wall height and wall stem, inclusion
connection on the seismic wall response. Finite element method computer program
named NIKE3D was used as a numerical analysis tool for this study. The Imperial
Valley ground motion time histories in both vertical and horizontal directions were
adopted in this study as a seismic loads. A total sixteen cases of analysis were
analyzed by NIKE3D program. All results were outputted by the GRIZ
postprocessor of NIKE3D, and subsequently analyzed to interpret the responses of
the hybrid retaining wall system.
1.3 Research Approach
Nonlinear finite element analyses were performed to assess the effects of
wall height, ground motion intensity, vertical components of ground motion, and
wallgeogrid connection conditions on the performance of hybrid MSE walls. An
extensive finite element analysis program was carried out using NIKE3D
computer code developed at the Lawrence Livermore National Laboratory
(LLNL). NIKE3D has an implicit formation, excellent interface formulation and
solution algorithm, and large number of material models. Its implicit formulation
2
produces stable solutions. Dr. NienYin Chang, Director of the Center for
Geotechnical Engineering Science (CGES) at the University of Colorado at
Denver has a collaborative agreement with the Lawrence Livermore National
Laboratory, University of California, and Berkeley. The agreement allows Dr.
Changs research group the use and further development of NIKE3D under the
condition that all improvement must be shared with the LLNL and all associated
institutions and agencies.
The performance of 10 and 20meter walls were investigated. The
isotropic linear elastic model is adopted for the TensarGeogrid, foundation soils
and concrete wall, the RambergOsgood model used for backfill soils. Both the
horizontal and vertical components of the 10/15/1979 Imperial Valley Earthquake
were used in the analysis. The former has a peak ground acceleration of 0.458G
and the latter has a peak ground acceleration of 0.136G. To study the effect of the
ground motion intensity, scaled motion records were also used with the scaling
factor of 1.0 and 1.5 for the horizontal component and 1.0, 2.0 and 3.0 for the
vertical component. Two different connection conditions were tried: connected
and detached were investigated.
Results of analyses in terms of earth pressure along the rear wall face, wall
base bearing pressure, wall displacements, and inplane stresses of Tensor geogrid;
wallgeogrid connection stresses were presented in figures and summarized in
tables. The contemporary approach of MononobeOkabe and current design
3
guideline 2001 were used to compute seismicinduced earth pressures, resultant
thrusts, and overturning moments. Comparisons were made on wall performance
and conclusions drawn. Finally, the major findings were summarized in the
concluding remarks and areas needing further study were recommended.
1.4 Engineering Significance
The retaining wall forms an integral part of bridge substructure and
elevated roadway support. Its performance under both gravitational and seismic
loads is of particular importance in a seismically active region. This study
provides an insight into the capability of a hybrid wall in resisting the seismic
force of different magnitudes. It also investigates the effect of the vertical seismic
ground motion on the performance of walls of different heights. The technical
information reveals in this study constitutes a large step in the seismic design of
retaining structures.
4
2. Literature Reviews
2.1 Introduction
In this literature review, three areas were discussed. First, Mononobe
Okabe method and its improvement on the seismic analysis of conventional
retaining wall design were reviewed. Second, the seismic performance of MSE
segmental retaining wall and MSE wall with full height rigid (FHR) facing is
explored. Potential failure modes of segmental retaining wall, construction stages
of FHR facing retaining wall were also included the second item. Finally, the
2001 design guideline for seismic analysis of MSE walls proposed by Victor Elias,
Barry R. Christoper and Ryan R.Berg was summarized.
2.2 MononobeOkabe Method
The MononobeOkabe method most frequently used for the calculation of
the net seismic soil thrust acting on a retaining structure. Mononobe and Okabe
were developed static earth pressure theory in 1929s. The MononobeOkabe
analysis is an extension of the Coulomb slidingwedge theory, taking into account
horizontal and vertical psuedostatic acceleration induced inertial forces acting on
the soil. A scheme of force equilibrium wedge is shown in Figure 2.1. Psuedo
static accelerations acting on the wedge mass are horizontal component of peak
5
ground acceleration, (ah=khG) vertical component of peak ground acceleration,
(av=kvG), where G is the gravitational acceleration.
Figure 2.1 Forces acting on active wedge in MononobeOkabe analysis
(after Kramer 1996)
Figure 2.2 Forces acting on passive wedge in MononobeOkabe analysis
(after Kramer 1996)
6
In an active earth pressure condition, active thrust with effect of earthquake PAe
from force equilibrium wedge can be determined following equation.
PAE=0.5KAEyH2(lkv) (2.1)
y is unit weight of the backfill, and H is the total wall height. KAe the dynamic
active earth pressure coefficient and is given by Equation 2.2.
COS2((p0y)
kae=
cosy cos20cos(8 + 0 + y)
1+ I sin(8 + (p)sin(cp (3 y)
y cos(5 + 0 + y)cos(P 0)
(2.2)
where: y, and y = arctan [kh/(lkv)], y is seismic inertia angle, is the soil
friction angle, 8 is the wallsoil interface friction angle. aAÂ£ is the critical failure
surface angle inclined from the horizontal direction. aAÂ£ in the static case can be
found by following Equation 2.3.
aAE=y+tan'1[( tan(
where
C1E = ^/tan((j> y P) [tan(cp y P) + cot(cp y 0)] [ 1 + tan(8 + y+0)cot(cp y 0)]
C2E = 1 + tan(8 + y + 0)[tan((p y P) + cot(cp y 0)]
The location of the resultant active thrust PAÂ£ from soil to retaining wall in
MononobeOkabe method is the same as the static Coulomb theory, and resultant
force acts at the height of H/3 from the wall base. Where H is the total wall height.
The resultant active thrust PAÂ£has two components: static and dynamic.
7
(2.4)
where: PA is static component of active thrust, APae is dynamic component of
active thrust. Seed and Whitman (1970) suggested that dynamic component acts at
approximately 0.6H. With known locations of static and dynamic thrust, we could
determine the location of resultant active thrust PAE by Equation 2.5.
where: h is the height of application above the wall base.
In the passive earth pressure condition, the horizontal component of
earthquake peak acceleration has reversed direction as shown in Figure 2.2. The
passive soil thrust PPE can be determined from force equilibrium wedge by
Equation 2.6 for the cohesionless backfill.
Kpe the dynamic passive earth pressure coefficient and is given by Equation 2.7.
PaH/3 + APae(0.6H)
(2.5)
Ppe =0.5Kpe yH2(lkv)
(2.6)
cos2(q> + 0\[/)
(2.7)
cost)/ cos20cos(8 + 9 + \/) 1 +
sin(S + cp)sin(cp + p\/)
cos(8 0 + v/)cos((3 0)
aPE is the critical failure surface angle inclined from the horizontal direction for the
passive condition. aPE can be calculated from Equation 2.8.
8
tan(cp + \j/ + (3) + C3E
(2.8)
aPE = \/q> + tan
C
4E
where
C3E = ^/tan((p + 0 \/)[tan((() + (3 v/) + cot((p t 0 t tan(5 + \\t 0)cot(q> + 0 \/)]
C4E = 1 + tan(8 + \/ 0)[tan(
The passive soil thrust has two components just like active thrust. One is static
(Pp), and other is dynamic component of soil thrust ( APpe ). The resultant passive
thrust PpE, can be determined by Equation 2.9.
Ppe=Pp+APpe (2.9)
The advantage of MononobeOkabe method is that a designer can obtain closed
form solution for total dynamic earth thrust, but not distribution of the lateral earth
pressure with depth.
2.2.1 Revision to MononobeOkabe Method
The improvements to the MononobeOkabe analysis by Seed and Withman
(1970), Richard and Elms (1979), and Bathurst and Cai (1995) were described in
the detail. Seed and Withman (1970) concluded that vertical accelerations could be
ignored when MononobeOkabe method is used to estimate PAe for typical wall
design. The backfill is unsaturated, so that liquefaction problem will not arise.
9
Figure 2.3 shows the total active dynamic pressure distribution due to soil
self weight proposed by Bathurst and Cai (1995). This total earth pressure
distribution is used in the seismic design of externally and internally stabilized
MSE walls. The point application of resultant total earth force depends on the
magnitude of dynamic earth pressure coefficient AKAe, and the location varies
over the range of l/3
to the wall height.
a) static component b) dynamic component c) total pressure distribution
Figure 2.3 Total earth pressure distributions due to soilweight
Dynamic active earth pressure coefficient Kae is the sum of static and dynamic
earth pressure coefficient.
O.SAKapyH
0.8AKA.yU
l
kae =ka + AKae
(2.10)
10
Once KAe and KA are known AKAe can be determined from Equation 2.10 by
subtraction of total and active earth pressure coefficients.
Horizontal peak ground acceleration coefficient kh is the key parameter of
the MononobeOkabe method. Selecting this seismic coefficient is a major issue
the seismic design of earth structure. Currently, there is no consensus view on
selecting a design value for kh. Bonaparte et al. (1986) suggested kh = 0.85Am/G for
reinforced slopes using MononobeOkabe method. Am is magnitude of the peak
ground acceleration. Whitman (1990) recommended value of kh could rangel/3 to
1/2 of the Am, which correspond to 0.05 to 0.15. AASHTO (1996) uses an
equation kh = 0.85 Am /G Am /G. In the 2001 AASHTO specifications, it is
recommended that kh=Am = (1.45A)* A where A is maximum earthquake
acceleration coefficient comes from AASHTO Division 1A contour map. In the
current design practice, the selection of kh is very important for the seismic design,
and its selection based on the engineering judgment, experience, and local
regulations.
2.3 Seismic Analysis of MSE Segmental Retaining Walls
In the recent years, segmental retaining walls with geosynthetic
reinforcement have been used widely in earth retaining structure construction.
A typical geosynthetic reinforced wall with segmental block facing, general view
is shown in Figure 2.4. The greatest advantages of MSE walls with block facing
11
are rapid construction, low cost, cheap labor, and less construction deformation. A
large number of these geosynthetic reinforced segmental retaining walls has been
built in seismically active areas. Based on observations in seismically active zone,
MSE structures have been demonstrated a higher resistance to seismic induced
loading than rigid concrete structures. Methods of analysis and design for
segmental retaining wall have been developed to ensure stability and tolerable
displacement under seismic loading (Bathrust et al. 1997; Ling et al. 1997).
2.3.1 Potential Failure Modes
Potential failure modes of reinforced segmental retaining wall under
seismic loading are shown in Figure 2.5. There are three general categories of
failure modes: the external failure modes, internal failure modes, and the facing
failure modes. External failure modes are base sliding, overturning about the toe,
and bearing capacity failure. Internal failure modes, include pullout, tensile over
stress, and internal sliding which occur within the reinforced soil mass. The third
category of failure modes, the facing failure consists of connection failure, column
shear failure, and toppling failure. The shear capacity in facing column can be
developed through interface friction between block and concrete keys and steel bar
connection through the facing hole in the vertical direction.
12
Figure 2.4 Typical geosynthetic reinforced retaining wall with segmental facing
(o) base sliding
(external foilure mode)
(d) pullout
(internal failure mode)
(g) connection failure
(focing failure mode)
(b) overturning
(ewternol failure mode)
(excessive settlement)
(externol foilure mode)
(e) tensile overstress
(internal foilure mode)
(f) internal sliding
(inlernol failure mode)
(h) column shear failure
(facing
(0 toppling
(facing failure mode)
Figure 2.5 Potential failure modes of MSE segmental retaining wall (after
Bathurst et al. 1997)
13
2.3.2 Seismic Performance of MSE Walls
with Full Height Rigid Facing
MSE walls and GRSW with full height rigid (FHR) facing have been
constructed in Japan since the last decade. These retaining walls serve as
embankments, bridge abutments, and support for train trucks in Japanese railways.
Figure 2.6 illustrates the staged construction of FHR facing wall. The construction
involves (1) a small foundation for the facing, (2) wraparound wall consists of
gravelfilled bag placed at the shoulder of each layer, and (3) a thin lightly steel
reinforced concrete facing connected to the geosynthetic reinforced soil wall. Note
that retaining wall with cohesionless soil use geogrid as the tensile inclusion
reinforcement. The vertical spacing between the reinforcement layers is about 30
cm, maximum thickness of wall stem 30 cm, anchorage length from 0.1 to 0.4 of
the wall height. A typical layout with the components of geosynthetic reinforced
soil retaining wall with full height rigid facing is shown in Figure 2.7.
Tatsuoka et al. (1997) evaluated several case histories for this type of FHR
facing walls. Geosynthetic retaining wall with full height rigid facing, in
comparison to geosynthetic reinforced segmental retaining wall, has greater wall
stability, lower wall deformation, and lower cost. (Tatsuoka et al. 1997).
In comparison of different type of walls during the earthquake 1995 in Japan, the
GRSW with FHR facing has demonstrating to be more stable and less damaging
against seismic force than other walls. (Tatsuoka et al. 1997)
14
Or o i noqc
(1) Uose Concrete
i
(3) OocWfilt ond Compoct'On
W1L
rSondbog
__  GcotextMe
Cl.. C__________
(?) Loyinq Gcote*tile and Sondboq
(4) Second Layer
Figure 2.6 Staged construction procedure for FHR facing retaining wall
Figure 2.7 Typical MSE retaining wall with FHR facing
15
2.4 Summary of Seismic Pressure Evaluation Method by
Victor Elias, Barry R. Christoper and Ryan B. Berg (2001)
The 2001 design guideline unlike the previous AASHTO, assumed inertial
force of earth mass in both external and internal stabilized wall systems. During an
earthquake, the retained fill exerts a dynamic horizontal thrust Pae, on the MSE
wall in addition to the static thrust. Moreover, the geosynthetic reinforced soil
mass is subjected to horizontal inertial force PiR=M*Am, where M is the mass of
the active portion of the reinforced wall section assumed at a base width of 0.5H,
and Am is the maximum horizontal acceleration in the reinforced soil mass, equal
to kh. Dynamic horizontal active thrust Pae can be evaluated by psuedostatic
MononobeOkabe analysis as shown in Figure 2.8. This is added to the static
forces to obtain a total thrust on a retaining wall. The equation PAe was developed
assuming a level backfill, a friction angle 30 degrees, horizontal acceleration
coefficient (kh) equal to Am> and vertical acceleration coefficient (kv) equal to zero,
a) The procedures for seismic external stability evaluation are as follows:
* Select a horizontal peak ground acceleration based on design earthquake.
The ground acceleration coefficient A may be obtained from contour map
of Division 1A of current AASHTO in Figure 2.9.
* Calculate the max acceleration Am developed in the wall:
Am =(1.45A)* A (2.11)
16
Reinforciiment L044O1
Mas* far Inartta) foro
Mas* for r**t*ttn9 foroaa
(b) Sloping bockfill condition
Figure 2.8 Seismic external stability of a MSE wall
17
Figure 2.9 Contour map of horizontal acceleration coefficient (Division 1 A).
* Calculation the horizontal inertia force Pir and seismic thrust APAe :
Pir = 0.5 Am yr H2 (level backfill) (2.12)
Pae =0.375 Am yf H2 (level backfill) (2.13a)
where: yr and yf are unit weight of reinforced soil mass and backfill respectively.
Note that add to the static forces (see in Figure 2.8a) acting on the structure, 50
percent of the seismic thrust PAe and the full inertia force Pir. The reduced PAe is
used because the inertia and seismic thrust are unlikely to peak simultaneously.
18
For the structure with sloping backfills, the inertial force (Pir) and the
dynamic horizontal thrust (Pae) will be based on a height H2 near the back
of the wall mass determined as follows:
H2 = H+(tanf3*0.5H)/( 1 0.5tanP) (2.14)
Pae may be adjusted for sloping backfills using MononobeOkabe method, with
kh = Am and kv = 0. A height of H2 should be used to calculate Pae in this case.
Pir for sloping backfills should be calculated as follows:
Pir Pir + Pis (sloping backfill) (2.15)
Pir 0.5 AmyrH2H (2.16)
PIS= 0.125 Amyr(H2)2 tan3 (2.17)
and Pae = 0.5 yf (H2)2 Kae (sloping backfill) (2.13b)
where: Pjr is the inertial force caused by acceleration of the reinforced backfill and
PjS is the inertial force caused by acceleration of sloping surcharge above
the reinforced backfill, with width of contributing to Pir equal to 0.5 H2.
Pir acts at the combined centroid of Pjr and Pjs as shown in Figure 2.8b. The total
seismic earth pressure coefficient Kae based on MononobeOkabe general
expression is computed from:
K
cos2 (9990+0)
AE '
cosn/co^(9O0)cos(&9O0+\/j 1+
(2.18a)
sin(^> + (p)sin((p [3 9)
y cosÂ§+90 0+\/)cos((390+ 0)
19
where: y = arctan [kh/(lkv)] is the seismic inertia angle
5 = is the wallsoil interface friction angle
(p = is the soil internal friction angle
P = is the backfill slope angle (see in Figure 2.1)
0= is the wall face slope angle (see in Figure 2.1)
The kh used for MononobeOkabe analysis of external stabilized walls may be
reduced to 0.5A, provided that displacements up to 250A [mm] are acceptable.
A is a horizontal acceleration coefficient comes from contour map Figure 2.9.
Kavazanjian et al. developed an expression for reduced kh and further simplified
the Newmark analysis. For MSE walls the maximum wall acceleration coefficient
at the centroid of the wall mass, computed as following Equation 2.18b. Am used
with this expression computed as Equation 2.11.
kh = 1.66 Am (Am / d)025 (2.18b)
where: d is the lateral wall displacement in [mm]. It should be noted that this
equation should not be used for displacements of less than 25 mm (1 inch) or
greater than approximately 200 mm (8 inches). It is recommended that this
reduced acceleration value only be used for external stability calculations, with
MSE wall behaving as a rigid block. Internally, the lateral deformation response of
the MSE wall is much more complex, and at present, it is not clear how much the
acceleration coefficient could decrease due to allowance of some lateral
deformation during seismic loading. In general, the states located in seismically
active areas is to design walls for reduced seismic pressure corresponding to 50 to
20
100 mm (2 to 4 inches) of wall displacement. It is recommended not to use this
simplified approach of kh in Equation 2.18b for walls with a complex geometry,
toll walls (over 15 m), and walls with peak ground acceleration A higher 0.3G.
b) Seismic load produce an inertial force P] (see Figure 2.10) acting
horizontally, in addition to the static forces in seismic internal stability of a
MSE wall. Inertial force will lead to incremental dynamic increases in
maximum tensile force in the reinforcement. Calculation steps for internal
stability analyses with respect to seismic loading are as follows:
* Calculate the maximum acceleration in the wall and the inertial force Pi :
Pi = Am*Wa (2.19)
Am= (1.45A)* A (2.11)
where: Wa is the weight of the active zone (shaded area on Figure 2.10) and A is
the AASHTO site acceleration coefficient in Figure 2.9.
* Calculate the total maximum static load applied to the reinforcements
horizontal Tmax as follows:
Calculate horizontal stress o>, using K coefficient
Oh = K av+ Actv K +A
where: av = yZ overburden pressure, Acjv is the increment of vertical stress due to
concentrated vertical loads using 2V:1H pyramidal distribution, Aah is the
increment of horizontal stress due to horizontal concentrated surcharges, if any
static equivalent loads should be included for traffic barriers.
21
Calculate the maximum static tensile load component Tmax:
(2.21)
where: Sv is vertical spacing of reinforcement.
Calculate the dynamic increment Tmd directly induced by the inertia force
Pi in the reinforcements by distributing Pi in the different reinforcements
proportionally to their resistant area (Le) on a load per unit width basis.
This leads to:
which is the resistant length of the reinforcement at level I divided by sum
of the resistant length for all reinforcement levels.
The maximum tensile force including static and dynamic component
applied to each layer is:
The extensibility of the reinforcements affects the overall stiffness of the
reinforced soil mass. As overall stiffness decreases, damping should increase and
amplification may also increase. Thus the resulting inertia force may not be much
different than for inextensible reinforcement. Additional research is needed to
justify any variation based on reinforcement extensibility.
(2.22)
i=l
(2.23)
22
Figure 2.10. Seismic internal stability of a MSE wall
where:
Pi internal inertia force due to soil weight of the backfill within the active zone
Lei the length of reinforcement in the resistant zone of the ith layer
Tmax the load per unit wall width applied to each reinforcement due to static force
Tmd the load per unit wall width applied to each reinforcement due to dynamic
force
The total load per unit wall width applied to each layer: Ttot = Tmax + Tmd
23
3. Theoretical Background of NIKE3D Program
3.1 Implementation of NIKE3D Program
NIKE3D is a computer program that performs finite element analysis. It is
a nonlinear analysis program with 2 and 3 dimensional finite element codes
specifically for solid and structural mechanics. NIKE3D originally developed and
has been used by the Lawrence Livermore National Laboratory (LLNL) for about
two decades. The 8nodes solid element and 4nodes membrane element were
implemented in this thesis study.
We can specify complete NIKE3D analysis following steps:
 Preprocessor: Ingrid and Truegrid mesh generation program
 Mainprocessor: NIKE3D program
 PostProcessor: GRIZ data processing program
 PostPostProcessor: Excel, AutoCad, Mathematica, MathCad, Math
Lab..etc, visualizing, plotting, and processing program using extracted data
from postprocessor GRIZ.
Mesh generation INGRID program was adopted in this thesis study as like input
program for NDCE3D. INGRID is a threedimensional mesh generator developed
by Lawrence Livermore National Laboratory as well. Besides the mesh generation,
could also use INGRID to specify external loads, element types, sliding interfaces,
24
boundary conditions and materia] models and parameters for the NIKE3D. Output
file from INGRID would then become the input file for NIKE3D.
NEKE3D is the mainprocessor; a postprocessor was used to extract results
from the main analysis. The postprocessor named GRIZ was developed by same
laboratory as well. The output file from NIKE3D then becomes the input for GRIZ
named N3PLOT. GRIZ could animate series of specified loading increments from
the analysis and digitized data could be printed to text file for other further
analysis. SI units were used in this study.
3.2 Interface Formulation
NIKE3D program has a significant feature of interface formulation
capability. We could define surfaces between different material meshes, and
surfaces could permit voids or frictional sliding during the analysis. There are two
main algorithms for interface capability; one is the Penalty formulation method,
and other is the Augmented Lagrandian method. For the Penalty method, penalty
springs are generated between contact surfaces when an intermaterial penetration
is detected. A penalty spring scale factor range 0.1 to 0.001 may be used to ensure
convergence. Scale factor one could allow more interpenetration; default value of
0.1 to 0.001 was adopted in this study.
In the current version of NIKE3D, ten interface types are available. The
frictional sliding with gaps interface was chosen for this study. Sliding interface
25
definition defined in the preprocessing program INGRID. Frictional sliding
interface with gaps could happen between two contacting surfaces, one is the
master surface, and the other is the slave surface. Selection of master or slave
contacting surface is arbitrary. The sliding surfaces in this study were defined all
planar.
3.3 Material Models of NIKE3D.
NIKE3D program includes twentytwo material models. These constitutive
models cover a wide range of elastic, plastic, viscous, and thermally dependent
material behavior. In the latest version of NIKE3D, soil and concrete materials
respectfully as RambergOsgood model or the Oriented Brittle Damage model,
where energy dissipation is allowed. RambergOsgood nonlinear model were
adopted in this study for the backfill soil.
There are four types of material used in the study. Foundation soil, concrete
wall, and inclusion materials were simulated using the isotropic elastic model. The
only material that used RambergOsgood model was backfill soil. The material
density is required for all materials. For isotropic elastic model, the required input
parameters are Modulus of Elasticity and Poisson's Ratio.
26
3.3.1 RambergOsgood Nonlinear Model
The RambergOsgood model is used to treat the nonlinear behavior of
many materials. In this model, five material model parameters required: (1)
reference shear strain yy, (2) reference shear stress xy, (3) stress coefficient a, (4)
stress component r, and (5) bulk modulus K. The stress strain relationship for
monotonic loading in RambergOsgood model is given by equation 3.1
ify>0
if y<0
(3.1)
where: x is the shear stress, and y is the shear strain. The model approaches perfect
plasticity as stress exponent r approaches infinity. Equation 3.2 is for model
unloading and reloading material behavior after the first reversal.
yy0
2yy
TXq
2x
 + a
TX
2x,
ify>0
YYo _^^o
2Yv
2x
a
XXq
2x
if y<0
(3.2)
where: xo and y0 represent values of shear stress and strain at the point of load
reversal. A computer program named RAMBO was developed specifically for
determining these five material model parameters.
27
3.4 Eigenvalue Analysis and Rayleigh Damping
NIKE3D has a capable of doing eigenvalue analysis on the proposed
model. Number of mode shapes can be specified in the input file for NIKE3D. In
thesis study total fifteen mode shapes were designed to the 10m wall system.
NIKE3D would return a natural frequency corresponding to each mode shape.
System natural frequency associated with a mode shape required coefficient for
Rayleigh damping. Rayleigh damping is a system damping. It considered as
damping matrix [C], and it is a linear combination of the mass matrix [M] and
stiffness matrix [K] according to the following equation.
[C]=a[M]+p[K] (3.3)
a and p are mass and stiffness proportional damping coefficient. Natural
frequencies of first and fifteenth mode were selected in the computation. Once
natural frequencies selected, coefficient for Rayleigh damping can be determined
following equations.
a = 2coC0j
2(g>2^2 ~C[Â£ )
(g>2 
(3.4)
P^CQ^CD^) (35)
(co* oof)
coi and C02 are the first and fifteenth mode system natural frequency, units for
radian/second. and are the fraction of critical damping corresponding to cox
and 2, respectively. 10% critical damping is adopted in this study for 10m wall.
28
4. Analysis Program and Input Parameters
4.1 Purpose
In this thesis, 10 and 20m hybrid Twall with small footing (16.5% of wall
height) were selected. Both the vertical and horizontal components of the Imperial
Valley strong ground motion were adopted to shake the wall with both ground
motion components. Sixteen different analyses were performed to investigate the
transient behavior, and the effect of wall heights, ground motion intensities and
wallgeogrid connection conditions.
Table 4.1 All analysis table
Walll [eight
10m 20m
Attached Attached Attached Detached
0.458* 0.687* t 0.458* 0.458*
0.458* (0.136)** 0.687* (0.136)** 0.458* (0.136)** 0.458* (0.136)** '
0.458* (0.272)** 0.687* (0.272)** 0.458* (0.272)** 0.458* (0.272)**
0.458* (0.408)** 0.687* (0.408)** t 0.458 (0.408)** 0.458 (0.408)**
where
* means horizontal peak ground acceleration ah in g
**() means vertical peak ground acceleration av in g
ttransient case analysis.
29
At the end of this thesis, some concluding remarks are provided on the effect of
influencing parameters on the performance of the hybrid walls.
4.2 Input Parameters
4.2.1 Applied Loading
Two types of loading were applied in each case of analysis: static loading
and dynamic loading. Both horizontal and vertical components of Imperial Valley
ground motion were adopted in the dynamic analysis. In the static loading,
gravitational acceleration (g) of 9.81 m/sec2 was applied linearly from 0 to lg in
ten seconds from the beginning of the entire load time history and stayed constant
lg till end of the analysis as shown in Figure 4.1a. The gravitational acceleration
imposes ydirection (vertical) body force to the elements within the model. There
were a total of 25 time steps in the static loading with time increment of 0.4
second. Time steps would change automatically in the dynamic analysis.
If some case of analysis subjected to vertical component of ground motion,
vertical acceleration body force in ydirection would be combined with gravity
acceleration. Once gravitational acceleration is applied completely, dynamic
vertical acceleration would then be applied from ten second to end of the analysis
as yacceleration body force, shown in Figure 4.1b.
30
I 121 flj l 4
Â£ 1 a>
o o , ,
CD
O 0 2
6
5 1 a. Static 0 1 Time [sec] Loading Time 5 2 History 0 25
Figure 4.1 Loading curves adopted in NIKE3D analysis
31
After the first ten seconds of static loading, horizontal dynamic loading
would then be applied to the system as xacceleration body force in Figure 4.1c.
The units of the input ground acceleration were m/sec2. The time increment of 0.04
second was selected for the dynamic analysis, but, if necessary, the time step was
decreased automatically until the numerical convergence was successfully reached.
4.2.2 Wall Geometries.
10m and 20meter hybrid retaining walls were designated for evaluating
the effect of wall heights on hybrid Twalls with small base (16.5%H) under
seismic shaking. Retaining wall system was comprised of four different materials:
foundation soil, concrete wall section, backfill soil and inclusion. Each material
and its properties would be presented in Section 4.2.5. Wall height was defined as
the height above the ground surface and it has onemeter embedment. Actual wall
height would be H+lm, where H is the height above the ground surface. The
concrete wall stem and footing thickness were 0.5m and 0.7m, respectively. The
dimension of footing was calculated proportion to the wall height, where toe
length was 1.5% H, and heel length was 15% H, i.e. the total base length of
16.5%H, where H is the wall height above ground surface in the front wall face.
The footing dimensions were selected after an extensive analysis for optimal
dimensions.
32
For the inclusion dimensions, vertical spacing between inclusions was kept
at 0.5m, and all inclusions had the uniform length of 1H. To avoid the effect of
boundary, a total backfill length of 3H was used. In other words, the backfill was
extended 2H beyond the end of inclusion. The thickness of the foundation soil
stratum in front of the wall was 6m. Along the wall base, the foundation soil
thickness is kept at 5 meter for both walls used in the analysis. The depth of
backfill was H+lm, the same as actual wall height. Figures 4.2a and 4.3a show the
dimensions and materials of 10m, and 20m wall system, respectively. Figures
4.2b and 4.3b show the mesh of 10m, and 20m wall system, respectively, for the
FEM analyses.
4.2.3 Boundary Conditions.
Figure 4.4 shows the boundary conditions and spatial coordinates adopted
in the finite element analysis for both walls. The twodimensional model with
plainstrain condition was used in this thesis. The plain strain condition was
applied in the zdirection normal to xy plane, thus no displacement was allowed
in the zdirection. The base of the model was fixed with constraints on x and y
direction displacement. Roller condition was applied along the left and right of the
mesh boundaries as shown in Figure 4.4. With roller condition, the sides could
have ydirection displacement but constrained on the xdirection displacement.
33
u>
4^
2Dn
0,5n
3 On
tOn
Concrete
Retaining
lOn Wall
' 0.5n Cspaclng)
r
Backfill Soil
Inclusion Re Inf orcenent
0,15n
1.65n
6n
Foundation Soil
5m
50.5n
Figure 4.2a 10m wall dimensions and materials
U)
20n
0.5j
T
10n
Ur
5r
U,15m
J i
4Ft 1 4m  4ro 1 4pi  2m  2m  2n  2n  2n  2m  2m  2m  4m I 4m  5m 5m
50.5m
Figure 4.2b 10m wall finite element mesh
40m 0.5m 60 m
Figure 4.3a 20m wall dimensions and materials
Figure 4.3b 20m wall finite element mesh
Roller Con.cMon
s / .
Figure 4.4 Boundary conditions used in analysis
4.2.4 Sliding Interfaces
Sliding Interface is one of the key features for NIKE3D. It is the contact
surface between two different materials. Four sliding surfaces were defined:
concretefoundation soil, foundation soilbackfill, concretebackfill, and inclusion
vs. backfill. NIKE3D requires the input parameters of static and kinetic friction
coefficients in sliding interface definition deck. In this study, the two coefficients
are assumed to have the same value. These coefficients of friction (p) are
calculated based on the relation between the internal friction angle of backfill ()
and interface friction angle (8).
With known internal friction angle the interface friction angle for concrete wall
and inclusion could be determined using Equation 4.1.
38
5 = cp
3
(4.1)
Thus friction coefficient (p) between two materials could be computed with
Equation 4.2.
p = tanÂ§ (4.2)
To determine coefficient of friction (p) for sliding interface between foundation
soil and backfill, the interface friction angle and the friction of soil are assumed
equal, i.e. 6 = <(>. The foundation soil was assumed to be an overconsolidated clay
with <(> = 28, and thus, p = 0.55.
For sliding interfaces between concrete wall and foundation soil and
between concrete and backfill, Equation 4.1 and 4.2 were used to determine the
friction coefficient with
The backfill soil was assumed to dense sand and gravel mix. In case of inclusion
backfill sliding interfaces, an interface friction angle (6 = 29) was selected from
direct shear test between geomembrane and granular soil performed by Lahti
(1998) and from Equation 4.2, the interface friction coefficient is 0.55.
Each sliding interface comprises of two contacting surfaces as discussed in
Section 3.3. The number of sliding interfaces depends on the number of contacting
surfaces. Each wall in this study has four concretefoundation soil interfaces, one
foundation soilbackfill interface and three concretebackfill interfaces around the
wall footing. The number of concretebackfill and inclusionbackfill sliding
39
interfaces depends on the number of inclusion layers. Each inclusion layer would
contribute two inclusionbackfill interfaces and one concretebackfill interface.
The total number of interfaces was 128 and 68 for 20m and lOmwall height,
respectively.
4.2.5 Material Models and Parameters
Foundation Soil
Hard clay was selected as the foundation soil with a sufficient bearing
capacity for the wall and under the bearing pressure from the wall it behaves
elastically. Its Youngs modulus of elasticity of foundation soil is 110 MN/m2,
Poissons ratio 0.35, and density 2100 kg/m3. The foundation soil overlies the
bedrock, which is assumed nondeformable as shown in Figure 4.4.
Concrete Wall Section
Concrete is also assumed an elastic material of medium strength with
Youngs modulus of 25 GN/m2, Poissons ratio of 0.15, and density of 2320
kg/m3.
Backfill
The backfill is assumed to behave nonlinearly and RambergOsgood
nonlinear model is adopted to simulate its behavior.
40
The Colorado Class 1 backfill is used in this study. It has a moist unit weight of
125 pcf (19.645 KN/m3 or 2001.5 Kg/m3.) The material model parameters are
calculated using RAMBO program and are tabulated in Table 4.1. The backfill
with density of 125 pcf is considered as dense sand and it has a shear wave
velocity (Vs) of 750 ft/sec. The four of the material parameters are determined
with known Vs using Table 4.1 generated by RAMBO.
The fifth parameter of RambergOsgood model, bulk modulus K, is
calculated using the known shear modulus Gmax from RAMBO and Poissons ratio
of 0.35 corresponds to cohesionless dense sand using Equation 4.3.
E = 2G(l + v) (4.3)
where E is Youngs modulus, v is the Poissons ratio, and G is the shear modulus.
With known E and v, the bulk modulus K could be computed with Equation 4.4.
K =
E
3[l2u]
The bulk modulus was calculated as K = 314 MN/m2.
(4.4)
41
Table 4.2 Results of RAMBO program for average sand of 125 psf
RambergOsgood Material Properties for Average Sand
Unit Weight 125 pcf
V. a r Tv
[fVsec] (10J psf) {1V*) (psf)
100 38.82 i.i 2.349 0.1052 4.09
150 87.34 i.i 2.349 0.1052 9.19
200 155.28 11 2.349 0.1052 16.34
250 242.62 i.i 2.349 0.1052 25.54
300 349.38 i.i 2.349 0.1052 36.77
350 475.54 i.i 2.349 0.1052 50.05
400 621.12 i.i 2.349 0.1052 65.37
450 786.10 i.i 2.349 0.1052 82.74
500 970.50 i.i 2.349 0.1052 102.14
550 1174.30 i.i 2.349 0.1052 123.59
600 1397.52 i.i 2549 0.1052 147,09
650 1640.14 i.i 2549 0.1052 172.62
700 1902.17 i.i 2.349 0.1052 200.2
750 2183.62 i.i 2.349 0.1052 229.82
800 2484.47 i.i 2549 0.1052 261.49
850 2804.74 i.i 2549 0.1052 295.19
900 3144.41 i.i 2549 0.1052 330.94
950 3503.49 i.i 2549 0.1052 368.74
1000 3881.99 i.i 2549 0.1052 40857
1050 4279.89 i.i 2549 0.1052 450.45
1100 4697.21 i.i 2549 0.1052 494.37
1150 5133.03 i.i 2549 0.1052 540.34
1200 5590.06 i.i 2549 0.1052 588.35
1250 6065.61 i.i 2549 0.1052 638.4
1300 6560.56 i.i 2549 0.1052 690.49
1350 7074.92 i.i 2549 0.1052 744.62
1400 7608.70 i.i 2549 0.1052 800.8
1450 8161.88 i.i 2549 0.1052 859.02
1500 8734.47 i.i 2549 0.1052 91929
1550 9326.47 i.i 2549 0.1052 981.6
1600 9937.89 i.i 2549 0.1052 1045.95
1650 10568.71 i.i 2549 0.1052 111254
1700 11218.94 i.i 2549 0.1052 1180.78
1750 11888.59 i.i 2549 0.1052 125125
1800 12577.64 i.i 2549 0.1052 1323.78
1850 13286 10 1.1 2549 0.1052 1398.34
1900 14013.97 i.i 2.349 0.1052 1474.95
1950 1476126 i.i 2549 0.1052 1553.6
2000 15527.95 i.i 2549 0.1052 163429
2050 16314.05 t.i 2.349 0.1052 1717.03
2100 17119.56 i.i 2.349 0.1052 1801.81
2150 17944 49 i.i 2.349 0.1052 1888.63
2200 18788.82 i.i 2.349 0.1052 1977.49
2250 19652.56 i.i . 2.349 0.1052 2068.4
2300 20535.71 i.i 2349 0.1052 2161.35
2350 21438.27 i.i 2549 0.1052 2256.34
2400 22360.25 i.i 2549 0.1052 2353.38
2450 23301 63 11 2549 0.1052 2452.46
2500 24262.42 11 2.349 0.1052 2553.58
42
Inclusion
A commercially available geogrid named Tensar SR2 was selected as the
inclusion for this analysis. Table 4.2 shows the mechanical properties of Tensar
SR2 geogrid. Elastic material model was used to simulate the inclusion behaviors.
The secant modulus of elasticity at 5% strain was used in the analysis.
Table 4.3 Mechanical properties of commercially available geogrid
Tensar (uniaxial)
Properties Test Method Units SR2 SR3
Tensile Strength at 2% Strain M TTM1.1 lb/ft 1465 2055
XM  
5% Strain M 3030 3810
XM  
Ultimate M 5380 7125
XM  
Initial Tangent Modulus M TTM1.1 kip/ft 136.2 175.9
XM  
Junction Strength TTM1.2 % 80 80
Weight lb/yd2 1.55 1.88
Aperture Size M in 3.9 4.5
Thickness rib in 0.05 0.06
Polymer HDPE HDPE
Width ft 3.3 3.3
Length ft 98 98
Weight lb 61 72
The secant Youngs modulus is determined by dividing the strength at 5% strain
by the geogrid thickness (0.003 m) and also by 5% strain. This gives Youngs
modulus of 6060 kips/ft2 (2900 MN/m2). Poissons ratio for highdensity
polyethylene (HDPE) ranges from 0.37 to 0.44 and a value of 0.4 was used.
43
The geogrid inclusions were simulated by fournode membrane elements with
thickness of 0.003m. Thus, no torsion or bending stiffness is allowed and the
rotational degree of freedom is constrained all directions. At connections, the
inclusion elements share the same nodal points with solid concrete elements. Table
4.3 summarizes all input parameters for the finite element analysis.
Table 4.4 Input material parameters for the thesis study
Elastic Material Model
Material Name P E V
[kg/nT] [MN/m2]
Foundation Soil 2100 110 0.35
Concrete 2320 25000 0.15
Inclusion 1030 290 0.40
RambergOsgood Model
Material Name P Yy Ty a r K
[kg/m3] (10J) [N/nr] [MN/m2]
Backfill Soil 2001.5 0.1052 11003 i.i 2.349 314
Sliding Interface
Interface 5 P
[degree] [degree]
foundation soilbackfill 28 0.55
concretefoundation soil 28 19 0.35
concretebackfill 39 26 0.50
inclusionbackfill 29 0.55
Rayleigh Damping
H=10m a = 3.2088 p = 0.0022654
44
5. Presentation and Interpretations of Analysis Results
5.1 Introduction
Chapter 4 presented the analysis program and associated input parameters.
This chapter will summarize the analysis results of the resultant thrust, overturning
moment and moment arm of earth pressure and bearing pressure, inclusion stress
and forward wall displacement. In studying the above items, usually only their
maximum values are presented. This causes some uncertainty of if these
maximum values exist simultaneously. Thus, the examination of their
synchronization with the peak ground acceleration is critical to the safety study of
MSE retaining walls under earthquake loads, and the issue of synchronization of
all the maximums with the peak ground acceleration will have to be verified. The
presentation of results is grouped as follows:
1. Transient variation
Time histories of resultant earth pressure; resultant overturning
moment, and the moment arm (the height of the point of application of
the resultant earth pressure from the wall base).
Time histories of resultant bearing pressure; resultant overturning
moment and moment arm (distance from the toe of the wall).
45
Time histories of wall forward displacement (at the wall top and
bottom).
Time histories of resultant inclusion forces and resultant inclusion
overturning moment.
2. Maximum earth pressures, bearing pressures, inclusion stresses, and wall
displacements.
Maximum static and dynamic earth pressure distribution, its resultant
earth pressure and point of application.
Maximum static and dynamic bearing pressure distribution, its resultant
and point of application.
Maximum static and dynamic wall displacement.
Maximum inclusion tensile stress.
All static loads including gravitational acceleration are applied quasistatically
over an appropriate period of time. One g gravitational acceleration was
imposed incrementally to obtain the static results. Then, the earthquake ground
motion was imposed with the complete accelerationtime history and the analysis
results are obtained for some selected nodal points as shown in Figure 5.1.
46
o nodo< point yd <' bockfin *nesi
ond *CCelprol^on do'O reduction
a rvodo* ooM used
on a oeceirotidn dot reduction
nodot DOint used (o' inclus1"  stress
doto reduction
nodoi point used (or foundation soil ysvess
doto 'eduction
5.2 Time Histories of Resultant Earth Pressure,
Resultant OTM and Moment Arm
For determining the time history of resultant earth pressure, the results at
the nodal points along the front face of backfill soil xstress were extracted from
GRIZ, the post processor. By getting summation of individual resultant force (Pi)
along the wall height acting on each wall section (Ah*), per time step (023.52 sec)
of analysis, Equation 5.1 was used to calculate time history of resultant force(p)
with units of kN/m.
47
(5.1)
1=1 p (<*xi +a*(i + l)) 2 1 (5.2)
Ah; = hi+1 h; (5.3)
where P is the resultant force, Pj is the individual resultant forces along the wall
height, oxi is the backfill nodal point xstress with unit of kN/m2, Ah; is the height
of a section of the wall between two neighboring nodal points, iindex shows
increment of the wall.
The resultant force was calculated for each time increment of analysis over
23.30 seconds. So, the time history of the resultant earth pressure (or thrust) was
calculated and presented in Figure 5.2.
The time history of the resultant overturning moment of earth pressure can
be calculated at each time increment using Equation 5.4 and results shown in
Figure 5.3.
OTM = Â£P,y, (5.4)
i=J
48
3.5 I ** n .
2.5  T i t
h 9 r> . 1 1
< *U C 1 . L J ill H ii /I iW vv LAi
I 1.0 5 05 N 4 IfVI yv nr r i
r T
n n . 1
0 5 10 1 Time [sec] Figure 5.4 Time History of Moment 10m wall under ah=0.68 5 2 Arm of Earth Pre 7g Motion 0 25 ssure
49
where: P, yi is the moment of individual thrust about the wall base
Pi is the individual thrust acting on center of wall section Ahj.
yi is the location of individual resultant application measured from the
wall base.
The time history of moment arm of lateral earth pressure could be calculated for
each time step using Equation 5.5 and the results were shown in Figure 5.4.
Figure 5.4 shows the moment arm of earth pressure. The moment arm varies from
0.5m to 3.25m from the wall base. The maximum values of resultant earth
pressure and resultant overturning moment synchronized with the peak horizontal
ground acceleration at the time of 15.23 second. Details are presented on in
Appendix A where all transient results are presented.
5.3 Time Histories of Resultant Bearing Pressure,
OTM and Moment Arm
The nodes along the foundation soil beneath the concrete wall footing were
chosen for the evaluation of the time histories of resultant bearing pressure at each
time increment of analysis. The ystresses at nodal points were extracted from
GRIZ as bearing pressure underneath concrete wall footing.
n
Moment Arm =
(5.5)
P
50
51
The calculation, time history of resultant bearing pressure, resultant
overturning moment and moment arm were obtained the same way as calculation
of earth pressure resultant using Equation 5.15.5 shown in Figure 5.55.7 by
substituting N, = P1; ayi = axi)Xi = y(, Abj = Ahj (section of footing length between
two nodal points). The wall toe was the center for overturning moment calculation.
Footing length varies from 0 to 16.5% H meter. Where 0 represents the location of
wall toe, 16.5%*H indicates the location of wall heel, and H is the wall height
above the ground surface from the wall base. The location of the bearing pressure
resultant varies from 0.68m to 0.88m from the wall toe, and its magnitude is
synchronized with the horizontal peak ground acceleration.
5.4 Time Histories of Wall Forward Displacement
The nodal points xdisplacement along the concrete face were selected to
extract wall forward displacement information. A negative xdisplacement
indicates the direction of wall movement against the positive direction of the local
xcoordinate system. Figures 5.8a and b show the time histories of forward
displacement at the bottom and the top nodal points of 10m wall. Analysis results
show that the forward displacement reaches maximum at wall top for the 10m
wall, but for the 20m wall at the middle of the wall. This difference in the relative
location of the maximum forward wall displacement is caused by the same wall
52
stem thickness used in both walls. As a result, the 20m wall is more flexible than
the 10mwall.
The monolithic nature of the wall provides a rigid connection between the
wall stem and wall base. This yields high shear and also flexural resistances.
However, the connection design becomes extremely critical in providing the
necessary resistances. Thus, a sufficient reinforcement is needed to prevent
connection yielding. Besides, the wall stem thick for the 20m wall should be
larger than that for the 10m wall. With this new design change, the forward wall
displacement may reach its maximum value at the wall top for both 10 and 20m
walls.
Time [sec]
0 5 10 15 20 25
Time History of Forward Displacement, (at toe)
10m wall under ah=0.687g Motion
Figure 5.8a Time histories of wall forward displacement (at bottom)
53
Figure 5.8b Time histories of wall forward displacement (at top)
5.5 Time Histories of Resultant Inclusion Stress
and Overturning Moment
In order to determine the time history of resultant inclusion stresses, the
inclusion connection xstress of all inclusion layers was extracted from GRIZ.
Once the inclusion connection xstress was gathered in spreadsheet, the time
history of resultant inclusion stresses and overturning moment for each time step
of analysis is calculated using Equations 5.65.8.
T^Tj (56)
i=l
Ti=oxi5 (5.7)
54
(5.8)
OTM = XT.yi
i=I
where T is the resultant tensile inclusion stresses, Tj is the individual resultant
tensile force for the inclusion i along the wall height in kN per m, aX] is the
inclusion nodal point xstress in kN/m2, 5 is the inclusion thickness equal to 0.003
meter for all inclusions, y, is the location of resultant inclusion stress for inclusion
i measured from the wall base, and n is the total number of inclusion layers
spaced at 0.5 m. Thus, the 10m and 20m walls have 20 and 40 inclusion layers,
respectively. The directions of resultant inclusion stresses and overturning
moment are opposite to those of earth pressure. Figures 5.9 and 5.10 show the
time histories of resultant inclusion stress and overturning moment. Also shown in
the title of the figures are wall height and the horizontal (H) and vertical (V)
ground motions used in the analysis and the numerical value in front of H and V
shows the scaling factor of 1.5 for H and 3 for V. The analysis result shows the
synchronization of the maximum values of resultant inclusion stress, and
overturning moment with the peak ground accelerations. All other transient results
are shown in Appendix A.
55
I E
a>
Z CL
50
40
30
20
10
0
0
i 10 15 20
Time [sec]
Figure 5.9 Time History of Inclusion Net Thrust
10m wall under ah=0.687g Motion
25
5.6 Maximum Stresses, Resultants, Shear, and Moment
Imparted on Concrete Wall Section
Stresses at the nodal points along the front face of backfill were extracted
for determining the lateral earth pressure distribution, resultant, shear and moment
imparted on the concrete wall section. The earth pressure distribution envelope
56
could be constructed by connecting these nodal point xstresses. By integrating
the area under the earth pressure distribution envelope, the resultant thrust is
calculated in terms of kN/m, the force per unit longitudinal length of the retaining
wall system. At the end of static and seismic loading, nodal point stresses in the x
direction were used to draw the pressure distribution diagrams for static and
dynamic earth pressures, respectively.
The inclusion nodal point xstress at the connection was used to calculate its
contribution to the earth pressure and thrust. The inclusion thrust acts in the
direction against earth pressure and affects the resultant thrust and its point of
application. Most often it counteracts the wall displacement.
Figure 5.11 shows the static and dynamic lateral pressure distribution on
the concrete wall section, imparted by both backfill and inclusions of the 20m
wall subjected to Imperial Valley earthquake. The static and dynamic lateral
pressure distributions of all sixteen cases are shown in Appendix B The title of
each figure gives the wall height, connection conditions and the ground motion
combinations. The wall height on each chart was defined as that 0 meter being the
wall base, 11 and 21 meters being the wall top for 10m and 20m walls,
respectively.
Figure 5.12 shows the static and dynamic thrust imparted on concrete wall
section by both the backfill and inclusions. Individual backfill compressive thrust
between two neighboring inclusions spaced at 0.5 m was calculated by finding
57
trapezoidal area formed by their nodal point xstresses. Individual soil thrust
would act through the mid height of the element if neighboring nodal point earth
pressures magnitude were close to each other. The inclusion tensile resultant was
determined by multiplying the nodal point xstress by the inclusion thickness of
0.003 meter. The point of application of each inclusion force is applied at the
layer location.
Figure 5.13 show shear and moment diagrams associated with individual
resultant forces indicated in Figure 5.12. Maximum shear and moment occurred at
the wall base. These diagrams are extremely important to design reinforced
concrete wall.
The location of the total static and dynamic thrusts and inclusion resultants
was calculated by finding center of the static and dynamic lateral earth pressure
distribution diagrams. The location of the total soil thrust and total inclusion
resultant were calculated using Equation 5.9.
ZP.Yi
y = ^ (5.9)
where P, yf is the moment of individual thrust about the wall base, P, is the
individual thrust see in Equation 4.6, y; is the point of application of each
individual resultant measured from the wall base, and i index shows the
increment of wall height.
58
Static Analysis
Nodal Point XStress (Static Lateral Earth Pressure Distribution)
Z0.5n
T0.5pi
Z0.5n
Z0.5n (backfill
^0.5n elenent
ZDSn thickness
J_0.5n
J u.
fs
To.
032J3kN/n2
\336.08kN/n*
\369.82kN/n* .
>_38824kN/n*
Dynanic Analysis
Nodal Point XStress (Dynanic Earth Pressure Distribution)
j 0.5b
To.5n (backfill
To.5 elenent
To.Sn thickness)
1339.81kN/n8^^"
1359.32kN/rn^
!229.84kN/nf\
1126.23kN/ni
26^3kN/nffX
1038.62kN/n*T
930^6kN/n
963.SlkN/8>
1029.38kN/n*/
lU3.65kN/ne/
U6S35kN/n/
1220.03kN/#Â£
l279.65kN/rA4
!34024kN/n*/
14ll.3lkN/i*A
M79.4kN/V^
J570.9kN/iAA
1658.9kN/r*4
17lL07kN/r*./
l786.41kN/fA/
1874.77kN/rA*
1922.79kN/n*f
l881.99kN/n*>
1992.55kN/n*^4
2198.54kN/n* <1 
9kN/n? V
l7859kN/4 ~T
I75l.72kN/nV^
104&Â£7kN/n*
I.Q6kN/n?^^
676^kN/rT>
x:
kN/nTX
354.08kN/nf"^
228.52kN/n8sN
93.59kN/n*s'
\
3Â£6kN/n*
5.10kN/n*
p.74kN/n*
[9.30kN/n*
lll.99kN/n*
l7.61kN/n*
,32.96kN/r*
t42.30kN/n>
k47.97kN/r*
.6t.04kN/n *
v71.67kN/n*
>8669kN/r*
V7l.67kN/n*
kB6.69kN/r*
3
05.9kN/n*
sJ25.9kN/n*
Xl46.5kN/n
iLl70.3kN/n*
XsJ97.4kN/n*
Xs225.7kN/(^
iv258.3kN/n2
S^96.8kN/n
_____________^^335.4kN/n2
____________ , ^.^376.SkN/n?
S&^l.lkN/n*
_________________________A478.4kN/ne
\496.9kN/n*
4S16.9kN/r*
rS25.3kN/n*
I /.ff*
:ST54!*
Figure 5.11 Static and dynamic earth pressure distribution
imparted on 20m wall under ah=0.458g Motion
59
All the resultants are shown in Figure 5.12 in dashed lines. Figure 5.14 shows the
static and dynamic resultant thrusts with the corresponding height of point of
application from the wall base. The points of application are much lower than
those from the conventional earth pressure calculations.
5.7 Maximum Bearing Pressure
All nodes along the foundation soil beneath the concrete wall
footing were chosen to present the static and dynamic bearing pressures in terms of
the nodal point ystresses at the end of static and dynamic analyses. The negative
ystress indicates the compressive stress. Figure 5.15 shows both static and
dynamic bearing pressure distributions beneath the concrete wall footing, where
0 represents the location of wall toe. Higher bearing pressures occurred
underneath the concrete wall stem. Appendix C contains the plots of bearing
pressure for all 16 cases.
Figure 5.16 shows the distribution of static and dynamic compressive
thrusts of each individual section of the wall base between two neighboring nodal
points imparted onto the concrete wall footing by evaluating the resultant of
bearing pressures for the abovesaid nodal points. Each individual resultant acts
through the mid width of the foundation soil element. Static and dynamic
resultants of bearing pressures were shown by dashed line in Figure 5.16. It shows
the resultant overturning moment about the wall toe as well.
60
Static Analysis
Static Thrust Calculated fron Nodal Point XStress
Â£0.5 n
v O.Sn
ia5n
^0.5n OoockfiU
\,05n elenent
v.05 thickness)
< 0.5n
Â£ 0.5n
jQ.5n
JO. 5n
V 0.5n
Â£<13"
Â£ 05n
J 0.5n
'0.5n
Â£0.5n
J 0.5n
^0.5n
?a5n
Â£0.5fi
^a5n
>0.5n
Â£0.5n
Jo5
Ja5n
'05n
vM(i
jQ.5n
C 0.5n
*0.5*
J 0.5n
v a5n
v0.5n
Jasn
>0.5n
J0.5n
' 0.5n
J 0.3n
v0.5n
i.'0.5n
58.1kN/n
(nenbrane
KStress
resultant)
0.09kN/n
Q.26kN/n 
O.07kN/n
0.12kN/n 
0.33kN/n
0.52kN/n
0.71kN/n 
0.9kN/n
1.08kN/n
l.27kN/r
\A5kH/n 
l.66kN/n
l89kN/n
2.llkN/n
2.3lUN/n
2.3kN/n
2.6?kN/n
2.79kN/n
2.86kN/n
2.96kN/n
3.02kN/n
3Q3kN/n
3.02kN/n
3.0k N/n
2.94kN/n
2.85kN/n
2.72kN/n
2.53kN/n
l.82kN/n 
M9kN/n 
UkN/n 
0.66kNA
O.IBkN/n
0.3kN/n 
Q.99kN/n
LSlkN/n
225kN/n
7.88kN/n
5.45kN/n
4.02kN/n
l56kN/
0.84kN/n
15kN/n
7.53kN/n
!2.l8kN/r>
17.33kN/n
22.93kN/n
2892kN/n
 35.04kN/n
41.7kN/n
48.79kN/n
 56.42kN/n
 64,38kN/n
 73.39kN/n
 92.9lkN/n
9335kN/n
 l04^8kN/n
~ Ti7,6fkN n " '
133.52kN/n
lS4,2kN/n
l72.lkN/rt
181.47kN/n
1813.79kN/n
(backfill
xstress
resultant)
 113.71kN/n
120.03kN/n
:..I0&21kJ!UA...
Dynanic Analysis
Dynanic Thrust Calculated fron Nodol Point XStress
;o.5n
' 0.5n
4 05n
>0.5* (backfill
^0.5n elenent
J 0.5n thickness)
>0.5n
140.98kN/n
(nenbrane
xstress
resultant)
V
3.12kN/n
2.85kN/n
289kN/n 
3.09kN/n
3.34kN/n
3.5kN/n
3.66kN/n
3.94kN/w....
4.02kN/n
4.23kN/n
4.44kN/n
4.7lkN/n 
4.98kN/n 
ITlTkN/n'
5.36kN/n
5.62kN/n
177kN/n___
5.65kN/n
5 98kN/n
6.6k N/n 
3.36kN/m
l.74kN/n
l.4 7kN/n
 3l.26kN/n
 27.26kN/n
 22.61kN/n
l6.l4kN/
10.96kN/n
*6.47kN/n
2.15kN/n
l06kN/n
0.69kN/n
0.28kN/n
036kN/'n
l.t8kN/n
2.09kN/n
2.96kN/n
4J))kN/n
 5.32UN/n
7.4kN/n
!2.64kN/n
!8.82kN/n
22.57kN/n
27^5kN/n
33.l8kN/n
39.59kN/n
4fi.J3kN/n
57.93kN/n
68.09kN/n
79.2lkN/n
91.94kN/n
!05.79kN/n
121.041
. J/n
81kN/n
2724.2lkN/n
(backfill
xstress
resultant)
158.05kN/n
l77.98kN/n
199.39kN/n
... 224.87kN/n
243.82kN/n
253.46kN/n
. l56.35kN/n
.i6056kN/n
Figure 5.12 Net thrusts imparted on 20m wall under ah=0.458g Motion
61
3000 25QQ J Shear Diagram 20m wall under ah=0.458g Motion
Â£ =5 2000
o l0UU u_ !S innn .
.C CO 500 .
0 c
< 1 W 0 1 all h 1 1 leig 2 1 ht [n 3 1 i] 4 15 1 6 1 7 1 8 1 9 2 0 2 1
Figure 5.13 Shear and moment diagram for 20m wall
62
Sta'tic Thruit and Static Ovd'Turnlng Me
Figure 5.14 Example of resultant static and dynamic thrusts and their point of
applications for 20m wall
0.3n 0.5n 1.25m 1.25m
Figure 5.15 Example of bearing pressure distributions for 20m wall
63
Figure 5.15 Example of bearing pressure distributions for 20m wall
S'tcx'tic T lo r lu s "t cxnci S"ta*tic Dverturning Monerrt
Dynamic Thrust and Dynamic Over turning Moment:
Figure 5.16 Static and dynamic resultant bearing pressure and resultant
overturning moment for 20m wall
5.8 Maximum Wall Deformation
Figure 5.17 shows both static and dynamic forward displacements of the
nodal points along the front face of the concrete wall section in the horizontal
direction for the 20m wall under horizontal ground motion. The forward
64
displacement is actually in the direction opposite to the positive direction of x
coordinate. Appendix D gives all of 16 forward displacement graphs.
The maximum wall deformation was occurred at the middle for the 20m
wall in Figure 5.17. For the 10m wall the maximum displacement takes place at
the wall top. This is most likely due to the same wall stem thickness was used in
the calculation and the 20m wall is less stiff than the 10m wall.
Wall tilt angles inclined with vertical direction were calculated at the wall
top and the middle of the wall where maximum displacement occurred. Wall tilt
angle was higher where displacement was higher. It will discuss detail in next
chapter for all case of analysis. Tilt was computed about the wall base. Wall
height 0 represents wall base.
Figure 5.17 Wall displacement for 20m wall under ah=0.458g Motion
65
5.9 Maximum Inclusion Stress
The inplane inclusion stresses are the nodal point xstresses along the
inclusion layer. Nodal point xstresses were extracted from GRIZ for each layer.
Figure 5.18a and b shows maximum dynamic inclusion stress versus inclusion
length for the 10 and 20m walls. The inclusions are spaced at 0.5 meters. Thus,
there are 20 and 40 inclusions for 10m and 20m wall, respectively. All 16 cases
of analysis graphs for inclusion stresses are included in Appendix E. The title of
each figure provides the information for the layer number (#1 for the top layer)
and the wallinclusion connection condition for each inclusion, wall height and
ground motion combination used in the analysis. Both static and dynamic
inclusion stresses are provided in the Appendix E graphs.
The top inclusion has the highest in plain tensile stress and decreases
drastically with the distance away from the wall face 2m, 6m and 10m in Figure
5.18a. The connection stress was higher in plain stress till 10th inclusion. After 10th
inclusion, the maximum inclusion stress was located somewhere in the backfill.
Beyond 2m distances from wall face the inclusion stress was much smaller than
connection stress.
Inclusion connection stress was higher till 7th inclusion then maximum
stress is located at the 8m from the connection till 23rd inclusion within depth in
Figure 6.8b for the 20m wall. Peak maximum inclusion stress occurred at 24th
inclusion then maximum stress moved to the end of the inclusion within the depth.
66
Very bottom 3 layers were worked in compression by effect of the wall heel
deformation in 20m wall. In the Figure 6.8b maximum tensile stress was zero till
2.5m from connection in the bottom 3 layers.
The Tensar SR2 Geogrid was used in all analysis. It has an ultimate tensile
strength of 5,380 kips/ft (78,511 kN/m) as shown in Table 4.2. With average
inclusion thickness of 3mm, ultimate tensile strength was computed to be 26,170
kN/m2. Thus, the factor of safety of the inclusion satisfies the 1996 AASHTO
requirement of 1.5 against inclusion rapture failure.
Figure 5.18a Maximum dynamic inclusion stresses for 10m wall
67
Inc 1
Inc 3
Inc 5
Inc 7
Inc 9
Inc 11
Inc 13
Inc 15
Inc 17
Inc 19
Inc 21
Inc 24
Inc 26
Inc 28
Inc 30
Inc 32
Inc 34
Inc 36
Inc 37
Inc 40
Inclusion Length [m]
Dynamic Inclusion Stress (attached)
20m wall under ah=0.458g Motion
Figure 5.18b Maximum dynamic inclusion stresses for 20m wall
68
6. Discussion of Results
6.1 Introduction
Chapter 5 is devoted to the interpretation of selected analysis results and
this chapter to the discussion and interpretation of all analysis results in three
separate groups. First, from the transient behavior of retaining walls under
different ground motions the synchronization of all maximums and the peak
ground acceleration is examined and verified. Second, the effect of wall height,
ground motion intensity and inclusionwall connection condition on earth pressure,
inclusion stress, and wall forward, displacement under static and seismic loading is
examined in detail. Third, the earth pressure from finite element analysis is
compared with the earth pressure from the M0 and current design specifications.
6.2 Transient Performance of 10m wall
under ah=0.687g Motion
Finite element analyses were performed to study the performance of hybrid
retaining walls with a small base under different earthquake ground motion. The
wall performance is measured by the lateral earth pressure acting on concrete wall,
bearing pressure underneath wall footing, wall face displacement, and inclusion
stress distribution along the inclusion length. Both the horizontal and vertical
components of the ground motion were used in this study.
69
6.2.1 Earth Pressure
The normal stresses in the x direction at all nodal points along the front
face of the backfill were extracted. The negative nodal point xstress indicates
compressive stress to both backfill and wall and the positive nodal point xstress
implies zero wall pressure. The static gravitational force corresponding to 1.0 g
was applied in 25 increments over 10 seconds. The increment magnitude (time
step size) was internally adjusted to enhance the convergence. After the
completion of the static analysis, the seismic analysis was initiated. The duration
of the seismic shaking is 13.52 seconds and the total time duration for the analysis
is 23.52 seconds.
Figure 6.1.a shows the ground motion history with the peak ground
acceleration at t = 5.32 seconds into the earthquake or 15.32 seconds into the total
analysis. Figure 6.1.b thru e show the earth pressure time histories at four different
heights of 3.0, 6.0, 9.0 and 11.0 meters from the wall base under a chosen ground
motion. The earth pressure magnitude decreases from its maximum at the wall
base level toward the wall top. In fact, the earth pressure higher than 6.5 meters
becomes insignificant.
The wallbackfill interface separation was observed from the wall top to a
depth of 4.5 meters. The instantaneous increase in earth pressure right at the
initiation of seismic shaking was observed at all nodal points close to the wall top
as shown in Figure 6.1.c, d and e. This could be resulted from the slapping effect
70
when the wall and backfill come together under seismic load after the separation
under static load. The tensile stress along the front face of the backfill implies the
wallbackfill separation. As shown in the Figure 6.1, maximum earth pressures
synchronize with the peak ground acceleration at time of 5.32 seconds. This
synchronization effect is very critical to the wall design. It implies that all
maximums do synchronize with the peak ground acceleration.
Figure 6.1 Synchronization of maximum earth pressure with HPGA
71
20 ro Pi 10 
2? 0 w _m .
M Ll_J.ll sic: 2
4
P cl 20 
t 30
W 40 J
5 10 15 20 25 Time [sec] c. Time History of Earth Pressure, (6m from base) 10m wall under ah=0.687g Motion
25 1 Of) _
ro 15 .
& 10 
Â£ 5 
3 0 8 0
Â£ _Â£>' _a n
T .
UJ 1 J m 20
25 J JJ
5 10 15 20 25 Time [sec] e. Time History of Earth pressure, (11m from base) 10m wall under ah=0.687g Motion
Figure 6.1 Synchronization of maximum earth pressure (contd)
72
6.2.2 Bearing Pressure
Nodal point ystresses beneath the concrete wall footing were extracted as
data for time history of the bearing pressure. Time histories of the bearing pressure
plots represented to wall toe. Figure 6.2 shows the synchronization of the
maximum bearing pressure with peak ground acceleration. Main title of the Figure
6.2 indicates point applications from the wall toe. Maximum bearing pressure
occurred right below the concrete wall stem, cause concentration of the stress
higher at this section. Compressive stress decreased rest of the footing length.
Length of the footing was 1.65m which is 16.5% H. Where H is the wall height
above the ground surface.
Figure 6.2 Synchronization of maximum bearing pressure with HPGA
73
Time [sec]
d. Time History of Bearing Pressure, (1.65m from toe)
10m wall under ah=0.687g Motion
Figure 6.2 Synchronization of maximum bearing pressure (contd)
74
6.2.3 Wall Deformation
Nodal point xdisplacements along the concrete wall face were selected to
plot time histories of the wall forward displacement. Figure 6.3 shows
synchronization of the maximum wall deformation with the horizontal peak
ground acceleration at the wall toe and the top. Maximum wall displacement was
occurred at the wall top for 10m wall.
Figure 6.3 Synchronization of the maximum deformation with HPGA
75
6.2.4 Inclusion Stress
In order to do reasonable comparison between transient analysis and
maximum connection stress envelope Figure 6.4a was placed before inclusion
stress time histories. Figure 6.4a shows that the maximum wallinclusion
connection stress occurred at the wall top and it decreases within the depth.
Nodal point xstresses at the wallgeogrid connection were selected to plot
time histories of the inclusion stress. Figure 6.4bi shows synchronization of
maximum inclusion stress with peak ground acceleration. Maximum inclusion
stress occurred at the inclusion #1, the very top inclusion layer for the 10m wall.
Inclusion numbers increase within depth. A total of 20 inclusions were placed in
the 10m wall with a spacing of 0.5 meters. Figures 6.4bf show a sudden increase
in connection stress after static loading and decreased within the depth. This
phenomenon could be caused by the imposition of seismic shaking at the end of
the static analysis where the wallbackfill separation took place in the top one third
of the wall height. All connection stresses are tensile except the for the bottom
three inclusions, where the maximum stresses become compressive in Figure 6.4g
and h because of the existence of the compression zone near the wall footing.
76
/innn
03 Q; ^nnn . I I I I I I l I ! I
Stat Connection Stress
1 2000
Dy lC onn ect ion Sti ess
CO c 1000 
o
= 0 ; O 1000
23456789 10 11 Wall Height [m] a. Max Inclusion Connection XStress along the wall height, 10m wall under ah=0.687g Motion
Time [sec]
b. Time History of Inclusion Stress (Inc # 1,at conn)
10m wall under ah=0.687g Motion
Figure 6.4 Synchronization of maximum inclusion stress with HPGA
77
Figure 6.4 Synchronization of maximum inclusion stress (contd)
78
nT 200 Q_
CO s>
c _4nn .
CO ^uu 3 c 600 
5 10 15 20 25 Time [sec] h. Time History of Inclusion Stress (Inc # 20, at conn) 10m wall under ah=0.687g Motion
Figure 6.4 Synchronization of maximum inclusion stress (contd)
6.2.5 Summary
Maximum earth pressure, bearing pressure, wall deformation, and inclusion
stresses are synchronized with horizontal peak ground acceleration at 5.32 sec of
dynamic analysis time history. A sudden increase observed after static loading in
earth pressure and connection stress time histories. This phenomenon could be
caused by the imposition of seismic shaking at the end of the static analysis where
the wallbackfill separation took place in the top one third of the wall height.
79
6.3 Transient Performance of 10m wall
under ah=0.687g and av=0.408g Motion
Both the horizontal and vertical component of the Imperial Valley
earthquake ground motion was selected in this study. Figure 6.6a and b
represented time histories of horizontal and vertical acceleration. The scaling
factor for the horizontal and vertical ground motion were 1.5 and 3. The peak
acceleration in the vertical direction (0.136g) is roughly equal to one third of the
peak acceleration in the horizontal direction (0.458g). Thus, with the scaling
factor of 3, the vertical peak ground acceleration becomes 0.408g. With the
scaling factor of 1.5, the peak horizontal acceleration becomes 0.687g.
6.3.1 Earth Pressure
Vertical acceleration caused more stress beginning of the dynamic analysis
time history. The maximum earth pressure occurred at the wall base and decreased
linearly till 8meter from the base. There was almost no compressive earth
pressure at the top 3meter of the wall, related to the wallbackfill separation.
Maximum earth pressures synchronized with horizontal ground motion except top
3meter of wall height. Figure 6.5 show time histories of earth pressure under
1.5H+3V motion. Title of the Figure 6.5 also indicated represented elevation from
the wall base as well. The wall completely separated from backfill at top 3m there
were almost no compressive stresses. The wall moves forward and backward. Top
80
of the wall at 11m from the base, there was very small compressive stress,
correlated to the wall backward movement and separation in Figure 6.5f.
6.3.2 Bearing Pressure
Time histories of the bearing pressure were not synchronized with
horizontal peak ground acceleration. Figure 6.6 shows time histories of bearing
pressure represented about wall toe. General shapes of the bearing pressure time
histories are pretty similar to vertical acceleration time histories. Maximum
bearing pressures were almost synchronized with vertical peak ground acceleration
not horizontal.
6.3.3 Wall Deformation
Time histories of wall forward displacement at the bottom, middle and top
were synchronized with horizontal peak ground acceleration shown in Figure 6.7a,
b and c. Maximum forward displacement occurred at wall top for 10m wall.
6.3.4 Inclusion Stress
Figure 6.8 was shown synchronization of maximum inclusion stresses with
horizontal peak ground acceleration. Bottom couple of inclusion layers was
compression stress affected by wall heel upward movement and stem tilt.
81
a. Horizontal Acceleration Time History
PGA=0.458G at 15.32 sec
& 0.2 1 C Â£ 01 . Time [sec] 5 10 15 20 25
ra u1 0) 8 o O < 0 1
Ujl ill Â§
IN
s  0.2 
b. Vertical Acceleration Time History PGA=0.136G at 13.04sec
Time [sec]
10 15 20
25
c. Time History of Earth Pressure, (1.5m from base)
10m wall under ah=0.687g ; av=0.408g Motion
Figure 6.5 Synchronization of maximum earth pressure with HPGA
82
TO
CL
&> 100
3
tA
(rt
a>
Â£ 200
TO
^ 300
Time [sec]
5 10 15 20 25

' Jii ikMUilL
y 1 1 mt 0 ''V \l
w f
d. Time History of Earth Pressure, (3m from base)
10m wall under ah=0.687g ; av=0.408g Motion
100 'to' CL Time [sec] ) 5 10 15 20 25
Earth Pressure tin c o o c
ui mm Ai ki m m ** m %
r T
e. Time History of Earth Pressure, (7.5m from base) 10m wall under ah=0.687g ; av=0.408g Motion
>
CL
e
ro
LLI
Time [sec]
10 15
20
25
f. Time History of Earth pressure, (11m from base)
10m wall under ah=0.687g ; av=0.408g Motion
Figure 6.5 Synchronization of maximum earth pressure (contd)
83
'to 0  CL ^ .mn . Time [sec] 5 10 15 20 25
1 i
=> tf) <8 200
CL o> _nnn .
TTf,T
C to Ann .
a. Time History of Bearing Pressure (0.15m from toe) 10m wall under ah=0.687g ; av=0.408g Motion
c 0 i Time [sec] 5 10 15 20 25
CO S: 100 
(1) 3 200  S
S tr
<0 d) n* _^nn . IL I il l Hr
1 inflil .kk J
JZ c 4Q0 . H rl r
f
to a> .son i
b. Time History of Bearing Pressure (0.4m from toe) 10m wall under ah=0.687g ; av=0.408gMotion
Time [sec]
c. Time History of Bearing Pressure (1.65m from toe)
10m wall under ah=0.687g ; av=0.408g Motion
Figure 6.6 Time histories of bearing pressure
84

PAGE 1
EFFECTS OF VERTICAL GROUND MOTION INTENSITY ON HYBRID RETAINING WALLS by Otgontulga Suidiimanan B.S., Mongolian Technical University 1993 M.S., Mongolian Technical University, 1995 A thesis submitted to the University of Colorado at Denver in partial fulfillment of the requirements for the degree of Master of Science Civil Engineering 2002
PAGE 2
This thesis for the Master of Science degree by Otgontulga Suidiimanan has been approved by Date
PAGE 3
Otgontulga Suidiimanan (M.S., Civil Engineering) Effects of Vertical Ground Motion Intensity on Hybrid Retaining Walls Thesis directed by Professor NienYin Chang ABSTRACT During last five years a hybrid retaining wall system has been investigated by Professor NienYin Chang and Dr ShingChun Trever Wang at the Center for Geotechnical Engineering Science (CGES), University of the Colorado at Denver. A hybrid wall adopts the features of continuous rigid facing from conventional retaining wall and reinforcement in the backfill from MSE retaining wall. It is a remarkable innovation of the retaining wall system. This thesis study was a continuation of previous research and focused on effects of vertical ground motion, real time history analysis, wall height and wall geogrid connection conditions for a 10 and 20m hybrid retaining walls. Numerical analysis of hybrid retaining wall system was performed using the NIKE3D finite element method computer program. Imperial Valley earthquake in both horizontal and vertical motion were selected as seismic loads. Real time history analyses were examined on 10m wall under ah=0.687g and ah=0.687g; av=0.408g motion using the GRIZ postprocessor, where ah and av are horizontal and vertical peak ground acceleration. lll
PAGE 4
Analysis results responded coefficient of vertical acceleration is one of the essential factors for the seismic resistant retaining wall. However, conventional externally stabilized wall and in the MononobeOkabe method were not assumed reinforcement in the backfill, neglecting vertical ground motion effect for the calculation of the seismic resultant force and their results could be wrong. This thesis study could consequently initiate first analysis of vertical acceleration effect on hybrid retaining wall This abstract accurately represents the content of the candidate's thesis I recommend its publication Signed lV
PAGE 5
ACKNOWLEDGEMENT This thesis was performed under the supervision of Professor NienYin Chang and Dr. ShingChun Trever Wang. I am grateful for their guidance, support and encouragement throughout my study at the University of Colorado at Denver. I also would like to thank Professor John R. Mays for serving on the final examination committee. Dr. NienYin Chang, Director of Center for Geotechnical Engineering Science (CGES) has established a collaborative agreement with Dr. Mike Puso at the Lawrence Livermore National Laboratory (LLNL), which allows the access to the NIKE3D source code for further development and its use in the nonlinear analysis of difficult soilstructure interaction problems. I would like to express my great appreciation for the permission to use the NIKE3D program Gratitude is also extended to our NIKE/SSI group members for sharing knowledge and information, particularly Dr. Fatih Oncul and Mr. Kevin ZehZon Lee. The financial support from the Government of Mongolia and Department of Civil Engineering at the University of Colorado at Denver in the forms of tuition scholarship and research assistantship through various CDOT research projects is also greatly appreciated
PAGE 6
Finally, I would like to thank to my father Suidiimanan Sodov, mother Orolmaa Sanjmyatav, wife Narantuya Amarbayar son Hashkhuu and Mitchell for their unfaltering understanding and support while I was working on my thesis.
PAGE 7
CONTENTS Figures .............................................................................................................. xii Tables ............................................................................................................... xvi Chapter 1 Introduction ..................... ..... ....... .... .............. ..... ........................................... I 1.1 Problem Statement ........................................................................................ 1 1.2 Objective ....................................................................................................... 2 1.3 Research Approach ....................................................................................... 2 1.4 Engineering Significance .............................................................................. 4 2 Literature Reviews .................... ... ... ................................................ .............. 5 2 I Introduction ... ................................ ............................................ ................... 5 2.2 MononobeOkabe Method ....................................... .... ........ ...... ............. ..... 5 2.2.1 Revision to MononobeOkabe Method ...................................................... 9 2.3 Seismic Analysis ofMSE Segmental Retaining Walls .................. .... ......... 11 2.3.1 Potential Failure Modes ..... ...................................................................... 12 2.3 2 Seismic Performance ofMSE Walls with Full Height Rigid Facing ................................................................. 14 Vll
PAGE 8
2.4 Summary of Seismic Pressure Evaluation Method by Victor Elias Barry R. Christopher and Ryan B. Berg (2001) .................... 16 3 Theoretical Background ofNIKE3D Program ........ .. ........ ........ .............. ..... 24 3.1 Implementation ofNIKE3D Program ........................................ .... .. ...... ..... 24 3.2 Interface Formulation ............ . ....... .............. ................ ................... ...... ... 25 3.3 Material Models ofNIKE3D .......................... ...... ..................................... 26 3.3 1 RambergOsgood Nonlinear ModeL. ... ...................................... .............. 27 3.4 Eigenvalue Analysis and Rayleigh Damping .............. .... .... .................... . 28 4. Analysis Program and Input Parameters .. ............. ... ............... ................. ..... 29 4 1 Purpose .... ......................... ... .. .. .... ..... .................................. .. .. ............. ... 29 4 2 Input Parameters ............... .... .. .... ... ............... ....... ......... ...................... .... 30 4.2.1 Applied Loading ................................ ..................................................... 30 4.2 2 Wall Geometries ....................... ........ .................................. .................... 32 4.2.3 Boundary Conditions ......... ....... ........................ ......... ........................... 33 4.2.4 Sliding Interfaces .... ....... .. ........................................................................ 38 4 2.5 Material Models and Parameters ....... ........ ........ ................... ... ................ 40 5 Presentation and Interpretations of Analysis Results ........... .... ... .. ............... .45 5 1 Introduction .......................... .. .... ........... ....... ....................... : ... .... .... .... ...... 45 5.2 Time Histories of Resultant Earth Pressure, Resultant OTM and Moment Arm ............................................................. .4 7 Vlll
PAGE 9
5.3 Time Histories of Resultant Bearing Pressure, OTM and Moment Arm ..... ..... .................................................................... 50 5.4 Time Histories of Wall Forward Displacement .......................................... 52 5 5 Time Histories of Resultant Inclusion Stress and Overturning Moment . ..... ... .... ... .......... .... ...................... ... ... .......... ... 54 5 6 Maximum Stresses, Resultants, Shear and Moment Imparted on Concrete Wall Section ......................... ... ...... ........... ... ..... ..... 56 5 7 Maximum Bearing Pressure ........................................................................ 60 5 8 Maximum Wall Deformation ... ... ................. ....... ................ .... .... ............... 64 5.9 Maximum Inclusion Stress ............................. ........................................... 66 6. Discussion ofResults ............ .... ........................ ........................................... 69 6 1 Introduction .... ... ...... ...... ............ . ...... .... ..... ....... ......... ........ ... ...... ....... ..... 69 6.2 Transient Performance of 10m wall under ah=0.687g Motion .................. 69 6.2.1 Earth Pressure ........................................... ... ..................... ...... ................. 70 6.2.2 Bearing Pressure ......... ............................................................................ 73 6.2 3 Wall Deformation ............ ....... ................. ..... ...................... ....... .............. 75 6 2.4 Inclusion Stress .............. ............. ............... .... ................. .... ..................... 76 6.2.5 Summary ........................ ..... ..................................................................... 79 6.3 Transient Performance of 10m wall under ah=0.687g and av=0 408g Motion ..................................................... 80 6 .3.1 Earth Pressure ............... ...... .............................................. ... ................. ... 80 lX
PAGE 10
6 3.2 Bearing Pressure .... ... .................................................... ... ........ .......... .... . 81 6.3.3 Wall Deformation ...... .... : .......... ......................................... ........... ..... ..... 81 6.3.4 Inclusion Stress ..... .......... ....... ............ ........ ...... .... ................. ......... ... ...... 81 6.3 .5 Surnrnary ... ............ ...... .......... ... ......... ..... .. .. ...... ........................ ...... ...... .... 87 6.4 Effect ofWall Height ................ ... ............................................................... 88 6.4.1 Earth Pressure ...... .. ...... ......... ............ ....................... ................ ........ ...... 88 6.4.2 Bearing Pressure ....... .... .... ...... ..... ...... ............................................. ....... 91 6.4.3 Wall Deformation .... ........................................... .................................... 93 6.4.4 Inclusion Connection Stress ...... ..................... ............ ... ..... ..... ..... ..... ...... 95 6.5 Effect of Ground Motion Intensity ............ ................... .... ... ............ .... ...... 99 6.5.1 Earth Pressure ........ ...... ........ ....... .......... ........................... ... .............. ... .... 99 6.5.2 Bearing Pressure ..... ............................ ......... ............... .... . ..... .............. 100 6.5.3 Wall Deformation ................ .... ........................................................ ..... 101 6.5.4 Maximum Connection Stress ................................................................. 101 6 6 Effect of Inclusion Connection Condition ................................................ 1 02 6.6.1 Earth Pressure ......... ... ....... ...... ............ ............... ..... ......... ... .................. 1 02 6.6.2 Bearing Pressure .................................................................................... 1 04 6 6.3 Wall Deformation .. ................. ............. .......... ...... ................ ..... ........... 106 6.6.4 Inclusion Stress ..................... ... ........... ... .......................... ....... ........ .... ... 108 6. 7 Comparison FEM Results with Conventional Method and Current Design Specification 2001 ....................................... 111 X
PAGE 11
6 .7.1 Comparison Results ofM0 Method with NIKE3D .... ........ ..... ........... 111 6. 7 2 Comparison Results ofNIKE3D with Current Design Guideline 2001 ................... ....... . ............ .... . ..... 112 7 Summary, Conclusions and Recommendation for Future Study ..... . ....... 120 7.1 Summary ............... ... ...... ....... ....... ....................................... .................. 120 7.2 Conclusions .... ....... .............................................................. ................... 121 7.3 Recommendation for Future Studies ..... ... ..... .... ....... .............. ................ 124 Appendix A 1. Transient Analysis of 10 m wall under 1.5H Motion ............................. 126 A2. Transient Analysis of 10m wall under 1.5H+3V Motion .. .. ................... 141 B. Lateral Earth Pressure Distribution Behind Concrete Wall Section .......... 155 C. Bearing Pressure Distribution Beneath the Wall Footing .......................... 160 D. Wall Face Deformation ........................................................................... ... 165 E 1 Inclusion Stress Distribution for 10m Wall ................. .... ....................... 170 E2. Inclusion Stress Distribution for 20m Wall ............ ........ ..... ....... ........ .. 213 F Coulomb and MononobeOkabe Active Thrust Calculation Spreadsheet .... ................ ..... ... .................. .... .... . .......... ....... . 326 References ..................... .... ............ ............ ................ ... ......... ......... . ...... ..... 329 Xl
PAGE 12
FIGURES Figure 2.1 Forces acting on active wedge in MononobeOkabe analysis .............. 6 2.2 Forces acting on passive wedge in MononobeOkabe analysis .... ........ 6 2.3 Total earth pressure distribution due to soilweight .... ..... ......... ........ 10 2.4 Typical geosynthetic reinforced retaining wall with segmental facing ..... ...................... ........ ..... . ..... ... ... ......... ......... 13 2.5 Potential failure modes ofMSE segmental retaining wall ......... ....... 13 2.6 Staged construction procedure for FHR facing retaining wa11 .... ........ 15 2. 7 Typical MSE retaining wall with FHR facing ...... .......... ................... 15 2.8 Seismic externally stability of a MSE wall ..................... ......... ....... . 17 2.9 Contour map ofhorizontal acceleration coefficient ................. ......... 18 2.10 Seismic internal stability of a MSE wall .... ....... ..... . ................ ........ ... 23 4.1 Loading curves adopted in NIKE3D analysis .. ... ......... ... ... ..... . .... .... 31 4 2.a 10m wall dimensions and materials ....... . . ......... ........................ .... 34 4.2.b 10m wall finite element mesh ............... . . ................ ........ ......... ... 35 4.3.a 20m wall dimensions and materials ..... ... .......................................... 36 4.3. b 20m wall finite element mesh .... ............ . ................ . . ....... ........... 37 4.4 Boundary conditions used in analysis ..... ..... ....... ............................ . 38 5.1 Selected nodal points for analysis result presentation ................ ....... .47 XII
PAGE 13
5.2 Time history oflateral earth pressure net thrust ................................. .49 5 3 Time history oflateral earth pressure net OTM ................................ .49 5.4 Time history of moment arm of earth pressure ........ .......................... 49 5.5 Time history of bearing pressure net thrust N ..................................... 51 5.6 Time history ofbearing pressure net OTM .............. ......................... 51 5.7 Time history ofbearing pressure net moment arm .............................. 51 5.8.a Time history ofwall forward displacement (at bottom) ..................... 53 5.8.b Time history ofwall forward displacement (at top) ............. ............. 54 5.9 Time history of inclusion net thrust ..................................................... 56 5.10 Time history of inclusion net OTM ............ . ......... .... . ....................... 56 5 .11 Static and dynamic earth pressure distribution imparted on 20m wall under ah=0.458g Motion ............. .................. 59 5 .12 Net thrusts imparted on 20m wall under ah=0.458g Motion ..... ......... 61 5.13 Shear and moment diagram for 20m wa11 .......................................... 62 5 .14 Example of resultant static and dynamic thrusts and their point applications for 20m wall ..... ..................................... 63 5.15 Example ofbearing pressure distributions for 20m wall ................... 63 5 .16 Static and dynamic resultant bearing pressures and resultant overturning moments for 20m wa11 .............................. 64 5.17 Wall displacement for 20m wall under ah=0.458g Motion ................ 65 5 .18a Maximum dynamic inclusion stresses for 10m wall .......................... 67 Xlll
PAGE 14
5 .18b Maximum dynamic inclusion stresses for 20m wall.. ........................ 68 6.1 Synchronization of maximum earth pressure with horizontal peak ground acceleration .......................................... 72 6.2 Synchronization of maximum bearing pressure with horizontal peak ground acceleration ............................................ 73 6.3 Synchronization of maximum deformation with horizontal peak ground acceleration ............................................ 75 6.4 Synchronization of maximum inclusion stress with horizontal peak ground acceleration ............................................ 77 6.5 Synchronization of maximum earth pressure with horizontal peak ground acceleration ............................................ 82 6.6 Time histories ofbearing pressure ....................................................... 84 6. 7 Synchronization of maximum wall deformation with horizontal peak ground acceleration ............................................ 85 6.8 Synchronization of maximum inclusion stress with horizontal peak ground acceleration ............................................. 86 6.9 Earth pressure distribution for 10 and 20m walls ............................... 89 6.10 Bearing pressure distribution for 10m wall ........................................ 92 6.11 Bearing pressure distribution for 20m wall attached case .................. 92 6.12 Wall forward displacement for 10 and 20m walls ............................. 94 6.13 Inclusion connection stress for 10m wall ........................................... 96 XIV
PAGE 15
6.14 Inclusion connection stress for 20m wall attached case ..................... 96 6.15 Seismic induced earth pressure ............................................................ 99 6.16 Seismic induced bearing pressure ...................................................... 1 00 6.17 Seismic induced forward displacement ........... ................................. 1 01 6.18 Seismic induced maximum connection stress ................................... 1 01 6.19 Earth pressure distribution for 20m wall (attached & detached) ...... 103 6.20 Bearing pressure distribution for 20m wall attached case ................ 1 05 6.21 Bearing pressure distribution for 20m wall detached case ............... 1 05 6.22 Forward displacement for 20mwall (attached & detached) ............ 107 6.23 Dynamic inclusion stress ( att) 20m wall under horizontal motion .. 1 09 6.24 Dynamic inclusion stress (det) 20m wall under horizontal motion ... 110 6.25 M0 maximum earth pressure ........................................................... 117 6.26 AASHTO maximum earth pressure ................................................... 117 6.27 NIKE3D maximum earth pressure .................................................... 117 6.28 Resultant OTM at wall base for 10m wall ....................................... 118 6.29 Resultant thrust imparted on wall for 10m wall ............................... 118 6.30 Point application from wall base for 10m wall ................................ 118 6.31 Resultant OTM at wall base for 20m wall ....................................... 119 6.32 Resultant thrust imparted on wall for 20m wall ............................... 119 6.33 Point application from wall base for 20m wall ................................ 119 XV
PAGE 16
TABLES Table 4 1 All analysis table ... ...... ....................... .......... .. ... ...... .................... ......... 30 4.2 Results of RAMBO program for average sand of 125 psf .. .. .. .. .. .... .42 4.3 Mechanical properties of commercially available geogrid ......... .. ...... .43 4.4 Input material parameters for the thesis study .. .. .. ..................... .......... 44 6.1 Resultant earth pressure for 10 and 20m walls ..... ................... .. ... ...... 90 6.2 Resultant bearing pressure for 10 and 20m walls ............................... 93 6.3 Resultant displacement for 10 and 20m walls ...... ............. ................. 95 6.4 Inclusion connection stress for 10m wall .................................. ........ 97 6.5 Inclusion connection stress for 20m wall ...... ... .... .... ............. ......... .. 97 6 6 Resultant earth pressure for attached and detached case ......... ....... . 1 03 6.7 Resultant bearing pressures for attached and detached case ........ ...... 106 6 8 Deformation and tilts for attached and detached case .................. ..... 1 08 6.9 Results ofMononobeOkabe method .. .......... ... ........ ....... ..... ..... . ... 113 6.10 Results ofNIKE3D analysis .... ... ....... ..... ....... ......... .. ....... .... ............. l14 6 .11 Results of current design guideline 2001 .... ...... .................... ... ......... 115 XVI
PAGE 17
1. Introduction 1.1 Problem Statement Retaining wall serves principally to support or resist lateral earth and water pressure. It can be found almost everywhere in civil related work, highway retaining walls, bridge abutments, building basement walls, earth dams, and waterfront bulkhead. Conventionally retaining walls are divided into two major groups, externally and internally stabilized walls. The externally stabilized walls include gravity and semigravity wall, cantilever wall, and sheet pile wall. The internally stabilized walls include wrapped around walls, mechanically stabilized earth (MSE) segmental walls, geosynthetic reinforced soil (GRS) walls. Typically advantages of internally stabilized MSE and GRS walls are low material cost, short construction period, and ease of construction. Externally stabilized conventional retaining walls require less excavation, however they are usually cost more. The Center for Geotechnical Engineering Science at University of Colorado at Denver has devoted the last four years of its research effort on a hybrid retaining wall system that combined advantage of externally and internally stabilized walls subjected to seismic loading. This study continues the previous research and focuses more on the effect of horizontal and vertical acceleration intensities, wall heights and wallgeogrid connection conditions.
PAGE 18
1.2 Objective The objectives of this thesis study are to numerically examine the seismic responses of 10 and 20m hybrid retaining walls and further to formulate the guidelines for the design. The study is focused on the effect of the combination of horizontal and vertical ground motion, wall height and wall stem, inclusion connection on the seismic wall response. Finite element method computer program named NIKE3D was used as a numerical analysis tool for this study. The Imperial Valley ground motion time histories in both vertical and horizontal directions were adopted in this study as a seismic loads. A total sixteen cases of analysis were analyzed by NIKE3D program. All results were outputted by the GRIZ postprocessor ofNIKE3D, and subsequently analyzed to interpret the responses of the hybrid retaining wall system. 1.3 Research Approach Nonlinear finite element analyses were performed to assess the effects of wall height, ground motion intensity, vertical components of ground motion, and wallgeogrid connection conditions on the performance of hybrid MSE walls. An extensive finite element analysis program was carried out using NIKE3D computer code developed at the Lawrence Livermore National Laboratory (LLNL). NIKE3D has an implicit formation, excellent interface formulation and solution algorithm and large number of material models. Its implicit formulation 2
PAGE 19
produces stable solutions. Dr. NienYin Chang, Director of the Center for Geotechnical Engineering Science (CGES) at the University of Colorado at Denver has a collaborative agreement with the Lawrence Livermore National Laboratory, University of California, and Berkeley. The agreement allows Dr. Chang's research group the use and further development of NIKE3D under the condition that all improvement must be shared with the LLNL and all associated institutions and agencies. The performance of 10 and 20meter walls were investigated. The isotropic linear elastic model is adopted for the TensarGeogrid, foundation soils and concrete wall, the RarnbergOsgood model used for backfill soils. Both the horizontal and vertical components of the 10/15/1979 Imperial Valley Earthquake were used in the analysis. The former has a peak ground acceleration of 0.458G and the latter has a peak ground acceleration of0.136G. To study the effect of the ground motion intensity, scaled motion records were also used with the scaling factor of 1.0 and 1.5 for the horizontal component and 1.0, 2.0 and 3.0 for the vertical component. Two different connection conditions were tried: connected and detached were investigated. Results of analyses in terms of earth pressure along the rear wall face, wall base bearing pressure, wall displacements, and inplane stresses of Tensor geogrid; wallgeogrid connection stresses were presented in figures and summarized in tables. The contemporary approach of MononobeOkabe and current design 3
PAGE 20
guideline 2001 were used to compute seismicinduced earth pressures, resultant thrusts, and overturning moments. Comparisons were made on wall performance and conclusions drawn Finally, the major findings were summarized in the concluding remarks and areas needing further study were recommended 1.4 Engineering Significance The retaining wall forms an integral part of bridge substructure and elevated roadway support Its performance under both gravitational and seismic loads is of particular importance in a seismically active region This study provides an insight into the capability of a hybrid wall in resisting the seismic force of different magnitudes. It also investigates the effect of the vertical seismic ground motion on the performance of walls of different heights. The technical information reveals in this study constitutes a large step in the seismic design of retaining structures 4
PAGE 21
2. Literature Reviews 2.1 Introduction In this literature review, three areas were discussed First, Mononobe Okabe method and its improvement on the seismic analysis of conventional retaining wall design were reviewed. Second, the seismic performance of MSE segmental retaining wall and MSE wall with full height rigid (FHR) facing is explored. Potential failure modes of segmental retaining wall, construction stages of FHR facing retaining wall were also included the second item. Finally, the 2001design guideline for seismic analysis ofMSE walls proposed by Victor Elias, Barry R. Christoper and Ryan R.Berg was summarized. 2.2 MononobeOkabe Method The MononobeOkabe method most frequently used for the calculation of the net seismic soil thrust acting on a retaining structure. Mononobe and Okabe were developed static earth pressure theory in 1929s. The MononobeOkabe analysis is an extension of the Coulomb slidingwedge theory, taking into account horizontal and vertical psuedostatic acceleration induced inertial forces acting on the soil. A scheme of force equilibrium wedge is shown in Figure 2.1. Psuedo static accelerations acting on the wedge mass are horizontal component of peak 5
PAGE 22
ground acceleration, ( ah=khG) vertical component of peak ground acceleration, ( av=kvG), where G is the gravitational acceleration. Figure 2.1 Forces acting on active wedge in MononobeOkabe analysis (after Kramer 1996) Figure 2.2 Forces acting on passive wedge in MononobeOkabe analysis (after Kramer 1996) 6
PAGE 23
In an active earth pressure condition, active thrust with effect of earthquake P AE, from force equilibrium wedge can be determined following equation (2.1) y is unit weight of the backfill, and H is the total wall height. KAE the dynamic active earth pressure coefficient and is given by Equation 2 2 K = cos 2 (
PAGE 24
(2.4) where: P A is static component of active thrust t.P AE is dynamic component of active thrust. Seed and Whitman (1970) suggested that dynamic component acts at approximately 0.6H With known locations of static and dynamic thrust, we could determine the location of resultant active thrust P AE by Equation 2 .5. h = PAH/3 + t.P AE (0.6H) PAE where: h is the height of application above the wall base. (2 5) In the passive earth pressure condition, the horizontal component of earthquake peak acceleration has reversed direction as shown in Figure 2.2 The passive soil thrust PPE can be determined from force equilibrium wedge by Equation 2.6 for the cohesionless backfill. (2.6) KPE the dynamic passive earth pressure coefficient and is given b y Equation 2.7. KPE = cos 2 (
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(2.8) where C3 E = +8\j/)(tan(cp \j/) + COt(cp +8\j/))[1 + tan(b + \j/9)C0t(cp +E)o/)] C4 E = 1 + Jtan(b + \jl8)[tan( Cj) + \jl) +COt( Cf> + 8'l')]J The passive soil thrust has two components just like active thrust. One is static (Pp ), and other is dynamic component of soil thrust ( 6PPE ). The resultant passive thrust PpE, can be determined by Equation 2 9 (2.9) The advantage of MononobeOkabe method is that a designer can obtain closedform solution for total dynamic earth thrust, but not distribution of the lateral earth pressure with depth 2.2.1 Revision to MononobeOkabe Method The improvements to the MononobeOkabe analysis by Seed and Withman (1970), Richard and Elms (1979), and Bathurst and Cai (1995) were described in the detail. Seed and Withman (1970) concluded that vertical accelerations could be ignored when MononobeOkabe method is used to estimate P AE for typical wall design. The backfill is unsaturated, so that liquefaction problem will not arise. 9
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Figure 2.3 shows the total active dynamic pressure distribution due to soil self weight proposed by Bathurst and Cai ( 199 5 ). This total earth pressure distribution is used in the seismic design of externally and internally stabilized MSE walls. The point application of resultant total earth force depends on the magnitude of dynamic earth pressure coefficient LlKAE, and the location varies over the range of As shown in Figure 2.3c, m is the proportion relative to the wall height. + a) static component b) dynamic component c) total pressure distribution Figure 2.3 Total earth pressure distributions due to soilweight Dynamic active earth pressure coefficient KAE is the sum of static and dynamic earth pressure coefficient. KAE = KA + LlKAE (2.10) 10
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Once KAE and KA are known can be determined from Equation 2.10 by subtraction of total and active earth pressure coefficients. Horizontal peak ground acceleration coefficient kh is the key parameter of the MononobeOkabe method. Selecting this seismic coefficient is a major issue the seismic design of earth structure. Currently there is no consensus view on selecting a design value for kh. Bonaparte et al. (1986) suggested kh = 0.85Am/ G for reinforced slopes using MononobeOkabe method. Am is magnitude of the peak ground acceleration. Whitman (1990) recommended value ofkh could range1/3 to 1/2 of the Am, which correspond to 0.05 to 0 .15. AASHTO (1996) uses an equation kh = 0.85 Am /G Am /G In the 2001 AASHTO specifications, it is recommended that kh=Am = (1.45A)* A where A is maximum earthquake acceleration coefficient comes from AASHTO Division 1A contour map. In the current design practice, the selection of kh is very important for the seismic design, and its selection based on the engineering judgment, experience, and local regulations 2.3 Seismic Analysis ofMSE Segmental Retaining Walls In the recent years, segmental retaining walls with geosynthetic reinforcement have been used widely in earth retaining structure construction. A typical geosynthetic reinforced wall with segmental block facing, general view is shown in Figure 2.4. The greatest advantages of MSE walls with block facing 11
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are rapid construction, low cost, cheap labor, and less construction deformation. A large number of these geosynthetic reinforced segmental retaining walls has been built in seismically active areas. Based on observations in seismically active zone, MSE structures have been demonstrated a higher resistance to seismic induced loading than rigid concrete structures. Methods of analysis and design for segmental retaining wall have been developed to ensure stability and tolerable displacement under seismic loading (Bathrust et al. 1997; Ling et al. 1997). 2.3.1 Potential Failure Modes Potential failure modes of reinforced segmental retaining wall under seismic loading are shown in Figure 2.5 There are three general categories of failure modes : the external failure modes, internal failure modes, and the facing failure modes External failure modes are base sliding, overturning about the toe, and bearing capacity failure. Internal failure modes, include pullout, tensile over stress, and internal sliding which occur within the reinforced soil mass The third category of failure modes. the facing failure consists of connection failure, column shear failure, and toppling failure. The shear capacity in facing column can be developed through interface friction between block and concrete keys and steel bar connection through the facing hole in the vertical direction. 12
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Geosynthe1i<: I !!Tit! f J I I t Backfill I I I / Re\ooned I (oth 1Eh+I I I Oroinoqe Collection Pipe J Limas Figure 2.4 Typical geosynthetic reinforced retaining wall with segmental facing ( o) ( ewlernol failure mode) (d) pullout (internal failure mode) (g) connect>on foilur., (toeing failure mode) (b) overturning (ewternol failure mode) (e) tensile OYerstress (internal foilure mode} (h) column gh.,or foilure (focinq loilure "'Ode) (c) bl!oring capacity (ewcessive setllement) (l!xternol loilure mode) (f) internal sliding (
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2.3.2 Seismic Performance of MSE Walls with Full Height Rigid Facing MSE walls and GRSW with full height rigid (FHR) facing have been constructed in Japan since the last decade. These retaining walls serve as embankments, bridge abutments, and support for train trucks in Japanese railways. Figure 2 6 illustrates the staged construction of FHR facing walL The construction involves ( 1) a small foundation for the facing, (2) wraparound wall consists of gravelfilled bag placed at the shoulder of each layer, and (3) a thin lightly steel reinforced concrete facing connected to the geosynthetic reinforced soil wall. Note that retaining wall with cohesionless soil use geogrid as the tensile inclusion reinforcement. The vertical spacing between the reinforcement layers is about 30 em, maximum thickness of wall stem 30 em, anchorage length from 0.1 to 0.4 of the wall height. A typical layout with the components of geosynthetic reinforced soil retaining wall with full height rigid facing is shown in Figure 2.7 Tatsuoka et al. (1997) evaluated several case histories for this type ofFHR facing walls. Geosynthetic retaining wall with full height rigid facing, in comparison to geosynthetic reinforced segmental retaining wall, has greater wall stability, lower wall deformation, and lower cost. (Tatsuoka et al. 1997) In comparison of different type of walls during the earthquake 1995 in Japan, the GRSW with FHR facing has demonstrating to be more stable and less damaging against seismic force than other walls (Tatsuoka et al. 1997) 14
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c:::::::J ______ Drainage (I) lJose Concrete (?) Laying Geote.tile ond Sandbag ( 3) (lockfdt and Cornpocton (4) Secor1d Loyer >+'"(5) Laying Completed (6) Concrete Facing [rected Figure 2.6 Staged construction procedure for FHR facing retaining wall Reinforcement for C.J. C.J.Anchor Element Construction (C.J.) Geotextile or Geogrid Sandbag or Gobion rilled with Grovel Figure 2. 7 Typical MSE retaining wall with FHR facing 15
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2.4 Summary of Seismic Pressure Evaluation Method by Victor Elias, Barry R. Christoper and Ryan B. Berg (2001) The 2001 design guideline unlike the previous AASHTO, assumed inertial force of earth mass in both external and internal stabilized wall systems. During an earthquake, the retained fill exerts a dynamic horizontal thrust P AE, on the MSE wall in addition to the static thrust. Moreover, the geosynthetic reinforced soil mass is subjected to horizontal inertial force P1R=M* Am, where M is the mass of the active portion of the reinforced wall section assumed at a base width of 0.5H, and Am is the maximum horizontal acceleration in the reinforced soil mass, equal to kh. Dynamic horizontal active thrust P AE can be evaluated by psuedostatic MononobeOkabe analysis as shown in Figure 2.8. This is added to the static forces to obtain a total thrust on a retaining wall. The equation P AE was developed assuming a level backfill, a friction angle 30 degrees, horizontal acceleration coefficient (kh) equal to Am, and vertical acceleration coefficient (kv) equal to zero. a) * The procedures for seismic external stability evaluation are as follows: Select a horizontal peak ground acceleration based on design earthquake The ground acceleration coefficient A may be obtained from contour map of Division 1A of current AASHTO in Figure 2.9. Calculate the max acceleration Am developed in the wall: Am= (1.45A)* A (2.11) 16
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Re1nfo..cement. Loy&,.. H (o) Level bockf"1ll condrt.1on i I I hi ! Hz i H (b) Sloptng bockftll cond1t1on R.ot. ....o _,,II <:>rYr K.r 0.6H Figure 2.8 Seismic external stability of a MSE wall 17
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Figure 2.9 Contour map of horizontal acceleration coefficient (Division 1A) Calculation the horizontal inertia force P1 R and seismic thrust M> AE : PIR = 0.5 AmYrH2 PAE= 0.375 AmyrH2 (level backfill) (level backfill) (2.12) (2.13a) where: Yr and Yr are unit weight of reinforced soil mass and backfill respectively. Note that add to the static forces (see in Figure 2.8a) acting on the structure, 50 percent of the seismic thrust P AE and the full inertia force P1 R. The reduced P AE is used because the inertia and seismic thrust are unlikely to peak simultaneously 18
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* For the structure with sloping backfills, the inertial force (PrR) and the dynamic horizontal thrust (P AE) will be based on a height Hz near the back of the wall mass determined as follows: H2 = H+(tani)*0.5H)/(10.5tanl)) (2.14) P AE may be adjusted for sloping backfills using MononobeOkabe method, with kh =Am and kv = 0. A height ofH2 should be used to calculate P AE in this case. PrR for sloping backfills should be calculated as follows: PrR = Pir + Pis (sloping backfill) (2. 15) Pir = 0.5 AmYrHz H (2.16) Pis= 0.125 AmYr(Hzi tan!) (2.17) and P AE = 0.5 Yr(Hz)z KAE (sloping backfill) (2.13b) where: Pir is the inertial force caused by acceleration of the reinforced backfill and Pis is the inertial force caused by acceleration of sloping surcharge above the reinforced backfill, with width of contributing to PrR equal to 0.5 Hz. PrR acts at the combined centroid of Pir and Pis as shown in Figure 2.8b. The total seismic earth pressure coefficient KAE based on MononobeOkabe general expression is computed from: KAE = cod(q>\j/90+9) 2 (2.18a) cosvcod (909)cos(&909+\j/J 1 + )sin( qr1)'l') ] 1 cos) + 909 + 90+ 9) 19
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where : \jf = arctan [kh/(1kv)] is the seismic inertia angle 8 = is the wallsoil interface friction angle q> = is the soil internal friction angle = is the backfill slope angle (see in Figure 2.1) e = is the wall face slope angle (see in Figure 2 .1) The kh used for MononobeOkabe analysis of external stabilized walls may be reduced to 0.5A, provided that displacements up to 250A [mrn] are acceptable. A is a horizontal acceleration coefficient comes from contour map Figure 2.9. Kavazanjian et al. developed an expression for reduced kh and further simplified the Newmark analysis For MSE walls the maximum wall acceleration coefficient at the centroid of the wall mass, computed as following Equation 2.18b. Am used with this expression computed as Equation 2 11. (2.18b) where : d is the lateral wall displacement in [mm) It should be noted that this equation should not be used for displacements of less than 25 mrn (1 inch) or greater than approximately 200 mrn (8 inches) It is recommended that this reduced acceleration value only be used for external stability calculations, with MSE wall behaving as a rigid block. Internally, the lateral deformation response of the MSE wall is much more complex, and at present, it is not clear how much the acceleration coefficient could decrease due to allowance of some lateral deformation during seismic loading. In general, the states located in seismically active areas is to design walls for reduced seismic pressure corresponding to 50 to 20
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100 mm (2 to 4 inches) of wall displacement. It is recommended not to use this simplified approach of kh in Equation 2.18b for walls with a complex geometry toll walls (over 15m), and walls with peak ground acceleration A higher 0.3G. b) Seismic load produce an inertial force P1 (see Figure 2.1 0) acting horizontally, in addition to the static forces in seismic internal stability of a MSE wall. Inertial force will lead to incremental dynamic increases in maximum tensile force in the reinforcement. Calculation steps for internal stability analyses with respect to seismic loading are as follows : Calculate the maximum acceleration in the wall and the inertial force P1 : Am= (1.45A)*A (2.19) (2.11) where: Wa is the weight of the active zone (shaded area on Figure 2.1 0) and A is the AASHTO site acceleration coefficient in Figure 2.9. Calculate the total maximum static load applied to the reinforcements horizontal Tmax as follows: Calculate horizontal stress crh using K coefficient (2.20) where: crv = yZ overburden pressure, is the increment of vertical stress due to concentrated vertical loads using 2V: 1 H pyramidal distribution, is the increment of horizontal stress due to horizontal concentrated surcharges, if any static equivalent loads should be included for traffic barriers 21
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Calculate the maximum static tensile load component T m ax : (2.21) where: Sv is vertical spacing of reinforcement. Calculate the dynamic increment T md directly induced by the inertia force P1 in the reinforcements by distributing P1 in the different reinforcements proportionally to their resistant area (Le) on a load per unit width basis. This leads to: (2.22) which is the resistant length of the reinforcement at level I divided by sum of the resistant length for all reinforcement levels The maximum tensile force including static and dynamic component applied to each layer is: (2.23) The extensibility of the reinforcements affects the overall stiffness of the reinforced soil mass. As overall stiffness decreases, damping should increase and amplification may also increase. Thus the resulting inertia force may not be much different than for inextensible reinforcement. Additional research is needed to justify any variation based on reinforcement extensibility. 22
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Rests tent Zone _______ Inextens1ble Retnf or cements Ext.enstble Retnf o.cements Figure 2.1 0. Seismic internal stability of a MSE wall where: P1internal inertia force due to soil weight of the backfill within the active zone Le;the length of reinforcement in the resistant zone of the i'th layer T max the load per unit wall width applied to each reinforcement due to static force T md the load per unit wall width applied to each reinforcement due to dynamic force The total load per unit wall width applied to each layer : T1 0 1 = T max + T md 23
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3. Theoretical Background of NIKE3D Program 3.1 Implementation of NIKE3D Program NIKE3D is a computer program that performs finite element analysis. It is a nonlinear analysis program with 2 and 3 dimensional finite element codes specifically for solid and stmctural mechanics. NIKE3D originally developed and has been used by the Lawrence Livermore National Laboratory (LLNL) for about two decades. The 8nodes solid element and 4nodes membrane element were implemented in this thesis study. We can specify complete NIKE3D analysis following steps: Preprocessor: Ingrid and Tmegrid mesh generation program Mainprocessor: NIKE3D program PostProcessor: GRIZ data processing program PostPostProcessor: Excel, AutoCad, Mathematica, MathCad, Math Lab .. etc, visualizing, plotting, and processing program using extracted data from postprocessor GRIZ. Mesh generation INGRID program was adopted in this thesis study as like input program for NIKE3D. INGRID is a threedimensional mesh generator developed by Lawrence Livermore National Laboratory as well. Besides the mesh generation, could also use INGRID to specify external loads, element types, sliding interfaces, 24
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boundary conditions and material models and parameters for the NIKE3D. Output file from INGRID would then become the input file for NIKE3D. NIKE3D is the mainprocessor; a postprocessor was used to extract results from the main analysis The postprocessor named GRIZ was developed by same laboratory as well. The output file from NIKE3D then becomes the input for GRIZ named N3PLOT. GRIZ could animate series of specified loading increments from the analysis and digitized data could be printed to text file for other further analysis SI units were used in this study. 3.2 Interface Formulation NIKE3D program has a significant feature of interface formulation capability We could define surfaces between different material meshes and surfaces could permit voids or frictional sliding during the analysis. There are two mai n algorithms for interface capability; one is the Penalty formulation method, and other is the Augmented Lagrandian method For the Penalty method, penalty springs are generated between contact surfaces when an intermaterial penetration is detected. A penalty spring scale factor range 0.1 to 0 001 may be used to ensure convergence. Scale factor one could allow more interpenetration; default value of 0.1 to 0.001 was adopted in this study. In the current version of NIKE3D, ten interface types are available The frictional sliding with gaps interface was chosen for this study. Sliding interface 25
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definition defined in the preprocessmg program INGRID. Frictional sliding interface with gaps could happen between two contacting surfaces, one is the master surface, and the other is the slave surface Selection of master or slave contacting surface is arbitrary. The sliding surfaces in this study were defined all planar. 3.3 Material Models of NIKE3D. NIKE3D program includes twentytwo material models. These constitutive models cover a wide range of elastic, plastic, viscous, and thermally dependent material behavior. In the latest version of NIKE3D, soil and concrete materials respectfully as RambergOsgood model or the Oriented Brittle Damage model where energy dissipation is allowed. RambergOsgood nonlinear model were adopted in this study for the backfill soil. There are four types of material used in the study. Foundation soil, concrete wall, and inclusion materials were simulated using the isotropic elastic model. The only material that used RambergOsgood model was backfill soil. The material density is required for all materials For isotropic elastic model, the required input parameters are Modulus of Elasticity and Poisson's Ratio. 26
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3.3.1 RambergOsgood Nonlinear Model The RambergOsgood model is used to treat the nonlinear behavior of many materials. In this model, five material model parameters required: (1) reference shear strain yy, (2) reference shear stress ty, (3) stress coefficient a, ( 4) stress component r, and (5) bulk modulus K. The stress strain relationship for monotonic loading in RambergOsgood model is given by equation 3.1 (3.1) where: t is the shear stress, and y is the shear strain. The model approaches perfect plasticity as stress exponent r approaches infinity. Equation 3.2 is for model unloading and reloading material behavior after the first reversal. (3.2) where : c0 and y0 represent values of shear stress and strain at the point of load reversal. A computer program named RAMBO was developed specifically for determining these five material model parameters. 27
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3.4 Eigenvalue Analysis and Rayleigh Damping NIKE3D has a capable of doing eigenvalue analysis on the proposed model. Number of mode shapes can be specified in the input file for NIKE3D. In thesis study total fifteen mode shapes were designed to the 10m wall system. NIKE3D would return a natural frequency corresponding to each mode shape. System natural frequency associated with a mode shape required coefficient for Rayleigh damping. Rayleigh damping is a system damping. It considered as damping matrix [C], and it is a linear combination of the mass matrix [M] and stiffness matrix [K] according to the following equation. [ (3.3) a and are mass and stiffness proportional damping coefficient. Natural frequencies of first and fifteenth mode were selected in the computation. Once natural frequencies selected, coefficient for Rayleigh damping can be determined following equations. = 2(co2s2 co1s1) (co;(3.4) (3.5) co1 and co2 are the first and fifteenth mode system natural frequency, units for radian/second. s1 and s2 are the fraction of critical damping corresponding to co1 and co2 respectively. 10% critical damping is adopted in this study for 10m wall. 28
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4. Analysis Program and Input Parameters 4.1 Purpose In this thesis, 10 and 20m hybrid T wall with small footing ( 16. 5% of wall height) were selected. Both the vertical and horizontal components of the Imperial Valley strong ground motion were adopted to shake the wall with both ground motion components. Sixteen different analyses were performed to investigate the transient beha v ior and the effect of wall heights ground motion intensities and wallgeogrid connection conditions. Table 4.1 All analysis table Wall Height 10m 20m Attached Attached Attached Detached 0.458* 0.687 t 0.458* 0.458* 0.458 0.687 0.458 0.458 (0.136)** (0.136)** (0.136)** (0.136)** 0.458. 0.687. 0.458. 0.458 (0.272)** (0.272)** (0.272)** (0.272) ** 0.458 0.687 0.458 0.458 (0.408)** (0.408) ** t (0.408)** (0.408)** where means horizontal peak ground acceleration ah in g **()means vertical peak ground acceleration av in g ttransient case analysis 29
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At the end of this thesis, some concluding remarks are provided on the effect of influencing parameters on the performance of the hybrid walls. 4.2 Input Parameters 4.2.1 Applied Loading Two types of loading were applied in each case of analysis: static loading and dynamic loading. Both horizontal and vertical components of Imperial Valley ground motion were adopted in the dynamic analysis. In the static loading gravitational acceleration (g) of 9 .81 rnlsec2 was applied linearly from 0 to lg in ten seconds from the beginning of the entire load time history and stayed constant 1 g till end of the analysis as shown in Figure 4.1 a The gravitational acceleration imposes ydirection (vertical) body force to the elements within the model. There were a total of 25 time steps in the static loading with time increment of 0.4 second. Time steps would change automatically in the dynamic analysis If some case of analysis subjected to vertical component of ground motion, vertical acceleration body force in ydirection would be combined with gravity acceleration Once gravitational acceleration is applied completely, dynamic vertical acceleration would then be applied from ten second to end of the analysis as yacceleration body force, shown in Figure 4.1 b. 30
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c 1.2 0 :;:::l Q) a; 0.8 (.) <(C) 0.6 ro c 0.4 0 :;:::l .l9 0.2 ::; v v ./ 0 C) v 0 1.25 c 0 "" Q) 0 75 uC) 0.5 13 'E 0.25 Q) > 0 1/ 0 12: 0.6 c 0 0.4 "" !! Q) 0.2 <( 0 c 0 2 0 N 0.4 ::c 0 v ./ ./ v ./ ./ 5 10 15 Time [sec) a. Static Loading Time History l .... jjU,j /" 11 ,,, 'WI 1''1' .., y v 5 10 15 5 Time [sec) b. Vertical Accreleration Time History PGA=0 136g at 13.04sec I. ..... IrA ,11 rll 1n 'l. llV ' 10 15 Time [sec] c. Horizontal Acceleration Time History PGA=0.458g at 15.32 sec 20 20 IIA. .... .... I 20 Figure 4.1 Loading curves adopted in NIK.E3D analysis 31 25 25 25
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After the first ten seconds of static loading, horizontal dynamic loading would then be applied to the system as xacceleration body force in Figure 4.1 c. The units of the input ground acceleration were rn!sec2 The time increment of 0.04 second was selected for the dynamic analysis, but, if necessary, the time step was decreased automatically until the numerical convergence was successfully reached. 4.2.2 Wall Geometries. 1Om and 20meter hybrid retaining walls were designated for evaluating the effect of wall heights on hybrid Twalls with small base (16.5%H) under seismic shaking. Retaining wall system was comprised of four different materials: foundation soil, concrete wall section, backfill soil and inclusion. Each material and its properties would be presented in Section 4.2.5. Wall height was defined as the height above the ground surface and it has onemeter embedment. Actual wall height would be H+ lm, where H is the height above the ground surface. The concrete wall stem and footing thickness were 0.5m and 0.7m, respectively. The dimension of footing was calculated proportion to the wall height, where toe length was 1.5% H, and heel length was 15% H, i.e the total base length of 16.5%H, where H is the wall height above ground surface in the front wall face. The footing dimensions were selected after an extensive analysis for optimal dimensions. 32
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For the inclusion dimensions vertical spacing between inclusions was kept at 0.5m, and all inclusions had the uniform length of lH. To avoid the effect of boundary, a total backfill length of 3H was used. In other words, the backfill was extended 2H beyond the end of inclusion. The thickness of the foundation soil stratum in front of the wall was 6m Along the wall base, the foundation soil thickness is kept at 5 meter for both walls used in the analysis. The depth of backfill wasH+ lm, the same as actual wall height. Figures 4 2a and 4 3a show the dimensions and materials of 10m, and 20m wall system, respectively Figures 4.2b and 4.3b show the mesh of 10m, and 20m wall system, respectively, for the FEM analyses. 4.2.3 Boundary Conditions. Figure 4.4 shows the boundary conditions and spatial coordinates adopted in the finite element analysis for both walls The twodimensional model with plainstrain condition was used in this thesis. The plain strain condition was applied in the zdirection normal to xy plane, thus no displacement was allowed in the zdirection. The base of the model was fixed with constraints on x and ydirection displacement. Roller condition was applied along the left and right of the mesh boundaries as shown in Figure 4.4. With roller condition, the sides could have ydirection displacement but constrained on the xdirection displacement. 33
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w eo,., o,s,., 30"' r Concrei;e Vall 101'1 101'l 1 0.51'1 (spo.dng) r Bo.ck fl\\ Sol\ l liM Inc\uslon Re lnf orcel'lent; I I Tl I 1.651'1 l Fo"oclotloo Soil 1 0.151'1 50.51'1 Figure 4.2a 1Om wall dimensions and materials
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V.J Vl 20" 0.5JI\ 301'1 1,r1Gn l llr> O.ISM I ___l L_ I T Tl I I I I II ill Ill I I I I I I I I 11 4, [ 4"' [ 4"' l 4,.., l 2"' l 2"' l 2n l 2n I eM I 21'> I 2n I eM j 4n I 4r'l l s,., [ 5r'l [ so.s,., Figure 4.2b 1Om wall finite element mesh
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I.,;.) 0\ 401'1 0.51'1 601'1 I I Concrete l Reta.lnlng Vall 201'1 ncl1.1slon Relnforcel"'t>nt ]o.ckflll elM 0 .31'1 0,5M (spa.cin g) r I ________ Fo,ndotlon Sdl}" L. IOO,:iM Figure 4.3a 20m wall dimensions and materials
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Ji c::i 0 .... 0 ru ... L.I ru 1 0 c 0 ru 37 E LJ); i1f: 1ID tIll "' ... !E ... 1' ... tE i. .... d t:::! ..1E ... != IIE: ... IItE ... E to 1: ID : ID : ID __
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/ __i___ . . . . :1 . /'"'" '"' .j_' _/ ....... ,/ / ///'/// /// /_/,. ." . '/'" .. Figure 4.4 Boundary conditions used in analysis 4.2.4 Sliding Interfaces "Sliding Interface" is one of the key features for NIKE3D. It is the contact surface between two different materials. Four sliding surfaces were defined: concretefoundation soil, foundation soilbackfill, concretebackfill, and inclusion vs. backfill. NIKE3D requires the input parameters of static and kinetic friction coefficients in sliding interface definition deck. In this study, the two coefficients are assumed to have the same value. These coefficients of friction (J.l) are calculated based on the relation between the internal friction angle of backfill ( and interface friction angle (8). With known internal friction angle the interface friction angle for concrete wall and inclusion could be determined using Equation 4.1. 38
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2 8=q> 3 (4.1) Thus friction coefficient between two materials could be computed with Equation 4 .2. = tan8 (4.2) To determine coefficient of friction for sliding interface between foundation soil and backfill, the interface friction angle and the friction of soil are assumed equal, i.e. 8 = $. The foundation soil was assumed to be an overconsolidated clay with$= 28, and 0.55. For sliding interfaces between concrete wall and foundation soil and between concrete and backfill, Equation 4 1 and 4.2 were used to determine the friction coefficient with$= 2839, 8 = 1926 to be 0.35 and 0.5 respectively. The backfill soil was assumed to dense sand and gravel mix. In case of inclusionbackfill sliding interfaces, an interface friction angle (8 = 29) was selected from direct shear test between geomembrane and granular soil performed by Lahti (1998) and from Equation 4.2, the interface friction coefficient is 0.55. Each sliding interface comprises of two contacting surfaces as discussed in Section 3.3 The number of sliding interfaces depends on the number of contacting surfaces. Each wall in this study has four concretefoundation soil interfaces, one foundation soilbackfill interface and three concretebackfill interfaces around the wall footing. The number of concretebackfill and inclusionbackfill sliding 39
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interfaces depends on the number of inclusion layers. Each inclusion layer would contribute two inclusionbackfill interfaces and one concretebackfill interface The total number of interfaces was 128 and 68 for 20m and 10mwall height respectively. 4.2.5 Material Models and Parameters Foundation Soil Hard clay was selected as the foundation soil with a sufficient bearing capacity for the wall and under the bearing pressure from the wall it behaves elastically Its Young's modulus of elasticity of foundation soil is 110 MN / m2 Poisson's ratio 0.35 and density 2100 kg/m3 The foundation soil overlies the bedrock, which is assumed nondeformable as shown in Figure 4.4 Concrete Wall Section Concrete is also assumed an elastic material of medium strength with Young's modulus of 25 GN/m2 Poisson's ratio of 0.15, and density of 2320 kg/m3 Backfill The backfill is assumed to behave nonlinearly and RambergOsgood nonlinear model is adopted to simulate its behavior. 40
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The Colorado Class 1 backfill is used in this study. It has a moist unit weight of 125 pcf (19.645 KN/m3 or 2001.5 Kg/m3.) The material model parameters are calculated using RAMBO program and are tabulated in Table 4.1. The backfill with density of 125 pcf is considered as dense sand and it has a shear wave velocity (Vs ) of 750 ft/ sec. The four of the material parameters are determined with known Ys using Table 4.1 generated by RAMBO. The fifth parameter of RambergOsgood model, bulk modulus K is calculated using the known shear modulus Gmax from RAMBO and Poisson's ratio of0.35 corresponds to cohesionless dense sand using Equation 4.3. E = 2G(1+v) (4. 3) where E is Young's modulus, vis the Poisson's ratio, and G is the shear modulus. With known E and v, the bulk modulus K could be computed with Equation 4.4. KE (4.4) The bulk modulus was calculated as K = 314 MN/m2 41
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Table 4.2 Results of RAMBO program for average sand of 125 psf Matenal for Average Sand Unit Weight .. 125 pet v. G..,., a. r l'y [t\lsec) (10) psfJ (1
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Inclusion A commercially available geogrid named Tensar SR2 was selected as the inclusion for this analysis. Table 4.2 shows the mechanical properties of Tensar SR2 geogrid. Elastic material model was used to simulate the inclusion behaviors The secant modulus of elasticity at 5% strain was used in the analysis. Table 4.3 Mechanical properties of commercially available geogrid Tensar (uniaxial) Properties Test Method Units SR2 SR3 Tensile Strength at 2 % Strain M TTMI.l lb / ft 1465 2055 XM 5% Strain M 3030 3810 XM Ultimate M 5380 7125 XM Initial Tangent Modulus M TTMl.l kip/ft 136.2 175.9 XM Junction Strength TTM1.2 % 80 80 Weight lb / yd2 1.55 1.88 Aperture Size M in 3.9 4.5 Thickness rib m 0 05 0 06 Polymer HDPE HDPE Width ft 3.3 3.3 Length ft 98 98 Weight lb 61 72 The secant Young's modulus is determined by dividing the strength at 5% strain by the geogrid thickness (0.003 m) and also by 5% strain This gives Young's modulus of 6060 kips /ft2 (2900 MN/m2). Poisson's ratio for highdensity polyethylene (HDPE) ranges from 0.37 to 0.44 and a value of0.4 was used. 43
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The geogrid inclusions were simulated by fournode membrane elements with thickness of 0.003m. Thus, no torsion or bending stiffness is allowed and the rotational degree of freedom is constrained all directions. At connections, the inclusion elements share the same nodal points with solid concrete elements. Table 4.3 summarizes all input parameters for the finite element analysis. Table 4.4 Input material parameters for the thesis study Elastic Material Model Material Name p E v [kg/m3J [MN /m2) Foundation Soil 2100 110 0.35 Concrete 2320 25000 0.15 Inclusion 1030 290 0.40 RambergOsgood Model Material Name p Yy" Ty a r K [kg/m3 ] (10"") [N!nl] [MN/m2 ] Backfill Soil 2001.5 0.1052 11003 1.1 2.349 314 Sliding Interface Interface 8 [degree] [degree] foundation soilbackfill 28 0.55 concretefoundation soil 28 19 0.35 concrete backfill 39 26 0.50 inclusionbackfill 29 0.55 Rayleigh Damping H=10m a= 3.2088 = 0.0022654 44
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5. Presentation and Interpretations of Analysis Results 5.1 Introduction Chapter 4 presented the analysis program and associated input parameters. This chapter will summarize the analysis results of the resultant thrust, overturning moment and moment arm of earth pressure and bearing pressure, inclusion stress and forward wall displacement. In studying the above items, usually only their maximum values are presented. This causes some uncertainty of if these maximum values exist simultaneously. Thus, the examination of their synchronization with the peak ground acceleration is critical to the safety study of MSE retaining walls under earthquake loads, and the issue of synchronization of all the maximums with the peak ground acceleration will have to be verified. The presentation of results is grouped as follows: 1. Transient variation Time histories of resultant earth pressure; resultant overturning moment, and the moment arm (the height of the point of application of the resultant earth pressure from the wall base). Time histories of resultant bearing pressure; resultant overturning moment and moment arm (distance from the toe of the wall). 45
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Time histories of wall forward displacement (at the wall top and bottom). Time histories of resultant inclusion forces and resultant inclusion overturning moment. 2 Maximum earth pressures, bearing pressures, inclusion stresses and wall displacements. Maximum static and dynamic earth pressure distribution, its resultant earth pressure and point of application. Maximum static and dynamic bearing pressure distribution, its resultant and point of application. Maximum static and dynamic wall displacement. Maximum inclusion tensile stress. All static loads including gravitational acceleration are applied quasistatically over an appropriate period of time One "g" gravitational acceleration was imposed incrementally to obtain the static results. Then, the earthquake ground motion was imposed with the complete accelerationtime history and the analysis results are obtained for some selected nodal points as shown in Figure 5.1. 46
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" j doto eduction dolo Figure 5.1 Selected nodal points for analysis result presentation 5.2 Time Histories of Resultant Earth Pressure, Resultant OTM and Moment Arm For determining the time history of resultant earth pressure, the results at the nodal points along the front face of backfill soil xstress were extracted from GRJZ, the post processor. By getting summation of individual resultant force (Pi) along the wall height acting on each wall section (Lilii), per time step (023.52 sec) of analysis, Equation 5.1 was used to calculate time history of resultant force (.P) with units ofkN/m. 47
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(5.1) ((J + (J ( ) p = XI X 1+1) 6h. 1 2 1 (5.2) (5.3) where P is the resultant force, P; is the individual resultant forces along the wall height, crxi is the backfill nodal point xstress with unit ofkN/m2 6h; is the height of a section of the wall between two neighboring nodal points, iindex shows increment ofthe wall. The resultant force was calculated for each time increment of analysis over 23.30 seconds. So, the time history of the resultant earth pressure (or thrust) was calculated and presented in Figure 5.2 The time history of the resultant overturning moment of earth pressure can be calculated at each time increment using Equation 5.4 and results shown in Figure 5.3. II OTM= IP;Y; (5.4) i=J 48
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0 E' 0 z 200 !!? 400 ::1 VJ VJ 600 !!? a. 800 0 iii 1000 2 1200 .r:. 1Q) 1400 z 0 0 !!? 200 ::1 VJ VJ 400 ,_ E 600 0 800 ..... 1000 0 Q) z 1200 1400 3 5 3.0 I 2 5 E 2 0 <( "E 1 5 CD E 1.0 0 0.5 0.0 0 tTime [sec] 5 10 15 20 t....... ....... .!1 An A II'AI I .A JV 'V Figure 5.2 Time History of Lateral Earth Pressure Net Thrust 10m wall under ah=0. 687g Motion Time [sec] 5 10 15 20 rtr.. 1'... ........ r..... .. l_ .. .. IV f. ., .. 1" Figure 5.3 Time History of Lateral Earth Pressure Net OTM 10m wall under ah=0.687g Motion lA n I .a Ji 'I I. Aft A lA LA. }. lf1 w ". rvv 5 10 15 20 Time [sec] Figure 5.4 Time History of Moment Arm of Earth Pressure 10m wall under ah=0.687g Motion 49 25 25 25
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where : P; Y; is the moment of individual thrust about the wall base Pi is the individual thrust acting on center of wall section L'l.hi. Y; is the location of individual resultant application measured from the wall base. The time history of moment arm of lateral earth pressure could be calculated for each time step using Equation 5.5 and the results were shown in Figure 5.4. n IP;Y; MomentArm= ....:...i=..:....I P; (5.5) Figure 5.4 shows the moment arm of earth pressure The moment arm varies from 0.5m to 3.25m from the wall base. The maximum values of resultant earth pressure and resultant overturning moment synchronized with the peak horizontal ground acceleration at the time of 15.23 second Details are presented on in Appendix A where all transient results are presented. 5.3 Time Histories of Resultant Bearing Pressure, OTM and Moment Arm The nodes along the foundation soil beneath the concrete wall footing were chosen for the evaluation of the time histories of resultant bearing pressure at each time increment of analysis The ystresses at nodal points were extracted from GRIZ as bearing pressure underneath concrete wall footing. 50
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:' z =. 1ii 2 .r:: Qj z e E z i!S ::::!! 0 Q) z I E 4: c Q) E 0 0 0 100 200 300 400 500 0 100 200 300 400 0.90 0 85 0.80 0.75 0.70 0.65 2 ...... 0 .......... 0 .._ Time [sec] 4 6 8 10 12 14 16 18 20 ........ 2 ......... .... ...... ..... ........ r... .. u 11.111 .II 1 ... IHII Figure 5.5 Time History of Bearing Pressure Net Thrust 10m wall under ah=0.687g Motion Time [sec] 4 6 8 10 12 14 16 18 ......... ........ ..... .......... I'.. r... !IIII.IOU ... '1" I,. r Figure 5.6 Time History of Bearing Pressure Net OTM 10m wall under ah=0. 687g Motion Time [sec] 5 10 15 20 11' It!'!/ IJ .... 20 .h Figure 5.7 Time History of Bearing Pressure Net Moment Arm 10m wall under ah=0.687g Motion 51 22 24 22 24 1 .. 25
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The calculation, time history of resultant bearing pressure, resultant overturning moment and moment arm were obtained the same way as calculation of earth pressure resultant using Equation 5.15.5 shown in Figure 5.55.7 by substituting N; =Pi, cryi = crxi, Xi= yi, (section of footing length between two nodal points). The wall toe was the center for overturning moment calculation. Footing length varies from 0 to 16.5% H meter. Where 0 represents the location of wall toe, 16.5%*H indicates the location of wall heel, and H is the wall height above the ground surface from the wall base. The location of the bearing pressure resultant varies from 0.68m to 0.88m from the wall toe, and its magnitude is synchronized with the horizontal peak ground acceleration. 5.4 Time Histories of Wall Forward Displacement The nodal points xdisplacement along the concrete face were selected to extract wall forward displacement information. A negative xdisplacement indicates the direction of wall movement against the positive direction of the local xcoordinate system. Figures 5.8a and b show the time histories of forward displacement at the bottom and the top nodal points of 10m wall. Analysis results show that the forward displacement reaches maximum at wall top for the 10m wall, but for the 20m wall at the middle of the wall. This difference in the relative location of the maximum forward wall displacement is caused by the same wall 52
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stem thickness used in both walls. As a result, the 20m wall is more flexible than the 10m wall. The monolithic nature of the wall provides a rigid connection between the wall stem and wall base. This yields high shear and also flexural resistances. However, the connection design becomes extremely critical in providing the necessary resistances. Thus, a sufficient reinforcement is needed to prevent connection yielding. Besides, the wall stem thick for the 20m wall should be larger than that for the 10m wall. With this new design change, the forward wall displacement may reach its maximum value at the wall top for both 10 and 20m walls. 0 5 0.0 r.... E' 0 5 t.2. 1.0 ..... c: Ql E 1. 5 2l m 2 0 0.. Ul i:5 2.5 3.0 Time [sec] 10 15 20 rI rII Ill LaJ ,, ll f.LLI 'll P' Time History of Forward Displacement, (at toe) 10m wall under ah=0.687g Motion ..A A lL. ll I_ Figure 5.8a Time histories of wall forward displacement (at bottom) 53 25
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0 5 2 'E 2 c Q) E 6 Q) (.) ro c. U) 10 0 14 Time (sec] 10 15 20 A JV Time History of Forward Displacement, (at top) 10m wall under ah=0. 687g Motion V' Figure 5.8b Time histories ofwall forward displacement (at top) 5.5 Time Histories of Resultant Inclusion Stress and Overturning Moment 25 In order to determine the time history of resultant inclusion stresses, the inclusion connection xstress of all inclusion layers was extracted from GRIZ. Once the inclusion connection xstress was gathered in spreadsheet, the time history of resultant inclusion stresses and overturning moment for each time step of analysis is calculated using Equations 5.65.8. (5.6) T=cr.8 I XI (5.7) 54
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n OTM= IT;Y; (5.8) i=l where T is the resultant tensile inclusion stresses, Ti is the individual resultant tensile force for the inclusion "i" along the wall height in kN per m, ()xi is the inclusion nodal point xstress in kN / m2 o is the inclusion thickness equal to 0.003 meter for all inclusions Y ; is the location of resultant inclusion stress for inclusion "i" measured from the wall base, and "n" is the total number of inclusion layers spaced at 0.5 m. Thus the 10m and 20m walls have 20 and 40 inclusion layers, respectively. The directions of resultant inclusion stresses and overturning moment are opposite to those of earth pressure. Figures 5.9 and 5.10 show the time histories of resultant inclusion stress and overturning moment. Also shown in the title of the figures are wall height and the horizontal (H) and vertical (V) ground motions used in the analysis and the numerical value in front of H and V shows the scaling factor of 1.5 for H and 3 for V. The analysis result shows the synchronization of the maximum values of resultant inclusion stress, and overturning moment with the peak ground accelerations. All other transient results are shown in Appendix A. 55
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50 tJ 40 2 IE 30 Q) z a. c:z 20 ::J 10 c 0 0 500 :;';! 400 0 E Q) 03 300 z a. .E UlZ 200 E 100 0 0 5 IJ ll 1'\/ y 10 15 Time [sec] Figure 5.9 Time History of Inclusion Net Thrust 10m wall under ah=0.687g Motion ll 'ij 5 10 15 Time [sec] Figure 5.10 Time History of Inclusion Net OTM 10m wall under ah=0.687g Motion 5.6 Maximum Stresses, Resultants, Shear, and Moment Imparted on Concrete Wall Section I ik '{\/' 1\. r""' v v 20 25 l U, N'i\ v 20 25 Stresses at the nodal points along the front face of backfill were extracted for determining the lateral earth pressure distribution, resultant, shear and moment imparted on the concrete wall section. The earth pressure distribution envelope 56
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could be constructed by connecting these nodal point xstresses. By integrating the area under the earth pressure distribution envelope, the resultant thrust is calculated in terms of kN / m, the force per unit longitudinal length of the retaining wall system. At the end of static and seismic loading, nodal point stresses in the x direction were used to draw the pressure distribution diagrams for static and dynamic earth pressures, respectively The inclusion nodal point xstress at the connection was used to calculate its contribution to the earth pressure and thrust. The inclusion thrust acts in the direction against earth pressure and affects the resultant thrust and its point of application. Most often it counteracts the wall displacement. Figure 5.11 shows the static and dynamic lateral pressure distribution on the concrete wall section, imparted by both backfill and inclusions of the 20m wall subjected to Imperial Valley earthquake. The static and dynamic lateral pressure distributions of all sixteen cases are shown in Appendix B The title of each figure gives the wall height, connection conditions and the ground motion combinations. The wall height on each chart was defined as that 0 meter being the wall base, 11 and 21 meters being the wall top for 10m and 20m walls, respectively. Figure 5.12 shows the static and dynamic thrust imparted on concrete wall section by both the backfill and inclusions. Individual backfill compressive thrust between two neighboring inclusions spaced at 0 5 m was calculated by finding 57
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trapezoidal area formed by their nodalpoint xstresses. Individual soil thrust would act through the mid height of the element if neighboring nodal point earth pressures magnitude were close to each other. The inclusion tensile resultant was determined by multiplying the nodal point xstress by the inclusion thickness of 0.003 meter The point of application of each inclusion force is applied at the layer location. Figure 5.13 show shear and moment diagrams associated with individual resultant forces indicated in Figure 5.12. Maximum shear and moment occurred at the wall base. These diagrams are extremely important to design reinforced concrete wall. The location of the total static and dynamic thrusts and inclusion resultants was calculated by finding center of the static and dynamic lateral earth pressure distribution diagrams The location of the total soil thrust and total inclusion resultant were calculated using Equation 5.9. n IP;Y; y=...:..:i=:..:....l __ P; (5.9) where P; Y; is the moment of individual thrust about the wall base, Pi is the individual thrust see in Equation 4.6, Y; is the point of application of each individual resultant measured from the wall base, and "i" index shows the increment ofwall height. 58
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St4tic At\Qtysis NOdQl Point XSt,.ess CStQtic Lote,.Ql [o,.th p,.essure Dlst,.lbution) CbQCkFilt ete,..."t thickness) 28.98kN/ 86.32kN/ 21.7lkN/ .C0.36kN/,..2 l09.1kN/"' 174.2kN/,..2 237.4kN/.Il 299.6kN/.Il 360.9kN/ 422.3kN/,.,I! .CS.C.JkN/J'll. SS3.2kN/,.,I! 628.7kN/.Il 70Z.2kN/"Z 77l.lkfr4/ 834.2kN/ 888.5kN/,.,I! 929.9kN/,.,I! 953.9kN/,.,I! 966.3kN/"2 986.6kN/"' 1006..3kN/,..Z 1009.6kN/"2: IOO? .CkN/"2 980.1kN/ 950.1kN/,.,I! 851.3kN/"' 782.2kN/..Z 699.1kN/"'Z 605.2kN/" 496.2kN/ 367.1kN/r. 58.46kN/ 603.8kN/,..Z 748.8kN/,.,I! Dy"a"ic Ano.lysls Nodal Poir"'t xst ... f'S!I CDyt\Gr'liC (a ... th p,..f'SSU,.. Dls1:,.1bution) Cbo.ckFIH ete"'nt thiCI<,_SS) 1539.81kN/,.,I! 1359.32kN/ 1229.84kN/ 1038.62kN/ 95DJI6kN/ 963.51kN/,.,I! 1029.58kN/..Z 1113.65kN/,.,I! lt65.35kN/"Z 1220.03kN/,.,I! 1279.65kN/,.,I! 1340.24kN/ .... 1411.31kN/,.,I! 1479 1570.9kN/ ... 1658.9kN/,.,I! 1711.07kN/,.,I! 1874.77kN/,.,I! 1922.79kN/ ... 1881.99kN/l"\l' 1992.55kN/ ... 2198.54kN/,.,I! 1785.9kN/P1 1751. 72kN/,2 1617.71kN/,.,I! l.C73.67kN/ 1241.06kN/ 1046.27kN/" 810.06kN/ 676.2kN/ 579.6SkN/..,r 490.41kN/ ... 354.08kN/ 228.52kN/.,Z 93.59kN/..Z 19.61kN/..Z 1.92kN/,..I .86kN/1"1 1 24kN/..Z 0.61kN/I"' l 9.53kN/I"'I 9.21kN/1"12 40.1kN/,I 51.63kN/.,Z 63.65kN/.,Z 76.53kN/..Z 9o.25kN/.,Z 04.91kN/,.I' 120.75kN/M2 137.59kN/"'I 155.9EikN/MI 175.6.CkN/,..I' l97.75kN/I'\I 68.19kN/,..2 85kN/ ... 2.t9ktu,..z 8.25kN/ ... 26.29kN/ ... 17.55kN/.,Z 8.35kN/..Z .24kN/f"'.l' 26kN/,..I 5.10kN/.,Z .?.CkN/,.,1' 9.30kN/,..I ll.99kN/P12 17.61kN/P'IZ 32.96kN/ ... o42.30kN/"'I 47.97kN/ ... 61.0<4kN/"I 7t.67kN/,..I 86.69kN/ ... 71.&7kN/,..z 20.98kN/I"'I 49.61kN/I"'I So4.47kN/,.2 32.33kN/ ... 56.08kN/,..I 69.82kN/..Z 9'1.,P!a.<,..:r"' 320.7kNl,..') 86.69kN/ ... 05.9kN/1"1 125.9kN/I"'I 1<46..5kN/,..I 170.3kN/"'Z 197.41kN/J'\I 225.7kN/ ... 258.5kN/.,Z 296.8kN/ ... 335.4kN/ ... 376.5kN/.,Z .C21.1kN/M 2 478.41kN/MI' 4'96.9kN/,.,2' 16.9kN/,.,I! ;,i25.3kN/ ... Figure 5.11 Static and dynamic earth pressure distribution imparted on 20m wall under ah=0.458g Motion 59
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All the resultants are shown in Figure 5.12 in dashed lines Figure 5 .14 shows the static and dynamic resultant thrusts with the corresponding height of point of application from the wall base. The points of application are much lower than those from the conventional earth pressure calculations 5. 7 Maximum Bearing Pressure All nodes along the foundation soil beneath the concrete wall footing were chosen to present the static and dynamic bearing pressures in terms of the nodal point ystresses at the end of static and dynamic analyses The negative ystress indicates the compressive stress Figure 5 .15 shows both static and dynamic bearing pressure distributions beneath the concrete wall footing, where "0" represents the location of wall toe. Higher bearing pressures occurred underneath the concrete wall stem. Appendix C contains the plots of bearing pressure for all 16 cases. Figure 5 .16 shows the distribution of static and dynamic compressive thrusts of each individual section of the wall base between two neighboring nodal points imparted onto the concrete wall footing by evaluating the resultant of bearing pr e ssures for the abovesaid nodal points Each individual resultant acts through the mid width of the foundation soil element. Static and dynamic resultants of bearing pressures were shown by dashed line in Figure 5 .16. It shows the result a nt overturning moment about the wall toe as well. 60
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Static Analysis Statlc Thrust Cotcutot. d t',.o" fl(odal Point XStrf'ss 4 7\kN /1"1 5.62kN/f'l 5 .65kN/1"1. 6.6kN/"' 5.36kN/I"\ 5.2&kN / "' 4 85kN/11 4 .o42kN/" 3.lo4kN/1'1 2.0JkN/" 1.7kN/" 1.47i
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: z Q) !::? 0 u... ... nl Q) ..c::; CJ) E' 'E z 'E! Q) E 0 Shear Diagram 20m wall under ah=0. 458g Motion 3000 2500 r.. 2000 1\ 1500 ... I' "" 1000 .... 500 / .,. ..._ ... .._ 0 0 1 2 3 4 5 6 7 8 9 1 0 11 12 13 14 15 16 17 18 19 20 21 Wall Height [m] 80000 70000 60000 50000 40000 30000 20000 10000 0 Moment Diagram 20m wall under ah=0. 458g Motion Ill \. \. lt lilt ..... Ill lila .... Ia. .. ..._ I .... ...... r0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Wall Height (m] Figure 5.13 Shear and moment diagram for 20m wall 62
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s... .. ,c ...... ,,... T ......... ... .,. S't:tc: o ............ """' (laAC04,111 ........... "..,rc ........ c .......... c ........ ,... c,.. ..... ...,c T ......... ..... .,. Dy"'"'"''c a .... .t: .... ,.......,CI 1'4o..,.,..,.._ "c"'':u ......... ..... ........ ) Figure 5.14 Example of resultant static and dynamic thrusts and their point of applications for 20m wall 326. 3kPa 429.3kPo. o .s ..... 1221.3kPo. }25M J .25M Static Pressure Dyno.Mic Pressure l48.7kPa. 161.4kPo. Figure 5.15 Example of bearing pressure distributions for 20m wall 63
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Figure 5.15 Example of bearing pressure distributions for 20m wall !697 62kN*M
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displacement is actually in the direction opposite to the positive direction of x coordinate. Appendix D gives all of 16 forward displacement graphs. The maximum wall deformation was occurred at the middle for the 20m wall in Figure 5.17. For the 10m wall the maximum displacement takes place at the wall top. This is most likely due to the same wall stem thickness was used in the calculation and the 20m wall is less stiffthan the 10m wall. Wall tilt angles inclined with vertical direction were calculated at the wall top and the middle of the wall where maximum displacement occurred. Wall tilt angle was higher where displacement was higher. It will discuss detail in next chapter for all case of analysis. Tilt was computed about the wall base. Wall height ''0'' represents wall base. Wall Height [m] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 0 I I I I I I I I 5 .... Static Displacement Dynamic Displacement f' "' 'E 10 .2. 'E:
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5.9 Maximum Inclusion Stress The inplane inclusion stresses are the nodal point xstresses along the inclusion layer. Nodal point xstresses were extracted from GRIZ for each layer. Figure 5.18a and b shows maximum dynamic inclusion stress versus inclusion length for the 10 and 20m walls The inclusions are spaced at 0.5 meters. Thus, there are 20 and 40 inclusions for 10m and 20m wall, respectively. All 16 cases of analysis graphs for inclusion stresses are included in Appendix E. The title of each figure provides the information for the layer number (#1 for the top layer) and the wallinclusion connection condition for each inclusion, wall height and ground motion combination used in the analysis. Both static and dynamic inclusion stresses are provided in the Appendix E graphs. The top inclusion has the highest in plain tensile stress and decreases drastically with the distance away from the wall face 2m, 6m and 1Om in Figure 5.18a. The connection stress was higher in plain stress till 101h inclusion. After lOth inclusion, the maximum inclusion stress was located somewhere in the backfill. Beyond 2m distances from wall face the inclusion stress was much smaller than connection stress. Inclusion connection stress was higher till 7th inclusion then maximum stress is located at the 8m from the connection till 23rd inclusion within depth in Figure 6.8b for the 20m wall. Peak maximum inclusion stress occurred at 241 h inclusion then maximum stress moved to the end of the inclusion within the depth. 66
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Very bottom 3 layers were worked in compression by effect of the wall heel deformation in 20m wall. In the Figure 6.8b maximum tensile stress was zero till 2.5m from connection in the bottom 3 layers. The Tensar SR2 Geogrid was used in all analysis. It has an ultimate tensile strength of 5,380 kips/ft (78,511 kN/m) as shown in Table 4.2. With average inclusion thickness of 3mm, ultimate tensile strength was computed to be 26,170 kN/m2 Thus, the factor of safety of the inclusion satisfies the 1996 AASHTO requirement of 1.5 against inclusion rapture failure. ro a. fJ) fJ) (/) c 0 c;; :::J u = 2500 2000 \ 1500 \\ 1000 r.... r. 500 r.. ::::: rr. 0 F= 0 Inc 1 lnc2 Inc 3 lnc4 Inc 5 1lnc6 Inc? lnc8 lnc9 Inc 10 1Inc 12 Inc 14 Inc 16 Inc 18 Inc 20 t2 I ii r, 3 4 5 6 7 Inclusion Length [m] Dynamic Inclusion Stress 1Om wall under ah=0.458g Motion 8 9 10 Figure 5.18a Maximum dynamic inclusion stresses for 10m wall 67
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ro c.. =. (/) (/) (/) c:: 0 o; ::I C3 = 2500 r"" 2000 11"" v b P" v 1500 t.. v v 1/ ...... 1v: 1000 K I'""' ...... ?D' \) "' 1 7 v v ,/ v I/ 500 I A P" / lr"' v/ / 0 0 2 4 ........ r... r..... r..::: r... b. r. f"... "" [".. _.. ...... r. t.. 1'. ...... ........ t:::: ...... rr.... ...... 11f. !'..... r.... 1:::; ......::: 1"' r. .....;;;:: r::::::: ....... r........ t..: ...... r1... t: / tt...... ,.,. v v I...11"" 1io< ...... """ ..... ? 0<. I...b:= ...... b ...... b::::: I/ """ """ ,. v / / / v / _... v 6 8 1 0 12 14 16 18 20 Inclusion Length [m] Dynamic Inclusion Stress (attached) 20m wall under ah=0.458g Motion lnc1 lnc3 lnc5 lnc7 lnc9 lnc11 Inc 13 lnc15 Inc 17 lnc19 lnc21 lnc24 lnc26 lnc28 lnc30 lnc32 lnc34 lnc36 lnc37 lnc40 Figure 5.18b Maximum dynamic inclusion stresses for 20m wall 68
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6. Discussion of Results 6.1 Introduction Chapter 5 is devoted to the interpretation of selected analysis results and this chapter to the discussion and interpretation of all analysis results in three separate groups. First, from the transient behavior of retaining walls under different ground motions the synchronization of all maximums and the peak ground acceleration is examined and verified. Second the effect of wall height, ground motion intensity and inclusionwall connection condition on earth pressure, inclusion stress, and wall forward displacement under static and seismic loading is examined in detail. Third, the earth pressure from finite element analysis is compared with the earth pressure from the M0 and current design specifications. 6.2 Transient Performance of 10m wall under ah=0.687g Motion Finite element analyses were performed to study the performance of hybrid retaining walls with a small base under different earthquake ground motion. The wall performance is measured by the lateral earth pressure acting on concrete wall, bearing pressure underneath wall footing, wall face displacement, and inclusion stress distribution along the inclusion length. Both the horizontal and vertical components of the ground motion were used in this study 69
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6.2.1 Earth Pressure The normal stresses in the x direction at all nodal points along the front face of the backfill were extracted. The negative nodal point xstress indicates compressive stress to both backfill and wall and the positive nodal point xstress implies zero wall pressure. The static gravitational force corresponding to "1.0 g" was applied in 25 increments over 10 seconds. The increment magnitude (time step size) was internally adjusted to enhance the convergence. After the completion of the static analysis, the seismic analysis was initiated The duration of the seismic shaking is 13.52 seconds and the total time duration for the analysis is 23.52 seconds. Figure 6.l.a shows the ground motion history with the peak ground acceleration at t = 5.32 seconds into the earthquake or 15. 32 seconds into the total analysis. Figure 6.l.b thru e show the earth pressure time histories at four different heights of 3.0, 6.0, 9.0 and 11.0 meters from the wall base under a chosen ground motion. The earth pressure magnitude decreases from its maximum at the wall base level toward the wall top. In fact, the earth pressure higher than 6.5 meters becomes insignificant. The wallbackfill interface separation was observed from the wall top to a depth of 4 5 meters. The instantaneous increase in earth pressure right at the initiation of seismic shaking was observed at all nodal points close to the wall top as shown in Figure 6.l.c, d and e. This could be resulted from the slapping effect 70
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when the wall and backfill come together under seismic load after the separation under static load. The tensile stress along the front face of the backfill implies the wallbackfill separation. As shown in the Figure 6.1, maximum earth pressures synchronize with the peak ground acceleration at time of 5.32 seconds. This synchronization effect is very critical to the wall design. It implies that all maximums do synchronize with the peak ground acceleration. : c 0.6 0 0.4 Q) 0.2 .;j_ 0 ]9 0.2 c 0 tJ) 0.4 J: 0 ro o c. =. 50 iil 100 tJ) 150 c. 200 250 0 rI Jli nil' ""' II' I 5 10 15 Time [sec] a. Horizontal Acceleration Time History PGA=0.458g at 15 .32 sec 20 rI ll l r11 5 10 15 20 Time [sec] ... ll" b. Time History of Earth Pressure, (3m from base) 10m wall under ah=0. 687g Motion 25 A 25 Figure 6.1 Synchronization of maximum earth pressure with HPGA 71
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ro 20 CL 10 0 ::l C/) 10 C/) 20 CL .c 30 t:: ro LU 40 ro 100 CL 80 60 ::l C/) 40 C/) 20 CL .c 0 t:: 20 ro LU 25 20 15 10 5 0 5 : 10 ro 15 LU 20 25 0 0 0 /It l7r I \A rl/1 WI '"' ....... IT .. to. ...... 5 10 15 20 Time [sec] c. Time History of Earth Pressure, (6m from base) 10m wall under ah=0.687g Motion 5 10 15 20 Time [sec] d. Time History of Earth Pressure, (9m from base) 10m wall under ah=0.687g Motion / v 1' .I Ill M "' ,. ri'T ... i1 "" ::JA. ld .. 5 10 15 20 Time [sec] e. Time History of Earth pressure, (11m from base) 1Om wall under ah=0.687g Motion .fT 25 25 25 Figure 6.1 Synchronization of maximum earth pressure (cont'd) 72
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6.2.2 Bearing Pressure Nodal pointystresses beneath the concrete wall footing were extracted as data for time history of the bearing pressure. Time histories of the bearing pressure plots represented to wall toe. Figure 6.2 shows the synchronization of the maximum bearing pressure with peak ground acceleration. Main title of the Figure 6.2 indicates point applications from the wall toe. Maximum bearing pressure occurred right below the concrete wall stem, cause concentration of the stress higher at this section. Compressive stress decreased rest of the footing length. Length of the footing was 1.65m which is 16.5% H. Where H is the wall height above the ground surface. ro a.. 0 =. 100 ::::! rn 200 a.. g> 300 Q) CD 400 r.... 0 ............... ......... r.... Iii Lo.ll. l'l I" ,., 5 10 15 20 Time [sec] a. Time History of Bearing Pressure, (0.15m from toe) 10m wall under ah=0.687g Motion 25 Figure 6.2 Synchronization of maximum bearing pressure with HPGA 73
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ro (L 0 =. 100 2! ill 200 rn 2! (L 300 Ol c: 400 Q) OJ 500 ro o 50 w 100 ::J 150 2! 200 (L Ol 250 c: 'fii 300 350 ro 0 (L " 50 2! ::J 100 rn rn 2! 150 (L Ol c: 200 Q) OJ 250 !'... 0 ............. 0 I' ...... 0 !'... ........ I""'....... I I IIU I P IW rt 5 10 15 20 Time [sec] b. Time History of Bearing Pressure, (0.4m from toe) 10m wall under ah=0.687g Motion ...... r... ....... ...... r... ....... ....... .a.! J l.il Ji. .,IY "' 'H 5 10 15 20 Time [sec] c. Time History of Bearing Pressure, (0.65m from toe) 1Om wall under ah=0.687g Motion ....... ........ ....... Ill\ 1 ... .. Ill I I 5 10 15 20 Time [sec] d. Time History of Bearing Pressure, (1.65m from toe) 10m wall under ah=0.687g Motion lA 25 25 25 Figure 6.2 Synchronization of maximum bearing pressure (cont'd) 74
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6.2.3 Wall Deformation Nodal point xdisplacements along the concrete wall face were selected to plot time histories of the wall forward displacement. Figure 6.3 shows synchronization of the maximum wall deformation with the horizontal peak ground acceleration at the wall toe and the top. Maximum wall displacement was occurred at the wall top for 10m wall 0 0 0 'E 0 5 rrr"E 1.0 Q) E 1.5 Q) () 2 0 Cll c. 2 5 fl) i:5 3 0 0 4 0 "E Q) 4 E Cll 8 a. 12 fl) i:5 16 Time [sec] 5 10 15 20 1o.. rr1o.. A ll l A '1' ' a. Time History of Forward Displacement, (at toe) 10m wall under ah=0 687gMotion Time [sec] 5 10 15 20 .AI '' IAI !"" b. Time History of Forward Displacement, (at top ) 10m wall under ah=0.687gMotion l.&_ 25 25 Figure 6.3 Synchronization of the maximum deformation with HPGA 75
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6.2.4 Inclusion Stress In order to do reasonable companson between transient analysis and maximum connection stress envelope Figure 6.4a was placed before inclusion stress time histories. Figure 6.4a shows that the maximum wallinclusion connection stress occurred at the wall top and it decreases within the depth. Nodal point xstresses at the wallgeogrid connection were selected to plot time histories of the inclusion stress. Figure 6.4bi shows synchronization of max1mum inclusion stress with peak ground acceleration. Maximum inclusion stress occurred at the inclusion #1, the very top inclusion layer for the 10m wall. Inclusion numbers increase within depth. A total of 20 inclusions were placed in the 10m wall with a spacing of 0.5 meters. Figures 6.4bf show a sudden increase in connection stress after static loading and decreased within the depth. This phenomenon could be caused by the imposition of seismic shaking at the end of the static analysis where the wallbackfill separation took place in the top one third of the wall height. All connection stresses are tensile except the for the bottom three inclusions, where the maximum stresses become compressive in Figure 6.4g and h because of the existence of the compression zone near the wall footing. 76
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4000 ro 3000 ro a.. =. Vl Vl (/) c: 0 u; ::l u E ro a.. =. Vl Vl (/) c: 0 u; ::l u E 2000 1000 0 1000 4000 3000 2000 1000 0 1000 2500 2000 1500 1000 500 0 1 0 0 I I I I I I I I I I +Stat Connection Stress I v ___, Dyn Connection Stress I / ___, ..JI"""' ./: t""' 2 3 4 5 6 7 8 9 10 Wall Height [m] a. Max Inclusion Connection XStress along the wall height, 10m wall under ah=0.687g Motion L ,al'l INI\11 jl\. ''"'' 11 r r"'1 5 10 15 20 Time [sec] b Time History of Inclusion Stress (Inc# 1 ,at conn) 10m wall under ah=0.687g Motion 'j R If u u '"' JV'I\, 11 rt"l v 'I 5 10 15 20 Time [sec] c. Time History of Inclusion Stress (Inc# 3, at conn) 10m wall under ah=0. 687g Motion ll 11 25 25 Figure 6.4 Synchronization of maximum inclusion stress with HPGA 77
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ro 500 a... 400 tl) tl) 300 (j5 200 c: 0 u; 100 :::l 13 = 0 ro 4oo a... tl) 300 en 200 c: 100 :::l 13 c: 0 ro 400 a... 300 tl) tl) 200 (/) c: 0 u; 100 :::l 13 = 0 0 0 0 I ru 'Ill ......... I .II I '\1 . v v ,., 5 10 15 20 Time [sec] d. Time History of Inclusion Stress (Inc# 10, at conn) 10m wall under ah=0.687g Motion .... .... lA I" .... "''I roN "" "" '\. "'"t / v v ,., 5 10 15 20 Time [sec] e. Time History of Inclusion Stress (Inc# 11, at conn) 10m wall under ah=0.687g Motion I w. ft / ., 1'11 ,.., v ./ ' v v 5 10 15 20 Time [sec] f. Time History of Inclusion Stress (Inc# 12) 10m wall with ah=0.687g Motion ,v 25 25 25 Figure 6.4 Synchronization of maximum inclusion stress (cont'd) 78
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'iii' 200 CL 100 =.. tl) 0 tl) 100 Ci5 c: 200 0 u; 300 :::J (3 = 400 'iii' 200 CL =.. tl) tl) 0 (/) 200 c: 400 :::J g 600 0 0 l &I II u! A '1 IJillN n' r vw I' 5 10 15 20 Time [sec] g. Time History of Inclusion Stress (Inc# 19, at conn) 10m wall under ah=0.687g Motion I I I .I j, lllAI!Il, IJ\ .... 111 I I IJI 5 10 15 20 Time [sec] h. Time History of Inclusion Stress (Inc# 20, at conn) 10m wall under ah=0.687g Motion 25 25 Figure 6.4 Synchronization of maximum inclusion stress (cont'd) 6.2.5 Summary Maximum earth pressure, bearing pressure, wall deformation, and inclusion stresses are synchronized with horizontal peak ground acceleration at 5.32 sec of dynamic analysis time history. A sudden increase observed after static loading in earth pressure and connection stress time histories. This phenomenon could be caused by the imposition of seismic shaking at the end of the static analysis where the wallbackfill separation took place in the top one third of the wall height. 79
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6.3 Transient Performance of 10m wall under ah=0.687g and av=0.408g Motion Both the horizontal and vertical component of the Imperial Valley earthquake ground motion was selected in this study. Figure 6.6a and b represented time histories of horizontal and vertical acceleration. The scaling factor for the horizontal and vertical ground motion were 1.5 and 3. The peak acceleration in the vertical direction (0.136g) is roughly equal to one third of the peak acceleration in the horizontal direction (0.458g). Thus, with the scaling factor of 3, the vertical peak ground acceleration becomes 0.408g. With the scaling factor of 1.5, the peak horizontal acceleration becomes 0.687 g. 6.3.1 Earth Pressure Vertical acceleration caused more stress beginning of the dynamic analysis time history. The maximum earth pressure occurred at the wall base and decreased linearly till 8meter from the base. There was almost no compressive earth pressure at the top 3meter of the wall, related to the wallbackfill separation. Maximum earth pressures synchronized with horizontal ground motion except top 3meter of wall height. Figure 6.5 show time histories of earth pressure under 1.5H+ 3V motion. Title of the Figure 6.5 also indicated represented elevation from the wall base as well. The wall completely separated from backfill at top 3m there were almost no compressive stresses. The wall moves forward and backward. Top 80
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of the wall at 11m from the base, there was very small compressive stress, correlated to the wall backward movement and separation in Figure 6.5f. 6.3.2 Bearing Pressure Time histories of the bearing pressure were not synchronized with horizontal peak ground acceleration. Figure 6.6 shows time histories of bearing pressure represented about wall toe. General shapes of the bearing pressure time histories are pretty similar to vertical acceleration time histories. Maximum bearing pressures were almost synchronized with vertical peak ground acceleration not horizontal. 6.3.3 Wall Deformation Time histories of wall forward displacement at the bottom, middle and top were synchronized with horizontal peak ground acceleration shown in Figure 6.7a, b and c. Maximum forward displacement occurred at wall top for 10m wall. 6.3.4 Inclusion Stress Figure 6.8 was shown synchronization of maximum inclusion stresses with horizontal peak ground acceleration. Bottom couple of inclusion layers was compression stress affected by wall heel upward movement and stem tilt. 81
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S[ c: 0 :;::; 'iii" a. 0 0.6 0.4 0.2 0 0.2 0.4 0 0.2 0.1 0 0.1 0.2 0 0 100 f!:! ::I 200 a. 300 111 w 400 rt. 5 5 5 Time [sec] 10 15 20 11'.1 ftA: :&i I'" '1 1'111 r1V II 11"1 I a. Horizontal Acceleration Time History PGA=0.458G at 15.32 sec Time [sec] 10 15 J 20 rr;oh ..... ..... I"" ,,. II ., I b. Vertical Acceleration Time History PGA=0.136G at 13.04sec Time [sec] 10 15 I 20 a, '"'' rll. rI. 11 .... 1 lll.ll d 1 ... .II I'INt Ill n lJ\j llr I I J1 c. Time History of Earth Pressure, (1.5m from base) 10m wall under ah=0.687g; av=0.408g Motion 25 ....... IV 25 25 lVII Figure 6.5 Synchronization of maximum earth pressure with HPGA 82
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0 0 ro r0.. =. 100 ::1 Vl Vl 200 0.. Cll w 300 0 100 ro 0.. =. 50 ::1 Vl Vl 0 0.. .s:: t:: Cll w 50 0 1Time [sec] 5 10 15 20 1.I. J .A 'll 1./V rv If' I d. Time History of Earth Pressure, (3m from base) 10m wall under ah=0.687g; av=0.408g Motion Time [sec] 5 10 15 20 I .. lot.. I 'I I r ,. ' e. Time History of Earth Pressure (7 5m from base) 10m wall under ah=0.687g; av=0. 408g Motion Time [sec] 5 10 15 20 f. Time History of Earth pressure, (11m from base) 10m wall under ah=0.687g; av=0.408g Motion 25 25 25 Figure 6.5 Synchronization of maximum earth pressure (cont'd) 83
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ro 0 a.. =.. 100 :;) (/) (/) 200 a.. Ol 300 c: c co Q) 400 lD ro 0 a.. 100 =.. :;) 200 (/) (/) 300 a.. .c c: 400 c: co Q) lD 500 ro 0 a.. ; 100 :;) (/) U) a.. 200 Ol c: c co Q) lD 300 0 0 I. 0 ....... ........ ........ Time [sec] 5 10 15 20 I ........ ...... Ill I I ; ...... ....... ...... 11111 Wj ... .loiJ ..J. llol. I 'I ... "" L I I 11 a. Time History of Bearing Pressure (0.15m from toe) 10m wall under ah=0.687g; av=0.408g Motion Time (sec] 5 10 15 20 ........... I I ....... II I, .l1 j r..... .l,fl ...... 1'111 IJ U lalllotlll .lol II IIW I I I J _l_l_ I I I I b. Time History of Bearing Pressure (0.4m from toe) 10m wall under ah=0. 687g ; av=0.408gMotion Time (sec] 5 10 15 20 ........ j. I r... ..J. lll ....... I ,, ..... I I' I c. Time History of Bearing Pressure (1. 65m from toe) 10m wall under ah=0.687g; av=0.408g Motion Figure 6.6 Time histories of bearing pressure 84 25 1 25 li 25 J r
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0 0 r'E 1 c Q) E 2 Q) (.) ro c. 3
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C? 8000 c.. =. 6000 en en en c 0 (ij ::> 0 4000 2000 0 E 2000 C? 1200 c.. =. en 800 en en c 400 0 (ij ::> 0 E 0 C? 300 c.. 200 =. 100 en en 0 100 en c 200 0 300 '(ij ::> 400 0 E 500 0 0 0 lA. u I" 5 10 15 20 Time [sec] a. Time History of Inclusion Stress (Inc# 1, at conn) 10m wall under ah=0.687g; av=0.408g Motion I. f\1\ t.. M iaal\. .,,, ... [T ..... ..... ;;;...5 10 15 20 Time [sec] b. Time History of Inclusion Stress (Inc# 10, at conn) 10m wall under ah=0.687g; av=0.408g Motion A '"k LU A uJ IJI l.i !/ Ia A 1.1 , '"' "'II'Y 5 10 15 20 Time [sec] c. Time History of Inclusion Stress (Inc# 20, at conn) 10m wall under ah=0.687g ; av=0.408g Motion '" 25 25 25 Figure 6.8 Synchronization maximum inclusion stress with HPGA 86
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6.3.5 Summary According to the horizontal ground motion record, acceleration amplitude was very low for the beginning of the dynamic analysis and increased within the time increment until reach peak and damped again, illustrated in Figure 6.5a. But the amplitude of the vertical acceleration was much higher than horizontal for the beginning of the dynamic analysis in Figure 6.5b. Correlated to the wallbackfill separation there was no compressive stress in the backfill soil, top one third of the wall height. In this section (top 3.0m) time histories of the earth pressure were not synchronized with peak ground acceleration. The maximum dynamic bearing pressures were occurred close to peak vertical acceleration time histories not synchronized with peak horizontal acceleration time histories at 15.32 second. General shape of the bearing pressure time histories were pretty similar to the vertical acceleration time history shown in Figure 6.5b. Maximum wall displacement and inclusion connection stress were occurred at the wall top for 10m wall. Very bottom couples of inclusion layers were worked in compression, correlated to the wall tilt and footing deformation. Except bearing pressure and top 3.0m of earth pressure time histories, all results synchronized with horizontal peak ground acceleration. 87
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6.4 Effect of Wall Height Once synchronization of maximum verified with peak ground acceleration, the performance of 10 and 20meter walls were investigated using maximum stress and displacement envelope. Scaled motion records were also used with the scaling factor of 1.0, 2.0 and 3.0 for the vertical component. Vertical acceleration scaling factor of 0,0 presented horizontal ground motion applied in retaining wall system. 6.4.1 Earth Pressure Figure 6. 9 shows earth pressure distribution for the 10 and 20m walls under different ground motion. Correlated to the wall separation there was no earth pressure, top one third of the wall height for the both 10 and 20m walls. Static and dynamic maximum pressures occurred at the wall base. Maximum dynamic earth pressure was greater than static. Earth pressure distributions results were close for the av<1g. Where av was peak vertical acceleration. Increasing av earth pressure and resultant force increased. When the wall height increased earth pressures and their resultant forces increased. Besides very small portion of earth pressure at the wall top 3m, there was almost no pressure one third of the wall height for the 20m wall in static and dynamic case of analysis. The increasing av, earth pressures and overall pressures increased as well for the 20m wall. Maximum static and dynamic pressures were occurred at ground surface where located 1m from the base for the 20m wall. 88
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11 10 9 8 7 1: CJ) "iii 6 I 5 4 3 2 ,. ... aa:ic I r_._ a.=0.4!fg ti aF0.4ttg, :i'i=O I a.=0.4S:g ; :rv=O 27'21; __._ 1+a"'=0.4!fg : \ .a1=04S:g: 3V=HCS!; l\ \ l . \""\. \ \ r\ ; \ \ \ \ 1\ \ i l \ \ '\ 1\. \ r\. \ 1 \\o. ll 1 \ \ \ : [', 21 20 19 18 17 16 15 14 I 13 .c 12 Gl ijj I 11 10 9 8 7 6 5 4 3 2 t&ali: tzh=l.453g oh= l453g: a;=1J'36g +';:h= l453g: a.=D :!72g +ch= l453g, a>=D.408y +ch=l.453g, a.=1 272g t +ch= l453g: av:'l 408g \ t__l\ r\ ..._ I ) llil [\ 1._ .. "" fl( li ..._ .... a 0 a 250 500 750 1ooo 0 500 100a 150a Blrth Ftessure [kPa] Earth Ftessure [kPa] Figure 6.9 Earth pressure distribution for 10 and 20m walls Table 6.1 summarized results of the earth pressure net thrust, net overturning moment and point application for the 10 and 20m wall under different motion. Dynamic maximum pressure, resultant thrust, point application and resultant overturning moment were higher than static results. 89
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Table 6.1 Resultant earth pressure for 10 and 20 m walls Ground Motion a. Earth Pressure for 10m wall ah o 0 .458' 0.458. 0.458' 0.458' na v (0)'* (O)*' (0.136)"' (0.272)'' (0.408)" Maximum Pressure [kPa] 255.04 495.01 513.22 528.25 541.79 Resultant Thrust [kN] 588.41 1220.82 1246.52 1247 .33 1308.98 Point Application from the base [ m] 1.84 1.95 1.92 1.85 2.01 Resultant OTM [kN*m) 1083 .17 2379.32 2398.04 2304.41 2625 .78 Ground Motion b. Earth Pressure for 20m wall, (attached) ah o 0 .458" 0.458. 0.458" 0.458" nav (0) (0) .. (0.136) .. (0.272) (0.408) Max Pressure [kPa] 388.24 525.34 530.99 524 36 519.30 Resultant Thrust [kN] 1755.69 2583.23 2480.14 2477 26 2456 76 Point Application from the base [ m] 3.18 3.68 3.15 3.15 3.29 Resultant OTM [kN*m) 5584.57 9517.87 7815.25 7791.44 8083 99 Where means peak horizontal acceleration ah in g **0 means peak vertical acceleration av in g nvertical acceleration scaling factors of 1.0, 2 0 and 3 0 Note that increasing av point applications of the resultant thrust were decreased. Because inclusion tensile stresses were reduced earth pressure that imparted onto concrete wall. Increasing wall height maximum pressure and their resultants were increased. 90
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The increasing a v magnitude of the maximum earth pressure, resultant thrust and overturning moment were increased in Table 6 .1. 6.4.2 Bearing Pressure Nodal point ystresses underneath wall base were selected to create the bearing pressure distribution envelope. Figure 6 10 presented maximum bearing pressure distribution envelopes for the 10m wall under different motion. Maximum pressures occurred under wall stem section There were close bearing pressure results when a v
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ro c.. ::::J en en c.. C> c:: Q) CD ro c.. ::::J en en c.. C> c:: Q) CD Base Length [m] 0 0 0.2 0.4 0 6 0.8 1.0 1.2 1.4 1.6 1.8 0 +Static ah=0.458g \ 400 s ....,._ah=0.458g ; \\ I' av=0 136g 11" Mah=0.458g ; \ .. / av=0 272g ..._ N v 800 1+ah=0.458g; av=0.408g 111I""'"' ,r;r i........_ah=0 458g : av=1.272g G. / ..._ ""'* v &ah=0. 458g ; 1200 av=2.408g Figure 6.10 Bearing Pressure Distribution for 10m wall Base Length [m] 0 0 0 5 1.0 1.5 2.0 2.5 3 0 3.5 0 ..... 1000 !'\. :2000 1\\ I \ L/, 3000 \ i'._ I 4000 P' ,..;rl.i. +Static ah=0.458g ....._ah=0.458g: av=0.136g Mah=0. 458g; av=0.272g +ah=0.458g; av=0.408g ........_ah=0.458g; av=1. 272g ......_ah=0.458g ; av=2 408g Figure 6.11 Bearing Pressure Distribtuion for 20m wall attached case 92
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Table 6.2 Resultant bearing pressure for 10 and 20m walls Ground Motion a. Bearing Pressure 1Om wall ah o 0 .458* 0.458* 0.458* 0.458* nav (o)** (0)** (0.136) .. (0.272) (0.408) .. Maximum Pressure [kPa] 272.84 373.14 377.96 392.88 435.45 Resultant Thrust [kN] 356.81 441.12 460.90 523.27 591.00 Point Application from toe [m] 0.80 0.77 0.79 0.80 0.80 Resultant OTM [kN*m] 284.38 341.70 362.67 418.68 475.61 Ground Motion b. Bearing Pressure 20m wall, (attached) ah o 0 .458. 0.458. 0.458* 0.458. nav (0)** (0) (0.136) .. (0.272) (0.408) Maximum Pressure [kPa] 937.33 1221.28 1204.76 1229.41 1263.52 Resultant Thrust [kN] 1356.97 1620.95 1703.10 1072.72 1143.13 Point Application from toe [m] 1.25 1.19 1.24 0.64 0.65 Resultant OTM [kN*m] 1697.62 1931.84 2115.87 682.88 743.98 6.4.3 Wall Deformation Figure 6.12 were shown wall forward displacements for the 10 and 20m walls under different ground motion combinations. Maximum wall displacement occurred at the wall top for the 10m wall. The 20m wall was more flexible than 10m wall thus, maximum wall deformation occurred at the middle of the wall section. Wall displacement increased when av increased. 93
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11 10 9 8 I 7 .1: lJl 6 'iii I 5 4 3 2 1 0 ... t .... 1 ) ,J, i :i 1 \ I ; i T I 1 ) ! [ I 1: [J) j +Static I J 1 ah=0458g 1ii I iii T 1 ah=0.458g; av=D 138g j ah=D.458g; I J' av=D272g J ah=0458g ; av=0408g ). +ah=0.458g; If/ av=1.272g eah=0.458g; 1 .JI!b av=2.408g 0 5 10 15 20 25 30 Cispacerrent [crf1 21 20 19 18 17 16 15 14 13 12 11 10 g 8 7 6 5 4 3 2 1 0 n .. .... .... ll "" :,. i ' .. +St
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Table 6.3 Resultant displacement for 10 and 20m walls Ground Motion a. Forward Displacement of 10m wall ah o 0.458. 0.458. 0.458. 0.458. nav (0) .. (0) (0.136) .. (0.272) .. (0.408) Max Displacement [em] 2.32 7.99 8.10 8.64 9.15 Location of the max from base [ m] 5.50 11.00 11.00 11.00 11.00 Wall Tilt 81 [degree] 0.03 0.29 0.28 0.32 0 34 Wall Tilt 82 [degree] 0.13 0.44 0.40 0.44 0.44 Ground Motion b. Forward Displacement of 20m wall, (attached) ah o 0.458. 0.458. 0.458. 0.458. nav cor (0) (0.136)". (0.272) .. (0.408) .. Max Displacement [em] 16.32 25.66 25.23 24.77 24.72 Location of the max from base [ m] 10.00 11.50 11.50 11.50 11.50 Wall Tilt 81 [degree] 0.14 0.41 0.40 0.40 0.39 Wall Tilt 82 [degree] 0.73 0.99 0.97 0.95 0.95 81=arctan(8d8,)/H; 8210=arctan(8d8,)/ 5.5m and 8/0=arctan(8d8,)/ 11.5m where 8d is dynamic displacement, 8, is static displacement, Hwall height, 5.5m and 11.5m distance from the wall base. 6.4.4 Inclusion Connection Stress Figure 6.13 show that inclusion connection stress within the dept for the 10m wall. Increasing av maximum connection stress increased at wall top and decreased within the depth linearly for the 10m wall. Tremendous stress concentration were observed at the wall top when ah=0.408g; av=l.272g and ah=0.408g; av=2.408g case of analysis for the 10m wall. 95
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The maximum connection stress occurred at the 12m from the wall top for the 20m wall in Figure 6.14. Connection stress distribution within the depth for the ah=0.408g; av=1.272g and ah=0.408g; av=2.408g cases were not uniform than others. Second and third mode shape of the structure may cause the performance of the retaining wall higher than 10m. Table 6.4 and 6.5 show spreadsheet for the inclusion connection stress plots. 25000 I 20000 IJl IJl (/) 15000 c: 0 10000 u Q) c: c: 5000 0 (..) 0 0 24000 20000 ro a. 16000 Vl Vl !!! 12000 U5 c: 8000 0 13 Q) 4000 c: c: 0 (..) 0 4000 0 \ ) "",. G) \ '\.... +Static ah=0.458g ......_ah=0.458g; av=0.136g """*'""ah=0.458g ; av=0.272g c, ........,._ah=0.458g ; av=0.408g ""1 .......,._ah=0.458g; av=1.272g eah0.458g; av=2.408g .,N ...:J 2 N 4 6 Wall Depth [m] Figure 6.13 Inclusion Connection Stress for 10m wall +Static ah=0.458g ......_ah=0.458g ; av=O. ah=0.458g; ........,._ah=0.458g ; ""=n LLflAn ..I. J. 8 ....... 1.2??9 eah av=2.40Rg .?' d' e. ..... .""5\,. t\.. I 0 I 5 10 15 Wall Depth [m] Figure 6.141nclusion Connection Stress for 20m wall attached case 96 10 ....20
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Table 6.4 Inclusion connection stress for 10m wall [kPa] ah o 0.458 0.458' 0.458' 0.458' na v (0)'' (0) (0.136)" (0.272) (0.408) Inc# 1 246.09 2328.43 2434.80 3503.64 4577.80 2 215.17 1926.47 2035 .52 3000 66 3981.14 3 201.25 1543.79 1677.39 2556.12 3429.61 4 201.49 1339.10 1342 .64 2145 .73 2904.10 5 210.22 1124.99 1106.44 1689 .62 2413.76 6 217.42 936.05 910.77 1333.28 1924.96 7 220.74 753.87 735.65 1105 07 1530.76 8 231 29 590.69 579.15 879 .14 1282.43 9 242 26 464.35 449.23 679 .52 1013.53 10 254.79 370.07 373.51 531.81 830 27 11 262 .19 323.76 328.00 442 .71 647.25 12 255.42 296.00 300 .62 395.97 525.12 13 236 .51 259.29 263.65 377.25 475.66 14 209.49 219.62 224.98 367.35 462 70 15 173.49 199.56 187 .05 351.58 474.24 16 128.60 164.23 155.21 335.28 475.85 17 81.34 136.86 146.78 340.41 464.49 18 31.68 113.02 127.08 364.49 470.84 19 30 .13 122.73 123.94 390.31 498.52 20 130.39 90 38 98. 66 446.52 557 .14 Table 6.5 Inclusion connection stress for 20m wall [kPa] ah o 0 .458' 0.458' 0.458' 0.458' na v (0) .. (O)'' (0 136) .. (0 272) .. (0.408) Inc# 1 28.98 1539.81 253.25 356 74 622.37 2 86.32 1359.32 253.17 363.67 649.81 3 21.71 1229.84 323.67 439.02 771.77 4 40.36 1126.23 410.91 536.73 912.60 5 109.02 1038.62 514 .19 642.94 1053 .65 6 174.23 950.06 606.10 753.98 1188.33 7 237.42 963.51 963.51 879 .9l 1325.83 8 299.62 1029.58 776.81 998.50 1441.93 9 360 .87 1113.65 851.68 1091.46 1538.13 10 422.33 1165.35 921.58 1177.75 1622 .67 11 484 27 1220.03 977 .95 1249.43 1689.44 97
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Table 6.5 Inclusion connection stress for 20m wall ( cont' d) 12 553 .15 1279 .65 1036 .01 1309 97 1733 .88 13 628.69 1340.24 1183.95 1408 .61 1767.69 14 702.21 1411.31 1199.10 1452.19 1772.18 15 771.07 1479.40 1287.96 1513 .33 1769.28 16 834.19 1570.90 1369.29 1575.41 1798.17 17 888.53 1658 90 1418 84 1612 93 1833.65 18 929.89 1711.07 1496.73 1645.04 1928.84 19 953 94 1786.41 1619.64 1702.36 1928.84 20 966.30 1874.77 1742.81 1764.92 1915.12 21 986.58 1922.79 1776.21 1719.44 1898.00 22 1006.33 1881.99 1856.47 1833.02 1940.02 23 1009 59 1992.55 1881.57 1908 66 2046.11 24 1007.37 2198.54 1879 70 1870 35 1971.46 25 998.91 1785.90 1792.18 1868.09 1881.45 26 980.03 1751.72 1674 70 1731.12 1817.25 27 950.13 1617.71 1617.71 1583.01 1684.80 28 907.47 1473.67 1376 .81 1407.39 1515.52 29 851.26 1241.06 1209.73 1216.57 1306.09 30 782.15 1046.27 1005.11 1004.83 1069.91 31 699.09 810.06 880.79 859.01 913.19 32 605.22 676.20 729.48 731.53 779.15 33 496.21 579.65 613.44 620.48 674.43 34 367.05 490.41 455.50 513 58 584.37 35 221.43 354.08 352.94 441.88 486.73 36 58.46 228.52 220.47 328.23 345.92 37 99.01 93.59 148.99 187.84 168.36 38 328.69 39 603 84 40 748.84 Where means peak horizontal acceleration ah in g **0 means peak vertical acceleration av in g nvertical acceleration scaling factors of 1.0, 2.0 and 3.0 98
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6.5 Effect of Ground Motion Intensity This section will discuss effect of the both horizontal and vertical ground motion intensity for the 10m wall. Scaled motion records were also used with the scaling factor of 1.0 and 1.5 for the horizontal component, 0.0, 1.0, 2.0 and 3.0 for the vertical component. Vertical acceleration scaling factor "0" presented only horizontal motion applied in the system. 6.5.1 Earth Pressure Figure 6 .15 shows seismic induced maximum earth pressure versus peak vertical acceleration for the 10m wall. Seismic induced maximum earth pressure was determined by subtracting maximum dynamic and static pressures from the earth pressure distribution diagram for the both ah=0.458g and ah=0.687g cases corresponding to av. 800 iii' c.. 600 ::::> V) 400 V) c.. .r: 200 t::: ro UJ 0 0 y = 205.86x + 304.78 R2 = 0 9923 0.5 y = 201.79x + 226.63 R2 = 0.9937 1.5 Peak Vertical Acceleration [g) +ah=0.408g ah=0.687g 2 Figure 6.15 Seismic Induced Earth Pressure 10m wall under D i fferent Motion 99 2 5
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Increasing av seismic induced earth pressure increased linearly for the all cases. The increasing ah magnitude of the seismic induced earth pressure increased as well. Where. ah and av are peak horizontal and vertical acceleration in g. 6.5.2 Bearing Pressure The same procedure was used as plot earth pressure graph, to plot seismic induced bearing pressure variation. Figure 6.16 illustrated this plot. 1000 (ij" 800 a.. =. ::J 600 (/) (/) a.. 400 Ol c::: 200 Q) m 0 0 0.5 y = 329.79x + 92.634 R2 = 0.9796 y = 346.11x + 51.608 R2 = 0.9915 1.5 2 Peak Vertical Acceleration [g) Figure 6.16 Seismic Induced Bearing Pressure 1Om wall under Different Motion 2.5 There was not much difference between ah=0.458g and ah=0.687g case of analysis. The results of the seismic induced bearing pressure after av=l.5g were almost same for the both ah=0.458g and ah=0.687g cases. It means horizontal acceleration magnitude could not effect for the result of the seismic induced bearing pressure at this moment. 100
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6.5.3 Wall Deformation Figure 6.17 presented seismic induced wall forward displacement for the 10m wall under different ground motion. Maximum occurred at the wall top. 30 E' 25 20 "E Q) E 15 Q) u ro 10 a. UJ i:5 5 0 0 +ah=0.408g 0.5 y = 7.4115x + 5.3346 R2 = 0.9892 1.5 2 Peak Vertical Acceleration [g] Figure 6.17 Seismic Induced Forward Displacement 1Om wall under Different Motion 6.5.4 Maximum Connection Stress 2.5 Maximum inclusion connection stress was occurred at the wall top where maximum displacement is high for the 10m wall in Figure 6.19. The shape of the graph was linearly. Stress increased within av. 25000 co c.. 20000 UJ UJ 15000 (/) c: 10000 0 13 Q) 5000 c: c: 0 (.) 0 0 + ah=0.408g ah=0.687g 0.5 y = 7788.5x + 1224.1 R2 = 0.9882 1.5 2 Peak Vertical Acceleration [g] Figure 6.18 Seismic Induced Max Connection Stress 1Om wall under Different Motion 101 2.5
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6.6 Effect of Inclusion Connection Condition Depending on the wallgeogrid connection condition, attached and detached case of analysis were completed on the 20m wall. Both horizontal and vertical ground motion with scaling factor were selected to investigate performance of the 20m retaining wall system. 6.6.1 Earth Pressure Figure 6.19 shows earth pressure distribution for the attached and detached case under different motion. Table 6.6 summarized the results of the maximum earth pressure, resultant thrust, point application and net overturning moment for the attached and detached case of analysis under different motion. Increasing av maximum earth pressure, resultant thrust and overturning moment increased in both attached and detached cases. There were close results when av
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Attached Case cetached C
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Table 6.6 Resultant earth pressures for attached and detached case (cont'd) Ground Motion b. Earth Pressure 20m wall, (detached) ah o 0.458. 0.458. 0.458. 0.458. nav (0) (0) (0.136)*. (0.272)"* (0.408) Max Pressure [kPa] 419.06 570 .38 645.46 695.32 612 .81 Resultant Thrust [kN] 1990.29 2613.76 4182.43 2283.53 2642.95 Point Application from base [ m] 3.46 3.49 6 90 3 .80 3 49 Resultant OTM [kN*m] 6886 20 9119.64 28858.73 8672.07 9235.33 6.6.2 Bearing Pressure Figure 6.20 presented bearing pressure distribution for the 20m wall attached case Maximum dynamic pressure was higher below the centerline of the wall stem 0.55m from the wall toe. But there was different bearing pressure distribution under ah=0.458g; av=0.272g motion Increasing peak vertical acceleration av, bearing pressure increased a lot for the ah=0.458g; av=l.272g and ah=0.458g; av=2.408g cases. Figure 6.21 shows bearing pressure distribution for the 20m wall detached case. Vertical dynamic stress was smaller than static at the 0.8m, 2 05m and 3.3m from the wall toe for the ah=0.458g; av=0.136g case. Wall top deformation was extremely higher in the detached case comparing with attached case. Thus bearing pressure was higher below the wall toe side and less below the wall heel. 104
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Maximum bearing pressure occurred at the 0.3m from the wall toe for the detached case. 0.0 0.5 0 .... ro a.. 1000 """ !.... l\ !If :::l (/) (/) 2000 a.. J \ ./ Ol c: 3000 Q) IIl \ .. I I ....... 4000 0.0 0.5 0 L.. Base Length [m] 1.0 1.5 2.0 2.5 3.0 ,.... l.i *" r J..+Static I.ah=0.458g 1.......... ah=0.458g; av=0.136g *ah=0.458g; av=0.272g ; av=0.408g +ah=0.458g; av=1.272g .ah=0.458g; av=2.408g Figure 6.20 Bearing Pressure Distribtuion for 20m wall attached case Base Length [m] 1.0 1.5 2.0 2.5 3.0 ro 500 a.. 1000 IL. / 11'1" "" :::l 1500 (/) (/) 2000 a.. Ol c: 2500 c "' 1\ \ !0 Q) 3000 IIl 3500 ......_ / I ll I. +Static ah=0.458g .......... ah=0.458g; av=0.136g ah=0.458g; av=0.272g av=0.408g +ah=0.458g; av=1.272g .ah=0.458g; av=2.408g Figure 6.21 Bearing Pressure Distribution for 20m wall detached case 3.5 3.5 Table 6. 7 summarized the results of the maximum bearing pressure, resultant thrust, point application from the toe and the resultant overturning moment for the attached and detached cases. Point application of the resultant bearing pressure 105
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was not same all the cases for the 20m wall. Increasing av bearing pressure resultant thrust and overturning moment increased. Table 6. 7 Resultant bearing pressures for attached and detached case Ground Motion a. Bearing Pressure 20m wall, (attached) ah o 0.458. 0.458. 0.458. 0.458. nav (0) (0) .. (0.136) .. (0.272) (0.408) .. Maximum Pressure [kPa] 937.33 1221.28 1204.76 1229.41 1263.52 Resultant Thrust [kN] 1356.97 1620.95 1703.10 1072.72 1143.13 Point Application from base [ m] 1.25 1.19 1.24 0.64 0.65 Resultant OTM [kN*m] 1697.62 1931.84 2115.87 682.88 743.98 Ground Motion b. Bearing Pressure 20m wall, (detached) ah o 0.458. 0.458" 0.458" 0.458. nav (o)'* (0) (0.136) .. (0.272) .. (0.408) .. Maximum Pressure [kPa] 937.33 1034.21 1024.34 1459.64 1002.85 Resultant Thrust [kN] 1356.97 1285.09 1344.33 2077.06 842.84 Point Application from base [ m] 1.25 1.17 1.21 0.88 0.63 Resultant OTM [kN*m] 1697.62 1499.07 1624.90 1834.04 529.06 6.6.3 Wall Deformation Figure 6.22 show wall forward displacement for the 20m wall attached and detached cases. Deformation shapes are so different in figure. The bulging deformation shape was observed in attached case, but unzipped deformation shape 106
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observed in detached case. Maximum deformation was four times higher in the detached case than attached. Table 6.8 summarized results of the wall deformation for the 20m wall both attached and detached cases. Wall tilt angle and deformation were extremely high at the wall top under ah=0.458g; av=l.272g and ah=0.458g; av=2.408g motion for detached case in Figure 6.22. Attached Case cetach ed Case 21 20 19 \ 18 I \ 17 t 16 \ 15 4 1 14 : 13 J: 12 Cl Qj 11 I 10 1 9 1 l 8 J J 7 j +stele 6 { + 5 j l! 3'FC 4 3 F I /<4 +a 'I=( c;:fl 2 j;( t3R!ffp: = 1 lr + 0 0 40 80 120 21 i 20 8:1 1 I I i 19 r l I ,; 18 /) f i 17 I + i 16 I 15 >:: l I I 14 i :s 13 lf I i 12 "ill ll J .s:: 11 10 . J I +Sl
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Table 6.8 Deformation and tilts for attached and detached case Ground Motion a. Forward Deformation 20m wall (attached) ah o 0.458. 0.458. 0.458. 0.458. nav (0) (0) (0.136) .. (0.272) (0.408) Max Displacement (em] 16.32 25.66 25.23 24.77 24 72 Point Application From base [m] 10.00 11.50 11.50 11.50 11.50 Wall Tilt 81 (degree] 0 14 0.41 0.40 0.40 0 39 Wall Tilt 8 2 [degree] 0.73 0.99 0.97 0.95 0.95 Ground Motion b. Forward Deformation 20m wall, (detached) ah o 0.458. 0.458. 0.458. 0.458. nav (0) .. (0) (0.136}". (0.272)". (0.408) .. Max Displacement [em] 16.32 95.85 115.45 8.89 81.04 Point Application from base [ m] 10. 00 21.00 21.00 21.00 21.00 Wall Tilt 81 [degree] 0.14 2.47 3.00 0.12 2.07 Wall Tilt 82 (degree] 0.73 2.00 2 25 0.02 1.49 81=arctan(od8s)IH; 82=arctan(od8s)/ 11.5m where od is dynamic displacement, Os is static displacement, Hwall height 11.5m distance from base where maximum occurred. 6.6.4 Inclusion Stress Figure 6.23 illustrated dynamic inclusion stress versus inclusion length for the attached case of 20m wall. In order to do better interpretation for this plot some inclusions with same stress changing shape within depth were eliminated. Cause total 40 inclusions were placed with 0.5m spacing for the 20m wall in both attached and detached case. 108
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Tension was high at the connection for the inclusion #l(very top), dropped linearly till 250 kPa and slowly increases at the backfill 12m from connection. Connection stress decreases within the depth till inclusion #6. Maximum stress occurred at the backfill 8m from connection for the inclusion #716. Peak connection stress occurred at the inclusion #24 where wall deformation was high section. Then maximum stress decreased for the inclusion #2536. Bottom four layers inclusion were worked in compression and maximum stress occurred at the end of the inclusion, 20m from connection for the inclusion #40. Inclusion stress may relate to the wall stiffuess and deformation shape. 2500 lnc1 t" lnc3 2000 I'. rttt... lnc5 ro ........ ll. ....... v rt"" lnc7 =. 1500 ....... rJ) f"". rrJ) I'rInc 11 !""r(/) v ........ rtrrc: r+tttlnc16 0 1000 iii ::l l ....... lnc24 u 1.E I'...... ....... :::::::: r""' lnc26 500 ......... / ...... ........ r1..' lnc36 / _. v lnc40 0 0 2 4 6 8 10 12 14 16 18 20 Inclusion Length [m] Figure 6.23 Dynamic Inclusion Stress (attached) 20m wall under ah=0.458g Motion 109
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Figure 6.24 shows dynamic inclusion stress for the 20m wall detached case under horizontal motion. Tension was high at the end of the inclusion for the top three layers and increased within the depth. Maximum stress occurred at the inclusion #22. The location of the maximum varies from end of the inclusion (20m from connection) to the 2.5m from connection, it may indicate failure surface of the inclusion. 3000 2500 ro 2000 c.. 6 r:;;._ ....... ......... I / v ........ ......... ..... ,;""' 1" ........ rI :;... / ,;""' / L. v / A / v '// ,;""' / L v / :::;;; ..... ':II' 0 / / ....... ....... ....... ? 5 10 lnlusion Length [m) 115 Figure 6.24 Dynamic Inclusion Stress (detached) 20m wall under ah=0.458g Motion 110 lnc1 lnc3 lnc6 lnc9 lnc12 lnc15 Inc 18 e ......... ....... lnc22 lnc29 lnc32 lnc36 lnc40 20
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6. 7 Comparison FEM Results with Conventional Method and Current Design Specification 2001 This section will discuss comparison NIKE3D results with Mononobe Okabe method and current design guideline for the MSE walls and RSS provided by Victor Elias, Barry R. Christopher and Ryan R. Berg in 2001. Al116 cases of analysis using NIKE3D program were performed on hybrid retaining wall with inclusions in the backfill. But MononobeOkabe conventional design method and current design guideline could not consider inclusion effect in the backfill, they assumed wall as externally stabilized. It is not realistic to compare hybrid wall with externally stabilized wall. 6.7.1 Comparison Results ofM0 Method with NIKE3D Table 6.9a and b summarized results of maximum earth pressure resultant thrust and point application of the resultant from wall base for the 10m wall under ah=0.458g and ah=0.687g motion using MononobeOkabe method. Horizontal ground motion was scaled with scaling factor of 0.0 and 1.5, vertical ground motion scaled with scaling factor of 1.0, 2.0 and 3.0. Dynamic earth pressures were higher than static. Dynamic resultant thrust, point application and overturning moment decreased with av in the Table 6.9a. Increasing a11 earth pressure and their resultants increased in Table 6.9b. Where ah is peak horizontal acceleration, av is peak vertical acceleration. Table 6.9c summarized results of the 111
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maximum earth pressure, point application, resultant thrust and overturning moment for the 20m wall under different motion. Increasing wall height magnitude of point application, resultant thrust and overturning moment increased than results of 10m wall. Table 6.1 Oa,b and c summarized results of the resultant earth pressure, point application, and overturning moment for the 10 and 20m walls using NIKE3D program Comparing results of the MononobeOkabe method with FEM analysis were quite different. MononobeOkabe method was neglected effect of the vertical acceleration and in Equation 2.2 seismic inertia angle \If was determined by \If= arctan [kh/(1kv)]. In terms of the Equation 2.2 increasing kv seismic earth pressure coefficient KAE and resultant active earth pressure thrust P AE decreased. But results of the finite element method computer code NIKE3D were totally different than conventional design method. Resultant thrust and overturning moment increased with increasing av. 6.7.2 Comparison Results ofNIKE3D with Current Design Guideline 2001 Table 6.1la,b and c summarized results of the resultant earth pressure and overturning moment and point application for the 1 0 and 20m walls using current design guideline provided by Victor Elias, Barry R. Christopher and Ryan R. Berg in 2001. Computation spreadsheet of the MononobeOkabe method including 112
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Coulomb active pressure calculation and current design specification of the wall design were included in Appendix F Necessary theoretical equation for the calculations were indicated in Chapter 2. Table 6.9 Results ofMononobeOkabe method Ground Motion a. M0 Active Thrust Calculation, lOrn wall ah o 0.458* 0.458* 0.458. 0.458. nav (0) cof (0.136}"* (0 272) (0.408) Max Pressure [kPa] 22.48 74.36 57.97 44.44 33.10 Active Thrust [kN] 247.30 758.52 645.85 552 .83 474.83 Point Application from base [ m] 3.67 5.64 5.48 5.29 5.07 OTM at wall toe (kN*m] 906.76 4280 .81 3537.20 2923 25 2408.49 Ground Motion b. M0 Active Thrust Calculation, lOrn wall ah o 0.687* 0.687* 0.687" 0.687" nav (0) (0) (0.136)"* (0 272) (0.408) Max Pressure [kPa] 22.48 185.98 125.76 87.56 60.63 Active Thrust [kN] 247.30 1525.94 1111.91 849.27 664.14 Point Application from base [ m] 3.67 6.12 5.95 5.75 5.51 OTM at wall toe [kN*m] 906.76 9345.82 6613.21 4879.81 3657.94 Ground Motion c. M0 Active Thrust Calculation, 20m wall ah o 0.458* 0.458. 0.458* 0.458* nav (O)"* (0)** (0.136) (0.272)"* (0.408) Max Pressure [kPa) 42 92 141.96 110 67 84 .84 63.18 Active Thrust [kN) 901.31 2110.50 1699.87 1360.84 1076.58 Point Application from base [ m) 7.00 11.94 11.79 11.58 11.31 OTM at wall toe [kN*m) 6309.14 25207.49 20033.51 15761.67 12180.04 113
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Table 6.10 Results ofNIKE3D analysis Ground Motion a. Earth Pressure for the 10m wall ah o 0.458. 0.458. 0.458* 0.458. nay (0) (0) .. (0 .136}'* (0 272) (0.408) Max Pressure [kPa] 255.04 495.01 513.22 528 25 541.79 Net Thrust [kN] 588.41 1220.82 1246.52 1247 33 1308.98 Point Application from base [ m] 1.84 1.95 1.92 1.85 2.01 NetOTM [kN*m] 1083.17 2379.32 2398.04 2304.41 2625.78 Ground Motion b. Earth Pressure for the 10m wall ah o 0.687" 0.687" 0.687. 0.687. llay (0) (0) (0 136)*. (0 272) (0.408) Max Pressure [kPa] 255 04 572.25 589.58 615.55 615.56 Net Thrust [kN] 588.41 1522.48 1556.92 1542.00 1564.14 Point Application from base [ m] 1.84 2.08 2 .01 1.90 1.92 NetOTM [kN*m] 1083.17 3167.36 3129.67 2935.52 2996.74 Ground Motion c. Earth Pressure for the 20m wall, (attached) ah o 0.458. 0.458. nay (0) (0) .. (0 136) .. Max Pressure [kPa] 388.24 525.34 530.99 Net Thrust [kN] 1755.69 2583.23 2480.14 Point Application from base [ m] 3.18 3.68 3.15 NetOTM [kN*m] 5584.57 9517.87 7815.25 Where : means peak horizontal acceleration ah in g **()means peak vertical acceleration a y in g 114 0.458. 0.458. (0.272) (0.408) 524.36 519.30 2477.26 2456 76 3.15 3 29 7791.44 8083.99
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Table 6.11 Results of current design guideline 2001 Ground Motion a. AASHTO Active Thrust Calculation, lOrn wall ah a 0.458. 0.458. 0.458. 0.458. nav (0) (o)* (0.136)** (0.272) (0.408) Max Pressure [kPa] 22.48 92.11 83.92 77.15 71.48 Active Thrust [kN] 247.30 1107.13 1050.80 1004 .29 965.29 Point Application from base [ m] 3 .67 6.87 6.53 6.22 5.94 OTM at wall toe (kN*m] 906.76 7604.05 6860.44 6246.48 5731.73 Ground Motion b. AASHTO Active Thrust Calculation, 1Om wall ah o 0.687. 0.687* 0.687. 0.687. nav (0) (0) .. (0.136) .. (0.272)** (0.408) Max Pressure [kPa] 22. 48 147.92 117.81 98 .71 85. 25 Active Thrust [kN] 247.30 1490.85 1283.83 1152.51 1059 .95 Point Application from base [ m] 3 .67 8.50 7.74 7.12 6 59 OTM at wall toe [kN*m] 906 76 12669.06 9936.45 8203.05 6981.18 Ground Motion c. AASHTO Active Thrust Calculation, 20m wall ah a 0.458. 0.458. 0.458. 0.458. nav (0) .. (0) .. (0.136) .. (0.272) .. (0.408) Max Pressure [kPa] 42 92 175.83 160 .19 147.27 136.44 Active Thrust [kN] 901.31 3380.80 3175.48 3005.96 2863.84 Point Application from base [ m] 7 00 14.29 13.59 12.93 12.33 OTM at wall toe [kN*m] 6309.14 48327.42 43153.44 38881.60 35299.97 Where means peak horizontal acceleration ah in g **() means peak vertical acceleration av in g 115
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Figure 6.25 shows maximum dynamic earth pressure versus peak vertical acceleration for the 10 and 20m walls using MononobeOkabe method. Increasing av maximum pressure, point application and resultant thrust decreased. Horizontal ground motion ah=0.687g, maximum pressure was higher than 20m wall pressure Figure 6.26 shows dynamic earth pressure diagram using current design guideline provided by Victor Elias etc for the 10 and 20m walls. Current design specification was made some change to MononobeOkabe method. They reduced dynamic earth pressure distribution by 50% and add an inertial force of the reinforced soil mass see Figure 2.8a in Chapter 2. Maximum dynamic earth pressure, point application, resultant thrust and overturning moment increases with wall height and decreases with vertical acceleration intensity Figure 6.27 presented results of maximum dynamic earth pressure versus av using NIKE3D program Figure 6.28 to 6.33 were summarized results of net overturning moment, net thrust and point application graph using M0 method, AASHTO and NIKE3D for 10 and 20m walls. Results of NIKE3D analysis resultant thrust were pretty close to conventional and current design specification for both 10 and 20m walls under ah=0.458g; av=0.136g motion. But for av>lg cases NIKE3D results increased with av and M0 and AASHTO results decreased linearly in Figure 6 29 to 6 32. 116
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200 ro 0.. =. 150 :::l Vl Vl 100 0.. <..> i: 50 (I) 1: >0 0 200 ro 0.. =. 150 :::l Vl Vl 100 a. <..> "i: 50 (I) 1: >0 0 800 ro a. =. :::l Vl Vl 600 a. <..> "i: (I) 1: >0 400 h. +10m ah=0.458g ........... ............. r_ ..... 10m ah=0.687g ....,._20m ah=0.458g 0 ::::::::::...... 0 1 0.2 0 3 Peak Vertical Acceleration [g) Figure 6.25 M0 Maximum Earth Pressure Ill 0.4 r'"' 1+10m ah=0 458g 10m ah=0 687g r....,._20m ah=0.458g 0 0 1 0 2 0.3 0 4 Peak Vertical Acceleration (g) Figure 6.26 AASHTO Maximum Earth Pressure I +1Om ah=0.458g 10m ah=0 687g ....,._20m ah=0.458g ..... 0 0.1 0.2 0.3 0.4 Peak Vertical Acceleration (g) Figure 6.27 NIKE3D Maximum Earth Pressure 117 0 5 0.5 0 5
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8000 'E 7000 6000 z 5000 4000 0 c 3000 .!9 :s 2000 rn Q) a:: 1000 0 0 3500 z 3000 2500 (ii 2 2000 .c c 1500 .!9 1000 :s rn Q) 500 a:: 0 0 8 7 I 6 c:: 0 5 4 c. c. 3 <( c 2 o 0... 0 0 0.5 +M0 .AASHTO .6.NIKE3D y = 1326.8x + 2155.2 R2 = 0.985 1.5 2 Peak Vertical Acceleration [g] Figure 6.28 Resultant OTM at Wall Base (10m) +M0 y = 738.83x + 1114.8 .AASHTO R2 = 0.9877 .6.NIKE3D 0.5 1.5 2 Peak Vertical Acceleration [g] Figure 6.29 Resultant Trust Imparted on Wall (10m) 0.5 +M0 MSHTO .6.NIKE3D y = 0.0379x + 1.9286 R2 = 0.2316 1.5 Peak Vertical Acceleration [g] 2 Figure 6.30 Point Application from Wall Base (1Om) 118 2.5 2.5 2.5
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60000 E' 50000 z =. 40000 130000 0 "E 20000 .l!l "5 Vl 10000 Q) a: 8000 z 7000 =. 6000 (ii 2 5000 ..r::: 14000 "E 3000 .l!l "5 2000 Vl Q) a: 1000 0 0 16 I 14 c: 12 0 10 c. 8 c. 6 od:: "E 4 5 Q_ 2 0 0 0 5 0 5 0 5 y = 6885.1 X + 7066 8 R2 = 0.9495 1 5 Peak Vertical Acceleration [g] 2 +M0 .AASHTO .&.NIKE3D Figure 6.31 Resultant OTM at Wall Base (20m) y = 2062 8x + 2105.9 R2 = 0 9723 +M0 .AASHTO .&.NIKE3D 1.5 2 2 5 Peak Vertical Acceleration (g] Figure 6 32 Resultant Thrust Imparted on Wall (20m) y = 0 0008x + 3.3395 R2 = 1E05 1.5 2 Peak Vertical Accelerat i on [g] +M0 .AASHTO .A.NIKE3D 2 5 Figure 6.33 Point Application from Wall Base (20m) 119 2 5 3 3
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7. Summary, Conclusions and Recommendations for Future Study 7.1 Summary The goal of this study was to evaluate the effect of the combined horizontalvertical ground motion on the hybrid retaining wall with 10 and 20m heights. A T wall with a small footing was adopted in this study. This is the extension of the study by my predecessor, Kevin Lee. The footing had a 15% H heel length and 1.5% H toe length. This wall type was found to have the highest performance rating among all wall types investigated and therefore, was selected for further study. The same wall thickness of 0.5m was used in both 10 and 20m walls. Both vertical and horizontal components of the Imperial Valley earthquake ground motion records were used in this study of seismic effect on MSE hybrid walls. Ground motion records were scaled with a scaling factor of 1.0 and 1.5 for the horizontal motion, and 1.0, 2.0, 3.0, 9.3 and 17.8 for the vertical motion. With the different combinations of ground motion and the wallgeogrid connection conditions, a total of 16 different analyses were performed using NIKE3D program. Two cases presented in detail for their transient behavior, the 10m wall under ah=0.687g and ah=0.687g; av=0.408g motion, where ah and av are, respectively, the horizontal and vertical peak acceleration of the Imperial Valley motion. 120
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In all other cases, only the maximum geogrid connection stresses, earth pressures, wall deformations, and bearing pressures are presented. Comparisons were made on the effects ofwall height between 10 and 20m walls, ground motion intensity between ah and av motion, and wallgeogrid connection conditions on all items of interest. Comparisons also made between the nonlinear FEM results and the results from conventional and current AASHTO design specifications. Final study conclusions and recommendations for future study are presented. 7.2 Conclusions The findings and conclusions of this study are: 1. Maximum stress and displacement envelopes represent the most critical conditions and could be used for the design of retaining walls under seismic forces knowing the synchronization of maximum stress and displacement with peak ground acceleration. 2. The coefficient of vertical acceleration kv is one of the most important parameters for wall design under seismic loading, particularly at a large vertical acceleration. 3. The neglecting vertical acceleration effect in the calculation of the resultant earth pressure using MononobeOkabe method in Equation 2.2 and using 121
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current design guideline in Equation of 2.18a would negatively affect to the design performance of the wall under seismic loading. 4. The difference in wall performance under ah= 0.458g and ah=0.458g; av = 0.136g is insignificant. However, tremendous increases in earth pressures, connection stresses, deformation and bearing pressure are observed when at higher vertical acceleration. 5. The dynamic resultant thrust imparted at the back of the wall section could be determined knowing the earth pressure distribution. Increasing peak ground acceleration in both horizontal vertical directions increased results of dynamic resultant thrusts. 6. Magnitude of the resultant thrust increases as wall height increases. 7. The point application of the resultant thrust about the wall base increases with wall height but decreases with increasing av. 8 The net thrust and overturning moment about the wall base determined from the results of NIKE3D analysis was different the net thrust and overturning moment determined from the MononobeOkabe method and current design guideline 200l.The conventional and current design specifications do not include inclusion effect in backfill. Show an opposing trend with the increase in the peak vertical acceleration. 122
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9 The location of the dynamic resultant thrust determined from FEM analysis was lower than MononobeOkabe method and current design guideline 2001 provided by Victor Elias, Barry R. Christopher and Ryan R Berg. 10. Time histories ofthe dynamic bearing pressure were not synchronized with horizontal peak ground acceleration Increasing av increased resultant dynamic bearing pressure and overturning moment about the wall toe. Point applications from wall toe were almost constant with increasing av. 11. At the greater wall height, the magnitude of dynamic bearing pressure was higher. Possible shear failure could be developed beneath the wall footing at a greater wall height. 12. Increasing ground motion intensity increased differential wall forward displacement. 13. The same wall thickness of0. 5m was selected for 10 and 20m walls. So the 20m wall was more flexible than 10m wall. Thus, the location of maximum differential displacement occurred at wall top for the 10m wall and at the middle of the wall height for 20m wall. 14. Direct proportional relation was observed between wall displacement and inclusion connection stress. Increasing wall displacement increased connection stress. Maximum connection stress occurred at the place where wall displacement was high. As the wall height increases, the dynamic tensile inclusion stress increases as well. 123
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7.3 Recommendations for Future Studies Parametric Studies Foundation soil stiffness is the one of the main factors in the performance of the hybrid retaining wall under seismic loads. Modulus of elasticity and Poisson's ratio could be changed for the foundation soil and inclusion. Inclusion serves as reinforcement in the backfill soil mass, and its strength also affects the performance of the hybrid retaining wall. Also soil friction angle is the most critical parameter for performance of the wall and stress strain relations. Another important parameter is the coefficient of the friction for the sliding interface between inclusion and backfill soil. There are different types of commercially available reinforcement and different types of backfill material. Wall Section and Inclusion Specifications In this thesis study rigid facing MSE walls with small footing were selected. Block facing MSE walls need to be examined in the future using the finite element method under both horizontal and vertical seismic motion. Optimal wall configuration, footing size and minimum required wall stem thickness would be redefined. More research is required on hybrid retaining wall system changing wall facing type, inclusion length and vertical spacing in the backfill. Current AASHTO 2001 recommended reasonable inclusion length should be 0 .7H and maximum vertical spacing of the inclusions should not exceed 800mrn. 124
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Input Ground Motion Imperial Valley earthquake ground motion records were selected as seismic motion. Results of the analysis will be different by using different earthquake ground motions for the foundation soil with different stiffuess. Critiques of the Current Specifications Current design and construction guideline 2001 for the MSE walls and RSS provided by Victor Elias, Barry R. Christopher and Ryan R. Berg made changes to psuedostatic MononobeOkabe method. They used the seismic earth pressure distribution diagram proposed by Bathurst and Cai in 1995, reduced dynamic resultant thrust by 50% and added an inertial force of the reinforced soil mass see Figure 2.8a This seems too conservative and how they derived this equation is unclear. The principle of this guideline was the same as MononbeOkabe classical theory However, the MononobeOkabe method and current design guideline could not assume the effect of inclusions and the results were totally different than FEM analysis results. Because in the Chapter 2 Equation 2.2 and equation 2 18a vertical acceleration effect ignored. Results of the FEM shown coefficient of vertical acceleration kv is one of the key parameters for the wall design as kh. 125
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Appendix Al. Transient Analysis of lOrn wall under l.S*Horizontal Motion Note: 126
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ro c._ (f) (f) (/) c: 0 "iii ::::1 0 .!:: ro 0 c._ 100 ::::1 I I LLIHfilHlJ I I I r I t I t i "' 200 (f) (f) 300 c._ .AI .c t 400 ro w v li! 500 2 / ro 600 ...J 0 ro 0 c._ 100 ::::1 (f) 200 (f) Q) .AI ./ ..... 300 c._ .r:: " t 400 ro w 500 v .. L Q) 600 ro ...J 0 4000 3500 3000 2500 2000 1500 1000 500 0 ...... 500 2 / t" 2 I""" / 2 _,A 3 1+Static Dynamic 1 l l I 4 5 6 7 Wall depth [m] Lateral Earth Pressure Distribution 1Om wall under 1 .5H Motion ......... !'""" j 8 ..,. +at 14 sec ,.. 3 at 15.32sec ........,_at 17 sec I 4 5 6 7 Wall Height [m) Lateral Earth Pressure Distribution 10m wall under 1 .5H Motion j 8 +Static Connection Stress Dynamic Connection Stress ......... ...,.......,.... ....3 4 5 6 7 8 Wall Height [m] Inclusion Connection XStress 9 9 / 9 along the wall height, 10m wall under 1.5H Motion 127 10 11 10 11 / v 10 11
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ro a.. =.. ::;:) Vl Vl a.. .c t ro UJ ::;:) Vl 0 50 100 150 200 250 0 20 40 60 80 a.. 100 ro UJ co a.. :::1 (/) (/) a.. .c. t co w 120 140 20 10 0 10 20 30 40 0 0 0 5 r5 5 AI l l 1/'V! IV ,., 10 15 20 Time [sec] Time History of Earth Pressure, (3m from base) 1Om wall under 1.5H Motion r.. .111.1 JJ 10 15 20 Time [sec] Time History of Earth Pressure, (4.5m from base) 1Om wall under 1.5H Motion Jl'l llfl .A ''
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50 'iii' 40 Ll. 30 f!? ::;, 20 rJ) 10 rJ) f!? 0 Ll. .r:. 10 t ra 20 w 30 100 ro 80 Ll. 60 ::;, rJ) 40 rJ) f!? Ll. 20 .r:. t 0 ra w 20 25 20 15 10 5 0 f!? 5 Ll. 10 15 w 20 25 0 5 0 5 0 5 ,j I ld l.i.t .. .., y r\/li nn '' 10 15 20 Time [sec] Time History of Earth Pressure, (7.5m from base) 1Om wall under 1 .5H Motion 1 .,, I' v f 10 15 20 Time [sec] Time History of Earth Pressure, (9m from base) 1Om wall under 1 5H Motion "" / v .... ,.a, "1. IN If"" ., ""'t' lUI ""' "'' I'"'' 10 15 20 Time [sec] Time History of Earth pressure, (11m from base) 10m wall under 1 .5H Motion 131 w M 'I '. 25 25 Ia,", 'I 25
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0 50 =. 100 150 200 250 a.. Cl 300 E 350 til 400 450 0.0 1\ \ Base Length [m] 0 2 0 4 0 6 0 8 1 0 1 2 I +Static Pressure Dynamic Pressure ........ """' 1 \ r..... ........... r' v Bearing Pressure Distribution 10m wall under 1 .5H Motion Time (sec] 1 4 1.6 1.8 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 250 'E 300 c. z =. 350 .....
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0 0.90 I 0.85 .?;0.80 o E c 0.75 Q) u u w 0.70 0.65 0 ro 0 c.. ....... t.... =. 100 :::J rJl rJl 200 c.. C) 300 c Q) CD 400 0 0 ro ...... rc.. 100 =. ....... :::J 200 rJl rJl 300 c.. C) c c 400 Cll Q) CD 500 r.,... r... Time [sec) 5 10 15 20 ra fl. !'""" Time History of Bearing Pressure Net Moment Arm 1Om wall under 1.5H Motion Time [sec] 5 10 15 20 5 I""r....... ...... ,......, IU l ...... JWIU l I IM II' "' I l Time History of Bearing Pressure, {0.15m from toe) 1Om wall under 1.5H Motion Time [sec] 10 15 20 'r... ......... r... II liM. A .. r N Time History of Bearing Pressure, {0.4m from toe) 10m wall under 1 5H Motion 133 25 25 25 'I\
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0 0 ro 50 c... .:.:. 100 ........ !'... ....... ......... :::l 150 rJ) rJ) !!? 200 c... Cl 250 c 300 Q) Ill 350 0 ro 0 c... 50 !!? ....... ........ ....... :::l 100 rJ) rJ) !!? 150 c... Cl c 200 Q) Ill 250 0 0 ......... ro c... 50 .:.:. !!? ...... ........ :::l 100 rJ) rJ) !!? c... 150 Cl c 200 Q) Ill 250 Time (sec) 5 10 15 20 ...... ......... ...... I'.... ........ ...l&JJ J lh. 1"1 I"' 1.,. ''"' 1r' I Time History of Bearing Pressure, (0.65m from toe) 1Om wall under 1 .5H Motion Time [sec] 5 10 15 20 ........ ["'.... ...... n liA I.A. ....... .t:lail u 111'1 .. '"' I I' ,., .. .. I' Time History of Bearing Pressure, (1.15m from toe) 1Om wall under 1 .5H Motion Time [sec] 5 10 15 20 ......... .............. ......... I .. 1an ill I Jill lllU '" .,r Time History of Bearing Pressure (1.65m from toe) 1Om wall under 1 .5H Motion 134 25 25 lA. 25
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0 2 E' 4 ,. ... ...... c 6 Q) E 8 ro Ci 10 U) i:5 12 14 0 2 0 5 0 E' rrr,_ c 1 Q) E Q) u 2 ro Ci U) i:5 3 1 +Numerical Static Numerical Dynamic t ...., 3 !"..... !"..... "ot """t 4 5 6 7 Wall height (m] Forward Displacement 10m wall under 1 .5H Motion Time [sec] 10 15 A. """t 8 9 10 20 ill l L A l A 'f' .... H .IV Time History of Forward Displacement, (at toe) 10m wall under 1.5H Motion 135 1'1 11 25
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0 5 0 E' 2 c 4
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4000 &. 3000 2!S rJ) rJ) 2000 (/) 1000 c;; ::I 0 0 ..!: 1000 50 1i) 40 2 .c tE 30 a; ..._ Q) z c_ cz 2!S 20 ::I 10 c 0 0 500 ::::E 400 0 E Q) Q; 300 Zc_ .E rJlZ ::I.:.< 200 n100 ..!: 0 1f1f111f1 0 .tr2mfrom w/face M6mfrom w/face 10mfrom w/face V" ./ 2 3 4 5 6 7 8 Wall Height [m] Inclusion XStresses, (parallel to wall face) 10m wall under 1.5H Motion I""" 5 5 .. 10 15 Time [sec] Time History of Inclusion Net Thrust 1Om wall under 1.5H Motion ..... 10 15 Time [sec] Time History of Inclusion Net OTM 10m wall under 1.5H Motion 137 ill I'\ I _l '\1 / II" ./ v ... 9 10 11 LJ l If l fk wr\ r v LI 20 25 II Ill LA 1\\ I N r .. t .. 20 25
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4000 'iii' a.. 3000 C/) C/) 2000 E! ii5 c 1000 0 "iii :;J 0 0 = 1000 0 3500 'iii' 3000 a.. 2500 C/) 2000 C/) E! ii5 1500 c 1000 0 "iii 500 :;J 0 0 = 500 0 2500 'iii' a.. 2000 C/) C/) 1500 (J) 1000 c 0 "iii :;J 500 0 = 0 0 n .11'\11, q r r ... 1 y 5 10 15 20 5 5 Time [sec] Time History of Inclusion Stress (Inc# 1 ,at conn) 1Om wall under 1.5H Motion ll lJ IV y 10 15 20 Time [sec] Time History of Inclusion Stress (Inc# 2, at conn) 1Om wall under 1 .5H Motion ill. N l v 10 15 20 Time [sec] Time History of Inclusion Stress (Inc# 3, at conn) 1Om wall under 1 5H Motion 138 '"' W'r\ v v 25 IAAtl '"" lV 25 l I\} rv v 25
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600 ro c.. =.
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200 ro c... =. 100 U) U) 0 il5 c: 0 "(ii 100 :::J (3 E 200 200 &' 100 =. U) U) 0 il5 100 c: 200 :::J (3 300 E 400 200 ro 100 a.. =.. 0 en en 100 Q) .... 200 U5 c:: 300 0 u; :::J 400 (3 500 E 600 0 0 0 5 5 5 ll l 1\. n IJ 10 15 20 Time [sec] Time History of Inclusion Stress (Inc# 18, at conn) 1Om wall under 1.5H Motion I an I 1\. W'\11 n. II"V II v ., 10 15 20 Time [sec] Time History of Inclusion Stress (Inc# 19, at conn) 10m wall under 1.5H Motion A, lAil A 1/'t\1 It 1JV 11'1 10 15 20 Time [sec] Time History of Inclusion Stress (Inc# 20, at conn) 1Om wall under 1.5H Motion 140 lt"\ Vv J\ 25 A U\ .I\ 25 J\ lA 'V 25
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Appendix A2. Transient Analysis of 1Om wall under l.S*Horizontal + 3*Vertical Motion Note: 1.5H+3V7 ah=0.687g; av=2.408g 141
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ro a_ 0 Q) 200 :; ffl 400 a_ 600 .c 1ij 800 UJ 1000 "* 1200 _J """"" ; 0 0 0 :::J Cl) 500 Cl) a_ 1000 E ro ..... UJ Q) 1500 c. oz ..>:: 2000 2 .c 2500 tQi 3000 z 0 0 :::J Cl) 1000 Cl) Q) C:E' 2000 .c ..... t:: Q) ro c. 3000 UJ E oz 4000 :::2:6 t5000 0 Qi 6000 z ....... u.1 r....... 2 5 t/ / ...... ...... +Static Dynamic 3 4 5 6 7 8 Wall Height [m] Lateral Earth Pressure Distribution 1Om wall under 1.5H+3V Motion Time (sec] 10 15 9 20 r5 li. j 1111\ """ ..to I ""' r' II .H r ll ",. I&JV ., Time History of Earth Pressure Net Thrust 10m wall under 1.5H+3V Motion Time [sec] 10 15 I 'Ill 'lllw., l. .. J. .I .. v ., ..., Time History of Earth Pressure Net OTM 10m wall under 1.5H+3V Motion 142 "' 20 10 11 25 'V 25
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2.5 I 2.o E 1.5 1.0 E 0.5 0.0 0 0 0 ro c.. ::::J UJ UJ c.. .r:. t:: ro UJ ro c.. ::::J UJ UJ c.. .r:. t:: ro UJ 200 400 600 800 0 0 100 200 300 400 500 600 5 5 ... n A IJII(' liP v ..,.. '" 10 15 Time [sec] Time History of Earth Pressure Moment Arm 1Om wall under 1.5H+3V Motion Time [sec] 10 15 II lA A J A l d r'f" 20 20 rr Jl "' l"ll t(VI JV r"V' If' V\1' 1/' 5 "' Time History of Earth Pressure, (1.5m from base) 1Om wall under 1.5H+3V Motion Time [sec] 10 15 20 .. ,,. "V' n1 ""1 1rrv j\ t/Ji Vv 'rJ v Time History of Earth Pressure, (3m from base) 10m wall under 1.5H+3V Motion 143 ""' r25 25 25
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0 5 0 "iii' 0.. 100 :J rn 200 rn 0.. .c. 300 1:: ro w 400 0 5 100 "iii' 0.. 50 :J rn rn 0.. 0 .c. 1:: ro w 50 0 5 150 "iii' 0.. 100 :J "' 50 "' 0.. .t::. 1:: 0 ro w 50 Time [sec] 10 15 20 I ll J 1f lV J\ w ,._ ..... Time History of Earth Pressure, (4.5m from base) 1Om wall under 1.5H+3V Motion Time [sec] 10 15 20 'Mt II ""' ... 1'' r'' ll l' Time History of Earth Pressure, (7.5m from base) 10m wall under 1.5H+3V Motion Time [sec] 10 15 20 ""'"" '. a lll\a ..... .... Time History of Earth pressure, (11m from base) 10m wall under 1.5H+3V Motion 144 25 25 25
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ro 0... =. :::l tJl tJl 0... 0) c Q) en 'E .... Q) 0. z =. Cii 2 .c 1Qi z 'E 0. E z =. :::!: 10 Qi z 0.0 0.2 0 200 400 600 800 1000 1200 0 0 200 400 600 800 1000 1200 1400 0 0 200 400 600 800 1000 1200 .......... \ \. \ \ .... 2 2 Base Length [m] 0.4 0.6 0.8 1.0 1.2 1.4 +Static Pressure Dynamic Presure 4 6 :v ....Bearing Pressure Distribution 10m wall under 1.5H+3V Motion Time [sec] 8 10 12 14 16 18 1.6 20 .,,... '" 4 6 111 J II Time History of Bearing Pressure Net Thrust 10m wall under 1.5H+3V Motion Time [sec] 8 10 12 14 16 18 r.. ,, .JI,rul. AI .... l. '" I I' '"' I' Time History of Bearing Pressure Net OTM 1Om wall under 1.5H+3V Motion 145 .. 20 1.8 22 24 22 24
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I .2:' '(3 :s c Q) u u w Cij' c... =. ::J rn rn c... Cl c Q) aJ Cl c 0 1.0 0.8 0.6 0.4 0.2 0.0 0 200 400 600 800 1000 1200 0 200 400 600 800 1000 Q) aJ 1200 5 0 0 r. Time [sec] 10 15 20 1\. y Time History of Bearing Pressure Moment Arm 1Om wall under 1.5H+3V Motion 5 5 Time [sec] 10 15 20 r+I. Ill II .n _l ... 10 I'''''' trrr r Time History of Bearing Pressure, (0.15m from toe) 1Om wall under 1.5H+3V Motion Time [sec] 10 15 20 rIUJI IINIA II Time History of Bearing Pressure, (0.4m from toe) 10m wall under 1.5H+3V Motion 146 25 25 25
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0 0 r..... ro 0... 200 ::::l 400 C/) C/) 0... 600 Cl c: 800 Q) co 1000 0 0 ro r1+0... 200 ::::l 400 C/) C/) 600 0... Cl I c: "fij 800 Q) co 1000 0 0 co 0... r200 ::::l C/) C/) 400 0... Cl c: 600 Q) co 800 Time [sec) 5 10 15 20 rd, I ( I II 1.11 ... ... I' ,, .,. I : Time History of Bearing Pressure, (0.65m from toe) 1Om wall under 1.5H+3V Motion 5 5 Time [sec] 10 15 20 r1a a . l1ll AI l.i.  11m. Ill' I rurr' '"'" '.,,. n I' I' .,1 Time History of Bearing Pressure, (1.15m from toe) 10m wall under 1.5H+3V Motion Time [sec) 10 15 20 illl lh .J lbi .. .. I P' ., I' IJI'UW1 '" r1 ,. Time History of Bearing Pressure, (1.65m from toe) 10m wall under 1.5H+3V Motion 147 25 25 25
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0 0 3 E' 6 9 55 12 E 15 2l 18 21 24 27 30 0 0 E' 1 2 c Q) E 3 Q) u ro 4 c. rn i5 5 6 0 E' 6 c Q) 12 E 2l 18 ro c. rn i5 24 30 0 2 I'&. 11... ......., 5 5 Wall Height [m] 3 4 5 6 7 8 9 I I I I I ......Static Dynamic """'1 "' """'! r"1 ........ Forward Displacement 1Om wall under 1 5H+3V Motion Time [sec] 10 15 20 tl In. I 1 Ill _I\ .U A l.M n _l ,, "" Time History of Forward Displacement, (at toe) 1Om wall under 1.5H+3V Motion Time [sec] 10 15 20 "" A j'_A_ ., .,.r .. \1 1\ At y I"' r' Time History of Forward Displacement, (at top) 1Om wall under 1.5H+3V Motion 148 .1\ 10 11 t 25 II\ 25 "' ll\
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25000 'iii' 20000 a.. IJ) 15000 IJ) Q5 c 10000 5000 :::J g 0 5000 4000 3500 'iii' 3000 a.. 2500 IJ) IJ) Q) 2000 = en 1500 c 0 1000 u; :::J u 500 E 0 500 1 2 v ..I v 2 +Static Connection Stress Dyn Connnection Stress ..... ..1 ..3 4 5 6 7 8 9 Wall Height [m] Inclusion Connection XStress along the wall height, 1Om wall under 1.5H+3V Motion ........... 3 It! .......... ...... ... v ...+Static Stress oyn Stress 4 5 6 7 8 Wall Height [m] Inclusion XStress, (2m from conn) 1Om wall under 1.5H+3V Motion 149 9 J 10 11 10 11
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3000 'iii' 2500 c.. =. 2000
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25000 ro 20000 a.. (/) (/) 15000 10000 Ci5 c 0 5000 o; :::1 13 0 = 5000 1 2 300 en 250 2 200 IE Q) (fi z a. 150 cz 100 :::1 50 0 0 3000 2400 0 E 'i) (i) 1800 Za. .E 1200 (/)z :::1.>< 600 = 0 0 3 l I I I I I static Connection Stress oyn Connnection Stress ......4 5 6 7 8 Wall Height [m] Inclusion Connection XStress J v v 9 along the wall height, 10m wall under 1 5H+3V Motion 5 5 A ft l/1\ ,..,. l"' \ y v I I 10 15 Time [sec) Time History of Inclusion Net Thrust 1Om wall under 1.5H+3V Motion l II 1\ I .A \. v / I 1 10 15 Time [sec] Time History of Inclusion Net OTM 10m wall under 1 5H+3V Motion 151 "' 20 II\ 20 / i/ / 10 11 25 25
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24000 ro 20000 0... (/) 16000 (/) 12000 (/) c:: 0 8000 c;; :::J u 4000 E 0 0 5 ro 18000 0... 15000 (/) 12000 (/) 9000 (/) c:: 6000 0 c;; :::J 3000 u E 0 0 5 15000 ro 12500 0... (/) 10000 (/) 7500 Ci5 c:: 5000 0 c;; :::J 2500 u E 0 0 5 A .. I"" u vr(IJ v r... /' { J I 10 15 20 Time [sec] Time History of Inclusion Stress (Inc# 1, at conn) 10m wall under 1.5H+3V Motion A ..A ... 'll\. \.t '"\._ / ,, I I v 10 15 20 Time [sec] Time History of Inclusion Stress (Inc# 2, at conn) 1Om wall under 1.5H+3V Motion rt, M"' .... "' ;' v I I 10 15 20 Time [sec] Time History of Inclusion Stress (Inc# 3, at conn) 1Om wall under 1.5H+3V Motion 152 v 25 v 25 .A 25
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4000 ro 0... 6 3000 Cf) Cf) 2000 (/) c 0 "iii 1000 :::J (3 .E: 0 0 5 ro 3000 0... 2500 6 Cf) 2000 Cf) 1500 Ci5 c 1000 0 "iii :::J 500 (3 .E: 0 0 5 ro 2500 0... 6 2000 Cf) Cf) 1500 (/) 1000 c 0 'iii 500 :::J (3 0 .E: 0 5 "' L... J'r v / r 10 15 20 Time [sec] Time History of Inclusion Stress (Inc# 9, at conn) 1Om wall under 1.5H+3V Motion ..... ,... v J....... 10 15 20 Time (sec] Time History of Inclusion Stress (Inc# 10, at conn) 1Om wall under 1.5H+3V Motion /"" I"'" 10 15 20 Time [sec] Time History of Inclusion Stress (Inc# 11, at conn) 10m wall under 1.5H+3V Motion 153 25 25 25
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500 ro 0.. 400 C/) C/) 300 Cii c:: 200 0 '(ii :::J 100 u E 0 0 600 ro 0.. 500 400 C/) C/) Cii c:: 0 '(ii :::J u c:: ro 0.. C/) C/) Cii c:: 0 '(ii :::J u E 300 200 100 0 100 0 200 400 600 800 5 0 5 0 5 II Ill, I& I.A. .IIJI A. II"'\ n lr11'l "fll"l l!V lJI 10 15 20 Time [sec] Time History of Inclusion Stress (Inc# 18, at conn) 1Om wall with 1.5H Motion .I ft.'l d A .. I r'1 1' rul 1lV 111 10 15 20 Time [sec] Time History of Inclusion Stress (Inc# 19, at conn) 1Om wall under 1.5H+3V Motion l .I 'J' A ,A I .ft ,N i' Ill' '" ll II' Vi 10 15 20 Time [sec] Time History of Inclusion Stress (Inc# 20, at conn) 10m wall under 1.5H+3V Motion 154 ... 1\ v 25 'II rvw 25 w 25
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Appendix B. Lateral Earth Pressure Distribution Behind the Concrete Wall Section Note: H7ah=0.458g H+V7ah=0.458g; av=0.136g H+2V7 ah=0.458g; a v =1.272g H+3V7 ah=0.458g; av=2.408g 1.5H+2V7 ah=0.687g; av=1.272g 1.5H+3V7 ah=0.687g; av=2.408g 155
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" 100 I!! ..... 200 a. 300 .A ./ / w i! 400 1;j 1 .. ' 500 Wall Height [m[ 5 6 ...... ..... +Static Dynamic Figura B1 Lateral Earth Pressure Distribution 1Om wall under Imperial Valley Horizontal Motion PGA=0.456G Wall Height [m] 5 10 11 10 11 200 Q. 300 i +Static +Dynamic w 400 j 500 600 2 100 a. .. 300 .. I!! 0.. .<: 400 .::: C1l 500 w 600 100 i 200 I 300 a. i 400 w 500 [. 600 4 ...... ...... JJ II Figure B2 Lateral Earth F"ressure Distribution 10m wall under Imperial Valley 1.5"Horizontal Motion HPGA=0.456G Wall Height [m] 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ... .. +Static Figura BJ Lateral Earth Pressure Distribution 20m wall under Imperial Valley Horizontal Motion PGA=0.458G WaiiHelght[m] ._ F= 10 11 12 13 14 15 16 17 18 19 20 21 ... .. ... r_. Ill rL +Static Dynamic Figure Lateral Earth Pressure Distribution, DetMem 20m wall under Imperial Valley Horizontal Motion HPGA=0.458G 156 If
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100 e 200 o._ .... ., A 300 '\j! .400 500 ,.. 600 ;;100 i 200 ...... 300 0. .400 "' '\j! 500 ./ ,/ IW' Jlj 600 100 200 i! 300 400 i 500 w 600 100 200 300 .400 _llo 0. 500 I w 600 ... 700 Wall Height [m[ 5 .... ..... ...... +Static Dynamic Figure B5 Lateral Earth Pressure Distribution 1Om waH under Imperial Valley H+V Motion HPGA=0.458G Wai!Height{m] 5 6 .... ..... +static Dynamic Figure B1 Lateral Earth Pressure Distribution 10m wall under Imperial Valley 1.5H+V Motion PGA=0.465G Wall Height {m] 10 11 10 11 9 10 11 12 13 14 15 18 17 18 19 20 21 +Static Oyrwnic Adu,.. B7 Lateral Earth Pressure Distribution 20m wall under Imperial Valley H+V Motion HPGA=0.458G Wall Height {m] 9 10 11 12 13 14 15 16 17 16 19 20 21 ..... +Static Dynamic Figure B1 Lateral Earth Pressure Distribution, DetMem 20m wall under Imperial Valley H+V Motion HPGA=0.458G 157 '"
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i e a. i w 'f. "'i e a. w .... 100 a. "'200 300 ... ........ ,.... e 400 a. 500 w 600 1! 700 ..... ,.... V" Jl 800 l 100 200 i 300 400 i 500 800 """ I"" .,. Wall Height [m] 5 6 I'""' ,/ ..... .... +Static __.,__Dynamic L I I I I I I Figure B1 Lateral Earth Pressure Distribution 1Om waH under Imperial H+2V Motion .,. Wall Height [m] 5 ..... 10 11 10 11 w i 700 +static __.,__Dynamic .... .... eoo IJ" 900 200 .. 400 ''\,; .... 600 & """ 600 1000 .. w200 IN 400 '"\. 600 1 ... ,. 600 1000 I Jill 1200 Flgu,. &.10 Lateral Earth Pressure Oistrbution 10m wall under Imperial Valley 1.5H+2V Motion HPGA=0.485G Wall Height [m] 9 10 11 12 13 1( 15 16 17 18 19 20 21 _.. l)IJ ... L.e' ... w+Static Dynamic Figure Blateral Earth Pressure Distribution 20m wall under Imperial Valley H+2V Motion HPGA=0.(58G WaiiHeight[m] 10 11 12 13 1( 15 16 17 18 19 20 21 .... ool .... _. LJrl _. ... +Static Dynamic t Figure B12 Lateral Earth Pressure Distribution, DetMem 20m wall under Imperial Valley H+2V Motion HPGA=0.(58G 158 I1
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"'" 400 a. w """ 1! ., Jll 400 a. 600 800 w 1! 1. r 400 "'" 600 iii e 800 a. 0 2 3 4 0 'ii' 400 600 i 800 e a. w 1200 1400 ...... ./ Wai/Height[m] 5 ........... ...,. .....,. 10 v +Static Figure 813 Lateral Earth Pressure Distribution 10m waa under lmperiaiVaney H+3V Motion Wai/Height[m] 11 ff10 11 .... ..... +Static Dynamic Figure 8 Lateral Earth Pressure Distribution 10m wall under Imperial Valley 1.5H+3V Motion HPGA=0.458G Wai/Height[m) rff9 10 11 12 13 14 15 16 17 18 19 20 21 +Static +Dynamic Figure B15 Lateral Earth Pressure Distribution 20m wall under Imperial Valley H+3V Motion HPGA.458G Wall Height[m] I= 10 11 12 13 14 15 16 17 18 19 20 21 +Static Figure B11 Lateral Earth Pressure Distribution, OetMem 20m wall under Imperial Valley H+3V Motion HPGA=0.458G 159
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Appendix C. Bearing Pressure Distribution Beneath the Wall Footing Note: H7ah=0 458g H+V7ah=0.458g; av=0.136g H+2V7 ah=0.458g; av=1.272g H+3V7 ah=0.458g; av=2.408g 1.5H+2V7 ah=0.687g; av=1.272g 1.5H+3V7 ah=0.687g; av=2.408g 160
PAGE 175
" a. c :z a. C) "' "' IX) .... i e 0. i .... e 0. !!' 'ii d! .... e 0. i Base Length [m] 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 l _L I I I 100 1\ H +Static Pressure __,.__Dynamic Presure 200 1\' l .. 300 1\. ....... 400 0.0 0.2 0.4 50 11/ rFig C Bearing Pressure Distribution 10m wall under Imperial Valley Horizontal Motion PGA=0.485G Base Length [m] 0.6 0.8 1.0 1.2 I I 150 H Pressure Pressure 250 I._ 350 1\. 1...... V" 450 Nl' 0.0 0.5 200 400 600 800 ....... Fig C Bearing Pressure Distribution 1om wan under Imperial Valley 1.SHorizontal Motion PGA=0.458G Base Length [m] 1.0 1.5 2.0 2.5 "" ,..1.6 """ 1.6 3.0 1000 'fll Pressure Dynamic Pressure 1200 "' 1 "" 1400 0.0 0.5 200 400 600 !'Fig C3 Bearing Pressure Distribution 20m wall under Imperial Valley Horizontal Motion HPGA=0.458G 1.0 rBase Length [m] 1.5 2.0 2.5 3.0 1.8 1.8 3.5 .. 3.5 800 I +Static Pressure __.,_Dynamic Pressure "'I 1000 ,. 1200 Fig Bearing Pressure Distribution, DetMem 20m wall under Imperial Valley Horizontal Motion HPGA=0.458G 161
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"[ !! !! Q. :? ill "' ;; :3. Q. r I .. r .! Base Length [m] 0 .0 0 2 0.4 0.6 0.8 1.0 1 2 1 4 50 100 I I I 150 +Static Pressure Dynamic Presure \' 200 250 300 350 l I\. 400 0 0 0 2 ..... r.,. .. ,r Fig C5 Bearing Pressure Distribution 1Om wall under Imperial Valley H+V Motion PGA=0. 485G Base Length [m] 0 4 0.6 0 8 1 0 1 2 1 4 100 II. +Static Pressure Dynamic Presun! 200 .. 300 400 500 0 0 0 200 400 \\.. aDO \.' 0 5 ...... .. Fig C..e Bearing Pressure Distribution 1om wall under Imperial Valley 1 .5H+V Motion PGA=0.485G 1 0 Base Length {m] 1.5 2 0 1 6 1 .8 ..... .. 1 6 1 8 3 0 3.5 000 "'Il +Static Pressure __.,_Oynamk: P ressure ... IJ f1400 0 .0 400 I"' 0 5 <100 1100 ... j tl 1000 1200 1.0 I I I I Fig C 7 Bearing Pressunt Dis1rtbUion 20m waif under Imperial Valley H+V Motion HPGA=0.458G Base length (mj 1.5 2 0 2.5 .,...,... I I 3 0 3 5 +Static Pressure Dynamic Pressure rI Fig Cl Bearing Pressure Distribution, DetMem 20m wall under lmperlll VIMey H+V Motion HPGA=0 458G 162 I I I
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"go l a. 6 ill go .: ill "' Base length [m] 0.0 0.2 o. 0.6 0.8 1.0 1.2 100 f' 200 .. 300 400 500 1\ Pressure Dynamic Pressure \ 600 700 ...... r800 0.0 200 ........ 400 \ 600 600 0.0 ...... 0.2 0.4 Fig C1 Bearing Pressure Olsribution 10m wan under Imperial Valley H+2V Motion Base Length [m] 0.6 0.8 1.0 1.2 1.4 Pressure Presure I I I I I .I l ....r0.5 Fig C.10 Bearing Pressure Distribution 10m wall under Imperial Valley 1.5H+2V Motion PGA=0.485G 1.0 Base Length [m] 1.5 2.0 2.5 500 a. 6 I!! 1000 1500 ._ \. 1.6 .. loll 1.6 ..... 3.0 a. 2000 go \ I Pressure Pressure L .: 2500 .I "' 3000 0.0 0.5 !! 500 e1000 ...... \ I I Fig C11 Bearing Pressure Dls11ib1Jtlon 2om waJI under Imperial Valley H+2V Motion HPGA=O .S8G 1.0 Base Length [m] 1.5 2.0 2.5 13.0 1.8 1.8 3.5 ill 3.5 .. l 1500 \ I Pressure 4Dynamic Pressure r .. I 2000 .... I I Fig C12 Bearing Pressure Distribution, OetMem 20m wall under Imperial Valley H+2V Motion HPGA=0 . 58G 163 I
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e e .. Base Length [m] 0.0 0 2 0.4 0.6 0.8 1.0 1 2 1.4 1 6 1 8 0 200 ..... 400 600 800 \ +Static Pressure ......,_Dynamic Pressure \ .. 1000 \ ... 1 .. ..... ..... 1200 0.0 0 2 0 4 0.0 0 5 1000 2000 e .. 3000 ] 4000 / IlL L 0 .0 0.5 1000 2000 e .. "/ 3000 4000 F1g C13 Bearing Pressure Oisribution 10m waiii.RSer Imperial Va!Wty H+3V Motion Base Length [m] 0.6 0.8 1 0 1.2 1 4 F"tg C14 Bearing Pressure Distribution 10m wall under Imperial Valley 1.5H+3V Motion PGA=0.458G Base Length [m] 1 0 1 5 2 .0 2.5 1.6 3.0 +Static PressLK"e Pressure 1.0 Fig C15 Bearing Pressure Distribution 20m wall under Imperial Valley H+3V Motion HPGA.458G Base Length [m] 1 5 2 0 2 5 3.0 1.8 3 5 13.5 Pressure Dynamic Fig C11 Beaing Pressure Dlslrbutlon 20m wal under Imperial Vllllay HJV Motion 164
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Appendix D. Wall Face Deformation Note: H 7ah=0.458g H+V7ab=0.458g; av=0.136g H+2V7 ab=0.458g; av=1.272g H+3V7 ab=0.458g; av=2.408g 1.5H+2V7 ab=0.687g; av=l.272g 1.5H+3V7 ab=0.687g; av=2.408g 165
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K ... i 6 i 6 0 10 .... .. K 0 1! ... o i 70 Q 60 100 f'o T'Wal Height (m) +Static Fig D1 Forward Displacement 10m wall under Imperial Valley Horizontal Motion WaJIHeight(m) s 5 +Static Fig 0 Forward Displacement 10m wan under Imperial Valley 1.5Horz MoUon Wall Height (m) 10 12 14 15 18 _..._Static Displacement Dynamic Displacement ,..... .,., ,... ,... Fig DS Forwanl Disptacement 20m wall under lmperlal Villley HorizorUI Motion HPGA=0 .458G Wal Height (m) 10 12 14 15 ..... ., +Static Displacement .., I Dynamic Displacement Fig 04 Forward Displacement, DetMem 20m wall under Imperial Valley Horizontal Motion HPGA=0.458G 166 .... .... 18 10 11 10 11 J 20 22 20 22
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1 1! B ! ... 0 1 c i 5 1 i i 5 0 0 t 2 3 roll 4 5 6 7 6 9 2 lo.. .... Wall He;ght [m[ 5 tO +Static Dynamic 1N N ...... Fig D5 Wall Forward Displacement 10m waU under Imperial Valley H+V Motion Wall Height [m[ 5 10 1 1 11 11 1 4 ..._ I I l! 6 8 i 0 10 12 1 0 0 5 jWll 10 15 20 25 30 20 40 60 60 100 120 """1 11't +Static Dynamic ft11't 11. N _,_ Fig Forward Displacement 10m wall under Imperial Valley 1.5H+V Motion WaiiHe;ght[mJ 10 12 16 18 +Static Displacement Dynamic Oisp4acement """ !"'a [', !"'a ..... rw, P'e. 1.& Fig 07 Forward Displacement 20m wall under Imperial Valley H+V Motion HPGA=0 . 58G Wall Height [mJ 10 12 1. +Static Displacement ......,_Dynamic Displacement Fig O..S Forward Displacement, OetMem 20m wall under Imperial Valley H+V Motion HPGA=0 . 58G 167 ..... ..... 18 18 20 20 t22 22
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K 1! 1! B i J!l 0 :[ .. ]0 Wall Height [m[ 5 6 10 11 2 1 I I 1 1 K 4 c 6 1! 8 T T ra. +Static Dynamic ...., i 10 12 0 ""'t ..... N .... N 1t 1( 16 Rg Dl Forward Displacement 10m wail under Imperial Valley H+2V Motion Wall Height [m] 5 6 10 11 3 Ml .._ I I I I K 8 N +Static __,._Dynamic Jc 9 1! 12 I 15 18 21 24 10 .... I .... 20 .. .... 30 40 50 60 50 100 1___, 150 1_, 200 ....... ....... ...... 11t ...., ...... Flg 0 0 Forward Displacement 10m wan under Imperial Valley 1.5H+2V Motion WaiiHeight[m[ 10 12 16 18 20 ..... +Static Displacement +Dynamic Displacement .... Fig D11 Forward Displacement 20m wall under Imperial Valley H+2V Motion HPGA=0.(58G Wall Height {m) 10 12 14 16 +Static Displacement I .... +Dynamic Displacement Fig 0.12 FOIWW'd Displacement, DeiMemb 20m wall under Imperial Valley H+2V Motion HPGA=0.458G 168 ... 18 20 .... .... '91 122 22
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0 0 .a I ...... c i 0 U K .a .g ... ta. :30 0 0 K 40 r.. c .ao i .ao 0 :[ c i 250 f0 f400 450 Wai Height(m] 5 6 10 11 I I I I ....,"' +Static Diplacement Dynamic Displacement r...... 1'1 FIG DU FOStatic Displacement ,_ Dynamic Displacement FIG D11 FO
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Appendix El. Inclusion Stress Distribution for 10m Wall Note: H7ah=0.458g H+ V 7 ah=0.458g; av=O.l36g H+2V 7 ah=0.458g; av=l.272g H+3V7 ah=0.458g; av=2. 408g 1.5H+V7 ah=0.687g; av=0.136g 1.5H+2V7 ah=0.687g; a v =1.272g 170
PAGE 185
c 0 :;:; ::I .0 ;:: 2500 u; 2000 tJ) C1l ti)Q.. .... U5 c 0 u; ::I u c 2000 :; .c 1500 i5 Ulro 1500 1000 500 0 "' \ 0 \. l' I I I I I I I I I I +Static Stress Max Tensile Stress ........ ...... 2 4 6 8 lnclision Length [m] Inclusion Stress Distribution (Inc# 1) 10m wall under Imperial Valley Horizontal Motion +Static Stress Max Tensile Stress 1 1000 l;500 "iii :J 0 1600 c: 0 1200 "" :J .c "t: ca .!!l a.. 800 tJl tJl 400 (J) 0 0 0 \ 'r.. 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc #2) 8 10m wall under Imperial Valley Horizontal Motion I I. 2 I I I +Static Stress Max Tensile Stress 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc #3) 8 10m wall under Imperial Valley Horizontal Motion 171 I110 10 10
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c .Q '5 .0 :sro .!!l a. rn rn Ul c 0 5 .0 E'Ci .!!l a. rn rn (/) c 0 :g .0 c l1l .!!l a. j (/) 1400 ........ 1050 )I. 700 350 0 0 1200 900 600 300 0 0 1000 .,, ..... 800 600 400 200 0 0 ........ 1+Static Stress Max Tensile Stress 2 rrtL 4 6 Inclusion Length (m] Inclusion Stress Distribution (Inc #4) 8 10m wall under Imperial Valley Horizontal Motion I +Static Stress Max Tensile Stress I ......... ..... II2 4 6 8 Inclusion Length (m] Inclusion Stress Distribution (inc# 5) 10m wall under Imperial Valley Horizontal Motion I I I r10 10 J +Static Stress Max Tensile StressF= r....... r1.._ ... 2 4 6 8 10 Inclusion Length [m] Inclusion Stress Distribution (Inc # 6) 10m wall under Imperial Valley Horizontal Motion 172
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800 c 700 0 600 :; .0 500 EC? .!:!! c.. 400 o=. 300 rJ) rJ) 200 Ul 100 0 700 600 c 500 0 :s .0 400 :sro .!:!! c.. 300 o=. rJ) rJ) 200 U5 100 0 500 c 450 0 :g 400 .0 :sro .!:!! c.. 350 o=. rJ) 300 rJ) Ul 250 200 t. I ....., 1+Static Stress Max Tensile Stress I', ............ 0 2 4 6 8 Inclusion Length [m] Inclusion Stress Distribution (Inc # 7) 10m wall under Imperial Valley Horizontal Motion . ..... v 0 t...... v 0 :r,_ l Static Stress Max Tensne Stress I 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 8) 8 1Om wall under Imperial Valley 1brizontal Motion .... r,_ ......""'1 / v ....... ........... I +Static Stress Max Tensile Stress I ......... I I I 2 4 6 8 Inclusion Length [m] Inclusion Stress Distribution (Inc # 9) 10m wall under Imperial Valley Horizontal Motion 173 rrr........ rI10 r"1 10 ....., 10
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c 0 :s .c :Sro :l .c a.. :l .c a.. !!:! Ci5 450 400 350 v v i'. ,.......... v v ......... .......... 300 v r250 200 0 450 400 350 ....... 300 250 ......... 200 0 450 400 350 300 ........ 250 200 0 !+Static Stress Max Tensile Stress I ./ / 2 4 6 Inclusion Length [m) Inclusion Stress Distribution {Inc# 10) 8 10m wall under Imperial Valley Horizontal Motion ,.,.. i'....... v ........... I', I +Static Stress Max Tensile Stress i 2 4 6 Inclusion Length (m] Inclusion Stress Distribution (Inc #11) 8 10m wall under Impe rial Valley Horizontal Motion _.. ...b.. ./ .... / ......... ./_ ./ +Static Stress _._Max Tensile Stress _I I 2 I I J j_ j_ I I I I I 4 6 Inclusion Length [m] Inclus ion Stress Distribution (Inc# 12) ......... 8 1Om wall under Imperial Valley Horizontal Motion 174 r10 .......... rr.... 10 r.. ............ 10
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400 c:: 0 350 .0 Ero 300 .!!1 c..
PAGE 190
300 c: 0 250 =s .0 c: ........ ro 200 .!!l a. Ul Ul 150 U5 100 320 c: 0 :s 240 .0 Eli .!!l a. Ul 160 Ul en 80 300 c: 0 ., ::> 200 .0 c: ro .!!l a. Ul 100 Ul en 0 ./ v v 0 :11 .Jttl+Static Stress Max Tensile Stress J 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 16) 8 10m wall under Imperial Valley Horizontal Motion ..,. ....... v .. 10 +Static Stress Max Tensile Stress 1 t1 r7 v 0 / / t1 v v ,...... 0 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc # 17) 10m wall under Imperial Valley Horizontal Motion ..,... V" ........... v ........ .......... 8 10 1+Static Stress Max Tensile 2 I I I I 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc # 18) I 8 10m wall under Imperial Valley Horizontal Motion 176 I I 10
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400 c 300 0 :s .c 200 :sro .!!l a.. v o=.. 100 "' v "' 0 (/) / v 100 0 400 300 c 0 200 :w ::::l .c 1/ cCll 100 .!!l a.. 0=., / I""' "' 0 (/) 100 / 200 0 ....:.... v ...... I' r1 Stress Max Tensile Stress t2 I I 4 6 Inclusion Length [m) Inclusion Stress Distribution (Inc# 19) 1Om wall under Imperial Valley Horizontal Motion I' ..... """' Jl""' r"""' 1/ I I 2 :.... Stress rI MaxTensile Stress I I' .... ..;..4 6 Inclusion Length [m) Inclusion Stress Distribution (Inc# 20) !", 8 8 10m wall under Imperial Valley Horizontal Motion 177 10 10
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c: 0 :; .0 i5 Cl)ro CI)Q.. ii5 c: 0 "iii ::l u c: 3000 2500 2000 1500 1000 500 0 1\. \.. 0 1\ \.. ....... ,....., 2 _1 _1 I _1 !+Static Stress Max Tensile Stress L 4 6 lnclision Length (m] Inclusion Stress Distribution (Inc# 1) 8 10m wall under Imperial Valley Horizontai+Vertical Motion I I I I I I I I I I I 1+Static Stress Max Tensile Stress 2500 2000 1500 1000 ,........ 500 0 2000 0 c: 0 :s 1600 ....... :g 1200 =. 800 Cl) en 400 0 0 1\. "\ ........ f"'... 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc #2) 8 1Om wall under Imperial Valley Horizontai+Vertical Motion I I I I l j+Static Stress Max Tensile Stress .._ 2 4 6 8 Inclusion Length [m] Inclusion Stress Distribution (Inc #3) 10m wall under Imperial Valley Horizontai+Vertical Motion 178 10 10 10
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c 0 .0 "<: co .!!l a. o=. U) U) (J) c 0 s .0 ;::: ........ co .!!l a. o=. U) U) Ci5 c .Q :; .0 t: ro a. o::s U) U) Ci5 1400 1050 700 350 0 1200 900 600 300 0 1000 900 800 700 600 500 400 300 200 100 0 r.. 0 0 ........ 0 1\. ........ !'... 2 I I 1+Static Stress Max Tensile Stress 1 rr4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc #4) 8 10m wall under Imperial Valley Horizontai+Vertical Motion 1\. Max Tensile Stress t 1 +Static Stress !', t1i .... r2 4 6 8 Inclusion Length [m] Inclusion Stress Distribution (inc # 5) 1Om wall under Imperial Valley Horizontai+Vertical Motion I I I I I I I "\ I+Static Stress Max Tens De Stress ........ !'.... I "1 .......... ..... ....2 4 6 8 Inclusion Length [m] Inclusion Stress Distribution (Inc# 6) 10m wall under lrrperial Valley 1brizontai+Verticall'vbtion 179 10 1r10 10
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800 c 700 0 600 +=' :J .0 500 :sro a_ 400 "" 1+Static Stress Max Tensile Stress t'rr. 300 IJ) IJ) 200 Ci5 100 0 0 700 c 600 0 :g 500 h ........ .0 ECO 400 300 IJ) IJ) 200 en 100 0 0 500 c 450 0 400 .0 ., :sco a_ 350 IJ) 300 IJ) 250 en v 200 0 2 4 6 8 10 Inclusion Length (m] Inclusion Stress Distribution (Inc # 7) 10m wall under Imperial Valley Horizontai+Vertical Motion +Static Stress Max Tensile Stress 1r2 4 6 8 Inclusion Length [m] Inclusion Stress Distribution (Inc# 8) 10m wall under Imperial Valley Horizontai+Vertical Motion ./ v ....... ......... +Static Stress Max Tensile Stress 2 L I _l 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 9) 8 1Om wall under Imperial Valley Horizontal+ Vertical Motion 180 r10 r. ...... 10
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450 c 400 0 .0 350 ECU .!a a.. o=. 300 Ul Ul 250 Ci5 200 450 c 400 0 .0 350 c ro .!a a.. o=. 300 Ul Ul 250 (J) 200 400 c: 350 0 :s .0 :sco .!a a.. 300 o=. Ul Ul (J) 250 200 f..i'v l/ / !".......... 1...' / 0 v v v 0 l./ / ......... / 0 ......... r+Static Stress Max Tensile Stress i"'2 4 6 8 Inclusion Length [m] Inclusion Stress Distribution (Inc# 10) 10m wall under Imperial Valley Horizontai+Vertical Motion ......., C::=="' r.... !".. l/ / f""'.. 1+Static Stress Max Tensile Stress l 2 4 6 8 Inclusion Length [m] Inclusion Stress Distribution (Inc #11) 1Om wall under Imperial Valley Horizontai+Vertical Motion / v ./' v v I'1+Static Stress Max Tensile Stress 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 12) '., 8 10m wall under Imperial Valley Horizontai+Vertical Motion 181 rI'10 i"'10 ......... "" 10
PAGE 196
400 c 0 350 .0 ECO f..r.... t""""' ....... ........... ........., .!1 a. 300 oe..
PAGE 197
300 c 0 250 .0 c .Cll 200 a.. Ul Ul 150 CIJ 100 320 c 0 :s 240 .0 :sro a.. Ul 160 Ul CIJ 80 300 c 0 :s 200 .0 :Sc;a.. Ul 100 Ul ii5 0 __. .... rr....r:...._ /v +Static Stress Max Tensile Stress I / 0 2 4 6 8 Inclusion Length [m] Inclusion Stress Distribution (Inc# 16) 10m wall under Imperial Valley Horizontai+Vertical Motion 1........ r.. r... ..../ r....... ,.,. +Static Stress Max Tensile Stress I""""' I 0 ./ t'1 / v 0 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 17) 8 10m wall under Imperial Valley Horizontai+Vertical Motion r.... v ..... .......... v 1+Static Stress Max Tensile Stress I 2 4 6 8 Inclusion Length [m] Inclusion Stress Distribution (Inc# 18) 10m wall under Imperial Valley Horizontai+Vertical Motion 183 10 10 10
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c .Q :; .c :sea !!l a. o=.. rJl rJl en c 0 .c :sea !!l a. rJl rJl Q) c?5 400 300 200 t"' 100 v 0 / 100 0 400 300 200 .... r./ ...!"'" r.... / 2 ........ ........., __. r...... 1"' I Static Stress l'vt3x Stress fI 4 6 hclusion Length [m] Inclusion Stress Distribution (Inc# 19) 8 1Om wall under fnlJerial Valley Horizontai+Vertical Mltion ...... :..r.. / ............ / ...._ t r10 L = 100 /'_ 1"' :0 ............... 100 :/ 1 Stat i c Stress l'vt3xTensile Stress J= 200 0 2 4 6 8 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 20) 10m wall under lnl>erial Valley Horizontai+Vertical Mltion 184
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12000 10000 8000 6000 4000 2000 0 Stress Max Tensile Stress I ll '....,L 0 2 4 6 8 8000 6000 4000 2000 0 7000 6000 5000 4000 3000 2000 1000 0 Inclusion Length [m] Inclusion Stress Distribution (lnc#1) 10m wall under Imperial Valley Horizontai+2Vertical Motion 1\. 0 I 0 u \ \ "" "'wL 2 Stress Max Tensile Stress r4 6 Inclusion Length [m] Inclusion Stress Distribution (lnc#2) 8 1Om wall under Imperial Valley Horizontai+2Vertical Motion ll \ l .... ....... 2 Stress Max Tensile Stress I I4 6 Inclusion Length [m] Inclusion Stress Distribution (lnc#3) 8 1Om wall under Imperial Valley Horizontai+2Vertical Motion 185 10 10 10
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c 6000 0 5 5000 .c ;:: Vi 4000 i5 ...... I I I I I I I +Static Stress Max Tensile Stress tl)ro t/)Q_ 3000 (/) 2000 c 0 1000 Ui :::> (3 0 = 0 c 5000 0 "" :::> .c 4000 ;:: Vi i5 (3 = 2000 1000 0 3500 3000 2500 2000 1500 1000 500 0 \ 1.. 0 ......... r2 4 6 8 Inclusion Length [m] Inclusion Stress Distribution (lnc#4) 1Om wall under Imperial Valley Horizontai+2Vertical Motion ...... 1\.. )IL ............ 2 I L I I I _l +Static Stress Max Tensile Stress I 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 5) 8 1Om wall under Imperial Valley Horizontai+2Vertical Motion 0 lh 1+Static Stress Max Tensile Stress I .... ..._ 12 4 6 Inclusion Length (m] Inclusion Stress Distribution (Inc# 6) 8 1Om wall under Imperial Valley Horizontai+2Vertical Motion 186 10 10 10
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c 0 3000 .a c: (ii i5 2000 mea 1000 c: 0 a; ::I (3 0 c c 0 :s .a :s II) i5 mea c 0 a; ::I (3 c 2500 2000 1500 1000 500 0 2000 :s .a c: (ii 1500 i5 mea II) a... 1000 500 0 a.... .,._ !+Static Stress Max Tensile Stress I 0 ........ 12 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 7) 8 10m wall under Imperial Valley Horizontai+2Vertical Motion ........ I +Static Stress Max Tensile Stress ..__ 0 t:t 0 1.._ ... I2 :4 6 Inclusion Length (m] Inclusion Stress Distribution (Inc# 8) 8 10m wall under Imperial Valley Horizontai+2Vertical Motion ,...., ... 1. 111+Static Stress Max Tensile Stress I 2 4 6 Inclusion Length (m] Inclusion Stress Distribution (Inc# 9) 8 1Om wall under Imperial Valley Horizontai+2Vertical Motion 187 10 10 10
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c: 0 2000 :; .0 :s 1500 fJ) 0 fJlro fJlQ.. 1000 C/) c: 500 0 "Cii ::::1 13 0 = 1600 :; .0 1200 0 fJlro fJ) a.. 800 e><= (i.jc: 0 "Cii ::::1 13 = 400 0 1600 1200 800 400 0 0 0 ,._ ,..._ I. +Static Stress Max Tensile Stress 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 1 0) 8 10m wall under Imperial Valley Horizontai+2Vertical Motion +Static Stress Max Tensile Stress 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 11) r8 10m wall under Imperial Valley Horizontai+2Vertical Motion Jlr0 2 +Static Stress Max Tensile Stress 1 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 12) 8 10m wall under Imperial Valley Horizontai+2Vertical Motion 188 10 ... 10 10
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1600 1200 800 400 0 1600 "5 .0 1200 0 1/lro (/) a. 800 (/) 400 u; :::J 0 .E 0 c: 1400 0 :g .0 :s 1050 (/) 0 1/lro 700 1/lQ. (/) c: 350 0 u; :::J 0 0 .E .A .r.) rrtU 0 2 +Static Stress Max Tensile Stress L 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 13) 8 1Om wall under Imperial Valley Horizontai+2Vertical Motion ..... 0 / 1rf1"" 11+StaticStress MaxTensileStress I 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 14) 8 1Om wall under Imperial Valley Horizontai+2Vertical Motion "" ... ........... 1+static Stress Max Tensile Stress I 0 2 I I 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 15) 8 1Om wall under Imperial Valley Horizontai+2Vertical Motion 189 110 rt 10 10
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c: 0 ..c c: u; i:5 rnro rna.. u; c: 0 u; ::;, 0 1200 900 600 300 0 1200 900 600 300 0 1000 800 600 400 200 0 0 Jr 2 .._. +Static Stress Max Tensile Stress I 4 6 Inclusion Length [m) Inclusion Stress Distribution (Inc# 16) 8 10m wall under Imperial Valley Horizontai+2Vertical Motion ./ / +Static Stress Max Tensile Stress I ..... h 0 0 2 4 6 Inclusion Length [m) Inclusion Stress Distribution (Inc# 17) 8 1Om wall under Imperial Valley Horizontai+2Vertical Motion Jr'""' v ......... h 2 .II,_. 11+Static Stress Max Tensile Stress I 4 6 Inclusion Length [m) Inclusion Stress Distribution (Inc# 18) 8 10m wall under Imperial Valley Horizontai+2Vertical Motion 190 10 10 10
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til 1000 c.. =. c: 0 :; .0 iS "' Ci) BOO 600 400 200 "iii :::1 0 .5 0 til 1000 c.. 800 c: 0 :s .0 :s "' iS 600 400 200 0 200 0 "iii :::1 0 .5 400 600 r 0 ..... 0 ./ "" _...... ...v / ...f._ _.... J +Static Stress Max Stress I v 2 I I 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 19) 8 1Om wall under lrrperial Valley lbrizontai+2Vertical M>tion ...v ,....v ../r......... I I 2 I+Static Stress Max Tensile Stress I I I 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 20) 8 1Om wall under lrrperial Valley lbrizontai+2Vertical M>tion 191 10 1 10
PAGE 206
24000 rn'i? 20000 rJla_ 16000 (/) c c .Q 12000 o::l rJl..C 8000 "t: TI(i) c 4000 0 I \ \ lh 0 0 16000 12000 \ II 8000 \ 4000 "' 0 0 c 12000 0 5 ..0 10000 ;:: 1ii 8000 0 rn'i? 6000 mo.. (/) 4000 \. \ \ \ ......... c 0 2000 "iii ::l u 0 E 0 ..., r+Static Stress Max Tensile Stress j 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (lnc#1) 1Om wall under Horizontai+3Vertical Motion 8 1+Static Stress Max Tensile Stress 2 4 6 8 Inclusion Length [m] Inclusion Stress Distribution (lnc#2) 10m wall under Horizontai+3Vertical Motion 1+Static Stress Max Tensile Stress ..,..._ 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (lnc#3) 10m wall under Horizontai+3Vertical Motion 192 8 10 10 10
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c 0 9000 :g .0 c Ui 0 6000 UJro 3000 c 0 v; ::J g 0 8000 5 .0 6000 i:5 UJro Ul a.. 4000 (j)2000 ;n ::J C3 0 E c 0 s .0 c Ui 0 UJro c 0 v; ::J C3 E 6000 4000 2000 0 "\_ \ \. ...... 0 ... ...... "\. '+Static Stress Max Tensile Stress ......... ...._ 2 4 6 Inclusion Length (m] Inclusion Stress Distribution (lnc#4) 10m wall under Horizontai+3Vertical Motion 8 I I I I I I I I +Static Stress Max Tensile Stress [ 0 " ,....._ 0 2 4 6 8 Inclusion Length [m] Inclusion Stress Distribution (Inc# 5) 1Om wall with Imperial Valley Horizontai+3Vertical Motion +Static Stress Max Tensile Stress 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc # 6) 10m wall under Horizontai+3Vertical Motion 193 8 10 10 10
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c 5000 0 :;::1 ::l .c 4000 .::: iii 1 ..... i5 3000 mro mo.. 2000 en 11c 0 1000 "iii ::> u 0 = 0 c 0 4000 .c E 3000 m ....... i5 mro mo.. 2000 en c 1000 0 "iii ::l 0 (3 = 0 c: 3000 Q :; .c ,JI..,1"" .::: iii 2000 i5 mro mo.. en 1000 c: 0 "iii ::> (3 0 E 0 1+Static Stress Max Tensile Stress I 2 I I I I I I I L 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc # 7) 1Om wall under Horizontai+3Vertical Motion 1+Static Stress Max Tensile Stress 2 l _..L. 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 8) 10m wall under Horizontai+3Vertical Motion ,.__ 8 8 r[t ..._ _!+Static Stress Max Tensile Stress 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 9) 1Om wall under Horizontai+3Vertical Motion 194 8 10 10 "1 10
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c: 0 3000 ..c :s IJ) i:5 2000
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c .Q 3000 "5 .c :s Vl i:5 2000 r.n';' U5 1000 c 0 ijj ::J (3 0 E c 0 3000 :s .c ;:::: 1i) i:5 2000 r.n'Cii' r.na.. !::1000 rn c:: 0 u; ::J 0 (3 .s c:: 0 :s 2500 .c ;:::: 2000 1i) i:5 1500 r.n';' Vla_ .. 0 .) .ti I0 1000 en r c 500 0 u; 0 ::J (3 E 0 rN 1+Static Stress Max Tensile Stress 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 13) 1Om wall under Horizontai+3Vertical Motion 8 .n1r. 1. '+static Stress Max Tensile Stress 2 I I I 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 14) 10m wall under Horizontai+3Vertical Motion Inclusion Stress Distribution (Inc # 15) 8 10m wall with Imperial Valley Horizontai+3Vertical Motion ..2 4 6 Inclusion Length [m) +Static Stress Max Tensile Stress 196 8 10 10 10
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c: 0 :s 2500 .0 2000 Ci 1500 rnro rna_ 1000 (/) c: 500 0 u; :::J 0 u E 2000 1500 1000 500 0 c: .Q 2000 :; .0 1500 i5 rnro VJ a.. 1000 500 0 / "" .......... 0 ..Stress Max Tensile Stress 2 I I I I I 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 16) 10m wall under Horizontai+3Vertical Motion .I ...8 .JI......... / ...... 0 2 ........ r_. ....... 0 2 Stress Max Tensile Stress 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 17) 1Om wall uder Horizontai+3Vertical Motion .II8 Stress Max Tensile Stress J4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 18) 1Om wall under Horizontai+3Vertical Motion 197 8 10 10 10
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c Q :; ..c :5 Ill 0 lllro lila_ en c 0 "iii ::J 0 = 2000 1500 1000 500 0 2000 :s 1500 i5 1000 lllro Ill a. 500 en 0 c 0 "iii ::J 0 = 500 1000 0 rr 0 +Static Stress Max Tensile ....I ...:/ """ ........ v 2 r4 6 Inclusion Length (m] Inclusion Stress Distribution (Inc# 19) 1Om wall under Horizontai+3Vertical Motion +Static Stress .....Max Tensile ........ put llili ........ 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 20) 10m wall under Horizonta1+3Vertical Motion 198 8 10 8 10
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rn 5000 ll. 6 c:: 4000 0 5 3000 :g ]j 2000 0 C/) 1000 C/) 0 (/) rn 4000 3000 :; :g 2000 C/) i5 1000 C/)
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ro c... 2400 1800 0 +=' ::J .c E rJ) i:5 rJ) en 1200 600 0 2000 1500 :; .c E 1000 rJ) i:5 500 0 ro 1600 c... 1200 .c E 800 rJ) i:5 400 0 II\. 0 ....... 0 ......... 0 )t Stress Max Tensile Stress i\. ..... 1 12 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc #4) 8 10m wall under Imperial Valley 1.5Horizontai+Vertical Motion n .. ........ ..._ 2 I I I I I Stress Max Tensile Stress 4 6 Inclusion Length [m] Inclusion Stress Distribution (inc# 5) 8 1Om wall under Imperial Valley 1.5Horizontai+Vertical Motion 1\. Stress Max Tensile Stress 1 )I. ........ 2 ...... r4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc # 6) 8 1Om wall under Imperial Valley 1.5Horizontai+Vertical Motion 200 10 10 10
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(ij' 1200 a. =.. ........ I I I 900 1+Static Stress Max Tensile Stress 600 300 0 0 (ij' 1000 a. =.. 800 c 0 ........... ........ :; 600 .0 ;:: 1ii 400 (5 (/) 200 (/) 0 en 0 (ij' 800 a. =.. c 0 600 +=> .... :J .0 ;:: 1ii 400 iS (/) (/) 200 en ,...... 0 ,._ 1= 2 r..... 4 6 Inclusion Length [m) Inclusion Stress Distribution (Inc# 7) 8 1Om wall under Imperial Valley 1.5Horizontai+Vertical Motion ... 2 I I I I +Static Stress Max Tensile Stress 1 :4 6 Inclusion Length [m) Inclusion Stress Distribution (Inc# 8) 8 1Om wall under Imperial Valley 1 5Horizontai+Vertical Motion ........ 2 1+Static Stress Max Tensile Stress I 14 6 Inclusion Length [m) Inclusion Stress Distribution (Inc# 9) 8 1Om wall under Imperial Valley 1.5Horizontai+Vertical Motion 201 _110 10 10
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ro 600 c.. 500 .0 400 i:5 C/) 300 C/) (J) 200 "tr ........ f"'" _.... 0 2 +Static Stress Max Tensile Stress r.. ........ r.... 1r.. 4 6 8 Inclusion Length [m] Inclusion Stress Distribution {Inc# 10) 1Om wall under Imperial Valley 1 5Horizontai+Vertical Motion ro 5oo 450 c 0 400 :s .0 E C/) .......... IIv ,/" "" rr......... r... ........... ""'tiL rr110 i:5 C/) 350 300 r' 1+Static Stress Max Tensile Stress I rrC/) 250 (J) 200 450 ro c.. 400 c 0 '5 350 .0 i:5 300 250 l!! Ci5 200 0 2 4 6 Inclusion Length [m] Inclusion Stress Distribution {Inc #11) 8 10m wall under Imperial Valley 1.5Horizontai+Vertical Motion Jl..... J( .......r... I'. r / / [".. I'. I. v .......... 1+Static Stress Max Tensile Stress 0 2 4 6 8 Inclusion Length [m] Inclusion Stress Distribution {Inc# 12) 10m wall under Imperial Valley 1.5Horizontai+Vertical Motion 202 10 .......... r... 10
PAGE 217
ro a... c: Q :; .0 i5 (/) (/) CJ) ro 400 a... c: .Q :; .0 300 E U) i5 U) U) CJ) 200 350 ro a... c: 0 .0 250 U) i5 U) U) (j) 150 400 350 300 r""". .......... ............ bot .. ........ ..,. ....... :r... 250 .......... 200 0 .) v 0 ....... kl 0 v 1+Static Stress Max Tensile Stress I 2 4 6 Inclusion Length [m) Inclusion Stress Distribution (Inc # 13) 8 10m wall under Imperial Valley 1.5Horizontai+Vertical Motion r.......... ...v 1+Static Stress Max Tensile Stress I 2 4 6 Inclusion Length [m) Inclusion Stress Distribution (Inc# 14) ........ r. 8 10m wall under Imperial Valley 1.5Horizontai+Vertical Motion ...... / ..r11 r1+Static Stress Max Tensile Stress I 2 4 6 8 Inclusion Length [m) Inclusion Stress Distribution (Inc# 15) 1Om wall under Imperial Valley 1 5Horizontai+Vertical Motion 203 ........ 10 rI' 10 rt. 10
PAGE 218
m 400 0.. =. c:: .Q 300 :; I I I I I I I ..I I I I J I I I I I I ,....0 ...... .:..._ E f/) i5 200 f/) f/) (/) 100 m 4oo 0.. =. 320 'S .0 c:: Cii 240 II"" 00 ..... v t::: 1+Static Stress Max Tensile Stress 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 16) 8 1Om wall under Imperial Valley 1.5Horizontai+Vertical Motion ..rr.......... r/ .. .n' 160 ttl" f/) (/) 80 m 0.. =. c:: 0 "" :::> .0 c:: Cii i5 f/) f/) Q) !:I (/) / ...,..A 0 2 1+Static Stress Max Tensile Stress 1 I I I I 4 6 Inclusion Length [m) Inclusion Stress Distribution (Inc# 17) 8 10m wall under Imperial Valley 1 5Horizontai+Vertical Motion 500 400 300 200 .JI'" ......... 100 v 0 0 ..,.... ....... Jt"""" "'t ......... 1+Static Stress Max Tensile Stress I 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc # 18) 8 1Om wall under Imperial Valley 1.5Horizontai+Vertical Motion 204 Ll 10 1"t 10 10
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(ij' c.. c: 0 :g .0 c: 1ii Ci Ill Ill en 600 400 kf.1/..1t ..... 200 Jr"' ........ ...... 0 r 200 0 800 (ij' c.. 600 c: 0 400 :s .0 c: 1ii 200 Ci H Ill Ill 0 en 200 0 J+Static Stress Max Tensile Stress r 2 4 6 8 Inclusion Length [m] Inclusion Stress Distribution (Inc # 19) 1Om wall under Imperial Valley 1 5Horizontai+Vertical Motion r;...... "'! ................ v J+Static Stress MaxTensile Stress ...... ..,...,.... 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc # 20) 8 1Om wall under Imperial Valley 1.5Horizontai+Vertical Motion 205 . 10 . 10
PAGE 220
14000 12000 10000 1'\ 8000 6000 4000 2000 0 0 10000 1\. 8000 6000 4000 2000 0 '\ 0 'iii' 9000 a. .. c: lt \ 1+Static Stress Max Tensile Stress I 1\ \ \ ...._, .... 2 4 6 lnclision Length [m] Inclusion Stress Distribution (Inc# 1) 8 10m wall under Imperial Valley 1.5Horizontai+2Vertical Motion \ 1+Static Stress Max Tensile Stress fu._ 2 I. 4 6 Inclusion Length [m] lndusion Stress Distribution (Inc #2) 8 10m wall under Imperial Valley 1.5Horizontai+2Vertical Motion 0 6000 .Cl ;:: \ +Static Stress Max Tensile Stress I 1ii i:5 3000 C/) C/) en 0 0 "'' .... 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc #3) 8 10m wall under Imperial Valley 1.5Horizontai+2Vertical Motion 206 10 f10 10
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ro 8ooo c.. 6000 .0 4000 2000 (/) en 0 ro 6ooo c.. c: g 4000 ::J .0 :s i5 2000 (/) (/) en 0 ro 5ooo c.. 4000 '5 3000 .0 2000 0 ::! 1000 en 0 I I I ., 11 \. Stress Max Tensile Stress 1 0 I ".{ 0 ..... .... 2 4 6 8 Inclusion Length [m] Inclusion Stress Distribution (Inc #4) 10m wall under Imperial Valley 1 .5Horizontai+2Vertical Motion \ ........ Stress Max Tensile Stress 1't ...._ 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (inc# 5) 8 10m wall under Imperial Valley 1.5Horizontai+2Vertical Motion .. """' 0 11 .. 1"""t 2 I I L J Stress Max Tensile Stress 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 6) 8 10m wall under Imperial Valley 1.5Horizontai+2Vertical Motion 207 10 10 r10
PAGE 222
ro 4000 a.. =.. c:: 3000 0 :g .0 2000 c ..... (/) i5 1000 (/) (/) Q) ..... ..... 0 (/) ro 3ooo a.. =.. c:: :8 2000 :J .0 c c;; i5 1000 (/) (/) e Ci5 0 J.. 0 I 0 Cii' 2500 Q_ rr... 2 L+Static Stress Max Tensile Stress 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 7) 8 1Om wall under Imperial Valley 1 5Horizontai+2Vertical Motion fr10 +Static Stress Max Tensile Stress f.._ ... f. 2 4 6 8 10 Inclusion Length [m) Inclusion Stress Distribution (Inc# 8) 10m wall under Imperial Valley 1.5Horizontai+2Vertical Motion I I 2000 11n I I I I +Static Stress Max Tensile Stress r0 :s 1500 .0 E Vl 1000 0 Vl 500 en o 0 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 9) 8 10m wall under Imperial Valley 1 5Horizontai+2Vertical Motion 208 10
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ro 2ooo a_ 1.!L c: 1500 .Q ::; .0 E 1000 Ul i5 Ul 500 (/) 0 ro a_ 0 1800 1400 0 'S .0 E 1000 Ul i5 Ul 600 (/) 200 co 1500 a_ c: 0 1000 .0 c iii 0 500 Ul U5 0 0 ....... 0 r1. +Static Stress Max Tens il e Stress 2 4 6 Inclusion Length [m] Inclusion Stress Distribut ion (Inc# 10) 8 10m wall under Imperial Valley 1.5Horizontai+2Vertical Motion .... r11+Static Stress Max Tensile Stress L 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc #11) r... 8 1Om wall under Imperial Valley 1.5Horizontai+2Vertical Motion ..t1. r . J1+Static Stress Max Tensile Stress I 2 4 6 8 Inclusion Length [m) Inclusion Stress Distribution (Inc# 12) 1Om wall under Imperial Valley 1.5Horizontai+2Vertical Motion 209 10 10 10
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'iii' a. =. c 0 :s .c
PAGE 225
ro c.. c: 0 .c ;:: ti 0 Ul Ul (/) ro c.. c: 0 !; .c ;:: ti 0 Ul Ul (/) 1200 800 ....1) ....... +Static Stress Max Tensile Stress 400 ( 0 0 1200 800 2 4 6 Inclusion Length [m) Inclusion Stress Distribution (Inc # 16) 8 10m wall under Imperial Valley 1.5Horizontai+2Vertical Motion v / 400 +Static Stress Max Tensile Stress / r0 0 1000 800 600 400 200 0 0 2 4 6 Inclusion Length [m) Inclusion Stress Distribution (Inc# 17) 8 1Om wall under Imperial Valley 1.5Horizontai+2Vertical Motion L/ ..1+Static Stress Max Tensile Stress I r 2 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 18) 8 10m wall under Imperial Valley 1.5Horizontai+2Vertical Motion 211 10 10 10
PAGE 226
ro c.. 900 600 c: 0 .c i5 300 r300 0 1000 ro c.. 800 c: 600 0 :s .c 400 c:: t; i5 200 rJ) rJ) 0 Ci5 200 ........ IL ,......... 0 / 2 *l+r _.1f1 ..,.. 1+static Stress Max Tensile Stress I 4 6 8 Inclusion Length [m] Inclusion Stress Distribution (Inc# 19) 10m wall under Imperial Valley 1.5Horizontai+2Vertical Motion / / _}I ,/ 2 1+Static Stress MaxTensile Stress 1 4 6 Inclusion Length [m] Inclusion Stress Distribution (Inc# 20) 8 10m wall under Imperial Valley 1.5Horizontai+2Vertical Motion 212 10 10
PAGE 227
Appendix E2. Inclusion Stress Distribution for 20m Wall Note: av=0.136g H+2V ah=0.458g; av=l.272g ah=0.458g; av=2.408g 213
PAGE 228
ro 0.. 2000 =.. 1500 c 0 1000 .0 ;:: 500 C5 rn 0 rn 500 Ci5 ro 15oo 0.. =.. c 1000 0 :s .0 ;:: C5 rn rn 500 0 Ci5 500 ro 0.. 1500 =.. 1000 c 0 "" :::l .0 :s rn C5 rn rn Ci5 500 0 500 ' I"'... 0 '.... 0 '\ 0 +Static Stress Dynamic Stress 5 10 Inclusion Length [m] 1rInclusion Stress Distribution (Inc# 1) 15 20m wall under Imperial Valley Horizontal Motion +Static Stress Dynamic Stress L 5 _.. 10 Inclusion Length [m] rInclusion Stress Distribution (Inc # 2) 15 20m wall under imperial Valley Horizontal Motion 1+Static Stress Dynamic Stress I .......... to' 5 ...10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 3) 15 20m wall under Imperial Valley Horizontal Motion 214 20 20 20
PAGE 229
1500 ro a.. c: 1000 .Q :; ..0 (5 500 Ul Ul (f) 0 ro 1500 a.. c: 0 1000 :s ..0 c: Cii (5 500 Ul Ul (f) 0 ro 1ooo a.. c: 0 :s ..0 ;::: Cii (5 Ul Ul (f) 500 0 '\ Ill "\ ... lA0 I ......... .. 1+Static Stress Dynamic Stress I ..IlL ...!""" 11 f.f.15 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 4) 15 20m wall under Imperial Valley Horizontal Motion +Static Stress Dynamic Stress ....... l'o... ..... ...f.L.o.. r...I"' 0 ....... ....... .. .....r 0 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 5) 15 20m wall under Imperial Valley Horizontal Motion ..5 ............. ....1+Static Stress Dynamic Stress I 10 Inclusion Length [m] Inclusion Stress Distribution (Inc # 6) 15 20m wall under Imperial Valley Horizontal Motion 215 20 20 20
PAGE 230
ro 1ooo 0... c 0 ..0 :s "' 15 "' "' Ci5 ro 0... c 0 :s ..0 15 "' "' en 500 0 1500 1000 500 0 ro 1500 0... c 0 1000 :s ..0 :s "' 15 500 "' "' Ci5 0 i'.. l'r / lv" 0 .... r 0 h ... r"W" AI' / 0 ...I""" ............1+Static Stress Dynamic Stress I 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 7) 15 20m wall under Imperial Valley Horizontal Motion It5 1+Static Stress Dynamic Stress I I 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 8) 15 20m wall under Imperial Valley Horizontal Motion I1+Static Stress Dynamic Stress I 5 I I I 10 Inclusion Length [m] I Inclusion Stress Distribution (Inc # 9) I 15 20m wall under Imperial Valley Horizontal Motion 216 20 20 20
PAGE 231
ro a. 6 c 0 .c ;:: 1ii 0 Vl Vl en 1500 1250 1000 .._ .... ' ...,..._. ... 750 500 ..;' !+Static Stress Dynamic Stress 250 0 0 ro 1500 a. 6 c .Q 1000 :; .c 0 500 ........ .. .... '""" ., ......... v 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 1 0) 20m wall under Imperial Valley Horizontal Motion ..J !I"" I!+Static Stress Dynamic Stress I en 0 0 1500 ... a. I. 6 c: 0 :B 1000 iii 500 .... .... / v 0 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 11) 15 20m wall under Imperial Valley Horizontal Motion tJt" ) v ........... .__ I +Static Stress Dynamic Stress I 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 12) 15 20m wall under Imperial Valley Horizontal Motion 217 20 20 120
PAGE 232
2000 ro ll.. =. c: 1500 0 :s .0 :s en i5 1000 en en (/) 500 ro 2ooo ll.. =. c: 0 1500 :s .0 ;:::: U5 i5 1000 en (/) 500 2000 ro ll.. =. 1500 +' ::l .0 i5 1000 (/) 500 11/ v 0 ..._ r.... "" v 0 ,_ l.' v j' 0 v ..JIL ...1I"' r1+Static Stress Dynamic Stress l .... 5 10 Inclusion Length [m) 15 Inclusion Stress Distribution (Inc# 13} 20m wall under Imperial Valley Horizontal Motion ._ rI;' 1/ v 1+Static Stress Dynamic Stress 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 14} 15 20m wall under Imperial Valley Horizontal Motion II'" )....r!.tiL 1+Static Stress Dynamic Stress 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 15} 20m wall under Imperial Valley Horizontal Motion 218 ,....__ +"1 20 :20 t20
PAGE 233
ro 2000 CL =. c: 0 1500 .0 c iii i:5 1000 t/) t/) I .v U5 500 0 ro zooo CL =. t: V"" / .... 1,,........,..., v r. 11 1+Static Stress Dynamic Stress 1 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 16) 15 20m wall under Imperial Valley Horizontal Motion r/ ...... IIr. .__ 0 1500 .0 K 1t ..._ rE t/) i:5 1000 t/) t/) U5 500 ro 2ooo CL =. 1500 :s .0 c iii i:5 1000 t/) t/) en 500 v 0 0 v ......v r+static Stress Dynamic Stress 5 10 15 Inclusion Length [m] Inclusion Stress Distribution (Inc# 17) 20m wall under Imperial Valley Horizontal Motion ......... ................. '+Static Stress Dynamic Stress 5 10 Inclusion Length [m] ........... 15 Inclusion Stress Distribution (Inc# 18) ...._ 20m wall under Imperial Valley Horizontal Motion 219 !r20 rt 20 20
PAGE 234
2000 1500 "" ::::l .0 ;::: ti 0 1000 IJ) en 500 ro 2ooo l:l. c: .Q 1500 "5 .0 :s IJ) 0 1000 IJ) IJ) U5 ro l:l. c: 0 :; .0 ;::: ti 0 IJ) IJ) en 500 2500 2000 1500 1000 500 / 0 r/ 0 "'" / 0 V"' / .,__ 1............ r.. 1+Static Stress Dynamic Stress I 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 19) ....... .._ 20m wall under Imperial Valley Horizontal Motion f+, ..... v rb 1+Static Stress Dynamic Stress [ 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 20) 15 20m wall under Imperial Valley Horizontal Motion """1 ....... / ............ ........ r:, 20 t20 r....... 1+Static Stress Dynamic Stress I I I I 5 10 15 20 Inclusion Length [m] Inclusion Stress Distribution (Inc# 21) 20m wall under Imperial Valley Horizontal Motion 220
PAGE 235
ro 25oo c.. c .Q 2000 :; .0 E c5 1500 Vl Vl l!! U5 1000 ro c.. 2500 2000 :; .0 :s Vl i:5 1500 Vl Vl C/) 1000 2500 ro c.. 2000 :s .0 E Vl i:5 1500 !I) C/) 1000 r,_. """"I v ................. r.... ./,r / 0 / / '/ 0 ...... .... /v ./ 0 i 1+Static Stress Dynamic Stress I 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 22) 20m wall under Imperial Valley Horizontal Motion pt v j'.. "'tiL 1+Static Stress Dynamic Stress I v 5 10 15 Inclusion Length [m] Inclusion Stress Distribution (Inc# 23) 20m wall under Imperial Valley Horizontal Motion """"I ........... 1'.11.. 1+Static Stress Dynamic Stress 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 24) 20m wall under Imperial Valley Horizontal Motion 221 r20 r.... 20 r.... 20
PAGE 236
ro 2000 a. ..... r=. 1750 ........ 1.... h. c 0 :; .c 1500 c Vi i:5 en 1250 en en 1000 v J' V"' J / 0 ro 2000 a. =. c 0 1500 .c i:5 1000 en t en 500 0 ro 2000 a. =. c Q 1500 :; .c c Vi i:5 1000 en en en 500 .. v / ..jr" / I' ...... 0 ......... ........... r..a. !+Static Stress Dynamic Stress I 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 25) 15 20m wall under Imperial Valley Horizontal Motion rr............. 1+Static Stress Dynamic Stress 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 26) 20m wall under Imperial Valley Horizontal Motion i"'i"'1+Static Stress Dynamic Stress 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 27) 20m wall under Imperial Valley Horizontal Motion 222 ......_ ......_ 1t 20 .... 20 I""'t 20
PAGE 237
ro 2ooo c.. ::!!:. c: 0 1500 .... r .c ;:: Cil 0 1000 t/) u; 500 ro 2ooo c.. ::!!:. c: 0 1500 :s .c :s C/) 0 1000 en 500 ,... 0 0 2000 c: 0 :s 1500 .c ..... JY ,./ """" ......... 11+Static Stress Dynamic Stress I 5 10 Inclusion Length [m) Inclusion Stress Distribution (Inc# 28) 15 20m wall under Imperial Valley Horizontal Motion . !+Static Stress Dynamic Stress 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc # 29) 15 20m wall under Imperial Valley Horizontal Motion 't: _.. ro .!!! c.. . ..._ lAIIt 0::!!:, t/) 1000 C/) u; ....... v 500 0 V'" 1+Static Stress Dynamic Stress I 5 10 Inclusion Length [m) Inclusion Stress Distribution (Inc# 30) 15 20m wall under Imperial Valley Horizontal Motion 223 20 1. 20 20
PAGE 238
'iii' a.. =. c 0 :s .c :s Vl i5 Vl Vl U5 'iii' a.. =. c 0 :; .c c Ui i5 Vl Vl U5 'iii' a.. =. 1500 1000 500 1500 1000 500 1500 1000 :; .c :s Vl i5 500 Vl Vl (J) 0 A 0 IJ" J7 0 ./ 0 ...IL . ..._ 1+Static Stress Dynamic Stress I 5 10 15 Inclusion Length [m] Inclusion Stress Distribution (Inc# 31) 20m wall under Imperial Valley Horizontal Motion 5 ,...... !+Static Stress Dynamic Stress 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 32) 15 20m wall under Imperial Valley Horizontal Motion 5 1+Static Stress Dynamic Stress 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 33) 15 20m wall under Imperial Valley Horizontal Motion 224 r1t 20 11"i 20 20
PAGE 239
"iii' a.. =. 1500 1000 :; ..c E rn 0 500 rn rn _g; (J) 0 1500 =. c: Q 1000 :; ..c E 5 5oo rn rn _g; (J) 0 "iii' 1000 a.. =. c: 0 5 ..c 0 rn (J) 500 0 .........: v 0 .:;::::: "'" 0 !I '7 r.... ./ 1/ 0 5 .:::: .,. J+Static Stress Dynamic Stress I 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 34) 20m wall under Imperial Valley Horizontal Mot ion 5 1+Static Stress Dynamic Stress I I 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 35) I 15 20m wall under Imperial Valley Horizontal Motion 5 1... .__ ......v / ....... !+Static Stress Dynamic Stress I 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 36) 20m wall under I mperial Valley Horizontal Motion 225 20 20 20
PAGE 240
1000 ro a. =.. c 500 0 .0 ;:: t5 i5 0 1/) 1/) !!:! ii5 500 0 1000 ro a. =.. c 500 0 .0 ;:: t5 i5 0 1/) 1/) !!:! ii5 .,/ r ;; 500 0 /... ............ v ..... 5 +Static Stress Dynamic Stress 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 37) 15 20m wall under Imperial Valley Horizontal Motion II.. _.....,.. r_.... ...... v .,.. ......... p ... 5 v 1+Static Stress Dynamic Stress I 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 38) 20m wall under Imperial Valley Horizontal Motion 226 20 20
PAGE 241
1000 c 500 0 'S ..c c ........ ro 0 .!!1 a.. C/) C/) Q) = 500 (/) v,_ ,X v 1000 0 1000 ro a.. 500 c: 0 :s ..c 0 / iS C/) C/) 500 Ci5 lr ./ ...1000 0 ...... ....... ...:. r::::v / p / ....... ........ 1+Static Stress Dynanic Stress I I I 5 10 hclusion Length [m] Inclusion Stress Distribution (Inc# 39) 15 20m wall under tl"l>erial Valley 1brizontal Mltion ......../ / ,____ 5 J +Static Stress Dynanic Stress I I I I 10 Inclusion Length [m] I I 15 Inclusion Stress Distribution (he# 40) 20m wall under hTperial Valley 1brizontal Mltion 227 20 t 20
PAGE 242
ro750 a. =. 500 c: 0 '5 250 .0 c tl 0 0 250 (/) 500 roa. =. 1000 500 :; .0 E rJl 0 0 rJl rJl Ci5 roa. =. c: 0 :s .0 c tl 0 rJl rJl Ci5 500 1000 500 0 500 r..... Ia. r. ..... 0 0 ...._ 0 ....1" v .......... ,.....I r......... v ....... I""' 1+Static Stress Dynamic Stress 5 10 Inclusion Length (m] Inclusion Stress Distribution (Inc# 1) 15 20m wall under Imperial Valley Horizontai+Vertical Motion ........ f.f""' ............ ,...:._ !+Static Stress Dynamic Stress L 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 2) 15 20m wall under Imperial Valley Horizontai+Vertical Motion ,.....I :,.....5 r......r_...... 1+Static Stress Dynamic Stress I 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 3) 20m wall under Imperial Valley Horizontai+Vertical Motion 228 20 20 20
PAGE 243
ro 1000 c.. c .Q ::; .0 500 c 1ii Ci en en U5 0 ro 1000 c.. c 0 :s .0 500 Ci en en U5 0 1000 ro c.. c 0 :s .0 500 E "' Ci "' "' (J) 0 ....rr_.. ..1.._ / ...... f.."r ,..;::: ....... 1+Static Stress Dynamic Stress _.....4 """"" 0 ...... Ia. .....0 h AI' 0 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 4) 20m wall under Imperial Valley Horizontai+Vertical Motion _.. i""'" ........... ......... _.. l." _.. "" .,..A ..5 1+Static Stress Dynamic Stress I 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 5) 20m wall under Imperial Valley Horizontai+Vertical Motion / / ..1 ..... v _.. f.' _.. 5 ........... ............ 1+Static Stress Dynamic Stress 10 Inclusion Length [m] Inclusion Stress Distribution (Inc # 6) 15 20m wall under Imperial Valley Horizontai+Vertical Motion 229 ..1 120 20 20
PAGE 244
ro 1000 Q._ c 0 :g .0 500 ;:: 1ii 0 Ill Ill (i5 0 ro15oo Q._ c 0 1000 :s .0 E 6 500 Ill Ill en 0 ro 15oo Q._ c 0 1000 :; .0 c:: 1ii 0 500 Ill Ill en 0 .... ... _, .K 0 it. ... ... .....f4' 0 ..._ . 0 ........ v v I....... lI.......... ........... 1+Static Stress Dynamic Stress 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 7) 15 20m wall under Imperial Valley Horizontai+Vertical Motion ...... ...5 '+Static Stress Dynamic Stress I I I 10 Inclusion Length [m] I I Inclusion Stress Distribution (Inc# 8) 15 20m wall under Imperial Valley Horizontai+Vertical Motion ........ / :..r1+Static Stress Dynamic Stress 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 9) 15 20m wall under Imperial Valley Horizontai+Vertical Motion 230 20 20 20
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'iii' 1500 a.. I I I 1250 <:: 0 1000 ...... ... .c 750 Ci 500 (/) 250 (/) 1....... K ii5 0 0 'iii' 1500 a.. <:: Q 1000 ::; .c ;:: 1ii Ci 500 v ...(/) (/) (/) 0 0 1500 'iii' a.. <:: 0 =s .c 1000 E '"' IL (/) Ci (/) (/) (/) I v v 500 0 I I I I I I I I I I I I .tit11+static Stress Dynamic Stress I 5 I I I I 10 Inclusion Length [m] I I 15 Inclusion Stress Distribution (Inc # 1 0) I 20m wall under Imper ial Valley Horizontai+Vertical Motion v _.... +Static Stress Dynamic Stress I 5 I I I 10 Inclus ion Length [m] I I 15 Inclus ion Stress Distribution (Inc# 11) 20m wall under Imperial Valley Horizontai+Vertical Motion ......... ... v .......... ,....,.... ....... v ......... r... .,...,. ........ I v "'1 ..._ rv 1+Static Stress Dynamic Stress I 5 10 Inclusion Length [m] 15 Inclusion Stress Distribut ion (Inc# 12) 20m wall under Imperial Valley Horizontai+Vertical Motion 231 I I 20 20 rN 20
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ro 2000 c... :!! c 0 1500 :s .0 c: Ui i5 1000 rJ) rJ) f!? Ci5 500 2000 1500 :s .0 c: Ui i5 1000 (/J 500 2000 ro c... =. t: Q 1500 "5 .0 :E rJ) i5 1000 rJ) rJ) f!? Ci5 500 .... / ,........ .... 0 0 I ......... 0 ...J ....... v ,. ...IL ....::::::: 1+Static Stress Dynamic Stress 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 13) 20m wall under Imperial Valley Horizontal+ Vertical Motion ..I r..... ......_ 41" +Static Stress Dynamic Stress I I I I 5 10 15 Inclusion Length [m] Inclusion Stress Distribution (Inc# 14) 20m wall under Imperial Valley Horizontai+Vertical Motion .... ....... .... [/ _.. ...... rr,.L 1+Static Stress Dynamic Stress 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 15) 20m wall under Imperial Valley Horizontai+Vertical Motion 232 20 rt 20 r"! 20
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m 2ooo a_ c 0 1500 :s .c c (ij i:5 1000 V) V) CJ') 500 m 2ooo a_ c 0 1500 .c E V) i:5 1000 V) V) U5 500 2000 m a_ c 1500 .Q "5 .c c (ij i:5 1000 V) V) CJ') 500 .. .L v 0 Itv .,.., 0 ........ ./__ 0 ..1 '... rv r'""1 11+Static Stress Dynamic Stress I I I I I 5 10 15 Inclusion Length [m] Inclusion Stress Distribution (Inc# 16) 20m wall under Imperial Valley Horizontai+Vertical Motion ..... ............ r.. N' I.Jr' .... N 1+Static Stress Dynamic Stress I 5 I I I 10 Inclusion Length [m] I 15 Inclusion Stress Distribution (Inc# 17) ...__ 20m wall under Imperial Valley Horizontai+Vertical Motion L ..._ v ... r..... "1 20 rt 20 ........ h r.... J+Static Stress Dynamic Stress I 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 18) 20m wall under Imperial Valley Horizontai+Vertical Motion 233 ......... 20
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ro2000 c.. 6 c: Q 1500 "5 .0 ;:: ti 1000 0 tJl tJl Ci) 500 2000 1500 s .0 E tJl 0 1000 tJl tJl en 500 ro 2500 c.. 6 c: 2000 0 :s .0 ;:: ti 0 1500 1000 Ci) 500 ..... r ....,. ttl 0 .... ..... v rilL ............ t... 1+static Stress Dynamic Stress I 5 I I 10 Inclusion Length [m] I I Inclusion Stress Distribution {Inc# 19) 15 ...... ...._ r20m wall under Imperial Valley Horizontai+Vertical Motion J,.r. .... ./v ............ r..... /'/" L 0 r ......... .., 0 .,..._ rt:J+Static Stress Dynamic Stress 5 10 Inclusion Length (m] 15 Inclusion Stress Distribution {Inc # 20) 20m wall under Imperial Valley Horizontai+Vertical Motion "" .. ....... r!+Static Stress Dynamic Stress 1 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution {Inc# 21) 20m wall under Imperial Valley Horizontai+Vertical Motion 234 . 20 20 20
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ro 25oo 0... =. c 0 2000 :s .0 c Ui i:5 1500 VI VI 1000 CJ) ro 25oo 0... =. c 0 2000 :s .0 c Ui i:5 1500 VI VI ii5 1000 ro 0... =. 2500 2000 "" :::l .0 i:5 1500 VI VI CJ) 1000 I'"" ,.... v ./ +Static Stress Dynamic Stress !"... II"'" r11 .L' 0 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 22) 15 20m wall under Imperial Valley Horizontai+Vertical Motion r ../ ./ 0 r I'"" /v v 0 ,.._ v r.......... 1+Static Stress Dynamic Stress I 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 23) 20m wall under Imperial Valley Horizontai+Vertical Motion )J. ........ I' r........... rr1+Static Stress Dynamic Stress 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 24) 20m wall under Imperial Valley Horizontai+Vertical Motion 235 20 ..... 20 Itt 20
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ro 2ooo c.. c: 0 1500 :s .0 0 1000 rn (J) 500 2000 c: .Q 1500 :5 .0 E i5 1000 rn rn (J) ro c.. 500 2000 1500 :s .0 :s rn 0 1000 rn rn (J) 500 ........ ....... P"'" /Y 0 / r1+Static Stress Dynamic Stress I 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc # 28) 20m wall under Imperial Valley Horizontai+Vertical Motion r....... ;.. ........ v 0 ...;: .,..., ;,r ._/ 0 1+Static Stress Dynamic Stress 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 29) 20m wall under Imperial Valley Horizontai+Vertical Motion .... J+Static Stress Dynamic Stress I 5 10 15 Inclusion Length [m) Inclusion Stress Distribution (Inc# 30) 20m wall under Imperial Valley Horizontai+Vertical Motion 237 . 20 20 20
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ro 1500 0.. e c: 0 "" :::1 1000 rJ) 0 rJ) rJ) (/) 500 ro 1500 0.. e 5 :g 1000 1ii 0 rJ) 500 1500 ro 0.. e c: 1000 0 .a :s rJ) 0 500 rJ) rJ) (/) 0 ./. ,. ......... / 7 0 'J' / v 0 !"' 0 ,...... 5 _,_ "'""I /+Static Stress Dynamic Stress 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 31) ...._ 20m wall under Imperial Valley Horizontai+Vertical Motion 5 /+Static Stress Dynamic Stress j 10 Inclusion Length [m] Inclusion Stress Distribution (Inc # 32) 15 20m wall under Imperial Valley Horizontai+Vertical Motion 5 J+Static Stress Dynamic Stress I 10 Inclusion Length [m) 15 Inclusion Stress Distribution (Inc# 33) 20m wall under Imperial Valley Horizontai+Vertical Motion 238 It 20 ., 20 20
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(ij' 1500 0... 6 c:: 0 1000 :; .c E "' i5 500 "' "' en 0 (ij' 1500 0... 6 c:: 0 1000 .0 E i:5 500 "' "' Ci5 0 1000 (ij' 0... c:: 0 :s .c 500 ;:: iii i5 "' "' en 0 r' r' 0 ..., ....... II" 0 rl ,.. ./ v 0 5 !" 1+Static Stress Dynamic Stress I I I I 10 Inclusion Length [m] I Inclusion Stress Distribution (Inc# 34) I 15 20m wall under Imperial Valley Horizontal+ Vertical Motion :...r!+Static Stress Dynamic Stress 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc # 35) 20m wall under Imperial Valley Horizontai+Vertical Motion ......... 5 1.... ....v '?' ......... J+Static Stress Dynamic Stress I 10 Inclusion Length [m] 15 Inclus ion Stress Distr i bution (Inc# 36) 20m wall under Imperial Valley Horizontai+Vertical Motion 239 20 20 20
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1000 ro 0.. c: 500 0 :s .c ..... o: :s rn i5 0 rn rn r(' en 500 0 1000 ro 0.. c: 500 0 :s .c . i5 0 (/) rn en tr /__ 500 0 5 ......... .......... v 1+Static Stress Dynamic Stress I 10 Inclusion Length [m) Inclusion Stress Distribution (Inc# 37) 15 20m wall under Imperial Valley Horizontai+Vertical Motion 1_... r....... v ,/" !+Static Stress Dynamic Stress J 5 10 Inclusion Length [m) Inclusion Stress Distribution (Inc # 38) 15 20m wall under Imperial Valley Horizontal Motion 240 20 20
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1000 ro c._ 500 c .Q :; .c 0 :s rn 0 rn 500 rn 1./) 1000 0 1000 ro c._ 500 c 0 :s .c 0 c iii .... r0 rn rn 500 1./) 1000 0 ..... ...r..... v ........ !+Static Stress Dynamic Stress I 5 I 10 Inclusion Length [m) 15 Inclusion Stress Distribution (Inc# 39) 20m wall under Imperial Valley Horizontai+Vertical Motion ......... 5 .. n....... / J+Static Stress Dynamic Stress I I I I 10 Inclusion Length [m) I 15 Inclusion Stress Distribution (Inc # 40) 20m wall under Imperial Valley Horizontai+Vertical Motion 241 20 ...... 20
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ro 3500 c.. 3000 c: 2500 0 2000 .0 1500 c: u; 1000 i:5 Ul 500 Ul 0 (J) 500 2500 ro 2000 1500 :s .0 :s Ul i:5 lll 1000 500 0 (J) 500 2500 ro 2000 c.. c: 1500 Q :; .0 1000 :s Ul i:5 500 Vl Vl 0 (J) 500 I 1\ \ "'\ \ 1\. 0 1+Static Stress Dynamic Stress 5 I""" k'1 ...... 10 Inclusion Length [m] 'II" 15 Inclusion Stress Distribution (Inc# 1) 20m wall under Imperial Valley Horizontai+2Vertical Motion 1+static Stress Dynamic Stress \ _..... ..... ....0 l \ 0 \ }, ...... 5 v ........ v ....... II" 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 2) 15 20m wall under Imperial Valley Horizontai+2Vertical Motion J+Static Stress Dynamic Stress [ ......... 5 ..... ..._.... ...r._._ ,.... 10 Inclusion Length [m] rInclusion Stress Distribution (Inc# 3) 15 20m wall under Imperial Valley Horizontai+2Vertical Motion 242 .1 20 120 .1 20
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ro 2500 c.. 2000 c: .Q 1500 "'5 .c E 1000 Ul Ci Ul 500 Ul en 0 ro 3ooo c.. 2500 c: 0 2000 .c E Ul Ci Ul Ul ii5 1500 1000 500 0 ro 3ooo 2500 f5 2000 5 .c ;:::: iii Ci Ul 1500 1000 500 en 0 '\. """'.. 0 0 I "" Ill'. .._... ..... I"'" 0 _... .1 ,... 5 ,....... .1 ..1+Static Stress Dynamic Stress 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 4) 20m wall under Imperial Valley Horizontai+2Vertical Motion "'"'" 120 ,..... +Static Stress Dynamic Stress C 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 5) 20m wall under Imperial Valley Horizontai+2Vertical Motion .......... ../" 5 ........ r +Static Stress Dynamic Stress 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 6) 20m wall under Imperial Valley Horizontai+2Vertical Motion 243 20 120
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ro 3000 c.. =.. c:: 0 2000 ..0 c:: 1i5 0 1000 (/) (/) U5 0 ..... I"" 0 4000 ro c.. =.. 3000 c:: 0 ..0 2000 0 ... r(/) 1000 (/) (/) 0 I'"' 0 4000 ro c.. =.. 3000 c:: 0 :; ..0 2000 c:: ... 1i5 0 (/) 1000 (/) Q) (/) 0 ..... I"" 0 ........... r........... v / 5 J+Static Stress Dynamic Stress 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 7) 15 20m wall under Imperial Valley Horizontai+2Vertical Motion _. v ./ r5 1+static Stress Dynamic Stress 10 Inclusion Length (m] Inclusion Stress Distribution (Inc# 8) 15 20m wall under Imperial Valley Horizontai+2Vertical Motion Jt"' 5 1+Static Stress Dynamic Stress I 10 Inclusion Length (m] 15 Inclusion Stress Distribution (Inc# 9) 20m wall under Imperial Valley Horizontai+2Vertical Motion 244 20 20 I 20
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'iij' a. 4000 3000 Q :; .c c: 1ii Ci 2000 1000 u; 0 'iij' 4500 a. : c: 0 3000 "" ::I .c c: 1ii 1500 Ci U) U) u; 0 5000 'iij' a. 4000 : c .Q 3000 :; .c :s 2000 U) Ci U) U) 1000 (/) 0 II..... 0 iL I'"' 0 0 _, l..r _., ..... "" v r...v .. 11+Static Stress Dynamic Stress J 5 10 lndusion Length [m] 15 Inclusion Stress Distribution (Inc# 10) 20m wall under Imperial Valley Horizontai+2Vertical Motion k' ,...... .) ...I'll. 1+Static Stress Dynamic Stress 5 10 15 Inclusion Length [m] Inclusion Stress Distribution (Inc# 11) 20m wall under Imperial Valley Horizontai+2Vertical Motion ..II. :..,IIJ./ l...t+""1+Static Stress Dynamic Stress 1 5 10 Inclusion Length (m] 15 Inclusion Stress Distribution (Inc# 12) 20m wall under Imperial Valley Horizontai+2Vertical Motion 245 20 20 20
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ro 5000 c... 4000 c 0 :s 3000 .0 ;::: iii i5 2000 IJl 1000 IJl (J) 0 6000 ro 5000 4000 :; .0 E 3000 IJl i5 2000 IJl 1000 (J) 0 ro 6000 c... 5000 c 0 4000 .0 3000 ;::: iii i5 2000 IJl IJl 1000 Ci5 0 r,__ .... 0 r.. _. [""' 0 / r. ... 1+Static Stress Dynamic Stress 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 13) 20m wall under Imperial Valley Horizontai+2Vertical Motion .II. ) ...1...... 1.. t 1+Static Stress Dynamic Stress I 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 14) ..._ 20m wall under Imperial Valley Horizontai+2Vertical Motion Vf I I I I I I I I I r/ .. .... 1+Static Stress Dynamic Stress toI"' 0 ..... 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc # 15) 15 20m wall under Imperial Valley Horizontai+2Vertical Motion 246 20 20 20
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ro 6000 c.. =. 5000 c: 0 4000 :s .0 3000 c iii 2000 i5 U) 1000 U) (/) 0 6000 '& =. 5000 4000 .0 3000 i5 2000 U) 1000 (/) 0 ro 6000 c.. 5000 =. c: 4000 0 :; .0 3000 c 1ii i5 2000 U) U) 1000 (/) 0 ... v ..... l...o.. 1 .... 0 ,., ..... ...... ....... 0 )1"' ./ .. v ..... r'+Static Stress Dynamic Stress 5 10 Inclusion Length [m] ...... 15 Inclusion Stress Distribution (Inc# 16) 20m wall under Imperial Valley Horizontai+2Vertical Motion /r rt11. r. ...... r.. '+Static Stress Dynamic Stress I 1" 5 10 15 Inclusion Length [m] Inclusion Stress Distribution (Inc# 17) 20m wall under Imperial Valley Horizontai+2Vertical Motion / ri':'t .... rr..... 1+Static Stress Dynamic Stress I !..1" 0 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc # 18) 20m wall under Imperial Valley Horizontai+2Vertical Motion 247 . 20 rt 20 rt 20
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ro 7000 a.. 6000 c: 5000 0 :s 4000 .0 ;:: 3000 iii i:5 2000 rJ) rJ) 1000 (/) 0 7000 ro 6000 a.. c: 5000 Q :; .0 4000 ;:: 3000 iii i:5 2000 rJ) rJ) 1000 (/) 0 8000 ro a.. 6000 c: 0 :s .0 4000 E rJ) i:5 rJ) 2000 rJ) (/) 0 llmllltfilflllllllll ./ I I I I I I I I I 1r... v Ill 1+Static Stress Dynamic Stress I 0 v 0 0 lA........... v lw....... ... 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 19) 15 20m wall under Imperial Valley Horizontai+2Vertical Motion rN ._ r........ 1+Static Stress Dynamic Stress I 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 20) 15 20m wall under Imperial Valley Horizontai+2Vertical Motion ""1 ...... tIlL 1+Static Stress Dynamic Stress """'" f.+r5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 21) 15 20m wall under Imperial Valley Horizontai+2Vertical Motion 248 "1 . 20 :t 20
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ro 7ooo c... =. 6000 c: 0 5000 .0 :s (/) i5 4000 3000 2000 en 1ooo 7000 ro c... 6000 =. c: 5000 Q :; .0 4000 :s (/) i5 3000 (/) (/) 2000 [!:! en 1000 7000 =. 6000 c: g 5000 :::l .0 c: (j) i5 4000 3000 (/) (/) 2000 (/) 1000 "' ,b ........ r'tiL 0 ...0 0 ....... 1+Static Stress Dynamic Stress I r1 5 l 10 Inclusion Length (m] Inclusion Stress Distribution (Inc# 22) 15 20m wall under Imperial Valley Horizontai+2Vertical Motion ..... 1. ...... rr.L 1+Static Stress Dynamic Stress I ...... r:........ 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 23) 15 20m wall under Imperial Valley Horizontai+2Vertical Motion :rN I... r.. 1+Static Stress Dynamic Stress I 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 24) 15 "1 20 . 20 20 20m wall under Imperial Valley Horizontai+2Vertical Motion 249
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7000 Cii' c.. 6000 6 c: 5000 0 :s .0 4000 ;:::: iii i5 3000 (/) (/) 2000 (i5 1000 Cii' 6000 c.. 6 5000 c: 0 4000 :s .0 3000 i5 2000 (/) 1000 (/) 0 CJ) Cii' 6000 c.. 5000 6 c: 4000 0 :s .0 3000 E (/) i5 2000 (/) (/) 1000 (i5 0 r0 0 ..._ ...... ....... 1w ...,._ r.f...... rr:t ..... ....._ btl. !+Static Stress Dynamic Stress I 5 10 Inclusion Length [m) Inclusion Stress Distribution (Inc# 25) 15 20m wall under Imperial Valley Horizontai+2Vertical MoUon !"" ,........... ... J+StaUc Stress Dynamic Stress I 5 10 Inclusion Length [m) Inclusion Stress Distribution (Inc# 26) 15 20m wall under Imperial Valley Horizontai+2Vertical Motion ,....... u..... rr..r.0 ... 1+StaUc Stress Dynamic Stress 5 10 Inclusion Length (m] Inclusion Stress Distribution (Inc# 27) 15 20m wall under Imperial Valley Horizontai+2Vertical Motion 250 ...... 20 20 ...... 20
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ro 6ooo 5000 c: 0 4000 :s ..0 :s 3000
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ro 5000 0... 4000 c 0 'S 3000 .0 :5 2000 rn i:5 rn 1000 rn (/') 0 ro 5ooo 0... 4000 5 'S 3000 .0 :s rn 2000 i:5 1000 0 (/') 5000 ro 0... 4000 c 0 3000 :s .0 :5 rn 2000 i:5 rn rn 1000 (/') 0 f'lr . .._ I........ ....... !""" 0 It""" 0 .... _..... ........ ..... 0 /+Static Stress Dynamic Stress I 5 10 Inclusion Length (m] Inclusion Stress Distribution (Inc# 31) 15 20m wall under Imperial Valley Horizontai+2Vertical Motion .5 ..I 1t 1+Static Stress Dynamic Stress ..I. 10 Inclusion Length [m] I 15 Inclusion Stress Distribution (Inc# 32) 120m wall under Imperial Valley Horizontai+2Vertical Motion ...... ....... r...... I"" ...._ r............ ........ II" 5 1+Static Stress Dynamic Stress 10 Inclusion Length (m] 15 Inclusion Stress Distribution (Inc# 33) 20m wall under Imperial Valley Horizontai+2Vertical Motion 252 . 20 20 20
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ro 4000 c._ 6 3000 c: 0 :s .0 2000 c: u; i:5 (/) 1000 (/) ii5 0 3000 ro c._ 6 c: 2000 0 .0 i:5 1000 (/) (/) en 0 ro 3000 c._ 6 c: 2000 0 :s .0 i:5 1000 (/) (/) en 0 r I( r t.r 0 .. v v _._ 0 / 5 ..... ...1+Static Stress Dynamic Stress I 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 34) 20m wall under Imperial Valley Horizontai+2Vertical Motion 5 ..II_.... 1+Static Stress Dynamic Stress 10 Inclusion Length [m] Inclus ion Stress Distribution (Inc# 35) 15 20m wall under Imperial Valley Horizontai+2Vertical Motion 1)1, 'I I J v..... 0 '1 .... .......... ...._ 5 ........'"" .,.vrI I 10 Inclusion Length [m] +Static Stress Dynamic Stress 15 Inclusion Stress Distribution (Inc# 36) 20m wall under Imperial Valley Hor i zontai+2Vertical Motion 253 20 20 f20
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2500 ro 2000 a. =. c 1500 0 :; .0 1000 :.s (/) i:5 500 (/) (/) 0 (/) 500 2500 ro 2000 a. =. c 1500 0 :s .0 1000 E (/) i:5 (/) 500 (/) 0 Ci5 500 / I 0 I I I I +Static Stress L J Dynamic Stress J ,.,..,. ...._..._ 5 .1 ,.. 10 Inclusion Length [m] f.15 Inclusion Stress Distribution (Inc# 37) 20m wall under Imperial Valley Horizontai+2Vertical Motion I +Static Stress l I Dynamic Stress It/ ...jt .._ / v I I"""" .. fr' 0 5 r' 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 38) 20m wall under Imperial Valley Horizontai+2Vertical Motion 254 20 20
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2500 ro 2000 a.. =. 1500 c 0 1000 .0 c Ui 500 Ci U) 0 U) 500 en 1000 2500 ro a.. 2000 =. 1500 c 0 :s 1000 .0 c Ui 500 Ci U) 0 U) 500 (i) 1000 I I H+Static Stress Dynamic Stress f..._... v 0 I 5 / i"" 1 v v ,_ 10 Inclusion Length (m] Inclusion Stress Distribution (Inc# 39) 15 20m wall under Imperial Valley Horizontai+2Vertical Motion I 4+Static Stress Dynamic Stress _....II" !;""" o' 0 5 .. ) ....... II" '/ __. ,.10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc # 40) 20m wall under Imperial Valley Horizontai+2Vertical Motion 255 20 1 20
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ro 2oooo a. 15000 :; 10000 .0 5000 Ci IJl 0 (/) 5000 14000 10000 :s .0 6000 Ci 2000 (/) 2000 ro 14000 a. 12000 10000 c: 0 8000 :; .0 6000 :s IJl 4000 Ci IJl 2000 IJl 0 (/) 2000 { \.. \.. \, 0 :\. \. ... "\ I".. 0 \. \.. Ill.,. ""' .... 0 I I I I I I I 1+Static Stress Dynamic Stress 1 5 10 Inclusion Length [m) Inclusion Stress Distribution (Inc# 1) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion 5 1+Static Stress Dynamic Stress 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 2) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion 5 1+Static Stress Dynamic Stress I 10 Inclusion Length [m) Inclusion Stress Distribution (Inc # 3) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion 256 20 20 20
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'iii' 12000 CL. 10000 =s c: 0 8000 .0 6000 c: Cii 0 4000 IJl IJl 2000 Q) en 0 'iii' 10000 CL. =s E :s IJl 0 8000 6000 4000 Ill 2000 en 0 10000 8000 6000 4000 2000 0 { \ \ .. 0 1\ \. Ill \. .. 0 I 1\ \ .. \. i\. 0 5 I+Static Stress Dynamic Stress I 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 4) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion 5 I I I 1+Static Stress Dynamic Stress 1 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 5) 20m wall under Imperial Valley Horizontai+3Vert ical Motion 5 +Static Stress Dynami c Stress 10 Inclusion Length (m] Inclusion Stress Distribution (Inc# 6) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion 257 20 20 20
PAGE 272
n; 10000 a. :. 8000 '\. ..... Jt6000 4000 2000 ..._..I' Stress Dynamic Stress 1 n; 8000 a. :. 6000 c: 0 :s 4000 c: iii 0 Cl) Cl) 2000 E (/) 0 8000 n; a. :. 6000 :s :s 4000 Cl) 0 j 2000 (/) 0 0 0 r\ \ .... 0 .. "'\ "" ... 0 5 I I I I j 10 Inclusion Length [m] I I Inclusion Stress Distribution {Inc# 7) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion rStress Dynamic Stress I 5 I 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# B) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion ..r,__ Static Stress Dynamic Stress I 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc # 9) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion 258 20 20 20
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10000 ro a_ 8000 c: .Q :; 6000 .0 c: (;) 4000 0 2000 0 10000 8000 c: 0 6000 .0 c: (;) 4000 0 C/) C/) Cll 2000 0 ro 1oooo a_ 8000 6000 .0 4000 0 2000 0 ..... 0 ..... ._ 0 .... 0 ..)II"" 5 1I+Static Stress Dynamic Stress l 10 lndusion Length [m] Inclusion Stress Distribution (Inc# 10) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion _, . ....: / +Static Stress Dynamic Stress 1 5 10 lndusion Length [m] 15 Inclusion Stress Distribution (Inc# 11) 20m wall under Imperial Valley Horizontai+3Vertical Motion "' ........ ...1+Static Stress Dynamic Stress 1 5 10 lndusion Length [m] Inclusion Stress Distribution (Inc# 12) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion 259 20 20 20
PAGE 274
ro 10000 0.. =. 8000 c: 0 :s 6000 .D ;:: iii 4000 Ci UJ 2000 UJ Ci5 0 '"'" 0 12000 ro 0.. 10000 =. c: 8000 0 :s .D 6000 ;:: iii ..... Ci 4000 UJ UJ 2000 en 0 [""" 0 ro 12000 0.. 10000 =. c: 8000 0 :s .D 6000 ;:: iii ..... Ci 4000 UJ UJ 2000 en 0 '"'" 0 r!,...... ....r. / 1+Static Stress Dynamic Stress 1 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 13) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion v 11".. ............ J+Static Stress Dynamic Stress 1 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 14) 15 ........ .... 20m wall under Imperial Valley Horizontai+3Vertical Motion / _,. ...+Static Stress Dynamic Stress 1 5 I I I J 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 15) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion 260 r:........... 20 r. 20 rt 20
PAGE 275
ro12000 c... 10000 (/) 8000 6000 4000 2000 Ci5 0 ro 12000 c... 10000 c: 8000 0 :s .0 6000 ti 0 4000 (/) (/) 2000 Ci5 0 12000 ro c... 10000 c: 8000 0 5 .0 6000 .::: ti 0 4000 (/) (/) 2000 (/J 0 / 0 '" / ,. 0 / / 0 ..,. J+Static Stress Dynamic Stress 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 16) r20m wall under Imperial Valley Horizontai+3Vertical Motion "' r. .._ 1+Static Stress Dynamic Stress 1 5 10 Inclusion Length (m] Inclusion Stress Distribution (Inc# 17) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion / .. ....... 1+Static Stress Dynamic Stress 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc # 18) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion 261 ""I 20 ""I 20 ..., 20
PAGE 276
ro 12000 c.. 10000 =. c: Q 8000 "S .0 6000 c Vi i5 4000 rn rn 2000 Ci5 0 12000 ro 10000 c: 0 :s .0 i5 rn rn (/) ro c.. =. c: 0 .0 :s rn i5 rn rn (/) 8000 6000 4000 2000 0 12000 10000 8000 6000 4000 2000 0 ./ v 0 /_ / r 0 ../_ .,/ ,... 0 1r ...._ r1+Static Stress Dynamic Stress 5 ...I. 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 19) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion _... ::........ 1.. to.... 1+Static Stress Dynamic Stress 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 20) 20m wall under Imperial Valley Horizontai+3Vertical Motion }/k"rt........ tor. 1+static Stress Dynamic Stress 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 21) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion 262 20 """1 20 20
PAGE 277
ro 12000 c... =: 10000 c: .Q 8000 :; D 6000 ;:: Ci) 4000 0 UJ 2000 UJ v.; 0 ro 12ooo c... 10000 c: 0 D ;:: Ci) 0 BODO 6000 4000 2000 v.; 0 ro 12000 c... 10000 c: 8000 .Q :; D 6000 ;:: Ci) i:5 4000 UJ UJ 2000 v.; 0 / .... .... 0 II'" I"' i'"" 0 I"' [""' 0 f.W r1....._ r.. 1+Static Stress Dynamic Stress I 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 22) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion ...... r1+Static Stress Dynamic Stress 5 10 Inclusion Length [m] .......... 15 Inclusion Stress Distribution (Inc# 23) ...... ... 20m wall under Imperial Valley Horizontai+3Vertical Motion ... 1"" r"'"" +Static Stress Dynamic Stress 5 10 Inclusion Length [m] 1. Inclusion Stress Distribution (Inc# 24) ........ ""' 15 20m wall with Imperial Valley Horizontai+3Vertical Motion 263 ........ 20 20 20
PAGE 278
12000 'iii' c._ 10000 c 8000 0 .0 6000 ;:: ti 0 4000 en en 2000 (/) 0 0 12000 'iii' c._ 10000 c 8000 0 :s .0 6000 :s en 0 4000 en en 2000 U5 0 0 'iii' 12000 c._ 10000 c 0 8000 11... .0 6000 ;:: ti 0 4000 en en 2000 (/) 0 0 f""" ...... . ..... ... .... ,.static Stress Dynamic Stress 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc # 25) 20m wall under Imperial Valley Horizontai+3Vertical Motion ...... NL I.static Stress Dynamic Stress 1 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 26) rn. 15 20m wall under Imperial Valley Horizontai+3Vertical Motion ""',.static Stress Dynamic Stress 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 27) 20m wall under Imperial Valley Horizontai+3Vertical Motion 264 ri 20 20 20
PAGE 279
ro 12ooo 10000 c: .Q "S .0 ;:: 1ii 0 fl) Ul 8000 6000 4000 2000 0 ro 1oooo a.. 6 8000 c: Q "S .0 ;:: 1ii 0 fl) fl) E en ro a.. 6 c: 0 .0 :s fl) 0 fl) fl) E en 6000 4000 2000 0 10000 8000 6000 4000 2000 0 r 11 .... 0 r0 ... rr 0 l.a" ........ ...._ r.. !+Static Stress Dynamic Stress I 5 10 Inclusion Length [m] Inclusion Stress Distribution {Inc# 28) 15 I20m wall under Imperial Valley Horizontai+3Vertical Motion ..... ...... r1+Static Stress Dynamic Stress 1 5 10 Inclusion Length [m] Inclusion Stress Distribution {Inc# 29) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion 1+Static Stress Dynamic Stress L 5 10 Inclusion Length [m] Inclusion Stress Distribution {Inc# 30) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion 265 20 20 20
PAGE 280
(ij' 8000 a.. =. 6000 c: 0 :s .J:I 4000 :s "' Ci "' 2000 "' (/) 0 (ij' 8000 a.. =. c: 6000 ::::l .J:I 4000 c: u; Ci 2000 "' "' u; 0 (ij' 8000 a.. =. 6000 c: 0 :s .J:I 4000 ;::: u; Ci "' 2000 "' u; 0 I LE f I I I t I I I IEIUE ......... ,... 0 .. ,...,... 0 ./ v ,...."'"' 0 J+Static Stress Dynamic Stress 5 10 Inclusion Length [m] Inclusion Stress Distr i bution (Inc# 31) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion ,... .. 5 ..IlL .... 1+Static St r ess Dynamic Stress I I 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Inc# 32) ..._ 20m wall under Imperial Valley Horizontai+3Vertical Motion _..II" 5 ...IL ..._.. :tL J+Stati c Stress Dynami c Stress 1 10 Inclusion Length [m] I 1 15 Inclusion Stress D i stribution (Inc# 33) 20m wall under Imperial Valley Horizontai+3Vertical Motion 266 20 :t 20 :........ 20
PAGE 281
8000 ro Q._ =. 6000 c: 0 :s .0 4000 c: iii i5 rn 2000 rn (/) 0 6000 ro Q._ =. c: 4000 0 :s .0 c: iii i5 2000 rn rn (/) 0 ro 60oo Q._ =. 4000 =s .0 E rn i5 2000 rn rn (/) 0 v rI"'" 0 ./ 0 I I 0 .......... .. I ........ ..5 ...... r....._ .......... I.......... I"'" Stress Dynamic Stress 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 34) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion / 5 1__. r Stress Dynamic Stress 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 35) 15 20m wall under Imperial Valley Horizontai+3Vert i cal Motion t' .. ..._ rf.f"""" _... t20 20 . Stress Dynamic Stress}....... 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc# 36) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion 267 I I 20
PAGE 282
5000 ro 4000 a.. c: 3000 .Q :; .0 2000 c: iii ./ .... II" i:5 tJl 1000 tJl 0 Ci5 1000 0 4000 ro a.. 3000 2000 :; .0 I :s tJl 1000 i:5 tJl '.1 ,...... tJl 0 (j) ......... 1000 0 I I I I +Static Stress I L 1 Dynamic Stress 1 v / ... ........ to. I .... 5 10 Inclusion Length [m] Inclusion Stress Distribution (Inc # 37) 15 20m wall under Imperial Valley Horizontai+3Vertical Motion '\. Ill" 5 ...,....r /_ v ............ 10 Inclusion Length [m) 1 +Static Stress E I Dynamic Stress 15 Inclusion Stress Distribution (Inc # 38) 20m wall under Imperial Valley Horizontai+3Vertical Motion 268 20 rr20
PAGE 283
4000 ro c.. 3000 6 c: 0 2000 :s .c ;::: ;;; 1000 i:5
PAGE 284
ro a.. =. c 0 .c c Cii iS UJ UJ ii5 ro a.. =. c .Q :; .c c Cii iS UJ UJ ii5 Cll a.. =. c 0 :s .c c Cii iS UJ UJ (/) 1500 1250 1000 750 500 250 0 250 500 1500 1000 500 0 500 +Static Stress I Dynamic Stress I v I" v ....... 1.... ..... !""' rr 0 r, ... 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 1) 20m wall under Imperial Valley Horizontal Motion I 1" +Static Stress ..... ..Dynamic Stress! ./ v ./ _..... ........0 5 10 Inclusion Length [m] 15 1500 1000 500 0 500 Inclusion Stress Distribution (Detached, Inc# 2) 20m wall under Imperial Valley Horizontal Motion II'"' j +Static Stress I Dynamic Stress I .,.,. ,.,...... ......... t..... r1 ... 0 ........ .5 1r .4t"" 10 Inclusion Length [m] 115 Inclusion Stress Distribution, (Detached, Inc# 3) 20m wall under Imperial Valley Horizontal Motion 270 20 20 20
PAGE 285
1500 (i a_ c: 1000 0 .c E Vl i5 500 Vl Vl _g; CIJ 0 1500 (i a_ =s c: 1000 0 5 .c E Vl i5 500 Vl Vl Ci5 0 1500 (i a_ c: 1000 0 :; .c :s Vl i5 500 Vl Vl _g; CIJ 0 I I 1U +Static Stress Dynamic Stress I .......... ............ rI"'" ..... 0 ..... ,... 0 1..... rr 0 ....... v .......... I_.... .... ... / 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 4) 20m wall under Imperial Valley Horizontal Motion .......... v ...... 5 v _.... ......... ',.,;' !+Static Stress 1 1 Dynamic Stress 1 I 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 5) 20m wall under Imperial Valley Horizontal Motion _. .. rrJV v ....5 ....!I 10 Inclusion Length [m] +Static Stress Dynamic Stress 15 Inclusion Stress Distribution (Detached, Inc# 6) 20m wall under Imperial Valley Horizontal Motion 271 20 20 , 20
PAGE 286
1500 ro a.. i:S c 1000 0 :g .0 c 1ii i:5 500 C/J C/J ./ It"""' """ ...... lA" (/) 0 0 1500 ro a.. i:S c 1000 0 :s .0 .. :s C/J i:5 500 C/J C/J .. ..... Ci5 0 0 1600 Ill a.. i:S 1200 c 0 .0 800 c 1ii i:5 C/J 400 C/J ...... Ci5 0 0 ..... v f..vf" ) y ,.....5 I +Static Stress I Dynamic Stress 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 7) 20m wall under Imperial Valley Horizontal Motion ....... I"""" ,...... .....5 ........ ,.... : +Static Stress 10 Inclusion Length [m] rtrDynamic Stress 15 Inclus i on Stress Distribution (Detached, Inc# 8) 20m wall under Imperial Valley Horizontal Motion Jt/ / ,.....,.....11+Static Stress Dynamic Stress I L 5 I I l 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 9) 20m wall under Imperial Valley Horizontal Motion 272 I rt t r120 I 20 20
PAGE 287
1750 "' 1500 a.. =. 1250 c:: 0 :s 1000 .D c:: en 750 0 (/) 500 (/) 250 en 0 2000 ro a.. =. 1500 c:: 0 :s .D 1000 0 (/) 500 (/) Ci5 0 2000 ro a.. =. c:: 1500 0 :s .D c:: en 0 1000 (/) (/) Ci5 500 1/ ......._ ...._ rr1../ / rv l.K """ j+Static Stress Dynamic Stress J 0 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 10) 20m wall under Imperial Valley Horizontal Motion J!r rtH I... .,/ ... ..,/ ,_ ..... 0 v I / k:0 ........... ...._ t.. Ir\+static Stress Dynamic Stress \ 5 10 Inclusion Length [m) 15 Inclusion Stress Distribution (Detached Inc# 11) 20m wall under Imperial Valley Horizontal Motion ...IL r. ........ I"'" ........ ...1+Static Stress Dynamic Stress 5 10 Inclusion Length [m) 15 Inclusion Stress Distribution (Detached, Inc# 12) 20m wall under Imperial Valley Horizontal Motion 273 ... ...... 20 20 20
PAGE 288
2000 ro Cl... =.. c 1500 .Q ::; .0 1000 c iii i5 II) 500 II) rJ) 0 2500 ro Cl... =.. c 2000 0 :s .0 1500 :s II) i5 II) 1000 II) Q) .:. rJ) 500 2500 ro Cl... =.. 2000 c 0 :g .0 1500 c:: iii i5 II) 1000 II) Q) .:. rJ) 500 1"'" ...v . h / rI'. v P" I l{_ 0 l_ .r 'r" 0 II' J'_ L .K :,......0 / 5 I +Static Stress I Dynamic Stress J 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 13) 20m wall under Imperial Valley Horizontal Motion r.._ "" r::= .... ./ +Static Stress Dynamic Stress 5 10 Inclusion Length [m) 15 Inclusion Stress Distribution (Detached, Inc# 14) 20m wall under Imperial Valley Horizontal Motion ........ I',......... !"',..._ '+Static Stress Dynamic Stress I 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached Inc# 15) 20m wall under Imperial Valley Horizontal Motion 274 I'20 .... 20 ...... 20
PAGE 289
2500 ro a.. 6 2000 r:::: .Q '5 .0 1500 E C/) 0 C/) 1000 C/) e U5 I v / 500 0 2500 ro a.. 6 2000 r:::: .Q '5 .0 1500 r:::: .I "" 'i ... / ""I ........... """"'= v i" 1+Static Stress Dynamic Stress I ./ I I 5 I I 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 16) 20m wall under Imperial Valley Horizontal Motion ..._ ........ r... ............ ....... _,) ..,. ._ Ui 0 L K .......:::: toC/) 1000 C/) 1,(' ./ .,..... U5 500 0 2500 ro a.. 6 2000 r:::: 0 :s .0 1500 c Ui 0 C/) 1000 C/) J / e U5 500 0 IT v l' +Static Stress Dynamic Stress I I 5 I I 10 Inclusion Length [m] I I 15 Inclusion Stress Distribution (Detached, Inc # 17) 20m wall under Imperial Valley Horizontal Motion ......... 1'.... ........... ...... ....... ......... 1+Static Stress Dynamic Stress 1 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 18) 20m wall under Imperial Valley Horizontal Motion 275 r.. 20 . 20 ... 20
PAGE 290
m 0.. c 0 :; .c 't: t) 0 (/) (/) (/) ro 0.. c 0 :s .c 't: iii 0 (/) (/) Q) .= (/) m 0.. c 0 :;::1 :::1 .c :s (/) 0 (/) (/) (/) 2700 2400 2100 1800 1500 L 1200 900 600 0 2700 2400 2100 1800 .. I I ... 2 r I _L Ill 1500 L ""' ./ 1200 / ._ 900 600 0 3000 2500 2000 / 'rtf ./" ..... ........ ...... ./ .........;: t. ......... '"""' +Static Stress Dynamic Stress I I 5 I 10 Inclusion Length [m] I 15 Inclusion Stress Distribution (Detached, Inc# 19) 20m wall under Imperial Valley Horizontal Motion ....... ri'""1 ./ ......::: :; +Static Stress Dynamic Stress 1 5 10 Inclusion Length [m] :...... 15 Inclusion Stress Distribution (Detached, Inc# 20) 20m wall under Imperial Valley Horizontal Motion .II. ......... ,... ..., r1500 / "" r.;: [ ...... 1000 500 0 I+Static Stress Dynamic Stress I I 5 I 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 21) 20m wall under Imperial Valley Horizontal Motion 276 20 20 20
PAGE 291
3000 ro a. =. 2500 c: .Q :; ..0 2000 E (/) 0 (/) 1500 (/) ij) 1000 .......... 0 3000 ro a. =. 2500 c: 0 :s ..0 2000 :s (/) 0 (/) 1500 (/) ij) 1000 0 3000 ro a. =. 2500 c: 0 :s ..0 2000 c::: II \ u; 0 rJ) 1500 rJ) (/) .,..,.... 1000 0 ._ 1+Static Stress Dynamic Stress f,... rN ..: ../ r.. r........ ..,v :.....:: rIff ,, / 1 / 'W M" /v 5 10 Inclusion Length [m] .......... 15 Inclusion Stress Distribution (Detached, Inc# 22) 20m wall under Imperial Valley Horizontal Motion rtf. 20 ........ J+Static Stress Dynamic Stress rrr.,r 5 t .... r.. ........ t10 Inclusion Length [m] ..... r............. "'1 I15 Inclusion Stress Distribution (Detached, Inc# 23) 20m wall under Imperial Valley Horizontal Motion I...... 20 J+static Stress Dynamic Stress rrv ,... 5 ""::1 I. r.. ....... 10 Inclusion Length [m] ............... i".... !'tiL 15 Inclusion Stress Distr i bution (Detached, Inc# 24) 20m wall under Imperial Valley Horizontal Mot ion 277 :r. rt:1 20
PAGE 292
3000 ro a.. =. 2500 c: Q "S .D 2000 ;:: iii i5 !/) 1500 !/) en 1000 2500 ro a.. =. 2000 c: 0 =s .D 1500 ;:: iii i5 !/) 1000 !/) en 500 2500 ro a.. =. 2000 c: .Q "S .D 1500 i5 !/) 1000 !/) en 500 .JI. . +Static Stress Dynamic Stress 1l rt".IL \ ......... r:... / ......... ..... v ......... rt""'.11 ......... 1'.L r...... lL 1 0 \ 'I ./ 0 \. \ I .,.. 0 ... I ,;r v f" v 5 10 Inclusion Length [m) 15 Inclusion Stress Distribution (Detached, Inc# 25) 20m wall under Imperial Valley Horizontal Motion rr11 ......... r.. .......... ...... r......... 1+Static Stress Dynamic Stress ..I 5 10 Inclusion Length [m) 15 Inclusion Stress Distribution (Detached, Inc# 26) 20m wall under Imperial Valley Horizontal Motion r. ........ ....... v r... ,_ I' 1+Static Stress Dynamic Stress 5 10 Inclusion Length [m) ......... r. 15 Inclusion Stress Distribution (Detached, Inc# 27) 20m wall under Imperial Valley Horizontal Motion 278 r"1 20 r...... r"1 20 . rt 20
PAGE 293
2500 'iii' 0.. =. 2000 <: 0 '3 .0 1500 c Ui Ci tl) 1000 tl) e: ii5 500 0 2500 'iii' 0.. =. 2000 <: 0 1\. ., :J .0 1500 ;::: Ui Ci tl) 1000 tl) v (/) 500 0 'iii' 2000 0.. =. ;::: 0 1500 ., :J .0 :s tl) Ci 1000 tl) tl) v (/) 500 0 J ... 1}6" rr........ r....... .... ...,;" ...... ........ !'.... 1+Static Stress Dynamic Stress I I K ........ I I 5 I I 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached Inc# 28) 20m wall under Imperial Valley Horizontal Mot ion . .... rr... ............ [:.... rrr.......... 20 v 11i:,v ..... / V"" ,....... +Stati c Stress Dynamic Stress J 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 29) 20m wall under Imperial Valley Horizontal Motion ......... ........ I'. r....... . 1+Static Stress Dynamic Stress 1 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached Inc# 30) 20m wall under Imperial Valley Hor izontal Motion 279 20 ;20
PAGE 294
2000 ro .. 0.. c 1500 0 ., ;:s .D J 'L c: 1ii i5 1000 vr 1" IJl IJl / (/) 500 0 2000 ro 0.. c 1500 0 '5 .D c: 1ii i5 1000 IJl IJl 500 ro 1eoo 0.. c 1200 0 :s .D :5 800 IJl i5 400 (/) 0 v v v v 0 ../ / ... ...... ttr ,.... 0 . 1)1...... r.......... ..._ !"". ....... h 1+Static Stress Dynamic Stress 5 10 Inclusion Length [m) 15 ..._ Inclusion Stress Distribution (Detached, Inc# 31) 20m wall under Imperial Valley Horizontal Mot ion h IIlL :r1r. .._ 5 1+Static Stress Dynami c Stress l 10 Inclusion Length [m) 15 Inclusion Stress Distribution (Detached, Inc # 32) 20m wall under Imperial Valley Horizontal Motion 5 rf. I+Static Stress Dynamic Stress 10 Inclusion Length [m) 15 Inclusion Stress Distr i bution (Detached Inc# 33) 20m wall under Imperial Valley Horizontal Motion 280 , 20 . 20 ""1 20
PAGE 295
1500 ro a.. =. c 1000 0 :g .c l)l. ..... v ;... c u; i:5 500 C/) C/) v v en 0 0 1500 ro a.. =. c 1000 .Q "S .c )1. r... / .... ;:: u; i:5 500 C/) C/) I rfl! L Ci5 0 0 ro 1000 a.. =. v )I.. c 0 :s .c 500 :s C/) i:5 C/) C/) / .... ... !'..... v / en 0 0 ._ 5 11+static Stress Dynamic Stress 10 Inclusion Length [m) 15 Inclusion Stress Distribution (Detached, Inc# 34) 20m wall under Imperial Valley Horizontal Motion ........... ...... 20 _I +Static Stress Dynamic Stress 5 I I 10 Inclusion Length [m) I I 15 Inclusion Stress Distribution (Detached, Inc# 35) 20m wall under Imperial Valley Horizontal Motion _,..... .....v / .,..,.. v I 1+Static Stress Dynamic Stress 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 36) 20m wall under Imperial Valley Horizontal Motion 281 I 20 120
PAGE 296
1000 C'O a. c:: 500 Q :; .... Ill.. ..... .. (ij i:5 0 (/) (/) v (/) 500 0 1000 C'O a. c:: 500 0 :s .c :.s / (/) 0 0 (/) (/) Ci5 ... 1 / / 500 0 5 I1" 1_... ,/ v ,.,. 1+Static Stress Dynamic Stress 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc # 37) 20m wall under Valley HOOzontal Mction 5 .......... _... f.v ,..... v ./ / v 1+Static Stress l>jnarric Stress 10 Inclusion Length [m] 15 hclusion Stress Distribution (Detached, he# 38) 20m wall under lrrperial Valley 1tlrizontal M>tion 282 20 I20
PAGE 297
1000 ctJ a... 500 c 0 5 .c 0 c ...Ul i5 v til til 500 Q) c?) .r 1000 0 1000 ctJ a... 500 c: 0 ___. .c 0 0 til til 500 (/) lT" v ...1000 0 1I_....A ......I1 ......,.,...... 1+Static Stress Dynarric Stress 5 10 Length [m] 15 Stress Distribution (Detached, # 39) 20m wall under l!ll>erial Valley Horizontal MJtion v / v r120 __. I+Static Stress Dynarric Stress 15 10 Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 40) 20m wall under !nl>erial Valley Horizontal MJtion 283 20
PAGE 298
2500 ro 2000 a. I c:: 1500 0 '5 .0 1000 :5
PAGE 299
2500 rn c.. 2000 =:. c: 0 1500 _, :::l .0 E Cll 1000 C:5 Cll Cll 500 en 0 ,..0 2500 rn c.. 2000 =:. c: 0 1500 .0 ;:: iii 1000 i:5 Cll Cll 500 Q) .!::> en ..... 0 I'"'" 0 2500 rn c.. 2000 =:. c: 0 1500 :s .0 ;:: iii 1000 C:5 Cll Cll 500 (j5 11..... 0 0 J +Static Stress Dynamic Stress J .....5 l.1 ...I10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 4) 20m wall under Imper ial Valley H+V Motion 1+Static Stress / v ./ /_ / i Dynamic Stress i v I I ...... ........ I 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 5) 20m wall under Imperial Valley H+V Mot ion +Static Stress I Dynamic Stress I 11 ...... r5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 6) 20m wall under Imperial Valley H+V Motion 285 / / ./ / 20 ....... 20 ...... 20
PAGE 300
2500 (ij' a.. 2000 c c 0 1500 .n E 1000 Vl 0 Vl Vl 500 en 0 2500 (ij' a.. 2000 c c 0 1500 :s .n E Vl 1000 0 Vl Vl 500 (/) 0 2500 (ij' a.. 2000 c c 0 1500 :s .n E Vl 1000 0 Vl Vl 500 (/) 0 rr.... 0 rr0 I I +Static Stress Dynamic Stress l 1,..A........ .... ....... l5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 7) 20m wall under Imperial Valley H+V Motion +Static Stress Dynamic Stress 1 ...I,.........A v 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 8) 20m wall under Imperial Valley H+V Motion r1/ ./ /_ ../ / ../ ......... .M' 1+static Stress Dynamic Stress :r 0 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 9) 20m wall under Imperial Valley H+V Motion 286 ........ / 20 ........ / 20 / v 20
PAGE 301
2000 Cii' a. =. 1500 c: 0 .0 1000 ;:: 1ii i5 (/) 500 (/) (/) 0 2500 Cii' a. 2000 =. c: 0 1500 =s .0 :s (/) 1000 i5 (/) (/) 500 (/) 0 2500 Cii' a. =. c: 2000 0 5 .0 1500 i5 (/) 1000 (/) (/) 500 L! .... r1V" ....... ..."' I"'" .K .... aoi""" 0 ... ..... / t:: *""" .... 0 v Jr ./ ./ .K ;....0 5 1+static Stress Dynamic Stress I 10 Inclusion Length (m] 15 Inclusion Stress Distribution {Detached, Inc# 10) 20m wall under Imperial Valley H+V Motion _.._ v r....... /_ 1+Static Stress Dynamic Stress 1 5 10 Inclusion Length [m) 15 Inclusion Stress Distribution {Detached, Inc# 11) 20m wall under Imperial Valley H+V Motion ..IL N ....... r. / 1+Static Stress Dynamic Stress I I 5 I 10 Inclusion Length [m] I I 15 Inclusion Stress Distribution {Detached, Inc# 12) 20m wall under Imperial Valley H+V Motion 287 v v ,..... 20 J v v 20 ) // v 20
PAGE 302
2500 ro a.. 2000 =.. c: .Q 1500 "S .c ;:: 1ii 1000 0 Vl Vl 500 U5 0 3000 'iii' a.. 2500 =.. c: 0 :s 2000 .c ;:: 1ii 1500 0 Vl Vl 1000 U5 500 'iii' 3000 a.. =.. 2500 c: 0 2000 :s .c 1500 ;:: 1ii 1000 0 Vl 500 Vl U5 0 .... I(' v r" ........ r""" 0 / lJI ....... fo!:"../ +Static Stress Dynamic Stress L 5 10 Inclusion Length [m) 15 Inclusion Stress Distribution {Detached, Inc# 13) 20m wall under Imperial Valley H+V Motion v 1+Static Stress Dynamic Stress I r..._ / v / ../ M'" r v 0 ... IIIII' ./ ... 0 5 10 Inclusion Length (m] 15 Inclusion Stress Distribution {Detached, Inc# 14) 20m wall under Imperial Valley H+V Motion +Static Stress Dynamic Stress 5 10 Inclusion Length (m] 15 I nclusion Stress Distribution (Detached, Inc# 15) 20m wall under Imperial Valley H+V Motion 288 ./ ..,. L_ / v 20 / L 20 ...... ./ 20
PAGE 303
3000 ro 0.. 2500 c: 2000 0 '"" :::J .D. 1500 ;:: 1il 0 1000 Vl Vl 500 Ci5 0 2500 ro 0.. 2000 c: 0 :s .D. 1500 ;:: 1il 0 Vl 1000 Vl (J) 500 3000 ro 0. 2500 c: 2000 0 '"" :::J .D. 1500 :5 Vl 0 1000 r/) Ill 500 Q) .=, (J) 0 / v 0 ../ / ,.. IL ""' !)"" ........ / 1" ....._ +Static Stress Dynamic Stress 1 I 5 I I I I 10 Inclusion Length [m] I I 15 Inclusion Stress Distribution (Detached, Inc# 16) 20m wall under Imperial Valley H+V Motion I.............. I.... r.... ........ ....... .......... ./ ._ II" +Static Stress Dynamic Stress I ,........ 0 !)"" / / / 1.# I 0 I 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 17) 20m wall under Imperial Valley H+V Motion 1'+Static Stress Dynamic Stress 1 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 18) 20m wall under Imperial Valley H+V Motion 289 ./ v v 20 L L v 20 / v L 20
PAGE 304
2700 ro 2400 a.. c: 2100 0 =s 1800 .0 ;:: 1500 1i) i5 1200 Ill Ill 900 I? I / v (/) 600 0 2700 ........ N bv ...... ""'=:::: I+Static Stress Dynamic Stress I I 5 I I 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 19) 20m wall under Imperial Valley H+V Motion ro 2400 a.. 2100 c: 1800 0 :; 1500 .0 1200 i5 900 .r / _,.Ill' ..... _..,.Ill 600 Ill 300 U5 0 0 2700 ro 2400 a.. 2100 c: '/ ......... .... .._ ::.. v "=' !+Static Stress Dynamic Stress I 5 10 15 Inclusion Length [m] Inclusion Stress Distribution (Detached, Inc# 20) 20m wall under Imperial Valley H+V Motion .., t. 1800 0 :s 1500 v .0 :s 1200 Ill i5 900 / ,.Ill 600 Ill 300 (/) 0 0 ,I+Static Stress Dynamic Stress I 5 10 Inclusion Length [m] 15 .r Inclusion Stress Distribution (Detached, Inc# 21) 20m wall under Imperial Valley H+V Motion 290 _,) l/ / r20 .J 20 ...II v 20
PAGE 305
3000 ro a. 2500 =.. I 'rc 2000 .Q "'5 .c 1500 ;:: Ui i5 1000 ....... I"' V) V) 500 U5 0 0 3500 ro 3000 a. '\. =.. c 2500 0 .. ... :s 2000 .c E Ul 1500 ..... i5 1000 Ul ... Ul 500 en 0 0 3000 ro a. 2500 =.. c 2000 0 :s .c 1500 Ui i5 1000 ..... / .....Ul V) 500 en 0 0 ...... rt r. ..... ....... J+Static Stress Dynamic Stress I I 5 I I I I I I 10 Inclusion Length [m] I I I I 15 .r Inclusion Stress Distribution (Detached, Inc# 22) 20m wall under Imperial Valley H+V Motion +Static Stress Dynamic Stress 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 23) 20m wall under Imperial Valley H+V Motion ,.... r.. +Static Stress Dynamic Stress 5 10 Inclusion Length [m] L 15 Inclusion Stress Distribution (Detached, Inc# 24) 20m wall under Imperial Valley H+V Motion 291 ........ 20 ,..20 ..I 20
PAGE 306
4000 ro c.. c:: 3000 0 :s .0 2000 c:: Cii i5
PAGE 307
3000 ro a... 2500 =. c:: 2000 0 :s ..c 1500 c 1ii i:5 1000 Vl Vl 500 "' 0 3000 ro a... 2500 =. c:: .Q 2000 :; ..c c iii 1500 i:5 Vl Vl 1000 "' 500 ro 6500 a... =. 5500 c:: 0 4500 'S ..c 3500 i:5 2500 Vl Vl 1500 "' 500 ..... I ... 1/ lK 0 / \ 1"\. trr........ +Static Stress Dynamic Stress I 5 I I L L 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 28) 20m wall under Imperial Valley H+V Motion ,...._ ......... r.. _,.. '+static Stress Dynamic Stress I 0 1\ \ _l ... ""\ ..... 0 J 5 I 10 Inclusion Length [m) I I 15 Inclusion Stress Distribution (Detached, Inc# 29) 20m wall under Imperial Valley H+V Motion 5 +Static Stress Dynamic Stress 10 Inclusion Length [m) 15 Inclusion Stress Distribution (Detached, Inc# 30) 20m wall under Imperial Valley H+V Motion 293 20 20 20
PAGE 308
2500 (ij' c.. =. 2000 c "\ 0 1500 .c c iii 1000 i5 ...... en en 500 ii5 0 0 2500 (ij' a.. 2000 =. c 0 l'a. :s .c 1500 c iii i5 en en 1000 (/) 500 v 0 1600 til .. c.. =. 1200 c 0 :s .c 800 :s en ., i5 en 400 en ., (/) 0 0 I+Static Stress Dynamic Stress _j_ I 5 I I I 10 Inclusion Length [m) I 15 Inclusion Stress Distribution (Detached, Inc# 31) 20m wall under Imperial Valley H+V Motion I I I I I t+Static Stress Dynamic Stress 1 .._ 1N 5 1'11 10 Inclusion Length [m) 15 Inclusion Stress Distribution (Detached, Inc# 32) 20m wall under Imperial Valley H+V Motion ..._ rr+Static Stress Dynamic Stress 5 10 15 Inclusion Length [m) Inclusion Stress Distribution (Detached, Inc# 33) 20m wall under Imperial Valley H+V Motion 294 20 20 20
PAGE 309
2000 ro a. =. 1500 c 0 1\ \ .0 1000 c: v ti i:5 1/) 500 1/) ... V" (/) 0 0 1500 ro a. =. t: 1000 0 :;:I ::J .0 / __. c: ti i:5 500 1/) 1/) r r. / (/) 0 0 1000 ro a. =. v t: 0 :s .0 500 c: ti i:5 1/) ( ..... v' ......... 1/) (/) v 0 0 5 I.static Stress Dynamic Stress 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached Inc# 34) 20m wall under Imperial Valley H+V Motion ..20 .static Stress Dynamic Stress 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 35) 20m wall under Imperial Valley H+V Motion _./" v v ........ I.static Stress Dynamic Stress 5 10 15 Inclusion Length [m] Inclusion Stress Distribution (Detached, Inc# 36) 20m wall under Imperial Valley H+V Motion 295 20 r20
PAGE 310
1000 ro a.. c: 500 0 :s ...... .a :s Ill iS 0 Ill Ill Q) '(" (/) 500 0 1200 ro a.. 800 c: Q :; .a 400 ;:: u; iS v Ill Ill 0 (/) 400 v 0 ."' "" ... / ............. !' 1f" ...I" ,.,..... v / / l +Static Stress Dynarric Stress 5 10 Inclusion Length [m) 15 klclusion Stress Distribution {Detached, klc # 37) 20m wall under k'rperial Valley H+V M:>tion 20 I+Static Stress Dynarric Stress I / /I' ..... 1 .... / / 5 ............. 1_.....A r/ v v 10 klclusion Length [m) ............. 15 Inclusion Stress Distribution {Detached Inc# 38) 20mw all under lrrperial Valley H+V M:>tion 296 / 20
PAGE 311
1200 C'O !l.. 800 =. c 0 400 :; .c E .VI 0 i:5 ... VI VI Q) fJ5 400 I/ v 800 0 1000 C'O !l.. 500 =. c: Q :5 ...r0 1ii i:5 VI VI 500 Q) .:. rn r / _.. 1000 0 ........ v / 1/ ,......... ......... v I+Static Stress Dynamc Stress 5 10 Inclusion Length [m] 15 klclusion Stress Distribution {Detached, Inc# 39) 20m wall under lrrperial Valley H+V M:ltion '5 ..,. / / v 1 +Static Stress Dynamc Stress I I 10 nclusion Length [m] I 15 Inclusion Stress Distribution {Detached, Inc# 40) 20m wall under lf11>erial Valley H+V M:ltion 297 20 r20
PAGE 312
6000 ro 5000 a.. =. c 4000 0 ..c 3000 c 2000 ti 0 1000 IJl IJl 0 U5 1000 6000 ro 5000 a.. =. c 4000 0 :s ..c 3000 :s 2000 IJl 0 1000 IJl IJl 0 (/) 1000 6000 ro 5000 a.. =. c 4000 0 ..c 3000 2000 0 1000 IJl IJl 0 (/) 1000 ./ / ..... v I I +Stati c Stress 1......... ............ I Dynamic Stress 0 .... 5 10 Inclusion Length [m) 15 Inclusion Stress Distribution (Detached, Inc# 1) 20m wall under Imperial Valley H+2V Motion +Static Stress ./ v Dynami c Stress ./ v n.r0 1 ; I0 5 10 Inclusion Length [m) 15 Inclusion Stress Distribution (Detached Inc# 2) 20m wall under Imperial Valley H+2V Motion JIL +Static Stress V" ......... Dynamic St r ess ....... II'" .... .... ...... ........... r""' 5 10 Inclus i on Length [m) 15 Inclusion Stress Distribution, (Detached Inc# 3) 20m wall under Imperial Valley H+2V Motion 298 . I I 20 r. 20 20
PAGE 313
6000 ro n. 5000 c 4000 0 :s ..0 3000 i:5 2000 rJ) rJ) 1000 (/) 0 6000 ro 5000 n. c 4000 .Q :; ..0 3000 '.5 rJ) i:5 2000 rJ) rJ) 1000 (/) 0 6000 ro n. 5000 c 4000 0 :s ..0 3000 i:5 2000 rJ) rJ) 1000 (i) 0 ...... It""': 0 _...... ..... .... 0 .J ...... rk1 .......... / ,...... ...... +Static Stress I"""" I Dynamic Stress I 5 10 15 Inclusion Length [m] Inclusion Stress Distribution (Detached, Inc# 4) 20m wall under Imperial Valley H+2V Motion ........... rl,J ......1'1 / v +Static Stress !Dynamic Stress 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 5) 20m wall under Imperial Valley H+2V Motion I .. .... ./ 11 .r"""' v 20 ..._ rI. 20 .._ I. +Static Stress .... v I I r... 0 5 Dynamic Stress I I I 10 Inclusion Length [m] I 15 Inclusion Stress Distribution (Detached, Inc # 6) 20m wall under Imperial Valley H+2V Motion 299 20
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6000 ro c.. 5000 =. c: 4000 0 :s .0 3000 i5 2000 IJl IJl 1000 U5 0 6000 ro c.. 5000 =. c: 4000 0 .0 3000 i5 2000 IJl IJl 1000 (/) 0 ro 6ooo 5000 c: 0 4000 :s .0 c: iii i5 3000 2000 1000 U5 0 r... 0 / ... ....0 "' ../ r""" 0 liL ...... ........ ...... v r.... ..._ / ) ....... 5 +Static Stress Dynamic Stress 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 7) 20m wall under Imperial Valley H+2V Motion ..... ......... ,.. ............. N ..._ v j+Static Stress Dynamic Stress j 5 10 15 Inclusion Length [m] Inclusion Stress Distribution (Detached, Inc# 8) 20m wall under Imperial Valley H+2V Motion ,.1'"' rN 1+static Stress Dynamic Stress I 5 I 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 9) 20m wall under Imperial Valley H+2V Motion 300 1t 20 20 ...... 20
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7000 ro 6000 0.. =. c 0 5000 :s 4000 .0 3000 iii 5 2000 U) U) 1000 en 0 7000 ro 6000 0.. =. c 5000 0 "" 4000 ::1 .c c 3000 iii 5 2000 U) U) !!:! 1000 (i; 0 7000 ro 0.. 6000 =. c 5000 Q :; .c c iii 4000 3000 2000 U) !!:! (i; 1000 0 ..JL )..t ._ v lJI .,., t""'" .... 0 1/ rl J fT 0 ../ vI ./ fT 0 5 rNl. 1 +Static Stress Dynamic Stress 1 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 1 0) 20m wall under Imperial Valley H+2V Motion r.... r. +Static Stress Dynamic Stress i 5 10 15 Inclusion Length [m] Inclusion Stress Distribution (Detached, Inc# 11) 20m wall under Imperial Valley H+2V Motion r1'.. """1 ........ ........ !+Static Stress Dynamic Stress I 5 10 15 Inclusion Length [m] Inclusion Stress Distribution (Detached, Inc# 12) 20m wall under Imperial Valley H+2V Motion 301 . 20 1. 20 r. 20
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8000 ro 0.. 6000 c: 0 ,. .0 4000 E U) 0 U) 2000 U) i.f ./ Ci5 iT 0 0 8000 ro 0.. 6000 c: .. 0 .0 4000 ;:: iii I 0 U) 2000 U) ./ ..... en .... 0 0 9000 ro 0.. c: 6000 0 :s ... 1 I .0 ;:: iii 0 3000 U) U) 1,( / en I"'" 0 0 / ...._ r.. !"r.... J +Static Stress Dynamic Stress I 5 10 15 Inclusion Length [m] Inclusion Stress Distribution (Detached, Inc# 13) 20m wall under Imperial Valley H+2V Motion ./ ......... V" ....... ........ ............. .... !"...... 1+Static Stress Dynamic Stress I 5 10 15 Inclusion Length [m] Inclusion Stress Distribution (Detached, Inc# 14) 20m wall under Imperial Valley H+2V Motion Jl...... !"...._ +Static Stress Dynamic Stress I 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 15) 20m wall under Imperial Valley H+2V Motion 302 , 20 20 20
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'iii' 0... c 0 :s .c c Ci) i:5 Ul Ul (/) 9000 'iii' 0... c 6000 0 :s .c i:5 3000 Ul Ul Ci5 0 10000 8000 6000 4000 2000 0 0 10000 'iii' 0... 8000 c 0 :s .c E Ul i:5 Ul Ul Ci5 6000 4000 2000 0 v t. ,. ............ !'... I !'... ./ 0 .I (0 1+Static Stress Dynamic Stress 5 10 Inclusion Length [m) 15 Inclusion Stress Distribution (Detached, Inc# 16) 20m wall under Imperial Valley H+2V Motion r:rII +Static Stress Dynamic Stress :2 4 ,.. I rl 6 8 10 12 14 16 Inclusion Length [m] Inclusion Stress Distribution (Detached, Inc# 17) 20m wall under Imperial Valley H+2V Motion I... r.. r..... ["""'....., i+Static Stress Dynamic Stress ........... ..... 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 18) 20m wall under Imperial Valley H+2V Motion 303 20 18 20 20
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12000 Cii' a.. 10000 6 c 8000 0 .0 6000 ;:: ii) i5 4000 IJ) IJ) 2000 (/) 0 12000 Cii' a.. 10000 6 c 8000 0 .0 6000 E IJ) i5 4000 IJ) IJ) 2000 ii5 0 12000 Cii' a.. 10000 6 c .. v rr.... 1,1 ..... ..... I' +Static Stress Dynamic Stress l ... !".. ,... 0 .. / ./ 5 10 15 Inclusion Length [m) Inclusion Stress Distribution (Detached, Inc# 19) 20m wall under Imperial Valley H+2V Motion r... ,.._ ..... ..._ r.... W+Static Stress Dynamic Stress r,.._ r""""'1 I"" I 0 .. 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 20) 20m wall under Imperial Valley H+2V Motion ..... r8000 Q ::; r" ....... ..... r. .0 6000 ;:: ii) i5 4000 IJ) IJ) 2000 (/) 0 0 .......... r. +Static Stress Dynamic Stress I r... ......... ,... 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc # 21) 20m wall under Imperial Valley H+2V Motion 304 20 ., 20 ., 20
PAGE 319
12000 ro CL 10000 =. .::: 8000 Q :; .0 6000 E Vl 0 4000 Vl Vl 2000 en 0 14000 ro 12000 CL c::. .::: 10000 0 :s 8000 .0 E 6000 Vl 0 4000 Vl Vl 2000 en 0 14000 ro 12000 CL =. .::: 10000 0 .0 8000 "I: 6000 iii 0 4000 Vl Vl Q) 2000 = en 0 ./ ,..... I.. v 1........... .... r.. ........ r. .... ...._ .... t+Static Stress Dynamic Stress I f""" 0 v / f""" 0 .. ./ 1'1 / I 0 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 22) 20m wall under Imperial Valley H+2V Motion I ...... +Static Stress Dynamic Stress .............. 5 ......... r. ...._ 10 Inclusion Length [m] ..... 15 Inclusion Stress Distribution (Detached, Inc# 23) 20m wall under Imperial Valley H+2V Motion ........ 5 1+Static Stress Dynami c Stress !".. r...._ 10 Inclusion Length [m] ..... ...... 15 Inclusion Stress Distribution (Detached, Inc# 24) 20m wall under Imperial Valley H+2V Motion 305 20 r20 r20
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14000 ro 12000 0.. c 10000 0 :s ..c 8000 :s 6000 Cll i:5 4000 Cll Cll 2000 Ci5 0 12000 ro 0.. 10000 c 8000 .Q "5 ..c 6000 :s Cll i:5 4000 Cll Cll 2000 en 0 12000 ro 0.. 10000 6 c 8000 0 ..c 6000 E Cll i:5 4000 Cll Cll 2000 Ci5 0 / / Ill T 0 ""' .l' ,.. .... 0 "' h 1+Static Stress Dynamic Stress ...... r.... "' 5 :r.,.._ 10 Inclusion Length [m) ........... 15 Inclusion Stress Distribution (Detached Inc# 25) 20m wall under Imperial Valley H+2V Motion 20 ..... +Static Stress Dynamic Stress[.......... r.... 5 "1.._ r.... """""1 10 Inclusion Length [m) t.... r. 15 Inclusion Stress Distribution (Detached, Inc# 26) 20m wall under Imperial Valley H+2V Motion 20 I rl' i'l+Static Stress Dynamic Stress r 1/ 0 r... 5 .., .._ :!"1 h 10 Inclusion Length [m) ........_ 15 Inclusion Stress Distribution (Detached, Inc# 27) 20m wall under Imperial Valley H+2V Motion 306 20
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Cii' a.. =. c: 0 :s ..0 :s
PAGE 322
8000 ro a_ 6000 c 0 s .0 4000 :s rJ) i5 rJ) 2000 rJ) en 0 7000 ro 6000 a_ 5000 c 0 5 4000 .0 c iii 3000 i5 rJ) 2000 rJ) 1000 Ci5 0 6000 4000 s .0 i5 2000 rJ) rJ) Ci5 0 ... ......., ._ ... v r.......... .... .. H+Static Stress Dynamic Stress r. I""' 0 .. v 5 10 Inclusion Length [m) 15 Inclusion Stress Distribution (Detached, Inc# 31) 20m wall under I mperial Valley H+2V Motion :.. ........... ,..._ r....... r. r!+Static Stress Dynamic Stress I 0 ./ .... / .. .... 0 5 J... 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 32) 20m wall under Imperial Valley H+2V Motion .. r...._ NL ...._ .... 1+Static Stress Dynamic Stress I 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached Inc# 33) 20m wall under Imperial Valley H+2V Motion 308 20 20 20
PAGE 323
6000 ro 5000 a.. c 4000 .Q ::; .c 3000 ;:: iii i5 2000 v 1./ / VI VI 1000 (/) 0 0 ro 4000 a.. ... c 3000 0 .c 2000 ;:: iii '.J /I i5 1000 VI VI Ci5 0 ...... ......... 0 3000 ro a.. .. c 2000 .Q ::; .c / / i5 1000 VI VI (/) v 0 0 1"1 .......... 5 L+Static Stress Dynamic Stress 1 r.. 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 34) 20m wall under Imperial Valley H+2V Motion !+Static Stress Dynamic Stress 1 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 35) 20m wall under Imperial Valley H+2V Motion +Static Stress Dynamic Stress I 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached Inc# 36) 20m wall under Imperial Valley H+2V Motion 309 20 20 20
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ro c.. 6 c: 0 .c E rn Ci rn rn ii5 ro c.. 6 c: 0 :s .c ;:::: Ci5 Ci rn rn (/) 3000 2000 / 1000 v 0 .., 1000 0 2400 2000 I I 1600 "' +Static Stress Dynarric Stress I 5 I10 hclusion Length [m] 15 Inclusion Stress Distribution {Detached, he# 37) 20m wall under llrperial Valley H+2V IVotion +stat1c Stress I Dynarric Stress I ./ / ./ 1200 1'\. v ..1 800 / 400 0 ./ 400 ............ 0 5 ....10 Inclusion Length [m] 15 hclusion Stress Distribution {Detached, Inc# 38) 20m wall under llrperial Valley H+2V IVotion 310 20 20
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2000 ro 1500 a.. :s 1000 c: 0 :g .c 500 .::: (i) .0 0 Ill Ill Q) U) 500 1000 0 2000 ro 1500 a.. :s 1000 c: 0 .c 500 .::: (i) 0 Ill 0 ............ Ill Q) c7) 500 ...1000 0 +Static Stress _....v Dynarric Stress / / r1 ... _..... :;r f"' 5 / ....f.10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 39) 20mw all under lrrperial Valley H+2V Wction f.5 1/ / / _. v ....1......... ........... [+Static Stress Dynarric Stress r 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 40) 20m wall under 1111Jerial Valley H+2V Wet ion 311 20 20
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10000 ro 8000 a... c:: 6000 0 :0:: :::l .c 4000 c:: .... iii i:5 2000 IJ) IJ) 0 (J) 2000 0 10000 ro a... 8000 c:: .Q 6000 "S .c 4000 :5 IJ) i:5 2000 IJ) IJ) 0 (J) 2000 10000 8000 6000 4000 2000 0 2000 0 0 T J ..... ......... 5 _,. ./ ./ / +Static Stress I I Dynamic Stress 10 Inclusion Length (m] 15 Inclusion Stress Distribution (Detached, Inc# 1) 20m wall under Imperial Valley H+3V Motion / r v / +Static Stress ,/ Dynamic Stress 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 2) 20m wall under Imperial Valley H+3V Motion ...... _l .......... _I I ....lr 1+Static Stress .......... l v 1Dynamic Stress I ..lr 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution, (Detached, Inc# 3) 20m wall under Imperial Valley H+3V Motion 312 11120 fr20 20
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ro c.. 6 c: Q :; ..0 E rn i5 rn rn (J) ro c.. 6 c: 0 ..0 E rn i5 rn rn (i5 ro c.. 6 c: 0 :p ::> ..0 i5 rn rn (J) 10000 8000 6000 4000 2000 0 0 10000 8000 6000 4000 2000 .II0 0 12000 8000 4000 ........ 0 0 ....... v ..,.,.. ..... I +Static Stress I ......... _I Dynamic Stress j 5 10 Inclusion Length [m) 15 Inclusion Stress Distribution (Detached, Inc# 4) 20m wall under Imper ial Valley H+3V Motion ...... v ........ rv ,.. J +Static Stress L ....... II" Stress I .... 5 10 Inclusion Length (m] 15 Inclusion Stress Distribution (Detached, Inc# 5) 20m wall under Imperial Valley H+3V Motion ......... v r5 ...IL ..... ..+Static Stress I Dynamic Stress I 1 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 6) 20m wall under Imperial Valley H+3V Motion 313 20 t 20 1i I I 20
PAGE 328
12000 ro a_ c 8000 .Q "5 .c E rn i:5 4000 rn rn ..... en 0 0 12000 ro a_ c 8000 0 :s .c i:5 4000 rn rn .. ... en 0 0 12000 ro a_ c 8000 0 :s .c ;::: ti i:5 4000 rn rn ./ ..en 0 0 .... ..t rv .......... +Static Stress v 5 Dynamic Stress l I 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 7) 20m wall under Imperial Valley H+3V Motion .IL r....._ ........... ......... t ._ r........ j+Static Stress Dynamic Stress: 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached Inc # 8) 20m wall under Imperial Valley H+2V Motion .......... ....._ r........ ""1 ..._ rv rv 5 +Static Stress Dynamic Stress 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 9) 20m wall under Imperial Valley H+3V Motion 314 20 20 20
PAGE 329
12000 (ij' 0.. c 8000 0 :g .c c:: ti i5 4000 Vl Vl (/) 0 14000 (ij' 0.. 12000 c: 10000 Q "5 .c E Vl i5 8000 6000 4000 2000 0 14000 12000 10000 :g 8ooo c:: ti i5 Vl Vl (/) 6000 4000 2000 0 ,.... 0 ./ .. 0 _/ ./ 0 .......... ...._ ........... / ......... ""'""1 J+Static Stress Dynamic Stress J 5 10 Inclus ion Length [m] 15 Inclusion Stress Distr i bution (Detached, Inc # 1 0) 20m wall under Imperial Valley H+3V Motion _. ....1!._ v ...... ]II' i +Static Stress Dynamic Stress ] 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 11) 20m wall under Imperial Valley H+3V Motion ...._ i.... ...... I+Static Stress Dynamic Stress I 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached Inc# 12) 20m wall under Imperial Valley H+3V Motion 315 ..._ 11 20 20 20
PAGE 330
16000 ro 0... 12000 c: Q "S .0 8000 c: iii i5 Vl 4000 Vl rt/ v (/) 0 0 16000 ro 0... 12000 c: 0 :s .0 8000 c: iii / i5 Vl 4000 Vl r"' (/) 0 0 16000 ro 0... 12000 c: 0 .0 8000 :s Vl /_ i5 Vl 4000 Vl "" Cll (/) 0 0 _..vV" : +Static Stress I 5 r.... ........... Dynamic Stress : I I T 10 Inclusion Length [m] ......... ........ 15 Inclusion Stress Distribution (Detached, Inc# 13) 20m wall under Imperial Valley H+3V Motion v r.1. I'..._ ......... t..I 1+Static Stress Dynamic Stress I 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 14) 20m wall under Imperial Valley H+3V Motion / .......... ......... NIL ........... !+static Stress Dynamic Stress 5 10 Inclusion Length [m] ...... ['1 15 ......... Inclusion Stress Distribution (Detached, Inc# 15) 20m wall under Imperial Valley H+3V Motion 316 t 20 :t. 20 11 20
PAGE 331
'iii' 18000 a.. 15000 =. c: 12000 0 :s .0 9000 i:5 6000 / / (/) (/) 3000 en 0 0 20000 'iii' a.. / ........ ... 1/ 1+Static Stress Dynamic Stress "" 5 10 15 Inclusion Length [m] Inclusion Stress Distribution (Detached, Inc# 16) 20m wall under Imperial Valley H+3V Motion Jl.. r.... 16000 =. c: rr r. 0 :s 12000 .0 I E 8000 (/) i:5 v (/) I (/) 4000 en 0 0 'iii' a.. 20000 =. 16000 c: .Q :; 12000 .0 8000 i:5 4000 0 I .. / 0 ......... rrt .._ [+Static Stress Dynamic Stress 1 I"" r 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 17) 20m wall under Imperial Valley H+3V Motion r. .... Nl. r,.., +Static Stress Dynamic Stress 1 Nl.. 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 18) 20m wall under Imperial Valley H+3V Motion 317 20 20 . 20
PAGE 332
24000 'iii' a. 20000 6 c 16000 0 .c 12000 ;:: 1ii i5 8000 (/) Ul 4000 Ci) 0 24000 'iii' 20000 a. 6 c 16000 .Q :; .c 12000 c 1ii i5 8000 (/) (/) _g 4000 (/) 0 24000 'iii' a. 20000 6 c 16000 .Q :; .c 12000 E Ul i5 8000 Ul Ul 4000 Ci) 0 ?0 ..1 r r"t ...... Ll r"'tiL rrH+Static Stress Dynamic Stress l 1"11.. I l I rl 5 T 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 19) 20m wall under Imperial Valley H+3V Motion ........ rrH+Static Stress Dynamic Stress I 0 ...... f0 .. II" .., l 5 l T 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 20) 20m wall under Imperial Valley H+3V Motion II ........ ......... .. ......... H+Static Stress Dynamic Stress ......... ........... I l 5 I I I I 10 Inclusion Length [m) 15 Inclusion Stress Distribution (Detached Inc# 21) 20m wall under Imperial Valley H+3V Motion 318 ..... 20 20 20
PAGE 333
24000 ro :g_ 20000 16000 "5 .0 c (i) i:5 1/) 1/) U5 ro a. c 0 :s .0 E 1/) i:5 1/) 1/) U5 ro a. c 0 :s .0 E 1/) i:5 1/) 1/) (/J 12000 8000 4000 0 24000 20000 16000 12000 8000 4000 0 25000 20000 15000 10000 5000 0 f0 v f0 / .. ./ ...._ ............ 1'i'.1. ....._ +Static Stress Dynamic Stress :........... I I l 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached Inc # 22) 20m wall under Imperial Valley H+3V Motion ...... ........ ..... l't ....... ...... ......... ....... ....... l+Static Stress Dynamic Stress rrII' I I I I I I I I I I I l I I I l l 1 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc # 23) 20m wall under Imperial Valley H+3V Motion ...... r...... r... ..... H+Static Stress Dynamic Stress 1 r0 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 24) 20m wall under Imperial Valley H+3V Motion 319 ..., 20 ..., 20 I 20
PAGE 334
30000 ro (l_ 25000 =. <: 20000 0 :s .c 15000 'C: ./ ,/ (ij 0 10000 IJ) IJ) 5000 (/) 0 0 30000 ro (l_ 25000 =. <: 20000 0 :s ..c 15000 :s .. v v IJ) 0 10000 IJ) IJ) 5000 (/) 0 0 30000 ro 25000 (l_ =. <: 20000 0 ..c 15000 E }J.. v v IJ) 0 10000 IJ) IJ) 5000 (/) 0 0 "1 1...... r5 I I I +Static Stress Dynamic Stress}......... ......... r..... ............. 10 Inclusion Length (m] rr.IL 15 Inclusion Stress Distribution (Detached, Inc# 25) 20m wall under Imperial Valley H+3V Motion I I I 20 .... .......... 1+Static Stress Dynamic Stress J"'1'1 5 ......... r.... 1'ta.. 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 26) 20m wall under Imperial Valley H+3V Motion I 20 ....... ........... 1+Static Stress Dynamic Stress f......... 1'1 5 ...... ........ r.......... 10 Inclusion Length [m] rtIlL 15 Inclusion Stress Distribution (Detached, Inc# 27) 20m wall under Imperial Valley H+3V Motion 320 20
PAGE 335
'iii' 0.. c: 0 :s .0 E C/) i:5 C/) C/) !!! Ci5 'iii' 0.. c: Q "5 .0 :s C/) i:5 C/) C/) !!! Ci5 'iii' 0.. c: .Q "5 .0 :s C/) i:5 C/) C/) !!! Ci5 30000 25000 .._ 20000 ../ "" 15000 / 10000 5000 0 0 28000 24000 Jll. 20000 16000 12000 8000 I rl L 4000 0 0 24000 I I I I I I 1+Static Stress Dynamic Stress 1.......... ......... I. r...._ """'til. r5 10 15 Inclusion Length [m] Inclusion Stress Distribution (Detached, Inc# 28) 20m wall under Imperial Valley H+3V Motion I I I I I 20 ., L.... +Static Stress Dynamic Stress ......... 1'5 .... ..._ ..... ..... .... ._ 10 Inclusion Length [m] ...._ 15 Inclusion Stress Distribution (Detached, Inc# 29) 20m wall under Imperial Valley H+3V Motion '"'"""'t 20 20000 II.... ....... 1+Static Stress Dynamic Stress _l 16000 12000 8000 4000 ..... 0 0 ..._ 5 "1 ......... ..._ . ._ 10 Inclusion Length [m] ...._ """'11. 15 Inclusion Stress Distribution (Detached, Inc# 30) 20m wall under Imperial Valley H+3V Motion 321 """1 20
PAGE 336
20000 '(ij' a. 16000 c: 0 12000 5 .c ;:: ti 8000 0 Vl Vl 4000 (/) 0 20000 '(ij' a. 16000 c: Q 12000 "5 .c :5 8000 Vl 0 Vl Vl 4000 (/) 0 '(ij' 14000 a. 12000 c: 10000 0 :s 8000 .c E 6000 Vl 0 4000 Vl Vl 2000 (/) 0 ,, 11 h r.... /_ ........ ........ 1...... ..... ......... h / / 0 0 r1+Static Stress Dynamic Stress I r..t ,. I .1 5 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 31) 20m wall under Imperial Valley H+3V Motion .IlL !'.... ...... r....... I...._ ........ r.. rj+Static Stress Dynamic Stress 1 r.... I IT I I I I 5 10 15 Inclusion Length (m] Inclusion Stress Distribution (Detached, Inc# 32) 20m wall under Imperial Valley H+3V Motion ........ ..... .......... r..... ..... ..... ...... ........ 0 +Static Stress Dynamic Stress .... I L L 5 I I _l I I 10 Inclusion Length [m] 15 Inclusion Stress Distribution (Detached, Inc# 33) 20m wall under Imperial Valley H+3V Motion 322 .... ., 20 ...... 20 20
PAGE 337
14000 'iii' 12000 a_ c: 10000 0 :s 8000 .a E 6000 tJJ i5 tJJ 4000 tJJ I 2000 (i) 0 0 10000 'iii' a_ 8000 c: .Q 6000 :; .a E 4000 tJJ i5 tJJ tJJ 2000 en 0 10000 'iii' a_ 8000 c: 0 :s 6000 .a E 4000 tJJ i5 tJJ tJJ 2000 (i) 0 IT I I / r I ..1 .......... !+Static Stress Dynamic Stress ........ 5 r::;L !"'"'10 Inclusion Length [m] r15 Inclusion Stress Distribution (Detached, Inc# 34) 20m wall under Imperial Valley H+3V Motion , r.... I'.. ........... !'..... ""'"1 .... 1..._ 11 20 "' / I+Static Stress Dynamic Stress I .... ..... 0 ... II I L 0 5 I I 10 Inclusion Length [m] I 15 Inclusion Stress Distribution (Detached, Inc# 35) 20m wall under Imperial Valley H+3V Motion ......... .......... 'r... j+Static Stress Dynamic Stress 1 5 I 10 Inclusion Length (m] 15 Inclusion Stress Distribution (Detached, Inc# 36) 20m wall under Imperial Valley H+3V Motion 323 20 20
PAGE 338
8000 8!. 6000 2!:. c :8 4000 :::J .a :5 iS 2000 C/) C/) ii5 0 2000 7000 6000 ro ll. 5000 2!:. c 4000 0 :s .a 3000 .:: 1ii i5 2000 C/) C/) 1000 ii5 0 1000 I .,/ 0 I I I I IIi / I ... 0 ,... ........... 1/ T'. I 1\. "" "' "' 5 : +Static Stress Dynarric Stress "k"" 1"' 10 k'lclusion Length [m] 15 Inclusion Stress Distribution (Detached, k'lc # 37) 20m wall under rrperial Valley H+3V IVbtion I I I I +Static Stress "\, II I Dynamc Stress II ........ r... 5 I"" ........ ............. 10 k'lclusion Length [m] I 15 Inclusion Stress Distribution (Detached, k'lc # 38) 20m wall under lrrperial Valley H+3V IVbtion 324 ,20 20
PAGE 339
5000 (1) 4000 a. 1/ =. c: 3000 \ 0 .0 2000 E en i:S 1000 en I I en Q) t5 0 !."' 1000 0 4000 (1) 3000 a. =. c: g 2000 ::J .0 ;:: iii 1000 i:S en en 0 (/) ... v ......., J' ..,..,... 1000 ....... 0 v ....... .......... / ............ ./ +:stat1c )tress I [)ynarric Stress I 5 r10 hclusion Length [m) 15 Inclusion Stress Distribution (Detached, he# 39) 20m wall under h"perial Valley H+3V Wotion v v / rt ff20 '+Static Stress [)ynarric Stress r _.4 .....r5 I,___ 10 Inclusion Length [m) 15 Inclusion Stress Distribution (Detached, Inc# 40) 20m wall under lrrperial Valley H+3V Wotion 325 20
PAGE 340
Appendix F. Coulomb and MononobeOkabe Active Thrust Calculation Spreadsheet 326
PAGE 341
Coulomb Active Thrust Calculation Spreadsheet for 10m wall K = cos2(
PAGE 342
MononobeOkabe Active Thrust Calculation Spreadsheet for 10m wall (Appx F cont'd) cos 2 (
PAGE 343
REFERENCES AASHTO, 1997. Standard Specifications for Highway Bridges, American Association of State Highway and Transportation Officials, Fifteenth Edition, Washington, D.C, USA, 686. Bathurst, R.J and M.C. Alfaro, 1996. "Review of seismic design, analysis and performance of geosynthetic reinforced walls, slopes and embankments,"(Invited keynote paper), ISKyushi '96, 3rd International Symposium on Earth Reinforcement, Fukuoka, Kyushi, Japan, 1214 November 1996, Vol. 2, 30p. Bathurst, R.J, Z.Cai, M.Alfaro and M Pelletier, 1997. "Seismic design issues for geosynthetic reinforced segmental retaining walls" Mechanically Stabilized Backfill (J.T H. Wu editor), Balkema, Proc Of the Int. Symp On Mechanically Stabilized Backfill, Denver, Colorado, February 1997, pp 7997. Bathurst, R.J. and Z.Cai, 1995. "PsuedoStatic Seismic Analysis of Geosynthetic Reinforced Segmental Retaining Walls Geosynthetics International, Vol. 2, No. 5, pp 787830. 329
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Bonoparte, R.,G.R. Schmertmann and N.D. Williams, 1986. "Seismic design of Slopes Reinforced with Geogrids and Geotextiles," Proceedings of the Third International Conference on Geotextiles, Vienna, Austria, Vol. 2, pp. 273278. Bowls, Joseph E., 1996 Foundation Analysis and Design Fifth Edition, McGraw Hill, New York. Christon, Mark A. and Donald J. Dovey, 1992. INGRID : A 3D Mesh Generator for Modeling Nonlinear SystemsUser's Manual, Lawrence Livermore National Laboratory, Livermore, California. Federal Highway Administration (FHWA), 1996. Mechanically Stabilized Earth Walls and Reinforced Soil Slopes Design and Construction Guidelines. FHW A Demonstration Project 82, (Elias.V and B.R. Christopher) Washington, D.C. USA pp. 364. Federal Highway Administration (FHWA), 2001 "Mechanically Stabilized Earth Walls and Reinforced Soil Slopes Design and Construction Guidelines" by Victor Elias, Barry R. Christopher and Ryan R. Berg. U.S. Department of Transportation Washington, D .C. Publication No FHWANHI00043. pp. 98115. 330
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Ling, H.I., D Leshchinsky, and E.B. Perry, 1997. "Seismic design and performance of geosyntheticreinforced soil structures" Geoteclmique, Vol. 47. No. 5, pp 933952. Maker, Bradley N., 1995. NIKE3D: A Nonlinear, Implicit, Three Dimensional Finite Element Code for Solid and Structural Mechanics User's Manual, Lawrence Livermore National Laboratory, Livermore, California. Seed, H.B. and R.V. Withman, 1970. "Design of Earth Retaining Structures for Dynamic Loads" Proceeding, ASCE Specialty Conference on Lateral Stress in the Ground and Design of Earth Retaining Structures, ASCE, pp. 103147. Segrestin, P. and M. Bastick, 1988. "Seismic Design of Reinforced earth Retaining Walls The Contribution of Finite Element Analysis," Proceedings Int. Geotech. Sym. On Theory and Practice of Earth Reinforcement, Japan, pp. 577582. Tatsuoka, F., M. Tateyama, and J. Koseki, 1995. "Performance of Geogrid Reinforced Soil Retaining Walls During the Great HashinAwaji earthquake, January17, 1995," The proceedings of the First international Conference on Earthquake Geoteclmical Engineering, ISTokio'95, 1416 November, 1995, Tokyo, Japan, p. 8. 331
