HYBRID RETAINING WALLS
UNDER SEISMIC LOADS
by
ZehZon Lee
B.S., University of Colorado at Denver, 1998
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
2000
!al!
3^._J
This thesis for the Master of Science
degree by
ZehZon Lee
has been approved
by
ZehZon Lee (M.S., Civil Engineering)
Hybrid Retaining Walls under Seismic Loads
Thesis directed by Professor NienYin Chang
ABSTRACT
Many mechanically stabilized earth (MSE) retaining walls have been
vigorously analyzed, designed, and constructed recently in many geotechnical
engineering applications. MSE retaining wall, being different from conventional
retaining wall, has attributes of reinforcements in the backfill soil and segmental
block facing. In attempt to revitalize conventional retaining wall, an innovative
concept of hybrid retaining wall has been put in place under the leadership of Drs.
NienYin Chang and Trever S.C. Wang in the Center of Geotechnical
Engineering Science at University of Colorado at Denver. Hybrid wall adopts the
features of continuous rigid facing from conventional retaining wall and
reinforcements in the backfill soil from MSE retaining wall. For hybrid retaining
wall to be viable and appealing, volume of continuous rigid facing section was
reduced by means of decreasing the wall footing size and wall stem thickness. To
have an efficient design of hybrid retaining wall and also the actual placement of
it, the responses of the system subjected to various loading need to be analyzed
and examined numerically beforehand. The primary theme of this thesis study
was thus to analyze and examine the responses of hybrid retaining wall under
seismic loading.
Numerical analyses of hybrid retaining wall system were performed using
NIKE3D finite element method (FEM) computer program. NIKE3D features real
time analysis, sliding interface capability, and elastoplastic RambergOsgood
material model. Furthermore, nine earthquake ground motions were selected and
HI
applied to the discretized models to simulate earthquake event. Ground motion
parameters were evaluated for each of the input ground motions. These ground
motion parameters were later correlated with reduced results output by NIKE3D
program. Though the output data were in terms of input ground motion time
history, only the highest amplitude values of interest were obtained and analyzed.
The reduced results were then considered to be the highest conceivable results.
As indicated by the analysis results, responses of hybrid retaining wall
subjected seismic loading can be predicted given the ground motion parameters,
such as peak ground acceleration and cumulative absolute velocity, of a design
earthquake and wall height. Also as indicated by the computed factor of safety
values, susceptible areas within the hybrid retaining wall system were depicted.
Recommendations for making hybrid retaining wall more viable and appealing
were thus stated. This thesis study could consequently initiate series of analysis
on hybrid retaining wall under seismic loading and could eventually optimize the
hybrid wall configurations.
This abstract accurately represents the content of the candidate's thesis. I
recommend its publication.
Signed
IV
ACKNOWLEDGEMENTS
The concept of "hybrid retaining wall" was initiated by Dr. NienYin
Chang. Author would like to show the appreciation to Dr. Chang for providing
the concept and study plan for this thesis study, along with his supervision,
guidance, spiritual and financial support, and encouragement throughout the
academic and research studies. I am also very grateful to Dr. ShingChun Trever
Wang for the retaining wall design concept that I have learned from him during
the NIKE/SSI Research Group deliberation and for his guidance and unselfish
sharing of practical and technical knowhow in retaining wall design and
construction. I also would like to thank Professor Brian Brady for serving on the
final exam committee. Gratitude is further extended to our NIKE/SSI Research
Group members for sharing knowledge and information. Particularly, I wish to
thank doctoral students Fatih Oncul and Kittichai Thanasupsin, and Dr. Lieu
Ching Jiang for their helps and guidance in understanding the NIKE3D program.
CONTENTS
Figures ..................................................................x
Tables ..................................................................xv
Chapter
1. Introduction .........................................................1
1.1 Problem Statement ................................................... 1
1.2 Objective ............................................................2
1.3 Scope of Study .......................................................3
1.4 Engineering Significance .............................................4
2. Literature Reviews ...................................................5
2.1 Introduction .........................................................5
2.2 Seismic Analysis of Conventional Retaining Walls ....................5
2.2.1 MononobeOkabe Method ..............................................6
2.2.2 Nonyielding Walls ..................................................8
2.3 Seismic Analysis of MSE Segmental Retaining Walls ..................10
2.3.1 Potential Failure Modes ...........................................11
2.3.2 Seismic Analysis Approaches .......................................11
2.4 Seismic Performance of MSE Retaining Walls with
Full Height Rigid Facing ............................................15
2.4.1 Advantages of Staged Construction Procedures ......................16
2.4.2 Seismic Stability of Retaining Walls ..............................18
3. Theoretical Background ofNIKE3D Program .............................19
3.1 Implementation of NIKE3D Program in the Study .......................19
3.2 Interface Formulation ..............................................20
VI
3.3 Material Models .....................................................21
3.3.1 RambergOsgood ElastoplasticModel ..................................22
3.4 Eigenvalue Analysis and Rayleigh Damping ............................23
4. Preliminary Study ....................................................26
4.1 Purpose ............................................................26
4.2 Study Parameters ............................................27
4.3 Ground Motions used in Preliminary Study ............................34
4.4 Material Models and Input Parameters ................................35
4.5 Sliding Interfaces and Boundary Conditions ..........................38
4.6 Data Analyses .......................................................38
4.7 Results .............................................................48
4.8 Discussion ..........................................................62
5. Ground Motions Used in the Study ....................................69
5.1 Introduction .........................................................69
5.2 Ground Motion Time Histories and Input Ground Motions ..............70
5.3 Response Spectra and Cumulative Absolute Velocities .................73
6. Analysis Programme ...................................................95
6.1 Purpose ..............................................................95
6.2 Input Parameters ............................................95
6.2.1 Applied Loading ....................................................95
6.2.2 Wall Heights and Dimensions ........................................96
6.2.3 Boundary Conditions ................................................98
6.2.4 Sliding Interfaces ................................................103
6.2.5 Material Models and Parameters ....................................104
6.3 Study Items ........................................................112
6.4 Data Analyses ......................................................114
6.4.1 Stresses and Resultants Imparted on
Concrete Wall Section .............................................116
vii
6.4.2 Backfill Soil Acceleration Profile ...............................118
6.4.3 Dynamic Bearing Pressure .........................................122
6.4.4 Wall Face Displacement ...........................................124
6.4.5 Inclusion Tensile Stress .........................................127
6.5 Results ..........................................................128
6.5.1 Data Reduction ...................................................131
6.5.2 Correlation with Ground Motion Parameters ........................132
6.5.3 Regression Analyses ..............................................148
6.6 Discussion ........................................................149
6.6.1 Comparison of Hybrid Wall and Conventional Wall ..................152
6.7 Conclusion ........................................................153
7. Summary, Conclusions, and Recommendations
for Future Studies .................................................156
7.1 Summary ..........................................................156
7.2 Conclusions .......................................................157
7.3 Recommendations for Future Studies ................................159
Appendix
A. Plots of Lateral Pressure Distribution Behind Wall Section .........165
B. Plots of Backfill Acceleration Profile .............................175
C. Plots of Bearing Pressure Distribution .............................185
D. Plots of Wall Face Displacement ....................................195
E. Plots of Inclusion Stress Distribution .............................205
F. Correlation between Study Items and Ground Motion
Magnitudes .........................................................305
G. Correlation between Study Items and Ground Motion
Duration ...........................................................310
H. Correlation between Study Items and
viii
Peak Ground Accelerations .............................................315
I. Correlation between Study Items and Predominant Periods ................320
J. Correlation between Cumulative Absolute Velocities .....................329
K. Plots of Regression Curves for Peak Ground
Acceleration Correlation ..............................................334
L. Plots of Regression Curves for Predominant
Period Correlation ....................................................337
M. Plots of Regression Curves for Cumulative Absolute
Velocity Correlation ..................................................342
N. Calculations for Thrust, Overturning Moment, and
Bearing Pressure using Limit State Method .............................345
O. Multiple Regression Analysis .........................................350
References ................................................................353
IX
FIGURES
Figure
2.1 Forces acting on active wedge in MononobeOkabe
analysis ...........................................................9
2.2 Forces acting on passive wedge in MononobeOkabe
analysis ...........................................................9
2.3 Typical geosynthetic reinforced soil retaining wall with
segmental facing ..................................................12
2.4 Potential failure modes of MSE segmental retaining wall ...........12
2.5 Total earth pressure distribution due to soil selfweight .........14
2.6 Staged construction procedure for FHR facing
retaining wall ....................................................17
2.7 Typical MSE retaining wall with FHR facing ........................17
4.1 Five hybrid walls dimensions and materials ........................28
4.2 Conventional gravity Twall dimensions and materials ..............29
4.3 MSE wrapped around wall dimensions and materials ..................30
4.4 MSE segmental wall dimensions and materials .......................31
4.5 Six hybrid wall dimensions and materials ..........................33
4.6a Original Loma Prieta acceleration time history ....................36
4.6b Modified Loma Prieta acceleration time history ....................36
4.7 Boundary conditions in preliminary analyses .......................39
4.8 Elements and nodes selected for data reduction ....................41
4.9a Static lateral pressure in hybrid Twall ..........................43
4.9b Dynamic lateral pressure in hybrid Twall .........................43
4.10a Static thrusts calculated from element stress
in hybrid Twall ..................................................44
x
4.10b Dynamic thrusts calculated from element stress
in hybrid Twall .......................................................44
4.1 la Net static thrust and overturning moment in
hybrid Twall ..........................................................45
4.1 lb Net dynamic thrust and overturning moment in
hybrid Twall ..........................................................45
4.12 Static and dynamic bearing pressure in hybrid Twall ...................49
4.13 Hybrid Twall deformation performances .................................50
4.14 Static and dynamic inclusion element stress distributions ..............51
4.15 Example of determining ranking value for static
thrust criterion .......................................................58
4.16 Effect of wall footing configuration on thrust imparted
on wall ................................................................63
4.17 Effect of wall footing configuration on total
overturning moment .....................................................63
4.18 Effect of wall footing configuration on maximum
total bearing pressure .................................................64
4.19 Effect of wall footing configuration on permanent wall tilt ............65
4.20 Effect of wall footing configuration on maximum
inclusion tensile stress ...............................................66
5.1a Mammoth Lakes Aftershock acceleration time history .....................74
5.1b Truncated Mammoth Lakes Aftershock acceleration
time history ...........................................................74
5.2a Whittier Narrows Earthquake acceleration time history ..................75
5.2b Truncated Whittier Narrows Earthquake acceleration
time history ...........................................................75
5.3a Morgan Hill Earthquake acceleration time history .......................76
xi
5.3b Truncated Morgan Hill Earthquake acceleration
time history ..........................................................76
5.4a Vrancea Earthquake acceleration time history ..........................77
5.4b Truncated Vrancea Earthquake acceleration time history ................77
5.5a Northridge Earthquake acceleration time history .......................78
5.5b Truncated Northridge Earthquake acceleration
time history ..........................................................78
5.6a Imperial Valley Earthquake acceleration time history ..................79
5.6b Truncated Imperial Valley Earthquake acceleration
time history ......................................................... 79
5.7a Kern County Earthquake acceleration time history ......................80
5.7b Truncated Kern County Earthquake acceleration
time history ..........................................................80
5.8a Santiago, Chile Earthquake acceleration time history ..................81
5.8b Truncated Santiago, Chile Earthquake acceleration
time history ......................................................... 81
5.9a Michoacan, Mexico City Earthquake acceleration
time history ..........................................................82
5.9b Truncated Michoacan, Mexico City Earthquake
acceleration time history .............................................82
5.10 Absolute acceleration response spectrum for
Mammoth Lakes Aftershock ..............................................84
5.11 Absolute acceleration response spectrum for
Whittier Narrows Earthquake ...........................................85
5.12 Absolute acceleration response spectrum for
Morgan Hill Earthquake ................................................86
5.13 Absolute acceleration response spectrum for
Vrancea Earthquake ....................................................87
xii
5.14 Absolute acceleration response spectrum for
Northridge Earthquake ...............................................88
5.15 Absolute acceleration response spectrum for
Imperial Valley Earthquake ..........................................89
5.16 Absolute acceleration response spectrum for
Kern County Earthquake ..............................................90
5.17 Absolute acceleration response spectrum for
Santiago, Chile Earthquake ..........................................91
5.18 Absolute acceleration response spectrum for
Michoacan, Mexico City Earthquake .................................. 92
6.1 Example of loading curves adopted in analysis .......................97
6.2a 10 m wall height dimensions and materials ...........................99
6.2b 10 m wall height finite element mesh ...............................100
6.3a 7 m wall height dimensions and materials ..........................101
6.3b 7 m wall height finite element mesh ...............................101
6.4a 4 m wall height dimensions ........................................102
6.4b 4 m wall height finite element mesh ...............................102
6.5 Boundary conditions used in analysis ...............................102
6.6 G/Gmax and damping ratio versus shear strain for
average sand .......................................................108
6.7 Selected nodal points for data reduction ...........................115
6.8 Example of static and dynamic pressures imparted
on 10 m wall .......................................................119
6.9 Example of static and dynamic thrust imparted
on 10 m wall .......................................................120
6.10 Example of net static and dynamic thrust imparted on
10 m wall with height of application ..............................121
6.11 Example of backfill acceleration profiles ..........................123
xiii
6.12 Example of bearing pressure distributions ............................125
6.13 Bearing capacity calculation work sheet for 10 m wall ................126
6.14 Example of wall face displacements ...................................129
6.15 Example of inclusion stress distributions ............................130
6.16 Overturning moment and thrust location discrepancy between numerical
and pseudostatic analysis of 10 m wall subjected to
magnitude 6, case no. 1 earthquake ..................................136
6.17 Variation in overturning moment between numerical and
pseudostatic analysis ...............................................137
6.18 Static stress distributions within 20 layers of inclusion
of 10 m wall .........................................................144
6.19 Static stress distributions within 14 layers of inclusion
of7mwall .............................................................145
6.20 Static stress distribution within 8 layers of inclusion
of 4 m wall ..........................................................146
7.1 Reinforced foundation soil ...........................................164
xiv
TABLES
Table
4.1 Material model parameters used in preliminary study .................39
4.2 Ranking of 8 wall types using original input
ground motion .......................................................53
4.3 Ranking of 8 wall types using modified input
ground motion .......................................................54
4.4 Ranking of 7 wall types using original input
ground motion .......................................................55
4.5 Ranking of 7 wall types using modified input
ground motion .......................................................56
4.6 Weight ranking of 7 wall types using original input
ground motion .......................................................60
4.7 Weight ranking of 7 wall types using modified input
ground motion .......................................................61
4.8 Results of performance criteria and ranking for second
stage analyses ......................................................67
5.1 Nine selected earthquake ground motion information ..................71
5.2 Summary of ground motion parameters .................................94
6.1 Value range for the static stressstrain modulus E for
selected soils .....................................................106
6.2 Values or value for Poissons ratio v ..............................106
6.3 Tabulated results computed by RAMBO for average
sand of 125 pcf ....................................................109
6.4 Typical values of compressive wave velocity and shear
wave velocity ......................................................Ill
xv
6.5 Physical and mechanical properties of commercially
available geogrid ..................................................Ill
6.6 Some values of Poissons ratio for elastically
isotropic solids ...................................................Ill
6.7 Inputted material parameters for the detailed study ................113
6.8 Results of net dynamic thrust and bearing pressure .................133
6.9 Comparison of static overturning moments between numerical
FEM and pseudostatic Coulomb analyses .............................134
6.10 Comparison of dynamic overturning moments between numerical
FEM and pseudostatic MononobeOkabe analyses ......................135
6.11 Results of maximum backfill forward acceleration and wall face
maximum differential forward displacement ..........................138
6.12 Results of maximum dynamic tensile stress within
inclusion ..........................................................139
6.13 Location of maximum dynamic tensile stress within
inclusion ..........................................................141
6.14 Results of eigenvalue analyses .....................................143
6.15 Results of linear regression analyses ..............................150
6.16 Results of 2nd order polynomial regression analyses ................151
6.17 Performance comparison of hybrid walls and walls
without inclusions .................................................154
xvi
1. Introduction
1.1 Problem Statement
Retaining wall, as a generic term, is used to retain soil mass for creating
space in the civil related work. Retaining walls can be found almost everywhere
in public and private civil projects. Examples of retaining wall are highway
retaining walls, building basement walls, and bridge abutments. Heretofore,
components within retaining wall vary from one system to another system.
Classification was thus created to distinguish various retaining walls. The first
group in the classification belongs to the externally stabilized wall. The
externally stabilized walls include gravity wall, semigravity wall, and sheet pile
wall. The second group in the classification is then the internally stabilized wall.
An example of internally stabilized wall is the mechanically stabilized earth
(MSE) segmental wall. A MSE segmental wall features geosynthetic
reinforcements in the backfill soil and facing column comprised of segmental
blocks. Where applicable, MSE segmental retaining wall is an extreme
competitor to those of the externally stabilized walls, due to its cost effectiveness.
MSE segmental wall is advantageous in aspects of low material cost, short
construction period, and ease of construction. On the other hand, externally
stabilized walls still have the merits of continuous rigid facet and the possibility
of less soil mass excavation.
The wall that cannot be classified as externally or internally stabilized wall
is then considered to be hybrid. The hybrid retaining wall was an innovation to
combine characteristics of externally and internally stabilized wall together. A
hybrid retaining wall inherits the continuous rigid facet from externally stabilized
wall and the geosynthetic reinforcements from internally stabilized wall. To
1
make hybrid retaining wall viable and appealing, volume of facing section must
be less than the one in externally stabilized wall, and the amount geosynthetic
reinforcements must also be less than the one in internally stabilized wall.
Reduction in the volume of facing section can be achieved by reducing the wall
footing size. The amount of geosynthetic reinforcements can be reduced by
means of shortening inclusion length and/or increasing vertical spacing between
inclusions.
Since hybrid retaining wall is merely at its introductory stage, there exists
unknowns in the actual design and even in the performance of the wall. The
Center for Geotechnical Engineering Science at University of Colorado at Denver
allocates part of its efforts in attempt to investigate the responses of the hybrid
retaining wall subjected to different types of loading via numerical analysis. This
particular thesis study was aimed toward the evaluation of the responses of hybrid
retaining wall when subjected to seismic loading. It is also the interest of this
study to examine the contribution of earthquake ground motion parameters to the
seismic responses of hybrid retaining wall. With the knowledge gained from the
results of this study and future studies, it is hoped that hybrid retaining wall can
be designed effectively and be performed safely.
1.2 Objective
The objective of this thesis study was to examine the seismic responses of
hybrid retaining wall numerically. A numerical analysis involves utilization of
computer program to solve the proposed problem. The finite element method
computer program named NIKE3D would be used as the numerical analysis tool
in this study. At this developing stage, many unknowns about the hybrid wall
exist. Therefore, the inductive procedure was adopted to determine an effective
configuration of the hybrid retaining wall prototype (or model). Once the wall
2
configuration was set, the prototype was discretized into finite number of
elements, along with material properties and boundary conditions assignment;
prototype was then analyzed numerically with NIKE3D. Real ground motion
time history was imposed onto the prototype as seismic loads. Data outputted by
NIKE3D were reduced and analyzed to interpret the responses of the hybrid
retaining wall system. Conclusions of the seismic responses of hybrid retaining
wall could thus be drawn from the limited cases that were analyzed.
1.3 Scope of Study
The scope of this thesis study is outlined as follows.
 Determination of wall configuration, specifically the wall footing size, for the
hybrid retaining wall prototype.
 Selection of material properties for components of hybrid retaining wall.
 Selection of nine earthquake ground motion records as input ground motion
time histories.
 Evaluation of ground motion parameters for each input ground motion time
history.
 Discretization of the three prototype: 10 m wall, 7 m wall, and 4 m wall with
inclusions attached to the back of concrete facing.
 Determination of wall responses such as thrust and location of thrust imparted
on the wall section, backfill acceleration amplification profile, bearing
pressure on foundation soil, wall face displacement, and inclusion tensile
stress from the outputted data.
 Determination of MononobeOkabe pseudostatic thrust, thrust location, and
overturning moment about the wall base.
 Correlation between the responses and inputted ground motion parameters.
3
 Prediction of the hybrid wall responses via inputted ground motion
parameters.
 Comparison between the numerical analysis (performance state) results and
pseudostatic analysis (limit state) results.
 Recommendations for future studies.
1.4 Engineering Significance
The engineering significance deduced from the conclusions of this thesis
study are included in the following.
 Although the values are of close magnitude, discrepancy was found between
numerical analysis and current pseudostatic analysis in the results of
overturning moment about the wall base.
 Seismic responses of retaining wall systems could be evaluated via NIKE3D
program.
 Optimized hybrid retaining wall system could be a feasible alternative to
externally and internally stabilized walls.
 One could use ground motion parameters such as peak ground acceleration
and cumulative absolute velocity of a design earthquake as indexes to predict
wall performances.
 The discretized finite element meshes and inputted material properties in this
study could serve as the basses for future studies.
4
2. Literature Reviews
2.1 Introduction
In this literature review, three items were discussed. First, the seismic
analysis of conventional retaining wall was reviewed where MononobeOkabe
method was introduced. The second item discussed was the seismic analysis of
mechanically stabilized earth (MSE) segmental retaining wall where the state of
practice in assigning thrust imparted on facing column was stated. The third item
considered the seismic performance of MSE retaining wall with full height rigid
(FHR) facing. Construction of the FHR facing retaining wall was also included in
the third item. Note that the term MSE is interchangeable with the term GRS,
which stands for geosynthetic reinforced soil.
2.2 Seismic Analysis of Conventional Retaining Walls
In an active seismic region, the seismic resistant design of externally
stabilized retaining walls, including gravity and cantilever walls, is of great
interest. Its purpose is to design the wall to resist the earthquake induced loading.
Simplified methods were developed to estimate these earthquake induced loading.
Here, retaining wall analyses are categorized into two groups: yielding wall and
nonyielding wall. Yielding wall is defined as the wall that develops minimum
active or maximum passive earth pressure. The pseudostatic method is utilized to
estimate the dynamic pressure on the yielding wall. In yielding wall, pseudostatic
seismic earth pressures could be determined using the MononobeOkabe method
as briefed in the next section.
5
2.2.1 MononobeOkabe Method
MononobeOkabe method is similar to static Coulomb theory with
additional pseudostatic accelerations applied to Coulomb active or passive force
equilibrium wedge. A scheme of such force equilibrium wedge is shown in
Figure 2.1. Pseudostatic accelerations that exert on the wedge mass are horizontal
component of earthquake peak acceleration, ah (= kj,G), and vertical component of
the earthquake peak acceleration, av (= kvG), where G is the gravitational
acceleration. In an active earth pressure condition, the active thrust with effect of
earthquake, Pae, from force equilibrium wedge can be determined using the
following equation.
PAE=KAEyH\\kv) (2.1)
y is the unit weight of the backfill, and H is the total wall height. Kae is the
dynamic active earth pressure coefficient and is given by Equation 2.2.
cos 2{9y/)
Kae =
cos ^ cos2 9cos(S + 0 + y/)
1 + .
/ sin(Â£ + ) sin(jf> p y/)
cos (S + 0 + i/s) cos (/? 9)
=r<2.2)
where P > \j/, and v/ = tan'1 [ kh / (1 kv)]. is the soil friction angle, and 6 is
the soilwall interface friction angle. (Xae is the critical failure surface angle
inclined from horizontal,
case, and the critical failure surface angle is found by Equation 2.3.
tan { y/ p)+C
<*ae =Â¥ + tan
i
'\E
2 E
(2.3)
where
ClE = yjtanty y/ /?)(tan(^ iff fi)+cot(j4 y/ 0)]\ + tan(S + ^ + 0)cot(^ y/6)J
C2E = 1 + {tan(<5 + y/ + 0)[tan(0 y/ 0) + cot(0 y/ 0)]}
6
The location of the resultant active thrust Pae from soil to retaining wall in
MononobeOkabe method is the same as the static Coulomb theory, and the
resultant thrust acts at height of H/3 above the wall base. H is the total wall
height. But experiment results for dynamic loading indicated that location of
thrust application is actually higher than H/3. The resultant active thrust Pae has
two components: static and dynamic. The static component is denoted by Pa, and
the dynamic component is denoted by APae Pae is then combination of Pa and
APae as shown in Equation 2.4.
The dynamic component APae would further be discussed in Section 2.3.2. Note
that static component acts at height of H/3. Seed and Whitman (1970) suggested
that dynamic component acts at approximately 0.6H. With known locations of
static and dynamic thrust, one 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 (ah) is pointed away from the retaining wall as
shown in Figure 2.2. Figure 2.2 shows the fore equilibrium wedge of passive
earth pressure condition. The passive soil thrust exerted on retaining wall from
the cohesionless backfill is given by Equation 2.6.
Kpe denotes the dynamic passive earth pressure coefficient and is given by
Equation 2.7.
(2.4)
h_PAHn + *PM(*.6H)
(2.5)
PPE=^KPEyH\\kv)
(2.6)
7
KPE =
co s2{tp + 0y/)
cosr cos; Bmjs g+y f 1 J S'" ^ + ^)sin^ +
V ^ Vco^fi + ricosO?#)
apE is the critical failure surface inclined from the horizontal for the passive
conditions. apE can be calculated from Equation 2.8.
tan {4> + y/ + p)+C2l
(2.7)
aPE = V' 0 + tan
C.
4E1
(2.8)
where
C3E = y]tan( + 9 ^)]l + tan(^ + iff #)cot(^ + Q y/)]
C4Â£. = 1 + {tan(^ + y/ #)[tan(^ + (5 y/) + cot(^ + 0 y/)]}
As in the active earth pressure condition, passive soil thrust also has two
components. One is static (Pp), and the other is dynamic (APpe). The resultant
passive thrust, Ppe, can be determined by Equation 2.9.
Ppe=Pp+APpe (2.9)
2.2.2 Nonyielding Walls
In the case of nonyielding walls, retaining walls are braced at top or
bottom. Examples are heavy gravity walls found on rock base and basement
walls. Mobilization of shear strength cannot be developed due to insufficient wall
movement. Consequently, minimum active and maximum passive earth pressure
limiting conditions cannot be developed. Wood (1973) presented the dynamic
thrust and dynamic overturning moment for rigid smooth walls in the following
equations.
APe, =yH2F (2.10)
g
8
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)
9
(2.11)
AA^=^3^Fm
g
ah here is the amplitude of the harmonic base acceleration. Fp and Fm are
dimensionless dynamic thrust and moment factors, respectively. Values of Fp and
Fm can be found in Figure 11.17 and 11.18, respectively, in the textbook by
Kramer. Dynamic thrust is acting at height of heq above the wall base and is
determined using Equation 2.12.
AM
Ka =
69 AP
eq
(2.12)
Typically, heq is approximately equal to 0.63 of the total wall height.
2.3 Seismic Analysis of MSE Segmental Retaining Walls
Segmental retaining walls with geosynthetic reinforcement have been used
widely in earth retaining structure constructions in the recent years. A typical
geosynthetic reinforced wall layout is shown in Figure 2.3. The primary
advantages of such walls are ease of construction and low cost. Modular masonry
blocks are stacked one on top of another to form the facing section of segmental
retaining wall. Large amount of these geosynthetic reinforced segmental
retaining walls has been built in seismically active areas. These structures have
performed satisfactorily during strong earthquake, and no catastrophic failures
have been reported, and the observed satisfactory seismic performance could be
due to the conservative design rather than an appropriate seismic design
(Tatsuoka et al. 1995). Methods of analysis and design for segmental retaining
wall have been developed to ensure stability and tolerable displacement under the
seismic loading (Bathrust et al. 1997; Ling et al. 1997).
10
2.3.1 Potential Failure Modes
Potential failure modes of reinforced segmental retaining wall subjected to
seismic loading are shown in Figure 2.4. There are three general categories of
failure modes, and they are the external failure modes, internal failure modes, and
the facing failure modes. The equivalent gravity structure comprising the facing
units, geosynthetic reinforcement, and the reinforced soil fill as a whole is
considered for the external failure modes. Examples of external failure modes are
base sliding, overturning about the toe, and bearing capacity failure. Internal
failure modes, on the other hand, consider modes of pullout, tensile overstress,
and internal sliding which occur within the reinforced soil mass. As for the third
category of failure modes, the facing failure modes consist of connection failure,
column shear failure, and toppling failure. The shear capacity in facing column
can be developed through interface friction, concrete keys, or mechanical
connectors in between the concrete blocks. The drystacked facing units provide
potential failure planes through the facing column (Bathrust et al. 1997). The
induced interface shear forces subjected to static and seismic loading are to be
compared with available shear capacity in determination of wall stability. Note
that the three categories stated do not include the global instability failure, and the
global failure could take place partially through or beyond the reinforced soil
mass.
2.3.2 Seismic Analysis Approaches
Analysis of geosynthetic reinforced segmental retaining walls subjected to
seismic loading can be categorized by the following three methods: pseudostatic
method, displacement method, and finite element method. Assumptions in the
seismic analysis are that the foundation of the retaining wall system is firm with
adequate bearing capacity and the reinforced soil fill is homogeneous,
11
Figure 2.3 Typical geosynthetic reinforced soil retaining wall with
segmental facing
(a) base sliding
(external foilure mode)
(d) pullout
(internol foilure mode)
(b) overturning
(external failure mode)
(e) tensile overstress
(internol failure mode)
(c) bearing copocily
(excessive settlement)
(external foilure mode)
(f) internal sliding
(internol failure mode)
(g) connection failure
(facing failure mode)
(h) column shear foilure
(focing foilure mode)
(i) toppling
(focing foilure mode)
Figure 2.4 Potential failure modes of MSE segmental retaining wall (after
Bathurst et al. 1997)
12
unsaturated, and cohesionless. Thus problems of excessive settlement and soil
liquefaction are excluded. The pseudostatic method would be discussed in the
following.
MononobeOkabe method is utilized in the pseudostatic analysis of earth
retaining structures. Dynamic earth forces acting on earth retaining structure can
be determined via MononobeOkabe. MononobeOkabe method, which is an
extension of Coulomb wedge analysis with additional seismic induced forces, was
presented in Section 2.2.1 of this thesis. The advantage of MononobeOkabe
method is that designer can obtain a closedform solution for Pae. The
MononobeOkabe method provides evaluation of the total dynamic earth force
(Pae) but not the distribution of the lateral earth pressure with depth.
Figure 2.5 shows the total active dynamic earth pressure distribution due
to soil self weight proposed by Bathurst and Cai (1995). This total earth pressure
distribution is used for external, internal, and facing stability analyses of
reinforced segmental retaining walls. The point of application of resultant total
earth force depends on the magnitude of incremental dynamic active earth
pressure coefficient (AKjyn), and the location varies over the range of 1/3 < m <
0.6 (Bathurst et al. 1997). As shown in Figure 2.5c, m is the proportion relative to
the wall height. Note that the dynamic component of earth force APdyn (=APae),
as shown in Figure 2.5b, acts at 0.6H above the base of the retaining wall system,
which is conservative for wide range of base motion frequency (Bathurst and
Alfaro, 1996). Again, Pae is the sum of Pa and APdyn as shown in Equation 2.4.
AKdyn can be determined using the following equation once Kae and Ka are
known.
KAE=KA+tJC^ (2.13)
Selecting an appropriate seismic coefficient is a major issue in the seismic
design of earth structures. The MononobeOkabe analyses show that the vertical
13
+1p
Figure 2.5 Total earth pressure distribution due to soil selfweight (after
Bathurst et al. 1997)
seismic coefficient (kv), when taken as 1/2 to 2/3 the value of the horizontal
seismic coefficient (kh), affects Pae by 10% (Bathurst et al. 1997). Seed and
Whitman (1970) concluded that vertical accelerations can be ignored when the
MononobeOkabe method is used to estimate Pae for typical wall designs.
Currently, there is no consensus view on selecting a design value for kh. Whitman
(1990) recommended values of kh range from 0.05 to 0.15 which correspond to
1/3 to 1/2 of the peak acceleration (am) of the design earthquake for the gravity
retaining wall. Bonaparte et al. (1986) suggested kh = 0.85am/g for geosynthetic
reinforced slopes using MononobeOkabe method of analysis. For the
geosynthetic reinforced soil walls, the FHWA guideline (1996) uses an equation
proposed by Segrestin and Bastic (1988) that relates kh to am according to kh =
(1.45 am/g) x am/g and results in kh > am/g for am < 0.45g. In the current design
practice, the selection of kh is more of an art than science and it is based on the
engineering judgment, experience, and local regulations.
2.4 Seismic Performance of MSE Retaining Walls
with Full Height Rigid Facing
Geosynthetic reinforced soil retaining walls (GRSRW) with castinplace
fullheight rigid (FHR) facing have been constructed in Japan since last decade.
These retaining walls serve as embankments, bridge abutments, and support for
train tracks in Japanese railways. Figure 2.6 illustrates the staged construction
procedure of such fullheight rigid facing wall. The construction involves (1) a
small foundation for the facing, (2) a geosynthetic reinforced soil wraparound
wall consists of gravelfilled bags placed at the shoulder of each soil layer, and (3)
a thin lightly steelreinforced castinplace concrete facing connected to the
geosynthetic reinforced soil wall. The concrete facing is cast in place after
deformation of the backfill and base soil layer has essentially completed. Note
15
that retaining walls with cohesionless soil use geogrid as the tensile
reinforcement, while those with cohesive soil use geotextile as reinforcement.
The vertical spacing between the reinforcement layers is about 30 cm, and the
minimum thickness of a fullheight rigid facing is 30 cm to ensure workability
during concrete placement. The anchorage lengths observed in literature range
from 1.0 to 0.4 of the wall facing height. A typical layout and 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 of geosynthetic
reinforced retaining wall with fullheight rigid facing based on the issues of (1)
cost performance, (2) deformability of wall, and (3) stability of wall.
Geosynthetic reinforced retaining wall with fullheight rigid facing, in comparison
to geosynthetic reinforced segmental wall, has greater wall stability and lower
wall deformation (Tatsuoka et al. 1997). Geosynthetic reinforced retaining wall
with fullheight rigid facing is also cost effective compared to conventional
retaining wall, because it is a self support structure and does not need pile
foundation to support the concrete facing.
2.4.1 Advantages of Staged Construction Procedures
By the staged construction method, potential damage due to differential
settlement between backfill and rigid facing and between connection at the back
of the facing and reinforcements can be avoided. In the staged construction
procedures, good compaction of the backfill at the back of the facing can be
achieved by allowing relatively large outward lateral displacement to occur at the
temporary wall face. Sufficient large tensile strains can thus be developed and
mobilized in the tensile reinforcement. Because the fullheight rigid facing is cast
in place after primary deformation of backfill and base soil layer is over, a good
16
__[ Drainage
(1) Base Concrete
eg : x
VM mr
(3) Backfill and Compaction
I Sondbag
(2) Laying Geotextile and Sandbog
(5) Laying Completed (6) Concrete Facing Erected
Figure 2.6 Staged construction procedure for FHR facing retaining wall
(after Tatsuoka et al. 1997)
Figure 2.7 Typical MSE retaining wall with FHR facing
17
alignment of the facing can be easily achieved. The erected facing at the later
stage will then experience minimal earth pressure and associated vertical force.
Laboratory tests also have confirmed that geosynthetic reinforced soil wall with
fullheight rigid facing can support very large vertical and lateral loads acting
behind the crest of the wall without exhibiting noticeable deformation (Tateyama
et al. 1994).
2.4.2 Seismic Stability of Retaining Walls
On January 17 of 1995, a devastating earthquake of Richter local scale 7.2
struck southern part of Hyogo Prefecture Japan. Retaining walls of various types
in the railway embankments located in severely earthquake affected areas were
evaluated. The retaining walls include masonry retaining walls, leaningtype
unreinforced concrete retaining walls, gravity type unreinforced concrete
retaining walls, and cantilevertype or inverted Tshaped type steelreinforced
concrete retaining walls. Most of the walls were seriously damaged, while the
damage to the cantilevertype steelreinforced concrete walls were less severe. In
comparison with the above four types of retaining walls, geosynthetic reinforced
soil retaining wall with fullheight rigid facing at Tanata was much less seriously
damaged, and some were not damaged at all (Tatsuoka et al. 1997). It is believed
that the reinforced soil zone can behave as a relatively flexible monolith having a
relatively large width/height ratio, which makes GRSRW with a FHR facing
more stable against seismic force than conventional gravity type retaining wall
(Tatsuoka et al. 1997).
18
3. Theoretical Background of NIKE3D Program
3.1 Implementation of NIKE3D Program in the Study
NIKE3D is a computer program that performs finite element analysis.
NIKE3D is a nonlinear, implicit, and threedimensional finite element code
specifically for solid and structural mechanics. NIKE3D was originally
developed and has been used by the Lawrence Livermore National Laboratory for
the last nineteen years. It has been used to study the static and dynamic response
of structures undergoing finite deformations. The available elements to achieve
spatial discretization in the program are the 8node solid element, 2node truss
and beam element, and 4node membrane and shell element. The 8node solid
element and 4node membrane element were implemented in this thesis study. A
preprocessor and a postprocessor were used in conjunction with NIKE3D to
complete a NIKE3D analysis.
As the primary numerical analysis tool, NIKE3D has been used
extensively to conduct researches at the Center for Geotechnical Engineering
Science, University of Colorado at Denver. Thus far, one Ph.D. thesis and two
M.S. theses were produced using NIKE3D in investigating the soilstructure
interactions. Besides being the users of NIKE3D, developments to the NIKE3D
kernel code were also conducted. Despite the twenty some constitutive models
available, many constitutive models in soil mechanics are not included in the
kernel code of NIKE3D. To make NIKE3D more applicable in other fields of
geotechnical engineering, several constitutive models were added to the kernel
code of NIKE3D, and these constitutive models are in the testing phase. The
constitutive models that had been constructed include DrukerPrager model,
MohrCoulomb model, Lades model, and Modified Cam Clay model. The
19
Bounding Surface model and Uncoupled Pore Pressure calculations are yet to be
developed in the near future.
Similar to common finite element program, a prototype (or model) of
interest should be discretized into finite number of elements. A preprocessing
program, INGRID, was developed for NIKE3D to generate such finite element
mesh. INGRID is a threedimensional mesh generator developed by Lawrence
Livermore National Laboratory as well. Besides the mesh generation, one could
also use INGRID to specify loads, element types, sliding surfaces, boundary
conditions, and material models and parameters to a prototype for the NIKE3D
analysis. Output file from INGRID would then become the input file for
NIKE3D. Sliding surfaces would be discussed in the Section 3.2 of this chapter.
Note that the units should be consistent through out the analysis. SI units were
adopted in the study.
With NIKE3D being the main processor, a postprocessor was used to
extract results from the main analysis. The name of the postprocessor is GRIZ,
and it was also developed by Lawrence Livermore Nation Laboratory. The output
file from NIKE3D then becomes the input file for GRIZ. With GRIZ, one could
visualize the analysis results directly on the terminal display. GRIZ could
animate series of specified loading increments from the analysis. Digitized data
could be printed to text file for plotting and other further analyses.
3.2 Interface Formulation
A significant feature of NHCE3D program is its interface formulation
capability. User could define surfaces between material meshes, and the surfaces
could permit gaps or frictional sliding during the analysis. Two algorithms are
utilized for the interface capability; one is the penalty formulation method, and
the other is the augmented Lagrangian method. For the penalty method, penalty
20
springs are generated between contact surfaces when an inter material penetration
is detected. A penalty stiffness scale factor can be specified to adjust the default
stiffness of the contacting interface, and the scale factor between 0.1 to 0.001 may
be used to ensure convergence. Scale factor less than one would allow more
interpenetration; default value of one was adopted in this thesis study for analyses
involved with penalty method. The augmented Lagrangian method is iterative
and is an addition to the penalty method for enforcing contact constraints. Penalty
stiffness factor is also applicable to the augmented Lagrangian method, and scale
factor of 0.05 was found to be compliant with general geotechnical problem.
In the current version of NIKE3D, ten interface types are available.
Among these interface types, the frictional sliding with gaps interface was chosen
for this thesis study. Sliding surfaces could be defined in the preprocessing
procedure using INGRID program. For interface type of frictional sliding with
gaps, a sliding surface is made up of two contacting surfaces. One contacting
surface is the master surface, and the other contacting surface is slave surface.
The selection of master or slave contacting surface is arbitrary. A contacting
surface is typically comprised of element faces. The nodes on the master surface
are the master nodes, while the nodes on slave surface are the slave nodes.
Although the designation of masterslave contacting surface is arbitrary, the
number of master nodes and slave nodes needs to be the same. The defined
sliding surfaces in this thesis study were all planar.
3.3 Material Models
Twentytwo constitutive models are included in the NIKE3D program.
These constitutive models cover a wide range of elastic, plastic, viscous, and
thermally dependent material behavior. For the 1995 version of NIKE3D,
geologic and concrete materials may be treated using the RambergOsgood model
21
or the Oritented Brittle Damage model, where dissipation of energy is allowed.
Only the isotropic elastic model and RambergOsgood elastoplastic model were
adopted in this thesis study. There are four types of material used in the study.
Foundation soil, concrete section, and inclusion materials were simulated using
the isotropic elastic model. The only material that used RambergOsgood model
was backfill soil. Input of material density is required for all material models.
For isotropic elastic model, the required input parameters are modulus of
elasticity and Poissons ratio.
3.3.1 RambergOsgood Elastoplastic Model
The RambergOsgood elastoplastic model is used to treat the nonlinear
hysterestic elastoplastic constitutive behavior of many materials. This model
allows a rateindependent representation of the hysterestic energy dissipation
observed in materials subjected to cyclic shear deformation. The model is
intended as a model for shear behavior, and it can be applied in soil dynamics and
seismic analysis of soilstructures. In RambergOsgood model, five material
model parameters are required: (1) reference shear strain yy, (2) reference shear
stress xy, (3) stress coefficient a, (4) stress exponent r, and (5) bulk modulus K.
The stress and strain relationship for monotonic loading in RambergOsgood
model is give by Equation 3.1.
Yy Ty
ify > 0
JL
ry
if y < 0
(3.1)
22
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 used to
model the unloading and reloading material behavior after the first reversal.
Y~Yo
try
rr
2 r
ify>0
YYo
2r,
2vy
a
r
2ry
if y < 0
(3.2)
where x0 and y0 represent the values of shear stress and strain at the point of load
reversal.
The five material model parameters are generally obtained based on the
test data or typical relationships in terms of shear modulus and damping ratios
versus shear strain. A computer program was developed specifically for
determining these five material model parameters given a relationship of shear
modulus and damping ratios versus shear strain. The name of the program is
RAMBO. This FORTRAN code was written by the Lawrence Livermore
National Laboratory to facilitate the determination of the RambergOsgood
material model parameters. In the detailed study of Chapter 6, relationship of
fractions of shear moduli (G/Gmax) and damping ratios with shear strain for
average sands were used as inputs for the RAMBO program to generate a set of
RambergOsgood material model parameters for the detailed study analyses.
3.4 Eigenvalue Analysis and Rayleigh Damping
NIKE3D is capable of doing eigenvalue analysis on the proposed
prototype (or model). Number of mode shapes can be specified in the input file to
NDCE3D. In the detailed study of Chapter 6, fifteen mode shapes were designated
to the hybrid retaining wall system. For each mode shape calculated, NIKE3D
23
would return a natural frequency corresponding to that mode shape. Knowing the
natural frequency of the system and natural frequency of the forcing motion,
amplification of the system could be calculated. System natural frequency
associated with a mode shape could be used to determine required coefficients for
Rayleigh damping.
Rayleigh damping is a system damping, and it was applied in the detailed
study of Chapter 6. Rayleigh damping is considered as a 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 the mass and stiffness proportional damping coefficient, respectively.
With system natural frequencies computed using eigenvalue analysis, a and P
coefficient for Rayleigh damping can be calculated. Natural frequencies of first
mode and fifteenth mode were selected in the computation. The Rayleigh
damping coefficients can be determined with the Equation 3.4 and 3.5.
a = 2a)x4\ ~ 2{oj2<
. (
o 2(qj2420) A)
P (2 2 (2 a), )
(3.4)
(3.5)
i and 0)2 are the first mode and fifteenth mode system natural frequency,
respectively. Note that units for i and 2 is radian/second. and Â£2 are the
fraction of critical damping corresponding to 1 and 2, respectively. User would
have to specify the fraction of critical damping. 5% critical damping is usually
adopted in the field of structural engineering. In the detailed study of the hybrid
retaining wall systems, Â£1 and Â£2 were entered as 10% (0.1) of critical damping.
The calculated a and P value were then specified in the material deck of NIKE3D
input file. Since Rayleigh damping is an overall system damping, the computed
24
value of a and P remained the same for all materials that comprised the prototype
(i.e. hybrid retaining wall system).
25
4. Preliminary Study
4.1 Purpose
In seeking an alternative retaining wall system, the hybrid wall was
considered. Hybrid wall lies in between an externally stabilized retaining wall
system and an internally stabilized retaining wall system. Unlike the conventional
gravity/cantilever retaining wall, a hybrid wall has reinforcements or inclusions at
the backfill. Unlike the internally stabilized retaining wall, hybrid wall has a rigid
facing instead of the stacked modular block facing as in the internally stabilized
wall. Hybrid wall is still at the developing stage. Research on the hybrid wall
system has been performed at the Center for Geotechnical Engineering Science,
University of Colorado at Denver. The research involves finding static and
dynamic behaviors of the hybrid wall. At this stage, numerical analysis using
NIKE3D program is the primary method of analyzing hybrid wall. With solid
understanding of hybrid wall behaviors, one could build and promote an
alternative wall that is structurally sound and economically competitive.
Preliminary study was performed before the commencement of a detailed
study programme of the hybrid wall subjected to strong ground motions. The
preliminary study was developed into two stages. Both stages involved the
numerical analysis of the retaining wall systems. In the first stage, five hybrid
wall types were compared with three other nonhybrid wall types. A total of eight
wall types were analyzed in the first stage, and the wall type that had the best
performance was chosen as the prototype for the second stage analysis. In the
second stage, four additional wall configurations were analyzed. The geometric
effect of the concrete facing section was considered in the second stage. In order
for the hybrid wall to be competitive with conventional gravity wall and MSE
26
3. Theoretical Background of NIKE3D Program
3.1 Implementation of NIKE3D Program in the Study
NIKE3D is a computer program that performs finite element analysis.
NHCE3D is a nonlinear, implicit, and threedimensional finite element code
specifically for solid and structural mechanics. NIKE3D was originally
developed and has been used by the Lawrence Livermore National Laboratory for
the last nineteen years. It has been used to study the static and dynamic response
of structures undergoing finite deformations. The available elements to achieve
spatial discretization in the program are the 8node solid element, 2node truss
and beam element, and 4node membrane and shell element. The 8node solid
element and 4node membrane element were implemented in this thesis study. A
preprocessor and a postprocessor were used in conjunction with NIKE3D to
complete a NIKE3D analysis.
As the primary numerical analysis tool, NIKE3D has been used
extensively to conduct researches at the Center for Geotechnical Engineering
Science, University of Colorado at Denver. Thus far, one Ph.D. thesis and two
M.S. theses were produced using NIKE3D in investigating the soilstructure
interactions. Besides being the users of NIKE3D, developments to the NIKE3D
kernel code were also conducted. Despite the twenty some constitutive models
available, many constitutive models in soil mechanics are not included in the
kernel code of NIKE3D. To make NIKE3D more applicable in other fields of
geotechnical engineering, several constitutive models were added to the kernel
code of NIKE3D, and these constitutive models are in the testing phase. The
constitutive models that had been constructed include DrukerPrager model,
MohrCoulomb model, Lades model, and Modified Cam Clay model. The
19
wall, the continuous concrete facing section should be as small as possible. In the
second stage, a single wall configuration would be selected for the detailed study
demonstrated in Chapter 6.
4.2 Study Parameters
In the first stage of the preliminary study, eight wall types were analyzed.
Five of the eight wall types were considered as hybrid walls. The five hybrid
walls were Twall, Lwall, invert Lwall, vertical wall, and Twall with small toe.
The dimensions of these hybrid walls are shown in Figure 4.1. Other three wall
types included a conventional gravity Twall, a (mechanically stabilized earth)
MSE wrapped around wall, and a MSE segmental wall. The dimensions for
conventional gravity Twall, MSE wrapped around wall, and MSE segmental wall
are shown in Figure 4.2, 4.3, and 4.4, respectively.
For the five hybrid walls and the conventional gravity Twall, the base of
the concrete facing was buried one meter (100 cm) below ground surface. SI
units were adopted throughout the study. These concrete facing walls all had the
same wall stem thickness and footing thickness. The footing thickness was 70
cm, while the wall stem thickness was 50 cm. For the MSE wrapped around wall
and MSE segmental wall, the base of the wall was elevated at the ground surface.
All eight walls had the same wall height. The wall height of 8 m was measured
from the ground surface to the wall top.
All wall types were reinforced with four layers of inclusion except the
conventional gravity Twall, where no inclusions were included. The inclusions
could be considered as geosynthetic reinforcements and specifically as geogrid
reinforcement. For the reinforced retaining wall types, the inclusions were
attached to the wall. No separation was allowed between the inclusion and the
wall facing. In addition, the length of the inclusions was kept at a constant length.
27
to
CO
Dimension [m]
Hybrid Wall Type a b c
T woll 0.95 0.95 0.5
Lwoll 0 0.95 0.5
Inverl L woll 0.95 0 0.5
Verlicol Woll 0 0 0.5
TwoH with Small Toe D. 145 0.95 0.5
Concrete
Retaining
Won
0.5rn i m
0.3m
H
0.7m~~
16m
> Inclusion f 0.0127m / i L_t 2m
r0.0127m 2m
r 0.0127m 2m
b i.99365m
r0.0127m
J 1m 1.00635m
BocUili Soil
Bose Soil
(Foundation Soil)
32.5m
Figure 4.1 Five hybrid wall dimensions and materials
Figure 4.2 Conventional Gravity Twall dimensions and materials
Figure 4.3 MSE wrapped around wall dimensions and materials
1.9619m
r 0.0127m 0.98095m
Concrete 1 Segmental Panel r~  0.0127m r nclusion 1.9619m BoCkliH Soil
1
f  0.0127m 1.9619m
0.2032m t c  0.0127m 1.9619m
0.1524m I f0.1524m 1.13335m
6m
Bose Soil
(Foundation Soil)
f 0.508m
0.1524m
32m
Figure 4.4 MSE segmental wall dimensions and materials
The inclusion length was set to be equal to the wall height of 8 m. The vertical
spacing between the inclusions was approximately 2 m (200 cm).
Besides the concrete facing and inclusions, the other material sitting above
the base soil (or foundation soil) was the backfill material. The backfill was
extended to be two times of the wall height. The backfill length was also kept
constant at 16 m for all eight wall types through out the first stage analysis. There
were two values of backfill depth. Wall types with concrete facing had backfill
depth of 9 m, while MSE wall types had backfill depth of 8 m. Backfill material
occupied the reinforcing zone reinforced by the inclusions and the retaining zone
behind the monolithic mass.
Foundation soil was the support for materials above ground surface, and it
was set on a fixed base. The total length of the foundation soil was 32.5 m.
Approximately 16 m was extended in front of the wall face, while the other 16 m
was then extend to the back of the wall face. The depth of the foundation soil was
6 m below ground surface and 5 m below the backfill base for the concrete facing
wall types. For MSE wall types, the foundation soil depth was kept at 6m.
Foundation soil was attached to the fixed base. The input ground motions were
then applied to the fixed base.
As for the second stage of the preliminary study, six hybrid wall
configurations were deployed. The dimensions of these six hybrid walls are
shown in Figure 4.5. The wall height was remained at 8 m. Similar to the hybrid
walls analyzed in the first stage analysis, these six hybrid wall configurations also
had the same wall stem thickness of 50 cm and wall footing thickness of 70 cm.
The base length for the wall footing was varied according to six combinations of
heel length and toe length that were proportional to the wall height. Figure 4.5
shows these base length combinations as well. Inclusions vertical spacing and
their lengths were the same as hybrid walls in the first stage analysis. Dimensions
32
u>
u>
T
Hybrid Woll Type Dimension (m]
Heel Length Toe Length o b c
15% H 1.5% H 0.12 0.7 0.5
15% H 5.0% H 0.4 0.7 0.5
15% H 10.0% H 0.0 0.7 0.5
15% H 0.0% H 0 0.7 0.5
10% H 1.5% H 0.12 0.3 0.5
25% H 1.5% H 0.12 1.5 0.5
Concrete
Retoining
Woll
0.5m
H=>8m
(Woll Height)
0.3m r:
Bose Soil
(foundoUon Soil)
0.7m~y~
Toe Length
16m
r 0.0127m
I r0.0127m
r0.01 27m
O.OI27m
Heel Length
2m
1.99365m
1.00635m
5m
32.5m
Figure 4.5 Six hybrid wall dimensions and materials
of backfill and foundation soil were also the same as the hybrid walls in the first
stage analysis.
4.3 Ground Motions used in Preliminary Study
Two input ground motions (acceleration time histories) were used in the
preliminary study. Ground motion record from Loma Prieta Earthquake was
selected as the first input acceleration time history in the analysis. This Loma
Prieta Earthquake ground motion amplitude was then amplified by 1.5 times to
serve as the second ground motion. With amplitude amplification, the second
ground motion had peak ground acceleration (PGA) 1.5 times higher than the
PGA of the original Loma Prieta ground motion record. The purpose of such
amplification is to have two comparable ground motion records with one being
stronger than the other. These two ground motions had the same frequency
content and duration, and the only difference was the acceleration amplitude. In
the first stage of the preliminary study, eight wall types were analyzed using these
two ground motions. Performances of the eight wall types could be compared
with respect to these two ground motions. In the second stage of the preliminary
study, six wall configurations would then be compared using only the original
Loma Prieta ground motion.
The original Loma Prieta ground motion had PGA value of 0.478 G, while
the second ground motion with amplitude amplification factor of 1.5 had PGA
value of 0.717 G. Note that G is the unit for 1 gravitational acceleration of 9.81
m/sec2. Loma Prieta Earthquake had the Richter Local Magnitude of 7.0. The
duration of both ground motions remained at 40.0 seconds in this preliminary
study. The time increment was 0.05 sec, and the total number of time steps for
both motions was 800. PGA occurred at the time of 4.05 sec. The input ground
motions were applied at the fixed base of the foundation soil. The acceleration
34
time history plots for the original and amplified Loma Prieta are shown in Figure
4.6.
4.4 Material Models and Input Parameters
In the preliminary study, four different materials were used in the analysis
to denote the four components of the hybrid wall system. These components were
wall facing section, foundation soil, reinforcing inclusions, and the backfill soil.
The wall facing section had properties of concrete material, except the MSE
wrapped around wall in the first stage analysis that had no facing section. The
concrete material was designated with elastic material model. Concrete material
could thus deform elastically with applied loads. Medium strength concrete
material properties were adopted for the concrete section. The density of the
medium strength concrete was 2320 kg/m3, and the modulus of elasticity was 25
GPa. The Poissons ratio of the medium strength concrete was 0.12.
Another material that employed the elastic material model was the
foundation soil. The foundation soil had density of 2100 kg/m3. The modulus of
elasticity and Poissons ratio were 110,000 kN/m2 and 0.35, respectively. This
combination of modulus of elasticity and Poissons ratio represented the dense
sand and gravel soil type. Table 6.1 gives typical values of modulus of elasticity
and Poissons ratio for various materials. The foundation material parameters
were kept constant through out the preliminary study. The only study item related
to the foundation soil was bearing capacity underneath the concrete wall footing.
Having a dense granular soil type as the stiff foundation soil, analysis could be
emphasized more on interactions in the system above the ground surface, and in
turn the effect of foundation stiffness was eliminated.
Elastic material model was also used for the tensile inclusion with
modulus of elasticity of 3,100,000 kN/m2 and Poissons ratio of 0.15. The density
35
0.8
0.6
0.4
0
 0.2
e
o
v 0
o
o
<
0.2
0.4
0.6
Acceleration Time History
Loma Prieta Earthquake
1 1 1 l~ Richter Local Magnitude (ML) = 7.0 Duration = 40 sec. dt = 0.05 sec.
r
M i c flk/UA.
JL l i I K
I TTj
10
20
Time (sec)
30
40
Figure 4.6a Original Loma Prieta acceleration time history
0.8
0.6
0.4
S 0.2
0.2
0.4
0.6
Acceleration Time History
Modified Loma Prieta Earthquake
zsz
Richter Local Magnitude (ML) = 7.0
Duration = 40 sec.
dt = 0.05 sec.
PGA = 0.717713G @ 4.05 sec.
10
20
Time [sec]
30
40
Figure 4.6b Modified Loma Prieta acceleration time history
36
was 1030 kg/m3. The tensile inclusion was comprised of hexahedron brick
elements. With hexahedron brick element, the thickness of inclusion was limited
to 1/4 inch (0.653 cm). Compared with commercially available geosynthetic
reinforcement products, this proposed inclusion thickness was considered large.
This unusual inclusion thickness was introduced to avoid divergence of the
numerical solution. If the thickness of inclusion element becomes considerably
smaller (i.e. aspect ratio of element length to thickness 1) than the neighboring
backfill element, then the convergence of the numerical solution was not possible.
In addition, the length of inclusion was set to be equal to the height of the
retaining wall. The inclusion length in the analysis was also larger than the
reinforcement length in geosynthetic reinforced soil structure practice. The
inclusion length being so long was initially intended to capture the interaction
between backfill soil and inclusion. The vertical spacing between tensile
inclusion in the preliminary comparative analysis was 2 m (200 cm), which was
also larger than the vertical spacing in typical geosynthetic reinforced soil
structures. With less layers of inclusion, the analysis time was greatly reduced.
Note that the 2 m spacing could compensate the large inclusion thickness to yield
a more realistic results.
The only material that used RambergOsgood Elastoplastic Model other
than the Elastic Material Model in the analysis was backfill material. In the
preliminary study of both stages, RambergOsgood Elastoplastic Model input
parameters were adopted from the research conducted by Thanasupsin (1998). A
rather stiff backfill soil was specified in Thanasupsins thesis study. The bulk
modulus had a value of 1,595,000 kN/m2. In the detailed study programme of the
hybrid wall subjected to strong ground motion of Chapter 6, the RambergOsgood
Elastoplastic Model input parameters would be changed according to the newly
adopted backfill material properties. All four material types and their
corresponding material model parameters were summarized in Table 4.1.
37
4.5 Sliding Interfaces and Boundary Conditions
Sliding interfaces were introduced wherever contacts between two
material types were present. Sliding interfaces were introduced between
contacting surfaces of foundation soil and concrete wall section, foundation soil
and backfill soil, concrete wall section and backfill soil, and backfill soil and
reinforcing inclusions. All sliding interfaces in the preliminary study had constant
static coefficient of friction. The value of static coefficient of friction was 0.5.
The coefficient of friction would be changed in the detailed study of hybrid wall
in chapters to follow.
The boundary conditions in the analyses are shown in Figure 4.7. Plane
strain condition was used in the preliminary study. All wall types and
configurations had a unit width and constrained zdirection displacement. Note
that zdirection is normal to the x and y axes shown in Figure 4.7. Roller
condition was applied at boundaries perpendicular to xaxis. In the case of roller
condition, nodes at the boundaries were constrained in both x and z displacement,
but nodes were free in y displacement. The fixed boundary condition was applied
at the base of the foundation soil. In fixed boundary condition, x, y, and z
displacement and rotation were constrained.
4.6 Data Analyses
All NIKE3D outputs were in terms of resulting quantity versus time
history. As mentioned in Chapter 3, gravity load was applied linearly from 0 to
10 second in the time history with time increment of 0.1 second. Dynamic loads
(input ground motions) would start after time history of 10 seconds. Since the
input ground motions used in the preliminary study had duration of 40 seconds, so
the entire analysis duration was 50 seconds. Static analysis results were selected
at time history of 10 second. The dynamic analysis results were selected from
38
Table 4.1 Material model parameters used in preliminary study
Eloslic Malenol Model:
Moleriol Nome Density [kg/m 3] Modulus of Eloslicity. E [MN/m2] Poisson's ratio, v
Concrele 2320 25000 0.12
Foundolion Soil 2100 1 10 0.35
Inclusion 1030 3100 0.15
Romberg Osgood Materol Model:
Moleriol Name Density [kg/m 3] Reference Sheor Stroin (10) Reference Shear Stress [N/m2] Stress Coefficient Stress Exponent Bulk Modulus [MN/m2]
Backfill Soil 2093.9 0.1092 38830 0.86 2.16 1595
/ J
2
/^V777777777777777777777777777777777777777777777V^
Figure 4.7 Boundary conditions in preliminary analyses
39
rest of analysis time history. Analysis results of hybrid Twall subjected to the
original Loma Prieta input ground motion were used as examples to demonstrate
data reduction procedures adopted in the preliminary study. Figure 4.8 shows the
elements and nodes selected for the data reduction in hybrid Twall; similar
element and node selections were made for other walls.
Stress Imparted on Wall Facing Section
Stress imparted on wall facing section by the backfill soil was determined
from the analysis outputs. Backfill soil elements next to the wall section in the
backfill soil mesh were selected for the lateral earth pressure and soil thrust
calculations. Backfill soil element stress in xdirection denoted stress exerted on
the wall facing section by that very backfill soil element. The positive stress
value represented tension, while negative stress value represented compression.
Since granular soil material cannot sustain much tensile stress, thus tensile stress
within soil is considered to have zero stress. Compressive stress was used for the
data reduction. Element normal stress in xdirection (or xstress) for each backfill
element behind the wall section could be connected to represent the lateral earth
pressure imparted on the wall section statically and dynamically. Integration of
the area under the lateral earth pressure curve along the wall depth determined the
soil thrust imparted on the wall section.
Sets of data reduction for hybrid Twall are shown in Figure 4.9, 4.10, and
4.11. Figure 4.9 shows the lateral earth pressure imparted by the backfill soil
element on the wall section both statically and dynamically. With reinforcing
inclusions attached to the wall section, inclusion element xstress also contributed
to stress imparted on the wall section. Stress distribution was laying against the
back face of the wall section. In the dynamic analysis of Figure 4.9b, results from
the original Loma Prieta ground motion were depicted. Maximum stress value in
40
o element used for finding xstress j~*j element used for finding ystress node used for finding xdisplocement e
0
0
0
e
0
e
0
"fr
0
0
A A & A A
Figure 4.8 Elements and nodes selected for data reduction
the dynamic analysis time history was selected as the dynamic stress. Both the
element xstress in backfill and inclusion in the dynamic analysis were greater
than the element xstress in static analysis. Note that the backfill element
thickness and inclusion thickness are shown in Figure 4.9 as well.
Individual element thrust was determined from the element xstress by
calculating area under xstress curve. Figure 4.10a shows individual static thrusts
from the backfill element and inclusion element, while Figure 4.10b shows the
dynamic thrusts. Since the inclusion element thickness was much smaller than
the backfill element thickness, the thrusts from inclusion elements were of less
thrust magnitude. It seems that backfill thrusts are pushing wall forward, while
inclusion thrusts are pulling the wall backward. The static and dynamic resultant
thrusts were determined by the summation of individual thrusts. Overturning
moment about the wall base was determined by multiplying each individual thrust
and its moment arm (perpendicular distance from wall base). Summation of all
individual moments gave a resultant overturning moment. The resultant thrust
and overturning moment for the hybrid Twall in static analysis and dynamic
analysis are shown in Figure 4.1 la and Figure 4.1 lb, respectively. Location of
the resultant thrust was then calculated by dividing resultant moment by the
resultant thrust. The locations of static and dynamic resultant thrust are also
shown in Figure 4.1 la and Figure 4.1 lb, respectively.
Bearing Pressure
Bearing pressure underneath the footing served as another index in
evaluating the performance of retaining wall system subjected to earthquake
loading. Element ystress time histories of foundation soil directly beneath wall
footing were extracted from the analysis outputs. The dynamic stress chosen was
the maximum stress in the dynamic analysis time history. Figure 4.12 shows
42
Slolic Anolysis
Elemenl Slress (Sialic Lalerol Earlh Pressure Distribution)
0.0127m 
(inclusion
elemenl
thickness)
0.0127m 
0.0127m
0.0127m
1 m
(bockfill elemenl
thickness)
0.99365m
0.99365m
0.99365m
0.99365m
0.99365m
0.99365m
0.9e73n
0.3m
0.35m
0.35m
667000 N/rn 
(tension)
492000 N/m w
251000 N/m ty
432000 N/m*
1 1400 N/m (compression)
14600 N/m
38000 N/m
16000 N/m
Figure 4.9a Static lateral pressure on hybrid Twall
1 46600 N/m
37000 N/m2
70900 N/m
2
92600 N/m
2
Dynomic Anolysis
Element x Stress (Dynomic Lotergl Earth Pressure Distribution)
1 m
(bockfill element
Ihickness) 1660000 N/
0.0127m 7 0.99365m (tension)
(inclusion 0.99365m
element
thickness) 0.99365m
1700000 N/
0.0127m
0.99365m
0 99365m 1170000 r
0.0127m 0.99365m
0.9673m 1000000
0.0127m r 0.3m ^ 0.33m 0.55m
21 300 N/m2 (compression)
32200 N/m2
16600 N/m2
4 7900 N/m2
9880 N/m2
77300 N/m2
3B700 N/m2
129000 N/m2
I O
146000 N/ml
HI 86300 N/m2
68500 N/m2
Figure 4.9b Dynamic lateral pressure on hybrid Twall
43
Stotic Analysis
Static Thrust Calculated tram Element .Stress
0.0127m 
(inclusion
element
thickness)
0.0127m 
1 m
(bockritl element
thickness)
0.99365m
0.99365m
0.99365m
0.99365m
0.0127m
0.99365m
0.99365m
0.0127m
0.9873m
' 0.3m
' 0.35m
' 0.35m
Figure 4.10a Static thrusts calculated from element stress in hybrid Twall
Dynomic Analysis
Dynomic Thrust Calculated from Element .Stress
0.0127m 
(inclusion
element
thickness)
0.0127m 
0.99365m
(bockfill element
thickness)
0.99365m
0.99365m
0.99365m
0.99365m
2I0B2 N/m
(tension)
21590 N/m
 21300 N/m (compression)
 31996 N/m
 1 6495 N/m
 47596 N/m
9817 N/m
0.0127m
0.99365m
0.99365m
76809 N/m
14859 N/m
38454 N/m
0.9873m
127362 N/m
0.0127m
0 3m
0.35m
0.35m
12700 N/m
 43800 N/m
 30205 N/m
23975 N/m
Figure 4.10b Dynamic thrusts calculated from element stress in hybrid T
wall
44
Stolic Anoiysis
Stolic Thrust ond Static Overturning Moment
0.0127m 
(inclusion
element
thickness)
0.0127m 
1 m
(backfill element
thickness)
0.99365m
0.99365m
0.99365m
0.99365m
0.0127m
0.99365m
0.99365m
0.0127m
0.9873m
' 0.3m
0.35m
0.35m
Figure 4.11a Net static thrust and overturning moment in hybrid Twall
Dynomic Analysis
Dynomic Thrust ond Dynomic Overturning Moment
0.99365m
(bockfill element
thickness)
0.99365m
0.0127m
(inclusion
element
thickness)
0.99365m
0.99365m
0.0127m
0.99365m
0.0127m
0.99365m
0.99365m
0.9B73m
0.0127m
0.3m
0.35m
0.35m
Figure 4.11b Net dynamic thrust and overturning moment in hybrid Twall
45
static and dynamic element ystress from the foundation soil elements, and these
are compressive stress. Element ystress was increased in the dynamic analysis as
earthquake loading was imposed to the system. The maximum element ystress
controlled the bearing capacity of the retaining wall system. The maximum static
bearing stress was 155 kPa, and the maximum dynamic bearing stress was 189
kPa.
Wall Deformations
Four wall deformation layouts were evaluated from the analysis outputs.
Each wall deformation layout was drawn with the corresponding wall top
deformation and wall bottom deformation. These layouts were static wall
deformation, permanent wall deformation, maximum forward wall displacement,
and maximum backward wall displacement. Figure 4.13 shows the four layouts
for the hybrid Twall. Static wall deformation was the wall deformation at the
end of static loading. Permanent wall deformation was then the deformation at
the end of the dynamic analysis. Maximum forward wall displacement was
defined by the maximum forward displacement at the wall top and wall bottom
ever possible in the entire analysis; maximum backward wall displacement was
the maximum backward displacement in the entire analysis.
Wall tilt from vertical was calculated using arctangent of wall top and
bottom deformation difference by the wall height. The four wall tilt angles are
shown and defined in the Figure 4.13. The wall tilt calculation is given by the
following equation.
6 = arctan
^ Ax'
\H)
(4.1)
Ax is the horizontal difference between wall top and wall bottom deformation. H
is the wall height. 0 is the wall tilt from vertical. Four wall tilt angles from
46
vertical were calculated for the four layouts. These wall tilt angles are shown in
Figure 4.12 as well. Static wall tilt and permanent wall tilt were calculated
directly from the corresponding wall top deformation and wall bottom
deformation. For maximum forward wall tilt from vertical, Ax is the horizontal
distance between top maximum forward displacement and bottom maximum
backward displacement. On the other hand, horizontal distance, Ax, between top
maximum backward displacement and maximum bottom forward displacement
was used to calculate maximum backward wall tilt from vertical.
Inclusion Stresses
Inclusion stresses were obtained from the inclusion element xstress
outputs. Similar to backfill soil element, positive xstress represented tension, and
negative was for compression. Inclusion was considered as reinforcement when it
was in tension. Figure 4.14 shows the inclusion xstress distribution, with respect
to element length, both in the static and dynamic analysis for the hybrid Twall.
Four layers of inclusion were arrayed from top to bottom. Top inclusion was
labeled number 1, and bottom inclusion was labeled number 4. As depicted in
Figure 4.14, inclusions had greater tensile stress when subjected to dynamic
loading than with static loading.
Inclusion stress performance was another criteria in evaluating the wall
system performance. Rather than plotting the xstress for all four layers of
inclusion, the maximum tensile stresses occurred at the end of static loading and
during the entire dynamic analysis were selected for the evaluating criteria. The
maximum tensile stress was selected among the four layers of inclusion, and the
location of the maximum tensile stress was considered irrelevant in the
preliminary study of both stages. The static maximum tensile stress was 739 kPa,
and the dynamic maximum tensile stress was 1,700 kPa.
47
4.7 Results
Results of First Stage Analyses
The following section describes the results from first stage analyses.
Stress imparted on wall section, bear capacity, wall deformations, and inclusion
stresses were the four wall performance criterion. Table 4.2, 4.3, 4.4, and 4.5 list
these four wall performance criterion and summarize the results of calculations
with respect to these criterion. Both static and dynamic results were presented.
The Magnitude columns appear in these tables show the magnitude of the
corresponding criterion. Criteria considered in the analysis are shown in the far
left column within each table. Stress magnitudes with negative sign stand for
compression. Deformation with negative sign shows that it is on the left side of
the position before the static analysis starts. Hybrid wall types are abbreviated
with their wall shapes. For example, hybrid Twall is abbreviated with Twall.
Table 4.2 and 4.3 show the responses of eight wall types subjected to the
original Loma Prieta input ground motion and the amplified Loma Prieta input
ground motion, respectively. Table 4.2 and 4.3 exclude the evaluation of
inclusion stresses criteria. Compared to Table 4.2 and 4.3, Table 4.4 and 4.5
include the evaluation of inclusion stresses criterion. Notice that since gravity T
wall of case 5 did not have reinforcing inclusions, so gravity Twall is not listed in
Table 4.4 and 4.5. Similar to Table 4.2 and 4.3, Table 4.4 and 4.5 summarize the
responses of seven wall types subjected to the original Loma Prieta input ground
motion and the amplified Loma Prieta input ground motion, respectively.
In order to differentiate the performance of the eight wall types, a ranking
procedure was adopted. Columns labeled Ranking in the tables were
designated to show the ranking results. A numerical ranking was assigned to each
performance criterion according to its magnitude. For each performance criterion,
the most desirable magnitude would have the highest ranking value, and the least
48
Bearing Pressure at Base of Wall Fooling
vo
(Foundation Soil Element yStress)
Static Anaylsis:
Dynamic Analysis:
ID m c c in n
m n
CM CM
o o o o o o
\ \ . \ , \ N \
\ \
E E E E
n n E t in n
U) n c
rj CM CM sT
o o o o d o
\ \ \ \
\ \
Figure 4.12 Static and dynamic bearing pressure in hybrid Twall
4.22mm 3.5mm
0.49mmJ H  0.15mm
BoUom Stolic
Oeformotion
^\_ BoUom Permonent
Deformation
Top Mok. Top Mov.
Figure 4.13 Hybrid Twall deformation performances
50
Sialic Anolysi$
(Inclusion Element irSlress)
Dynomic Anolysis
(inclusion Element tSlress)
mo*.
o
o.
o>
O
a
CD
o
CL
JL
(N
O)
o
a
jr
to
o
a
n
to
m
Cl
6
Inclusion (lop)
Inclusion j}2
Inclusion Â§Z
 r O
_Q_1 CL run 0. o o o 0
O o Jt JL o
h* CN (0 m
rO O cn to 00 m
00 CD
Inclusion ft 1 (top)
Inclusion ff2
Inclusion ft3
Inclusion ft4 (bottom)
Inclusion ff4 (bottom)
Figure 4.14 Static and dynamic inclusion element stress distribution
desirable magnitude would have the lowest ranking value. Tables (i.e. Table 4.2
and 4.3) that had eight wall types would have 8 as the highest ranking value, and
1 being the lowest ranking value, because eight comparisons could be made. On
the other hand, tables (i.e. Table 4.4 and 4.5) that had seven wall types would
have 7 as the highest ranking value.
Accordingly, the smallest wall thrust is most desirable, and the largest
thrust is least desirable. Therefore the smallest thrust would score with the
highest ranking value of 8 in Table 4.2 and 4.3 and 7 in Table 4.4 and 4.5, and the
largest thrust would then score the lowest value of 1. Similar to the thrusts
imparted on wall section, the smallest bearing pressure, wall deformation, and
inclusion stress are the most desirable and would score a value of 8 or 7
depending on the number of comparisons. Small magnitudes of the evaluating
criteria could lead to the most economical design in engineering practice and
application.
The ranking value determination is described as follows. First, difference
between the highest magnitude and the lowest magnitude of a criterion (or
performance factor) among all wall types is calculated. The difference is then
divided by number of wall types in question to serve as the equal incremental
value. A series of reference scale was then defined by the following equation.
5, = x. + /'
i min
(x X ^
max min
n
(4.2)
where i = 1, 2, 3, ..., n. n is the total number of wall types in question. The
quantity (xmax  )/ is the equal incremental value, where xmax and xmin is the
highest and the lowest magnitude of a criterion, respectively. Note that the last
value in the reference scale is equal to x^x Each 6, is assigned with a ranking
value ric, where k = n, n1, n2, ...,1. 8i values are in ascending order, while the r*
values are in the descending order. Magnitude of a criterion is then compared
52
Table 4.2 Ranking of 8 wall types using original input ground motion
Rankings on Performance of Various Retaining Walls
(Excluding Evaluation of Inclusion Tensile Stress Parameter)
PGA: 0.478475G
Case 1 T*wall Case 2 Lwall Case 3 Invert Lwal Case 4 Vertical wal
Rankina / Meonilude Rankina / Magnitude Rarridna / Maanilude Rankina / Maanilude
Active Soil Thrust (Static) INAnl 2 t 198053 3 / 179297 2 / 194809 4 / 161089
Over Timing Moment (Static) INmAnl 3 ( 397802 3 / 345426 1 / 471991 4 / 287308
Total Active Soil Thrust [NAnl 1 / 397577 2 / 356564 1 / 372980 2 / 366359
Total Over Turrina Moment INmAnl 1 / 1135698 3 / 897867 1 / 1090731 2 / 1018067
Bearina Pressure at Base (Static) INAn*2l 8 / 155000 1 / 214000 8 / 156000 1 / 21S000
Mar Total Bearina Pressure at Base INA*21 e / 189000 1 / 262000 8 / 191000 1 / 265000
Top Deformation (End of Sialic) fml 7 1 0.0004680 1 / 0.0007630 2 / 0.0004710 1 / 0.0007720
Bottom Deformation (End ol Static) Iml 3 / 0.0028900 7 / 0.0027100 2 / 0.0029800 6 / 0.0027600
Too Permanert Deformation Iml 6 / 0.0001540 8 / 0.0000916 8 / 0.0000744 3 / 0.0002370
Bottom Pemanert Deformation (ml 6 / 0.0021300 6 / 0.0020600 7 / 0.0022900 8 / 0.0020600
Top Mannun Forward Displacement (ml 6 / 0.0042200 6 / 0.0040700 S / 0.0042400 7 / 0.0039400
Bottom Maidmum Forward Displacement Iml S / 0.0064100 8 / 0.0061800 3 / 0.0064800 8 / 0.0062000
Too Marl mm Backward Displacement Iml 1 / 0.003S000 3 / 0.0032700 2 / 0.0033500 1 / 0.0035800
Bottom Merimm Backward Displacemenl Iml 8 / 0.0017200 5 / 0.0019500 6 / 0.0015900 5 / 0.0019300
Wal Trl from Vertical {Static) Ideareel 4 / 0.0152916 6 / 0.0123950 2 l 0.0159728 8 / 0.0126560
Wat Tit from Vertical (Permanent) Ideareel 8 / 0.0125796 8 / 0.0136975 7 / 0.0150522 7 / 0.0146232
Mar Forward Wal Til from Vertical Ideareel 8 / 0.0378152 7 / 0.0383245 6 / 0.0371149 8 / 0.0373696
Min. Backward Well Till from Vertical Ideareel 3 / 0.0630890 6 / 0.0601605 4 / 0.0625797 4 / 0.0622614
Total Poirt 90 ee 79 80
Case 5 orav. Twal Case 6 MSE warperoutd wal Case 7 Twal with smal toe Cased MSE seonertalwal
Rankina / Magnitude Rankina / Maanilude RenMno Maori lude Rankina Msarritude
Active Sail Trims* (Static) INAnl 1 t 219044 8 / 82210 3 175188 6 133229
Over Tunina Moroert (Static) INmAnl 2 / 406825 8 / 84627 4 265109 4 303246
Total Active Soil Thrust (NAnl 1 / 397212 8 / 196261 3 342659 7 245797
Total Over Ttfrino Momert INmAnl 3 / 917323 8 / 446210 3 887550 5 784800
Bearina Pressrn et Base (Static) INAn*21 8 / 153000 3 / 193000 3 196000 1 210000
Max. Total Bearina Pressure et Base INAnA21 6 / 188000 4 / 234000 3 242000 2 255000
Too Deformation (End of Static) (ml 8 / 0.0008630 3 / 0.0008070 2 0.0007100 6 0.0003340
Bottom Deformation (End of Static) (ml 1 / 0.0030400 8 / 0.0026200 6 0.0027600 7 *0.0027200
Too Permanert Deformation fml 1 / 0.0002980 1 1 0.0002610 8 0.0000820 7 0.0001300
Bottom Permanert Deformation Iml 6 / 0.0024000 8 / 0.0021100 8 0.0020800 1 0.0033600
Top MaxJmm Forward Displacement Iml 1 / 0.0052900 8 / 0.0037300 6 0.0041400 9 0.0035800
Bottom Maximum Forward Displacemert Iml 3 / 0.0065000 6 / 0.0063900 8 0.0061900 1 0.0066500
Too Marirrun Backward Displacemert Iml 8 / 0.0023700 6 / 0.0023700 2 0.0033900 e 0.0026700
Bottom Maximum Backward Displacement Iml 8 / 0.0016700 1 / 0.0023200 5 / 0.0019300 4 / 0.0020300
Wal Til from Vertical (Static) Ideareel 6 / 0.0137319 7 / 0.0129847 7 0.0130507 1 / 0.0170885
Wei Til from Vertical (Permanert) Ideareel 8 / 0.0133817 8 / 0.0130992 8 0.0127197 1 0.0231332
Max. Forward Wal Til from Vertical Ideareel 1 / 0.0443067 2 ! 0.0433299 7 0.0386428 5 t 0.0401787
Min. Backward Wal Til from Vertical Idee?eel 8 / 0.0564682 4 / 0.0627389 5 0.0609682 1 0.0667496
Total Poirt 62 103 91 75
Table 4.3 Ranking of 8 wall types using modified input ground motion
Ranting; on Performance of Various Retailing WaH
(Excluding Eva ballon of Inclusion Tensile Stress Parameter)
PGA: 0.717713G (Input Acceleration Magnitude Amplified by 1.5)
Case 1 T*weB Case 2 Lwal Case 3 Invert Lwal Case 4 Vertical wal
Rankino 7 Macxiitude Rartona / Meanilude Rankino / Maonitude Rankino 7 Meanilude
Active Soil Thrust (Static) INAnl 2 / 198053 3 / 179297 2 / 194809 4 / 161089
Over Tumi no Momert (Stalk) (NmAnl 2 / 397802 3 / 345426 1 / 471991 4 / 287308
Total Active Soil Thrust INAnl 1 / 461193 2 / 424052 2 7 423986 2 7 382601
Total Over Turrina Moment INmAnl 1 / 1335023 2 7 1195407 1 / 1264601 3 / 1059980
Bearino Pressure at Base (Slatic) INAn*21 6 / 155000 1 / 214000 8 7 156000 1 7 215000
Max. Total Bearino Pressure at Base IN/m*21 8 / 215000 6 7 294000 6 / 210000 6 7 296000
Too Deformation (End of Static) (ml 6 / 0.0004880 2 / 0.0007630 7 / 0.0004710 2 / 0.0007720
Bottom Deformation (End of Static) fml 3 / 0.0028900 7 / 0.0027100 2 / 0.0029800 6 / 0.0027600
Tod Permanent Deformation Iml 3 / 0.0008310 4 / 0.0006100 6 / 0.0004620 7 / 0.0003770
Bottom Permanent Deformation fml 8 / 0.0027500 8 / 0.0023600 8 / 0.0025700 8 7 0.0024300
Tod Madman Forward Oisolacement (ml 2 / 0.0072600 4 7 0.0066500 2 / 0.0073300 5 / 0.0064500
Bottom Madman Forward Oisolacement fml 8 / 0.0093600 8 7 0.0092800 8 / 0.0093900 8 / 0.0092300
Tod Madmun Backward Displacement Iml 1 / 0.0055900 2 / 0.0055300 2 7 0.0054300 1 7 0.0056500
Bottom Mailman Backward Displacement Iml 7 / 0.0038900 6 / 0.0040200 8 / 0.0037400 7 / 0.0039700
Wat Tilt from Vertical (Stalk) fdeareel 3 / 0.0152916 7 7 0.0123950 2 / 0.0159728 7 / 0.0126560
Wal TIK from Vertical (Permanert) fdegreel 8 / 0.0122167 8 / 0.0098676 7 / 0.0134199 7 / 0.0130698
Max. Forward Wal Tilt from Vertical fdeareel 4 / 0.0709831 7 / 0.0679273 4 / 0.0704738 6 / 0.0663358
Min. Backward Wal Til from Vertical fdeareel 7 / 0.09S1746 B l 0.0942833 8 / 0.0943470 7 7 0.0947289
Total Poirt 82 86 86 93
Case 5 orav. Twal Case 6 MSE warp*around waD Case 7 Twafl with smel toe Case8 MSE seonertal wal
RanWno / Maonitude Rantino / Magnitude RenWna Maonitude Rankino Marntude
Active Soil Thrust (Static) INAnl 1 / 219044 8 / 62210 3 175188 6 133229
Over Turlna Momert (Static) INmAnl 2 / 406825 0 / 64827 4 285109 4 303246
Total Active Soil Trust INAnl 1 7 475843 1 7 462869 1 431143 8 99960
Total Over Turrina Momert (NmAnl 2 7 1178234 2 7 1177038 2 1183435 8 543527
Bearino Presstae at Base (Static) INAn*21 8 / 153000 3 / 193000 3 198000 1 7 210000
Max. Total Bearino Pressure at Base NAnA2l 8 7 206000 1 7 489000 6 280000 6 283000
Tod Deformation (End of Static) Iml 1 / 0.0006830 2 / 0.0008070 3 0.0007100 8 0.0003340
Bottom Deformation (End of Static) fml 1 / 0.0030400 8 / 0.0026200 6 0.0027600 7 0.0027200
Too Permanent Deformation [ml 1 / 0.0012000 B 1 0.0001660 3 0.0008410 6 0.0002480
Bonom Permanent Deformation Iml 7 / 0.0028800 1 7 0.0050500 8 0.0024100 2 0.0046300
Top Mailman Forward Dtsotocemenl Iml 1 7 0.0078700 8 7 0.0052300 4 0.0067300 8 0.0052600
Bottom Madman Forward Displacement Iml 7 / 0.0096500 6 / 0.0097500 8 / 0.0092400 1 0.0111000
Top Maid man Backward Disotacemert Iml 8 / 0.0047400 3 7 0.0053400 1 7 0.0056200 8 0.00S0500
Bottom Maiiman Backward Displacement fml 8 / 0.0037400 1 7 0.0046600 6 / 0.0040000 5 0.0041800
Wal Tit from Vertical (Static) Iderreel S 7 0.0137319 8 / 0.0115419 6 7 0.0130507 1 0.0170865
Wal Tit from Vertical (Permanent Ideoreel 8 / 0.0106952 2 / 0.0310925 8 / 0.0099886 1 0.0349361
Max. Forward Wal Tit from Vertical fdeareel 1 / 0.0739115 4 7 0.070B319 6 / 0.0683093 7 0.0677522
Min. Backward Wal Tit from Vertical Ideoreel 6 7 0.0916095 3 7 0.1000740 8 7 0.0946016 1 0.1156657
Total Poirt 78 77 86 90
Table 4.4 Ranking of 7 wall types using original input ground motion
Rankings on Performance of Various Retaining Wals
(Incfcrfng Evacation of Inclusion Tensile Stress Parameter)
PGA: 0.478475G
Case 1 TwaB Case 2 Lwafl Case 3 Invert LwaD Case 4 Vertical wal
Rank) no 1 Maonitude Rankino / Maonitude Rankino / Maonitude Rankino t Maordtude
Active Soil Thrust (Static) (N/ml 1 / 168053 2 / 179267 1 / 194806 3 / 161086
Over Tmrino Moment (Static) INm/ml 2 / 397802 3 / 345426 1 / 471991 4 / 267308
Total Active Soil Thrust INfml 1 / 367577 2 / 356584 1 / 372960 2 / 366359
Total Over Ttrrina Moment INmfm] 1 / 1135898 3 1 897887 1 / 1090731 2 / 1018067
Bearing Pres so e at Base (Static) IN/m*2l 7 1 155000 1 1 214000 7 / 156000 1 / 215000
Mae. Total Bearino Pressure at Base INfm*21 7 1 189000 1 / 262000 7 / 191000 1 / 265000
Top Deformation (End of Sialic) fml S I 0.0004660 1 / 00007630 S / 0.0004710 1 / 0.0007720
Bottom Deformation (End of Static) Iml 2 / 0.0028600 8 / 0.0027100 1 / 0.0029800 5 / 0.0027600
Top Permanert Defonnalion (ml 5 / 0.0001540 7 / 0.0000916 7 / 0.0000744 2 / 0.0002370
Bottom Permanent Defonnation Iml 7 / 0.0021300 7 1 0.0020600 6 / 0.0022900 7 / 0.0020600
Top Mariimm Forward Disolacement fml 1 / 0.0042200 2 / 0.0040700 1 / 0.0042400 4 1 0.0039400
Bottom Marinin Forward Disolaeemert Iml 4 / 0.0084100 7 / 0.0001800 3 / 0.0064600 7 / 0.0062000
Tod Marimun Backward Displacement Iml 1 / 0.0035000 2 / 0.0032700 2 / 0.0033500 1 / 0.0035800
Bottom Marinin Backward Disolacement Iml 0 / 0.0017200 4 f 0.0019500 7 / 0.0015900 4 / 0.0016300
Wal Tit from Vertical (Sialic) (decree! 3 / 0.0152916 7 / 0.Q1236S0 2 / 0.0159728 7 / 0.0126560
Wal Tit from Vertical (Permanent) Ideoreel 7 / 0.0125796 7 / 0.0136975 6 / 0.0150522 6 / 0.0146232
Mai. Forward Wal Tit from Vertical Idearee] 7 / 0.0378152 8 / 0.0383245 7 / 0.0371149 7 / 0.0373696
Min. Backward Wal Til from Vertical (decree) 4 . / 0.0030890 7 / 0.0801605 5 / 0.0625707 5 / 0.0822614
Mai. InckisJon Tensile Stress rEnd of Static) IN/rrr*2l 3 / 739000 4 / 698000 7 / 565000 e / 642000
Max. Total Inclusion Tensile Stress (N/m*21 6 / 1700000 6 / 1750000 6 / 1660000 7 / 1390000
Total PcrfrX 80 85 83 82
Case 8 MSE waroaround wal Case 7 Twal with smal toe Case 8 MSE seomental wall
Rankino / 1 i Rankino Maonitude Rank) no Maonitude
Active Sell Thrust (Static) fN/ml 7 / 82210 2 175188 4 133226
Qrer Tummo Momerd (Static) fNm/ml 7 / 64827 4 2BS106 4 303248
Total Active Soil TTvusf (Nfrnl 7 / 168281 2 342059 6 245797
Total Over Turrina Momerd ffkn/ml 7 / 448210 3 887550 4 784800
Bearino Pressure at Base (Static) fN/m*21 3 f 193000 2 198000 1 / 210000
Max. Total Bearino Pressire at Base rNfrrr*2l 3 1 234000 3 242000 1 255000
Top Defamation (End of Static) Iml 1 1 0.0006070 2 0.0007100 7 0.0003340
Bottom Deformation (End of Static) Iml 7 / 0.0028200 S 0.0027600 6 0.0027200
Too Permanent Defonnation Iml 1 t 0.0002610 7 0.0000620 6 0.0001300
Bottom Permanerd Deformation (ml 7 t 0.0021100 7 0.0020600 1 / 0.0033600
Top Maxlmm Forward Disolacement Iml e t 0.0037300 2 0.0041400 7 0.0035800
Bottom Marinin Forward Dtsotaeemerd Iml 4 / 0.0063900 7 0.0061900 1 / 0.0066500
Tod Marinwn Backward Oisobeemerd (ml 7 / 0.0023700 2 0.0033600 e 0.0026700
Bottom Marinin Backward Disolaeement (ml 1 / 0.0023200 4 0.0016300 3 0.0020300
Wal Til from Vertical (Static) Iderree) 7 / 0.0126647 7 0.0130507 1 0.0170685
Wal Til from Vertical (Permanerd) Ideoreel 7 t 0.0130992 7 0.0127167 1 / 0.0231332
Max. Forward Wal Til from Vertical Ideoreel 1 / 0.0433299 6 0.0368428 4 0.0401787
Mn. Backward Wal Til from Vertical Ideoreel S l 0.0827386 7 0.0609882 1 / 0.0607499
Max. InefcisJon Tensile Stress (End of Static) IN/m*2l 3 / 754000 4 722000 1 / 835000
Max. Total tneknlon Tensile aress INhn21 7 / 1650000 7 1460000 1 / 3270000
Total Port 68 60 68
Table 4.5 Ranking of 7 wall types using the modified input ground motion
Rankings on Performance of Various Retaining WaBs
(Inducing Evaluation of Inclusion Tensile Stress Parameter)
PGA: 0.7177130 (Input Acceleration Magnitude Amplified by 1.5)
Case 1 Twal Case 2 Lwafl Casa 3 Invert Lwal Case 4 Vertical wal
RanMno / Maoritude RarJdna 1 Magnitude Ranking / Magnitude Rank) no 1 Macrilude
Active Soil Thrust (Static) IN/ml 1 / 168053 1 / 179297 1 / 194609 3 / 161089
Om Tumi no Moment (Static) iNmfml 1 / 397802 2 / 345426 1 / 471991 3 / 287308
Total Active Soil Thrmi IN/ml 1 1 461193 1 / 424052 1 / 423988 2 / 382801
Total Over Turirto Momerd INm/ml 1 / 1335023 1 / 1195407 1 / 1284001 6 l 1059960
Bearino Pressue at Base (Static) IN(m*2l 7 l 155000 1 / 214000 7 / 158000 1 / 215000
Max. Total Bearino Pressue al Base IN/m*21 7 1 215000 5 1 204000 7 / 210000 5 / 268000
Top Deformation (End of Sialic) Iml 5 1 0.0004880 1 / 0.0007630 5 / 0.0004710 1 / 0.0007720
Bottom Deformation (End of Static) Iml 2 t 0.0028900 6 / 0.0027100 1 / 0.0029800 5 / 0.0027600
Too Permanerd Deformation Iml 1 / 0.0008310 1 / 0.0008100 4 1 0.0004620 5 l 0.0003770
Bottom Pemunerd Deformation Iml 6 / 0.0027SOQ 7 / 0.0023600 7 / 0.0025700 7 / 0.0024300
Too Maximun Forward Disotacemerd 1ml 1 / 0.0072800 3 / 0.0086500 1 1 0.0073300 3 1 0.0064500
Bottom Marinun Forward Dtsotacement Iml 7 / 0.0093600 7 / 0.0092600 7 l 0.0093900 7 / 0.0092300
Too Maximun Backward Disolacement Iml 1 / 0.00SS600 2 / 0.0055300 3 1 0.0054300 1 / 0.0058500
Bottom Maxinun Backward Disotacemerd (ml 8 1 0.0030900 5 t 0.0040200 7 1 0.0037400 6 / 0.0039700
Wal Til from Vertical (Static) Fdeareel 3 f Q.01S2916 6 / 0.0123950 2 / 0.01S6728 6 / 0.0126560
Wat Tit from Vertical (Permanerdl (deoreel 7 ( 0.0122187 7 f 0.0098676 7 t 0.0134199 7 / 0.0130696
Max. Forward Wal Til from Vertical (deoreel 1 / 0.0709831 5 f 0.0679273 1 / 0.0704736 7 / 0.0663358
Min. Backward Wal Til from Vertical (deoreel 7 / 0.0951746 7 / 0.0942833 7 1 0.0943470 7 / 0.0947289
Max. Inclusion Tensile Stress (End ol Static) INtm*21 3 \ 739000 4 f 698000 7 1 595000 8 / 642000
Max. Total Inclusion Tensile Stress INlm*2l 7 1 1950000 7 / 1800000 8 / 2420000 8 / 2100000
Total Point 75 79 83 94
Cased MSE waroaroutd wal Case 7 TwaB with smal loe Case 8 MSE seomerdal wal
RanMno 1 Maori tude Ranking Magnitude Ranking Magnitude
Active Soil TNust (Static) fN/ml 7 1 82210 2 175188 4 133229
Dver Turing Moment (Static) INnVml 7 / 84627 3 285109 3 303246
Total Active Soil Thrust INAnl 1 l 462866 1 / 431143 7 96960
Total Over Tumino Momerd IfkiVml 1 / 1177038 1 / 1183435 7 543527
Bearira Pres sue at Base (Static) fN/m*21 3 l 193000 2 168000 1 / 210000
Max. Total Bearino Pres sue at Base IN/m*21 1 / 489000 a 280000 6 283000
Top Deformation (End of Static) Iml 1 / 0.0006070 2 0.0007100 7 0.0003340
Bottom Deformation (End of Static! Iml 7 / 0.0026200 5 0.0027800 6 0.0027200
Too Pemanert Deformation (ml 7 / 0.0001880 1 / 0.0008410 7 0.0002480
Bottom Permanerd Deformation Iml 1 / 0.0050500 7 0.0024100 2 0.0046300
Too Maximun Forward Disotaeemerd Iml 7 / 0.0052300 3 0.0087300 7 0.0052800
Bottom Maximun Forward Dhokcemert Iml 6 1 0.0097500 7 0.0092400 1 / 0.0111000
Too Maidmun Backward Disotaeemerd Iml 4 1 0.0053400 1 1 0.0056200 7 0.0050500
Bottom Maxinun Backward Disotaeemerd (ml 1 1 0.0046600 6 0.0040000 4 0.0041800
Wal Til Pom Vertical (Statfe) fdeueel 7 ! 0.0115419 6 0.0130507 1 0.0170885
Wal TiR from Vertical (Permanerdl (deoreel 2 1 0.0310925 7 0.0099866 t / 0.0349381
Max. Forward Wal Til from Vertical (deoreel 1 / 0.0708319 S 0.0663093 5 0.0677522
Mn. Backward Wal Tit from Vertical idecreel 3 / 0.1080740 7 0.0946016 1 / 0.1156657
Max. Inehfslon Tensile Stress (End of Stalk) fN/nr2l 3 / 754000 4 722000 1 / 835000
Max. Total Inckislon Tensile Stress fWm*2l 1 / 4380000 7 1650000 8 2190000
Total Polrd 71 83 04
within the reference scale. Magnitude of a criterion was also assigned with the
ranking value r* with the following comparative condition.
S,
where Xj is the magnitude of a criterion and j = 1, 2, 3, ..n. If the condition is
true, then Xj would be designated with the ranking value rk. Figure 4.15 shows the
ranking value determination of the static soil thrust criterion for the hybrid Twall.
Following the above procedure, each wall type is assigned a ranking value
for each criterion (or performance factor) considered in the preliminary study.
Total Point appeared at the end of Ranking column shows the summation of
all ranking values for a wall type. The summations of ranking values were used
as indexes to compare the performance of all the wall types. The wall type with
the highest points is considered the wall type with the most desirable over all
performance. Note that the criteria evaluated all had the same weight. So,
summation of ranking values could only give a general performance of a wall
type subjected to both static and dynamic loading.
Weight factors was implemented to the ranking values of several criteria.
Selected criteria could control the ultimate performance of hybrid walls. These
criteria included total (dynamic) soil thrust, total (dynamic) overturning moment,
maximum total (dynamic) bearing pressure at wall base, the permanent wall tilt
from vertical, and maximum total (dynamic) inclusion tensile stress. A weight
factor of 1.5 was applied to total soil thrust, total overturning moment, maximum
total bearing pressure at wall base, and maximum total inclusion tensile stress.
Weight factor of 1 was applied to permanent wall tilt from vertical criterion.
Criteria with weight factor of 1.5 were considered more dominant than weight
factor of 1 in evaluation of the ultimate wall performance. Summations of the
weighted ranking values were computed and are listed in Table 4.6 and 4.7 for
original and modified input ground motion, respectively. Note that gravity Twall
57
Ranking Value Determination lor Static Soil Thrust Criterion
Slolic Soil Thrust *i
T wall 198055 N/m X 1
L woll 179297 N/m *2
Invert Lwall 194809 N/m * J
Verticol wall 161089 N/m X4
Gravity Twall 219044 N/m X 5
MSE wrapped around wall 82210 N/m x6
Twall with small toe 175188 N/m X 7
MSE segmental wall 133229 N/m X 6
xmo, = 219044 N/m
Xmin = 82210 N/m
n = 8
= 17104.25 N/m 6, = xmin + i ( *m' Xmin )
n
<5i r k
<51 99314.25 N/m ' 8 8
<52 116418.5 N/m r 7 7
<53 133522.75 N/m r 6 6
64 150627 N/m r 5 5
<55 167731.25 N/m r 4 4
<5e 184835.5 N/m r 3 3
67 201939.75 N/m r 2 2
<5a 219044 N/m r 1 1
<5; < x j < 6 i+1 x j r n_l+,
Static Soil Thrust Xj r lr
Twall 198053 N/m X 1 2
Lwall 179297 N/m X 2 3
Invert Lwall 194809 N/m X 3 2
Vertical wall 161089 N/m X4 4
Gravity T wall 219044 N/m X5 1
MSE wrappedaround wall 82210 N/m x6 8
Twall with small toe 175188 N/m <7 3
MSE segmental wall 133229 N/m X B 6
Figure 4.15 Example of determining ranking value for static thrust criterion
58
was not included in Table 4.6 and 4.7 due to its poor rank status appeared in Table
4.2 and 4.3. MSE wraparound wall was showed in Table 4.6 and 4.7, but it was
not evaluated due to its poor longterm performance and aesthetic appearance.
MSE segmental wall was showed but not evaluated in Table 4.7 due to the large
wall displacement when subjected to relatively large earthquake loading.
Results of Second Stage Analyses
Hybrid Twall with small toe was ranked first on wall performance
evaluation in the first stage analyses, and the scores are shown in Table 4.6 and
4.7. Thus, the hybrid Twall with small toe was selected as the wall type for the
second stage analyses. The purpose of the second stage analyses was to
determine the most desirable wall configuration. Hence wall footing length,
specifically toe length and heel length, was varied so that one wall configuration
of the best performance could be used in the detailed study. Figure 4.5 in section
4.2 of Study Parameters shows the six wall configurations adopted in the second
stage analyses.
The toe length and heel length were varied according to the percentage of
wall height. The wall height, H, for all six configurations remained at 8 m. Four
wall configurations had the same heel length of 15% wall height and the only
variance being the toe length; four different toe lengths were 1.5% H, 5% H, 10%
H,andO%H. The 0% H was simply the Lwall. The other two configurations
had the same toe length of 1.5% H, and the heel lengths were 10% H and 25% H.
Dimensions of the six wall configuration are again shown in Figure 4.5.
Digital outputs were plotted in Figure 4.16, 4.17,4.18, 4.19, and 4.20 for
the evaluation criteria of the total soil thrust, total overturning moment, maximum
total bearing pressure, permanent wall tilt from vertical, and maximum total
inclusion tensile stress, respectively. In each figure, two plots were presented.
59
Table 4.6 Weighted ranking of 7 wall types using original input ground
motion
Rankings on Performance of Various Retaining Walls
(Including Evaluation of Inclusion Tensile Stress Parameter)
PGA: 0.478475G
Case 1 Twall Case 2 Lwall Case 3 Invert Lwall Case 4 Vertical wall
Ranking Magnitude Ranking Magnitude Ranking Magnitude Ranking Magnitude
Total Actto Sou Thrust IN/ml X 1.5 * 1.5 .397577 2 x 1.5 a 3 >356564 1 x 1.5 1.5 372980 2 x 1.5 a 368359
Total Over Turning Moment INm/ml X 1.5 1.5 .1135698 5 x 1.6 a 7.5 897867 1 x 1.5 1.5 1090731 3 x 1.5 4.5 1018067
Max Total Beartnq Pressure at Base IN/m*2l 6 x 1.5 9 .189000 X 1.5 a 1.5 262000 6 X 1.5 9 .191000 1 X 1.5 1.5 265000
Wall m from Vertical (Permanent) Idea reel 6 x 1 6 0.0125796 6 x 1 a 6 0.0136975 5 x 1 6 0.0150522 5 X 1 5 0.0146232
Max. Total Inclusion Tensile Stress IN/m*21 6 x 1.5 9 1700000 5 x 1.5 a 7.5 1750000 6 x 1.5 9 1660000 6 x 1.5 9 1390000
Total Point 27 26 26 23
Case 6 Case 7 Case 8
MSE wraparound wall Twall wttfi small toe MSE seamental wall
Ranking / Maanltude Ranklno / Magnitude Ranklno / Maanltude
Total Active Soil Thrust (N/mt N/A. x 1.5 0 / 196281 3 x 1.5 4.6 1 342659 6 X 1.5 * 9 / 245797
Total Over Turning Moment INm/ml N/A X 1.5 0 / 446210 5 X 1.5 7.5 / 887550 6 x 1.5 9 / 784800
Max Total Beahno Pressure at Bas IN/m*21 N/A X 1.5 0 / 234000 2 x 1.5 3 / 242000 1 x 1.5  1.5 / 255000
Wall Tfft from Vertical (Permanent) [degree] N/A X 1 * 0 / 0.0130992 6 x 1 6 / 0.0127197 1 X 1  1 / 0.0231332
Max. Total Inclusion TensHe Stress IN/mA21 N/A X 1.5 0 / 1650000 6 x 1.5 9 / 1460000 1 x 1.5  1.5 / 3270000
Total Point 0 30 22
Table 4.7 Weighted ranking of 7 wall types using modified input ground
motion
Rankings on Performance of Various Retaining Walls
(Including Evaluation of Inclusion Tensile Stress Parameter)
PGA: 0.717713G (Input Acceleration Magnitude Amplified by 1.5)
Case 1 Twall Case 2 Lwall Case 3 Invert Lwall Case 4 Vertical wall
Ranking Magnitude Ranking Magnitude Ranking Magnitude Ranking Magnitude
Total Active Soil Thrust IN/ml X 1.4  1.5 461193 3 x 1.6 4.5 424052 3 x 1.5 4.5 423966 5 X 1.5 7.5 382601
Total Over Turning Moment INm/ml X 1.5  1.5 1335023 3 x 1.5 * 4.5 1195407 2 x 1.5 * 3 1264601 5 x 1.5 * 7.5 1059980
Max. Total Beartog Pressure at Base N/mA2l 5 X 1.5 7.5 215000 X 1.5 * 1.5 294000 5 x 1.6 7.5 210000 X 1.5 1.5 298000
Wall Tift from Vertical (Permanent) Idea reel 2 X 1  2 0.0122167 5 x 1 * 5 0.0098676 X 1  1 0.0134199 X 1 1 0.0130696
Max Total Inclusion Tensile Stress IN/mA21 3 x 1.5  4.5 1950000 4 X 1.5 * 6 1600000 X 1.5  1.5 2240000 2 X 1.5  3 2100000
Total Point 17 22 16 21
Case 6 MSE wraparound wall Case 7 Twall with small toe CaseS MSE segmental wall
Ranking Magnitude Ranking Magnitude Ranking Magnitude
Total Active SoH Thrust (N/ml N/A x 1.5 * 0 462669 2 x 1.5 a 3 431143 N/A x 1.5 * 0 99960
Total Over Turning Moment INm/ml N/A X 1.5 b 0 / 1177036 3 X 1.5 4.5 / 1163435 N/A x 1.5 * 0 543527
Max Total Bearina Pressure at Base [N/mA2l N/A x 1.5 0 / 469000 2 x 1.5 3 / 260000 N/A x 1.5 * 0 283000
Wall Tift from Vertical (Permanent) Idegreel N/A x 1 * 0 0.0310925 5 x 1 s 5 / 0.0099866 N/A x 1 0 / 0.0349361
Max Total Inclusion Tensile Stress (N/mA21 N/A x 1.5 * 0 4360000 5 x 1.6 B 7.5 / 1650000 N/A x 1.5 * 0 2190000
Total Point 0 23 0
The plots labeled a of Figure 4.16 through 4.20 compared four wall
configurations that had the same heel length of 15% wall height. Plots that
labeled b would then compare the three wall configurations that had the same
toe length of 1.5% wall height. These figures would identify the wall
performance criteria with respect to the base length variations.
Magnitudes of the performance criteria were listed in Table 4.8. Criterion
magnitudes of all six wall configurations were compared to each other. The same
ranking procedure adopted in the previous section also was applied here. Since
there were six wall configurations, the highest ranking value was 6. Table 4.9
shows the ranking results among all six wall configurations. One could depict the
best wall performance wall configuration by comparing the summation of ranking
values in the Total Points column of Table 4.9. Wall configuration of 15% H
heel length and 1.5% toe length of case number 1 scored the most points and
hence be the most desirable wall configuration. This combination of heel length
and toe length would be selected for the detail study programme of Chapter 6.
4.8 Discussion
A series of analyses was performed to determine wall type and
configuration for the detail study of hybrid wall under seismic loads. The
analyses were divided into two stages. The first stage was to select a particular
wall type, while the configuration of that wall type was determined from the
second stage. Performance criteria were first defined for the wall types and
configurations. Calculations from digital outputs were performed for the selected
performance criteria. In determining the wall performances, a ranking procedure
was adopted, where the best wall type and configuration would score the most
points in comparison to other wall types and configurations. Weight factors were
62
On
u>
Toe% of Wat HdgH Va. Net Thrust Heel 15% of Wal Height
i 3
! } s
\ /
\ /
\ /
\ /
\ >
/
\ /
\/
G 2 A Toc %ofV /all He ght G 1
Heel% of Wal Height Vs. Net Thrust Toe = 1.5% of Wei HelgN
6
\
\
\
\
v
\
Y
\
1
1 3 1 2 1 4 1 H 6 l% 1 OfV B Vail 2 Helg 0 7 fth 2 2 4 2
Figure 4.16 Effect of wall footing configuration on thrust imparted on wall
Toe% of Wal Hettft Va. Total Moment Heel* 15% of Wal Hdrft
/
/
l /
\ / 0
i \ i
\ /
Â£ A /
\ /
V
c 3 A Toe % of Wall He 1 ight 1
Heef% of Wal HelgN Vs. Total Momert Toe *1.5% of Wal H etf*
V 6
v
N
\
Z \ i
v
\
a V
\
v
V
\
1 3 1 2 1 4 1 H 6 wl% 1 ofV B Vail 2 Hole 0 ht 2 2 2 4 2
Figure 4.17 Effect of wall footing configuration on total overturning
moment
Toe% of Wall Ht. Vs Mu. Total Bearing Heel s 15% of Wall Height
0
V
s
s
3 y
CL
\
c' \ ,
d)
C 2 4 T0 %0fV 6 /all He 3ht 6 1
Toe% of Wall Ht Vs Max. Total Bearing Toe 1.5% of Wall Height
?7 V 7 6
/
u 3 Â£ 7
/
c 1 m V > /
\ 7
1 2 \ / /
S /
1 0 1 2 1 4 1 H 6 eel% 1 of V /all Hek 0 2 ht 2 2 4 2
Figure 4.18 Effect of wall footing configuration on maximum total bearing
pressure
Os
Us
Heel% x Wall Ht Vs Permanent Wall Tilt Toe = 1.5% of Wall Height
6
N
s
n 5
C ra g
1 D 1 2 1 4 1 H 6 eel* 1 of V 8 Vail 2 Heig 0 2 ht 2 2 4 2
Figure 4.19 Effect of wall footing configuration on permanent wall tilt
Ov
Os
Toe% of Wall Ht Vs Max. Tensile Stress Heel = 15% of Wall Height
0
'
2 r
\
0) \
\ /
\
V
h
( * 2 t T %ofV ( Vail He ghl f 1
Figure 4.20 Effect of wall footing configuration on maximum inclusion
tensile stress
Table 4.8 Results of performance criteria and ranking for second stage
analyses
Case No. Heel % Toe % Total Force [N/m] Total Moment [Nm/m] Maximum Total Bearing Pressure [N/mA2] Maximum Tensile Stress [N/mA2] Permanent Wall Tilt [degree]
1 15 1.5 337494 832741 245137 1477252 0.013521
2 15 5.0 382690 1073231 223000 1910000 0.013260
3 15 10.0 363829 973772 196000 1640000 0.014754
4 15 0.0 381734 996424 265000 2230000 0.013757
5 10 1.5 437809 1146627 246000 2280000 0.014237
6 25 1.5 367565 1036168 247000 1920000 0.012264
Case No. Heel % Toe % Total Force Total Moment Maximum Total Bearing Pressure Maximum Tensile Stress Permanent Wall Tilt Total Points
1 15 1.5 6 6 2 6 3 23
2 15 5.0 4 2 4 3 4 17
3 15 10.0 5 4 6 5 1 21
4 15 0.0 4 3 1 1 3 12
5 10 1.5 1 1 2 1 2 7
6 25 1.5 5 3 2 3 6 19
also applied to several of the most dominant criteria anticipated in determining the
most desirable wall type.
From this preliminary study, wall type of hybrid Twall with small toe
ranked first and hence was targeted as the wall type for the second stage analysis.
As for the wall configuration in the second stage analysis, the combination of heel
length of 15% wall height (H) and toe length of 1.5% wall height (H) had the
highest score in competition with other five configurations of hybrid Twall with
small toe. Thus, hybrid Twall with small toe with 15% H heel length and 1.5%
H toe length was selected as the prototype to be analyzed in the detail study
programme. Though the number of cases analyzed in this preliminary study was
limited, but by selecting a feasible wall prototype before the detail study was
carried forward, future analyses could be more focused and less time consuming.
68
5. Ground Motions Used in the Study
5.1 Introduction
In order to determine the effect of earthquake motions on the retaining
wall system, nine different magnitude earthquakes were selected. These nine
earthquake records were then implemented in the detailed study of Chapter 6.
Three of the earthquake records selected had magnitude close to 6, three with
magnitude close to 7, and the other three had magnitude close to 8. The intent for
using earthquake magnitude to categorize these earthquake records was to be able
to produce wall performance design chart based on earthquake magnitude 6, 7,
and 8. Earthquake magnitude is a quantitative measurement of earthquake size,
but earthquake magnitude does not necessary reflect direct proportion of the
measured earthquakes motion amplitude, frequency content, and the motion
duration. Availability of the digitized earthquake motion was limited to the
instruments installed in the field. Unless the digitized earthquake motion is
corrected for epicentral distance, hypocenter depth, and site geology, magnitude
itself alone could not be used to characterized earthquake motion.
Each earthquake motion exhibits its own ground motion parameters.
Three ground motion parameters of engineering significance are amplitude,
frequency content, and the duration of the motion. With ground motion
parameters, one could define the characteristics of an earthquake motion. The
ground motion parameters were depicted and determined in the following
sections. Ground motion parameters would then serve as indexes for evaluating
the wall performances in the detailed study programme later in Chapter 6.
69
5.2 Ground Motion Time Histories and Input
Ground Motions
National Geophysical Data Center of National Oceanic and Atmospheric
Administration (NOAA) located at Boulder Colorado published a CDROM
collection of earthquake strong motion records. The collection contains over
15,000 digitized and processed accelerograph records dating from 1933 to 1994.
Three types of processed record on the CDROM are uncorrected, corrected, and
response spectra record. All nine earthquake records utilized in the detailed study
of Chapter 6 were selected from this CDROM collection. This CDROM
collection could be purchased at the NOAA Boulder Colorado.
The ground motions (or acceleration time histories) selected were all
corrected records. The term corrected record stands for filtered record. The
corrected strong motion had been corrected from the uncorrected (raw) strong
motion by filtering out high frequency or low frequency background noise,
correcting the measurement errors, and calibrating the instrument transducer or
sensor. Correction of the accelerogram errors was not performed in this thesis
study, since all nine records selected were already corrected.
A database software named SMC AT3 (Strong Motion Data Catalog) is
included in the earthquake strong motion CDROM. Nine acceleration time
histories were selected using SMC AT3 quarry capability, and the records were
listed in Table 5.1. Also included with each earthquake name in Table 5.1 were
its date, magnitude, intensity, depth, epicentral distance, and peak ground
acceleration (PGA). Note that the unit for earthquake intensity is Modified
Mercalli (MM) intensity scale. The type of structure that strong motion
instrument resided on and the site geology were also included in Table 5.1.
Structure type of free field indicates that strong motion instrument is located far
away from the influence of large structures.
70
Table 5.1 Nine selected earthquake ground motion information
Category Magnitude 6 Magnitude 6 Magnitude 6
Case No. 1 2 3
Name Mammoth Lakes Aftershock Whittier Narrows Earthquake Morgan Hill Earthquake
Dale 05/25/80 10/01/87 04/24/84
Magnitude 6.0 [ML] 5.9 [ML] 6.2 [ML]
Intensity 0 [MM] 8 [MM] 7 [MM]
Depth 14 Km 9 Km 9 Km
Structure Building Free Field Dam
Site Geology Glacial Debris (50100m) Alluvium (9m), Sillslone Conglomerate, Sandstone, Shale
Epicentra! Distance 3 Km 43 Km 25 Km
PGA 0.380 G 0.537 G 0.652 G
PF*: 0% dampinq 3.23 G at 7.69 hertz 7.30 G at 3.33 hertz 5.03 G at 3.57 hertz
2% damping 1.87 Gal 7.14 hertz 3.73 G at 3.33 hertz 3.36 G at 3.57 hertz
5% damping 1.31 Gat 6.67 hertz 2.36 Gat 3.13 hertz 2.39 G at 3.57 hertz
10% damping 0.9B G at 6.67 hertz 1.56 G at 3.13 hertz 1.70 Gat 3.33 hertz
20% dampinq 0.65 G at 6.67 hertz 1.02 Gat 3.33hertz 1.21 Gat 3.57 hertz
Category Magnitude 7 Magnitude 7 Magnitude 7
Case No. 1 2 3
Name Vrancea Earthquake Northridge, California Earthquake Imperial Valley Earthquake
Date 08/30/86 01/17/94 10/15/79
Magnitude 7.0 [ML] 6.8 [MS] 6.6 [ML]
Intensity 0 [MM] 9 [MM] 9 [MM]
Depth 131 Km 18 Km OKm
Structure Unknown Free Field Free Field
Site Geology Unknown Unknown Alluvium (>300m)
Epicentral Distance Unknown 19 Km 27 Km
PGA 0.303 G 0.390 G 0.493 G
PF*: 0% dampinq 2.66 Gat 3.57 hertz 3.43 G at 6.25 hertz 3.07 G at 2.63 hertz
2% damping 1.54 G at 3.57 hertz 2.13 Gat 4.17 hertz 1.39 Gat 2.63 hertz
5% dampinq 0.91 G at 3.57 hertz 1.54 G at 4.17 hertz 1.08 Gat 5.26 hertz
10% damping 0.69 G at 2.00 hertz 1.04 G at 4.17 hertz 0.96 G at 4.55 hertz
20% damping 0.54 G at 2.08 hertz 0.76 G at 6.25 hertz 0.80 G at 4.55 hertz
71
Table 5.1 (Cont.) Nine selected earthquake ground motion information
Category Magnitude 8 Magnitude 8 Magnitude 8
Case No. 1 2 3
Name Kern County Earthquake Santiago, Chile Earthquake Michoacan, Mexico City Earthquake
Date 07/21/52 07/09/71 09/19/85
Magnitude 7.7 [ML] 7.9 [MS] 8.1 [MS]
Intensity 11 [MM] 0 [MM] 9 [MM]
Depth 16 Km 58 Km 16 Km
Structure Misc. Building Free Field
Site Geology Alluvium Alluvium Bedrock
Epicentral Distance Unknown 119 Km 27 Km
PGA 0.179 G 0.159 G 0.141 G
PF*: 0% dampinq 1.84 Gat 2.27 hertz 1.90 Gat 6.25 hertz 2.08 G at 5.00 hertz
2% dampinq 0.97 G at 2.27 hertz 0.77 G at 6.25 hertz 0.73 Gat 11.1 hertz
5% dampinq 0.60 G at 2.27 hertz 0.49 G at 3.85 hertz 0.43 G at 2.27 hertz
10% damping 0.37 G at 2.27 hertz 0.34 G at 3.85 hertz 0.31 G at 5.00 hertz
20% damping 0.27 G at 2.38 hertz 0.24 G at 8.33 hertz 0.24 G at 4.55 hertz
* PF is (he predominant frequency determined from absolute acceleration response
spectrum.
72
Peak ground acceleration (PGA) is a ground motion parameter of
amplitude. This is the most commonly used amplitude parameter in
characterizing a particular ground motion. PGA is defined as the largest absolute
value of acceleration from a given acceleration time history. Note that all PGA
listed in Table 5.1 are of the horizontal component. Values of PGA would be
used as indexes in determining hybrid wall performance relationships. In general,
an earthquake motion with a high PGA would indicate a strong ground motion but
not necessarily more destructive. A high peak acceleration with a very short
duration may not be as destructive as a lower peak acceleration with long
duration. Since PGA alone could not solely characterize ground motion, other
ground motions parameters were introduced later in the section 5.3.
Nine digitized acceleration time histories were plotted in part (a) of Figure
5.1 through Figure 5.9. Duration of the nine acceleration time histories selected
were quite long. Thus definition of strong motion duration was applied to these
nine acceleration time histories to reduce the real analysis duration. Specifically,
the bracketed duration definition was adopted in determining the real analysis
duration. Bracketed duration is defined as the time between the first and last
exceedances of 5% G, where G is the gravitational acceleration of 9.81 m/s2. Part
(b) of Figure 5.1 through Figure 5.9 show the truncated acceleration time history
according to the bracketed duration definition. These nine truncated acceleration
time histories were used as the input ground motion in the detail study of Chapter
6.
5.3 Response Spectra and Cumulative Absolute
Velocities
Acceleration Response Spectra
73
Figure 5.1a Mammoth Lakes Aftershock acceleration time history
Figure 5.1b Truncated Mammoth Lakes Aftershock acceleration time
history
74
Figure 5.2a Whittier Narrows Earthquake acceleration time history
Figure 5.2b Truncated Whittier Narrows Earthquake acceleration time
history
75
Figure 5.3a Morgan Hill Earthquake acceleration time history
Morgan Hill Earthquake (Mag.6,#3)
Analysis Duration = 9.74 sec.
0.8
0.6
_ 0.4
(3
Â§ 0.2
S o nM
' 0.2
0.4
0.6 +
y\j\r
4 6
Time [sec]
10
Figure 5.3b Truncated Morgan Hill Earthquake acceleration time history
76
Figure 5.4a Vrancea Earthquake acceleration time history
Figure 5.4b Truncated Vrancea Earthquake acceleration time history
77
Figure 5.5a Northridge Earthquake acceleration time history
Figure 5.5b Truncated Northridge Earthquake acceleration time history
78
Imperial Valley Earthquake (Mag.7,#3)
PGA=0.493G @ 5.34sec.
Figure 5.6a Imperial Valley Earthquake acceleration time history
Figure 5.6b Truncated Imperial Valley Earthquake acceleration time history
79
Figure 5.7a Kem County Earthquake acceleration time history
Figure 5.7b Truncated Kem County Earthquake acceleration time history
80
Figure 5.8a Santiago, Chile Earthquake acceleration time history
Figure 5.8b Truncated Santiago, Chile Earthquake acceleration time history
81
Figure 5.9a Michoacan, Mexico City Earthquake acceleration time history
Figure 5.9b Truncated Michoacan, Mexico City Earthquake acceleration
time history
82
Response spectrum is a ground motion parameter of frequency content.
Response spectrum can be generated for each of the ground motion selected. A
computer program named Basic StrongMotion Accelerogram Processing
Software (BAP) was used to generate the response spectrum for each of the
selected input ground motion. BAP was developed by the U.S. Geological
Survey (USGS) of U.S. Department of the Interior. BAP program is distributed in
the public domain, and it could be obtained from the USGS NationalStrong
Motion Program (NSMP) internet website. A digitized ground motion needs to
be arranged into a specific input format in order for BAP to read and run properly.
Response spectrum reflects the characteristics of a ground motion. The
amplitude and frequency content of the ground motion would influence the
spectral values. In a response spectrum, the maximum response of single degree
of freedom (SDF) damped system subjected to the input ground motion is
calculated. The computed spectral values include absolute acceleration response,
relative velocity response, relative displacement response, and their corresponding
natural period. Damping ratios of 0.0, 0.02, 0.05, 0.1, and 0.2 were specified in
the response spectrum calculations. Damping ratio is simply defined as the
fraction of critical damping. The absolute acceleration response (spectral
acceleration) and its corresponding natural period for the nine selected input
ground motions were illustrated in Figure 5.10 through Figure 5.18. Note that
only the spectral acceleration with 0%, 5%, 10%, and 20% damping ratios were
plotted.
Predominant period could be determined from the response spectrum of
different damping value. Predominant period is defined as the natural period
corresponding to the maximum spectral value. Again, the spectral acceleration in
the response spectrum was selected as the spectral value in this thesis study.
Predominant period served as an index that could be related to the performance of
hybrid retaining wall system. Predominant periods of response spectra with
83
