REVITALIZING T AND L WALLS
WITH INCLUSIONS
by
Kittichai Thanasupsin
B. Eng., Khon Kaen University, 1992 .
M. Eng., Asian Institute of Technology, 1995
A thesis submitted to the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Civil Engineering
1998
This thesis for the Master of Science
degree by
Kittichai Thanasupsin
has been approved
by
NienYin Chang
ShingChun Trever Wang
John R. Mays
/ft?
Date
Kittichai Thanasupsin (M.S., Civil Engineering)
Revitalizing T and L Walls with Inclusions
Thesis directed by Professor Nien Yin Chang
ABSTRACT
The mechanically stabilized earth(MSE) wall is getting more popular due to
its cost effectiveness, simplicity and rapid construction. However, this type of wall
still has some drawbacks such as lack of an aesthetic appearance, the requirement for
selected granular backfill, and for a relatively large space behind the wall. On the
other hand, the cantilever wall is better than the MSE wall in terms of aesthetics and
less space requirement behind the wall, but it is not as cost effective as the MSE wall.
A hybrid wall combines the advantages of both MSE and cantilever walls.
The backfill is mechanically stabilized by using inclusions and is termed MSB. The
soil stability is enhanced by the mechanism of interface friction between soil and
inclusions. The hybrid wall is subject to less earth pressure than the cantilever wall.
Thereby, the hybrid wall with MSB can have a thinner wall stem, and this naturally
results in cost saving. Furthermore, the hybrid wall has less displacement, settlement,
and wall rotation, and it also can support impact guard rails. These are the advantages
of the hybrid wall over the MSE and conventional castinplace cantilever wall.
In this study, the nonlinear finite element program, NIKE3D, is selected
because of its excellent capability of simulating the interface slippage, debonding,
and rebonding. The MSE, the MSE wall with segmental panel facing,
the hybrid T wall, the hybrid invert L wall, and the hybrid invert L wall with shear
key were analyzed under different surcharges. The effects of connection condition
either attached or detached inclusions to the wall face also were studied. The rear wall
face earth pressure, passive earth pressure, bearing pressure at wall base, stress
in
distribution, horizontal displacement of the wall, wall settlement, wall rotation, and
point of application of resultant earth pressure were investigated.
The findings show that the rear wall face earth pressure decreases from
Rankine and Coulomb earth pressures. The wall performance is also found to be very
sensitive to soil types. Tensions in inclusions are usually small and reduce drastically
to near zero away from the rear wall face in many cases except in walls with soft soil.
The ratio of height of point of application of resultant pressure from a wall base to the
wall height(Hr/H) is higher in invert L walls with inclusions than in T walls with
inclusions. However, it is much lower than one third of wall height from the base as
in the Rankine and Coulomb theories.
This abstract accurately represents the content of the candidates thesis. I recommend
its publication.
SignedJ
Nien Yin Chang
IV
ACKNOWLEDGEMENTS
This study was preformed under the supervision of Professor Nien Yin Chang
and Dr. ShingChun Wang. I am grateful for their support and encouragement
throughout my academic and research studies. Gratitude is also extended to our NIKE
group members for sharing knowledge and information.
CONTENTS
Chapter
1. Introduction...............................................................1
1.1 Problem Statement.........................................................2
1.2 Objectives................................................................2
1.3 Scope of Study........................................................... 2
1.4 Engineering Significance..................................................3
2. Conventional T Wall and Invert L Wall Designs and AASHTO
Design criteria............................................................4
2.1 Introduction..............................................................4
2.2 Design of Retaining walls................................................5
2.2.1 Lateral Earth Pressure..................................................6
2.2.2 Coulombs Theory........................................................7
2.2.3 Rankines Theory.......................................................10
2.2.4 Comparison of the Horizontal Earth Pressure Between Coulomb and
Rankines Theories....................................................15
2.3 AASHTO Design Criteria..................................................17
2.3.1 General Considerations.................................................17
2.3.2 Bearing Resistance and Stability at the Strength.......................17
3. Design of Mechanically Stabilized Earth Walls And AASHTO Criteria.........21
3.1 Mechanically Stabilized Earth Wall.......................................21
3.2 Advantages and Disadvantages of Mechanically Stabilized Earth(MSE) wall.22
3.3 Reinforced Soil Concepts................................................23
3.4 Geotextiles.............................................................25
3.5 AASHTO Design Criteria..................................................26
3.5.1 Movement Under Service Limit State.....................................27
3.5.2 Safety Against Soil Failure............................................28
vi
3.5.3 Internal Stability...................................................29
3.5.4 Pullout Design Parameters............................................33
3.6 Design Example.........................................................35
4. NIKE3D, Material Parameters, And Wall Dimensions........................38
4.1 Introduction............................................................38
4.2 Interface formulation..................................................38
4.3 RambergOsgood Elastoplastic Model.....................................42
4.4 Material Parameters....................................................49
4.5 Wall Dimensions........................................................50
5 Mechanically Stabilized Earth............................................53
5.1 Horizontal Displacement.................................................54
5.2 Vertical Displacement..................................................56
5.3 Walls Rotation........................................................56
5.4 Stress Distribution in Inclusions......................................56
5.5 Comparison Between MSE with Wrapped and Unwrapped Inclusions...........58
5.6 Effects of Soft Soil...................................................58
5.7 Summary................................................................59
6 MSE Wall with Segmental Panel Facing....................................69
6.1 The Effects of the Variation of Applied Surcharge......................70
6.1.1 Horizontal Resultant Force............................................70
6.1.2 Locations of Resultant Force(Hr/H.....................................70
6.1.3 Maximum Horizontal Displacement.......................................71
6.1.4 Wall Settlement.......................................................71
6.1.5 Degree ofRotation................................................... 71
6.2 Active Earth Pressure and Passive Earth Pressure......................71
6.3 Bearing Pressure at Wall Base..........................................72
6.4 Stress Distribution in Inclusions......................................72
6.5 Horizontal Displacement of Wall Face...................................72
Vll
6.6 Vertical Displacement of Wall Face.....................................72
6.7 The Analysis of Segmental Panel Facing with Soft Soil..................73
6.8 Summary................................................................73
7. T Wall With Mechanically Stabilized Backfill(MSB.........................87
7.1 Active Earth Pressure and Shear Diagram.................................88
7.2 Passive Earth Pressure............................................... 90
7.3 Bearing Pressure at Wall Base..........................................90
7.4 Stress Distribution in Inclusions..................................... 91
7.5 Maximum Displacement and Rotation......................................91
7.5.1 Horizontal Displacement..............................................91
7.5.2 Wall Settlement......................................................91
7.5.3 Rotation of the Wall.................................................92
7.6 Location of Resultant Force(Hr/H.......................................92
7.7 Conventional Factor of Safety for the Wall Without Inclusions..........93
7.8 Equivalent Cohesive Soil..............................................100
7.9 Effects of Soil Parameters............................................102
7.10 Summary and Conclusions..............................................103
8. Invert L Wall With Mechanically Stabilized Backfill(MSB)................163
8.1 Rear Wall Face Earth Pressure and Shear Diagram.........................164
8.2 Passive Earth Pressure................................................165
8.3 Bearing Pressure at Wall Base.........................................165
8.4 Stress Distribution in Inclusions.....................................166
8.5 Maximum Displacement and Rotation.....................................166
8.5.1 Horizontal Displacement.............................................166
8.5.2 Wall Settlement.....................................................167
8.5.3 Wall Rotation.......................................................167
8.6 Location of Resultant Force (Hr/H)....................................168
vm
8.7 Conventional Factor of Safety for the Wall Without Inclusions........168
8.8 Equivalent Cohesive Soil.............................................170
8.9 Effects of Soil Parameters...........................................172
8.10 Summary and Conclusions.............................................172
9. Invert L Wall With Shear Key And MSB..................................252
9.1 Rear Wall Face Earth Pressure and Shear Diagram.......................253
9.2 Passive Earth Pressure...............................................254
9.3 Bearing Pressure at Wall Base........................................254
9.4 Stress Distribution in Inclusions....................................255
9.5 Maximum Displacement and Rotation....................................255
9.5.1 Horizontal Displacement............................................255
9.5.2 Wall Settlement....................................................255
9.5.3 Wall Rotation......................................................256
9.6 Location of Resultant Force (Hr/H)...................................256
9.7 Conventional Factor of Safety for the Wall Without Inclusions........256
9.8 Equivalent Cohesive Soil.............................................260
9.9 Effects of Soil Parameters...........................................261
9.10 Effects of Shear Key Depth..........................................262
9.11 Summary and Conclusions.............................................262
10. Summary, Conclusions, And Recommendation for Future Study.......;.....309
10.1 Summary..............................................................309
10.2 Conclusions..........................................................310
10.3 Recommendation for future study......................................312
Appendixes
A. Retaining wall designLoad factor design..............................319
B. Applied surcharge and its equivalent height...........................325
IX
References
...326
x
FIGURES
Figure
2.1 Illustration of the concept of elastic and plastic equilibrium............6
2.2 The schematic for coulomb theory..........................................7
2.3 The schematic for Rankine theory.........................................10
2.4 The plots of Ka values...................................................16
2.5 Earth load and stability criteria for walls with clay soils in the backfill
or foundation..........................................................18
2.6 Earth loads and stability criteria for walls with granular backfills and
foundations on sand and gravel..........................................18
2.7 Earth loads and stability criteria for walls with granular backfills and
foundations on rock.....................................................19
3.1 Stress transfer mechanism for soil reinforcement.........................24
3.2 Types of polymeric fibers or yams........................................25
3.3 Determination of failure plane location and earth pressure coefficient for
inextensible reinforcements.............................................32
3.4 Pullout factor for inextensible mesh and grid reinforcement..............34
3.5 Schematic of the wall used in this study.................................35
4.1 Typical interface........................................................40
4.2 Contact of node m with segment jk........................................40
4.3 The comparision of relation of G/Gmax and damping ratio versus
shear strain............................................................42
4.4 Hysteresis loop according to RambergOsgood model........................45
4.5 Shows the equivalent linear modulus and damping ration of soils..........45
4.6 The variation of shear modulus with shear strain for sands...............46
4.7 The variation of damping ratio with shear strain for sands...............46
4.8 Plot of log(Gmax/G01) versus log (GoY/GmaxYy)...........................47
4.9 Invert L wall............................................................51
xi
4.10 Invert L wall with shear key.................................................51
4.11 T wall.......................................................................52
5.1 The schematic and boundary conditions of MSE ................................53
5.2 The finite element mesh for MSE..............................................54
5.3 Plots of the variation of parameters with surcharge..........................61
5.4 Plots of investigated parameters for MSE with 0 KPa surcharge
and unwrapped inclusions....................................................62
5.5 Plots of investigated parameters for MSE with 25 KPa surcharge
and unwrapped inclusions....................................................63
5.6 Plots of investigated parameters for MSE with 100 KPa surcharge
and unwrapped inclusions....................................................64
5.7 Plots of investigated parameters for MSE with 0 KPa surcharge and
wrapped inclusions..........................................................65
5.8 Plots of investigated parameters for MSE with 25 KPa surcharge
and wrapped inclusions......................................................66
5.9 Plots of investigated parameters for MSE with 100 KPa surcharge
and wrapped inclusions......................................................67
5.10 Plots of investigated parameters for MSE with 25 KPa surcharge,
unwrapped inclusions, and soft soil.........................................68
6.1 (a) The schematic and boundary conditions of segmental panel facing............69
6.1 (b) The finite element mesh of segmental panel facing..........................70
6.2 Plots of the variation of parameters with surcharge..........................75
6.3 Plots of investigated parameters for SPF with 0 KPa surcharge...............77
6.4 Plots of investigated parameters for SPF with 50 Kpa surcharge..............79
6.5 Plots of investigated parameters for SPF with 100 Kpa surcharge.............81
6.6 Plots of investigated parameters for SPF with 200 KPa surcharge.............83
6.7 Plots of investigated parameters for SPF with 50 KPa surcharge and
soft soil...................................................................85
Xll
7.1 (a) The schematic of T wall with MSB and boundary conditions........87
7.1 (b) The finite element mesh of T wall with MSB......................88
7.2 Wall stabilty against overturning and sliding.....................98
7.3 Plots of investigated parameters with various surcharge..........105
7.4 Plots of the investigated parameters for T8A1ER0100.3.........107
7.5 Plots of the investigated parameters for T8A1ERO1250.3...... 110
7.6 Plots of the investigated parameters for T8A1ER01500.3........113
7.7 Plots of the investigated parameters for T8 A1ERO11000.3......116
7.8 Plots of the investigated parameters for T8 A1 ERO 101.5......119
7.9 Plots of the investigated parameters for T8A1ER01251.5........122
7.10 Plots of the investigated parameters for T8A1ERO1501.5........125
7.11 Plots of the investigated parameters for T8A1ER011001.5....;..128
7.12 Plots of the investigated parameters for T8D1ER0100.3.........131
7.13 Plots of the investigated parameters for T8D1ERO1250.3........134
7.14 Plots of the investigated parameters for T8D1 ERO 1 500.3.....137
7.15 Plots of the investigated parameters for T8D1ER011000.3.......140
7.16 Plots of the investigated parameters for T8D1ERO101.5.........143
7.17 Plots of the investigated parameters for T8D1 ERO 1251.5......146
7.18 Plots of the investigated parameters for T8D1ERO1501.5........149
7.19 Plots of the investigated parameters for T8D1 ERO 1 1001.5....152
7.20 Plots of the investigated parameters for T8A1ER0200.3.........155
7.21 Plots of the investigated parameters for T1 ERO 1 00.3........157
7.22 Plots of the investigated parameters for T1 ER0200.3..........159
7.23(a) The interface separation for the wall with attached inclusion,
0.3m embedment depth and 100 KPa surcharge.........................161
(b) The interface separation for the wall with detached inclusion,
0.3m embedment depth and 100 KPa surcharge......................162
8.1 (a) The schematic of L wall with MSB and boundary conditions.......163
xm
8.1(b) The finite element mesh of L wall with MSB.....................164
8.2 Plots of investigated parameters with various surcharge.........175
8.3 Plots of the investigated parameters for L8 A1ERO100.3.......178
8.4 Plots of the investigated parameters for L8A1ERO1250.3.......180
8.5 Plots of the investigated parameters for L8A1ER01500.3.......182
8.6 Plots of the investigated parameters for L8A1ER011000.3......184
8.7 Plots of the investigated parameters for L8 A1 ERO 101.5.....186
8.8 Plots of the investigated parameters for L8 A1 ERO 1251.5....188
8.9 Plots of the investigated parameters for L8A1ERO1501.5 ......190
8.10 Plots of the investigated parameters for L8A1ER011001.5......192
8.11 Plots of the investigated parameters for L8D1 ERO 1 00.3.....194
8.12 Plots of the investigated parameters for L8D1ERO1250.3.......196
8.13 Plots of the investigated parameters for L8D1ER01500.3.......198
8.14 Plots of the investigated parameters for L8D1ER011000.3......200
8.15 Plots of the investigated parameters for L8D1 ERO 1 01.5.....202
8.16 Plots of the investigated parameters for L8D1 ERO 1251.5 ....204
8.17 Plots of the investigated parameters for L8D1 ERO 1501.5 ....206
8.18 Plots of the investigated parameters for L8D1ER011001.5......208
8.19 Plots of the investigated parameters for L8A5ER01 00.3.......210
8.20 Plots of the investigated parameters for L8A5ERO 1250.3......212
8.21 Plots of the investigated parameters for L8A5ER01500.3.......214
8.22 Plots of the investigated parameters for L8A5ER011000.3......216
8.23 Plots of the investigated parameters for L8A5ERO101.5........218
8.24 Plots of the investigated parameters for L8A5ERO1 251.5 .....220
8.25 Plots of the investigated parameters for L8A5ERO1501.5 ......222
8.26 Plots of the investigated parameters for L8A5ER011001.5 .....224
8.27 Plots of the investigated parameters for L8D5ER0100.3........226
8.28 Plots of the investigated parameters for L8D5ERO1250.3 ......228
xiv
8.29 Plots of the investigated parameters for L8D5ER01500.3 ....230
8.30 Plots of the investigated parameters for L8D5ER011000.3....232
8.31 Plots of the investigated parameters for L8D5ERO101.5...:..234
8.32 Plots of the investigated parameters for L8D5ERO1251.5 ....236
8.33 Plots of the investigated parameters for L8D5ERO1501.5 ....238
8.34 Plots of the investigated parameters for L8D5ER011001.5....240
8.35 Plots of the investigated parameters for L8A1 ER0200.3 ....242
8.36 Plots of the investigated parameters for L1ERO101.5....... 244
8.37 Plots of the investigated parameters for L1ERO201.5........246
8.38 Plots of the investigated parameters for L8A1ER011002.5....248
8.39 Plots of the investigated parameters for L8D1ER011002.5 ...250
9.1 (a) The schematic of invert L wall with shear key with MSB and
boundary conditions..........................................252
9.1(b) The finite element mesh for invert L wall with shear key....253
9.2 Plots of investigated parameters with various surcharge......265
9.3 Plots of the investigated parameters for LSK8A1ER0100.3....267
9.4 Plots of the investigated parameters for LSK8A1ERO 1250.3 .269
9.5 Plots of the investigated parameters for LSK8A1ER01500.3...271
9.6 Plots of the investigated parameters for LSK8A1ER011000.3..273
9.7 Plots of the investigated parameters for LSK8A1ERO101.5....275
9.8 Plots of the investigated parameters for LSK8A1ER01251.5...277
9.9 Plots of the investigated parameters for LSK8A1ERO1501.5 ..279
9.10 Plots of the investigated parameters for LSK8A1ER011001.5..281
9.11 Plots of the investigated parameters for LSK8D1ER0100.3....283
9.12 Plots of the investigated parameters for LSK8D1ERO1 250.3 .285
9.13 Plots of the investigated parameters for LSK8D1ER01500.3...287
9.14 Plots of the investigated parameters for LSK8D1ER011000.3 .289
9.15 Plots of the investigated parameters for LSK8D1ERO101.5....291
xv
9.16 Plots of the investigated parameters for LSK8D1ER01251.5......291
9.17 Plots of the investigated parameters for LSK8D1ERO 1501.5.....295
9.18 Plots of the investigated parameters for LSK8D1ERO11001.5 ....297
9.19 Plots of the investigated parameters for LSK8A1ER0200.3.......299
9.20 Plots of the investigated parameters for LSK1ER0100.3.........301
9.21 Plots of the investigated parameters for LSK1ER0200.3.........303
9.22 Plots of the investigated parameters for LSK8A1ER011001.52.0.305
9.23 Plots of the investigated parameters for LSK8D1ER011001.52.0.307
xvi
TABLES
Table
2.1 Coulomb active earth pressure coefficients, Ka.............................11
2.2 Coulomb passive earth pressure coefficients, Kp............................12
2.3 Rankine acitve earth pressure coefficients, Ka.............................14
2.4 Rankine passive earth pressure coefficients, Kp............................15
3.1 Relationship between joint width and limiting distortion of the face of MSE
walls.....................................................................27
3.2 Minimum Front Face Embedment...............................................29
3.3 Load Factors for Permanent Loads...........................................31
3.4 Calculation of Ti and Lei..................................................36
7.1 Summary of resultant earth pressure at wall faces by using Rankine and
Coulomb theories..........................................................95
7.2 Summary of resultant earth pressure at wall heels by using Rankine and
Coulomb theories..........................................................95
7.3 Summary of resultant force of passive earth pressure by using Rankine and
Coulomb theories..........................................................97
7.4 The Calculation of moment for the wall with 1.5 m embedment depth and
without surcharge.........................................................98
7.5 Factor of safety against overturning.......................................99
7.6 Factor of safety against sliding..........................................100
7.7 Depth of tension gap in meters............................................101
7.8 The value of equivalent cohesion, c.......................................101
7.9 Summary of parameters for all cases.......................................103
8.1 The calculation of moment for the wall with 1.5m embedment depth and
without surcharge........................................................168
8.2 Factor of safety against overturning......................................168
xvn
8.3 Factor of safety against sliding.........................................169
8.4 Depth of tension gap in meters...........................................170
8.5 The values of equivalent cohesion, c.....................................170
8.6 Summary of the selected parameters for the wall with EjncUSj0n = 1 *E...172
8.7 Summary of the selected parameters for the wall with Exclusion = 5 E...173
9.1 Summary of resultant earth pressure......................................257
9.2 Summary of passive earth pressure........................................258
9.3 The calculation of moment for the wall with 2.5m embedment depth and
without surcharge........................................................258
9.4 Factor of safety against overturning.....................................259
9.5 Factor of safety against sliding.........................................260
9.6 The depth of tension gap in meters.......................................260
9.7 The values of equivalent cohesion, c.....................................261
9.8 Summary of the selected parameters for all cases.......................263
xvm
1. Introduction
1.1 Problem Statement
The applications of retaining walls are diverse and they have been used for a
various types of structures. For instance, Abutment, which is a particular type of
retaining wall that supports the end of a bridge superstructure, is mostly used in
highway projects. The conventional retaining walls, gravity and semigravity, are a
cost effective application. In recent years, A retaining wall with soil reinforcement or
mechanically stabilized earth (MSE) wall has evolved and is now getting more
popular than other types of retaining structures. This approach offers numerous
advantages of MSE walls over conventional walls such as cost effectiveness,
simplicity and rapid construction procedures. To fully utilize these advantages of soil
reinforcement characteristics, it is important to comprehend behaviors of soil and
geotexiles interaction and their impact on walls stability. Moreover, to select the wall
type, there are various parameters to be considered. The volume of excavation plays
an important role in terms of economics. Therefore, sometimes considering invert L
walls instead of Twall may be a better decision.
The implicit nonlinear finite element code, NIKE3D, is a powerful program,
which can deal with various types of materials including interface interaction between
different materials. This program has been developed by the Lawrence Livermore
National Laboratory (LLNL). With the collaboration with LLNL, the Center for
Geotechnical Engineering Science at the University of Colorado at Denver has the
authorization to use and enhance this program for research.
In this study, the NIKE3D program was used to investigate performance of
tensile inclusions, the effects of detached and attached tensile inclusion on the
retaining wall, active earth pressure on the wall back face, passive earth pressure on
1
the wall front face, settlement and horizontal displacement, rotation, and normal
bearing pressure at the wall base for walls with or without a shear key. Included in
the study are three different types of retaining walls: invert Lwall, invert Lwall with
shear key and Twall.
1.2 Objectives
The objectives of this study are many. They included investigating the
following :
0 The advantages and disadvantages of invert Lwall and Twall including
the effects of shear key on invert Lwall.
0 Behaviors of tensile inclusions including the required length of tensile
inclusion.
0 The altering of characteristics of active and passive earth pressure due to
tensile inclusion.
0 The effect of embedment depth.
0 The behavior of walls corresponding to applied surcharge.
0 The effects of Youngs Modulus for Inclusions.
0 Properties of soils and inclusions
1.3 Scope of Study
The three different types of MSE walls with eight layers of inclusions, invert
Lwall, invert Lwall with shear key, and Twall, have been investigated. The
following factors that effect wall performance have been studied:
0 Attached and detached inclusions to the wall face
0 Invert Lwall with and without shear key
0 Invert Lwall and Twall performance
0 Modulus of Elasticity of inclusions
0 Depth of embedment: 0.3 m. and 1.5 m.
2
0 Variations of applied surcharge: 0 KPa, 25 KPa, 50 KPa, and lOOKPa
1.4 Engineering Significance
Walls can be classified into three categories: externally stabilized system,
internally stabilized system, and hybrid system. The last two types of walls are
associated with soil reinforcement. Mechanically stabilized earth (MSE) wall has
become increasingly popular due to its cost effectiveness, simplicity and speedy
construction. Studies are still lacking in the microscopic load transfer mechanism and
its effects on wall performance. A better understanding of soil reinforcement
interaction is needed to fully employ the benefit of soil reinforcement. Invert Lwalls
and Twalls have become less popular because of their high cost and long
construction time. This study is designed to show that these conventional retaining
walls can regain their popularity by using hybrid walls with mechanically stabilized
backfill(MSB).
2. Conventional T Wall and InvertL wall Designs
and AASHTO Design Criteria
2.1 Introduction
Retaining walls used widely especially in highway project can be classified
into various categories. According to how they produce stability, retaining walls can
be categorized as;
1. Mechanically stabilized earth
2. Gravity
3. Cantilever
4. Anchored
or they can be classified according to basic mechanisms of retention and source of
support as following (Bridge Design Manual, CDOT, 1991);
1. An externally stabilized system uses a physical structure to hold the
retained soil.
2. An internally stabilized system involves reinforced soils to retain fills and
sustained loads.
3. A hybrid or mixed system is the combination of both externally and
internally stabilized systems.
Selection of wall type is based on the following parameters.(Richard M.
Barker, et al., 1997)
1. Construction and maintenance cost
2. Cut or fill earthwork situation
3. Traffic maintenance during construction
4. Construction period
5. Safety of construction worker
6. Availability and cost of backfill materials
4
7. Superstructure depth
8. Size of retaining wall
9. Horizontal and vertical alignment change
10. Area of excavation
11. Aesthetic and similarity to adjacent stresses
12. Previous experience with that type of retaining wall
13. Ease of access for inspection and maintenance
14. Anticipated life, loading conditions and acceptability of deformation
Aesthetic is one of factors for selecting type of retaining wall for instance,
some projects may need wall with monolithic fronts not broken by horizontal joints.
Thereby, a fullheight facing unit should be used.
If the cost of excavation as well is a concern, use Lwall instead of Twall.
2.2 Design of retaining walls
The general considerations of wall stability are :
0 Stem shear and bending due to lateral earth pressure on the stem
0 Base shear and bending moments at the stem caused by the wall loading
produced earth pressure on the wall footing.
0 Overall wall stability
0 Sliding
0 Overturning
0 Rotational stability
0 Stability against a bearing capacity failure
0 Settlement and horizontal deformation
5
2.2.1 Lateral earth pressure
The lateral earth pressure is the most important parameter in the design of
retaining wall. Figure 2.1 illustrated the concept of elastic and plastic equilibrium.
a) Mohrs circles for the Ko and at plastic equilibrium(or rupture)
b) Initial Ko stake c) Active pressure d) Passive pressure
Figure 2.1 Illustration of the concept of elastic and plastic equilibrium
(Joseph E. Bowles, 1988)
6
There are two popular theories for calculating Ka and Kp coefficient of active
and passive earth pressure, respectively: Coulomb theory and Rankine theory.
2.2.2 Coulomb Theory
The assumptions in this analysis are
1. Soil is isotropic, homogeneous, and has both internal friction and
cohesion.
2. The surface of sliding through the soil is a straight line.
3. The full strength of the soil is mobilized to resist sliding (shear failure)
through the soil.
4. The friction resistance is distributed uniformly along the rupture surface
and the soil to soil friction coefficient / = tan cj)
5. There is wall friction, i.e. as the failure wedge moves with respect to the
backface of the wall as friction force is developed between soil and wall.
This friction angle is usually term 8
6. Failure is a plane strain problem consider a unit slice from an infinity
long wall.
The schematic for coulomb theory shown in Figure 2.2
180
(0
Figure 2.2 The schematic for coulomb theory (Joseph E. Bowles, 1988)
7
Active Pressure
The resultant force of active earth pressure can be express as:
r.=^rH2K.
Where
Pa = active earth pressure force (force/length)
K =
sin2 {a + 0)
sin2 <2sin(a Â£)
1 +
I sin(^ + 8) sm{(/> /?)
' sin(a 8) sin(a + /?)
y = unit weight of backfill soil (force/length3)
H = wall height (length)
cj) = the internal friction angle of soil (degrees)
a = the slope of stem face (degrees)
8 = the friction angle between wall and soil (degrees)
P = the slope of backfill surface (degrees)
(2.1)
(2.2)
For cohesive soil, the active earth pressure can be written as
p. = K.rHIcJT.
(2.3)
If p = 8 = c = 0 and a = 900 which is a smooth vertical wall with horizontal backfill,
the above equation can be simplified to
n rH
Pa =t tan
2 f
2
45*'
V
(2.4)
8
The basic assumption in the Coulomb theory is that the surface of sliding is a
plane. This assumption does not affect appreciably the accuracy for the active case.
However, for the passive case, values of Pp calculated by the Coulomb theory can be
much larger than mobilized, especially when the value of 8 exceeds about onehalf of
Passive earth pressure
For the cohesive soil, the passive earth pressure can be written as:
(2.5)
If c = 0, The resultant force of active earth pressure can be express as:
(2.6)
Where
Pp= passive earth pressure force (force/length)
K
sin2 (a (/>)
(2.7)
p
If p = 5 = 0 and a = 90 0 which is a smooth vertical wall with horizontal backfill, the
above equation can be simplified to
The values for Ka and Kp for selected angular values of (j), a, 5, and
(3 calculated from above equations are listed in Table 2.1 and 2.2
2.2.3 Rankine Theory
Rankine (1857) essentially used the same assumptions as Coulomb, except
the he assumed no wall friction or soil cohesion. The schematic for Rankine is
illustrated in Figure 2.3
Figure 2.3 The schematic for Rankine theory (Joseph E. Bowles, 1988)
10
!.l
6
0
16
1?
20
22
s
o
16
17
20
22
o
16
17
20
22
5
o
16
17
20
22
6
o
16
17
20
22
d
0
16
17
20
22
Coulomb active earth pressure coefficients, K;
ALPHA = 90 BETA = 10
S 2b 26 30 32 34 36 38 40
0.354 0.328 0.304 0.281 0.259 0.239 0.220 0.201
0.311 0.290 0.270 0.252 0.234 0.216 0.200 0.184
0.309 0.289 0.269 0.251 0.233 0.216 0.200 0.184
0.306 0.266 0.267 0.249 0.231 0.214 0.198 0.183
0.304 0.265 0.266 0.246 0.230 0.214 0.198 0.183
ALPHA 90 BETA * 5
= 26 26 30 32 34 36 36 40
0.371 0.343 0.318 0.293 0.270 0.249 0.226 0.209
0.326 0.306 0.264 0.264 0.245 0.226 0.209 0.192
0.327 0.305 0.283 0.263 0.244 0.226 0.206 0.192
0.324 0.302 0.281 0.261 0.242 0.224 0.207 0.191
0.322 0.301 0.260 0.260 4.242 0.224 0.207 0.191
ALPHA = 90 BETA  0
= 26 26 30 32 34 36 36 40
0.390 0.361 0.333 0.307 0.283 .0.260 0.238 0.217
0.349 0.324 0.300 0.278 0.257 0.237 0.216 0.201
0.348 0.323 0.299 0.277 0.256 0.237 0.218 0.200
0.345 0.320 0.297 0.276 0.255 0.235 .0.217 0.199
0.343 0.319 0.296 0.275 0.254 0.235 0.21? 0.199
ALPHA 9C 1 BETA * 5
= 26 26 30 32 34 36 36 40
0.414 0.382 0.352 0.323 0.297 0.272 0.249 0.227
0.373 0.345 0.319 0.295 0.272 0.250 0.229 0.210
0.372 0.344 0.318 0.294 0.271 0.249 . , 0.229 0.210
0.370 0.342 0.316 0.292 0.270 0.248 0.228 0.209
0.369 0.341 0.316 0.292 0.269 0.248 0.228 0.209
ALPHA 90 BETA 10
= 26 26 30 32 34 36 38 40
0.443 0.407 0.374 0.343 0.314 0.286 0.261 0.238
0.404 0.372 0.342 0.315 0.289 0.265 0.242 0.221
0.404 0.371 0.342 0.314 0.288 0.264 0.242 0.221
0.402 0.370 0.340 0.313 0.287 0.263 0.241 0.220
0.401 0.369 0.340 0.312 0.287 0.263 0.241 0.220
ALPHA = 90 BETA = 15
= 26 28 30 32 34 36 3B 40
0.482 0.440 0.402 0.367 0.334 0.304 0.276 0.251
0.447 0.406 0.372 0.340 0.310 0.283 0.258 0.234
0.447 0.407 0.372 0.339 0.310 0.282 0.257 0.234
0.446 0.406 0.371 0.336 0.309 0.282 0.257 0.234
0.446 0.406 0.371 0.338 .0.309 0.282 0.2S7 0.234
11
Table 2.2 Coulomb passive earth pressure coefficients, Kp
ALPHA = 90 BETA 10
A = 26 28 30 32 34 36 36 40 42
0 1 .914 2.053 2 .204 2.369 2 .547 2 .743 2 .957 3 .193 3 .452
ib 2 .693 2.956 3 .247 3.571 3 .934 4 .344 4 .607 5 .335 5 .940
17 2 . 760 3.034 3 .339 3.679 4 .062 4 .493 4 .983 S .543 6 .187
20 2 .980 3.294 3 .645 4.041 4 .466 4 .997 5 .581 6 .255 7 .039
22 3 .145 3.490 3 .878 4.317 4 .616 5 . 389 6 .050 6 .619 7 .720
ALPHA 90 BETA * 5
A *  26 26 30 32 34 36 36 40 42
0 2 .223 2.392 2 .577 2.761 3 .004 3 .250 3 .523 3 .826 4 .163
16 3 .367 3.709 4 .094 4.529 5 .024 S .591 6 .243 7 .000 7 .663
17 3 .469 3.626 4 .234 4.694 5 .216 S .620 6 .516 7 . 326 B .277
20 3 .606 4.226 4 .704 5.250 5 .679 6 .609 7 .462 e .468 9 .665
22 4 .064 4.532 5 .067 5.684 b . 399 7 .236 8 .222 9 . 397 10 .609
ALPHA = 90 BETA 0
A 26 28 30 32 34 36 36 40 42
0 2 .561 2.770 3 . 000 3.2SS 3 .537 3 .652 4 .204 4 .599 S .045
16 4 .195 4.652 S . 174 5.775 6 .469 7 .279 8 .229 9 .356 10 .704
17 4 . 346 4.630 5 . 365 6.025 6 . 767 7 .636 8 .661 9 .662 11 . 351
20 4 .6S? 5.436 6 .105 6.686 7 .604 e .692 10 .194 11 .771 13 .705
22 S .253 5.910 6 .675 7.574 6 .641 9 .919 11 .466 13 . 364 15 .726
ALPHA 1 90 BETA * 5
A
0 2 .943 3.203 3 .492 3.815 4 .177 4 .565 5 .046 5 .572 6 .173
16 S .250 5.676 6 .609 7.464 8 .474 9 .676 11 .128 12 .694 15 .076
17 s .475 6.146 6 .929 7.650 0 .942 10 .251 11 .636 13 .761 16 .201
20 6 .249 7.074 6 .049 9.212 10 .613 12 . 321 14 .433 17 .063 20 . 468
22 6 .864 7.820 6 .960 10.334 12 .011 14 .063 16 .665 20 .011 24 .352
ALPHA 90 BETA = I 10
A = 26 26 30 32 34 36 3B 40 42
0 3 .385 3.712 4 .0B0 4.496 4 .968 5 .507 6 .125 6 .640 7. .673
16 6 .652 7.545 8. .60S 9.876 11, .417 13 .309 15 .665 16. .647 22 .497
17 6 .992 7.956 9 .105 10.492 12 .163 M .274 16 .699 20 .254 24 .633
20 8 .166 9.414 10 .903 12.733 15. .014 17 .903 21 .636 26. .569 33 .270
22 9 .164 10.625 12 .421 14.659 17, .497 21 .164 2*6 .012 32. .601 41 .663
ALPHA 90 BETA 1 15
A 4> = 26 28 30 32 34 36 38 40 42
0 3 .913 4.331 4. .607 5.352 5. .960 6. .710 7 .563 6. .570 9. .766
16 A. .611 9.936 11 .555 13.557 16. .073 19, .291 23 .494 29. .123 36, .694
17 9 .139 10.590 12, .373 14.595 17. .413 21. .054 25, .667 32. .409 41, .603
20 11 . Q49 12.966 15. .422 10.541 22. 617 26. ,060 35. .629 46. .456 62. ,759
22 12 .676 15.067 16. .130 22.136 27. ,506 34. 930 45. .584 61. 626 87. ,954
12
Active earth pressure
The coefficient of active earth pressure, Ka can be expressed as
K = cos^/ "
COS f3 + ^COS P COS (}>
(2.9)
when the ground surface is horizontal, that is, when i=0, Ka can be expressed as
For cohesive soil, the active earth pressure can be written as
If c= 0, The resultant force of active earth pressure, Pa can be expressed as
Where
Pa = the active pressure (force/length )
Ka= the active pressure coefficient
y = the unit weight of soil(force/length )
Passive Pressure
The passive earth pressure can be expressed as
1 sin ^
1 + sin^
(2.10)
pa=Ka7H2c^Ka
(2.11)
Pa=\rH2K(
(2.12)
(2.13)
Kp = cos^/ =;  2 =
cos P ~ COS P~ cos ^
13
When the ground surface is horizontal, Kp can be expressed as
K 1 + sip#
p 1sin^
(2.14)
For the cohesive soil, the passive earth pressure can be written as:
p=KprH+2cjrp (2.15)
If c=0, The total resultant force of passive pressure can be expressed as
P=^rH2Kr (2.16)
Where
Pp = the passive pressure(force/length2)
Kp= the passive pressure coefficient
Table 2.3 and 2.4 show the active and passive coefficients for Rankine earth pressure
theory of specific parameters of soil.
Table 2.3 Rankine active earth pressure coefficients, Ka
6 *26 28 30 32 34 36 38 40 42
0 0.3905 0.3610 O. 3333 0.3073 0.2827 0.2596 0.2379 0.2174 0.1982
s 0.3959 0.3656 0.3372 0.3105 0.2855 0.2620 0.2399 0.2192 0.1997
10 0.4134 0.3802 0.3495 0.3210 0.2944 0.2696 0.2464 0.2247 0.2044
15 0.4480 0.4086 0.3729 0.3405 0.3108 0.2834 0.2581 0.2346 0.2129
20 0.5152 0.4605 0.4142 0.3739 0.3381 0.3060 0.2769 0.2504 0.2262
25 0.6999 0.5727 0.4936 0.4336 0.3847 0.3431 0.3070 0.2750 0.2465
30  0.8660 0.5741 0.4776 0.4105 0.3582 0.3151 0.2784
35    0.5971 0.4677 0.3906 0.3340
40        0.7660 0.4668
14
Table 2.4 Rankine passive earth pressure coefficients, Kp
6 ~ 26 26 30 32
0 2.5611 2.7698 3.0000 3.2546
5 2.5070 2.7145 2.9431 3.1957
10 2.3463 2.5507 2.7748 3.0216
IS 2.0626 2.2836 2.5017 2.7401
20 1.7141 1.9176 2.1318 2.361B
25 1.1736 1.4343 1.6641 1.8942
30 35   0.8660 1.3064
40 
34 36 36 40 42
3.5371 3.6S16 4.2037 4.5989 5.0447
3.4757 3.7875 4.1360 4.5272 4.9684
3.2946 3.5980 3.9365 4.3161 4.7437
3.0024 3.2926 3.6154 3.9766 4.3827
2.6116 2.6857 3.1688 3.5262 3.9044
2.1352 2.3938 2.6758 2.9867 3.3328
1.5705 1.8269 2.0937 2.3802 2.6940
1.1239 1.4347 1.7177 2.0088
0.7660 1.2570
2.2.4 Comparison of the Horizontal Pressure Between
Coulomb and Rankine Theories
The active earth pressure coefficient, Ka, for Coulomb and Rankine theories
can be calculated from Eq. 2.2 and Eq. 2.9, respectively. Figure 2.4 (a), (b), (c), and
(d) show the plots of Ka vulues for (3 = 0,5,10, and 15
From the graphs, The Ka values for Coulomb theory at different interface
friction angle(5) are not different significantly and usually lower than those from
Rankine theory except at 8 = 0. When the friction angle(
will decrease.
15
Comparison of horizontal pressure between
Coulomb and Rankine theories(P=0)
Friction angle(degree)
Rankine
Couiomb((tJ6)
Coulotnb(
Coulorob{d=22)
(a)
Comparison of horizontal pressure between
Coulomb and Rankine theories(P=5)
26 28 30 32 34 36 38 40 42
Friction angle(degree)
Rankine
Coubmb(d=l6)
CouIotnWd^O)
Coulomb(d=22)
(b)
Comparison of horizontal pressure between
Coulomb and Rankine theories((l=15)
26 28 30 32 34 36 38 40 42
Friction angle(degree)
Rankine
Couk>inb(dl6)
Coulomb(d=0)
Coulomb(d=22)
(d)
Fig. 2.4 The Plots of Ka Values
16
2.3 AASHTO Design Criteria
2.3.1 General Considerations
Abutment and retaining walls shall be investigated for:
0 lateral earth and water pressures, including any live and dead load
surcharge,
0 the self weight of the wall
0 temperature and shrinkage deformation effects, and
0 earthquake loads
Gavity and semigravity walls shall be dimensioned to ensure stability against
possible failure modes by satisfying the following factor of safety(FS) criteria:
0 Sliding FS > 1.5
0 Overturning 
FS > 2.0 for footing on soil
FS >1.5 for footing on rock
0 The factor of safety against sliding and overturning failure under seismic
loading may be reduced to 75% of the factors of safety listed above.
2.3.2 Bearing Resistance and Stability at the Strength
Stability criteria for walls with respect to various modes of failure shall be as
shown in Figures 2.5 through 2.7. where the horizontal earth pressure is computed
using the Coulomb theory, and where the horizontal earth pressure is not applied
directly to the back of the wall, a vertical component load acting on the vertical plane
extending upward from the heel shall be considered.
17
Effective
Width
Earth i Stability Criteria
Figure 2.5 Earth loads and stability criteria for walls with clayey soils in the backfill
or foundation, Duncan(1990)
Earth Loads
Stability Criteria
Thraugti Hal of Wall
q ^  HI ^Used for bearing resistance check
I Factored Gearing Resistance
Figure 2.6 Earth loads and stability criteria for walls with granular backfills and
foundations on sand and gravel, Duncan(1990)
18
77T&77
Effective
" Width
9max
\)fKUsed for bearing resistance check
__J_N...............
Factored Bearing Resistance
Stability Criteria
Figure 2.7 Earth loads and stability criteria for walls with granular backfills and
foundations on rock, Duncan(1990)
2.3.2.1 Bearing Resistance
Bearing resistance shall be investigated at the strength limit state, assuming
the following soil pressure distributions:
0 If the wall is supported by a soil foundation: a uniformly distributed
pressure over the effective base area, as shown in Fig 2.5 and 2.6
0 If the wall is supported by a rock foundation: a linearly varying
distribution of pressure over the effective base area, as shown in Fig 2.7
2.3.2.2 Overturning
For foundation on soil, the location of the resultant of the reaction forces shall
be within the middle onehalf of the base.
19
For foundation on rock, the location of the resultant of the reaction forces
shall be with in the middle threefourths of the base.
2.3.2.3 Overall Stability
The overall stability of the retaining wall, retained slope and foundation soil
or rock shall be evaluated for all walls using limiting equilibrium methods of analysis.
2.3.2.4 Passive Resistance
Passive resistance shall be neglected in stability computations, unless the base
of the wall extends below the depth of maximum scour, freezethaw or other
disturbances. Where passive resistance is utilized to ensure adequate wall stability,
the calculated passive resistance of soil in front of conventional walls shall be
sufficient to prevent unacceptable forward movement of the wall.
20
3. Design of Mechanically Stabilized Earth
Walls And AASHTO Criteria
3.1 Mechanically Stabilized Earth Wall
The functions of soil reinforcement which depends on soil reinforcement
interaction, strength and stiffness of the reinforcement, the bond between soil and
reinforcement can improve the stability of soil. MSE wall consists of 3 main
components:
0 reinforcing inclusion
0 backfill
0 facing
Reinforcing materials such as geotextile are used to carry tension stresses
developed by applied loads and the friction stress or shear resistance along the
reinforcing inclusion help to resist pullout based on the angle of friction between soil
and reinforcement. The example of the use of MSE wall are such as temporary detour
structures for highway reconstruction projects, bulk materials using sloped walls and
dam and seawalls.
Mechanically stabilized earth (MSE) wall and gravity wall are most often
used. The MSE wall, have various advantages over conventional system. The cost is
one of reasons that cause the cast in place walls to be taken over by MSE walls. A
simple and rapid construction procedure is the another advantage of MSE walls
introducing them to be more popular. The research by Timothy G. Hess, et aL, 1995
shows that MSE walls are the most frequently used by the transportation engineers.
21
3.2 Advantages and Disadvantages of Mechanically
Stabilized Earth (MSE) Wall
( Victor Elias and Barry R. Christopher, 1997)
Advantages of Mechanically Stabilized Earth(MSE) Wall
0 Use simple and rapid construction procedures and do not require large
construction equipment.
0 Do not require experienced craftsman with special skills for construction.
0 Require less site preparation than other alternatives.
0 Need less space in front of the structure for construction operation
0 Reduce rightofway acquisition
0 Do not need rigid, unyielding foundation support because MSE structures
are tolerant to deformations
0 Are cost effective.
0 Are technically feasible to heights in excess of 25 m.
Disadvantages of Mechanically Stabilized Earth (MSE) Walls
0 Require a relatively large space behind the wall or outward face to obtain
enough wall width for internal and external stability
0 MSE walls require selected granular fill. (At sites where there is a lack of
granular soils, the cost of importing suitable fill material may render the
system uneconomical).
0 Suitable design criteria are required to address corrosion of steel
reinforcing elements, deterioration of certain types of exposed facing
elements such as geosynthetics by ultra violet rays, and potential
degradation of polymer reinforcement in the ground.
22
0 Since design and construction practices of all reinforced system are still
evolving, a designer will have to continue on updating his knowledge on
specifications and contracting practices.
3.3 Reinforced soil concepts
The mainly objective of reinforced soil is to enhance soils on tensile strength
which is the result of the interaction between the reinforcement and the soil. The
composite material has the following characteristics:
0 Stress transfer between the soil and reinforcement takes place
continuously along the reinforcement
0 Reinforcement are distributed through the soil mass with a degree of
regularity and must not be localized
Stress transfer mechanisms
Friction develops at locations where is a relative shear displacement and
corresponding shear stress between soil and reinforcement surface. Reinforcing
elements where friction is important should be aligned with the direction of soil
reinforcement relative movement. Example of such reinforcing elements are steel
strips, longitudinal bar in grids, geotextile and some geogrid layers.
Passive resistance occurs through the development of bearing type stresses on
transverse reinforcement surface normal to the direction of soil reinforcement
relative movement. Passive resistance is generally considered to be the primary
interaction for rigid geogrids, bar mat, and wire mesh reinforcements. The transverse
ridges on ribbed strip reinforcement also provide some passive resistance. ( Victor
Elias, et. al., 1997)
23
PULL OUT FORCE
NORMAL PRESSURE
a) Friction stress transfer between soil and reinforcement surfaces
FRICTIONAL RESISTANCE
FRICTIONAL RESISTANCE
b) soil passive(bearing) resistance on reinforcement surfaces
Figure 3.1 Stress Transfer Mechanisms for Soil Reinforcement
24
3.4 Geotextiles
Geotextiles are usually made from polypropylene or polyester polymers
formed into fibers or yams and finally into a woven or nonwoven fabric. The choices
of fabric styles are the following:
0 Woven monofilament
0 Woven multifilament
0 Woven slitfilm monofilament
0 Woven slitfilm multifilament
0 Nonwoven continuous filament heat bonded
0 Nonwoven continuour filament needle punched
0 Nonwoven staple needle punched
0 Nonwoven resinbonded
0 Other woven or nonwoven combinations
0 Knitted(rare)
Figure 3.2 shows the type of polymeric fibers(or yams) used in the construction of
geotextiles.
ENLARGED VIEW OF GEOTEXTILE FIBERS
Figure 3.2 Types of polymeric fibers or yams
25
There are three factors to concern for the fabric manufacturer: the type of
polymer, the type of fiber and the fabric style. The polymers used in the manufacture
of geotextile fibers are made from the following polymeric materials,
polypropylene(83%), Polyester(14%), Polyethylene(2%) and Polyamide(nylon)(l%).
So the polypropylene is the most important component in the geotextiles production.
The fabric when placed in the ground is a geotextile. In generally, the words fabric
and geotextile will be used interchangeably.
Because of a widely different properties and applications of geotextile, design
method or design philosophy is a critical decision. There are mainly three different
design method as following:
1. Design by cost and availability; This method is obviously weak
technically but is still sometimes practiced.
2. Design by specification; In this method several application categories are
listed together with critical fabric properties and it is usually used when
dealing with public agencies.
3. Design by function; consists of assessing the primary function that the
geotextile will be asked to serve and then calculating the required
numerical value of that particular property.
3.5 AASHTO Design Criteria
MSE wall may be used where conventional garvity, cantilever, or
counterforted concrete retaining walls are considered, and are particularly well suited
where substantial total and differential settlements are anticipated. Based on
AASHTO, SI unit, 1994, the MSE walls shall not be used under the following
conditions:
0 Where utilities other than highway drainage are to be constructed with in
reinforced zone
26
0 Where floodplain erosion or scour may undermine the reinforce fill zone,
or any supported footing.
0 With galvanized metallic reinforcements exposed to surface or ground
water contaminated by acid mine drainage or other industrial pollutants as
indicated by low pH and high chlorides and sulfates.
The following minimum factors of safety shall be satisfied:
Pullout resistance  FS > 1.5
Ultimate bearing capacity FS > 2.0
Factor of safety against overturning =
Z Moments resisting > ^
Z Moment overturning
r c . .... ^Horizontal resisting force ,
Factor of safety against sliding = >1.5
Z Horizontal driving force
3.5.1 Movement Under Service Limit State
For system with panel areas less than 2.8 million mm and with a minimum
joint width of 19 mm, the maximum slope resulting from calculated differential
settlement shall be taken as Table 3.1
Table 3.1 Relationship between joint width and limiting distortion of the face of MSE
walls
Joint width (mm) Limiting vertical distortion
19 1/100
12.7 1/200
6.4 1/300
27
3.5.2 Safety Against Soil Failure
3.5.2.1 Sliding
The coefficient of sliding friction at the base of the reinforced soil mass shall
be determined using the friction angle of the foundation soil. In the absence of
specific data, a maximum friction angle of 30 may be used.
3.5.2.2 Bearing Resistance
For the purpose of computing strength bearing capacity, an equivalent footing
shall be assumed whose length is the length of the wall, and whose width is the length
of the reinforcement strip at the foundation level. For overturning and overall
stability, the criteria are the same as conventional walls.
3.5.2.3 Minimum Length of Soil Reinforcement
For both strip and grid type reinforcement, the minimum soil reinforcement
length should be taken as the greater of either 70% of the wall height as measured
from the leveling pad or 2400 mm. Reinforcement length shall be increased for
surcharges and other external loads.
3.5.2.4 Minimum Front Face Embedment
Unless constructed on rock foundations, the embedment at the front face of
the wall in mm shall not be less than:
0 the value specified in Table 3.2, in which H is the height of structure
above the top of the leveling pad in mm
0 a depth based on the prevailing depth of frost penetration and the external
stability requirement, and
0 600 mm.
28
Table 3.2 Minimum Front Face Embedment
Slope in Front of structures Minimum Embedment
Horizontal For walls H/20.0
For abutments H/10.0
3.0H:1.0V Walls H/10.0
2.0H:1.0V Walls H/7.0
1.5H:1.0V Walls H/5.0
3.5.2.5 Panels
The minimum panels thickness at, and in the vicinity of, embedded
connections shall be 140 mm and 90 mm elsewhere. The minimum concrete cover
shall be 38 mm. Reinforcement shall be provided to resist the average loading
conditions for each panel.
3.5.3 Internal Stability
MSE walls shall be evaluated for internal failure by slip or rupture of the
reinforcements. The factored horizontal force acting on the reinforcement at any
reinforcement level, Pi, shall be:
p, = hK (3.1
Where:
hi = height of reinforced soil zone contributing horizontal load to the
reinforcement at level i, determined as the vertical distance from the midpoint
between layer i and the next overlying layer to the midpoint between layer i and the
next underlying layer(mm)
an = factored horizontal stress at layer i
29
3.53.1 Inextensible Reinforcements
The failure surface shall be assumed to be as specified in Figure 3.3 The
factored horizontal stress, gh at each reinforcement level shall be:
h = rPovk (3.2)
where :
yp = the load factor for earth pressure in Table 3.3
k = horizontal pressure coefficient. Structures shall be designed using k = ko
at Hi above the top of the leveling pad and decreasing linearly to k = ka at
6000 mm as shown in Figure 3.3. Below a 6000 mm depth, k = ka shall be
used.
gv = pressure due to resultant vertical forces at reinforcement level being
evaluated, determined using a uniform pressure distribution over an effective
width
The maximum friction angle used for the determination of horizontal force
within the reinforced soil zone shall be taken as 34, unless the specific project select
backfill is tested for frictional strength by triaxial or direct shear testing methods.
Figure 3.3 shows the determination of failure plane and earth pressure
coefficients for MSE wall with inextensible reinforcements.
3.5.3.2Extensible Reinforcements
Internal stability for structures constructed with polymeric reinforcements
shall be analyzed using a tieback wedge method approach. A failure plane may be
assumed to be defined by Rankine active earth pressure zone defined by a straight
line passing through the wall toe and oriented at an angle of 45 + $/2 from the
horizontal, for both horizontal and sloping backfill conditions.
30
Table 3.3 Load Factors for Permanent Loads, yp
Type of Load Load Factor
Maximum Minimum
DC: Component and Attachments 1.25 0.90
DD: Downdrag 1.80 0.45
DW: Wearing Surface and Utilities 1.50 0.65
EH: Horizontal Earth Pressure
 Active 1.50 0.90
 At Rest 1.35 0.90
EV: Vertical Earth Pressure
 Overall Stability 1.35 N/A
 Retaining Structure 1.35 1.00
 Rigid Buried Structure 1.30 0.90
 Rigid Frames 1.35 0.90
 Flexible Buried Structures other than Metal 1.95 0.90
Box Culverts
 Flexible Metal Box Culverts 1.50 0.90
ES: Earth Sucharge 1.50 0.75
3.5.3.3PuIlout Design Parameters
The minimum length in the resistant zone shall be 900 mm. The reinforcement
length at all levels shall be equal. Minimum total length shall be 2400mm. The
ultimate pullout capacity of ribbed or smooth steel reinforcing strips, PfS, shall be
taken as:
Pfi=gf'rsZAs* IQ"9 (3.3)
where:
g = acceleration of gravity(m/s2)
f* = apparent coefficient of friction at each reinforcement level
As = total top and bottom surface area of reinforcement along the effective
pullout length beyond the failure plane specified in Figure 3.3, less any
sacrificial thickness (mm2)
31
H,
H tan 3 x ,3H
(1.3 tan 0)
Fig. 3.3 Determination of failure plane location and earth pressure coefficient
for inextensible reinforcements
32
Z = depth below effective top of wall or to reinforcement (mm)
ys = unfactored soil density(kg/m )
For smooth steel reinforcing strips, the apparent codfficient of friction shall be
constant at all depths and may be taken as:
i/ = soilreinforcement angle of friction(DEG)
For steel grid reinforcing systems with transverse bar spacing of 150 mm. or
greater, the generalized relation for ultimate pullout capacity, Pfg, shall be taken as:
where:
g = acceleration of gravity(m/s2)
Np = passive resistance factor taken either from backfill specific pullout tests
or in lieu of such test data, as a function of depth as specified in Figure 3.4
ys = unfactored soil density(kg/m3)
Z = depth below effective top of wall or to reinforcement(mm)
n = number of transverse bearing members behind failure plane
Ab= surface area of transverse reinforcement in bearing, less any sacrificial
a
thickness of cross bars(diameter times length)(mm )
/* = tan^ < 0.4
(3.4)
where:
(3.5)
33
Np Passive Resistance Factor
Figure 3.4 Pullout Factor for Inextensible Mesh and Grid Reinforcement
For steel grid reinforcements with transverse spacing less than 150 mm., the
ultimate pullout capacity, Pfg, shall be taken as:
P/g = 2gwlysZfd tanf 10"9 (3.6)
where:
/ = length of mat beyond failure plane(mm)
fa = internal friction angle of the reinforced soil zone(DEG)
3.6 Design Example
The walls used in this study were seven meters in height with eight layers of
inclusions as shown in Fig. 3.5 The followings are the design example of that wall.
34
Z._l
L
Le
Sb
Ti
A I
Le; 
H
/X
/ 62.5
Fig 3.5 Schematic of the wall used in this study
where
Tj = Maximum pullout force
Lei = Required anchoring length
S = 0.5(Su+Sb)
Assume = 35 0, y = 20.54 kN/m3, p = 0.5
K
a
lsin
1 + sin (p
= 0.2710
= 0.5*20.54*72*0.2710 = 136.375 kN/m
Tj = KayZiSi
35
and 1.5 Tj <2yZi.tan(j) Ci. Lei
Therefore,
I., =
1.57)
2yZ} tan ^*(0.6)
The following table shows the calculation of Tj and Lei
Table 3.4. The calculation of Tj and Le,
Inclusion No. Zj m Si m Ti=yZjKaSi kN Lei m
1 0.81 0.77 3.46 0.37
2 1.58 0.77 6.78 0.37
3 2.35 0.77 10.09 0.37
4 3.12 0.77 13.40 0.37
5 3.89 0.77 16.71 0.37
6 4.66 0.77 20.02 0.37
7 5.44 0.77 23.34 0.37
8 6.21 0.77 26.65 0.37
Lr = H*tan(90p)
p = 45+(
Therefore
Lr= 7*tan(27.5) = 3.65 m.
L0 = LR+Le =3.65+0.37 = 4.02 m or0.57H
In this study, use L0 = 7.75 m
F.S. against pull out is approximately (7.753.65)/0.37 = 11.08
F.S. against sliding = (yLH)(tan<))/Pa
= 20.54*7.75*7*0.5/136.375
= 4.08 >1.5
F.S. against overturning = (Resisting Moment)/(Overtuming Moment)
= (3 l2)/ KaH2
36
= (3*7.752)/(0.271 *72)
= 13.57 >2.0
In this study, the length of inclusion was 7.75m or 1.1 m. which provided the
high factor of safety against pull out. The reason why we need that long inclusion is
to study the stresses distribution in inclusion.
The results from FEM analysis for this particular soil show that only the
length of 0.3H of inclusions were in tension. According to AASHTO, the minimum
length of inclusion is 0.7H which is longer than that from FEM results for this
particular soil. The results also show that the inclusion in bottom layer experienced
less stresses than those in top layer so maybe the inclusions in bottom layer can be
reduced the length.
37
4. NIKE3D, Material Models, and Wall Dimensions
4.1 Introduction
The NIKE3D is a non linear finite element code developed by the Lawrence
Livermore National Laboratory(LLNL). The University of Colorado at Denver has a
signed collaborative agreement with LLNL to use and develop this program. The
NIKE3D program was developed in 1980. A typical NIKE analysis is concerned
structural vibration, low velocity dynamics and static loading of complex mechanical
systems. This program can also account for the response of structures to
earthquakes. One of the many advantages of this program is many different material
models are available.
The NIKE3D program has INGRID and TAURUS as preprocessor and
postprocessor, respectively. INGRID is used to define the finite element mesh, slide
lines, etc. The material models and properties including boundary conditions need to
be assigned in this step. The output from INGRID is fed into the NIKE3D program
for analysis. The output from NIKE3D then is used as input for TAURUS for post
processing including graphing.
4.2 Interface Formulation(LieuChing Jiang, 1996)
NIKE3D contains interface models capable of simulating the interface
slippage, debonding, and rebonding. One side of the contact surface is named master
surface and the other the slave surface. The nodes on the slave are called slave
nodes and the nodes on the master surface master nodes. A typical slide line in a
contact region is shown in Figure 4.1 and 4.2.
38
Figure 4.2 shows an isolated portion of an interface where the node m is
penetrating through the segment jk. A local equilibrium conditions can be expressed
in the following equation:
KsAus=PsFs (4.
where Ks = the spring stiffness
Fs = spring internal force
Ps = the external force arising from internal states of stress in the interface
elements.
Aus = [Avm, Awm, Avj, Awj, Avk, Awk]
Ks can be defined as in the following matrix, where c = cos 0, s = sin 0 a is the
ratio of the contact surface to the length of jk, as shown in Figure 4.1, and k is the
panalty stiffness:
s2 sc a ~a)s2 (1 a)sc as2 asc
sc c2 (1 a)sc (1 ~a)c2 asc ac2
(1 ay (1 a)sc (l)V (1 a)2 sc (1 a)as2  (1 a)asc
(1 a)sc (1 ~a)c2 (lar)2.ye (1 ~a)2c2  (1 a)asc (1 a)ac2
2 as asc (1 a)as2 (1 a)as2 a2s2 a2 sc
asc ac2  (1 a)asc (1 a)ac2 a2 sc a2c2
Fs is internal spring force defined as
39
MASTER SURFACE
MASTER NODE
LAVE SURFACE
CONTACT REGION
SLAVE NODES
Fig. 4.1 Typical Interface (NIKE2D User Manual, 1991)
Fig 4.2 Contact of Node m with Segment jk (NIKE2D User Manual, 1991)
40
s
Fs =kS
c
(la>
(1 ~a)c
as
ac
(4.3)
where 5 is the amount of penetration of node m through segment jk.
The algorithm of the interface friction at yielding, Fy, can be expressed as the
following mathematical equations:
Fy= p,fn
Ae = xn+1(sn+1, tn+1)xn+1(sn, tn)
f* = f"k Ae
f+1 = f* if f*
f+1 = Fyf*/f= if f*> Fy
where
f* = the trial force,
fn = normal force,
K = interface stiffness,
jli = coefficient of friction,
f1 = the frictional force at time n,
fn+1 = the frictional force at time n+1,
sn+1 = the local coordinate at time n+1,
sn = the local coordinate at time n,
tn+1 = the local coordinate at time n+1,
tn = the local coordinate at time n,
xn+1 = the global coordinate at time n+1, and
xn = the global coordinate at time n.
41
4.3 RambergOsgood Elastoplasetic Model
4.3.1 Equation for Monotonic Loading
The RambergOsgood model is based on the nonlinear relative between shear
modulus and damping ratio at various shear strains. Figure 4.3 shows the relation of
G/Gmax and damping ratio versus shear strain between input data and Ramberg
Osgood model.
Fig 4.3 comparision of relations of G/Gmax and damping ratio versus shear strain
(TzouShin Ueng, et al., 1992)
42
The RambergOsgood model is used to describe the nonlinear hysteretic constitutive
relation of the onedimensional elastoplastic behavior of many materials, including
the dynamic soil behavior. Four parameters are needed for the model: reference shear
strain(yv), reference shear stress(Ty), stress coefficient(a), and stress exponent(r).
The backbone(monotonic loading) strainstress relation of the Ramberg
Osgood elastoplastic model can be express by:
^(l +
Yy
r\
(4.1)
where y = shear strain,
x = shear stress,
yy = reference shear strain,
Ty = reference shear stress,
a = stress coefficient > 0, and
r = stress exponent > 1.0
4.3.2 UnloadingReloading Relation
For unloading and reloading, according to Masings rule, the relation
becomes:
YYo
2Yy
2ry
(1+a
rr0
2ty
r1
)
where yo = shear strain at point of stress reversal, and
To= shear stress at point of stress reversal.
(4.2)
43
The dynamic hysteretic properties, such as dynamic soil behavior, are
commonly given in terms of equivalent linear(secant) modulus, Go, and equivalent
critical damping ratio, p. Fig. 4.4 shows the hysteresis loop according to Ramberg
Osgood model. Fig. 4.5 shows the equivalent linear modulus and damping ratio of
soils. Fig 4.6 and 4.7 show the variation of shear modulus and damping ratio with
shear strain, respectively.
By rearranging Eq 4.1 the secant modulus for the backbone curve can be
expressed as:
1
7 Yy
r1
1+a
T
V
y 7
(4.3)
At a very small strain, i.e., y 0 and x  0, since r > 1,
T
y
(4.4)
(Go)ro =3
max
Then the backbone relation can be written as:
rl
(4.5)
Therefore, the other three parameters, yy, a, and r, need to be determined.
Shear strain
Fig. 4.4 Hysteresis loop according to RanbergOsgood model
x
Fig. 4.5 The equivalent linear modulus and damping ratio of soils.
(TzouShin Ueng, et al., 1992)
45
SHEAR MODULUS OF SHEAR STRAIN i
DAMPING RATIO PERCENT SHEAR MODULUS OF t 10'4 PERCENT
SHEAR STRAIN, y PERCENT
Fig 4.6 The variation of shear modulus with shear strain for sands
(Seed and Idriss, 1970)
, A Weissman and Hart 0961) Hardin (1965) O Drnevich, Hall and Richarl (1966) O Matsushita, Kishida and Kyo(l967) Silver and Seed (1969) A Oonavan (1969) a'"0 a X 4 B 
m / / X / / X
Hardin and v Kishida and Drnevich (1970) Takono (1970) / / / f / J } / / / / / / / / /
V / / / / /
> / A Xir r / / O
V
n t=~ 1______________________________________________
IO"1 I03 I0_z 10"' I
SHEAR STRAIN PERCENT
Fig 4.7 The variation of damping ratio with shear strain for sands
(Seed, et al., 1984)
46
4.3.3 Evaluation of Stress Coefficient^) and Stress Exponent(r)
Substituting t = Goy and rearranging Eq. 4.5 we obtain
1 = a
G0y
r1
(4.6)
log(%^l) = loga+(rl)log(^) ,
^0 ^mayJ?y
The values of a and r can be determined from the intercept and the slope,
respectively, of the straight line and the ordinary leastsquare method is used in
finding tbe best fit straight line. Fig 4.8 shows the plot of log (Gmax/Gol) versus
log(Goy/GmaxYy)
Ie( 1)
47
4.3.4 Evaluation of Equivalent Critical Damping Ratio, (3
The equivalent critical damping ratio,[3, for a hysteresis loop with the tip at (yo,
to) can be express as:
AE 2a(rY) ( r V r \ 7o
2 7TT0r0 n{r +1) ^^max j
where AE=energy dissipation in one loading cycle.
The value of P computed from Eq 4.8 may not necessarily fit well with the
soil damping data obtained in the tests. The difference may be significant in some
cases. For better fit of both modulus and damping data, the following need to be
considered.
Substituting Eq. 4.6 in Eq 4.8, we obtain
2frl)
n(r +1)
iG
G
, or
max J
(4.9)
Go _1 fa(r+1)
Graax 2(11)
substitute Eq. 4.10 in Eq. 4.7 then
log
Pn(r+1)
2(rY) f37t(r+ Y)
log a + (rY) log
Tj Prtr+\) r
IL 2(r1) J r>)
(4.10)
(4.11)
Depending on the type of soils and the loading conditions, the reference stress,
Ty, usually ranges approximately from 0.6 to 0.9 of the shear strength of the soils.
Then yy can be calculated by multiplying xy with Gmax according to Eq. 4.4 and also
48
the value of yy can be determined based on the modulus and damping data by
iteration procedure as following:
1. Assume a value for yy and obtain the values of a and r by plotting the data
according to Eq.4.7
2. Compute yy according Eq 4.8 from the given modulus and damping data
and obtain an average value of yy
3. Compare the new value of yy with the previous value. Repeat step 1 and 2
if the difference is too great.
4.4 Material Parameters
Soil: RambergOsgood Model
Stiff soil Soft soil Ratio
Reference shear strain,yy = 1.09* 104 0.49*1 O'4 2.22
Reference shear stress,xy,N/m2 = 3.88*104 0.62* 104 6.26
Stress Coefficient,a = 0.86 0.94 
Stress exponent, r = 2.16 2.27 
Bulk modulus, K, N/m2 = 1.59*109 1.83* 10s 8.74
Gmaxs N/m = 3.57 *108 1.24* 108 2.88
E, N/m2 = K*3(l2v) = 2.39*109 1.65*108 14.48
vs, m/s = 391 248 1.57
Density, p, kg/m = 2322 2002 1.16
Concrete : Elastic Model
Youngs Modulus, E, N/m2 =2.618*1010
Poissons Ratio, v = 0.35
Density, p kg/m3 =2511.42
49
Inclusions : Elastic Model
Youngs Modulus, E, N/m2 = 5.10*10'
5*E, N/m2 = 2.55*10l
Poissons Ration, v = 0.25
Density, p, kg/m = 900
4.5 Walls Dimensions
The walls dimensions, used in this study, are:
Wall height = 7.0 m.
Stem thickness = 0.2 m.
Base thickness = 0.3 m.
Base length
 Invert Lwall and invert Lwall with shear key = 1.6 m.
Twall = 3.6 m.
The backfill is mechanically stabilized backfill(MSB) with 8 layers of
inclusions. The slope of the backfill is zero and the length of inclusions are about 8
m. The Youngs modulus for soil is 2.3925*109 Pa. while that values for
inclusions(Ei) are 5.10* 107 Pa. and 2.55* 108 Pa.( for 5*Ei). So, the Youngs
modulus for soil is higher than that for inclusions about 9 to 45 times.
The inclusions can be considered as an extensible inclusions due to their
strength are much lower than those of soil.
Figure 4.9,4.10 and 4.11 show the dimensions of the walls.
50
/0.20m.
0.3Orv
]_
1.20n.
0.30m.
1.00 m.
0.50m.
K.~
1 1.60m. 7.75n.
16.00n.
Figure 4.9 The schematic of invert Lwall
8.50m.
/0.20m.
8.30n.
1.20m.
0.30m.i
1.00m.
0.50m.:
h*.
8.50m.
16.00m.
Figure 4.10 The Schematic of invert Lwall with shear key
51
yf050n.
8.30m.
8.50n.
Figure 4.11 The schematic of Twall
52
5. Mechanically Stabilized Earth
The mechanically stabilized earths with 4 layers of inclusions and with the
variation of applied surcharge were analyzed. The height and width for those MSE
are 8 m. by 8.30 m. The effects of wrapped and unwrapped inclusions also were
investigated. The parameters that were studied are horizontal displacement, vertical
displacement, and stresses distribution in inclusions. Fig 5.1 shows the boundary
conditions for MSE with wrapped and unwrapped inclusions. Fig. 5.2 shows the
finite element mesh.
Applied surcharge
(a) (b)
Fig 5.1 The Schematic and Boundary Conditions of MSE with (a) Wrapped
Inclusions, (b) Unwrapped Inclusions.
53
Fig. 5.2 The Finite element mesh for MSE
5.1 Horizontal Displacement
Fig. 5.3(a) shows the maximum horizontal displacement for the cases with
different applied surcharge and wrapped and unwrapped inclusions. For the
unwrapped inclusions cases, the maximum horizontal displacement are 1.02, 1.58,
and 3.70 mm. for 0,25, and 100 KPa applied surcharge, respectively. Furthermore,
for the wrapped inclusions, the maximum horizontal displacement are 0.975,1.40,
and 3.52 mm. for 0,25, and 100 KPa of applied surcharge which are lower than those
of unwrapped inclusions cases by about 4 to 5 percent. Obviously, As the result of an
increasing of applied surcharge, the horizontal displacement increased.
Figs. 5.4(a), 5.5(a), and 5.6(a) show the horizontal displacement of MSE with
unwrapped inclusions and with 0,25, and 100 KPa of applied surcharge, respectively.
It is obviously that the locations of maximum horizontal displacement shift upward
54
when the applied surcharge increases. The locations of maximum horizontal
displacement are at the depth of 6, 6, and 0 m for 0,25, and 100 KPa of applied
surcharge, respectively.
Fig. 5.4 (a) shows the horizontal displacement of MSE with unwrapped
inclusions and 0 KPa of surcharge. The horizontal displacement at the top is about
0.40 mm and it increases with depth to 1.02 mm. at the depth of 6m. It then decreases
to about 0.25 mm. at the depth of 8 m. The maximum value is 1.02mm at the depth of
6 m.
Fig. 5.5 (a) shows the horizontal displacement of MSE with unwrapped
inclusions and 25 KPa of surcharge. The deformed shape is similar to that with 0
KPa applied surcharge. The maximum horizontal displacement is 1.58 mm at the
depth of 6 m.
Fig 5.6(a) shows the horizontal displacement of MSE with unwrapped
inclusions and with 100 KPa of surcharge. The top of the wall provides the
maximum horizontal displacement and reduces linearly with depth. The maximum
value is 3.70 mm. the top of the wall.
The MSE with wrapped inclusions are shown in Fig. 5.7(a), 5.8(a), and 5.9(a)
for 0,25, and 100 KPa surcharge, respectively. The locations of maximum horizontal
displacement are at the depth of 5.7, 5, and 0 m for 0,25, and 100 KPa of applied
surcharge, respectively.
Fig. 5.7 (a) shows the horizontal displacement of MSE with wrapped
inclusions and with no surcharge. The displacement increased with depth and
provided maximum horizontal displacement of 0.975 mm at the depth of 5.7 m.
From the depth of 5.7 m to 8 m, the horizontal displacement reduced from 0.975mm
to 0.1 mm.
Fig. 5.8 (a) shows the horizontal displacement of MSE with wrapped
inclusions and with 25 KPa of surcharge. The deformed shape of the wall is similar to
55
that with unwrapped inclusions. The maximum horizontal displacement is 1.40 mm at
the depth of 5 m.
Fig. 5.9 (a) shows the horizontal displacement of MSE with wrapped
inclusions and with 100 KPa of surcharge. The deformed shape also is similar to that
with unwrapped inclusions. The maximum horizontal displacement is at the top of
the wall, which is 3.520 mm.
5.2 Vertical Displacement
The plots of vertical displacement are shown in Fig. 5.4(b), 5.5(b), and 5.6(b)
for unwrapped inclusion cases and are shown in Fig. 5.7(b), 5.7(b), and 5.9(b) for
wrapped inclusions cases. Fig. 5.3(b) shows the vertical displacement for two cases
with applied surcharges. For the unwrapped inclusions cases, the settlements are
2.35, 3.34, and 8.69 mm. for 0,25, and 100 KPa of applied surcharge, respectively.
For the wrapped inclusions cases, the settlements are 2.17, 3.09, and 7.83 mm. for 0,
25, and 100 KPa of applied surcharge, respectively, which are about 7.5 to 10 percent
lower than those of unwrapped inclusions cases.
5.3 Walls Rotations
Fig. 5.3(c) shows the degree of rotation of the walls. The degree of rotation
increases when the applied surcharge increases. For the unwrapped inclusion cases,
the degree of rotation ranges between 0.0214 to 0.0677 degree for 0 to 100 KPa of
surcharge. For the wrapped inclusions cases, the degree of rotation range between
0.0205 to 0.0634 degree which are a little bit lower than those of unwrapped cases.
5.4 Stresses Distribution In Inclusions
Fig. 5.4(c) shows the stresses distribution in inclusion for MSE with
unwrapped inclusions and with 0 KPa of applied surcharge. From the plot, only the
first element in the top experiences both tension and compression stresses, which are
56
in between 37 KPa to 13 KPa. The element in first layer that provided highest
tension stress is the first element. The inclusions can be ranked in term of highest
compression stresses as following: inclusions in fourth, third, second and first layers.
The inclusion in second layer is subject to stresses between 5 to 13 KPa. The
inclusion in third layer experienced stresses between 3 to 30 KPa. and between 13
to 48 KPa for that in fourth layer.
Fig. 5.6 (c) shows the stresses distribution in inclusions for MSE with
unwrapped inclusion and with 100 KPa of applied surcharge. The first two elements,
in the top layer and the first element in the second layer are subject to tension
stresses. The rest are all in compression. The inclusion in the fourth layer experiences
the highest compression stresses and is subject to higher compression in the elements
that close to another end, which the boundary condition is set to restrict in horizontal
direction. The stresses in inclusions are in the range of 55 to 78 KPa for this case.
The stresses distribution for MSE with wrapped inclusions are shown in Fig.
5.7(c), 5.8(c), and 5.9(c). The fifth layer of inclusion is added to MSE at the bottom.
The stresses distribution for MSE with wrapped inclusion and 0 KPa of applied
surcharge case, as shown in Fig. 5.7(c), most inclusions are in compression stresses
except the inclusion in first layer which some elements along the length of inclusion
were in tension stresses. The inclusion in fifth layer experienced highest compression.
On the contrary, the inclusion in first layer experience lowest compression stresses
and even tension stresses in some elements. The range of stresses are in between 10 to
75 KPa. for this case.
Fig. 5.8(c) shows the plot for MSE with 25 KPa of surcharge. All inclusions
are in compression stresses. The inclusion in first layer experience lowest
compression stresses and the fifth layer shown the highest compression stresses. The
compression stresses are in the range of 5 to 88 KPa.
Fig. 5.9(c) shows the stresses distribution in inclusion of MSE with wrapped
inclusions and 100 KPa of surcharge. All inclusions are in compression stresses. For
57
the inclusion in first layer, the first element experiences compression stresses about 
20 KPa and decreases to about 5 KPa. For the second to fourth layer, the stresses in
their first element are about 20 KPa and increased to about 30, 50, and 70 KPa at
another end of inclusions for those in second, third and fourth layers, respectively.
The inclusions in fifth layer experience stresses in the range of80 to 130 KPa
which is the layer that is subject to highest compression stresses.
5.5 Comparison Between MSE With Wrapped
And Unwrapped Inclusions
From Figs. 5.3(a) and (b), it is obviously that the MSE with wrapped
inclusions provide the smaller horizontal and vertical displacement; especially at the
high applied surcharge. The deviation of vertical displacement between these two
cases are higher at high applied surcharge.
The soil along the front face is retained by the wrapped inclusions so that it
provided a smaller deformation.
5.6 Effects of Soft Soil
The softer soil were used in the analyzed to compare the effects to soil
behaviors. The parameters that used for this soft soil is listed in Chapter 4. The MSE
with 25 KPa of surcharge was selected to compare the horizontal displacement,
settlement, and stress distribution in inclusions as shown in Figs. 5.10(a), (b), and (c),
respectively.
From Fig. 5.10(a), At the depth 0 to 5.5 m., the horizontal displacement
increases with depth and the maximum horizontal displacement is 24.30mm. at the
depth of 5.5m. At the depth from 5.5 to 8 m., the horizontal displacement reduces
nonlinearly to 5 mm. In comparison, the maximum horizontal displacement of this
soft soil is 24.30mm. whereas the maximum horizontal displacement of strong soil is
1.58mm.
58
The settlement reduces nonlinearly with depth as shown in Fig. 5.10(b). The
maximum settlement is at the top which is 62.9mm whereas that for strong soil is
3.340mm.
Fig. 5.10(c) shows the stress distribution in inclusions. The stress in top three
layers are all in tension which are in the range of 30 KPa to 250 KPa. For the fourth
layer inclusion, the first element experiences tension stress of 80 KPa and from
second element to the first six meter of the length of inclusion experience tension
from 430 KPa to 0 KPa at six meter. From the length 6m., the inclusion experiences
compression of 0 KPa and increases nonlinearly to 50KPa at the length of 7.75
KPa.
5.7 Summary
The results of study of MSE can be summarized as the following
1 .The location of maximum horizontal displacement shifts upward when the
applied surcharge increases.
2. The maximum horizontal displacement increases almost linearly as the
surcharge increases.
3. The settlement increases almost linearly with an increasing of an applied
surcharge.
4. The horizontal displacement, settlement, and rotation for the MSE with
wrapped inclusions are less than those of the MSE with unwrapped inclusions.
5. For the softer soil, both the horizontal displacement and the settlement are
much higher than those of strong soil.
6. Inclusions in the soft soil experience more tension than those in the strong
soil.
7. Only at fourth layer where either the surcharge is the highest or the soil is
soft, the assumption of Rankine failure plan is maybe valid.
59
8. The wrapped case is a close resemblance of MSB with wire basket wall
face or wire gabion wall that explains why almost all inclusions are in compression.
60
MSE
Material model: SoilRO; InclusionsElastic
No. of inclusions's laye4
E of inclusions : lEti
The variaiton of max. horizontal disp. with
applied surcharge
Applied surcharge(KPa)
(a)
Rotation of the front face
Applied surcharge(KPa)
The variation of max. vertical disp. with
applied surcharge
Applied surcharge(KPa)
(b)
(c)
Fig. 5.3 The variation of parameters with applied surcharges:
(a) Max. horizontal displacement, (b) Max. settlement, (c) Rotation
61
MSE
Material model: SoilRO; Inclusions Elastic
No. of inclusion's la4
Surcharge : 0 KPa
E of inclusions : 1 Eti
MSB
0.000
2.000
s
Â£
6 4.000
a
u
Q
6.000
8.000
1.500 1.000 0.500 0.000
Horizontal displacement(mm)
(a)
Stresses distribution in inclusions
50.0
Â£ 25.0
V
1 25.0
0
1
50.0
0.0 2.0 4.0 6.0 8.0
Distance(m)
(C)
Fig. 5.4 Plots of investigated parameters for MSE with 0 KPa of surcharge
62
MSE
Material model: SoilRO; Inclusions Elastic
No. of inclusion's layers : 4
Surcharge: 25 KPa
E of inclusions : 1 Eti
Stresses distribution in inclusions
I
(C)
Fig. 5.5 Plots of investigated parameters for MSE with 25 Kpa of surcharge
63
MSE
Material model: SoilRO; Inclusions Elastic
No. of inclusion's layers : 4
Surcharge: 100 KPa
E of inclusions : 1 Eti
Stresses distribution in inclusions
80.0
60.0
S' 40.0
Â£
Â£ 20.0
u
0.0
{20.0
E 40.0
I
60.0
80.0
0 2 4 6 8
Distance(m)
MSB
0.000
2.000
?
Â£ 4.000
a
o
O
6.000
8.000
10.00 8.000 6.000 4.000 2.000 0.000
0
Vertical displacement(mm)
(b)
(c)
Fig.5.6 Plots of investigated parameters for MSE with 100 KPa of surcharge
64
MSE(wrapped)
Material model:
No. of inclusion's layers :
Surcharge:
E of inclusions:
SoilRO; Inclusions Elastic
4
OKPa
1 Eti
Stresses distribution in inclusions
I Til TI2 t Til Â¥ T14 M T1S 
Distance(m)
MSB

Max. v :rt disp. e 2.170mr
2.500 2.000 1.500 1.000 0.500 0.000
Vertical displacement(mm)
(b)
(c)
Fig. 5.7 Plots of investigated parameters for MSE with wrapped inclusions and 0 KPa
65
MSE(wrapped)
Material model: SoilRO; Inclusions Elastic
No. of inclusion's layers : 4
Surcharge : 25 KPa
E of inclusions : 1 Eti
(a)
Stresses distribution in inclusions
Til TI2 ATI3 X TI4 TI5
Distance(m)
MSB
4.00 3.00 2.00 1.00 0.00
Vertical displacement(nun)
(b)
(c)
Fig. 5.8 Plots of investigated parameters for MSE(wrapped) with 25 KPa
66
MSE(wrapped)
Material model: SoilRO; Inclusions Elastic
No. of inclusion's layers : 4
Surcharge : 100 KPa
E of inclusions : 1 Eti
Stresses distribution in inclusions
0.000 2.000 4.000 6.000 8.000
Distance(m)
(C)
Fig. 5.9 Plots of investigated parameters for MSE (wrapped) with 100 KPa
67
MSE
Material model: SoilRO(soft); Inclusions Elastic
No. of inclusion's layers : 4
Surcharge: 25 KPa
E of inclusions : 1 Eti
Stresses distribution in inclusions
(C)
Fig. 5.10 Plots of investigated parameters for MSE with 25 KPa of surcharge
for soft soil
68
6. MSE Wall With Segmental Panel Facing
The four layers of inclusions with segmental panel facing with the height of
1.8 m. were used in this study. Surcharge: 0, 50,100 and 200 KPa, were applied. Fig.
6.1 shows the finite element mesh and boundary conditions.
Fig. 6.1 (a) The schematic and boundary conditions of segmental panel facing
69
Fig. 6.1(b) The finite element mesh of segmental panel facing
6.1 The Effects of the Variation of Applied Surcharge
6.1.1 Horizontal Resultant Forces at Back of Wall
From Fig. 6.2(a), the resultant force varies linearly with the applied surcharge.
When the surcharge increases, the resultant force also increases. The resultant force
at 0, 50, 100, and 200 KPa are 153,225,299, and 446 KPa, respectively. Those
resultant forces are lower than Rankine active earth pressure as calculated in chapter
7.
6.1.2 Locations of Resultant F orces (Hr/H)
From Fig. 6.2(b), the locations of resultant forces shift upward as the applied
surcharge increases which caused the reduction in overturning stability. As observed
70
from the graphs slope, the changing of location of resultant force is affected to a
lesser degree at a high surcharge than that at a low surcharge. The value of those
Hr/H are 0.254, 0.272, 0.281, 0.284 for 0, 50,100, and 200 KPa of applied
surcharge.
6.1.3 Maximum Horizontal D isplacement
The maximum horizontal displacement increases with the increase in applied
surcharge as shown in Fig. 6.2(c). At a high surcharge, the changing rates are higher
than those at a low applied surcharge. The values of maximum horizontal
displacement are 0.291, 0.885, 1.960, and 5.220 mm. for 0, 50, 100, and 200 KPa of
applied surcharge.
6.1.4 Maximum Vertical Displacement
As show in Fig 6.2(d), the maximum vertical displacement varies with the
applied surcharge almost linearly. Those maximum vertical displacements are 0.755,
1.080,1.490, and 2.160 mm. for 0, 50,100, and 200 KPa of applied surcharge.
6.1.5 Degree of Rotation
From Fig 6.2(e), The rate of change of rotation to applied surcharge increases
as an increasing rate as the surcharge increases. The rotation angle ranges from 0.002
to 0.037 degree.
6.2 Active Earth Pressure and Passive Earth Pressure
Figs. 6.3(a) to 6.6(a) show the active earth pressure at different applied
surcharges. The soil elements neighboring the wall face are in compression and
higher compression when the depth increases. The values of maximum active earth
pressure are 64, 120, 159, and 246 KPa for 0, 50,100, and 200 KPa of surcharge,
respectively
71
The passive earth pressure varies almost linearly with depth as shown in Fig
6.3(b) to 6.6(b). The maximum passive earth pressures are at the bottom which are
78,120,148, and 215 KPa for 0, 50, 100, and 200 KPa of surcharge, respectively.
6.3 Bearing Pressure At Wall Base
The highest bearing pressure occurs at the element right under the wall stem
and it decreases with the distance from the wall stem as shown in Fig 6.3(c) to 6.6(c).
The bearing pressures at wall bases are in the range of 102 to 180, 129 to 231,152 to
277 and 196 to 375 KPa for 0, 50,100, and 200 KPa of surcharge, respectively.
6.4 Stresses Distribution in Inclusions
The stresses in inclusions are mostly in compression and almost constant
along the length of inclusions except in the first elements in top two layers. The
highest compression stresses was in fourth layer inclusion and lowest compression
stress is in first layer inclusions. As shown in Figs. 6.3(d) to 6.6(d), The stresses are
in the range of 13 to 32, 50 to 44,184 to 51, and 352 to 73 KPa for 0, 50,100,
and 200 KPa of surcharge, respectively.
6.5 Horizontal Displacement of Wall Face
The locations of maximum horizontal displacement are at the bottom of walls
with 0 KPa surcharge and shift upward when the surcharge increased as shown in Fig
6.3(f) to 6.6(f) For the wall with 200 KPa surcharge, the maximum horizontal
displacement is at the top of the wall. The horizontal displacements are in the range of
0.091 to 0.291, 0.388 to 0.885, 0.603 to 1.960, and 1.140 to 5.220 mm for 0, 50, 100,
and 200 KPa of surcharge, respectively.
6.6 Vertical Displacement of Wall Face
Figs. 6.3(g) to 6.6 (g) show the vertical displacement of wall face. When the
surcharge increases, the vertical displacement also increases corresponding to that
72
additional load. The vertical displacement values are in the range of 0.699 to 0.755,
0.967 to 1.080,1.270 to 1.490, and 1.970 to 2.610 mm. for 0, 50,100, and 200 KPa of
surcharge, respectively.
6.7 The Analysis of Segmental Panel Facing with Soft Soil
The segmental panel facing with 50 KPa of surcharge was selected to
analyzed with softer soil. Fig. 6.7 shows the investigated parameters for soft soil.
The plot of active earth pressure is shown in Fig.6.7(a). The active earth
pressures are in compression and increase with depth except the top three elements
above the first inclusion which are in tension. Those active earth pressures range
between 80 KPa to 75 KPa. Fig. 6.7(b) shows the passive earth pressure. The values
for passive earth pressure vary in the range of10 KPa to 135 KPa. Fig. 6.7(c)
shows the bearing pressure at wall base. The element that close to back wall face
experiences highest compression. The values are in the range of140 KPa to 240
KPa. Fig. 6.8(d) shows the stress distribution in inclusions. The stresses in those
inclusions range between 30 KPa to 75 KPa.
Fig 6.7(e) shows the shear diagram. The maximum value or total resultant
force is 290 KPa which is higher than that for stiff soil (225KPa). The horizontal
displacement for soft soil is 9.44mm. whereas the horizontal displacement for stiff
soil is 0.885mm. as shown in Fig. 6.7(f). Fig. 6.7(g) shows the settlement for soft
soil. The maximum settlement is 19.30 mm which is much higher than that of stiff
soil.
6.8 Summary
The results from this analysis can be summarized as the following :
1. Horizontal resultant force increases linearly with the increase of an applied
surcharge.
73
2. Horizontal displacement, settlement and degree of rotation increase almost
linearly with an increase of a applied surcharge.
3. Location of resultant force shifts upward as the applied surcharge
increases.
4. The degree of rotation increases with an increase of applied surcharge and
the rate of change increase as the applied surcharge increases also.
74
Wall type :
Material model:
No. of inclusions's layer
Attached/Detached:
E of inclusions :
Segmental panel facing
SoilRO; InclusionsElastic
4
Attached
lEti
The variaiton of max. horizontal disp. with
applied surcharge
(C)
(d)
Fig. 6.2 Plost of the variation of parameters with surcharge
75
Wall type :
Material model:
No. of inclusions's layer :
Attached/Detached:
E of inclusions :
Segmental panel facing
SoilRO; InclusionsElastic
4
Attached
lEti
Fig. 6.2(cont.)Plost of the variation of parameters with surcharge
Wall type: Segmental panel facing
Material model: SoilRO; InclusionElastic
No. of inclusion's layers : 4
Attached/Detached: Attached
Surcharge: no surcharge
E of inclusion: lEti
The variation of activeearth pressure against
wall face
0.0
1.0
2.0
_3.0
S,
5 4.0
c.
6.0
7.0
8.0
50.0 0.0 50.0 100.0
Active earth pressure(KPa)
(a)
The variation of bearing pressure at wall base
0.0 0.5 1.0 1.5 2.0 2.5
Distance(m)
(c) (d)
Fig. 6.3 The plots of investigated parameters for SPF with 0 KPa surcharge
77
Wall type:
Material model:
No. of inclusion's layers :
Attached/Detached :
Surcharge :
E of inclusion:
Segmental panel facing
SoilRO; InclusionElastic
4
Attached
no surcharge
lEti
Horizontal displacement of wall face
0.40 0.30 0.20 0.10 0.00
Displ acement(mm)
(f)
(g)
Fig. 6.3(cont.) The plots of investigated parameters for SPF with 0 KPa surcharge
78
Wall type:
Material model:
No. of inclusion's layers :
Attached/Detached :
Surcharge:
E of inclusion:
Segmental panel facing
SoilRO; InclusionElastic
4
Attached
50KPa
lEti
The variation of active earth pressure against
100.0 50.0 0.0 50.0 100.0 150.0
Active earth pressure(KPa)
0.0 50.0 100.0 150.0
Passive earth pressure(KPa)
(a)
(b)
The variation of bearing pressure at wall base
0.0 0.5 1.0 1.5 2.0 2.5
Distance(m)
o
*3
(A
rt
C
_N
C
X
The variation of horizontal stresses in TI.
0.0 2.0 4.0 6.0 8.0
Distance(m)
(C) (d)
Fig. 6.4 The plots of investigated parameters for SPF with 50 KPa surcharge
79
Wall type:
Material model:
No. of inclusion's layers :
Attached/Detached:
Surcharge :
E of inclusion:
Segmental panel facing
SoilRO; InclusionElastic
4
Attached
50KPa
lEti
Shear diagram(KN/m)
50.0 0.0 50.0 100.0 150.0 200.0 250.0
Shear (KN/ra)
(e)
Vertical displacement of wall face
1.100 1.050 1.000 0.950
Displacement (mm.)
(g)
Fig. 6.4 (cont.)The plots of investigated parameters for SPF with 50 KPa surcharge
80
Wall type:
Material model:
No. of inclusion's layers :
Attached/Detached:
Surcharge :
E of.inclusion:
Segmental panel facing
SoilRO; InclusionElastic
4
Attached
lOOKPa
lEti
The variation of active earth pressure against
wall face
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
f?
1 1 it
&=
l < 4
* "rV
h
J _U
300.0 200.0 100.0 0.0 100.0 200.0
Active earth pressure(KPa)
(a)
(d)
Fig. 6.5 Plots of the investigated parameters for SPF with 100 KPa surcharge
81
Wall type:
Material model:
No. of inclusion's layers :
Attached/Detached:
Surcharge :
E of inclusion:
Segmental panel facing
SoilRO; InclusionElastic
4
Attached
lOOKPa
lEti
(f)
Fig. 6.5(cont.) Plots of the investigated parameters for SPF with 100 KPa surcharge
82
