i APPLICATION OF HORIZONTAL SLICE METHOD ON GEOSYNTHETICS REINFORCED SLOPE SHARON LEE FUNG CHOO Master of Engineering (Civil) 2013 Faculty of Engineering
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i
APPLICATION OF HORIZONTAL SLICE METHOD ON
GEOSYNTHETICS REINFORCED SLOPE
SHARON LEE FUNG CHOO
Master of Engineering
(Civil)
2013
Faculty of Engineering
ii
APPLICATION OF HORIZONTAL SLICE METHOD ON
GEOSYNTHETICS REINFORCED SLOPE
SHARON LEE FUNG CHOO
A dissertation submitted in partial fulfilment of the requirements
for the degree Master of Engineering (Civil)
Faculty of Engineering
UNIVERSITI MALAYSIA SARAWAK
2013
i
ACKNOWLEDGEMENT
First and foremost, I would like to thank my almighty God for giving me the strength and
wisdom to complete this thesis for my master’s degree. Besides, thanks to my mother, Madam
Liaw and my family members who encouraged me to pursue my studies.
With this opportunity, I would like to extend my appreciation to many individuals for their
gracious support to me. Without them, this thesis would not be completed as planned.
My deepest appreciation goes to my supervisor, Assoc. Prof. Dr. Siti Noor Linda Taib for her
personnel guidance, supervision and comments throughout this thesis. With her encouragement,
I had a better understanding towards the topic chosen for my thesis and also have a clearer
direction towards the work that needs to be done.
I would like to thank all the lecturers who taught me the geotechnical courses, Prof. Kaniraj,
Dr. Norazzlina bt M. Sa’don, Dr. Fauzan b. Sahdi and Puan Dayangku Salma for sharing their
knowledge with me as it has enhanced my understanding in this discipline of Civil Engineering.
Besides, I would like to express my appreciation to my coursemates, Lee Shyue Leong and Lim
Hung Ling for their help and support throughout the period of completing this thesis. In addition
to that, I would like to thank another coursemate, Mr. Bong Shun Tat who is a Geotechnical
Engineer with seven years of experience in this field, for sharing his practical knowledge in
slope construction and slope stability analysis. Apart from that, I would like to express my
ii
sincere appreciation to him for guiding me in using Plaxis Version 8.2 for the validation work
in this thesis.
Not forgetting my ex-coursemates such as Gilbert Wong, Willie Chai, Ivy Sii, Gillan Lio and
Law Dah Lit for recommending me a great supervisor in this discipline of Civil Engineering. I
will cherish the good times we had studying, struggling and playing together. Best wishes for
their future undertakings.
My gratitude goes to Executive College for granting me the study leaves to pursue my master’s
degree. Many thanks for the tolerance from my Director of Study and Heads of Department
throughout these periods, especially in the arrangement of time table for my teaching. Thanks
to my colleagues who are very supportive in many areas too.
Special thanks for this group of friends who prayed faithfully for my studies such as Lai Sia
Ing and Lydia Tan.
Last but not least, I would like to say a prayer of blessing to those who supported me throughout
these periods.
iii
ABSTRACT
The purpose of the study is to apply the Horizontal Slice Method (HSM) in slope stability
analysis for slope reinforced with geotextile. This is a new method which can resolve the
problem of direct influence of reinforcement on the inter-slice forces encountered in the
Vertical Slice Method. This new method had been used in past researches done by Nouri et al.
(2006) and Taib & Craig (2007). The results from their research had shown close values with
the conventional methods. The simple formulation of the HSM comprising of (2N+1)
unknowns and (2N+1) equations suggested by Shahgholi et al. (2001) were used in this study.
Factors contributing to slope instability were identified as the factors would influenced the
formulating of the equations for vertical forces and horizontal forces in the slope. The factors
were slope geometry, soil properties, groundwater condition and configuration of reinforcement.
A spreadsheet had been designed using Microsoft Excel 2007. There are four sections in the
spreadsheet. Namely the data input, data generation, data analysis and result. With the trial and
error method, the factor of safety is found when the equilibrium of the horizontal forces for the
whole wedge of slope is achieved. Validation work using Plaxis Version 8.2 was carried out to
test the reliability of the spreadsheet. Six slopes had been designed for the validation work. The
deviations between the factors of safety from Plaxis and the factors of safety from spreadsheet
were ranged from 0.6 % to 3.27 %. The deviations were considered low, thus the HSM can give
values close to the existing software. The results from the spreadsheet had same pattern as the
results from Plaxis Version 8.2. This also confirmed that the spreadsheet had been prepared
with no error.
iv
ABSTRAK
Tujuan kajian ini adalah untuk mengaplikasikan Kaedah Hirisan Mendatar ke dalam analisis
kestabilan cerun yang diperkukuh oleh geotekstil. Kaeadah in merupakan kaedah baru yang
digunakan untuk menyelesaikan masalah pengaruh lansung tetulang terhadap daya – daya
antara hirisan yang dijumpai dalam Kaedah Hirisan Menegak. Kaedah baru ini pernah dikaji
oleh Nouri et al. (2006) dan Taib & Craig (2007). Keputusan-keputusan daripada kajian mereka
mendekati keputusan-keputusan daripada kaedah konvensional. Ini membuktikan Kaedah
Hirisan Mendatar dapat memberi keputusan yang memuaskan. Rumusan ringkas daripada
Kaedah Hirisan Mendatar yang terdiri daripada (2N+1) anu dan (2N+1) persamaan yang
dicadangkan oleh Shahgholi et al. (2001) telah digunakan dalam kajian ini. Faktor-faktor yang
mempengaruhi ketidakstabilan cerun telah dikenalpasti kerana ia akan mempengaruhi
pembentukan persamaan untuk daya-daya menegak dan daya-daya mendatar. Faktor-faktor
tersebut adalah geometri cerun, sifat-sifat tanah, keadaan air bawah tanah dan konfigurasi
tetulang. Pengiraan telah direka menggunakan Microsoft Excel 2007. Terdapat empat seksyen
di dalam pengiraan yang direka, iaitu input data, penjanaan data, analisi data dan keputusan.
Dengan ujian percubaan dan kesilapan, faktor keselamatan cerun akan didapati apabila
keseimbangan daya-daya mendatar untuk keseluruhan baji cerun tercapai. Kerja pengesahan
pengiraan yang direka telah dilakukan dengan perisian Plaxis versi 8.2 untuk menguji
kebolehpercayaan pengiraan tersebut. Enam cerun telah direka untuk kerja pengesahan.
Deviasi-deviasi daripada perbandingan faktor keselamatan yang didapati daripada Plaxis dan
pengiraan Excel merangkumi 0.6 % hingga 3.27 % untuk keenam-enam cerun ini. Deviasi
tersebut dianggap rendah, maka ini membuktikan Kaedah Hirisan Mendatar dapat memberi
keputusan yang mendekati keputusan daripada perisian yang sedia ada. Keputusan daripada
v
pengiraan Excel mempunyai corak yang sama dengan Plaxis. Ini membuktikan pengiraan
tersebut telah direka dengan tepat.
vi
TABLE OF CONTENTS
ACKNOWLEDGEMENT .......................................................................................................... i
ABSTRACT .............................................................................................................................. iii
ABSTRAK ................................................................................................................................ iv
LIST OF TABLES .................................................................................................................. viii
LIST OF FIGURES ................................................................................................................... ix
1 INTRODUCTION ....................................................................................................... 1
1.1 PROBLEM STATEMENT ........................................................................... 1
1.2 AIMS AND OBJECTIVES .......................................................................... 2
1.3 SCOPE OF RESEARCH .............................................................................. 3
1.4 THESIS OUTLINE ....................................................................................... 3
2 LITERATURE REVIEW ............................................................................................ 5
2.1 SLOPE STABILITY ANALYSIS ................................................................ 5
2.1.1 Factor of Safety ................................................................................... 5
2.1.2 Limit Equilibrium Method .................................................................. 6
2.1.3 Finite Element Method ........................................................................ 7
2.2 VERTICAL SLICE METHOD AND ITS LIMITATION ........................... 8
2.3 HORIZONTAL SLICE METHOD............................................................. 12
2.3.1 Horizontal Slice Method and the Basic Assumptions ....................... 12
2.3.2 Formulation of Horizontal Slice Method .......................................... 14
2.4 APPLICATION OF HSM IN THE PAST RESEARCHES ....................... 18
2.4.1 Application of Horizontal Slice Method on Soil Nailed Slopes ........ 18
2.4.2 Development of Horizontal Slice Method for Seismic Stability
Analysis of Reinforced Slopes and Walls ................................................... 21
2.5 GEOTEXTILE AS REINFORCING MATERIAL .................................... 23
2.5.1 Advantages of using Geotextile......................................................... 23
2.5.2 Characteristic of Geotextile ............................................................... 25
2.5.3 High Strength Geosynthetics and Soil Compatibility ....................... 26
2.6 PLAXIS VERSION 8.2 .............................................................................. 27
3 METHODOLOGY ..................................................................................................... 28
3.1 INTRODUCTION ...................................................................................... 28
3.2 SLOPE GEOMETRY ................................................................................. 30
vii
3.3 SOIL PROPERTIES ................................................................................... 32
3.4 GROUNDWATER CONDITION .............................................................. 33
3.5 CONFIGURATION OF REINFORCEMENT ........................................... 34
3.6 COMPUTATION OF NORMAL FORCE AND SHEAR FORCE UPON
BASE OF SLICE ...................................................................................................... 36
3.7 EQUILIBRIUM OF HORIZONTAL FORCES FOR WHOLE WEDGE . 37
3.8 DEVELOPMENT OF SPREADSHEET .................................................... 38
3.9 VALIDATION WORK .............................................................................. 39
3.9.1 Data for validation ............................................................................. 39
3.9.2 Analysis through Plaxis Version 8.2 ................................................. 40
4 RESULTS AND CONCLUIONS .............................................................................. 43
4.1 GENERAL .................................................................................................. 43
4.2 VALIDATION RESULTS ......................................................................... 43
4.2.1 Comparison between Factor of Safety from Plaxis and Factor of
Safety from Spreadsheet for Slopes with Height of 5 m ............................ 43
4.2.2 Comparison between Factor of Safety from Plaxis and Factor of
Safety from Spreadsheet for Slopes with Inclination Angle of 60˚ ........... 45
4.3 SPREADSHEET FOR HORIZONTAL SLICE METHOD ....................... 46
4.3.1 Introduction to Spreadsheet ............................................................... 46
4.3.2 Guideline for Using Spreadsheet ....................................................... 52
5 CONCLUSION AND RECOMMENDATIONS ....................................................... 53
5.1 GENERAL REMARKS.............................................................................. 53
5.2 CONCLUSIONS......................................................................................... 53
5.3 RECOMMENDATIONS ............................................................................ 54
REFERENCES ......................................................................................................................... 56
APPENDIX .............................................................................................................................. 58
Appendix A: Results from Plaxis Version 8 ............................................................................ 58
Appendix B: Results from Spreadsheet ................................................................................... 64
Appendix C: Results for Comparison ...................................................................................... 85
viii
LIST OF TABLES
Table 2.1: Method of limit equilibrium. 6
Table 2.2: Notation for Figure 2.1 9
Table 2.3: Notation for Figure 2.2 9
Table 2.4: Equations and unknowns of Vertical Slice Method of Analysis.
(Shahgholi et al., 2001)
10
Table 2.5: Notation for Figure 2.3 11
Table 2.6: Notation for Figure 2.5 14
Table 2.7: Equations and Unknowns of Complete Formulation of HSM of
Analysis. (Shahgholi et al., 2001)
14
Table 2.8: List of Equations and Unknowns in Two Simple Formulations.
(Shahgholi et al., 2001; Fakher et al., 2002)
17
Table 2.9a: Notation for Figure 2.7 19
Table 2.10: List of Equations and Unknowns in the First and Second 3N
Formulation. (Nouri et al., 2006)
22
Table 2.11: List of Unknowns and Equations in Rigorous 5N – 1 Formulation.
(Nouri et al., 2006)
22
Table 2.12: Summary of Types of High Strength Geosynthetics and Soil
Compatibility. (Tencate Geosynthetics Asia Sdn. Bhd.)
26
Table 3.1: Slope Conditions for Validation Work 37
ix
LIST OF FIGURES
Figure 2.1: Traditional Method of Slice 8
Figure 2.2: Forces Acting at A Typical Vertical Slice 9
Figure 2.3: Forces Developed on A Single Vertical Slice Containing
Reinforcement
11
Figure 2.4: Horizontal Slice Method 13
Figure 2.5: Forces Acting on A Single Horizontal Slice Containing
Reinforcement
13
Figure 2.6: (a) The Geometry of Log-spiral Failure Mechanism and Horizontal
Slice Method and (b) The Geometry of Acting Forces of Each Slice
16
Figure 2.7: Configuration of HSM Slicing for Soil Nailed Slope with Inclined
Reinforcement.
18
Figure 2.8: Distribution of Forces and Dimensions of Horizontal Slice (Taib &
Craig, 2007)
19
Figure 2.9 (a) Conventional Structure and (b) Reinforced Soil Structure
(Tencate Geosynthetics Asia Sdn. Bhd.)
24
Figure 2.10 (a) Conventional Slope and (b) Reinforced Soil Slope (Tencate
Geosynthetics Asia Sdn. Bhd.)
24
Figure 3.1: Analysis Procedure 29
Figure 3.2: Log-spiral Failure Surface 31
Figure 3.3: Geometry and Acting Forces for Each Slice 32
Figure 3.4: Distribution of Pore Pressure Forces of Each Slice 33
Figure 3.5: Dimensions for Reinforcing Force 34
Figure 3.6: Distribution of Normal Force and Shear Force upon Base of Slice 36
Figure 3.7: Flow of Spreadsheet 38
Figure 3.8: Input of Soil Parameters 40
Figure 3.9: Input of Material 40
Figure 3.10: Output of Factor of Safety 41
Figure 3.11: Output of Reinforcing Forces 41
Figure 3.12: Output of Total Displacement 42
Figure 4.1: Comparison between FOS from Plaxis and FOS from Spreadsheet
for Slopes with Height of 5 m
42
x
Figure 4.2: Comparison between FOS from Plaxis and FOS from Spreadsheet
for Slopes with Inclination Angle of 60˚
45
Figure 4.3: Input of Geometry and Geotechnical Characteristics 47
Figure 4.4: Input of Slope Geometry 47
Figure 4.5: Input of Location of Reinforcing Material 48
Figure 4.6: Chart for Failure Surface 48
Figure 4.7: Dimensions and Angles 49
Figure 4.8: Computation of Forces 50
Figure 4.9: Computation of Reinforcing Forces 50
Figure 4.10: Data Analysis 51
Figure 4.11: Result 51
1
CHAPTER 1
1 INTRODUCTION
1.1 PROBLEM STATEMENT
There are numerous methods used to analyse the stability of a slope. Limit equilibrium
methods adopting the vertical slice method are conventionally used to determine the factor of
safety of a soil wedge against sliding. In this method the soil wedge is usually divided into a
number of vertical slices during the analysis. In the reinforced slope, the orientation of the
reinforcement has a direct influence on the inter-slice forces, the force mobilised in the
reinforcement will intersect the vertical slices and additional unknown horizontal tension forces
from the reinforcement will appear in the vertical slice method of analysis. Thus, the solution
becomes complicated and time consuming. As a result, vertical slice method has the limitation
in analysing the reinforced soil slope.
A new limit equilibrium method known as Horizontal Slice Method (HSM) has been
identified and used to resolve the problem (Shahgholi, 2001). In this method, the sliding soil
wedge is divided into a number of horizontal slices, which do not intersect the reinforcements,
thus the reinforcement has no direct influence on the inter-slice force.
The factor of safety from HSM analysis is compared with values produced from program
slope, which utilises Janbu’s Simplified Method had shown reasonably close values (Taib &
Craig, 2007).Other than this, the HSM analysis was compared with the published procedures
2
for verification of its reliability. Result has shown that the HSM analysis using the rigorous
formulation (5N-1) are similar to the procedure based on pseudo-static limit stability analysis
by Ling et al. (1997) in which the internal and external stability analyses are conducted to
determine the required strength and length of the reinforcement considering different modes of
failure (Nouri et al., 2006). Therefore reinforced slope analysis using Horizontal Slice Method
can be used.
1.2 AIMS AND OBJECTIVES
The aim of this project is to apply the Horizontal Slice Method for stability analysis on
reinforced slope with geotextile.
The specific objectives of this study are:
1. to apply Horizontal Slice Method to formulate mathematical equations for finding the factor
of safety (FOS) on reinforced slope with geotextile,
2. to design spreadsheet for stability analysis on reinforced slope with geotextile and
3. to validate the safety factor (output) produced from the designed spreadsheet with existing
software Plaxis version 8.2.
3
1.3 SCOPE OF RESEARCH
Simple formulation of the Horizontal Slice Method comprises (2N+1) unknowns and
(2N+1) equations by Shahgholi et al. (2001) are used in slope stability analysis. The simple
formulation only considered the vertical equilibrium for individual slices together with overall
horizontal equilibrium for the whole wedge, no account being taken for moment equilibrium.
The scenario such as pore pressure will be considered in the formulation. Type of reinforcing
material for slope will be focused on geotextile. Microsoft Excel 2007 will be used to design
the spreadsheet for stability analysis on reinforced slope with geotextile. Validation work using
Plaxis version 8 is carried out to test the reliability of the spreadsheet.
1.4 THESIS OUTLINE
Chapter 1 covered problem statement, aim and objectives and scope of work. This chapter
explained the problem encountered in the calculation of reinforced slope through the
conventional Vertical Slice Method. A new method known as Horizontal Slice Method has
been identified to resolve this problem.
Chapter 2 covered the literature review done for the Vertical Slice Method and its
limitation in reinforced slope analysis, Horizontal Slice Method and the simplified formulation,
application of HSM in reinforced slope in the past research and detail of geotextile material.
Chapter 3 covered the procedure undertaken to achieve the objectives of the study. A flow
chart showed the overall process to conduct the study. Formulation of mathematical equation
for stability analysis on reinforced slope with geotextile by applying Horizontal Slice Method
4
was carried out in this chapter. Reinforcement force was analysed and calculated. Explanation
on the development of the spreadsheet was done.
Chapter 4 covered the analysis of the validation work and explanation of the designed
spreadsheet.
Chapter 5 covered the conclusion of the overall study that had been made.
5
CHAPTER 2
2 LITERATURE REVIEW
2.1 SLOPE STABILITY ANALYSIS
2.1.1 Factor of Safety
Factor of safety for a slope is defined as shear strength of soil divided by the shear stress
developed along the potential failure of surface. If the shear stress of the soil along the potential
failure surface is more than the shear strength of soil, the slope will fail. This happens when the
factor of safety is less than 1. Meanwhile, factor of safety of 1 indicates the slope is in critical
condition. For a stable and safe slope, the factor of safety is more than 1.
FOS =shear strength of soil, Tf
shear stress developed along the potential failure surface,Td (Equation 2.1)
There are two methods used to analyse the factor of safety for a slope. The first method
is called limit equilibrium method and the second is called finite element method.
6
2.1.2 Limit Equilibrium Method
Limit equilibrium method can be divided into two major classes. The first class
considers the equilibrium of the whole failing mass above the surface of sliding. This method
is merely suitable to analyse the slope which is formed by homogeneous soil. In the second
class, the soil above the surface of sliding is divided into a number of vertical parallel slices.
The stability of each slice is calculated separately. This is a method in which the non-
homogeneity of soil and pore water pressure can be taken into consideration. It also takes
account for the variation of the normal stress along the potential failure surface.
Limit equilibrium method consists of several methods of analysis as summarised in
Table 2.1. These methods search for the most critical slip surface that gives the minimum factor
of safety. The differences between these methods are each method need to make an assumption
for the shape of the sliding wedge whether circular, plane, etc. and satisfy the equilibrium
equation either for force, moment and both.
Table 2.1: Method of Limit Equilibrium
Limit Equilibrium Method Developer Description
Ordinary method of slices Fellenius, 1936 The simplest method where the resultant
of inter-slice forces is parallel to the
average inclination of the slice.
Bishop Method Bishop, 1955 The resultant of inter-slice forces is
assumed to be equal and opposite.
Morgenstern-Price Method Morgenstern-Price,
1965
The inclination of inter-slice resultant
forces is assumed to be varied based on
selected part.
Janbu Method Janbu, 1968 Resultant of inter-slice shear forces is
assumed where the correction factor is
taken into account.
Spencer Method Spencer, 1967
& 1968
The resultant inter-slice forces are
assumed to be constant.
7
2.1.3 Finite Element Method
Finite element method is an effective method which is an alternative to the limit
equilibrium method. This method is widely used nowadays. The advantage of this method is
that no assumption needs to be made in advance about the shape or location of the failure surface,
slice side forces and their directions. This method can be applied to complex slope
configurations and soil deposits in two or three dimensions to model virtually all types of
mechanisms. The equilibrium stresses, strains and the associated shear strengths in the soil mass
can be computed very accurately. This method can be extended to account for seepage induced
failure.
Generally, finite element method consists of two approaches. One approach is to
increase the gravity load until the slope fails. In this approach, the ratio of the gravitational
acceleration in failure time and actual gravitational acceleration is used to determine the safety
factor of the slope. Another approach is to reduce the strength characteristics of the soil mass
until slope fails. The safety factor is determined when the actual strength parameters divided
with the critical strength parameters.
8
2.2 VERTICAL SLICE METHOD AND ITS LIMITATION
Vertical slice method is one of the limit equilibrium method used in slope stability
analysis. This vertical slice method has been traditionally used to analyze the stability of slopes
with or without reinforcements. The method can be used to analyze both circular and general
slip surface. It can satisfy both force and moment equilibrium.
In this method, a sliding soil wedge is divided into a number of vertical slices, and the
equilibrium of the individual slice is considered during the analysis. Figure 2.1 shows a sliding
soil wedge of an embankment without any reinforcement and the notations for the figure are
shown in Table 2.2. A typical slice with the forces that act on it are shown in Figure 2.2 and the
notations for the figure are shown in Table 2.3.
Figure 2.1: Traditional Method of Slice
r sin α
r
l
h
b
α
O
9
Table 2.2: Notations for Figure 2.1
Symbol Definition
Α Angle of base of slice
B Length of base of slice
H Vertical distance between any point in soil mass and external
border of soil mass
L Length of vertical slice
R Radius
O Centre of rotation
Figure2.2: Forces Acting at A Typical Vertical Slice
Table 2.3: Notations for Figure 2.2
Symbol Definition
HA, HB Horizontal inter-slice forces
N Normal force upon base of slice
S Shear force upon base of slice
VA, VB Vertical inter-slice forces
W Weight of slice
N α
W
HB
S
α
HA VB
VA
10
Table 2.4 shows a list of governing equations and unknown parameters in the vertical
slice method of analysis. From Table 2.4, it can be concluded that the number of unknown
parameters (6N-2) is greater than the number of equations (4N + 3). Thus, further simplified
assumptions need to be made to reduce the number of unknowns.
Table 2.4: Equations and Unknowns of Vertical Slice Method of Analysis
(Shahgholi et al., 2001)
Equations Number Unknowns Number
∑Fx = 0 (each slice) N Horizontal inter-slice forces N -1
∑Fy = 0 (each slice) N Vertical inter-slice forces N -1
∑M = 0 (each slice) N Normal forces upon base of each
slice.
N
Trequired =Tfailure
FS (each
slice)
N Shear forces upon base of each slice. N
Equilibrium equations for
whole mass
3 Location of horizontal inter-slice
forces
N-1
Location of shear and normal forces
upon base of each slice.
N-1
Factor of safety 1
Sum 4N + 3 Sum 6N - 2
In the analysis of the reinforced soil slope, the tension force (Tj) from the reinforcing
material needs to be considered. These forces are usually acted horizontally due to its method
of construction and its usual orientation of the reinforcement. In Figure 2.3, it can be observed
that the orientation has a direct influence on the inter-slice forces, therefore the tension forces
of the reinforcement are additional unknowns in the vertical slice method of analysis. As a
11
result the vertical slice method is not particularly suited to the analysis of reinforced soil slopes
(Shahgholi et al., 2001). Table 2.5 shows the notations for Figure 2.3.
Figure 2.3: Forces Developed on A Single Vertical Slice Containing Reinforcement
Table 2.5: Notations for Figure 2.3
Symbol Definition
Hj, Hj+1 Horizontal inter-slice force
Vj, Vj+1 Vertical inter-slice force
Nj Normal force upon base of slice
Sj Shear force upon base of slice
Tj, Tj+1, Tj+2 Tensile force of reinforcement
ΔTj+1 Change in tensile force of reinforcement
Tj+2–ΔTj+2
Tj+1–ΔTj+1
Tj–ΔTj
Tj+2
Tj+1
Tj
Hj+1
Vj+1 Vj
Sj
Nj
Hj
12
2.3 HORIZONTAL SLICE METHOD
2.3.1 Horizontal Slice Method and the Basic Assumptions
Shahgholi et al. (2001) had introduced the horizontal slice method in the reinforced
slope analysis to solve the limitation of vertical slice method. The idea of using horizontal slices
was also proposed by Lo & Xu (1992) (Nouri et al., 2006). In this method, the sliding soil
wedge is divided into a number of horizontal slices and the orientation of the reinforcing
elements still maintain as horizontal as shown in Figure 2.4. A single horizontal slice containing
reinforcement as shown in Figure 2.5 is extracted from the sliding soil wedge as shown in
Figure 2.4 and Table 2.6 shows the notations for Figure 2.5. It can be observed that no inter-
slice forces are generated by the reinforcing element for this method. The advantages of this
approach include simplification of the analytical procedures and less numerical effort.
In the horizontal slice method, Shahgholi et al. (2001) had made the following
assumptions during the stability analysis:
(i) The vertical stress on an element in the soil mass is equal to the overburden
pressure.
(ii) The factor of safety (FOS) is equal to the ratio of the available shear resistance
to the required shear resistance along the failure surface.
(iii) The factor of safety for all slices is equal.
(iv) The failure surface can have any arbitrary shape, but it does not pass below the
toe of the slope and wall.
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