CHAPTER 1: INTRODUCTION
A slope is a ground surface that inclines either may be natural or man-made. Each slope has its own soil characteristics and geometric features, in order to resist gravity or collapse. Soil mass will move slowly or suddenly without any signage downward and outward when slope failure occurred. Slides usually begin from hairline tension cracks, which propagate through the soil layers (Das,1994). Slope failures have caused an unquantified number of causalities and economic loss. However, in rural area and less populated less effect of mass movements, only being part of natural degradation of the land surface. In the case of coastal cliffs instability involving the destruction of property is often accepted due to the costs of resisting natural erosion process with cliff stabilization measures are prohibitive.
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Factors that Influence Slope Stability
Figure 1, (Tulane University, Prof. Stephen A. Nelson, 6 oct 2010)
Gravity is the main force for mass wasting. Its acts everywhere on the earth’s surface, and then pulls everything in direction towards the middle of the earth’s. By looking at the figure 1, gravity acts downwards on the flats surface. Therefore the materials will not moving under the force of the gravity. It will be different case when a material is placed on a slope, by resolving the force of gravity to two component acting perpendiculars and tangential to the slope.
The figure 2 below shows the steps of how the two components resolved:-
Figure 2, (Tulane University, Prof. Stephen A. Nelson, 6 oct 2010)
The Perpendicular component of gravity, gp, acts to hold the material in place on it position. Meanwhile the tangential component of the gravity, gt, and cause shear stress parallel to the slope pulls the material acting downwards direction as shown in figure 2.
When the angle slope increase, the shear stress or the tangential component of gravity, gt also increases but the perpendicular component of gravity, gp will decreases.
Force that resisting the movements down the slope are classified as shear strength as it involves the cohesion and frictional resistance surrounded by the particles that make up the object.
The material will move down-slope when the sheer stress is larger than the total forces holding the object on the slope. However, when the materials like soil, clay, sand, silts and etc, the shear stress will become higher than the cohesional forces which hold, the particles will flow down slope and separate.
Consequently, the down-slope movement is preferential by the steeper slope angles the stress also increase and everything that decreases the shear strength for example by lowering the cohesion among the particles or the frictional resistance. In other words, it is often known as the safety factor, Fs, the ratio of shear strength to shear stress.
Fs = Shear Strength/Shear Stress
When the value of safety factor less than 1.0, it indicates that slope failure is expected.
To perform the different method of slope stability analysis used by both programs.
To design the suitable parameters of soil
To obtain factor of safety which should be equal to one (FOS= 1.0)
To compare the outcome run by both software.
CHAPTER 2: LITERATURE REVIEW
Due to the consequences of slope failure, the topic has received extensive treatment in the literature. Several models and analytical techniques have been developed to describe a variety of geometric and soil characteristics. The majority of literature focuses on deterministic evaluation of slope stability, however, with the new technology nowadays slope stability can be determine or predict factor of safety of the soil strength just simply entering the parameters.
For this project the programmed used to analysis the slope stability had used different method approached to solve the factor of safety required for the problems being analysed. In Limitstate:Geo 2.0,Discontinuity Layout Optimization (DLO) method was used to approaches the problems. Meanwhile, in Geostudio 2007 the method use was General Limit Equilibrium. Thereafter, the factors of safety equations were presented to highlight the importance of modelling assumptions.
This chapter presents a review of slope stability analysis methods, including determining the factor of safety for the soil strength and the designing the soil parameters. The variability within soil parameters is summarized in this review. Finally, several case studies of slope stability analysis are summarized.
The slope stability can be analyse nowadays by using a computer program. LimitState: Geo 2.0 and Geostudio 2007 are examples programs can be used to analyse the slope stability. Drained and un drained analysis is required to be analyse to find out the factor of safety of the soil strength such that the slope collapses with soil parameters .The parameters of the soil properties have to be design until the factor of safety obtained equal to one (F.O.S =1).
2.2 Background study
For this project, there were two computer softwares used for modeling the slope stability problems named Limitstate: Geo 2.0 and GeoStudio 2007. By using this new technology being developed, modelling and calculating the factor of safety and the adequacy factor of the soil have been made easier to be obtained.
These both softwares produce the same aim to produce the outcome of the slope stability analysis but the term used for the results were different. In LImitState: Geo 2.0 the output produced was the adequacy factor and Geostudio 2007 gave factor of safety as it results.
Adequacy factor is the factor by which specified load, material self weight must be multiplied by to cause collapse (Limitstate: Geo 2.0, 2010).
Factor of safety is defined as the ratio of the available shear resistance (capacity) to that required for equilibrium (Geostudio, 2007).
In GeoStudio 2007 (SLOPE/W), the minimum factor of safety of moment and force produced was obtained by using different method such as Bishop simplified method, Ordinary method, Janbu method and M-P method. In this software, the minimum factors of safety to be focus only the Morgenstern-Price method. Meanwhile, in Limitstate: Geo 2.0 the outcome produced was obtained by using the discontinuity layout optimize method (DLO).
2.2.1 How Discontinuity Layout Optimized works?
In Limitstate:Geo 2.0, Discontinuity Layout Optimization is a solution engine to analyse the slope stability problems. This procedure was developed at University of Sheffield. Beside that this method can be used to identify critical transitional sliding block failure mechanism with no limitations.
Discontinuity layout optimization is a limit analysis method that effectively allows free choice of slip-line orientation, and the critical solution identified may involve the failing soil mass being divided into a large number of sliding blocks. Accuracy can be assessed by determining the influence of nodal refinement. DLO also readily handles variation of soil parameters, and heterogeneous bodies of soil.
Discontinuity Layout Optimized procedures occupy a few steps as shown in diagram below.
There are number of steps of procedure involved in DLO. The initial step of the procedure is by identifying complex failure patterns through the set of potential discontinuities. In terms of equilibrium relations or in terms of displacements, DLO can be formulated. The aim of the mathematical optimization problem in the’ kinetic’ formulation(i.e DLO which is formulated in terms of displacement) is to minimize the internal energy degenerate along discontinuities, focus in the direction on nodal compatibility constraints. This can be solved via resourceful linear programming techniques and, when combined with an algorithm initially developed for bind layout optimization problems, where modern computer power can be used to directly search through very large numbers of different malfunction mechanism topologies.
2.2.2 How General Limit Equlibrium works?
Formulation used in general limit equilibrium was developed by Fredlund at the University of Saskatchewan in the 1970s (Fredlund and Krahn 1977; Fredlund et al. 1981). This technique includes the key elements of all the other methods available in the slope stability analysis in Geostudio 2007.
There are several general limit equilibrium (GLE) methods have been developed for slope stability analyses purposes. They are:-
i) Fellenius (1936) which introduced the first method. It is also known as the Ordinary or the Swedish method and used for a circular slip surface.
ii) Bishop (1955) had advanced the first method by introducing a new relationship for the base normal force. Hence, the equation for the FOS hence became non-linear.
iii) Janbu (1954a) developed a simplified method for non-circular failure surfaces, dividing a potential sliding mass into several vertical slices. The generalized procedure of slices (GPS) was developed at the same time as a further development of the simplified method (Janbu, 1973).
iv) Morgenstern-Price (1965),
v) Spencer (1967),
vi) Sarma (1973) and;
Several others made further assumptions and modification on the interslice forces. As for example, a procedure of General limit equilibrium (GLE) was developed by Chugh (1986) through the extension of the Spencer and Morgenstern-Price methods, which satisfying both moment and force equilibrium conditions (Krahn 2004, Abramson et al. 2002).
In this general limit equilibrium, the formulation is based on two factors of safety equations. The equations are:
i) Factor of safety with respect to moment equilibrium (Fm).
ii) Factor of safety with respect to horizontal force equilibrium.
The terms in the equations are:
c’= effective cohesion
?’= effective angle of friction
U= pore-water pressure
N = slice base normal force
W = slice weight
D = concentrated point load
?, R, x, f, d, ? = geometric parameters
? = inclination of slice base
Both moment and force equilibrium have to be achieves by finding the cross-over point of the Fm and Ff curves.
18.104.22.168 Morgenstern-Price Method
For the analysis Morgenstern-Price Method was used to determine the Factor of Safety of the slope due to it allowed for various user-specified inter-slice force functions. The inter-slice functions available in SLOPE/W for use with the Morgenstern-Price (M-P) method are (1) Constant, (2) Half-sine, (3) Clipped-sine, (4) Trapezoidal and (5) Data-point specified. By selecting the Constant function makes the M-P method identical to the Spencer method (Geo-Studio, 2007).
Morgenstern and Price proposed an equation to be used to handle the interslice shear forces. The equation is:
The terms are:-
f(x) = a function,
l = the percentage (in decimal form) of the function used,
E = the interslice normal force, and
X = the interslice shear force.
In SLOPE/W the values of lambda is varies from -1.25 to +1.25 but sometimes it is needs to be narrowed due to it is not possible to reached a achieved solution at the boundaries of the range. Consequently, the general limit equilibrium helps in understand the differences between the various methods and understand what is happening behind the scenes.
Figure XX shows how the moment and force factors of safety vary with lambda. The M-P Factor of safety occurs where the two curves across.
Once the X value obtained it must match with the inter-slice shear value (E2) on the free body diagram as shown in figure…. As with the Spencer method, the force polygon closure is very good with the M-P method, since both shear and normal inter-slice forces are included (Geo-Studio, 2007).
CHAPTER 3: RESULTS
In this chapter, it presents the results obtained from the analysis done using both programmed. There were some cases analyzed to compare the results produce by both programmed. First case, the problems to modeling the analysis must obtained the factor of safety equal to one. The parameters given for each drain and undrained analysis stated in the problem. Meanwhile the rest of the case shows the different value obtained for factor of safety with same case using both programmed.
3.2 Case 1: one layer of soil and changing parameters to obtain F.O.S is 1
Material strength properties:
Table 1: soil material strength properties
Results for drained analysis
Table 3: Minimum factor of safety for undrained analysis
From the results obtained from the data shown above does not give the factor of safety of the slope stability equal to one. Hence tables below shows the changes of parameters for both drained and undrained analysis in order to obtained the factor of safety equal or near to one.
Outcome produce by both programmed as the phi is changing but the remaining parameters stay constant.
Outcome produce by both programmed as the slope is increase but the rest of the parameters stay the same.
The table below the results obtained for the undrained analysis to obtained factor of safety equal or nearly to one as changing the undrained shear strength:-
3.3 Case 2: two different layers of soil with different parameters.
Material strength properties:
CHAPTER 5: DISCUSSION
5.1 Case 1
In the case scope 1, with the materials properties given as shown in table……its shows that the minimum factor of safety obtained for drained analysis by using limitstate: Geo 2.0 is 2.225 compare to Geostudio 2007 which is 1.064. Meanwhile for undrained analysis the results obtained was only slightly different which is different by 0.013. The main point for this case 1 was to obtain minimum factor of safety equal to one for both drained and undrained analysis.
Therefore in order to obtain the factor of safety equal to one for the slope stability for drained analysis there are two factors to be considered. Firstly, change the drained friction angle (phi) but maintained the other soil parameters constant. Secondly, maintained drained friction angle and the other parameters constant but change the angle slope of the problems. Meanwhile for the undrained analysis the same analysis was carried out but in this case was to obtain the factor of safety equal to one; only the undrained shear strength was changed.
From the results gathered in table….It shows that when the phi was changed and the others parameters remain the same, the results obtained was different in order to obtained the near ideal factor of safety, where by using Limitstate: Geo 2.0 the phi values to obtain was 29.5°. Meanwhile, Geostudio 2007 produced the factor of safety nearly to one when the phi was 30°.
For the case of changing the slope angles and the remaining material strength properties stay the same, the results was tabulated in table….It shows that in Limitstate: Geo 2.0 the factor of safety close to one was 29.5°. Meanwhile, in Geostudio 2007 the slope angles obtained was one degree smaller than the Limitstate: Geo 2.0.
5.2 Case 2
In the case scope 2, the minimum factor of safety produced by Limitstate: Geo 2.0 was 75 % higher than Geostudio 2007 due to different highest inter-slice forces obtained during stimulate the analysis. In Geostudio 2007, the highest forces was…..Meanwhile, the biggest forces value in Limitstate: Geo 2.0 was……
5.3 General discussion different FOS obtained from both programmed.
As mentioned earlier, the method approached to find the factor of safety by both programmed were different make the solutions obtained from any analysis also different. Hence, the solution obtained might small or huge differences between the outcomes produce by both programmed.
In Geostudio 2007, Morgenstern-Price (M-P) method was used to perform the analysis. In this method, shear and normal inter-slice forces were considered and satisfies both moment and force equilibrium. Not only that, it allows variety of user-selected inter-slice force function. Simpler methods do not include all inter-slice forces and do not satisfy all equations of equilibrium sometimes can be on the unsafe side (Geostudio, 2007).
In Limitstate: Geo 2.0, the accuracy of solution controlled by specified nodal density. Within the set of all possible discontinuities linking pairs of nodes, all potential transitional failure mechanism was considered. Failure Mechanisms involving rotations along the edges of the solid bodies can be identified. The critical mechanism and collapse factor of safety were determined based on upper bound theorem of plasticity.
CHAPTER 5: CONCLUSION
The results has fulfilled the aims of the study in determine the minimum factor of safety equal to one for drained and undrained analysis for case 1. Base on the FOS simulated, the both programmed give different results for the same case analysed due to the method used to run the programmed. However, though in case 1 the factor of safety produce almost similar values, it inter-sliced forces produced by both programmed will be different due to the shape of interslice form by each method will be not the same.
Safe fill slope construction required a geotechnical input by the engineers with relevant geotechnical experience during planning, design, construction and maintenance. Therefore, high factor of safety produce will give high cost but will bring up good quality over period of time.
CHAPTER 6: COMPARISON BETWEEN LIMITSTATE: GEO 2.0 AND GEOSTUDIO 2007
From the desk study analysis using both limitstate:Geo 2.0 and Geostudio 2007 programmed, there are strengths and limitations of each programmed to run slope stability analysis which are summaries in the table shown below:-
CHAPTER 7: REFERENCES
Limitstate Ltd. (October 4, 2010). LimitState:GEO Manual VERSION 2.0 http://www.limitstate.com/files/pdf/geo/GEO_Manual.pdf. Last accessed 14/3/2011.
D.G. Fredlund.(2001) The relationship between Limit Equilibrium Slope Stability Methods, Department of Civil Engineering, University of Saskatchewan, Saskatoon, Saskatchewan, Canada.
Geostudio.(2010) Stability Modeling with SLOPE/W 2007 Version, Geo-Slope International Ltd., Calgary, Alberta, Canada.
Geotechnics 2 Notes: Slope stability. Belfast: Queen’s University of Belfast.
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