"Geotechnical Stability Analysis Using StudentVersions of FLAC, PLAXIS and SLOPE/W AbstractSlope stability analysis is of particular importance to Geotechnical Engineers asslope failures can have devastating social and economic impacts. There areseveral software packages developed for stability analysis which utilise the LimitEquilibrium (LE) Method, Finite Element (FE) method and Finite Difference(FD) method.The majority of published information is in regards to the slope stability analysismethods of Limit Equilibrium, Finite Element and Finite Difference and not thesoftware packages themselves. Several studies have suggested that the FE and FDmethods provide greater benefits than the LE method; however other studies havesuggested that the simplicity of the LE method outweighs the complexity of theFE and FD methods.The purpose of this research project is to compare the student versions of FLAC,PLAXIS and SLOPE/W and their use in Geotechnical stability analysis. FLAC isa software package using the FD method; PLAXIS the FE method and SLOPE/Wthe LE method.From this report it can be concluded that for software packages using the FE orFD method the type of „mesh? generated and utilised in calculating the FOS valuehas a significant effect on accuracy of the results. Due to the limit in the amountof zones allowed within the FLAC student version and in general only allowing acoarse mesh analysis it can be considered that the FOS values calculated are lessaccurate compared to the student versions of PLAXIS and SLOPE/W.Each package has its own benefits and limitations and it is recommended that theusers choose the package that best suits the models requirements and itscomplexity. The student versions should be used as an indication only and anydetailed analysis requires the use of a full licensed version of the chosen softwarepackage. Page iiENG 4111/2 Research Project ContentsABSTRACT............................................................................................................................... IIACKNOWLEDGEMENTS .................................................................................................VCONTENTS .............................................................................................................................VILIST OF FIGURES ..............................................................................................................XILIST OF TABLES ............................................................................................................. XIVNOMENCLATURE ............................................................................................................ XVCHAPTER 1: INTRODUCTION ...................................................................................... 11.1 INTRODUCTION .................................................................................................................... 11.2 BACKGROUND ...................................................................................................................... 21.3 METHODOLOGY ................................................................................................................... 21.4 OBJECTIVES .......................................................................................................................... 31.5 REPORT STRUCTURE .......................................................................................................... 3CHAPTER 2: LITERATURE REVIEW ....................................................................... 52.1 INTRODUCTION .................................................................................................................... 52.2 LIMIT EQUILIBRIUM (LE) METHOD ................................................................................ 52.2.1 Vertical Slices .......................................................................................................... 62.2.2 Benefits ....................................................................................................................... 82.2.3 Limitations ................................................................................................................ 82.2.4 Factor of Safety (FOS) .......................................................................................... 82.3 FINITE ELEMENT (FE) METHOD .................................................................................... 102.3.1 Finite Difference (FD) Technique .................................................................... 112.3.2 Benefits ..................................................................................................................... 122.3.3 Limitations .............................................................................................................. 132.3.4 Factor of Safety (FOS) ........................................................................................ 13 Page viENG 4111/2 Research Project CHAPTER 3: SOFTWARE PACKAGES ................................................................... 153.1 OVERVIEW .......................................................................................................................... 153.2 SLOPE/W ......................................................................................................................... 153.2.1 Required Soil Properties ..................................................................................... 163.2.2 Slip Surface Entry & Exit ................................................................................... 163.2.3 SOLVE Process ..................................................................................................... 163.2.4 Morgenstern-Price Method ................................................................................ 173.3 FLAC ................................................................................................................................. 183.3.1 Required Soil Properties ..................................................................................... 193.3.2 FLAC/Slope............................................................................................................. 203.4 PLAXIS ............................................................................................................................. 213.4.1 Required Soil Properties ..................................................................................... 223.4.2 Elastic Modulus (E) .............................................................................................. 223.4.3 Staged Construction ............................................................................................. 233.4.4 Phi-c Reduction ..................................................................................................... 23CHAPTER 4: SCENARIO 1 – SIMPLE HOMOGENEOUS SOILSLOPE AT VARYING HEIGHTS 244.1 GEOTECHNICAL MODEL .................................................................................................. 244.1.1 Material Properties .............................................................................................. 254.1.2 Units .......................................................................................................................... 254.2 FLAC/SLOPE ANALYSIS ................................................................................................. 264.2.1 Methodology ........................................................................................................... 264.2.2 Results ...................................................................................................................... 284.3 SLOPE/W ANALYSIS ..................................................................................................... 304.3.1 Methodology ........................................................................................................... 304.3.2 Results ...................................................................................................................... 314.4 PLAXIS ANALYSIS ......................................................................................................... 334.4.1 Methodology ........................................................................................................... 334.4.2 Results ...................................................................................................................... 344.5 SUMMARY OF SIMPLE HOMOGENEOUS SOIL SLOPE RESULTS ................................. 38 Page viiENG 4111/2 Research Project CHAPTER 5: SCENARIO 2 – SIMPLE RESERVOIREMBANKMENT WITH A CLAYEY SOIL OFVARYING PLASTICITY ......................................................................... 395.1 GEOTECHNICAL MODEL .................................................................................................. 395.1.1 Material Properties .............................................................................................. 405.1.2 Units .......................................................................................................................... 405.2 FLAC/SLOPE ANALYSIS .................................................................................. 415.2.1 Methodology ........................................................................................................... 415.2.2 Results ...................................................................................................................... 435.3 SLOPE/W ANALYSIS ...................................................................................... 455.3.1 Methodology ........................................................................................................... 455.3.2 Results ...................................................................................................................... 465.4 PLAXIS ANALYSIS .......................................................................................... 485.4.1 Methodology ........................................................................................................... 483.4.2 Results ...................................................................................................................... 495.5 SUMMARY OF SIMPLE HOMOGENEOUS SOIL SLOPE RESULTS ................................. 53CHAPTER 6: SCENARIO 3 – EARTH DAM SUFFERING RAPIDDRAWDOWN ................................................................................................ 546.1 GEOTECHNICAL MODEL .................................................................................................. 546.1.1 Material Properties .............................................................................................. 556.1.2 Units .......................................................................................................................... 566.2 FLAC/SLOPE ANALYSIS .................................................................................. 566.2.1 Methodology ........................................................................................................... 566.2.2 Results ...................................................................................................................... 586.3 SLOPE/W ANALYSIS ..................................................................................................... 596.3.1 Methodology ........................................................................................................... 596.3.2 Results ...................................................................................................................... 616.4 PLAXIS ANALYSIS ......................................................................................................... 626.4.1 Methodology ........................................................................................................... 626.4.2 Results ...................................................................................................................... 646.5 SUMMARY OF EARTH DAM RESULTS ............................................................ 66 Page viiiENG 4111/2 Research Project CHAPTER 7: RESULTS AND DISCUSSION .......................................................... 677.1 RESULTS ............................................................................................................................. 677.1.1. Simple Homogeneous Soil Slope at Varying Heights ................................ 677.1.2. Simple Reservoir Embankment with a Clayey Soil of VaryingPlasticity Factor of Safety 687.1.3. Earth Dam Suffering Rapid Drawdown ........................................................ 707.2 FLAC ................................................................................................................................. 727.2.1 Student Version Specific Limitations ............................................................... 727.2.2 Modelling ................................................................................................................ 727.2.3 Materials.................................................................................................................. 727.2.4 Solving Process ..................................................................................................... 737.2.5 Results ...................................................................................................................... 747.2.6 Discussion ............................................................................................................... 747.3 SLOPE/W ......................................................................................................................... 757.3.1 Student Version Specific Limitations ............................................................... 757.3.2 Modelling ................................................................................................................ 757.3.3 Materials.................................................................................................................. 757.3.4 Solving Process ..................................................................................................... 757.3.5 Results ...................................................................................................................... 767.3.6 Discussion ............................................................................................................... 777.4 PLAXIS ............................................................................................................................. 777.4.1 Student Version Specific Limitations ............................................................... 777.4.2 Modelling ................................................................................................................ 777.4.3 Materials.................................................................................................................. 787.4.4 Solving Process ..................................................................................................... 787.4.5 Results ...................................................................................................................... 787.4.6 Discussion ............................................................................................................... 79CHAPTER 8: CONCLUSIONS ....................................................................................... 808.1 CONCLUSIONS .................................................................................................................... 808.2 FURTHER WORK ............................................................................................................... 81 Page ixENG 4111/2 Research Project CHAPTER 9: REFERENCES .......................................................................................... 82APPENDIX A: PROJECT SPECIFICATION .......................................................... 86APPENDIX B: SOFTWARE VALIDATION .......................................................... 104APPENDIX C: SIMPLE HOMOGENEOUS SOIL SLOPE WITHAPPLIED SURCHARGE (ATTEMPT) 112 Page xENG 4111/2 Research Project List of FiguresFigure 1 Static Scheme – Morgenstern-Price Method (Fine-CivilSoftware Package 2013). 7Figure 2 Rectangular mesh showing nodal points used in the finitedifference technique. 11Figure 3 Image of the Las Colinas Landslide (U.S. Geology Survey2010). 4Figure 4 Moment and Force FOS as a Function of the Inter-slice ShearForce (GEO-SLOPE International 2004) 18Figure 5 Basic explicit calculation cycle (ITASCA Consulting Group2011b). 19Figure 6 Simple Homogeneous Soil Slope 24Figure 7 Image of a Road Embankment (Terracon 2013) 24Figure 8 FLAC/Slope Slope Parameters for Case 1 - SimpleHomogeneous Soil Slope 27Figure 9 FLAC/Slope Material Properties - Simple Homogeneous SoilSlope 27Figure 10 FLAC/Slope Finite Element Mesh for Case 1 - SimpleHomogeneous Soil Slope 28Figure 11 FLAC/Slope Critical Slip Surface for Case 1 - SimpleHomogeneous Soil Slope 28Figure 12 FLAC/Slope Critical Slip Surface for Case 2 - SimpleHomogeneous Soil Slope 29Figure 13 FLAC/Slope Critical Slip Surface for Case 3 - SimpleHomogeneous Soil Slope 29Figure 14 SLOPE/W Material Properties - Simple Homogeneous SoilSlope 31Figure 15 SLOPE/W Critical Slip Surface for Case 1 - SimpleHomogeneous Soil Slope 31Figure 16 SLOPE/W Critical Slip Surface for Case 2 - SimpleHomogeneous Soil Slope 32Figure 17 SLOPE/W Critical Slip Surface for Case 3 - SimpleHomogeneous Soil Slope 32 Page xiENG 4111/2 Research Project Figure 18 PLAXIS Finite Element Mesh for Case 1 - SimpleHomogeneous Soil Slope 34Figure 19 PLAXIS Case 1 - Simple Homogeneous Soil Slope (a)Deformation, and (b) Total Displacement 35Figure 20 PLAXIS Case 2 - Simple Homogeneous Soil Slope (a)Deformation, and (b) Total Displacement 36Figure 21 PLAXIS Case 3 - Simple Homogeneous Soil Slope (a)Deformation, and (b) Total Displacement 37Figure 22 Simple Reservoir Embankment with a Clayey Soil 39Figure 23 Image of a Reservoir Embankment (VirginiaTech 2007). 40Figure 24 FLAC/Slope: Slope Parameters for all Cases - SimpleReservoir Embankment 41Figure 25 FLAC/Slope: Material Properties for Case 1 - SimpleReservoir Embankment 42Figure 26 FLAC/Slope Finite Element Mesh - Simple ReservoirEmbankment 42Figure 27 FLAC/Slope Critical Slip Surface for Case 1 - SimpleReservoir Embankment 43Figure 28 FLAC/Slope Critical Slip Surface for Case 2 - SimpleReservoir Embankment 44Figure 29 FLAC/Slope Critical Slip Surface for Case 3 - SimpleReservoir Embankment 44Figure 30 SLOPE/W Material Properties for case 1 - Simple ReservoirEmbankment 46Figure 31 SLOPE/W Critical Slip Surface for Case 1 - Simple ReservoirEmbankment 46Figure 32 SLOPE/W Critical Slip Surface for Case 2 - Simple ReservoirEmbankment 47Figure 33 SLOPE/W Critical Slip Surface for Case 3 - Simple ReservoirEmbankment 47Figure 34 PLAXIS Finite Element Mesh - Simple ReservoirEmbankment 49Figure 35 PLAXIS Case 1 - Simple Reservoir Embankment (a)Deformation, and (b) Total Displacement 50 Page xiiENG 4111/2 Research Project Figure 36 PLAXIS Case 2 - Simple Reservoir Embankment (a) Deformation, and (b) Total Displacement 51Figure 37 PLAXIS Case 3 - Simple Reservoir Embankment (a) Deformation, and (b) Total Displacement 52Figure 38 Earth Dam before Rapid Drawdown. 54Figure 39 Earth Dam after Rapid Drawdown. 54Figure 40 Image of an Earth Dam (U.S. Army Corps of Engineers 2013). 55Figure 41 FLAC/Slope Slope Parameters for all Cases – Earth Dam 57Figure 42 FLAC/Slope Material Properties – Earth Dam 57Figure 43 FLAC/Slope Finite Element Mesh for Case 1 – Earth Dam 58Figure 44 FLAC/Slope Critical Slip Surface before Drawdown – Earth Dam 58Figure 45 FLAC/Slope Critical Slip Surface after drawdown – Earth Dam 59Figure 46 SLOPE/W Material Properties – Earth Dam 60Figure 47 SLOPE/W Critical Slip Surface before drawdown – Earth Dam 61Figure 48 SLOPE/W Critical Slip Surface after drawdown – Earth Dam 61Figure 49 PLAXIS Finite Element Mesh - Earth Dam 63Figure 50 PLAXIS - Earth Dam before drawdown (a) Deformation, and (b) Total Displacement 64Figure 51 PLAXIS - Earth Dam after drawdown (a) Deformation, and (b) Total Displacement 65Figure 52 Results Comparison - Simple Homogeneous Soil Slope 68Figure 53 Results Comparison - Simple Reservoir Embankment 70Figure 54 FLAC/Slope allowed models. 72Figure 55 FLAC coarse mesh of an Open Cut Mine Pit Wall. 74Figure 56 SLOPE/W Critical Slip Surface before drawdown (incorrect direction) – Earth Dam 76Figure 57 Image of the Kalgoorlie „Super Pit? (The Super Pit 2009) 81 Page xiiiENG 4111/2 Research Project List of TablesTable 1 SLOPE/W Mohr-Coulomb Model Properties 16Table 2 FLAC Mohr-Coulomb Model Basic Properties 20Table 3 FLAC Mohr-Coulomb Model Advanced Properties 20Table 4 PLAXIS Mohr-Coulomb Model Properties 22Table 5 Unsaturated Sand Material Properties - Simple Homogeneous Soil Slope 25Table 6 Cases and corresponding Embankment Heights - Simple Homogeneous Soil Slope 25Table 7 Parameters for Analysis 26Table 8 FLAC/Slope FOS Results - Simple Homogeneous Soil Slope 30Table 9 SLOPE/W FOS Results - Simple Homogeneous Soil Slope 33Table 10 PLAXIS Finite Element Modelling Construction Stages 34Table 11 PLAXIS FOS Results - Simple Homogeneous Soil Slope 38Table 12 Summary of FOS Results - Simple Homogeneous Soil Slope 38Table 13 Clayey Soil Material Properties - Simple Reservoir Embankment 40Table 14 FLAC/Slope FOS Results - Simple Reservoir Embankment 45Table 15 SLOPE/W FOS Results - Simple Reservoir Embankment 48Table 16 PLAXIS Finite Element Modelling Construction Stages 49Table 17 PLAXIS FOS Results - Simple Reservoir Embankment 53Table 18 Summary of FOS Results - Simple Reservoir Embankment 53Table 19 Clayey Soil Material Properties - Simple Reservoir Embankment 55Table 20 FLAC/Slope FOS Results – Earth Dam 59Table 21 SLOPE/W FOS Results – Earth Dam 62Table 22 PLAXIS Finite Element Modelling Construction Stages 63Table 23 PLAXIS FOS Results – Earth Dam 66Table 24 Summary of FOS Results – Earth Dam 66Table 25 FOS Differences (%) - Simple Homogeneous Soil Slope 67Table 26 FOS Differences (%) - Simple Reservoir Embankment 69Table 27 FOS Differences (%) before Rapid Drawdown – Earth Dam 71Table 28 FOS Differences (%) after Rapid Drawdown – Earth Dam 71Table 29 Parameters for Analysis 73Page xivENG 4111/2 Research Project NomenclatureFOS Factor of safetyLE Limit EquilibriumFE Finite ElementFD Finite DifferenceSRF Strength Reduction FactorZ Depths Shear strengtht Shear stresss Normal stresss' Effective normal stress? Density?unsat Unsaturated unit weight ?sat Saturated unit weightu Pore water pressurec'Drained cohesion?' Drained friction anglec Undrained cohesion? Undrained friction angle ? E Undrained Elastic (Young?s) modulus?' Poisson?s ratioPage xvENG 4111/2 Research Project Chapter 1: Introduction1.1 IntroductionThe purpose of this report is to compare the student versions of FLAC, PLAXISand SLOPE/W and their use in Geotechnical stability analysis.The instability of a slope is an ongoing concern in most construction andinfrastructure projects, as slope failures can result in significant repair andmaintenance costs and can endanger both the workers and the general public.There are a number of software packages that have been developed forgeotechnical stability analysis which utilise the Limit Equilibrium (LE) Method,Finite Element (FE) method and Finite Difference (FD) method. The LE methodis the most widely used approach; however it does contain several limitations andinconsistencies. With the advancement in technology software packages utilisingthe FE and FD methods have increased in popularity as they tend to possess awider range of features (Hammouri et al. 2008).This research project intends to compares three software packages and theirrespective methods of stability analysis.LE method:? SLOPE/W is a software package created by GEO-SLOPE InternationalLtd. as part of their GeoStudio bundle. ? FE/FD methods:? PLAXIS is a software package created by Plaxis bv.. ? ? ? FLAC is a software package created by ITASCA Consulting Group Inc. ?Page 1ENG 4111/2 Research Project 1.2 BackgroundOver the years there has been an increase in construction and infrastructureprojects and consequently a growth in the requirements for excavation, footingsand road design. Engineers must take into account all geotechnical aspectsaffecting their design including soil material properties, slope stability andpossible natural disasters which can have devastating social and economicimpacts. Incorporating the analysis of slope stability within the design will helpin the prevention of any geotechnical failures throughout construction and the lifeof the design (Bromhead 1992).Slope stability is important throughout all aspects of construction and a smalldifference in the calculated Factor of Safety (FOS) can result in a significantincrease in costs both in construction and ongoing maintenance. For many yearsthe LE method has been the most common approach due to its simplicity andrequiring minimal properties; however with the advancement in technology therehas been an increase in the use of the FE and FD methods; as they are able toaccommodate a wider range of geometries and can progressively calculate thedeformation and stresses on the model up to and including the FOS. Currentlythere is no evidence into which software packages produce the most acceptableresults. This research project intends to assist the engineering industry incomparing the student versions of SLOPE/W, PLAXIS & FLAC; three packageswidely used (Aryal 2008).1.3 MethodologyThe methodology employed in addressing this report involves:i) Studying the background into the methodology of the 3 softwarepackages; PLAXIS, FLAC & SLOPE/W. i.e. Finite Element Method,Finite Difference Method & Limit Equilibrium Method.ii) Familiarise with each package and their capabilities.iii) Understand the limitations of the student versions.Page 2ENG 4111/2 Research Project iv) Research scenarios of geotechnical stability in which the softwarepackages can be used.v) Create concepts for each scenario to analyse.vi) Research each scenario?s parameters and soil properties.vii) Create detailed scenarios including the geometry, details or actionsand soil properties.viii) Analyse each scenario using FLAC, PLAXIS & SLOPE/W anddiscuss the results.ix) From all the above steps discuss the limitations and benefits of each ofthe software packages and make recommendations.1.4 ObjectivesThe objectives of this report include:? Gain a better understanding of factors that cause slope instability and theirimportance in the geotechnical analysis. ? ? ? Gain a better understanding of the student versions of FLAC, PLAXISand SLOPE/W. ? ? ? Discuss the benefits and limitations of each packages student version. ? ? ? Evaluate my own personal experiences and preferences in the packages. ? 1.5 Report StructureThis report details background information of slope stability analysis throughreviewing literature, analysing slope stability methods, experimental techniques,results and recommendations on the student versions of FLAC, PLAXIS andSLOPE/W software programs. These are outlined in the following sections: Page 3ENG 4111/2 Research Project Chapter 1: IntroductionOutlines the problemexplored within the report.Chapter 2: Literature Review Reviews the current literature that has been published.Chapter 3: Software Packages Outlines the softwarepackages used for the report.Outlines the scenario andChapter 4: Scenario 1 - Simple Homogeneousresults.Soil Slope at Varying Heights.Chapter 5: Scenario 2 - Simple reservoir Outlines the scenario andembankment with a clayey soil of varying results.plasticity.Chapter 6: Scenario 3 - Earth Dam suffering Outlines the scenario andrapid drawdown. results.Chapter 7: Results and Discussion Analysis of the results anddiscussion of the softwareused.Chapter 8: Conclusion Conclusion andrecommendations for furtherwork. Page 4ENG 4111/2 Research Project Chapter 2: Literature Review2.1 IntroductionThis chapter serves to review the current literature that has been publishedregarding FLAC, PLAXIS and SLOPE/W and their corresponding stabilityanalysis methods. The majority of published information is in regards to theanalysis methods of Limit Equilibrium, Finite Element and Finite Difference andnot the software packages themselves. This literature review intends to establishan understanding of each of these methods.2.2 Limit Equilibrium (LE) MethodCurrently the LE method is the most widely used approach within thegeotechnical industry in solving modern day slope stability scenarios. The LEmethod requires the plastic Mohr-Coulomb criterion where a materials failure isdue not from the maximum normal or shear stress alone but a combination ofboth. The LE method establishes the required soil properties; slope geometry andthen using the Mohr-Coulomb criterion calculates the stability of the slope bycomparing the forces causing failure against the resisting forces. Throughout thisprocedure an FOS is computed using the equations of static equilibrium. “Thefundamental assumption…is that failure occurs through sliding of a block or massalong a slip surface” (RocScience 2004a, p.2) and in order to compute theappropriate FOS a number of slip surfaces need to be postulated to find thecritical slip surface. (Duncan & Wright 2005; Hammouri et al. 2008; Chen & Liu1990, Das 2010).The LE method requires the following assumptions:i) “The soil behaves as a Mohr-Coulomb material.ii) The FOS of the cohesive component of strength and the frictionalcomponent of strength are equal for all soils involved” (GEO- SLOPE International 2004, p.427).Page 5ENG 4111/2 Research Project iii) Each block within the slip surface has the same FOS.iv) Inter-slice forces are assumed; to deem the problem determinate(Griffiths & Lane 1999; Cheng & Lau 2008; Aryal 2008).2.2.1 Vertical SlicesThe LE method utilises the method of vertical slices, the vertical slices method iswhere “the entire sliding mass is divided into a reasonable number of slices andthe inter-slice forces are computed based on an assumed inter-slice forcefunctional relationship” (Aryal 2008, p.4509). Slip surfaces are assumed and thestatic equilibrium equations are used to calculate the stresses and FOS on eachslice (Chen & Lau 2008).The static equilibrium conditions are:1. “Equilibrium of forces in the vertical direction,2. Equilibrium of forces in the horizontal direction, and3. Equilibrium of moments about any point” (Duncan & Wright 2005, p.56).The slip surface is a surface where sliding is assumed to occur; this slip surfacemay be circular, or a shape defined by straight lines. Duncan and Wright, 2005states that when using the LE method the Morgenstern-Price procedure should beadopted as it satisfies all requirements for static equilibrium requirements forboth forces and moments. The Morgenstern-Price procedure creates „blocks’dividing the soil above the slip surface.Fine – Civil Engineering Software (2013) states that “Forces acting on individualblocks are displayed in the following figure: Page 6ENG 4111/2 Research Project Figure 1 Static Scheme – Morgenstern-Price Method (Fine-Civil Software Package 2013).The following assumptions are introduced in the Morgenstern-Price method tocalculate the limit equilibrium of forces and moment on individual blocks:? dividing planes between blocks are always vertical; ? ? ? the line of action of weight of block W passes through the center of thei th i segment of slip surface represented by point M; ? ? th ? the normal force N is acting in the center of the i segment of slipi surface, at point M; ? ? ? inclination of forces Eacting between blocks is different on each block ? i ? (d ) at slip surface end points is d = 0.” (Fine-Civil Software Package,i 2013) ? An assumption is then made that each „block? along the slip surface is believed tohave the same FOS value, representing the average FOS for the slip surface andis taken as the appropriate value for that slip surface. The minimum or criticalFOS is determined by calculating the FOS for all assumed slip surfaces and thesmallest value being accepted; this is identified as the critical slip surface. Failureshould not occur if the design is based on this calculated FOS (Duncan & Wright2005; Hammouri et al. 2008). Page 7ENG 4111/2 Research Project 2.2.2 BenefitsThe LE method has the following benefits:? It is a simplistic approach. ? ? ? Requires minimal soil properties and slope geometry. ? ? ? An adequate design based upon the calculated FOS ensures that slidingalong the slip surface should not occur. ? 2.2.3 LimitationsThe LE method has several limitations, including:? Numerical inconsistencies. ? ? ? The analysis method is the same for all scenarios; i.e. the same method isused for a “slope of a newly constructed embankment, a slope of a recentexcavation, or an existing natural slope” (Zheng et.al. 2008, p.629). ? ? ? Neglects the stress-strain behaviour of the material. ? ? ? The user needs an understanding of the geotechnical and slope stabilityprincipals involved within the analysis i.e. the direction of the slip surface. ? ? ? Unable to model the progressive failure and deformation of the surfacewithout assumptions being made. (Cheng & Lau 2008; Hammouri et al.2008; RocScience 2004a). ? 2.2.4 Factor of Safety (FOS)The FOS provides a “quantitative indication of slope stability” (Duncan & Wright2005, p.199). A calculated FOS value equal to 1 represents the forces on the slopebeing in equilibrium; that is the forces within the slope causing stablility(resisting forces) are in balance with those which cause the slope to be unstable(driving forces). A calculated FOS value greater than 1.0 represents the slopebeing stable under the given conditions (resisting forces > driving forces), and aFOS value less than 1.0 represents that the slope is unstable (failing); that is thedriving forces out way the resisting forces (Duncan & Wright 2005). Page 8ENG 4111/2 Research Project "