Geotechnical Slope Analysis

1 Aims and overview – slopes, geology and materials

• 1.1 Introduction
• 1.2 Overview of recent developments and trends
• 1.2.1 Increasing frequency and impact of disasters from slope failures and landslides
• 1.2.2 Climate change, global warming and sea level rise
• 1.2.3 Built slopes – lessons from the catastrophic impacts of Hurricane Katrina
• 1.2.4 New developments related to slope analysis
• 1.2.5 Importance of probabilistic analysis
• 1.2.6 GIS-based methods and analyses
• 1.2.7 Assessments concerning very large landslides
• 1.2.8 Landslide frequency related to magnitude
• 1.2.9 Assessing regional landslide susceptibility and hazard
• 1.2.10 Development and use of slope stability software
• 1.2.11 Need to strengthen the fundamentals of geomechanics and slope analysis
• 1.3 Main aim and scope of this book
• 1.4 Aims of geotechnical slope analysis
• 1.5 Natural slopes – regional and site-specific analyses
• 1.6 Natural slopes – factors affecting stability
• 1.7 Built slopes, unreinforced and reinforced
• 1.7.1 Unreinforced slopes
• 1.7.2 Reinforced slopes
• 1.8 Geomorphology and slopes
• 1.9 Types of slope movement and landslides
• 1.9.1 Processes and types of slope movement
• 1.9.2 Pre-failure and post-failure movements
• 1.9.3 Failures of slopes in poorly compacted fill
• 1.9.4 Some observed data concerning magnitude of movements in soil and rock slopes
• 1.9.5 Rainfall as a triggering factor for slope failures or for the occurrence of landslides
• 1.9.6 Available methods for seepage analysis
• 1.10 Geology and slopes
• 1.10.1 Fabric
• 1.10.2 Geological structure
• 1.10.3 Geological structure and tendency of slope movement
• 1.10.4 Ground water
• 1.10.5 Seismic effects
• 1.10.6 Ground stresses or ‘initial’ stresses
• 1.10.7 Weathering
• 1.10.8 Previous landslide activity
• 1.11 The nature of soils
• 1.12 The nature of rocks

Appendix to chapter 1

2 Basic geotechnical concepts

• 2.1 Introduction
• 2.2 Stress and strain
• 2.2.1 Elastic (recoverable) stresses and strains in soil and rock
• 2.2.2 Irrecoverable strains in soil and rock
• 2.3 The principle of effective stress in soil and rock
• 2.3.1 Saturated soil
• 2.3.2 Unsaturated soil
• 2.3.3 Different types and sources of pore water pressure
• 2.3.4 Reservoir filling and artesian pressures – an example, the 1963 Vaiont slide
• 2.4 Shear strength of soils
• 2.4.1 Dry or saturated soils
• 2.4.2 Unsaturated soils
• 2.4.3 Slope failures involving unsaturated soil slopes
• 2.4.4 Factors influencing shear strength parameters
• 2.4.5 Measurement of shear strength under different drainage conditions
• 2.4.6 Peak, ultimate and residual shear strength
• 2.4.7 Factors influencing residual shear strength
• 2.4.8 Undrained strength of fissured clays
• 2.5 Mohr-Coulomb criterion in terms of principal stresses and stress path concept
• 2.5.1 Stress paths
• 2.5.2 Failure plane inclination and intermediate principal stress
• 2.5.3 Coulomb failure criterion for compression and extension tests
• 2.6 Shear strength of rocks
• 2.6.1 A rock mass as a discontinuum
• 2.6.2 Example of the importance of discontinuities in rock – the occurrence of catastrophic landslides
• 2.6.3 Griffith theory of rock fracture
• 2.6.4 Shear failure along rough discontinuity
• 2.6.5 Continuity of jointing and actual area of contact
• 2.6.6 Curved strength envelopes
• 2.6.7 Strength of filled discontinuities
• 2.6.8 Shear strength of closely jointed or fractured rock
• 2.6.9 Determination of shear strength
• 2.7 Plasticity and related concepts
• 2.8 Excess pore water pressures
• 2.9 Relationships between drained and undrained strength of cohesive soils
• 2.9.1 Unique w-p-q relationships at peak and ultimate strength
• 2.9.2 Undrained strength and pore pressure parameterat failure
• 2.9.3 Relative magnitude of drained and undrained strength
• 2.9.4 "φ 0" concept
• 2.9.5 Anisotropy of shear strength
• 2.10 Progressive failure of slopes
• 2.11 Residual strength and other factors in progressive failure
• 2.12 Progressive failure and the stress field
• 2.13 Numerical examples

3 Performance indicators and basic probability concepts

• 3.1 Introduction and scope
• 3.1.1 Preliminary decisions concerning type of analysis
• 3.1.2 Choice of performance indicators
• 3.1.3 Contents of this chapter
• 3.2 Deterministic approach
• 3.2.1 Global and local factors of safety
• 3.2.2 Critical seismic coefficient as alternative to factor of safety
• 3.2.3 Progressive failure and system aspects
• 3.2.4 Performance indicators for stress-deformation analyses
• 3.2.5 Threshold or allowable values of factor of safety
• 3.3 Probabilistic approach
• 3.3.1 Uncertainties and the probabilistic framework
• 3.3.2 Systematic uncertainties and natural variability of geotechnical parameters
• 3.4 Reliability index, probability of failure and probability of success (reliability)
• 3.5 Considering thresholds – minimum reliability index, maximum probability of failure
• 3.6 Spatial, temporal and system aspects
• 3.7 Susceptibility, hazard and risk
• 3.8 Further comments on geotechnical uncertainties
• 3.8.1 Introduction
• 3.8.2 Basic statistical parameters
• 3.8.3 Variability of soil properties and errors
• 3.9 Variance of F for simple slope problems
• 3.10 Using probabilistic analysis
• 3.10.1 Requirements and limitations: discussions during early phase of development
• 3.10.2 Example of a probabilistic slope study, De Mello (1977)
• 3.10.3 Errors and probability of failure, Wu and Kraft (1970)

Appendix I to chapter 3

• C3I.1 Axioms and rules of probability
• C3I.2 Conditional probability and statistical independence
• C3I.3 Total probability and Bayes’ theorem
• C3I.4 Random variables and probability distributions
• C3I.5 Moments of a random variable
• C3I.6 The normal distribution
• C3I.6.1 The standard normal variate
• C3I.6.2 Application of standard normal variate
• C3I.7 Logarithmic normal distribution
• C3I.8 Joint distribution, covariance and correlation
• C3I.9 Moments of functions of random variables
• C3I.9.1 Sum of variates x1, x2 etc.
• C3I.9.2 Product of independent variates x1, x2, x3, etc.
• C3I.9.3 First order approximation for general functions

Appendix II to chapter 3

• C3II.1 Equations for a capacity – demand model (after Harr, 1977)
• C3II.1.1 Safety margin and factor of safety
• C3II.1.2 Defining probability of failure and reliability
• C3II.1.3 Probability of failure with normal distribution
• C3II.1.4 Probability of failure with lognormal distribution
• C3II.1.5 Safety margin required for given reliability

Appendix III to chapter 3

4 Limit equilibrium methods I – planar failure surfaces

• 4.1 Introduction to limit equilibrium methods
• 4.1.1 Methods considered in chapters 4 and 5
• 4.1.2 Scope of limit equilibrium studies
• 4.1.3 The concept of slip surfaces
• 4.1.4 Defining factor of safety as per concept of limit equilibrium
• 4.1.5 Alternatives to conventional safety factor
• 4.1.6 Saturated and unsaturated soil slopes
• 4.2 Infinite slopes in cohesionless soils
• 4.2.1 Dry cohesionless soil
• 4.2.2 Submerged cohesionless soil
• 4.2.3 Cohesionless soil with seepage parallel to slope
• 4.2.4 Rapid drawdown of water level in a slope of cohesionless soil
• 4.3 Infinite slopes in cohesive soil
• 4.3.1 Seepage through a slope – simple cases
• 4.3.2 Rapid drawdown of water level in a slope of cohesive soil
• 4.4 Ultimate inclination of natural slopes
• 4.5 Vertical cuts in cohesive material
• 4.5.1 Unsupported height of a vertical cut and tension crack depth
• 4.5.2 Tension crack depth for use in stability analysis
• 4.6 Plane failure in rock slopes
• 4.7 Plane failure with water in tension crack
• 4.7.1 Conventional analysis
• 4.7.2 Alternative ways of defining F
• 4.8 Interpretation of strength data for use in stability calculations
• 4.9 Two-dimensional sliding along one of two joint sets
• 4.10 Continuity of jointing
• 4.11 Wedge method or sliding block method of two-dimensional analysis
• 4.11.1 Bi-planar slip surface
• 4.11.2 Tri-planar sliding surface
• 4.12 Failure of three-dimensional wedge
• 4.13 Layered natural deposits and the effect of water pressure
• 4.13.1 Interbedded sand and clay layers
• 4.13.2 Interbedded sandstones and shales
• 4.14 Earth dams – plane failure analyses
• 4.14.1 Introduction
• 4.14.2 Simple sliding block analysis
• 4.14.3 Hydraulic fill dam
• 4.15 Slurry trench stability
• 4.15.1 Cohesionless soil
• 4.15.2 Cohesive soil – soft clay

5 Limit equilibrium methods II – general slip surfaces and beyond critical equilibrium

• 5.1 Introduction and scope
• 5.1.1 Drainage conditions – choice between effective stress and total stress analysis
• 5.1.2 Shapes of slip surfaces
• 5.1.3 Estimating minimum factor of safety associated with a critical slip surface
• 5.1.4 Tension crack location and depth as part of optimization process
• 5.1.5 Back analysis of failed slopes and landslides
• 5.1.6 The concept of a resistance envelope
• 5.2 Short-term stability of clay slopes
• 5.2.1 Slopes in soft clay – circular failure surfaces
• 5.2.2 Undrained strength of soft clay in relation to analysis (simple and advanced ‘total stress’ approaches)
• 5.2.3 Stiff clays
• 5.2.4 Proportion of fissures from back analysis
• 5.3 Friction circle method (c, φ soils)
• 5.4 Method of slices – Fellenius and Bishop simplified methods
• 5.4.1 Ordinary method of slices (Fellenius method)
• 5.4.2 Bishop simplified method
• 5.4.3 Convergence problems and possible numerical errors
• 5.4.4 Pore pressures and submergence
• 5.4.5 Effective stress charts and average pore pressure ratio
• 5.4.6 Inclusion of additional external forces such as soil reinforcement
• 5.5 Slip surfaces of arbitrary shape
• 5.5.1 Janbu’s generalised method
• 5.5.2 Convergence problems
• 5.5.3 Extended Janbu method (Zhang, 1989)
• 5.6 Other methods for general slip surfaces
• 5.6.1 Developments before 1978
• 5.6.2 Developments over the last three decades
• 5.6.3 Availability of geotechnical software for slopes
• 5.6.4 Non-vertical slices in limit equilibrium analysis
• 5.6.5 A variation of the method of slices and its application to the 1963 Vaiont slide
• 5.7 Morgenstern and price method
• 5.8 Simplified calculation and correction factor
• 5.9 Some early applications
• 5.10 Special analyses
• 5.10.1 Slope underlain by very weak soil layer such as soft clay
• 5.10.2 Considering calculated F in the context of the method of analysis
• 5.10.3 Clay slope underlain by water-bearing seam of fine sand
• 5.11 An early comparison of different limit equilibrium methods
• 5.12 Three-dimensional effects
• 5.12.1 Developments over the last four decades
• 5.12.2 Weighted average procedure
• 5.12.3 Inclusion of end effects
• 5.12.4 A general three-dimensional approach
• 5.12.5 Lateral curvature (curvature in plan) of a slope
• 5.12.6 Shape or curvature of slope profile or slope face
• 5.12.6 An example of 3D factor of safety calculations – analysis of the 1963 Vaiont slide
• 5.13 ‘Total stress’ versus ‘effective stress’ analyses
• 5.14 choice and use of limit equilibrium methods – guidelines
• 5.14.1 Essential first steps
• 5.14.2 Choice of method of analysis
• 5.14.3 Sensitivity of calculated F
• 5.14.4 Sensitivity of F to tension cracks
• 5.14.5 The factor of safety in practice
• 5.14.6 Important considerations in all types of analysis
• 5.15 Variational calculus and slope stability
• 5.16 Simulating progressive failure within the framework of limit equilibrium – the effect of stress redistribution in slopes of strain-softening soil
• 5.16.1 Applications of the above procedure
• 5.17 Lessons from case studies of clay slopes
• 5.17.1 End-of-construction failures in clay
• 5.17.2 Long-term failures in intact clays, progressive failure and renewed movement
• 5.17.3 Long-term failures in fissured clays
• 5.17.4 Time to failure
• 5.18 Post-failure behaviour of landslides with particular reference to exceptional rockslides
• 5.18.1 Broad categories of landslides
• 5.18.2 Suggested mechanisms for exceptional landslides
• 5.18.3 Travel angle of landslides based on completed motion after detachment
• 5.19 Understanding ordinary slope failures beyond critical equilibrium
• 5.19.1 Stability to critical equilibrium and failure
• 5.19.2 The importance of very small movements of a failed but undetached mass
• 5.19.3 Estimating deformations
• 5.19.4 Rainfall-induced debris flow initiation
• 5.19.5 Methodology for analysing a rock avalanche
• 5.20 Improving slope stability
• 5.20.1 Introduction
• 5.20.2 Preliminary steps for slope improvement
• 5.20.3 Brief outline of some stabilisation methods

Appendix to chapter 5

• C5.1 Slope analysis including anisotropy
• C5.2 For φ = 0 conditions
• C5.3 For φ > 0 cases

6 Stress-deformation analyses and their role in slope analysis

• 6.1 Introduction
• 6.1.1 Range of advanced numerical methods for stress-deformation analysis
• 6.1.2 Need for stress-deformation analysis
• 6.1.3 Specific advantages of stress-deformation analyses
• 6.1.4 Beginnings of a numerical approach for embankment stress analysis
• 6.2 The finite element method
• 6.2.1 Basis of the method
• 6.2.2 Two-dimensional displacement formulation
• 6.2.3 Review of linear, non-linear and sophisticated models for FEM Solutions
• 6.2.4 Features of the simpler models: linear elastic, multi-linear elastic, hyperbolic elastic
• 6.2.5 Features of elastoplastic and viscoplastic models
• 6.2.6 General comments about all models
• 6.2.7 Range and complexity of data and parameters required for some sophisticated models
• 6.3 Material parameters for stress analysis
• 6.3.1 Isotropic parameters
• 6.3.2 Anisotropic parameters
• 6.3.3 Influence of deformation parameters on stresses and deformations
• 6.4 Incremental body force stresses
• 6.4.1 Embankment analysis in stages
• 6.4.2 Multi-stage excavation in linear and non-linear material
• 6.4.3 Simulation of excavation
• 6.5 Non-linear material behaviour and special problems
• 6.5.1 Introduction
• 6.5.2 Alternative approaches for non-linear problems
• 6.5.3 Equations based on hyperbolic response
• 6.5.4 Joints and discontinuities and interface elements
• 6.5.5 Incompressibility
• 6.5.6 Analysis of mining spoil pile stability (Richards et al., 1981; Richards, 1982)
• 6.6 Post excavation stresses
• 6.7 Computed stresses and safety factor
• 6.8 Modelling progressive failure in slopes of strain-softening soil
• 6.8.1 Brief overview of available methods
• 6.8.2 Overstressed elements in a slope and calculating excess shear stress
• 6.8.3 Iterative FEM analyses in strain-softening soil
• 6.9 Changes in water table and pore pressures
• 6.10 Limit equilibrium analysis with known falure zone

7 Natural slope analysis considering initial stresses

• 7.1 Introduction
• 7.1.1 Importance of in-situ stresses
• 7.1.2 Magnitude and measurement of in-situ stresses
• 7.2 Relationship between K0, shear strength and pore pressure coefficients
• 7.3 Estimating K0 from the back analysis of a failed slope
• 7.4 Initial stresses in sloping ground
• 7.5 Limiting values of K
• 7.6 Stresses on any plane
• 7.7 The concept of inherent stability
• 7.8 Planar failure
• 7.9 Ultimate stable angle of natural slopes
• 7.10 Bi-planar surfaces of sliding
• 7.11 Potential slip surface of arbitrary shape
• 7.12 Example – circular failure surfaces
• 7.13 Simulating progressive change in stability
• 7.13.1 The simulation process 385
• 7.13.2 Defining an overall factor of safety at any stage
• 7.13.3 Change in stability considering two alternative modes of progression
• 7.13.4 An alternative method for simulation of progressive change in the stability of an idealized embankment
• 7.14 Application to altered slopes
• 7.15 Rock-slide at the site of the vaiont dam and a summary of some analyses carried out after its occurrence
• 7.15.1 Unusual nature of the catastrophic landslide
• 7.15.2 Back-calculated shear strength based on critical equilibrium
• 7.15.3 Shear strength of rock materials
• 7.15.4 Pore water pressure assumptions
• 7.16 Simulation of progressive failure based on initial stress approach (Chowdhury, 1978a)
• 7.16.1 Assumption of a reasonable initial stress field
• 7.16.2 Estimation of factors of safety
• 7.16.3 Approximate estimation of accelerations
• 7.16.4 Approximate estimation of velocities
• 7.16.5 Supporting comments
• 7.16.6 Conclusion
• 7.17 An alternative approach for analysis of the vaiont slide (Hendron and Patton, 1985)
• 7.17.1 Introduction
• 7.17.2 2-D static analyses
• 7.17.3 3-D static analyses
• 7.17.4 Analyses for the dynamics of the landslide
• 7.18 Final comment on the two alternative explanations
• 7.18.1 Approach based on initial stress field and simulation of progressive failure
• 7.18.2 Approach based on assumed high artesian pressures and heat – generated pore water pressures

8 Plasticity and shear band analyses – a brief review

• 8.1 Plasticity
• 8.1.1 Introduction
• 8.1.2 Scope
• 8.1.3 Material idealisation and types of solutions
• 8.2 Classical analyses
• 8.2.1 Introduction
• 8.2.2 Critical profile of a slope with loading on the crest
• 8.2.3 Finding the non-uniform surcharge for a uniform slope of given critical inclination
• 8.2.4 Slopes curved in plan
• 8.2.5 Uniform slope of soil in which shear strength increases with depth
• 8.3 Limit analysis
• 8.3.1 Upper and lower bound theorems
• 8.3.2 Example-a vertical slope
• 8.3.3 Lower bound solution
• 8.3.4 Scope of solutions for general cases
• 8.3.5 Extension of solutions to more realistic or complex problems
• 8.3.6 Possible future extension to modeling of progressive failure
• 8.3.7 Extension of upper bound method
• 8.4 Plasticity solution by finite elements
• 8.4.1 Introduction
• 8.4.2 Strength reduction technique
• 8.4.3 Non-homogeneous slopes and realistic material behaviour
• 8.4.4 Simple and advanced soil models
• 8.4.5 A slope in homogeneous soil resting on a rough base
• 8.5 Shear band concept
• 8.5.1 Questions relevant to formation and significance of shear bands or slip surfaces
• 8.5.2 Some relevant applications reported in theliterature
• 8.5.3 Cases in which internal deformations of soil mass must be considered
• 8.6 Palmer and rice approach – the shear box problem
• 8.6.1 Introduction
• 8.6.2 Energy balance equation
• 8.7 Long shear box and infinite slope
• 8.7.1 Long shear box
• 8.7.2 Long slope with a step or cut
• 8.8 Non-uniform shear stress on band
• 8.8.1 Introduction
• 8.8.2 Long shear box
• 8.8.3 Long slope with step or cut
• 8.8.4 Relatively flat slope – gravitational stress less than residual strength
• 8.9 Shear band of arbitrary inclination (after Chowdhury, 1978b)
• 8.9.1 Introduction
• 8.9.2 Considering the energy balance
• 8.9.3 The propagation criterion
• 8.9.4 Results for an example case
• 8.10 Rate of propagation
• 8.11 A simple progressive failure model
• 8.12 Application of shear band concepts

Appendix to chapter 8

• C8.1 Slope studies for anisotropic soil

9 Earthquake effects and seismic slope analysis

• 9.1 Seismic slope stability and deformations – an introduction
• 9.1.1 Aims and scope
• 9.1.2 Introducing pseudo-static analysis
• 9.1.3 Critical seismic coefficient (or yield value of seismic coefficient)
• 9.1.4 Introducing Newmark approach of sliding block analysis
• 9.1.5 Three stages of change in stability and permanent deformation
• 9.2 Soil behaviour under cyclic loading conditions
• 9.2.1 Introduction
• 9.2.2 Cyclic shear strength from laboratory tests
• 9.2.3 Field tests and model tests
• 9.2.4 Shear strength parameters for seismic slope analysis
• 9.2.5 Rate effects on the shear strength along existing slip surfaces
• 9.3 Seismically-induced soil liquefaction and residual strength of cohesionless soil
• 9.3.1 Seismic liquefaction phenomena
• 9.3.2 Liquefaction-related strains and deformations
• 9.3.3 Undrained residual shear strength
• 9.3.4 Flow liquefaction contrasted with cyclic mobility
• 9.4 Pseudo-static analysis
• 9.4.1 Planar slip surfaces
• 9.4.2 Circular slip surface in saturated soil slope
• 9.4.3 Slip surfaces of arbitrary shape
• 9.4.4 Seismic coefficient and factor of safety for pseudo-static analysis
• 9.4.5 Beyond pseudo-static analysis
• 9.5 Critical seismic coefficient
• 9.5.1 Introduction – the range of methods and solutions
• 9.5.2 Critical seismic coefficient for slip surfaces of planar or log spiral shapes
• 9.5.3 Critical seismic coefficient for circular slip surface
• 9.5.4 Critical seismic coefficient for homogeneous slope considering slip surface of arbitrary shape
• 9.6 Sliding block solution for permanent displacements
• 9.6.1 The Newmark approach
• 9.6.2 Typical estimated values of seismic displacement
• 9.6.3 Considering variable critical seismic coefficient
• 9.7 Empirical/regression equations for permanent displacements
• 9.7.1 Introduction and scope of equations from regression analysis
• 9.7.2 An equation based on (i) the ratio of critical seismic coefficient and peak ground acceleration coefficient and (ii) the predominant period
• 9.7.3 An equation based only on the ratio of critical seismic coefficient and peak ground acceleration coefficient
• 9.7.4 An equation based on arias intensity and critical seismic acceleration
• 9.7.5 Seismic Destructiveness Potential Factor and its use in numerical analyses
• 9.8 Dynamic analyses
• 9.8.1 Introduction
• 9.8.2 Basic concepts and equations
• 9.8.3 Example of analyses for a failed dam
• 9.8.4 Other procedures developed and used in the 1970s
• 9.8.5 The Seed-Lee-Idriss procedure for dams or embankments which include saturated cohesionless materials
• 9.8.6 Analysis of Lower San Fernando Dam – Seed’s approach
• 9.8.7 Alternative explanation for failure of Lower San Fernando Dam
• 9.8.8 Effective stress approach for analysis of Lower San Fernando Dam
• 9.9 Occurrence of earthquake-induced landslides
• 9.9.1 Landslides related to some major earthquakes – key findings
• 9.9.2 Some empirical relationships between earthquake magnitude M, landslide volume V, and landslide area A
• 9.9.3 Summary of a subsequent study (Keefer, 2007)
• 9.9.4 Topographic amplification effects
• 9.10 Effect of earthquakes on earth dams and embankments
• 9.10.1 Examples of dams that failed during earthquakes
• 9.10.2 Example of a dam surviving a strong earthquake
• 9.10.3 Failure modes and earthquake resistant design
• 9.11 Role of probabilistic analysis
• 9.11.1 Numerous uncertainties
• 9.11.2 Probability of failure conditional on earthquake occurrence
• 9.11.3 Probability of failure over the design life of a slope
• 9.11.4 Estimating annual probability of earthquake occurrence
• 9.11.5 Probability of landsliding based on observation and calculated values
• 9.11.6 Increase in existing landslide hazard due to earthquakes Appendix to chapter 9

Appendix to chapter 9

• C9.1 Some discussions during the period (1960–1973) concerning the seismic coefficients
• C9.1.1 Factors influencing pseudo-static factor of safety
• C9.1.2 Estimating seismic coefficient based on visco-elastic response analysis
• C9.1.3 Seismic coefficients related to inertia forces

10 Probabilistic approaches and reliability analyses

• 10.1 Basic probabilistic approach for slopes
• 10.1.1 Introduction
• 10.1.2 Numerical examples
• 10.1.3 Aspects of probabilistic analysis covered in published work – a sample
• 10.2 Elements of a basic probabilistic approach
• 10.2.1 Recalling the basic resistance – load probability model
• 10.2.2 Probabilistic approach based on general limit equilibrium models of slope stability
• 10.2.3 Probability distribution of a function of several variables such as the factor of safety, F
• 10.3 The big picture – role and benefitsof a probabilistic approach
• 10.4 Numerical methods for evaluating statistical moments of factor of safety or for simulating its probability distribution
• 10.4.1 First Order Second Moment Method (FOSM)
• 10.4.2 Point Estimate Method or Rosenblueth method (PEM)
• 10.4.3 Monte-Carlo Simulation Method (MSM)
• 10.4.4 Summing up – comparison of results from use of different methods
• 10.5 Essential questions and elementary calculations for probabilistic analysis
• 10.5.1 Select random variables: which parametersare significant?
• 10.5.2 Statistical moments of F: which numerical methods are to be used?
• 10.5.3 Alternative definition of reliability index: is a simple definition of reliability index good enough?
• 10.5.4 Meaning of probability of failure as usually defined
• 10.5.5 Options for evaluating probability of failure based on the assumption that F follows a normal probability distribution
• 10.5.6 Probability distribution of F: which PDF to assume for F, Normal or Lognormal?
• 10.5.7 Probability of failure based on Lognormal distribution
• 10.5.8 Estimating standard deviations of basic variables
• 10.5.9 Final comment
• 10.6 Uncertainty components and issues for uncertainty analysis
• 10.6.1 Introduction
• 10.6.2 Spatial variation of a geotechnical parameter
• 10.6.3 Length of slope failure – insight provided by spatial variability
• 10.6.4 Systematic uncertainty of a geotechnical parameter
• 10.6.5 Summing up
• 10.7 Probability of successive failures
• 10.7.1 Introduction
• 10.7.2 Formulation in terms of safety margins along two discontinuities within a slope
• 10.7.3 Joint normal distribution
• 10.7.4 Trend of results for probability of successive failure along rock discontinuities
• 10.7.5 Trend of results for probability of successive failures in a soil slope
• 10.8 Systems reliability
• 10.9 Probability of progressive failure along a slip surface
• 10.9.1 Basic model considering local safety margins
• 10.9.2 Advanced model for probability of sliding by progressive failure
• 10.9.3 Further development of the model for probability of sliding by progressive failure
• 10.10 Simulation of sliding probability of a progressively failing slope
• 10.11 Bayesian updating
• 10.11.1 Introduction
• 10.11.2 Updating the reliability of an open-cut mining slope
• 10.11.3 Back-analysis through reliability updating
• 10.12 Reliability analysis for a three-dimensional slope problem
• 10.13 Target failure probabilities
• 10.13.1 Introduction
• 10.13.2 Suggested target values of reliability index and failure probability for slopes
• 10.13.3 Discussion and limitations
• 10.14 Hazard and risk concepts and site-specific assessments
• 10.14.1 The basic terminology
• 10.14.2 Types of risk and risk assessments
• 10.14.3 Acceptable or tolerable risk levels
• 10.14.4 Calculations and simple examples concerning risk
• 10.15 Regional assessment of hazard and risk
• 10.15.1 Introduction
• 10.15.2 Purpose
• 10.15.3 Key assumptions in regional studies
• 10.15.4 Defining the scope
• 10.15.5 Qualitative and quantitative approaches for regional analysis
• 10.15.6 Role of an observational approach – monitoring of slopes and landslides
• 10.16 Additional numerical examples As described for Case (a), calculations are done in a tabular form and presented in Appendix to chapter 10

11 Case studies of urban slope stability

• 11.1 Aims of this chapter
• 11.2 Regional perspective
• 11.3 Landslide inventory
• 11.4 Stability analyses of three sites
• 11.4.1 Introduction
• 11.4.2 Available information and assumptions
• 11.4.3 Failure mechanism
• 11.4.4 Drainage conditions
• 11.4.5 Observed shapes of landslides and slip surfaces
• 11.4.6 Software used for the Case Studies
• 11.5 Case study 1 – site 64 in the suburb of Scarborough
• 11.5.1 Introduction
• 11.5.2 Background
• 11.5.3 Geotechnical model for Site 64
• 11.5.4 Pore water pressure assumptions
• 11.5.5 Results of analysis
• 11.5.6 Shear strength at failure on the basis of the above analyses
• 11.6 Case study 2 – site 77, Morrison Avenue, Wombarra
• 11.6.1 Introduction
• 11.6.2 Background
• 11.6.3 Geotechnical model for Site 77
• 11.6.4 Pore water pressure assumptions
• 11.6.5 Results of analyses
• 11.6.6 Shear strength at failure based on resultsof analyses
• 11.7 Case study 3 – site 134, Woonona Heights
• 11.7.1 Introduction
• 11.7.2 Background
• 11.7.3 Geotechnical model for site 134
• 11.7.4 Pore water pressure assumptions
• 11.7.5 Results of analyses
• 11.8 Concluding remarks on the three case studies
• 11.9 Landslide-triggering rainfall
• 11.9.1 Rainfall as triggering factor – thresholdand variability
• 11.9.2 Analyses of the 1998 rainstorm and associated landsliding
• 11.10 Landslide susceptibility and hazard
• 11.10.1 Introduction and scope
• 11.10.2 Regional risk assessment outside the scope of this chapter
• 11.10.3 Data-sets relevant to the study area
• 11.10.4 Knowledge based approach and Data Mining (DM) model
• 11.10.5 Analysis of DM results and landslide susceptibility zoning
• 11.10.6 Landslide hazard assessment and zoning
• 11.11 Observational approach and monitoring
• 11.11.1 Introduction and definition
• 11.11.2 Why an observational approach?
• 1.11.3 Example of landslide management based on monitoring
• 11.11.4 Field monitoring – periodic
• 11.11.5 Field monitoring – continuous
• 11.12 Concluding remarks

12 Summing up

• 12.1 Introduction and brief overview
• 12.2 Seeking emerging themes
• 12.3 Geotechnical slope analysis in a regional context
• 12.4 Choice between conventional and advanced methods of analysis
• 12.5 Understanding and modelling important phenomena
• 12.6 Appropriate use of probabilistic analysis
• 12.7 Observational approach
• 12.8 Meeting emerging challenges
• 12.9 Concluding remarks

Appendix I Shear strength parameters of residual soils, weathered rocks and related minerals

Appendix II Slope stability charts and their use for different conditions including rapid draw down

• AII.1 Chart for parameter min Bishop simplified method (also Janbu’s method)
• AII.2 Introduction to slope stability charts
• AII.3 Taylor’s charts and their use
• AII.3.1 Special conditions considered by Taylor (1948)
• AII.4 Cousins’ (1977) charts – studies in terms of effective stress
• AII.5 Example concerning use of cousins’ charts
• AII.6 Charts by Hoek (1970) and Hoek and Bray (1974, 1977)
• AII.7 Rapid draw down-effective stress approach (after Bishop, 1954 and Skempton, 1954)
• AII.8 Construction pore pressures in impervious fill of earth dam (after Bishop, 1954)

Appendix III Morgenstern and price approach – some additional particulars

• AIII.1 Side force assumptions
• AIII.2 Admissibility criteria for morgenstern and price solution
• AIII.3 Typical comparisons
• AIII.3.1 Brilliant cut slide
• AIII.3.2 Navdocks example problem
• AIII.4 Conclusions

References

Subject index

Colour plates