Geotechnical Slope Analysis

Freshly updated and extended version of Slope Analysis (Chowdhury, Elsevier, 1978). This reference book gives a complete overview of the developments in slope engineering in the last 30 years. Its multi-disciplinary, critical approach and the chapters devoted to seismic effects and probabilistic approaches and reliability analyses, reflect the distinctive style of the original. Subjects discussed are: the understanding of slope performance, mechanisms of instability, requirements for modeling and analysis, and new techniques for observation and modeling. Special attention is paid to the relation with the increasing frequency and consequences of natural and man-made hazards. Strategies and methods for assessing landslide susceptibility, hazard and risk are also explored. Moreover, the relevance of geotechnical analysis of slopes in the context of climate change scenarios is discussed. All theory is supported by numerous examples. ''...A wonderful book on Slope Stability....recommended as a refernence book to those who are associated with the geotechnical engineering profession (undergraduates, post graduates and consulting engineers)...'' Prof. Devendra Narain Singh, Indian Inst. of Technology, Mumbai, India ''I have yet to see a book that excels the range and depth of Geotechnical Slope Analysis... I have failed to find a topic which is not covered and that makes the book almost a single window outlet for the whole range of readership from students to experts and from theoreticians to practicing engineers...'' Prof. R.K. Bhandari, New Delhi, India

Table of Contents:
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