Degree Name

Doctor of Philosophy


Department of Civil and Mining Engineering


The basic concepts and methods for the stability and reliability assessment of a soil slope or an earth structure, under static and dynamic loading conditions, have been discussed in some detail in this thesis. A number of improvements and extensions to the current state-of-the-art approaches have been proposed and implemented with particular emphasis on both 'simplified' and 'rigorous' limit equilibrium models. The simplified Bishop method, the Generalised Procedure of Slices (with the Morgenstern and Price side force function) and the Sarma method have been used extensively in this thesis.

An optimisation procedure, based on the conjugate gradient algorithm, was developed for locating the critical slip surface with either the minimum factor of safety or the minimum critical seismic coefficient. This optimisation procedure can be used to search not only circular and non-circular slip surfaces in homogeneous or layered soil slopes but also including situations in which part of the potential slip surface is controlled by a weak soil zone or a weak surface. A very effective numerical technique, the rational polynomial technique (RPT), was introduced for solving non-linear equations and estimating the partial derivatives of inexplicit functions which are often encountered in geotechnical reliability assessments.

A comprehensive framework has been presented for improving or updating the current probabilistic methods of analysis for earth structures. This framework includes the availability of the three main method used for geotechnical reliability analysis, i.e., (a) First Order and Second Moment Method (FOSM), (b) Point Estimation Method (PEM) and (c) Monte Carlo Simulation Method (MCSM).

The performance function was expressed in terms of the factor of safety and may be defined on the basis of either the simplified or 'rigorous' limit equilibrium methods. The proposed probabilistic framework includes some new concepts and new approaches. An orthogonal transformation has been introduced in the Monte Carlo Simulation Method so that correlated basic random variables can be considered. A comparison of the conventional definition of reliability index, β, with the so called 'invariant' reliability index, β*, has been presented. The influence of spatial correlations of basic random variables on the reliability index has also been investigated. Comprehensive comparisons based on the three methods, i.e., FOSM, PEM and MCSM, have been carried out.

The evaluation of geotechnical system reliability is important for earth structures because of the spatial variability of soil properties. Comprehensive procedures have been developed for estimating the reliability bounds, 'upper' and 'lower' bounds of slope reliability taking into consideration the fact there are many potential slip surfaces in any slope. These evaluations of geotechnical system reliability can be carried out on the basis of either the simplified or the relatively 'rigorous' limit equilibrium methods. Therefore, reliability bounds have been evaluated by considering not only circular slip surfaces but also non-circular slip surfaces. Moreover, both independent and correlated basic random variables can be included in the proposed analysis procedures. The influence of spatial variation of basic random variables on the reliability bounds was also investigated.

On the basis of the limit equilibrium concept and the Newmark-type dynamic response approach, an innovative procedure was developed for the earthquake analysis of earth structures such as embankments and earth dams. The proposed analysis procedure can consider not only the critical seismic coefficient but also the dynamic properties of materials, such as damping ratio and natural frequency. More importantly the change in the critical seismic coefficient with time is included in the analysis and simulation process. The degradation of shear strength parameters during earthquake shaking may occur due to strain-softening characteristics of the earth materials. A method has been proposed and implemented to include this post-peak shear strength decrease in the earthquake analysis process. Shear strength may also decrease in some soils due to the development of dynamic excess pore water pressure during earthquake shaking. A different procedure has been used to include this type of shear strength decrease in the analysis procedure. The factor of safety and critical seismic coefficient are considered as functions of time after the start of an earthquake. The permanent displacements of earth structures due to earthquake excitations can also be evaluated and illustrative examples are presented to show the influence of material properties on the estimated magnitudes of permanent deformations. Based on Gaussian non-stationary random process a procedure has been presented for simulating earthquake motion and, in particular the time acceleration histories for an earthquake of specified magnitude and duration.