University of Wollongong Research Online University of Wollongong Thesis Collection University of Wollongong Thesis Collections 1994 Stability and reliability assessments of earth structures (under static and dynamic loading conditions) Dawei Xu University of Wollongong Recommended Citation Xu, Dawei, Stability and reliability assessments of earth structures (under static and dynamic loading conditions), Doctor of Philosophy thesis, Department of Civil and Mining Engineering, University of Wollongong, 1994. http://ro.uow.edu.au/theses/1269 Research Online is the open access institutional repository for the University of Wollongong. For further information contact Manager Repository Services: [email protected]. STABILITY AND RELIABILITY ASSESSMENTS OF EARTH STRUCTURES (under static and dynamic loading conditions) A thesis submitted in fulfilment of the requirements for the award of the degree of DOCTOR OF PHILOSOPHY from \ UNIVERSITY OF I WOLLONGONG | LIBRARY . THE UNIVERSITY OF WOLLONGONG DEPARTMENT OF CIVIL AND MINING ENGINEERING AUSTRALIA By DA WEI XU, B.E., M.E.(Honours.) January, 1994 DECLARATION I hereby declare that the research work described in this thesis is my own work and has not been submitted for a degree to any university or institute except where specifically indicated. Dawei Xu January, 1994 -1 - ACKNOWLEDGMENTS I wish to express my sincere gratitude to Professor Robin Chowdhury who directed my interests in probabilistic geomechanics and geotechnical earthquake engineering and supervised the whole research work of my Ph.D. thesis. His invaluable guidance, useful suggestions and discussions and constant encouragements are gratefully acknowledged. Special thanks are also extended to Professor Chuanzhi Xiong who allowed me to undertake research in geotechnical engineering and supported my application to come to Australia for further study. I am indebted to the University of Wollongong for a postgraduate award and the Water Engineering and Geomechanics Research Group in the Department of Civil and Mining Engineering for continual support. I record my gratitude to all members of my family. Special acknowledgement is due to my parents, and my wife, Heng Wang, for their constant support and encouragements. My lovely son, Ferris Xu, who was born on January 15, 1993, gave me a lot of happiness during a period of my intense study. Finally, I would like to thank the Department of Civil and Mining Engineering for providing all the necessary facilities and good conditions for my research work. -ii - ABSTRACT 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 -iii - that correlated basic random variables can be considered. A comparison of the conventional definition of reliability index, p\ with the so called 'invariant' reliability index, P , 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 -iv- 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. - v - NOTATION The following symbols are used in this thesis: A = Vector of constants in a linear performance function; A^ = A parameter corresponding to n cycles of loading; [C] = Covariance matrix of basic random variables or parameters; [C ] = Covariance matrix of the reduced or normalised random variables X = (Xj, X2, • • -, Xn); [CY] = Covariance matrix of vector Y; D = Distance from a point X' on the failure surface to the origin of X'; E = Interslice normal force; F = Factor of safety Ff = Factor of safety based on force equilibrium equation; Fm = Factor of safety based on moment equilibrium equation; f(X) = A model for calculating the factor of safety of a slope; Fx(xl5 x2, ..., xn) = Cumulative probability density function; g = Gradient vector; G(X) = Performance function in X space (e.g., safety margin of a slope); I(t) = Intensity function; I = Identity matrix; K = Seismic coefficient; Kj. = Critical seismic coefficient; K(t) = Time history of earthquake acceleration coefficient; Lj or lj = Length of the base of a slice; p^ = Conjugate direction (k = 1, 2, ..., n); Pf = Probability of failure of a slope; P+ and P. = Weight coefficients in Point Estimate Method; Q = A symmetric and positive-defined matrix with constant components; - vi - R = Radius of a circular slip surface; S(co) = Power spectrum density function; T = Interslice shear force; T = Orthogonal transformation matrix; x0 = Abscissa of the centre of a circular slip surface; X = Vector of basic random variables or parameters; X = Vector of reduced or normalised random variables; X = Vector representing the most probable failure point on the failure surface; AXj = Width of a vertical slice; y0 = Ordinate of the centre of a circular slip surface; Y = Vector of uncorrected transformed variables; Y' = Reduced or normalised vector corresponding to vector Y; Z = Uncorrected standard normal random vector; <|)(X) = A joint probability density distribution; u\G = Mean value of performance function; px = Vector of mean values of random parameters;