1 NUMERICAL AND OBSERVATIONAL METHODS OF DETERMINING. THE BEHAVIOUR OF ROCK SLOPES IN OPENCAST MINES A Thesis submitted to the University of London (Imperial College of Science and Technology) for the Degree of Doctor of Philosophy in the Faculty of Engineering by Christopher Michael St. John, B.Sc.(Eng.), A.R.S.M. January 1972 ABSTRACT 2 This thesis is intended to be a study of methods of determining the behaviour of rock slopes, particularly as resulting from opencast mining excavations. Numerical and observational methods are discussed and are shown to be linked via displacement studies on model and prototype. The majority of numerical work was carried out using the Finite Element Method. As far as is relevant to the main theme of the thesis, attention is given to this method. The exposition, given primarily in Chapter 2, provides sufficient information. to follow the computer programs given in Appendices B and D for the analysis of two and three dimensional structures respectively. Chapters 3, 4 and 5 deal with studies carried out using the Finite Element Method to explore its application in slope stability investigations. For simple examples sufficient cases have been studied to permit general conclusion to be drawn. In many situations, in particular the jointed three dimensional problem, only simple models were amenable to solution. Where possible comparison is made with limiting equilibrium models. Chapter 6 deals exclusively with observational methods and gives some current examples of their use. Field trials designed to measure displacements around a small opencast mining operation are described and general proposals for monitoring systems are outlined. Finally, in Chapter 7, an attempt is made to apply the methods discussed in Chapters 3 and 4 to a simulation of a physical model of a systematically jointed rock slope. ACKNOWLEDGEMENTS The author would like to express his gratitude to all those who made this work possible. In particular, thanks are due to: All the members of the Rock Mechanics Project at Imperial College over the years 196? - 1971, and especially to the author's supervisor, Professor E. Hoek. The Rio Tinto Zinc. Corporation Ltd, for generous financial support, together with Anglo American International (U.K.) Ltd, Bougainville Copper Pty Ltd, Consolidated Gold Fields Ltd, Ehglish China Clays Ltd, Iranian Selection Trust Ltd, National Coal Board Opencast Executive, Palabora Mining Co. Ltd, and seven member companies of the Australian Mineral Industries Research Association Ltd. Professor R.E. Goodman, of the'University of California, for his interest and for computer programmes that provided a basis for the author's research. Dr. J.W, Bray for his valuable comments and critical study of this manuscript. Dr. T.L. Thomas for anything connected with surveying. Mr. L.D. Wilson for arranging everything from transport to optical reflectors. Gortdrum Mines (Ireland) Ltd, and their staff for permission to carry out field measurements and assistance whilst doing so. The Mining Department, Imperial College, for leaving the author almost uninterrupted during the final stages of the preparation of this thesis. Those involved in the production of the thesis, and especially to Mrs. R. Smith who typed the manuscript. The author's wife for patience. GENERAL INDEX 4 Page ABSTRACT 2 ACKNOWLEDGEMENTS 3 GENERAL INDEX CHAPTER 1 - Introduction 5 CHAPTER 2 - The Finite Element Method 23 Part I - Continuum Mechanics Part II - Special Considerations for Jointed 41 Materials CHAPTER 3 - The Elastic Analysis of Rock Slopes - 69 Plain Strain Conditions CHAPTER 4 - Two Dimensional Analysis of Jointed Rock 108 Slopes CHAPTER 5 - Three Dimensional Analysis of Rock Slopes 159 CHAPTER 6 - Observational Methods 198 CHAPTER 7 - A Study of a Physical Model and the 231 Modelling Material APPENDIX A - Plotting Input and Output of Two 261 Dimensional Finite Element Studies APPENDIX B - Two Dimensional Simulation of Jointed Rock 274 Structures by Finite Elements APPENDIX C - Wedge Stability Analysis by Vector Methods 300 APPENDIX D - Three Dimensional Analysis of Jointed Rock 307 Masses by Finite EJements 5 CHAPTER INTRODUCTION Chapter Index 5 Synopsis 6 1.1 Object and Outline 7 1.2 Description of the Problem 8 1.3 Existing Methods of Analysis - An Outline 9 1.4 Conclusion 20 References 21 CHAPTER 1 INTRODUCTION 6 Synopsis SYNOPSIS An outline of the aim and nature of this thesis is followed by a brief description of the rock slope problem to be studied. An attempt is made to review methods used to estimate the behaviour of rock slopes. These methods range from simple limiting equilibrium calculations, through numerical techniques to observational studies. The aim of this discussion is to place the remainder of the work reported in this thesis in the context of current slope stability research and practice. CHAPTER 1 INTRODUCTION 7 Object and Outline 1.1 OBJECT AND OUTLINE A rock slope may be designed prior to excavation, or it may be designed by observation and experience during the early stages of the work. In the context of opencast mining the latter approach is relatively common but initial estimates may be essential since the viability of a project can be closely related to the angle at which the rock. slopes are mined (Ref. 1). Estimates of bench behaviour may also govern the choice of heavy mining machinery. The primary purpose of this thesis is to draw together the body of knowledge concerning the application of numerical methods in rock slope design and to place these in context with other current methods. It further aims to show how such work maybe coupled with field measurements and how these may be carried out in a real situation. Comments on the latter are based on field trials carried out at a small open pit mine and on relevant technical literature. The majority of work in this thesis is based upon the Finite Element Method of structural analysis. The method has been widely reported in scattered literature and this thesis to some extent reviews its current uses in estimating rock slope behaviour. When this study began relatively little work in this field had been reported. Since then there has been very rapid development, much of which will be referenced where relevant. Instead of reporting other researcher's work the author has attempted to cover the whole range of possible approaches himself. Where computer programs were already available in the literature they have been used, modified and extended where necessary. In some cases, new approaches required the writing of completely new programs. Although some of this work may have been repetitive, it is believed that it should all be included in order to cover the whole of this relatively new field, and to make informed criticism where necessary. Since the object of this thesis is not a study of Numerical Methods themselves, discussion of the Finite Element Method is restricted almost entirely to a single chapter. Only when the method itself, CHAPTER 1 INTRODUCTION a Description of the Problem or the computer programming, have a direct bearing on the assumptions inherent in the analysis, are these discussed within the main body of the text. The mathematical content of even the chapter on the Finite Element Method is extremely limited since the emphasis is on a user tool rather than a research topic. In order to be consistent with this aim, computer programs, with input instructions, are given in the appendices. The collection is fairly comprehensive, but avoids duplication with other publications. 1.2 DESCRIPTION OF THE PROBLEM The behaviour of a rock mass when an excavation is made in it will depend upon the characteristics of the rock material itself and its state prior to disturbance. The geological history will have determined both the initial conditions and the rock characteristics, but the latter may be considerably modified by the process of excavation if it involves heavy blasting. 1.2.1 Initial Conditions A considerable amount of effort has been given to the study of the state of stress in the earth's crust. It is usually accepted that the vertical stresses in undisturbed material may be deduced from self weight alone. Horizontal stresses vary considerably, according to the environment. Measurements by Hast (Ref. 2) in the Fennoscandian mountain ranges showed considerable horizontal stresses even at the surface, and a much higher rate of increase with depth than normally is assumed. Where possible measurements of initial stress conditions should be made since they are an important parameter that may be included in the numerical design techniques. 1.2.2 Rock Mass Classification In most cases, the material constituting a rock slope is a discontinuum. The spatial orientation and frequency of fractures, together with the relative strength and deformability of the rock material and the discontinuities, are the major factors that control CHAPTER 1 INTRODUCTION Existing Methods of Analysis - An Outline the behaviour of the rock mass during and after excavation. The method of analysis required will depend on the above considerations, since these control the mode of failure. A number of classifications of rock masses relating to surface excavations, have been presented. Miller and Hoffmann (Ref. 3) drew the distinction between quasi-monolithic, jointed, cracked, and shattered rock. Duncan and Goodman (Ref. 4) have given a more comprehensive classification that is reproduced (Table 1.1) together with comments on the pertinent method of analysis. 1.3 EXISTING METHODS OF ANALYSIS - AN OUTLINE There are three basic methods of estimating the behaviour of a rock slope. The first of these is Limit Equilibrium. This finds extensive use since it provides a simple method of calculating a Factor of Safety and, hence, the required YES/NO answer. In addition, the calculations, in some cases, may be done on'the back of an envelope' or reduced to a graphical or tabular presentation.