Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol. 20, No. 4, p. 201, 1983 0148-9062'83 S3.00+0.00 Pergamon Press Ltd. Printed in Great Britain Copyright ,~ 1983 Pergamon Press Ltd

Book Review

Boundary Element Methods in Solid Mechanics--by S. L. Crouch and A. M. Starfield. Allen & Unwin, London, 1983. 322 pp. £20.00 (hard cover).

The world can be divided into two groups of people: those who understand the boundary element technique and those who do not. Because the second group is several orders of magnitude larger than the first group, a book which clearly and simply explains the technique is more than welcome, and in the context of this Journal especially a book which is illustrated with rock mechan- ics examples. In their Preface, the authors state that their objective is "to enable readers to develop a familiarity with boundary element methods which will encourage them to delve deeper after they have laid aside this book". Knowing the reputation of both authors for their intelligence and the clarity of their presentation, it was with some anticipation that I started reading this book. In particular, and as a result of belonging to the second group mentioned above, I wanted to know what the boundary element technique is, what value it has in rock mechanics and mining sciences, and how easy it would be for someone to use the methods after reading the book.

The first three Chapters are introductory in nature. The first Chapter explains the conceptual basis of the boundary element technique; the second concisely re- views aspects of the theory of linear elasticity; and the third introduces the technique itself using the solution to Flamant's problem for a line of concentrated force on the surface of an elastic half-plane.

The second three Chapters explain separately the fictitious stress method, the displacement discontinuity method and the boundary integral method. The fictitious stress method is based on influence functions derived from Kelvin's problem of a line of force in an infinite elastic solid. The displacement discontinuity method is a companion method used for problems containing slits or cracks. Both methods are illustrated by the traditional rock mechanics geometries of the diametrally com- pressed disc and the circular hole in a plate. I found that the explanation of the boundary integral method, which is based on the reciprocal theorem, required more time and courage in the face of some rather daunting integral equations.

The last two Chapters and the Appendices comprise improvements and extensions to the theoretical meth- ods, practical applications in rock mechanics and geo- logical engineering, and listings of computer programs for each of the main methods. The theoretical discussion

embraces higher-order formulations of the direct bound- ary integral method, crack tip elements, and modelling inhomogeneity and anisotropy. The practical applica- tions demonstrate that the boundary element technique is a flexible computational tool, being adaptable to the idiosyncrasies of geomechanics problems. The examples include modelling joints--with the extension to stratified rock--and mining in seams or tabular ore bodies. Ap- pendices A, B and C contain listings and clear expla- nations for the use of computer programs TWOFS, TWODD and TWOBI which are acronyms of TWO- dimensional Fictitious Stress, Displacement Discon- tinuity and Boundary Integral methods. These programs are relatively short and could be used directly from the book.

I was not disappointed in my expectations of this book. The boundary element technique is explained simply and succinctly with illustrative examples and with listings of computer programs for three different meth- ods. All my questions were answered. The book is a delight to read. The authors use a system of highlighting key words in italic or bold lettering which is most effective. There are many attractive diagrams that ap- pear just when required. As a result of reading the book I have now moved, hesitantly but definitely, from the group that does not understand the boundary element technique to the group that does.

In fact, it is difficult to fault this book on any grounds. There are aspects of the presentation which could be improved (each heading in the Contents list has been centralized resulting in a very visually disturbing effect) and some aspects which must be corrected (there is something wrong with the index indentation system starting at f). Certainly one needs to understand elas- ticity theory before reading the book-the review in Chapter 2 is really only an aide-memoire. The physical interpretation, which the authors emphasize, could be amplified in several of the explanations, e.g. for the reciprocal theorem. Also, I should have liked to have read a concluding Chapter which summarized the ideas and indicated "the way ahead" for theoreticians and practitioners and those wondering if the programs will fit on their micro. However, these are all very minor points compared to the excellence of the information contained in the book.

This book is recommended as essential reading for anyone in rock mechanics and mining sciences who has some grounding in the theory of elasticity.

J.A.H.

.... 2O/~o 201