ABSTRACT:

The analytical solutions involving the distribution of stresses around a small hole in an infinite elastic plate have been extensively applied for the elastic stress analysis of underground openings or excavations with simple geometry. Although these solutions are widely known and used in rock engineering, some of the people behind these solutions are vaguely known, if at all. The paper gives a chronological account of the lives and the mathematical solutions of the following scientists: Lamé and Clapeyron, two Frenchmen who presented the solution for elastic stresses occurring in thick-walled cylinders; Kirsch, who developed the famous solution for a circular hole in an infinite plate; Kolosov and Inglis, both of whom were recognized for the solution regarding to an elliptical hole; Greenspan, who was responsible for the solution involving an ovaloidal hole; and Savin, who presented solutions covering a variety of hole shapes applied in underground openings. For each instance, a brief biography of the person is given along with the details of his particular contribution to the subject. Also, some significant applications of such solutions in rock engineering are mentioned.

1 INTRODUCTION

The mathematical solutions for elastic stresses around underground openings or excavations with simple geometry were extensively used and applied in rock engineering between the 1950s and 1970s when rock mechanics was at the beginning of its maturation period (Terzaghi & Richart 1952, Talobre 1957, Coates 1966, Obert& Duvall 1967, Morrison 1970, Dharetal. 1970, Jaeger & Cook 1976). Thanks to the availability of highly capable and friendly numerical stress analysis codes supported by the developments in numerical methods and computing technologies, these mathematical solutions, nowadays, seem to have lost their prominence and attractiveness among the engineers. Indeed, compared to the present-day numerical methods, the success of such solutions is limited when they are utilized in realistic design applications. Yet, in many respects, they are among the indispensable tools of rock engineering when it comes to checking the accuracy of numerical stress analysis codes and practical stability evaluations of underground openings (Bray 1987).

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