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SUMMARYIn this paper we introduce a method to reduce the solution cost for Boundary Element (BE) models from 0"') operations to O(NZlogN) operations (where N is the number of elements in the model). Previous attempts to achieve such an improvement in efficiency have been restricted in their applicability to problems with regular geometries defined on a uniform mesh. We have developed the Spectral Multipole Method (SMM) which can be used not only for problems with arbitrary geometries but also with a variety of element types. The memory necessary to store the required influence coefficients for the spectral multipole method is O(N) whereas the memory required for the traditional Boundary Element method is O(N2) . We demonstrate the savings in computational speed and fast memory requirements in some numerical examples. We have established that the break-even point for the method can be as low as 500 elements, which implies that the method is not only suitable for extremely large-scale problems, but that it also provides a useful bridge between the small-scale and large-scale problems. We also demonstrate the performance of the multipole algorithm on the solution of large-scale granular assembly models. The large-scale BE capacity provided by this algorithm will not only prove to be useful in large macroscopic models but it will also make it possible to model microscopic damage processes that form the fundamental mechanisms in plastic flow and brittle fracture.

SUMMARYA symmetric-Galerkin boundary element framework for fracture analysis with frictional contact (crack friction) on the crack surfaces is presented. The algorithm employs a continuous interpolation on the crack surface (utilizing quadratic boundary elements) and enables the determination of two important quantities for the problem, namely the local normal tractions and sliding displacements on the crack surfaces. An e ective iterative scheme for solving this non-linear boundary value problem is proposed. The results of test examples are compared with available analytical solutions or with those obtained from the displacement discontinuity method (DDM) using linear elements and internal collocation. The results demonstrate that the method works well for di cult kinked=junction crack problems.

Sensitivity of the Kaiser effect to the deviations of the directions of s 1 -principal stress experienced by rock in successive loading cycles has an important impact on the application of this effect for stress measurements in rocks. The paper presents an analysis of the gradual Kaiser effect degradation with increasing deviation of the principal stress axes between loading cycles in Brazilian experiments. An experimental study was carried out to investigate the Kaiser effect in cyclic loading tests of disk specimens of a brittle limestone in diametrical compression with acoustic emission measurement. Tests were performed in which disks were loaded in two cycles without or with rotations between successive cycles. The rotation angle varied between 01 and 901. The Kaiser effect became gradually less pronounced with increasing rotation angle, but remained detectable for angles o101. Rotation by more than 101 resulted in complete disappearance of the effect. These experimental results were confirmed by numerical simulations using the displacement discontinuity method. r

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