ANALYSIS OF PROBABILISTIC DISTRIBUTION AND RANGE OF AVERAGE STRESS INEACH PHASE OF HETEROGENEOUS MATERIALS

The estimation of the crust stress is essential for the prediction of an earthquake. However, the in situ measurement of stress is difficult since data often show large variance, probably, due to the heterogene ity in the rock mass. To clarify the effects of the material heterogen eity on the stress distribution, this paper carries out two analyses, the prediction of a probability density function (PDF) from a given PD F of the material heterogeneity, and the computation of a range which bounds possible maxmum/minimum values. Recursive formulae for computin g the PDF are derived from the perturbation analysis of fields disturb ed by the heterogeneity, and the range is determined from approximate solutions which bound the strain energy of an infinite body with arbit rary ellipsoidal inclusions. Analytic expressions for the recursive fo rmulae and the approximate solutions are obtained by applying new tech niques that are based on the equivalent inclusion method. Monte-Carlo computation of the stress distribution in a heterogeneous body is made to verify the validity of the present analyses. It is shown that the predicted PDF and range are in good agreement with those obtained from the simulation. (C) 1998 Elsevier Science Ltd. All rights reserved.