M. Hori et J. Kubo, ANALYSIS OF PROBABILISTIC DISTRIBUTION AND RANGE OF AVERAGE STRESS INEACH PHASE OF HETEROGENEOUS MATERIALS, Journal of the mechanics and physics of solids, 46(3), 1998, pp. 537-556
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.