Fuzzy-random probabilistic analysis of rock mass responses to explosive loads

This paper addresses the effects of randomness of initial damage in a rock mass and the critical tensile strain of the rock material on its dynamic re sponses and damage under explosive loads. A fuzzy definition is proposed to describe the fuzzy nature of failure phenomenon in a rock mass. The initia l damage of the rock mass is estimated using the longitudinal and transvers e elastic wave velocities. By using statistical analysis, the initial damag e of the rock mass is found having the Beta distribution. The statistical e stimation of a damage state and properties of randomly damaged rock mass ar e evaluated by the Rosenbluth's point estimate method. In numerical calcula tion, an isotropic continuum damage model with the initial damage and the c umulative damage dependent on an equivalent tensile strain is suggested to model the rock mass behavior under blast loads. A Beta distribution is prop osed to represent the probabilistic distribution of the damage variable of the rock mass under explosive loads. Several types of membership functions are suggested to represent the fuzziness of material failure. Based on the fuzzy-random probabilistic theory, a model including both the effects of ra ndomness and fuzziness is proposed for the failure analysis of rock mass un der explosive loads. The suggested models are coded and linked with an avai lable computer program AUTODYN2D through its user's subroutine capacity. Th e fuzzy failure probability and dynamic responses of the rock mass are calc ulated. Numerical results are compared with those obtained from independent held tests. (C) 1999 Elsevier Science Ltd. All rights reserved.