Distinctive and fuzzy failure probability analysis of an anisotropic rock mass to explosion load

This paper estimates failure probability of an anisotropic rock mass with random initial damage and random critical tensile strain to explosion loads. The initial random damage and critical tensile strain of the rock mass are estimated by approximate statistical methods. They are incorporated into the constitutive law of the anisotropic damage model. The statistical estimation of the rock-mass response to underground explosion is evaluated by the Rosenblueth’s point estimate method. A statistical anisotropic continuum damage model considering both the anisotropic initial damage and cumulative damage dependent on tensile strain is suggested. A beta distribution is proposed to represent the probabilistic distribution of the damage variable of the rock mass under blasting loads. Using the theory of reliability, failure probabilities are calculated according to di erent levels of failure criteria of the rock mass. A fuzzy de nition is also proposed to describe the fuzzy nature of failure phenomenon of the rock mass. Based on the fuzzy random probabilistic theory, a model including both the e ects of randomness of the rock-mass properties and fuzziness of its failure criterion is proposed for the failure analysis of the rock mass. The suggested models are coded and linked with an available computer programe Autodyn3D as its user’s subroutines. Using the Autodyn3D together with the suggested model, a series of eld blasting tests are simulated. Numerical results of stress wave propagation are compared with eld-recorded data. The failure probabilities of the rock mass around the charge hole are estimated