Changes in crack density and wave velocity in association with crack growth in triaxial tests of Inada granite

摘要

A nondimensional second-rank tensor F ij , called the crack tensor, has successfully been introduced to deal with geometrical aspects of microcracks (fabric) such as anisotropy and crack density. Unfortunately, however, its usage for practical purposes is rather limited because its determination involves tedious and time-consuming laboratory work. We seek the possibility of using the directional change of longitudinal wave velocities to conquer the difficulty associated with the determination of crack tensors. A new second-rank tensor V ij is introduced, such that the directional change in the longitudinal wave velocities is represented in terms of the tensor, and the crack tensor F ij is then given as a function of V ij . On the basis of the analyses of the crack tensors for one intact and several damaged samples of Inada granite, we then discuss how microcracks grow through the whole inelastic process, terminating at brittle failure. The conclusions are summarized as follows: The second-rank symmetrical tensor V ij (or its inversion tensor V ij ?1) can be determined experimentally, with sufficient accuracy from the directional change in the squared longitudinal wave velocity. It is found that the tensor changes markedly so as to reflect the fabric of the damaged Inada granite formed by open microcracks. The principal axes of V ij ?1 are coaxial with the principal axes of F ij so that both tensors are correlated in terms of their principal values F i and V i ?1. Four successive stages can be distinguished in regard to the crack growth as follows: In stage 1, the rock behaves like an elastic solid. In stage 2, microcracks start to grow so that inelastic volumetric strain is slowly accumulated, along with microcracking. However, crack growth does not occur globally but rather is limited within some local zones (probably in each grain). In stage 3, microcracking is considerably accelerated, suggesting that the micromechanism leading to crack growth changes substantially at the boundary stress between stages 2 and 3. In stage 4, the crack density, as well as the dilatancy, increases explosively in association with a drop of a few percent in the differential stress after the peak stress is reached. Interestingly, this explosive increase is always associated with the development of a few fault zones. Experimental evidence seems to support the postulate that Inada granite starts to collapse once the crack density, F 0 (f), the first invariant of F ij , attains a threshold value of 7–8, regardless of the applied confining pressure. This can be a failure criterion in terms of the crack density, and be an extended expression for the so-called “critical dilatancy” for creep failure suggested by Kranz and Scholz (1977).