Analysis of a microcrack model and constitutive equations for time-dependent dilatancy of rocks

Abstract

SUMMARY Based on experimental observations and theoretical analyses, the author introduces an ideal microcrack model in which an array of cracks with the same shape and initial size is distributed evenly in rocks. The mechanism of creep dilatancy for rocks is analysed theoretically. Initiation, propagation and linkage of pre-existing microcracks during creep are well described. Also, the relationship between the velocity of microcrack growth and the duration of the creep process is derived numerically. The relationship agrees well with the character of typical experimental creep curves, and includes three stages of creep. Then the damage constitutive equations and damage evolution equations, which describe the dilatant behaviour of rocks, are presented. Because the dilatant estimated value is taken as the damage variable, the relationship between the microscopic model and the macroscopic constitutive equations is established. In this way the mechanical behaviour of rocks can be predicted.