Abstract
A failure probability model is developed to describe the effect of the intermediate principal stress on rock strength. Each shear plane in rock samples is considered as a micro-unit. The strengths of these micro-units are assumed to match Weibull distribution. The macro strength of rock sample is a synthetic consideration of all directions’ probabilities. New model reproduces the typical phenomenon of intermediate principal stress effect that occurs in some true triaxial experiments. Based on the new model, a strength criterion is proposed and it can be regarded as a modified Mohr-Coulomb criterion with a uniformity coefficient. New strength criterion can quantitatively reflect the intermediate principal stress effect on rock strength and matches previously published experimental results better than common strength criteria.
Highlights
The stress state in three-dimensional space is defined by three mutually perpendicular stress components (σ1, σ2, σ3) and it is an important subject in rock mechanics to study the rock failure behavior under complex stress conditions
New model reproduces the typical phenomenon of intermediate principal stress effect that occurs in some true triaxial experiments
The failure probability model in this paper is observed to reproduce the typical phenomenon of intermediate principal stress effect that occurs in some true triaxial experiments
Summary
The stress state in three-dimensional space is defined by three mutually perpendicular stress components (σ1, σ2, σ3) and it is an important subject in rock mechanics to study the rock failure behavior under complex stress conditions. Researchers have developed many numerical models or used commercial software to study the failure processes of rocks under polyaxial stress conditions [7,8,9,10,11] In these numerical tests, it was clear that the intermediate principal stress has an effect on rock strength and the mechanism of such an effect is discussed. The rock will be weaker where the stress state is more symmetric and there are several equivalent directions of the failure plane to choose These considerations are supported by Chang and Haimson’s observations [1]. By combining the new model with Mohr-Coulomb criterion, a new strength criterion is developed, which can quantitatively describe the effect of intermediate principal stress on rock strength
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