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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 960973, 7 pages
Research Article

Failure Probability Model considering the Effect of Intermediate Principal Stress on Rock Strength

College of Civil Engineering, Tongji University, Shanghai 200092, China

Received 8 July 2015; Revised 1 November 2015; Accepted 8 November 2015

Academic Editor: Yakov Strelniker

Copyright © 2015 Yonglai Zheng and Shuxin Deng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.