A theoretical derivation of the Hoek-Brown failure criterion for rock materials  

作　　者：Jianping Zuo Huihai Liu Hongtao Li 

机构地区：[1]State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology [2]Institute of Rock Mechanics and Fractals, School of Mechanics and Civil Engineering, China University of Mining and Technology [3]Aramco Research Center

出　　处：《Journal of Rock Mechanics and Geotechnical Engineering》2015年第4期361-366,共6页岩石力学与岩土工程学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (No. 51374215);Fok Ying Tung Education Foundation (No. 142018);Beijing Major Scientific and Technological Achievements into Ground Cultivation Project;the 111 Project (No. B14006)

摘　　要：This study uses a three-dimensional crack model to theoretically derive the HoekeBrown rock failure criterion based on the linear elastic fracture theory. Specifically, we argue that a failure characteristic factor needs to exceed a critical value when macro-failure occurs. This factor is a product of the micro-failure orientation angle （characterizing the density and orientation of damaged micro-cracks） and the changing rate of the angle with respect to the major principal stress （characterizing the microscopic stability of damaged cracks）. We further demonstrate that the factor mathematically leads to the empirical HoekeBrown rock failure criterion. Thus, the proposed factor is able to successfully relate the evolution of microscopic damaged crack characteristics to macro-failure. Based on this theoretical development, we also propose a quantitative relationship between the brittleeductile transition point and confining pressure, which is consistent with experimental observations.This study uses a three-dimensional crack model to theoretically derive the HoekeBrown rock failure criterion based on the linear elastic fracture theory. Specifically, we argue that a failure characteristic factor needs to exceed a critical value when macro-failure occurs. This factor is a product of the micro-failure orientation angle （characterizing the density and orientation of damaged micro-cracks） and the changing rate of the angle with respect to the major principal stress （characterizing the microscopic stability of damaged cracks）. We further demonstrate that the factor mathematically leads to the empirical HoekeBrown rock failure criterion. Thus, the proposed factor is able to successfully relate the evolution of microscopic damaged crack characteristics to macro-failure. Based on this theoretical development, we also propose a quantitative relationship between the brittleeductile transition point and confining pressure, which is consistent with experimental observations.

关 键 词：Failure criterionTriaxial compressionMicro-failure orientationFracture mechanicsBrittle--ductile transition 

分 类 号：TU45[建筑科学—岩土工程]