岩石强度准则的主应力显式表达式几何推导及应用  

A GEOMETRIC DERIVATION OF THE EXPLICIT EXPRESSIONS WITH RESPECT TO THE PRINCIPAL STRESSES FOR ROCK STRENGTH CRITERIA AND ITS APPLICATIONS

作　　者：付自国 李化 王佳信[3] 邓建辉 陈菲[4] FU Ziguo;LI Hua;WANG Jiaxin;DENG Jianhui;CHEN Fei(State Key Laboratory of Hydraulics and Mountain River Engineering,Sichuan University,Chengdu 610065,China;Institute of Geo-engineering and Geohazards,Sichuan University,Chengdu 610065,China;Faculty of Land Resource Engineering,Kunming University of Science and Technology,Kunming 650093,China;College of Architecture and Civil Engineering,Chengdu University,Chengdu 610065,China)

机构地区：[1]四川大学水力学与山区河流开发保护国家重点实验室,成都610065 [2]四川大学地质工程与地质灾害研究所,成都610065 [3]昆明理工大学国土资源工程学院,昆明650093 [4]成都大学建筑与土木工程学院,成都610065

出　　处：《力学与实践》2023年第3期526-534,共9页Mechanics in Engineering

基　　金：国家自然科学基金青年基金项目(42102320);区域创新发展联合基金(U19A2098)资助。

摘　　要：主应力是岩石强度准则的基本量,然而,给定应力张量求解主应力的三次特征方程通常难以求解。本文通过几何关系将主应力的三次代数方程转化为三元一次方程组的求解,最终建立了三个主应力关于应力张量不变量的显式表达式,并着重推演了其在静水压力效应的刻画、三维强度准则的推导和空间屈服面的绘制中的应用。可为岩石真三轴试验数据可视化提供参考,同时丰富了弹塑性力学教学内容。Principal stresses are essential variables to establish strength criteria for rocks.However,it is usually difficult to solve the cubic characteristic equation to obtain the principal stresses for a given stress tensor.In this paper,explicit expressions of the principal stresses with respect to stress invariants are derived by transforming the cubic algebraic equation of principal stresses into the three-dimensional first-order equations through a geometric relation.Then,we emphatically introduce the applications of the derived formula in the domain of rock strength criteria,including quantitative characterization of hydrostatic pressure effect for rocks,derivation of three-dimensional failure criteria and drawing yield surface of the rock in the principal stress space.The research not only presents a visualization method for triaxial test data of rock samples but also enhances the teaching content of elastic-plastic mechanics.

关 键 词：岩石 主应力公式 强度准则 屈服面 

分 类 号：O34[理学—固体力学]