基于二阶损伤张量的节理岩体各向异性屈服准则  

ANISOTROPIC YIELD CRITERION FOR JOINTED ROCK MASSES BASED ON A TWO-ORDER DAMAGE TENSOR

作　　者：杨强[1] 陈新[1] 周维垣[1] 

机构地区：[1]清华大学水利水电工程系,北京100084

出　　处：《岩石力学与工程学报》2005年第8期1275-1282,共8页Chinese Journal of Rock Mechanics and Engineering

基　　金：国家重点基础研究发展规划(973)项目(2002CB412708);国家自然科学基金资助项目(50279016)

摘　　要：为了在节理岩体的本构关系中反映岩体几何特征的影响,采用一个二阶损伤张量,将岩体各方向截面的连通率表示为其截面法向的连续函数。根据连通率将完整岩体与完全裂隙的内摩擦系数与粘聚力加权平均得到节理岩体的各向异性抗剪材料参数,从岩体的面抗剪强度准则(莫尔–库仑条件)出发,建立了各向异性节理岩体的抗剪屈服准则隐式表达式。在主应力轴空间内,将损伤张量分解为各向同性部分和偏量部分,以损伤张量为各向同性时的临界屈服面单位法向量和显式屈服准则的解为基础,导出了一般情况下具有一阶精度的临界屈服面单位法向量的解,相应的显式各向异性屈服准则表达式为主应力的二次式,其系数是损伤张量的函数。研究了二阶损伤张量的6个独立参量:3个主值及其主轴与主应力轴的Euler角对岩体屈服各向异性的影响。针对6个参量取值的几种代表性情况,分别采用隐式屈服准则和具有一阶精度的显式屈服准则计算出屈服应力,绘出了偏平面和子午面内岩体屈服曲线的形状。研究表明,提出的节理岩体各向异性显式屈服准则具有很高的精度。In order to include the geometrical characteristics of jointed rock masses in its constitutive relations, a two-order tensor is adopted as damage variable. Joint connectivity at any direction of jointed rock masses is expressed as a continuum function of its normal vector and the damage tensor. Consequently, shear strength parameters of jointed rock masses, i.e., friction factor and cohesion are weighted average of those of entire rock and entire fissures respectively according to joint connectivity, and implicit anisotropic yield criterion for jointed rock masses can be obtained through the Mohr-Coulomb yield condition for plane in every direction. In principal stresses space, the damage tensor is divided into two parts: the isotropic part and deviatoric part. According to rigor analytical solution to critical normal vector of the most disadvantage section for isotropic damage tensor, explicit yield criterion for isotropic joint rock masses is obtained, and an approximate analytical solution with one order precision to critical normal vector of the most disadvantage section for general damage tensor is obtained. The explicit anisotropic yield criterion for jointed rock masses is a form of quadratic equation of principal stresses in which its coefficients are functions of the damage tensor. The anisotropic yield criterion can be fully determined by the two-order damage tensor which has six independent variables, i.e., the three principal values of damage tensor and the three Euler angles which represent the relations of principal vectors of damage tensor and those of principal stresses. In four examples, how the six variables affect the anisotropic properties of rock yield stresses in principal stresses space is analyzed by figuring out yield curve in deviatoric plane and meridian plane through the implicit and the explicit anisotropic strength criterion respectively. It is concluded that the explicit anisotropic yield criterion for jointed rock masses which is obtained by approximate analytical method has high p

关 键 词：岩石力学 损伤 节理岩体 莫尔-库仑屈服准则 

分 类 号：TU452[建筑科学—岩土工程]