圆形硐室广义Hoek-Brown围岩弹塑性交界面上径向应力的近似解  

Approximate solution of the radial stress at the generalized Hoek-Brown elastic-plastic zone interface for surrounding rocks of circular openings

作　　者：曾钱帮[1,2] 马平[1,2] 刘彤[1,2] 

机构地区：[1]交通运输部公路科学研究院,北京100088 [2]北京交科公路勘察设计研究院有限公司,北京100191

出　　处：《土木工程学报》2011年第12期85-92,共8页China Civil Engineering Journal

摘　　要：基于广义Hoek-Brown剪切强度包络线与Mohr应力圆、Mohr-Coulomb强度直线均相切的几何性质,引进一个与瞬时内摩擦角有关的参数——最大剪应力模数,获得最大和最小主应力、潜在破坏面上的正应力和剪切力、Mohr应力圆半径和瞬时内聚力与该参数的函数关系,为轴对称平面应变条件下遵守广义Hoek-Brown破坏准则的圆形硐室围岩塑性区半径及重分布应力场的解答提供了简捷途径。通过弹塑性交界面上环向应力和径向应力之和一定的条件,结合最大剪应力模数与由弹塑性交界面上的径向应力与环向应力决定的Mohr圆半径间的关系,得到最大剪应力模数与正规化初始应力满足的非线性表达式,进而运用Newton-Raphson迭代法求得弹塑性交界面上的径向应力的接近于真实值的近似解,并研究弹塑性交界面上的瞬时内摩擦角、正规化瞬时内聚力和正规化径向环向应力比随正规化初始应力和Hoek-Brown物性参数的变化关系。结果表明,随着正规化初始应力的增大,相同岩体质量的围岩弹塑性交界面上的应力状态由近似单轴压缩过渡到两向压缩应力状态,瞬时内摩擦角逐渐变小,而正规化内聚力逐渐变大。Based on the geometric characteristics that the generalized Hoek-Brown shear strength envelope is tangent to both the Mohr stress circle and the Mohr-Coulomb strength line, the maximum shear stress modulus （MSSM）, a parameter relevant to the instantaneous friction angle, is introduced, and the maximum and minimum principle stresses, the normal and shear stresses on the potential failure surface, the Mohr circle radius and the instantaneous cohesion, as various functions with the MSSM, are obtained by a succinct approach to analyzing the plastic zone radius and stress redistribution under axisymmetric plane strain condition in surrounding rocks that is assumed to obey the generalized Hoek-Brown failure criterion for a circular opening. With the sum of the radial and tangential stresses given at the elastic-plastic zone interface, a non-linear formula for the MSSM and the normalized initial stress is acquired by combining with the relationship between the MSSM and the radius of the Mohr stress circle determined by radial and tangential stresses, and then an approximate solution of the true radial stress is obtained by using the Newton-Raphson iteration method. Moreover, the instantaneous friction angle, the normalized instantaneous cohesion and the normalized radial to tangential stress ratio at the elastic-plastic zone interface are studied with various normalized initial stresses and the Hock-Brown parameters, and the results show that as the normalized initial stress increases, the stress state undergoes a gradual transition from a uniaxial compressive stress state to a two-directional compressive stress state, the instantaneous friction angle decreases, and the normalized instantaneous cohesion increases.

关 键 词：广义Hoek-Brown剪切强度包络线 Mohr应力圆 最大剪应力模数 瞬时强度参数 圆形硐室 塑性区半径 弹塑性交界面 径向应力 

分 类 号：TU452[建筑科学—岩土工程]