广义Hoek-Brown破坏准则平面应变问题的滑移线场理论

Slip Line Field of Plane Strain Problem Obeying the Generalized Hoek-Brown Failure Criterion

根据弹塑性力学平面应变问题的特点,推导广义Hoek-Brown破坏准则平面应变问题应力分量的双参数表达式。代入静力平衡微分方程,得到双曲型一阶拟线性偏微分方程组。运用行列式方法,在适当的变量代换后,获得应力偏微分方程组的特征方向和特征上的微分关系。特征方向表明塑性区中的共轭斜交剪切滑移面形成两族非正交滑移线,其共轭角随极限应力状态和Hoek-Brown岩体材料物性参数而变化。由于对称初始应力场条件下圆形硐室理想弹塑性围岩塑性区内最大主应力方向为环向,而滑移线切线方向与最大主应力方向的夹角是最小主应力(径向应力)的函数,结合圆形硐室理想弹塑性围岩的应力分布的分析解,获得滑移线的极坐标曲线所满足的微分方程,进而得到其极坐标曲线方程。

According to the characteristics of plane strain problem of elastic and plastic mechanics, the bi parametric expressions were derived for stress components satisfying the generalized Hock-Brown failure criterion. Being substituted into the static equilibrium partial differential equations, a group of first order hyperbolic pseudo-linear differential equation partial differential equations was obtained. Utilizing the determinant method and proper variable transformation, the characteristic direction and the differential relation equation for the stress partial differential equations were acquired. The characteristic direction indicted that in plastic zone obliquely-intersecting conjugate shear slip surfaces formed two families of non- orthogonal slip lines, in which conjugate angle varied with the limit stress state and the material physical properties of Hoek Brown rock mass. Since the principal direction of the maximum principal stress was circumferential in perfectly elasto-plastic surrounding rock of the plastic zone around a circular opening suffering the symmetric initial stress field, the angle between the tangential direction of slip line with the principal direction of the maximum principal stress was the function of the minimum principal stress（i, e. the radial stress）. Combined with the analytical solution, the polar coordinate differential equation was derived and furthermore, the polar coordinate curve equation for the slip line was obtained.