单轴压缩非贯通节理岩石尖端塑性区及弹塑性断裂模型研究

基于Drucker-Prager（下简称D-P）准则，建立压缩载荷作用下的非贯通节理岩石的弹塑性断裂模型。针对节理岩石小范围屈服翼裂纹尖端塑性区，推导了D-P屈服准则的纯I、纯II及I、II复合型3种翼裂纹无量纲塑性区径长函数，并与Mises准则的塑性区进行对比；结果表明，D-P准则的I型和复合型塑性区较Mises屈服准则的塑性区大，且其II型及I、II复合型塑性区在翼裂纹上下表面不连续。进一步，引入断裂软化因子以表征节理岩石裂隙断裂扩展后的断裂软化规律，考虑非贯通节理岩石复合型断裂软化，是由于节理尖端翼裂纹应变能密度超过最小应变能密度导致其成核扩展引起的，提出用应变能密度的指数函数形式表征断裂软化变量的演化；塑性屈服函数采用Borja等的应力张量3个不变量的硬化/软化函数，反映塑性内变量及应力状态对硬化函数的影响；建立节理岩石的弹塑性断裂本构关系及其数值算法，并用回映隐式积分算法编制了弹塑性断裂模型的程序。以单轴压缩下非贯通节理岩石为例，分析岩石断裂韧度、节理摩擦系数和节理倾角等参数的影响，结果表明，所提出的弹塑性断裂模型与数值和试验结果比较吻合。

Crack tip plastic zone and elastoplastic fracture model for nonpenetrating jointed rock mass under uniaxial compression

An elastoplastic fracture model for jointed rock mass under compressive loading is presented.In order to account for the mixed mode plastic zone model of wing crack tip of jointed rock under small scale yielding,the dimensionless function of the plastic zone diameter based on the Drucker-Prager(D-P) criterion is derived.The plastic zone models of mode Ⅰ,mode Ⅱ and mixed-mode(Ⅰ+Ⅱ) are compared with plastic zones obtained by Mises criterion and the influences of different Poisson’s ratios for mixed-mode plastic zones of wing crack tip are studied.It is shown that the mode Ⅰ and mixed-mode plastic zones of D-P criterion are larger than that of Mises criterion;and its mode Ⅱ and mixed-mode plastic zones are not continuous between the upper and lower surfaces of wing crack.Moreover,plastic yield criterion is employed simultaneously with the fracture softening to describe the behaviors of jointed rock based on D-P criterion.The conception of fracture softening factor is introduced to characterize the softening feature of crack propagation.Regarding the strain energy density of wing cracks at joint-tip is responsible for the evolution of fracture softening of jointed rock.Thus,the behavior of fracture softening can be developed by proposed function of strain energy density.Borja’s strain hardening/softening function is employed as the plastic yield function,regarding the plastic inner variables and stress as two impact factors of the hardening function.The elastoplastic fracture model with its numerical algorithm is proposed;and the code of elastoplastic fracture model is implemented by using return mapping implicit integration algorithm.The influences of friction coefficients,initial joints orientation and stress intensity factor on the constitutive response under uniaxial compression are studied.The results are generally in good agreement with experimental data of uniaxial compression tests of jointed marble.