双轴应力下非贯通节理岩体压缩损伤本构模型

针对目前节理岩体损伤变量定义中大多仅考虑节理长度、倾角等几何性质，而未考虑节理抗剪强度等力学性质的不足，基于断裂力学中的由于单个节理存在引起的附加应变能增量与损伤力学中的损伤应变能释放量相关联的观点，推导出了在双轴应力下含单条非贯通闭合节理岩体的损伤变量计算公式，并根据断裂力学理论对双轴压缩荷载下的单个节理尖端应力强度因子计算方法进行了研究，得出了应力强度因子KⅠ、KⅡ的计算公式；同时考虑多节理间的相互作用，给出了单组单排及单组多排非贯通节理尖端应力强度因子计算公式，由此建立了相应的节理岩体双轴压缩损伤本构模型，并利用该模型进行了相应的算例分析。结果表明：对含单条非贯通闭合节理的岩体而言，当节理倾角小于其内摩擦角时，岩体强度与完整岩石相同，岩体损伤为0，而后随着节理倾角增加，岩体强度、损伤随节理倾角的变化分别呈开口向上及向下的抛物线，当节理倾角约为60°时，岩体损伤最大，强度最低。随着节理长度增加，岩体损伤增加，而随着节理内摩擦角的增加，岩体损伤则减小；对含单组单排非贯通闭合节理的岩体而言，当节理总长度一定时，随着单条节理长度的减小及节理条数的增加，岩体损伤则逐渐减小，但其减小幅度与节理条数并不呈线性关系。

A biaxial compression damage constitutive model for rock mass with non-persistent joints

Currently, most definitions of the damage variable for jointed rock mass only use geometrical factors of joints such as the length and dip angle, but cannot consider joint shear strength. Due to this limitation, a new damage variable formulae is firstly deduced to calculate rock mass with a non-persistent closed joint, based on the connection between the increment of additional strain energy caused by the existence of one joint in fracture mechanics and the emission of damaged strain energy in damage mechanics. Secondly, the calculation method of the stress intensity factor (SIF) of a single joint tip under biaxial compression is studied according to fracture mechanics theory, and then the calculation SIF formulae of KⅠ and KⅡ are obtained. Thirdly, the calculation formulae of the tip SIF of a set of one or more-rowed joints are given by considering the interaction among the joints. Finally, a biaxial compression damage constitutive model for the jointed rock mass is developed, which is further employed to analyze an example. It is found that for rock mass with a single non-persistent closed joint, the strength of rock mass is the same as that of the intact rock, and the damage is 0 when the joint dip angle is less than its internal friction angle. Furthermore, with the increase in joint dip angle, the change laws of rock mass strength and the damage with the joint dip angle are parabola with the hatch up and down, respectively. The strength of rock mass is the lowest and its damage is the highest when the joint dip angle is about 60°. With the increase of joint length, the damage of rock mass increases; while with the increase of the internal friction angle of joint, the damage of rock mass decreases. For the rock mass with a set of one-rowed non-persistent closed joint, when the total length of the joint is the same, the damage of rock mass gradually decreases with the decrease of a single joint length and the increase of the joint number, however the relationship between the decrease amplitude and the joint number exhibits nonlinear response.