基于颗粒离散元法的连接键应变软化模型及其应用

基于颗粒间的有限接触假设,提出了可表述颗粒间力、力矩传递的连接键模型.为了表征连接键的塑性、损伤及断裂过程,在连接键中引入了考虑应变软化效应的Mohr--Coulomb准则及最大拉应力准则.单一连接键的单向拉伸测试及直剪测试表明了上述连接键应变软化模型的计算精度.研究了颗粒体系的宏观应变能与颗粒平均配位数的对应关系.通过计算发现,对于二维颗粒体系,当平均配位数为5时,颗粒体系的宏观应变能与相同参数下连续介质方法 (如有限元等)计算获得的应变能基本一致.利用上述连接键应变软化模型对岩石的单轴压缩过程进行了模拟,计算结果表明:岩石单轴压缩的应力应变曲线经历了线性上升段、非线性上升段、非线性下降段及缓变段等4个阶段,并给出了上述4个阶段与岩石内部损伤破裂状态的内在联系.计算结果还表明,随着断裂应变的增大,岩石的破裂模式逐渐由拉剪复合型破裂向单一压剪型破裂转化;随着断裂应变的增大,峰值应力及达到峰值应力时的应变均逐渐增大,但峰值时的破裂度及终态时的破裂度将逐渐减小.

PARTICLE-DEM BASED LINKED BAR STRAIN SOFTENING MODEL AND ITS APPLICATION

Based on finite contact assumption between particles, a linked bar model to transmit the force and moment between particles is proposed. To represent the plastic, damage and fracture process of linked bar, the Mohr-Coulomb model and maximal tensile stress model considering strain softening e ect is introduced. The numerical results of uniaxial extension test and direct shear test with single linked bar show the accuracy of the model. The relationship between equivalent macro strain energy of particles system and the average coordination number is studied. Numerical results show that, for 2D particles system, when the average coordination number equals 5, the equivalent macro strain energy of particles system coincides well with the strain energy computed by approaches based on continuous media (i.e. FEM). The uniaxial compression process of rock is simulated based on the linked bar strain softening model. The results show that, the strain-stress curve of rock during uniaxial compression could be divided to four stages, which are linear stage, hardening stage, softening stage and sliding stage, and the relationships between four stages and damage fracture status of rock are also studied. From the results, with the increase of fracture strain, the failure mode of rock changes from tensile-shear composite fracture pattern to purely compression shear fracture pattern. With the increase of fracture strain, the peak stress and corresponding critical strain increases gradually, however, the fracture degree at peak point and at final state decreases gradually.