平面应变压缩岩样侧向变形特征数值模拟

Numerical simulation of lateral deformation of rock specimen in plane strain compression

在平面应变压缩条件下,采用拉格朗日元法对岩样的应变局部化启动、传播、形成及侧向位移特征进行了数值模拟。在数值计算中,采用了莫尔—库仑剪破坏与拉破坏复合的破坏准则,峰后岩石的本构关系为线性应变软化。研究发现,试样的侧向位移具有非均匀性。由于端面约束的作用,接近试样上、下端面的节点的侧向位移远小于试样中部节点的侧向位移。在试样的上、下端面附近,由于弹性应变的恢复快于塑性应变的增加,因而,轴向压缩应力—侧向位移曲线出现了快速回跳现象。通常,可以通过检测岩样不同位置的侧向位移—时步曲线识别出变形局部化启动的时刻。相同高度的侧向位移—时步曲线最先发生分离的时刻,即为局部化启动的时刻。局部化启动之后,试样两侧的侧向位移具有非对称性,侧向位移变化具有非同步性。

Onset, propagation, formation of shear band and lateral displacement of rock specimen with a material imperfection in the form of a null element at left edge in plane strain compression were modeled numerically by FLAC. The failure criterion was a composite Mohr-Coulomb criterion with tension cut-off. Linear post-peak strain-softening constitutive relation of rock was adopted. It is found that lateral displacement of specimen is non-uniform. Lateral displacement near top and base of specimen is lower than that close to the middle. In the vicinity of top and base of specimen, compressive stress-lateral displacement curve exhibits snap-back behavior (Class II behavior) once peak stress is reached, owing to that the recovery of elastic strain is faster than increase of plastic strain. Generally, onset of strain localization can be identified by lateral displacement-time step curves measured at different locations within specimen. Strictly speaking, onset of strain localization corresponds to the beginning of separation of the curves at the same height. After localization begins, lateral displacements at two edges are asymmetry and change in displacements is non-synchronism. If time steps of transition from symmetry with respect to veridical axis of specimen to non-symmetry are obtained, then onset of strain localization can be identified numerically.