饱和脆性岩石在反平面剪切条件下的应变局部化分析

LOCALIZATION OF SATURATED BRITTLE ROCKS UNDER ANTI-PLANE SHEAR

对反平面剪切条件下饱和脆性岩石中单个剪切带的空间发展进行了分析。将饱和岩石视为固液两相介质，用小扰动方法进行稳定性分析。固相视为弹塑性介质，是应变、应变率和孔隙水压力或应力历史的函数，而液体满足达西定律。考虑惯性效应和相间作用，假设固相是可压的。研究结果表明，如果比例加载路径与局部化方向的夹角为π／2，则变形是稳定的，这相当于中性加载：夹角大于π／2的情况相当于弹性卸载；而夹角小于π／2的情况相当于加载，且当夹角等于0°时，失稳发展最快。扰动频率础正值的条件是要求孔压软化效应超过应变硬化效应。在两种极端情况下——长波和短波，饱和脆性岩石总是稳定的。

The spatial development of a single shear band in saturated brittle rocks for anti-plane shear deformation is investigated. The saturated rock is taken as a solid-liquid two-phase medium. Perturbation method is used to analyze the stability conditions. The solid medium is taken to be elasto-plastic, and is the function of strain, strain ratio and pore pressure or stress history. The solid medium is compressible, and the liquid satisfies the Darcy law. The inertial effects and the force between two media are considered in the analysis. It is shown that, if the angle between the proportional loading path and the direction of the localization is π/2, then the deformation is stable. This agrees well with the case of neutral loading. The case that Δθ is more than π/2 corresponds to elastic unloading, while the one that Δθ is less than π/2 corresponds to loading and the instability develops the fastest when Δθ is equal to zero. Positive solutions for α require that the rate of pore pressure softening exceeds that of strain hardening. Under two limit conditions, namely, long wave and short wave, the saturated brittle rock is stable.