考虑应变率及应变梯度效应的断层岩爆分析

ANALYSIS ON FAULT ROCKBURST CONSIDERING STRAIN RATE AND STRAIN GRADIENT

从理论上研究了考虑应变率效应及微小结构相互影响的断层带-弹性岩石系统的剪切不稳定性。在经典弹-塑性理论的屈服函数中引入应变梯度及考虑应变率效应的函数。将断层岩爆简化为一维动态剪切问题,利用:局部塑性剪应变的对称性;在断层带的边界上,其应变值为零;断层带的宽度由塑性剪切应变取极值来确定等条件,得到了断层带内部的局部塑性剪切应变及局部塑性剪切位移,二者都随应变率的增加而趋于明显增加。同时,还得到了应变软化阶段系统结构响应的理论表达式。令峰后刚度为无穷大,则可得到岩爆发生的临界加载应变率,该参数不仅与岩石材料的本构参数有关,而且还与岩石结构的几何尺寸(即弹性区域的尺寸)有关。应变率增加使断层-弹性岩石系统容易发生失稳回跳。此外,若不考虑应变率效应,则本文的理论结果可以退化为对断层岩爆的静力分析结果。

Dynamic shear instability of fault rockburst is analyzed with considering the effect of strain rate and interaction among microstructures. The second shear strain gradient and the function reflecting the effect of strain rate are introduced into the yield function of classical elastoplastic theory. The fault rockburst is simplified as the one-dimensional dynamic shear problem and shear localization is initiated at the peak shear stress. Symmetry of local plastic shear strain in shear band is considered and in the boundary of the band the strain is zero. In addition, the thickness of band is determined according to the maximum local plastic shear strain. Local plastic shear strain and local plastic shear displacement analytically obtained show that these two local parameters increase with strain rate. Beyond the peak shear stress, the structural response of the system composed of fault band and elastic rock outside the fault is proposed. If the post-peak stiffness of the structural response is infinity, the critical loading strain rate of rockburst can be deduced. Once the critical value is achieved, the rock burst occurs certainty. It is found that the critical parameter is dependent on both constitutive parameters of rock materials and the size of structure. Larger strain rate can lead to snap-back of instability of the system. Besides, if the effect of strain rate is neglected, the static results based on gradient-dependent plasticity by Wang et al. can be obtained by simplifying the present theoretical results.