断层地震孕育和发生的不稳定性模型

在以前的工作中，考虑直立走滑型断层地震，假设断层面微元破裂强度遵循Weibull概率分布，由细观力学方法推导出断层面的宏观本构关系是一个非线性函数，表现为弹性-软化塑性特征，在此基础上用稳定性理论研究了地震稳定性问题.而实际断层大多是倾斜的，为此，本文首先建立了由围岩和倾斜断层构成的平面地震力学模型，采用宏观的断层载荷-变形的全过程曲线，详细讨论了倾斜断层地震的不稳定性问题.结果表明，远场一旦施加位移，断层也同时错动，这可能与实际情况不符合.为了更好的模拟断层的初始能量累计过程，进一步对断层本构模型进行改进.考虑断层面破裂强度，采用Coulomb破裂准则，则断层表现为刚塑性本构关系，只有当断层面剪应力达到一个临界值时，断层才开始错动.研究表明，对于倾斜断层地震，与直立走滑型断层地震一样，系统刚度比β（围岩切线刚度与断层刚度最大值之比）是决定地震失稳的重要参数，只有当ββ≥1时，仅仅是断层无震滑动，不会发生地震.在远场应施以位移形式边界条件，以致地震失稳发生在平衡路径的位移转向点并伴有应力突跳.

An instability model for fault earthquake genesis and occurrence

In previous work, considering vertical strike-slip fault earthquake and assuming the strength of fault local micro elements follows Weibull probability distribution, the macro fault constitutive relation is derived using micromechanics method. It is a nonlinear function, behaving as elastic-plastic softening characters. Based on it and applying the stability theory, the problem of earthquake instability is investigated. While the actual faults are mostly inclined, therefore in this paper, the plane earthquake mechanical model is established firstly, which is composed of the surrounding rock and the inclined fault. Then adopting the macro complete load-deformation process constitutive curves, the earthquake instability problem is discussed thoroughly. The result indicates that the fault begins to slip once a displacement is applied on the far field, which may be inconsistent with the actual situation. In order to better simulate the process of fault initial energy accumulation, the macro fault constitutive model is improved by considering fault rupture strength and using Coulomb fracture criterion. The modified fault constitutive relation is rigid plasticity. The fault begins to slip only when the shear stress on fault plane reaches the critical value. The research result shows that, as the same as the vertical strike-slip fault earthquake, for inclined fault earthquake, the system stiffness ratio (ratio of surrounding rock stiffness to fault maximum stiffness) β is the important parameter for earthquake occurrence. The earthquake instability occurs only when β<1, accompanied by a stress drop and strain energy release of surrounding rock. When β≥1, earthquake does not occur and the fault only slips slowly without an earthquake. The displacement boundary conditions should be applied on the far field to induce an earthquake at the displacement turning point of the equilibrium path curve, where accompanied by sudden stress jump.