断层系统摩擦动力学行为的有限元模拟分析

绝大多数大地震发生在先存断层构造上，被广泛认为是一种断层摩擦失稳行为.研究断层上的摩擦动力学行为对地震数值预报具有重要意义.本文围绕地震断层动力学行为，首先回顾了断层摩擦动力学有限元模拟相关的进展，尤其是有限元模拟过程中断层摩擦行为的处理方法，重点分析比较了不同时间积分方案在有限元模拟计算中的差异，探讨了传统有限元方法在模拟断层摩擦失稳非线性的收敛性等难题.考虑到相关差异及问题，本文主要简明介绍了基于R-minimum策略自适应地控制时间步长方案及其有限元计算算法和相关软件，其兼顾了静态隐式与动态显式的优点，将不稳定的隐式迭代计算转变为显式计算；同时利用库仑摩擦定律及速率和状态相关的摩擦本构方程，通过节点-点任意接触单元模拟变形体之间的三维非线性接触摩擦动力学行为，并小结了相关的成功应用实例.此外，为了构建刻画复杂断层形态的有限元网格模型，本文在总结了相关有限元网格生成算法基础上，举例说明了我们最近发展的基于图像的复杂断层约束下非连续四边形和六面体网格的生成方法.最后以此为例，对生成的复杂断层系统模型进行了有限元数值模拟分析.

Finite element simulation and analysis of frictional dynamic behavior of fault system

Most large earthquakes occurred along pre-existing faults and are widely regarded as a kind of frictional instability behavior on faults. It is of great significance to study the interacting fault system involving frictional instability dynamics for numerical prediction of earthquakes. Firstly, the related progress on finite element simulation of interacting fault dynamics is reviewed, especially the treatment methods of friction dynamic behavior and the contact interface. The characteristics of different time integration schemes in the finite element simulation calculation are comprehensively compared and analyzed. The non-convergence issue is discussed due to high nonlinearity in simulating fault friction instability using the conventional finite element method. Considering the relevant differences and difficulties as above, the R-minimum strategy based adaptive control scheme of time step size, its related finite element algorithm and software are proposed and briefly introduced, which takes into account the advantages of static implicit and dynamic explicit, and transforms the unstable implicit iterative calculation into the explicit one; At the same time, using Coulomb's friction criteria together with the rate and state-dependent friction law, the three-dimensional nonlinear contact friction dynamic behavior between deformable bodies are simulated by node-to-point arbitrary contact element. The relevant successful application examples are summarized. In addition, to construct a finite element mesh model with complex faults, the appropriate finite element mesh generation algorithms are reviewed. The application presents our recently developed image-based mesh generation methods of quadrilateral and hexahedral meshes subjected to complex fault constraints. It is simulated and analyzed using our R-minimum strategy-based finite element algorithm and code to investigate the fault friction behavior and its effects on the fault system to demonstrate its capability and usefulness.