﻿ 强震孕育、发生及其复发循环过程的有限单元法模拟
 地球物理学报  2021, Vol. 64 Issue (2): 537-545 PDF

1. 应急管理部国家自然灾害防治研究院, 北京 100085;
2. 清华大学水利水电工程系, 北京 100084

Finite element method simulation of the earthquake preparation, occurrence, and recurrence cycles
YUAN Jie1,2, CUI ZeFei1, ZHU ShouBiao1, WANG JinTing2
1. National Institute of Natural Hazards, Ministry of Emergency Management of China, Beijing 100085, China;
2. Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China
Abstract: The study of the quasi-periodic recurrence behavior of strong earthquakes is important for predicting and mitigating earthquake disasters. Reasonably and continuously simulating the interseismic-coseismic cycle process is the key to researching the spontaneous earthquake sequences. Based on the finite element dynamic implicit algorithm, this work develops a new methodology for simulating the interseismic-coseismic cycle processes. Our approach has the following advantages:(1) Continuously simulate the interseismic-coseismic cycle process without switching algorithms, and the time step size is automatically and smoothly scaled between quasi-static and dynamic states. (2) The stress field of the calculation model can be obtained under slow tectonic loading and gravity without artificially assigned. (3) The nucleation process of each earthquake event is formed slowly and naturally, and does not need to be given artificially. The simulation results show that the new methodology can continuously and steadily simulate the fault interseismic-coseismic cycle behavior, recurrence interval of strong earthquake, and the detailed coseismic rupture process. In addition, we study the influence of friction coefficient on the recurrence interval of strong earthquake. It turns out that the difference between the static and dynamic friction coefficients on the fault directly affect the recurrence interval of strong earthquake. The smaller the difference, the shorter the recurrence period is.
Keywords: Pregnant process of strong earthquake    Coseismic rupture    Seismic cycle    Continuous simulation    Finite element method
0 引言

1 计算原理及有限元模型 1.1 动力学方程

 (1)

(1) 式又称为平衡方程.其中σij是应力张量，fi是体力，ρ是弹性介质的密度，c是阻尼系数，ui表示位移，ui, tui, tt分别是uit的一次导数和二次导数，即分别是速度和加速度；－ρui, tt和－cui, t分别代表惯性力和阻尼力.具体的动力学基本方程和有限元方法见我们之前的文章(袁杰和朱守彪，2014)，以及相关有限元理论文献(王勖成，2003)，此处不再赘述.

1.2 摩擦本构关系

 (2)

1.3 动力学方程求解方法

1.4 模型几何及有限元网格剖分

 图 1 模型几何及边界条件 Fig. 1 Model geometry and boundary conditions

2 模拟结果

 图 2 断层上盘上的典型点(中间点)的位移随时间的变化曲线 Fig. 2 Displacements change with time at the typical point on the hanging wall of the fault
 图 3 断层典型点位置上下盘之间的位错随时间的变化曲线 Fig. 3 Sliding distance at the typical point on the fault vary with time

 图 4 孕震期间和同震期间的自动增量步时间的变化 Fig. 4 The change of the automatic time increments during interseismic and coseismic periods

 图 5 每次地震事件断层上各点滑移随时间的变化 Fig. 5 Snapshots of the slip profiles at every node along the fault vary with time in each event
 图 6 地震事件五中不同时刻断层周边介质的振动速度云图 Fig. 6 Contour distributions of particle velocities at different times around the fault in event 5

3 问题讨论 3.1 初始场的设定

 图 7 重力作用下，垂直于地表方向应力云图 (a)对整个模型施加重力; (b)自由地表至地下2 km处施加重力. Fig. 7 The vertical stresses of the models under applying gravity (a) Gravity is applied to the whole model; (b) Gravity is applied to the region between free surface and 2 km underground.
3.2 摩擦系数对地震准周期的影响

 图 8 不同摩擦系数下，断层典型点位置上下盘之间的位错随时间的变化 Fig. 8 Slip between hanging wall and footwall at the typical point on the fault vary with time in different models in which friction coefficients are different

(1) 比较图 8a图 8b图 8d，在动摩擦系数相同时，当断层上的静摩擦系数越大，断层的强震复发周期越长.

(2) 比较图 8b图 8c图 3，在静摩擦系数相同时，当断层上的动摩擦系数越大，断层的强震复发周期越短.

(3) 比较图 8c图 8d，可以看出，当断层上的静、动摩擦系数差值相同时，断层的强震复发周期也相当.

4 结论

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