水库触发地震研究中二维与三维有限元模拟结果比较

紫坪铺水库蓄水载荷引起的库仑应力变化以及是否可以触发汶川M_S8.0地震是地学界关注的一个热点问题。 已有较多研究均建立在二维有限元模拟基础上, 然而二维与三维结果存在较大差异, 本文定量给出了该差异的大小。 首先比较了有限元方法与解析方法求解半无限空间点载荷下弹性问题结果, 确认了三维有限元计算在百万网格下具有足够的计算精度; 然后数值计算并比较了二维、 三维模型中紫坪埔水库蓄水的弹性力学及渗流效应。 结果表明, 总体上弹性加载会造成逆断层更趋安全, 而水压渗透使其趋于危险, 两者叠加仍然没有导致增加汶川地震危险性; 但现有的二维有限元模拟夸大了真实结果, 在汶川震源位置三维计算的应力大小仅为二维计算的1/3到1/4, 因此在严格的讨论中必须使用三维建模。

Comparison of 2D and 3D Finite Element Simulations in the Research of Reservoir Induced Earthquakes

It has been widely discussed in geoscience community whether Coulomb stress change caused by Zipingpu reservoir loading activities has triggered the 2008 Wenchuan M_S8.0 earthquake. Many conclusions have come from 2D finite element simulations, which are quite different with the 3D results. In this paper, we quantitatively discussed the difference of the 2D and the 3D results. First, a comparison of the 3D finite element solutions and the analytic solutions was given to ensure the enough precision of the 3D finite element simulation with 1 million grid points. Then, the 2D and the 3D numerical solutions of the elastic effect and the seepage effect caused by Zipingpu reservoir were compared. The simulation results show that elastic load caused the thrust fault to be more secure, while the water pressure caused it to be more dangerous. The superimposed effect, however, didn't result an increase in the risk of Wenchuan earthquake. The comparison of the 2D and the 3D results show the 2D result exaggerated the truth. At the hypocenter of the Wenchuan earthquake, the computed stress of the 3D result is only 1/3 to 1/4 of the 2D result, thus in a serious study, 3D modeling is necessary.