隧道地震预报波场的有限元数值模拟

Wavefield Modeling Based on the Finite Element Method for the Tunnel Seismic Prediction

在勘探地球物理领域中,能快速、有效地数值模拟2D和3D的地震全波场,包括同时模拟P波、S波、面波多分量波场特征的软件并不是很多;但在结构力学领域中,已有多种成熟的多波多分量有限元数值模拟大型商用软件用于求解弹性本构方程,如ANSYS,PLAXIS等。从方程结构来看,弹性本构方程与完全弹性波动方程相比,只多一项对时间的一阶微分项——阻尼项。因此,调整合理的介质参数——Rayleigh系数,令阻尼项近似为0,弹性本构方程就蜕化为完全弹性波动方程。隧道地震波场是在岩体中传播,具有弹性参数较好、无常规地震勘探中覆盖层等低速带干扰等的优点,采用ANSYS软件对隧道地震波场进行数值模拟,研究了频散、阻尼与吸收边界等数值模拟的相关技术。针对介质吸收,比较了数值模拟中有无阻尼的时间记录和波场快照,对隧道地震预报来说,将阻尼系数设定为0是一种合理的假设;比较了实例中不同网格长度与频散的关系,当网格长度小于波长的1/π倍时,才能消除频散;通过由波方程的推导,引入了黏弹性边界条件,通过实例计算证明它可以有效地吸收边界反射;最后对隧道地震预报进行了实例计算,算例表明采用ANSYS软件可以有效地模拟隧道复杂地质条件下全波场的激发传播过程。

In the field of exploration geophysics,the software packages that can fast and efficiently simulate 2D and 3D seismic full-wavefield,including simultaneously simulate P-wave,S-wave,and surface wave are not very much.In the structure mechanics,however,many sophisticated commercial software packages based on the finite element method including ANSYS and PLAXIS for multi-wave and multi-component have been employed for the solutions of the elastic constitutive equations.Compared to the complete elastic wave equations,the elastic ones include a damping term,which is a first-order differential term time.Therefore,by adjusting the parameter of the medium,that is,the Rayleigh coefficient to make the damping to zero,the elastic constitutive equations will degenerate into full elastic wave equation.The wavefields propagating in the rocks of a tunnel are free of the disturbance of low velocity resulting from the cover layer in the conventional seismic exploration. We simulated the wavefields of the tunnel seismic prediction using the ANSYS software,and researched the dispersion, damping and absorbing conditions etc.in the numerical modeling.For medium absorption,we compared time records and snapshots of the wavefields in the numerical simulation for the cases with and without the damping.In the tunnel seismic prediction,setting the damping to zero is a reasonable assumption. By comparing the relation of different grid length and dispersion in the numerical example,we find that the dispersion disappears when the mesh size is smaller than the wavelength of 1/π.By introducing a viscoelastic boundary condition deduced from the wave equation,boundary reflections can be effectively absorbed.Finally,an numerical example of the tunnel seismic prediction shows that the usage of the ANSYS software can effectively simulate the propagation of waves in the complicated geological conditions.