基于柱坐标系的隧道空间全波场数值模拟与分析

Full wave filed numerical simulation and analysis of tunnel space based on cylindrical coordinate system

不同于地面地震,隧道空间的特殊结构使得其波场十分复杂,基于实际隧道模型的全波场数值模拟是有效认识隧道空间内波场传播规律的重要手段。关于这方面的研究以往多是基于直角坐标系,而隧道作为类似空气柱的特殊地质模型,采用柱坐标系下的全波场数值模拟对认识隧道空间的波场特征更有意义。基于柱坐标系下的一阶弹性波速度-应力方程,推导任意偶数阶交错网格差分格式,设计了人工截断边界和隧道自由边界,对岩性分界面、断层破碎带、溶洞等隧道典型不良地质模型进行数值模拟与波场特征分析。研究结果表明:基于柱坐标系下的一阶弹性波速度-应力方程,采用交错网格有限差分算法结合FCT技术,可实现隧道空间全波场高精度数值模拟,波场特征符合波的运动学与动力学特征,为隧道空间复杂波场特征的认识和资料解译提供有效的依据。

Differing from ground seismic exploration, the special structure of tunnel space makes its wave field very complex. Full-wave field numerical simulation based on actual tunnel model is an important method to effectively understand the propagation law of wave field in tunnel space. Previous studies on this field are mostly based on Cartesian coordinate system. As a special geological model similar to air column, numerical simulation of full wave field in cylindrical coordinate system is more meaningful for understanding the characteristics of wave field in tunnel space. An arbitrary even-order staggered grid difference scheme was deduced, artificial truncated boundary and tunnel free boundary were designed, and numerical simulation and wave field characteristics analysis were performed for typical problematic geological models of tunnels such as lithologic interface, fault fracture zone and karst cave based on the first-order elastic wave velocity-stress equation in cylindrical coordinates. The results show that the staggered grid finite difference method based on the first-order elastic wave velocity-stress equation in cylindrical coordinates combined with FCT technology can achieve high-precision numerical simulation of the full-wave field in tunnel space. The wave field characteristics are in accordance with the kinematic and dynamic characteristics of the wave, which provides an effective basis for understanding the complex wave field characteristics in tunnel space and interpreting the data.