ABSTRACT

A complicated natural topography, such as a cavity beneath a canyon, can cause considerable ground motion during earthquakes. This phenomenon is referred to as a site effect. An awareness of site effects can help to reduce damage to property and loss of life. However, modeling the highly complex interactions between a cavity and a canyon requires considerable mesh skills. In this study, we developed a novel, systematic approach to meshing this kind of complicated topography, wherein irregularities are meshed via arithmetic progression, the formula of the internal division point, and the transfinite interpolation (TFI) function. We then implemented a hybrid method combining Lamb’s series with the finite element method (FEM) in conjunction with the proposed meshing skill to resolve the problem of anti-plane scattering. The results were verified using two degenerated models: a semi-circular canyon and a cavity beneath a planar surface. We made a detailed account of how the responses of $\left|u_y\right|$ at the surface of the semi-circular canyon and around the surface of the circular cavity were affected by the incident angle of SH waves ($\mathrm{\Theta }$), dimensionless frequency ($\eta$), and variations in the radius of the circular cavity ($a_1$). Interestingly, the responses of $\left|u_y\right|$ were affected by the following site effects: (1) plate-like effects related to the buried depth of the circular cavity, (2) canyon-decay effects due to the existence of the canyon, and (3) creep effects associated with the curvature and size of circular cavity. The patterns of $\left|u_y\right|$ at the free surface and surface of the circular cavity are affected by each of the aforementioned site effects, which all depend profoundly on $\mathrm{\Theta }$, $\eta$ and $a_1$.

摘要

复杂的自然地形，例如峡谷下方的空洞，会在地震期间引起相当大的地面运动。这种现象被称为站点效应。了解场地影响有助于减少财产损失和生命损失。然而，对空腔和峡谷之间高度复杂的相互作用进行建模需要相当多的网格技能。在这项研究中，我们开发了一种新颖的、系统的方法来对这种复杂的地形进行网格划分，其中通过算术级数、内分割点的公式和超限插值 (TFI) 函数对不规则性进行网格划分。然后，我们实施了一种混合方法，将 Lamb 级数与有限元法 (FEM) 结合提出的网格技术来解决反平面散射问题。使用两个退化模型验证了结果：半圆形峡谷和平面下方的空腔。我们详细说明了$\left|{你}_{\mathrm{是的}}\right|$半圆形峡谷表面和圆形空腔表面周围受到SH波入射角的影响（$\mathrm{\theta }$），无量纲频率（$\eta$)，以及圆形空腔半径的变化 (${\mathrm{一种}}_1$）。有趣的是，$\left|{你}_{\mathrm{是的}}\right|$受到以下场地效应的影响：（1）与圆形空腔埋深相关的板状效应，（2）由于峡谷的存在而产生的峡谷衰减效应，以及（3）与曲率相关的蠕变效应和圆形腔的尺寸。的图案$\left|{你}_{\mathrm{是的}}\right|$圆形空腔的自由表面和表面受到上述每种场地效应的影响，这些都深深地依赖于$\mathrm{\theta }$,$\eta$和${\mathrm{一种}}_1$.