基于改进比例边界有限元法的成层场地中峡谷-地下孔洞体系的散射分析

A modified scaled boundary finite element method for scattering analysis of canyon-underground cavity system in horizontally layered site

基于相似拼接线的比例坐标变换,提出了能精确模拟成层半空间的改进比例边界有限元法,在频域中建立了复杂成层场地散射场分析的高精度模型。该方法采用相似拼接线作为比例缩放中心,克服了比例边界有限元法(scaled boundary finite element method,简称SBFEM)由相似性导致求解范围受限的困难,成功地将比例边界有限元法的求解范围扩展到水平及倾斜成层半空间。基于改进比例边界有限元法,建立了复杂成层半空间散射场的求解模型,其中采用子结构法将复杂边界条件的散射问题转化为土-结构相互作用问题,降低了地震波散射问题的计算复杂度,这种转化在线弹性框架内严格成立。通过计算典型算例,验证了提出模型的准确性。采用提出的新模型,分析了水平成层场地中峡谷-地下孔洞耦合体系的散射问题。数值算例表明:与峡谷下无孔洞的情况相比,地下孔洞的存在会放大峡谷表面散射位移幅值,并且对于方形截面孔洞这种放大作用更明显。

Based on the scaled boundary coordinate transformation of scaling splicing lines, an improved scaled boundary finite element method is proposed to accurately model the layered half-space, and a high-precision analysis model for the scattering field response of a complex layered site is established in the frequency domain. This method adopts the splicing lines as scaling center,which overcomes the difficulty due to the scaling requirements, and extends the scope of application of the scaled boundary element method to horizontal and inclined layered sites. Furthermore, based on the modified scaled boundary element method, a solution model for the complex layered half-space scattering field is established. In this model, the substructure method is used to transform the scattering problem with complex boundary conditions into the soil-structure interaction problem, which reduces the complexity of the seismic wave scattering problem. This transformation is strictly true in linearly elastic range. The accuracy of the proposed model is verified by comparing with the reference examples. In addition, the scattering field response of the canyon-underground cavity system in horizontally layered site is conducted. The results show that, compared with the case of no cavity under the canyon, the underground cavity will amplify the scattering displacement amplitude of the canyon surface, and this amplification effect is more obvious for the square cavity.