基于比例边界有限元法的成层半空间中斜坡场地地震响应计算模型

李艳朋; 李志远; 胡志强; 林皋

doi:10.11779/CJGE20211387

基于比例边界有限元法的成层半空间中斜坡场地地震响应计算模型 English Version

李艳朋^{1, 2,},
李志远^3, ,,
胡志强^{1, 2},
林皋^{1, 2}

1.
大连理工大学海岸与近海工程重点实验室, 辽宁大连 116024
2.
大连理工大学建设工程学部水利工程学院工程抗震研究所, 辽宁大连 116024
3.
中国水利水电科学研究院工程抗震研究中心, 北京 100048

基金项目:

国家自然科学基金项目 52209157

西藏自治区重点研发计划项目 XZ202101ZY0002G

详细信息

作者简介:
李艳朋(1994—)，男，博士研究生，主要从事地震工程和工程波动等方面的研究工作。E-mail: liyanp@mail.dlut.edu.cn

通讯作者:
李志远, E-mail: zhiyuanli@dlut.edu.cn

中图分类号: TU435
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出版历程
- 收稿日期: 2021-11-22
- 网络出版日期: 2023-05-18
- 刊出日期: 2023-04-30

Model for seismic dynamic response of slope terrain site in layered half-space based on scaled boundary finite element method

LI Yanpeng^{1, 2,},
LI Zhiyuan^3, ,,
HU Zhiqiang^{1, 2},
LIN Gao^{1, 2}

1.
State Key Laboratory of Coast and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
2.
Institute of Earthquake Engineering, Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China
3.
Earthquake Engineering Research Center, China Institute of Water Resources and Hydropower Research, Beijing 100048, China

摘要

摘要: 由于左右侧不对称且不规则的边界条件延伸到远场，斜坡地形场地的地震波动场求解存在一定困难。为得到成层半空间中斜坡地形场地的地震动力响应，基于波场理论提出一种以相似拼接线为缩放中心的比例边界有限元法计算模型：首先将待求波动场分解为具有规则边界条件的已知波场和由已知波场在真实不规则边界处引起的散射波场，然后通过在斜坡场地的不规则边界处施加等效地震荷载将散射波场的求解由外源输入问题转化为内源辐射问题，最后推导了适用于水平及倾斜成层、左右岸不对称等复杂地基的比例边界有限元法，可沿径向解析地求解斜坡场地的内源辐射问题。通过与文献中均质和成层弹性半空间中凹陷地形场地在SH波入射条件下地表动力响应进行对比，表明了计算模型的准确性，并通过分析成层半空间中斜坡地形场地的波动响应验证了模型的有效性。提出的计算模型，为复杂地基-结构相互作用分析的输入波动场计算提供了新的技术手段。
- 斜坡地形 /
- 成层半空间 /
- 地震动输入 /
- 比例边界有限元法 /
- 地震波动响应
Abstract: For the slope terrain site, the asymmetric and irregular boundary conditions at the left and right sides extend to the far field, which makes it difficult to solve the ground motion waves. In order to obtain the seismic dynamic response of the layered slope terrain sites, based on the wave field theory, a computational model proposed for the scaled boundary finite element method (SBFEM) whose scaling center is the splicing lines. Firstly, the wave field to be determined is decomposed into the known wave field with regular boundary conditions and the scattered wave field caused by the real irregular boundary of the slope-shaped site in the known wave field. Then, the solution of the scattered wave field is transformed from the wave scattered problem to the internal radiation one by applying the equivalent seismic loads on the irregular boundary of the slope terrain site. Finally, the SBFEM, which is suitable for the foundation with horizontal and inclined layes and asymmetric left and right sides, is derived for the internal radiation problem of the slope terrain site analytically along the radial direction. The accuracy of the model is demonstrated by comparing the surface dynamic responses of the depressed terrain site in the uniform and layered elastic half-space under the SH wave incident in the literature, and the validity of the model is verified by analyzing the wave response of the slope terrain site in the layered half-space. The proposed model provides an alternative technique for calculation of the input wave field of the complex soil-structure interaction analysis.
- slope terrain /
- layered half-space /
- seismic wave input /
- SBFEM /
- seismic wave response

HTML全文

图 1 成层场地中斜坡等地表不规则地形震区示意图

Figure 1. Schematic diagram of asymmetric topographical earthquake zone at left and right banks of layered site

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图 2 计算模型分析过程示意图

Figure 2. Schematic diagram of analysis process

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图 3 不同坐标系的映射关系

Figure 3. Mapping relationship of different coordinate systems

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图 4 均质半空间中半圆形河谷示意图

Figure 4. Schematic diagram of a semi-circular valley in homogeneous half-space

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图 5 SH波入射时地表位移响应

Figure 5. Surface displacements induced by incident SH waves

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图 6 成层半空间中梯形河谷横截面示意图

Figure 6. Cross section of canyon in layered half-space

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图 7 SH波入射时地表位移响应

Figure 7. Surface displacements induced by SH waves

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图 8 成层半空间中斜坡地形场地

Figure 8. Slope terrain site in layered elastic half-space

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图 9 不同入射波频率下各观测点位移幅值截断距离nλ收敛情况

Figure 9. Convergence of displacement amplitude versus cutoff distance at some positions with different incident frequencies

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图 10 斜坡上台阶地表位移幅值

Figure 10. Amplitudes of ground surface displacement of steps on slope

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