基于波场分离的不规则地形下地震波输入方法

张佳文; 李明超; 韩帅; 闫文钰

doi:10.6052/j.issn.1000-4750.2022.02.0138

基于波场分离的不规则地形下地震波输入方法

doi: 10.6052/j.issn.1000-4750.2022.02.0138

张佳文^1,,
李明超^1, ,,
韩帅^2,,
闫文钰^1,

1.
水利工程仿真与安全国家重点实验室，天津大学，天津 300350
2.
香港理工大学建筑与房地产学系智能建造实验室，香港 999077

基金项目: 国家自然科学面上基金项目(51879185)；天津市研究生科研创新项目(2021YJSB138)

详细信息

作者简介:
张佳文(1995−)，女，安徽人，硕士生，主要从事水工抗震方向的研究 (E-mail: 2018205341@tju.edu.cn)

韩　帅(1992−)，男，河北人，博士生，主要从事水利工程数据挖掘与分析研究(E-mail: hs2015205039@tju.edu.cn)

闫文钰(1998−)，女，山西人，硕士生，主要从事水利工程数值仿真分析研究(E-mail: 987765184@qq.com)

通讯作者:
李明超(1979−)，男，湖北人，教授，博士，博导，主要从事水利工程仿真与优化分析研究(E-mail: LMC@tju.edu.cn)

中图分类号: P315.9；TV312
计量
- 文章访问数: 607
- HTML全文浏览量: 37
- PDF下载量: 67
- 被引次数: 0
出版历程
- 收稿日期: 2022-02-09
- 修回日期: 2022-05-15
- 网络出版日期: 2022-05-20
- 刊出日期: 2023-11-25

INPUT METHOD OF SEISMIC WAVE IN IRREGULAR TERRAIN BASED ON WAVE FIELD SEPARATION

1.
State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300350, China
2.
Smart Construction Laboratory, Department of Architecture and Real Estate, The Hong Kong Polytechnic University, Hong Kong 999077, China

摘要

摘要: 不规则地形条件下斜入射地震波场求解难度较大，以往的方法在计算精度和适用范围方面仍有不足。该文结合解析推导和有限元模拟，提出了一种基于波场分离技术的不规则地形条件下地震波输入方法，将地震P波和SV波在不同边界下进行波场分离：垂直入射时在侧面边界上分离为自由波场和散射波场，底部边界上分离为入射波场和边界外行场；斜入射时将输入侧对面的边界改为分离成入射波场和边界外行场；并充分考虑局部地形条件的影响，还基于改进的波动方法以便捷地输入节点力。同时对比了多组不同地震入射角度下规则场地和不规则场地的振动反应。结果表明：该方法在多类地形条件下计算精度与效率均较高，适用范围广且易于推广至复杂场地条件，并发现地震波入射角度和局部场地条件对地表位移响应影响较大。该研究可为不规则地形条件下的振动响应分析提供有效的手段。
- 场地反应 /
- 不规则地形 /
- 地震波输入 /
- 地震波场分离 /
- 入射角度
Abstract: Solving the oblique incident seismic wave field under irregular terrain conditions is challenging, and previous methods are limited in calculation accuracy and application range. A ground motion input method was proposed for irregular terrains based on wave field separation by combining analytical derivation and finite element simulation. Seismic P waves and SV waves are separated under different boundary conditions. When incident vertically, they are decomposed into free wave field and scattered wave field at the side boundary, and incident wave field and boundary outer field at the bottom boundary. For oblique incidence, the seismic wave at the opposite boundary of the input side is separated into incident wave field and outer boundary field. In this paper, the influence of local topographic conditions was fully considered, and the improved wave method was used to input nodal force conveniently. Besides, the vibration responses of regular and irregular terrains under different incidence angles were analyzed. The results show that the method has high computational accuracy and efficiency under multiple topographic conditions and can be applied to complex site conditions. Moreover, the incident angle and local site conditions are found to have significant effects on surface displacement response. The study can provide an effective way for response analysis under irregular terrain conditions.
- site response /
- irregular terrain /
- seismic wave input /
- seismic wave field separation /
- incident angle

HTML全文

图 1 不规则地形下各边界地震波场输入

Figure 1. Input of seismic wave field at each boundary under irregular terrain

下载: 全尺寸图片幻灯片

图 2 斜入射P波作用下的地震波场

Figure 2. Seismic wave field under obliquely incident P waves

下载: 全尺寸图片幻灯片

图 3 斜入射地震波传播规律

Figure 3. Propagation law of obliquely incident seismic waves

下载: 全尺寸图片幻灯片

图 4 离散化后的弹性半空间模型

Figure 4. Discrete model of elastic half-space

下载: 全尺寸图片幻灯片

图 5 基于人工边界子结构的波动输入方法

Figure 5. Wave input method based on substructure of artificial boundaries

下载: 全尺寸图片幻灯片

图 6 不规则地形场地的有限元模型　/m

Figure 6. Finite element model of irregular terrain site

下载: 全尺寸图片幻灯片

图 7 远置边界法中的有限元模型　/m

Figure 7. Finite element model in remote boundary method

下载: 全尺寸图片幻灯片

图 8 入射脉冲波的位移时程和傅里叶谱

Figure 8. Displacement and Fourier spectrum of the incident seismic wave

下载: 全尺寸图片幻灯片

图 9 P波入射下自由表面点位移

Figure 9. Displacement of free surface under incident P waves

下载: 全尺寸图片幻灯片

图 10 SV波入射下自由表面点位移

Figure 10. Displacement of free surface under incident SV waves

下载: 全尺寸图片幻灯片

图 11 场地关键点的位移输入情况

Figure 11. Input displacement of key points in the site

下载: 全尺寸图片幻灯片

图 12 P波垂直入射时的波场快照

Figure 12. Wave field snapshot of site under vertical incident P waves

下载: 全尺寸图片幻灯片

图 13 P波入射角度30°时的波场快照

Figure 13. Wave field snapshot of site under P waves with the incident angle of 30°

下载: 全尺寸图片幻灯片

图 14 规则地形场地的有限元模型　/m

Figure 14. Finite element model of regular terrain site

下载: 全尺寸图片幻灯片

图 15 地震波入射下规则场地自由表面点位移

Figure 15. Displacement of free surface of regular site under seismic waves

下载: 全尺寸图片幻灯片

图 16 地震波入射下阶梯型场地自由表面点位移

Figure 16. Displacement of free surface of stepped site under seismic waves

下载: 全尺寸图片幻灯片

图 17 P波不同入射角度下阶梯型场地A₁点位移

Figure 17. Displacement of A₁ on the stepped site under P waves with different incident angles

下载: 全尺寸图片幻灯片

图 18 SV波不同入射角度下阶梯型场地A₁点位移

Figure 18. Displacement of A₁ on the stepped site under SV waves with different incident angles

下载: 全尺寸图片幻灯片

表 1 场地模型参数

Table 1. Model parameters of the site

场地模型	密度/ (kg·m⁻³)	泊松比	弹性模量/ GPa	SV波波速/ (m·s⁻¹)	P波波速/ (m·s⁻¹)
阶梯型场地	2000	0.25	0.2000	200	346
V字河谷型场地	1500	0.25	0.3375	300	520
梯形河谷型场地	1500	0.25	0.3375	300	520

下载: 导出CSV

表 2 两种方法的结果对比

Table 2. Comparison of the two methods

入射角度/(°)	远置边界方法			本文方法
入射角度/(°)	模型网格数	计算时长/ min	结果文件大小/GB	模型网格数	计算时长/ min	结果文件大小/GB
θ_P=0	43 550	29	2.84	4550	4.2	0.38
θ_P=30	89 700	56	5.72	3700	4.5	0.32
θ_SV=0	43 550	28	2.84	4550	4.1	0.38
θ_SV=15	90 000	56	5.74	4500	4.6	0.37

下载: 导出CSV

表 3 P波入射时不同地形条件下自由表面A₁点位移

Table 3. Displacement of A₁ under different terrain conditions when P waves incident

入射角度/(°)	横向位移幅值			竖向位移幅值
入射角度/(°)	规则地形/m	阶梯型/m	相差/(%)	规则地形/m	阶梯型/m	相差/(%)
0	0.00	0.17	−100.00	2.00	2.07	−3.35
15	0.59	0.84	−29.50	1.92	2.50	−23.34
30	1.12	1.28	−12.39	1.69	1.96	−13.86
45	1.52	2.26	−32.67	1.36	1.36	0.14
60	1.73	2.48	−30.25	1.00	0.85	18.05
75	1.60	2.25	−28.82	0.65	0.52	25.71
90	0.73	0.97	−24.90	0.52	0.27	89.50

下载: 导出CSV

表 4 SV波入射时不同地形条件下自由表面A₁点位移

Table 4. Displacement of A₁ under different terrain conditions when SV waves incident

入射角度/(°)	横向位移幅值			竖向位移幅值
入射角度/(°)	规则地形/m	阶梯型/m	相差/(%)	规则地形/m	阶梯型/m	相差/(%)
0	2.00	1.98	0.86	0.00	−0.12	−99.98
5	1.99	1.96	1.46	−0.16	−0.15	7.55
10	1.95	1.90	2.75	−0.31	−0.20	51.98
15	1.89	1.81	4.59	−0.45	−0.26	70.47
20	1.81	1.77	2.36	−0.58	−0.40	46.42
25	1.71	1.70	0.37	−0.70	−0.51	35.32
30	1.59	1.72	−7.10	−0.79	−0.68	16.66

下载: 导出CSV

参考文献(36)

[1]	郜新军, 赵成刚, 刘秦. 地震波斜入射下考虑局部地形影响和土结动力相互作用的多跨桥动力响应分析[J]. 工程力学, 2011, 28(11): 237 − 243. GAO Xinjun, ZHAO Chenggang, LIU Qin. Seismic response analysis of multi-span viaduct considering topographic effect and soil-structure dynamic interaction based on inclined wave [J]. Engineering Mechanics, 2011, 28(11): 237 − 243. (in Chinese)
[2]	MAUFROY E, CRUZ-ATIENZA V M, GAFFET S. A robust method for assessing 3-D topographic site effects: A case study at the LSBB underground laboratory, France [J]. Earthquake Spectra, 2012, 28(3): 1097 − 1115. doi: 10.1193/1.4000050
[3]	田林, 徐则民, 张家明. 局部地形下入射波散射效应对场地地震响应的影响[J]. 地球物理学进展, 2012, 27(1): 122 − 130. doi: 10.6038/j.issn.1004-2903.2012.01.014 TIAN Lin, XU Zemin, ZHANG Jiaming. Seismic response for local landform subjected to scattering of incident wave [J]. Progress in Geophysics, 2012, 27(1): 122 − 130. (in Chinese) doi: 10.6038/j.issn.1004-2903.2012.01.014
[4]	TIAREN G P, FERREIRA A, GONZALO Y, et al. Effects of topography and basins on seismic wave amplification: The Northern Chile coastal cliff and intramountainous basins [J]. Geophysical Journal International, 2021, 227(2): 1143 − 1167. doi: 10.1093/gji/ggab259
[5]	BARON J, PRIMOFIORE I, KLIN P, et al. Investigation of topographic site effects using 3D waveform modelling: Amplification, polarization and torsional motions in the case study of Arquata del Tronto (Italy) [J]. Bulletin of Earthquake Engineering, 2022, 20(2): 677 − 710. doi: 10.1007/s10518-021-01270-2
[6]	张建毅, 薄景山, 王振宇, 等. 汶川地震局部地形对地震动的影[J]. 自然灾害学报, 2012, 21(3): 164 − 169. ZHANG Jianyi, BO Jingshan, WANG Zhenyu, et al. Influence of local topography on seismic ground motion in Wenchuan earthquake [J]. Journal of Natural Disasters, 2012, 21(3): 164 − 169. (in Chinese)
[7]	LYU D, MA S, YU C, et al. Effects of oblique incidence of SV waves on nonlinear seismic response of a lined arched tunnel [J]. Shock and Vibration, 2020: 8093804: 1 − 12.
[8]	ZHANG J W, ZHANG M X, LI M C, et al. Nonlinear dynamic response of a CC-RCC combined dam structure under oblique incidence of near-fault ground motions [J]. Applied Science, 2020, 10: 10030885. doi: 10.3390/app10030885
[9]	ZHANG J W, LI M C, SHUAI H, et al. Estimation of seismic wave incident angle using vibration response data and stacking ensemble algorithm [J]. Computers and Geotechnics, 2021, 137(5): 104255.
[10]	BAO X, LIU J B, WANG D Y, et al. Modification research of the internal substructure method for seismic wave input in deep underground structure-soil systems [J]. Shock and Vibration, 2019: 5926410: 1 − 13.
[11]	SAHEBKAR K, ESKANDARI-GHADI M. Time-harmonic response of saturated porous transversely isotropic half-space under surface tractions [J]. Journal of Hydrology, 2016, 537: 61 − 73. doi: 10.1016/j.jhydrol.2016.02.050
[12]	BA Z N, LIANG J W. Fundamental solutions of a multi-layered transversely isotropic saturated half-space subjected to moving point forces and pore pressure [J]. Engineering Analysis with Boundary Elements, 2017, 76: 40 − 58. doi: 10.1016/j.enganabound.2016.12.006
[13]	KEAWSAWASVONG S, SENJUNTICHAI T. Poroelasto dynamic fundamental solutions of transversely isotropic half-plane [J]. Computers and Geotechnics, 2019, 106: 52 − 67. doi: 10.1016/j.compgeo.2018.10.012
[14]	巴振宁, 彭琳, 梁建文, 等. 任意多个凸起地形对平面P波的散射[J]. 工程力学, 2018, 35(7): 7 − 17, 23. doi: 10.6052/j.issn.1000-4750.2017.03.0181 BA Zhenning, PENG Lin, LIANG Jianwen, et al. Scatter and diffraction of arbitrary number of hills for incident plane P-waves [J]. Engineering Mechanics, 2018, 35(7): 7 − 17, 23. (in Chinese) doi: 10.6052/j.issn.1000-4750.2017.03.0181
[15]	李明超, 张佳文, 张梦溪, 等. 地震波斜入射下混凝土重力坝的塑性损伤响应分析[J]. 水利学报, 2019, 50(11): 1326 − 1338, 1349. LI Mingchao, ZHANG Jiawen, ZHANG Mengxi, et al. Plastic damage response analysis of concrete gravity dam due to obliquely incident seismic waves [J]. Journal of Hydraulic Engineering, 2019, 50(11): 1326 − 1338, 1349. (in Chinese)
[16]	LEE V W, LIU W Y. Two-dimensional scattering and diffraction of P- and SV-waves around a semi-circular canyon in an elastic half-space: An analytic solution via a stress-free wave function [J]. Soil Dynamics and Earthquake Engineering, 2014, 63: 110 − 119. doi: 10.1016/j.soildyn.2014.02.005
[17]	ZHANG N, GAO Y F, PAK RONALD Y S. Soil and topographic effects on ground motion of a surficially inhomogeneous semi-cylindrical canyon under oblique incident SH waves [J]. Soil Dynamics and Earthquake Engineering, 2017, 95: 17 − 28. doi: 10.1016/j.soildyn.2017.01.037
[18]	LIU J B, TAN H, BAO X, et al. Seismic wave input method for three-dimensional soil-structure dynamic interaction analysis based on the substructure of artificial boundaries [J]. Earthquake Engineering and Engineering Vibration, 2019, 18(4): 747 − 758. doi: 10.1007/s11803-019-0534-5
[19]	宝鑫, 刘晶波, 李述涛, 等. 土-结构相互作用对储液结构动力反应的影响研究[J]. 工程力学, 2021, 38(增刊): 125 − 132. doi: 10.6052/j.issn.1000-4750.2020.06.S022 BAO Xin, LIU Jingbo, LI Shutao, et al. Influence analysis of soil-structure interaction on the dynamic response of storage tanks [J]. Engineering Mechanics, 2021, 38(Suppl): 125 − 132. (in Chinese) doi: 10.6052/j.issn.1000-4750.2020.06.S022
[20]	林皋. 地下结构地震响应的计算模型[J]. 力学学报, 2017, 49(3): 528 − 542. LIN Gao. A computational model for seismic response analysis of underground structures [J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 528 − 542. (in Chinese)
[21]	赵密, 苏成坤, 王丕光, 等. 地震作用下水-结构-土动力相互作用分析[J]. 工程力学, 2022, 39(3): 51 − 63. doi: 10.6052/j.issn.1000-4750.2021.01.0031 ZHAO Mi, SU Chengkun, WANG Piguang, et al. Analysis of water-structure-soil dynamic interaction under earthquakes [J]. Engineering Mechanics, 2022, 39(3): 51 − 63. (in Chinese) doi: 10.6052/j.issn.1000-4750.2021.01.0031
[22]	ASHFORD S A, SITAR N. Analysis of topographic amplification of inclined shear waves in a steep bluff [J]. Bulletin of the Seismological Society of America, 1997, 87: 692 − 700. doi: 10.1785/BSSA0870030692
[23]	李山有, 廖振鹏. 地震体波斜入射情形下台阶地形引起的波型转换[J]. 地震工程与工程振动, 2002, 22(4): 9 − 15. LI Shanyou, LIAO Zhenpeng. Wave-type conversion caused by a step topography subjected to inclined seismic body wave [J]. Earthquake Engineering and Engineering Vibration, 2002, 22(4): 9 − 15. (in Chinese)
[24]	顾亮, 丁海平, 于彦彦. SV波斜入射陡坎地形对地面运动的影响[J]. 自然灾害学报, 2017, 26(4): 39 − 47. GU Liang, DING Haiping, YU Yanyan. Effects of scarp topography on seismic ground motion under inclined SV waves [J]. Journal of Natural Disasters, 2017, 26(4): 39 − 47. (in Chinese)
[25]	赵密, 孙文达, 高志懂, 等. 阶梯地形成层场地的斜入射地震动输入方法[J]. 工程力学, 2019, 36(12): 62 − 68. doi: 10.6052/j.issn.1000-4750.2018.10.0574 ZHAO Mi, SUN Wenda, GAO Zhidong, et al. Input method of obliquely incident earthquake for step-shaped layered site [J]. Engineering Mechanics, 2019, 36(12): 62 − 68. (in Chinese) doi: 10.6052/j.issn.1000-4750.2018.10.0574
[26]	BAO X, LIU J B, TAN H. Hybrid wave field method for seismic wave input in dynamic soil-structure interaction problems [C]// 17th World Conference on Earthquake Engineering. Sendai, Japan: NICEE, 2020.
[27]	杜修力, 赵密. 基于黏弹性边界的拱坝地震反应分析方法[J]. 水利学报, 2006, 37(9): 1063 − 1069. DU Xiuli, ZHAO Mi. Analysis method for seismic response of arch dams in time domain based on viscous-spring artificial boundary condition [J]. Journal of Hydraulic Engineering, 2006, 37(9): 1063 − 1069. (in Chinese)
[28]	ZHANG J W, LI M C, HAN S. Seismic analysis of gravity dam-layered foundation system subjected to earthquakes with arbitrary incident angles [J]. International Journal of Geomechanics, 2022, 22(2): 04021279.
[29]	李述涛, 刘晶波, 宝鑫, 等. 采用粘弹性人工边界单元时显式算法稳定性分析[J]. 工程力学, 2020, 37(11): 1 − 11, 46. doi: 10.6052/j.issn.1000-4750.2019.12.0755 LI Shutao, LIU Jingbo, BAO Xin, et al. Stability analysis of explicit algorithms with visco-elastic artificial boundary elements [J]. Engineering Mechanics, 2020, 37(11): 1 − 11, 46. (in Chinese) doi: 10.6052/j.issn.1000-4750.2019.12.0755
[30]	刘晶波, 吕彦东. 结构–地基动力相互作用问题分析的一种直接方法[J]. 土木工程学报, 1998, 31(3): 55 − 64. LIU Jingbo, LYU Yandong. A direct method for analysis of dynamic soil-structure interaction [J]. China Civil Engineering Journal, 1998, 31(3): 55 − 64. (in Chinese)
[31]	刘晶波, 谭辉, 宝鑫, 等. 土–结构动力相互作用分析中基于人工边界子结构的地震波动输入方法[J]. 力学学报, 2018, 50(1): 32 − 43. doi: 10.6052/0459-1879-17-336 LIU Jingbo, TAN Hui, BAO Xin, et al. The seismic wave input method for soil-structure dynamic interaction analysis based on the substructure of artificial boundaries [J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(1): 32 − 43. (in Chinese) doi: 10.6052/0459-1879-17-336
[32]	张奎, 夏佩林, 李伟华, 等. 斜入射下水下地基场地地震输入的一维化时域方法[J]. 工程力学, 2019, 36(11): 91 − 101. doi: 10.6052/j.issn.1000-4750.2018.09.0523 ZHANG Kui, XIA Peilin, LI Weihua, et al. 1D time-domain method for 2D wave motion in underwater site with obliquely incident plane wave [J]. Engineering Mechanics, 2019, 36(11): 91 − 101. (in Chinese) doi: 10.6052/j.issn.1000-4750.2018.09.0523
[33]	张季, 谭灿星, 叶国涛, 等. SV波超临界角斜入射时层状地基地震动输入在ABAQUS中的实现[J]. 工程力学, 2021, 38(4): 200 − 210. doi: 10.6052/j.issn.1000-4750.2020.06.0378 ZHANG Ji, TAN Canxing, YE Guotao, et al. Realization of ground motion input in ABAQUS for layered foundation under SV wave of oblique incidence over critical angle [J]. Engineering Mechanics, 2021, 38(4): 200 − 210. (in Chinese) doi: 10.6052/j.issn.1000-4750.2020.06.0378
[34]	BI Z H, CUI B H, ZHAI Y F. Research on seismic input method of layered ground foundation [J]. IEEE Access, 2021, 99: 3070479.
[35]	SOTOUDEH P, GHAEMIAN M, MOHAMMADNEZHAD H. Seismic analysis of reservoir-gravity dam-massed layered foundation system due to vertically propagating earthquake [J]. Soil Dynamics and Earthquake Engineering, 2019, 116: 174 − 184. doi: 10.1016/j.soildyn.2018.09.041
[36]	LIU T J, ZHENG S Y, TANG X W, et al. Time-domain analysis of underground station-layered soil interaction based on high-order doubly asymptotic transmitting boundary [J]. Computer Modeling in Engineering and Sciences, 2019, 120(3): 545 − 560. doi: 10.32604/cmes.2019.05043