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
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- 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

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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

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图 3 斜入射地震波传播规律

Figure 3. Propagation law of obliquely incident seismic waves

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图 4 离散化后的弹性半空间模型

Figure 4. Discrete model of elastic half-space

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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

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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

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图 7 远置边界法中的有限元模型　/m

Figure 7. Finite element model in remote boundary method

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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

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图 9 P波入射下自由表面点位移

Figure 9. Displacement of free surface under incident P waves

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图 10 SV波入射下自由表面点位移

Figure 10. Displacement of free surface under incident SV waves

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图 11 场地关键点的位移输入情况

Figure 11. Input displacement of key points in the site

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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

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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°

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图 14 规则地形场地的有限元模型　/m

Figure 14. Finite element model of regular terrain site

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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

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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

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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

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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

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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

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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

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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

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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

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