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三维局部场地地震波散射问题谱元并行模拟方法

于彦彦 芮志良 丁海平

于彦彦, 芮志良, 丁海平. 三维局部场地地震波散射问题谱元并行模拟方法. 力学学报, 2023, 55(6): 1-13 doi: 10.6052/0459-1879-23-052
引用本文: 于彦彦, 芮志良, 丁海平. 三维局部场地地震波散射问题谱元并行模拟方法. 力学学报, 2023, 55(6): 1-13 doi: 10.6052/0459-1879-23-052
Yu Yanyan, Rui Zhiliang, Ding Haiping. Parallel spectral element method for 3D local-site ground motion simulations of wave scattering problem. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(6): 1-13 doi: 10.6052/0459-1879-23-052
Citation: Yu Yanyan, Rui Zhiliang, Ding Haiping. Parallel spectral element method for 3D local-site ground motion simulations of wave scattering problem. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(6): 1-13 doi: 10.6052/0459-1879-23-052

三维局部场地地震波散射问题谱元并行模拟方法

doi: 10.6052/0459-1879-23-052
基金项目: 国家自然科学基金资助项目(51808371)
详细信息
    通讯作者:

    于彦彦, 副教授, 主要研究方向为场地地震效应及近场波动数值模拟. Email: yyy2016@usts.edu.cn

PARALLEL SPECTRAL ELEMENT METHOD FOR 3D LOCAL-SITE GROUND MOTION SIMULATIONS OF WAVE SCATTERING PROBLEM

  • 摘要: 针对平面波入射下三维局部场地的波动散射问题, 利用解析法实现了考虑非均匀分布谱元节点的自由场计算, 将其作为谱元波动数值模拟的输入波场. 利用高阶谱元方法模拟内域节点的运动, 采用多次透射边界(MTF)模拟边界节点的运动, 同时基于消息传递接口(MPI)技术完成跨节点的并行计算, 进而实现基于谱元法的三维散射波动问题并行模拟, 最后基于典型数值算例验证了方法的精度及稳定性表现. 结果表明: 本方法对于不同偏振方向入射体波下的局部场地三维散射问题均具有较高的模拟精度. 直至3阶MTF, 在满足内域计算稳定的前提下, 取MTF人工波速接近介质剪切波速即可实现长持时稳定计算, 而无需其他消除高频振荡的附加措施. 取较小的消飘因子即可消除MTF的低频飘移失稳且基本不影响模拟精度. 本方法在平面波入射下区域性三维地震动数值模拟分析中具有较好的应用前景.

     

  • 图  1  三维平面波斜入射示意图

    Figure  1.  Schematic diagram of oblique incidence of three-dimensional plane wave

    图  2  不同体波入射时的振动方向规定

    Figure  2.  Regulation of vibration direction under different body wave incidence

    图  3  三维谱元节点及MTF计算点示意图

    Figure  3.  3 D spectral element node and MTF calculation point

    图  4  三维均匀半空间验证模型

    Figure  4.  3 D uniform half-space verification model

    图  5  入射波时程(a)及其频谱(b)

    Figure  5.  Incident wave (a) and its spectrum (b)

    图  6  不同平面波入射时3个观测点的位移时程与解析解对比

    Figure  6.  Comparison of displacement time histories and analytical solutions of three observation points under plane wave incidence

    6  不同平面波入射时3个观测点的位移时程与解析解对比 (续)

    6.  Comparison of displacement time histories and analytical solutions of three observation points under plane wave incidence (continued)

    图  7  三维半球形沉积盆地模型

    Figure  7.  Three-dimensional hemispherical sedimentary basin model

    图  8  SV和P波入射时剖面1的谱放大系数与Mossessian等[34]结果的对比

    Figure  8.  Comparison of spectral amplification coefficient of profile 1 with Mossessian et al. [34]

    8  SV和P波入射时剖面1的谱放大系数与Mossessian等[34]结果的对比 (续)

    8.  Comparison of spectral amplification coefficient of profile 1 with Mossessian et al.[34] (continued)

    图  9  SH波入射时剖面1、2的谱放大系数与Sanchez-Sesma等[35]结果的对比

    Figure  9.  Comparison of spectral amplification coefficient of profile 1 and 2 with Sanchez-Sesma et al. [35]

    图  10  垂直入射SV波时测线1沿x分量的位移时程

    Figure  10.  Displacement time history of line 1 in the x component under vertical incident SV wave

    图  11  2阶MTF, 施加不同小量时均匀半空间模型观测点B的位移时程

    Figure  11.  Displacement time history of point B of the homogeneous halfspace model when different γ values are applied (second-order MTF)

    图  12  3阶MTF, 施加不同小量时均匀半空间模型观测点B的位移时程

    Figure  12.  Displacement time history of point B of the homogeneous halfspace model when different γ values are applied (third-order MTF)

    图  13  半球形盆地模型, 施加不同小量时测点B的位移时程

    Figure  13.  Displacement time history of point B of the hemisperical basin model when different γ values are applied

    13  半球形盆地模型, 施加不同小量时测点B的位移时程 (续)

    13.  Displacement time history of point B of the hemisperical basin model when different γ values are applied (continued)

    图  14  长持时计算时

    Figure  14.  Displacement time history of observation point B of different model under long duration calculation

    图  15  不同MTF人工波速下均匀半空间模型观测点B的位移时程(SH波20°斜入射)

    Figure  15.  Displacement time histories of point B in the homogen- eous halfspace model when different apparent velocities used (SH wave inclined incident with an angle of 20°)

  • [1] Jayalakshmi S, Dhanya J, Raghukanth STG, et al. 3D seismic wave amplification in the Indo-Gangetic basin from spectral element simulations. Soil Dynamics and Earthquake Engineering, 2020, 129: 105923
    [2] 冯广军, 刘忠宪, 陈頔等. 近断层山体地形三维地震动放大效应谱元法模拟. 防灾减灾工程学报, 2020, 42(4): 778-787 (Feng Guangjun, Liu Zhongxian, Chen Di, et al. Analysis on the 3D ground motion amplification of mountain topography near the fault using SEM. Journal of Disaster Prevention and Mitigation Engineering, 2020, 42(4): 778-787 (in Chinese) doi: 10.13409/j.cnki.jdpme.20201218001
    [3] 万远春,于彦彦,丁海平等. 考虑不均匀地壳构造的四川盆地地震动模拟研究. 自然灾害学报, 2022, 31(2): 204-214 (Wan Yuanchun,Yu Yanyan, Ding Haiping, et al. Seismic simulation of Sichuan Basin considering inhomogeneous crustal structure. Journal of Natural Disasters, 2022, 31(2): 204-214 (in Chinese)
    [4] 孔曦骏, 邢浩洁,李鸿晶. 流固耦合地震波动问题的显式谱元模拟方法. 力学学报, 2022, 54(9): 2513-2528 (Kong Xijun, Xing Haojie, Li Hongjing. An explicit spectral-element approach to fluid-solid coupling problems in seismic wave propagation. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(9): 2513-2528 (in Chinese)
    [5] Boore DM, Larner KL, Aki K. Comparison of two indepent methods for the solution of wave-scattering problem: response of a sedimentary basin to vertically incident SH waves. Journal of Geophysical Research, 1971, 76(2): 558-569 doi: 10.1029/JB076i002p00558
    [6] Tong P, Komatitsch D, Tseng T, et al. A 3-D spectral-element and frequency-wave number hybrid method for high-resolution seismic array imaging. Geophysical Research Letters, 2014, 41: 7025-7034 doi: 10.1002/2014GL061644
    [7] Poursartip B, Fathi A, Kallivokas LF. Seismic wave amplification by topographic features: A parametric study. Soil Dynamics and Earthquake Engineering, 2017, 92: 503-527 doi: 10.1016/j.soildyn.2016.10.031
    [8] Poursartip B and Kallivokas LF. Model dimensionality effects on the amplification of seismic waves. Soil Dynamics and Earthquake Engineering, 2018, 113: 572-592 doi: 10.1016/j.soildyn.2018.06.012
    [9] 廖振鹏, 黄孔亮, 杨柏坡, 等. 暂态波透射边界. 中国科学A辑, 1984, 26(6): 50-56 (LIAO Zhenpeng, HUANG Kongliang, YANG Baipo. Transient wave transmission boundary. Chinese Science Series A, 1984, 26(6): 50-56 (in Chinese)
    [10] Huang J J. An incrementation-adaptive multi-transmitting boundary for seismic fracture analysis of concrete gravity dams. Soil Dynamics and Earthquake Engineering, 2018, 110: 145-158 doi: 10.1016/j.soildyn.2017.12.002
    [11] 陈少林, 孙杰, 柯小飞. 平面波输入下海水-海床-结构动力相互作用分析. 力学学报, 2020, 52(2): 578-590 (Chen Shaolin, Sun Jie, Ke Xiaofei. Analysis of water-seabed-structure dynamic interaction excited by plane waves. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(2): 578-590 (in Chinese)
    [12] 陈少林, 伍锐, 张娇等. 地形和土-结相互作用效应对三维跨峡谷桥梁地震响应的影响分析. 力学学报, 2021, 53(6): 1781-1794 (Chen Shaolin, Wu Rui, Zhang Jiao. et al Topography and soil-structure interaction effects on the seismic response of three-dimensional canyon- crossing bridge. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(6): 1781-1794 (in Chinese)
    [13] 丁海平, 朱重洋, 于彦彦. P, SV波斜入射下凹陷地形地震动分布特征. 振动与冲击, 2017, 36(12): 88-92+98 (Ding Haiping, Zhu Chongyang, Yu Yanyan. Characteristic of ground motions of a canyon topography under inclined P and SV waves. Journal of Vibration and Shock, 2017, 36(12): 88-92+98 (in Chinese)
    [14] 周国良, 李小军, 侯春林等. SV波入射下河谷地形地震动分布特征分析. 岩土力学, 2012, 33(4): 1161-1166 (Zhou Guoliang, Li Xiaojun, Hou Chunlin, et al. Characteristic analysis of ground motions of canyon topography under incident SV seismic waves. Rock and Soil Mechanics, 2012, 33(4): 1161-1166 (in Chinese)
    [15] 李平, 薄景山, 肖瑞杰等. 地震动河谷场地效应研究. 震灾防御术, 2018, 13(2): 331-341 (Li Ping, Bo Jingshan, Xiao Ruijie. et al The Study of Effect by the Valley Site on Ground Motion. Technology for Earthquake Disaster Prevention, 2018, 13(2): 331-341 (in Chinese)
    [16] 于彦彦,丁海平,刘启方. 透射边界与谱元法的结合及对波动模拟精度的改进. 振动与冲击, 2017, 36(2): 13-22 (Yu Yanyan, Ding Haiping, Liu Qifang. Integration of transmitting boundary and spectral-element method and improvement on the accuracy of wave motion simulation. Journal of Vibration and Shock, 2017, 36(2): 13-22 (in Chinese)
    [17] Xing HJ, Li XJ, Li HJ, et al. Spectral-element formulation of multi-transmitting formula and its accuracy and stability in 1 D and 2 D seismic wave modeling. Soil Dynamics and Earthquake Engineering, 2021, 140: 106218 doi: 10.1016/j.soildyn.2020.106218
    [18] Yu YY, Ding HP, Zhang XB. Simulations of ground motions under plane wave incidence in 2D complex site based on the spectral element method (SEM) and multi-transmitting formula (MTF): SH problem. Journal of Seismology, 2021, 25(3): 967-985
    [19] 刘晶波,王艳. 成层半空间出平面自由波场的一维化时域算法. 力学学报, 2006, 38(2): 219-225 (Liu Jingbo,Wang Yan. A 1-D time-domain method for 2-D wave motion in elastic layered half-space by antiplane wave oblique incidence. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(2): 219-225 (in Chinese)
    [20] 刘晶波,王艳. 成层介质中平面内自由波场的一维化时域算法. 工程力学, 2007, 24(7): 16-22 (Liu Jingbo,Wang Yan. A 1-D time-domain method for 2-D wave motion in elastic layered half-space by inplane wave oblique incidence. Engineering Mechanics, 2007, 24(7): 16-22 (in Chinese)
    [21] 赵密, 杜修力, 刘晶波等. P-SV波斜入射时成层半空间自由场的时域算法. 地震工程学报, 2013, 35(1): 84-90 (Zhao Mi, Du Xiuli, Liu Jingbo. Time-domain method for free field in layered half space under P-SV waves of oblique incidence. China Earthquake Engineering Journal, 2013, 35(1): 84-90 (in Chinese)
    [22] 高智能, 卓卫东, 谷音. SH波斜入射时有阻尼成层介质自由场的一维化时域算法. 振动与冲击, 2017, 36(16): 37-43+84 (Gao Zhineng, Zhuo Weidong, Gu Yin. A 1 D time-domain method for free field motion in layered media with damping under obliquely incident SH wave. Journal of Vibration and Shock, 2017, 36(16): 37-43+84 (in Chinese)
    [23] 谢志南, 王立刚, 章旭斌等. 斜入射出平面自由波场勒让德谱元时域模拟方法. 岩土力学, 2021, 42(12): 3467-3474+3484 (Xie Zhinan, Wang Ligang, Zhang Xubin, et al. Time-domain Legendre spectral element method for free-field wave simulation in layered media under obliquely incident plane wave. Rock and Soil Mechanics, 2021, 42(12): 3467-3474+3484 (in Chinese)
    [24] 孙纬宇,汪精河,严松宏等. SV波斜入射下河谷地形地震动分布特征分析. 振动与冲击, 2019, 38(20): 237-243+265 (Sun Weiyu, Wang Jinghe, Yan Songhong, et al. Characteristic analysis of ground motions of a canyon topography under obliquely incident SV waves. Journal of Vibration and Shock, 2019, 38(20): 237-243+265 (in Chinese)
    [25] 赵源,杜修力,李立云. 地震动入射角度对地下结构地震响应的影响. 防灾减灾工程学报, 2010, 30(6): 624-630 (Zhao Yuan, Du Xiuli, Li Liyun. The Effect of obliquely Incident Seismic Waves on Dynamic Responese of underground Structures. Journal of Disaster Prevention and Mitigation Engineering, 2010, 30(6): 624-630 (in Chinese)
    [26] 章小龙, 李小军, 陈国兴等. 黏弹性人工边界等效荷载计算的改进方法. 力学学报, 2016, 48(5): 1126-1135 (Zhang Xiaolong, Li Xiaojun, Chen Guoxing. et al An improved method of the calculation of equivalent nodal forces in viscous-elastic artificial boundary. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(5): 1126-1135 (in Chinese)
    [27] 杜修力, 黄景琦, 赵密等. SV波斜入射对岩体隧道洞身段地震响应影响研究. 岩土工程学报, 2014, 36(8): 1400-1406 (Du Xiuli, Huang Jingqi, Zhao Mi, et al. Effect of oblique incidence of SV waves on seismic response of portal sections of rock tunnels. Chinese Journal of Geotechnical Engineering, 2014, 36(8): 1400-1406 (in Chinese)
    [28] 王飞, 宋志强, 刘云贺等. SV波斜入射不同自由场构建方法下水电站地面厂房地震响应研究. 振动与冲击, 2021, 40(7): 9-18 (Wang Fei, Song Zhiqiang, Liu Yunhe, et al. Seismic response of ground powerhouse of hydropower station based on different free field construction methods with oblique incidence of SV wave. Journal of Vibration and Shock, 2021, 40(7): 9-18 (in Chinese)
    [29] Aki K, Richards PG. Quantitative Seismology. California: University Science Books, 2002.
    [30] 廖振鹏. 工程波动理论导论. 北京: 科学出版社, 2002

    Liao Zhen-peng. Introduction to Engineering Wave Theory. Beijing, Science Press. 2002. (in Chinese))
    [31] He CH, Wang JT, Zhang CH. Nonlinear spectral-element method for 3 D seismic-wave propagation. Bulletin of the Seismological Society of America, 2016, 106(3): 1074-1087 doi: 10.1785/0120150341
    [32] Komatitsch D, Vilotte JP. The spectral element method: an efficient tool to simulate the seismic response of 2 D and 3 D geological structures. Bulletin of the Seismological Society of America, 1998, 88(2): 368-392 doi: 10.1785/BSSA0880020368
    [33] Komatitsch D, Tromp J. Introduction to the spectral element method for three-dimensional seismic wave propagation. Geophysical Journal International, 1999, 139(3): 806-822 doi: 10.1046/j.1365-246x.1999.00967.x
    [34] Mossessian TK, Dravinski M. Amplification of elastic waves by a three dimensional valley. Part1: Steady state response. Earthquake Engineering & Structural Dynamics, 1990, 19(5): 667-680
    [35] Sánchez-Sesma FJ, Eduardo Pérez-Rocha L, Chávez-Pérez S. Diffraction of elastic waves by three-dimensional surface irregularities. Part II. Bulletin of the Seismological Society of America, 1989, 79(1): 101-112
    [36] 谢志南, 廖振鹏. 透射边界高频失稳机理及其消除方法——SH波动. 力学学报, 2021, 44(4): 745-752 (Xie Zhinan, Liao Zhenpeng. Mechanism of high frequency instability caused by transmitting boundary and method of its elimination—SH wave. Chinese Journal of Theoretical and Applied Mechanics, 2021, 44(4): 745-752 (in Chinese)
    [37] 章旭斌, 廖振鹏, 谢志南. 透射边界高频耦合失稳机理及稳定实现——SH波动. 地球物理学报, 2015, 58(10): 3639-3648 (Zhang Xubin, Liao Zhenpeng, Xie Zhinan. Mechanism of high frequency coupling instability and stable implementation for transmitting boundary -SH wave motion. Chinese Journal of Geophysics, 2015, 58(10): 3639-3648 (in Chinese)
    [38] 周正华, 廖振鹏. 消除多次透射公式飘移失稳的措施. 力学学报, 2001, 33(4): 550-554 (Zhou Zhenghua, Liao Zhenpeng. A measure for eliminating drift instability of the multi-transmitting formula. Acta Mechanica Sinica, 2001, 33(4): 550-554 (in Chinese)
    [39] 李小军, 廖振鹏. 时域局部透射边界的计算飘移失稳. 力学学报, 1996, 28(5): 116-121 (Li Xiaojun, Liao Zhenpeng. The drift instability of local transmitting boundary in time domain. Acta Mechanica Sinica, 1996, 28(5): 116-121 (in Chinese)
    [40] 李小军,杨宇. 透射边界稳定性控制措施探讨. 岩土工程学报, 2012, 34(4): 641-645 (Li Xiaojun,Yang Yu. Measures for stability control of transmitting boundary. Chinese Journal of Geotechnical Engineering, 2012, 34(4): 641-645 (in Chinese)
    [41] 孔曦骏,邢浩洁,李鸿晶等. 多次透射公式飘移问题的控制方法. 力学学报, 2021, 53(11): 3094-3109 (Kong Xijun, Xing Haojie, Li Hongjing, et al. An approach to controlling drift instability of multi-transmitting formula. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(11): 3094-3109 (in Chinese)
    [42] 章旭斌, 谢志南. 波动谱元模拟中透射边界稳定性分析. 工程力学, 2022, 39(10): 26-35 (Zhang Xubin, Xie Zhinan. Stability analysis of transmitting boundary in wave spectral element simulation. Engineering Mechanics, 2022, 39(10): 26-35 (in Chinese)
    [43] 章旭斌, 廖振鹏, 谢志南. 透射边界高频失稳机理及稳定实现——P-SV波动. 地球物理学报, 2021, 64(10): 3646-3656 (Zhang Xubin, Liao Zhenpeng, Xie Zhinan. Mechanism of high frequency instability and stable implementation for transimtting boundary--P-SV wave motion. Chinese Journal of Geophysics, 2021, 64(10): 3646-3656 (in Chinese)
    [44] Basabe D Jonás D, Sen MK. Grid dispersion and stability criteria of some common finite-element methods for acoustic and elastic wave equations. Geophysics, 2007, 72(6): 81-95
    [45] Pozrikidis C. Introduction to Finite and Spectral Element Methods using MATLAB, Second Edition. CRC Press, 2014
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  • 收稿日期:  2023-02-21
  • 录用日期:  2023-05-08
  • 网络出版日期:  2023-05-09

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