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流固耦合地震波动问题的显式谱元模拟方法

孔曦骏 邢浩洁 李鸿晶

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(7): 1-16 doi: 10.6052/0459-1879-22-068
引用本文: 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(7): 1-16 doi: 10.6052/0459-1879-22-068
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(7): 1-16 doi: 10.6052/0459-1879-22-068
Citation: 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(7): 1-16 doi: 10.6052/0459-1879-22-068

流固耦合地震波动问题的显式谱元模拟方法

doi: 10.6052/0459-1879-22-068
基金项目: 国家自然科学基金委员会-中国地震局地震科学联合基金项目(U2039208)和中国地震局地球物理研究所基本科研业务费专项(DQJB22B22)资助
详细信息
    作者简介:

    李鸿晶, 教授, 主要研究方向: 地震工程. E-mail: hjing@njtech.edu.cn

  • 中图分类号: TU435

AN EXPLICIT SPECTRAL-ELEMENT APPROACH TO FLUID-SOLID COUPLING PROBLEMS IN SEISMIC WAVE PROPAGATION

  • 摘要: 流固耦合地震波动问题主要研究由流体和固体构成的复杂系统中地震波传播特性及其规律. 传统模拟方法中一般以声波方程、弹性波方程的数值解分别描述理想流体和弹性固体中的波动, 并实时地处理两种不同性质介质之间的相互耦合作用, 数值格式复杂且限制数值模拟精度与计算效率. 本文采用谱元法结合多次透射公式人工边界条件实现了一种流固耦合地震波动问题的高阶显式数值计算方法. 该方法利用了流固耦合问题统一计算框架,可将饱和多孔介质的Biot波动方程分别退化为理想流体的声波方程和弹性固体的弹性波方程. 通过P波垂直入射的水平成层理想流体-饱和多孔介质-弹性固体场地模型、P波斜入射的不规则层状界面以及任意形状界面的理想流体-饱和多孔介质-弹性固体场地模型等三个算例, 与传递函数法解析解以及集中质量有限元法计算结果进行对比分析, 证明了本文方法的正确性与有效性. 数值模拟结果表明, 本文方法相较传统有限元法可以少得多的节点数量获得更高的数值精度, 并且在较宽的频率范围内都能可靠地模拟出流固耦合系统的动力响应, 充分体现出本文方法兼顾高精度、计算效率和复杂场地建模灵活的特点.

     

  • 图  1  流固耦合地震波动问题示意图

    Figure  1.  Schematic diagram of seismic wave motion problem in a fluid-poroelastic-solid model

    图  2  流固耦合问题的不同介质交界面

    Figure  2.  Different interfaces in the fluid-poroelastic-solid problem

    图  3  界面连续条件的谱元离散

    Figure  3.  Spectral-element discretization of the continuous condition on the interface

    图  4  多次透射公式人工边界条件与地震动输入

    Figure  4.  Artificial boundary condition and seismic wave input based upon multi-transmitting formula

    图  5  输入样条脉冲波

    Figure  5.  The input wave of a spline impulse

    图  6  二维水平成层场地模型

    Figure  6.  Two-dimensiona model of horizontal layered site

    图  7  各测点的竖向位移

    Figure  7.  Vertical displacement at measuring points

    图  8  不同方案情况下C点的位移谱比

    Figure  8.  Spectral ratio of displacement at point C with different scheme

    图  9  不规则层状界面模型

    Figure  9.  Irregular layered interface model

    图  10  各测点的位移

    Figure  10.  Displacement at measuring points

    图  11  各测点的法向位移

    Figure  11.  Normal displacement at measuring points

    图  12  土体表面的位移幅值

    Figure  12.  Surface displacement amplitude of soil

    图  13  任意形状界面模型

    Figure  13.  Arbitrary shape interface model

    图  14  各测点的法向位移

    Figure  14.  Normal displacement at measuring points

    图  15  饱和多孔介质表面的位移幅值

    Figure  15.  Surface displacement amplitude of saturated porous medium

    表  1  透射边界(MTF)谱元离散格式中插值点的局部坐标

    Table  1.   Local coordinates of the interpolation points in the spectral-element formulation of multi-transmitting formula

    Number
    (ngllξ)
    Local coordinates
    (sk (k = 0, …, ngllξ−1))
    20, 2
    30, 1, 2
    40, 0.55278, 1.44721, 2
    50, 0.34535, 1, 1.65465, 2
    60, 0.23494, 0.71477, 1.28523, 1.76506, 2
    下载: 导出CSV

    表  2  介质参数表

    Table  2.   Parameters of medium

    Mediaβμ0ρs/kg·m−3ρw/kg·m−3νμ/MPaEw/GPaM/GPaαk0/m·s−1
    ideal fluid10010000.4902.252.2511
    saturated soil0.260.001200010000.4983.22.254.780.69710−7
    bedrock00250000.24800-00
    $ \lambda=2 \mu i f(1-2 v) $
    下载: 导出CSV
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  • 收稿日期:  2022-02-13
  • 录用日期:  2022-04-07
  • 网络出版日期:  2022-04-07

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