基于等效零时刻点的水平层状场地黏弹性边界方法研究

贾忠明; 赵伯明; 王子珺; 赵天次; 冯俊

doi:10.11779/CJGE202212020

基于等效零时刻点的水平层状场地黏弹性边界方法研究 English Version

贾忠明^{1, 2,},
赵伯明^{1, 2, ,},
王子珺^{1, 2},
赵天次^{1, 2},
冯俊^{1, 2}

1.
北京交通大学城市地下工程教育部重点实验室，北京 100044
2.
北京交通大学土木建筑工程学院，北京 100044

基金项目:

国家自然科学基金项目 51778046

国家自然科学基金项目 51808035

国家自然科学基金重点项目 U1434210

详细信息

作者简介:
贾忠明(1996—)，男，博士研究生，主要从事结构抗震方面的研究。E-mail：zhmjia@bjtu.edu.cn

通讯作者:
赵伯明, E-mail: bmzhao@bjtu.edu.cn

中图分类号: TU435
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出版历程
- 收稿日期: 2021-10-25
- 网络出版日期: 2022-12-13
- 刊出日期: 2022-11-30

Viscoelastic boundary method of horizontal layered site based on equivalent zero-time point

JIA Zhong-ming^{1, 2,},
ZHAO Bo-ming^{1, 2, ,},
WANG Zi-jun^{1, 2},
ZHAO Tian-ci^{1, 2},
FENG Jun^{1, 2}

1.
Key Laboratory of Urban Underground Engineering, Ministry of Education, Beijing Jiaotong University, Beijing 100044, China
2.
School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China

摘要

摘要: 针对黏弹性边界下水平层状场地地震动输入中的时间延迟计算问题，提出了水平层状场地的等效零时刻点迭代时间延迟计算方法，并依托斯涅尔方程及地震波在分层界面上的连续性条件推导了人工边界上等效节点力的计算公式，得出了黏弹性边界下的水平层状场地斜入射地震动输入方法。建立两层地层三维有限元计算模型，进行动力响应分析，并将计算结果与理论值进行对比，验证了方法的有效性和实用性。应用方法进行等效节点力计算的过程中，可根据所求目标地震波的具体信息及其所在地层的具体条件直接求解，无需对所求地震波的全部来源依次进行分析，使得公式更为统一，在简化计算的同时保证计算精度及准确性，并拓展了黏弹性边界理论在水平层状场地斜入射地震动上的应用。
- 地震波斜入射 /
- 水平层状场地 /
- 黏弹性边界 /
- 时间延迟
Abstract: An equivalent zero-time point iterative time delay method for horizontal layered strata is proposed to solve the problem of time delay calculation in ground motion input of layered strata under viscoelastic boundary. It assignes an equivalent zero-time plane to each generated seismic wave. An appropriate point on the plane can be selected as the equivalent zero-time point, and the time delay can be calculated. Based on the Snell equation and the continuity condition of seismic waves at the layered interface, the formula for calculating the equivalent nodal force of the artificial boundary is derived, and the viscoelastic boundary input method for oblique incidence ground motion of the layered strata under the viscoelastic boundary is deduced. The finite element model for a double-layer horizontal layered stratum is established for dynamic response analysis. The calculated results are compared with the theoretical values. The deviation between them is relatively small, which shows the effectiveness and practicability of the method. By using the method it can be solved directly according to the specific information of the seismic wave and the stratum, without analyzing all the sources of the desired seismic wave in turn, which makes the formula unified. It is a way to simplify the calculation without affecting the accuracy. Meanwhile, it can extend the application of the viscoelastic boundary to the oblique incidence ground motion of layered stratum.
- oblique incidence of seismic wave /
- layered stratum /
- viscoelastic boundary /
- time delay

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图 1 反射波时间延迟计算示意图

Figure 1. Time delay calculation of reflected waves

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图 2 透射波时间延迟计算示意图

Figure 2. Time delay calculation of transmission waves

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图 3 三维模型时间延迟计算示意图

Figure 3. Time delay calculation of 3D model

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图 4 计算流程图

Figure 4. Flow chart of calculation

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图 5 计算模型示意图

Figure 5. Computational model

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图 6 输入位移时程曲线

Figure 6. Time histories of input displacement

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图 7 MD5计算结果

Figure 7. Results of MD5

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图 8 地表中点处的位移时程

Figure 8. Time histories of displacement at midpoint of surface

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图 9 不同时刻位移场云图

Figure 9. Cloud diagram of displacement field at different time

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