﻿ 地震和波浪共同作用下斜坡式防波堤的动力响应分析
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 应用科技  2019, Vol. 46 Issue (2): 19-24  DOI: 10.11991/yykj.201807009 0

### 引用本文

ZHANG Yunce, ZHANG Guixin, MAO Jize, et al. Dynamic response analysis for mound breakwaters under the action of earthquake and wave loads[J]. Applied Science and Technology, 2019, 46(2), 19-24. DOI: 10.11991/yykj.201807009.

### 文章历史

1. 哈尔滨工程大学 航天与建筑工程学院，黑龙江 哈尔滨 150001;
2. 中国地震局工程力学研究所，黑龙江 哈尔滨 150080

Dynamic response analysis for mound breakwaters under the action of earthquake and wave loads
ZHANG Yunce1, ZHANG Guixin2, MAO Jize1, GUO Qingyong1, LIU Zongmin1
1. College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China;
2. Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China
Abstract: For mound breakwaters, the structural analysis of dynamic response is the main method to study the seismic performance of structures. Since the mound breakwater is affected by waves during the earthquake, the seismic response analysis of the mound breakwater needs to consider the interaction of earthquake and waves. In this paper, the corresponding finite element model is established by using ABAQUS software, and the model is verified by comparison. The dynamic response of the mound breakwater under the combined action of earthquake and the wave is simulated. The results show that the interaction between earthquake and the wave has a significant effect on the vertical residual deformation of the mound breakwater structure compared with the individual earthquake action. Waves will have different effects on the vertical residual deformation of the mound breakwater structure.
Keywords: earthquake action    wave action    mound breakwater    dynamic response    finite element analysis    numerical simulation    constitutive model    Rayleigh damping

1 基本方程

 $\begin{array}{l} { M}{{\ddot u}_s}\left( t \right) + { C}{{\dot u}_s}\left( t \right) + { K}{u_s}\left( t \right) = - { M}{{\ddot u}_g}\left( t \right) + p + P \end{array}$

 $\begin{array}{l} {p_{x = 0}}\left( {y,t} \right) = \displaystyle\frac{{4{{\ddot u}_0}\rho }}{{\text π} }\cos \omega t\sum\limits_{n = 1,3,5, \cdots }^\infty {\frac{1}{{\sqrt {\lambda _n^2 - \displaystyle\frac{{{\omega ^2}}}{{{c^2}}}} }}\sin {\lambda _n}y} \end{array}$

 \left\{ {\begin{aligned} & {{P_{{h_1}}} = \alpha \rho g{h_1}}\\ & {{h_1} = {h_w}\left( {1 - \frac{Z}{{{R_u}}}} \right)}\\ & {\alpha = 2.9{{\left( {\frac{{{R_u}}}{{{H_u}}}\cos \;\; \beta } \right)}^2}} \end{aligned}} \right.

 ${u_q} - {u_s} = 0 \;\; \left( {{\text{在}}{S_{qs}}{\text{上}}} \right)$

 ${T_q} + {T_s} = 0 \;\; \left( {{\text{在}}{S_{qs}}{\text{上}}} \right)$

2 斜坡式防波堤的有限元模型 2.1 参数及边界的选择

2.2 有限元建模

2.3 本构模型及阻尼的选择

 ${ C} = \alpha { M} + \beta { K}$

 $\alpha = \frac{{2{\omega _{\text{i}}}{\omega _j}({\xi _i}{\omega _j} - {\xi _j}{\omega _i})}}{{\omega _j^2 - \omega _i^2}}$
 $\beta = \frac{{2({\xi _j}{\omega _j} - {\xi _i}{\omega _i})}}{{\omega _j^2 - \omega _i^2}}$

3 斜坡式防波堤的动力响应分析 3.1 荷载

 Download: 图 4 $y = h$ 时，动水压力时程曲线
3.2 模型的验证和对比

3.3 地震和波浪共同作用下斜坡式防波堤的动力响应

3.4 地震和波浪共同作用下斜坡式防波堤的竖向残余变形

4 结论

1）在地震和波浪共同作用下，斜坡式防波堤残余变形机理十分复杂。向海侧坡脚在地震和波浪共同作用下的竖向残余变形大于单独地震作用下的竖向残余变形；而前后挡浪墙和背海侧坡脚在地震和波浪共同作用下的竖向残余变形均小于单独地震作用下的竖向残余变形。由此可见，地震发生时波浪的存在将对斜坡式防波堤结构竖向残余变形造成不同程度的影响。

2）波浪荷载分别按总波浪力和规则波的方式加载，但从竖向残余变形的仿真结果来看，两者的差别很小。

3）地震和波浪共同作用与单独地震作用相比，斜坡式防波堤结构的水平残余变形无明显差异，所以水平方向的残余变形只考虑地震荷载即可。

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