Structure-soil-structure coupling in seismic excitation and city effect
Structure-soil-structure coupling in seismic excitation and city effect
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DOI：
10.1016/j.ijengsci.2008.11.005
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发表时间：
2009-03
影响因子：
6.6
通讯作者：
M. Ghergu;I. Ionescu
中科院分区：
文献类型：
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作者：
M. Ghergu;I. Ionescu
通过结构-土-结构全耦合模型研究城市建筑间的相互作用。主要问题是强调建筑物在地震激励下的集体行为（城市效应），并计算城市的整体响应。考虑弹性半空间的反平面剪切，其边界部分由建筑物的刚性基础构成。将建筑物建模为两个集中质量的弹性弹簧。相关的数学问题是一个偏微分方程与一个常微分方程通过一类特殊的边界条件耦合。为了关注结构-土-结构耦合（城市频率），将相关的频谱问题重写为包含对称矩阵特征值的非线性标量方程。提出了一种涉及积分法的数值方法，对城市效应进行数值研究。主特征值对建筑物宽度与城市宽度之比的渐近极限指出了城市的主频率。这个值并不取决于组成城市的建筑数量，而是取决于每个城市的建筑属性。通过第一特征函数的形状强调了建筑物在地震激励下的集体行为。最后给出了一个数值例子，说明了其中一栋建筑物顶部的撞击在城市中的传播（9/11类型的事件）。
We study the interaction between the buildings of a city through a fully coupling structure–soil–structure model. The main issues are to emphasize the collective behavior of the buildings during a seismic excitation (city effect) and to compute the global response of the city. The anti-plane shearing of an elastic half space with a part of its boundary formed by the rigid foundations of the buildings is considered. The buildings are modeled as elastic springs which relate two concentrated masses. The associated mathematical problem is a partial differential equation coupled with an ordinary differential equation through a special class of boundary conditions. To focus on the coupling structure–soil–structure (city frequencies) the associated spectral problem is rewritten in terms of a nonlinear scalar equation involving the eigenvalues of a symmetric matrix. A numerical approach, involving an integral method, is proposed to numerically investigate the city effect. The asymptotic limit of the principal eigenvalue with respect to the ratio between the width of the building and the width of the city points out the principal frequency of the city. This value does not depended on the number of buildings which compose the city but it is specific to each city via the specific properties of the buildings. The collective behavior of the buildings during a seismic excitation is emphasized through the shape of the first eigenfunction. Finally a numerical illustration of a the propagation in the city of the impact on the top of one of the buildings (a 9/11 type event) is presented.