Abstract This paper presents an approximate analytical solution for the vertical dynamic impedance and shaft resistance of rectangular closed diaphragm walls (RCDWs) embedded in a homogeneous soil medium and resting on rock base. The vertical continuous displacement model for the steady-state response of RCDWs is proposed to ensure proper RCDWs-soil contact and satisfy the boundary condition of soil at infinite horizontal distance. The soil horizontal displacement is neglected and the effect is indirectly taken into account by the modification of soil modulus. The functional of system potential and kinetic energies is established via the soil and RCDWs displacement functions. The governing equations of the system and the relevant conditions are obtained and the vertical shaft resistance of RCDWs is established by employing Hamilton’s variational principle for RCDWs-soil system and thin layer element, respectively. Some representative numerical examples are presented to portray the influences of soil core ratio, height–width ratio, diaphragm wall-soil stiffness ratio, and aspect ratio of RCDWs cross sections on the dynamic impedances and stiffness of the shaft resistance.

中文翻译：

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轴向受力端承矩形封闭连续墙的动力响应

摘要 本文提出了嵌入在均质土壤介质中并搁置在岩基上的矩形封闭连续墙（RCDWs）的垂直动态阻抗和轴阻力的近似解析解。提出了RCDWs稳态响应的垂直连续位移模型，以确保RCDWs与土壤的适当接触并满足无限水平距离土壤的边界条件。忽略土壤水平位移，通过修改土壤模量间接考虑影响。系统势能函数和动能函数是通过土壤和 RCDWs 位移函数建立的。分别对RCDWs-土壤系统和薄层单元应用Hamilton变分原理，得到了该系统的控制方程和相关条件，并分别建立了RCDWs的竖井阻力。给出了一些代表性的数值例子来描述土芯比、高宽比、连续墙土刚度比和 RCDW 横截面的纵横比对轴阻力的动态阻抗和刚度的影响。