端承桩‑土动力相互作用的频域子结构分析方法∗

A Frequency Domain Substructure Analysis Model for Dynamic Interaction between End Bearing Piles and Soil

摘要:

对动力荷载作用下桩‐土相互作用问题，将桩和结构等效为一维杆、土体假定为黏弹性介质，提出了一种桩‐土动力相互作用的频域子结构分析方法。首先，基于连续介质力学方法，通过引入势函数对土体振动方程进行解耦， 根据边界条件推导桩周土体位移和应力的表达式，并结合桩‐土耦合连续性条件推导出均质土体中水平抗力表达式。之后，基于有限元方法将桩和结构采用梁单元离散，进一步通过有限元离散得到土体水平抗力与桩位移之间的动力刚度矩阵，并将其与桩和结构的动力刚度矩阵耦合形成耦合有限元方程，从而建立了结构‐桩‐土体系动力响应的频域子结构模型。最后，通过 Abaqus 软件中的三维有限元模型对该方法进行了验证；利用提出的模型分析了土体动力刚度、土体阻尼和土体模型等对结构动力响应的影响，并分析了地震动一致和非一致激励对结构地震响应的影响。

Abstract:

In order to solve the problem of pile-soil interaction under dynamic loads， a frequency domain substructure analysis method was proposed based on the assumption that the pile and structure were equivalent to one-dimensional rods and the soil was assumed to be a viscoelastic medium. Firstly， based on the continuum mechanics method， the soil governing equation was decoupled by introducing the potential function. The expressions of displacement and stress of the soil around the pile were derived from the boundary conditions， and the expressions of horizontal resistance in the homogeneous soil were derived from the pile-soil coupling continuity conditions. Then， the pile and structure were discretized using beam elements and a dynamic-stiffness matrix between the soil resistance and the structural displacement was obtained through finite element discretization. The dynamic-stiffness matrix was further combined with the finite element model of the pile and the structure to form the coupled finite element equation. Thus， the frequency domain substructure model for the dynamic response of the structure-pile-soil system was established. Finally， the method was verified by the threedimensional finite element model in ABAQUS software. The proposed model was used to analyze the effects of soil dynamic stiffness， soil damping and soil model on the dynamic response of the structure， and the effects of uniform and non-uniform ground motion excitation on the seismic response of the structure.