A Simple Model for Vertical Dynamic Interactions among a Group of Strip Footings Rested on Homogeneous Half-Space

Jue Wang,Ding Zhou

doi:10.1155/2018/7382392

Abstract

A simple model for vertical dynamic interactions among a group of strip footings rested on half-space is presented in this paper. An analytical method is presented to obtain the contact pressures and the impedance matrix for a group of surface strip footings. In order to conveniently solve the unknown contact pressures between the soil and footings, the soil-footing interfaces are discretized into a series of strip elements. The Green function for each element under uniform harmonic force is derived and calculated by the piecewise integration and Cauchy principal value integral. The influences of footing and soil parameters on contact pressures and vertical dynamic impedances of footing groups are discussed in detail. The SSSI effect between adjacent footings increases with the decrease of the distance ratioS/L. For three footings in a group, the middle footing experiences greater cross-interactional effect than the side ones. The present method has high accuracy, which is not only simple but also suitable for the high-frequency analysis.

Highlights

General Formulation of SSSI ProblemFor the strip footings such as track footings, dams, or building footings with high ratio of length to width, it is reasonable to consider the problem as a plane strain case with a coordinate system (x-z) where the z-axis is normal to the space surface
In this paper, the Green function of uniform harmonic vertical force is derived and numerically calculated by the piecewise integrations and the Cauchy principal value integral
Contact pressures and the impedance matrix of multiple strip footings considering the SSSI effect are obtained by combining the Green function with the element discretization technique

Summary

General Formulation of SSSI Problem

For the strip footings such as track footings, dams, or building footings with high ratio of length to width, it is reasonable to consider the problem as a plane strain case with a coordinate system (x-z) where the z-axis is normal to the space surface. Consider a group of strip footings with different width Lm Where Hm represents the vertical displacement of the mth footing. E impedance Rmn in matrix [R] is a complex number in the matrix, which describes the coupling interaction effect between the mth fo√ot i ng and the nth footing. Based on the above formulations, an equivalent simplified model as shown in Figure 2 visually describes the dynamic interaction among strip footings in a group through the soil. For the simplification in analysis, the interface between the supporting medium and each footing is divided into a number of surface strip elements.

Green Function for Elastic Half-Space

Impedance Matrix of a Strip Footing Group

Convergence and Comparison Studies

Numerical Examples and Discussions

Findings

Conclusions