Dynamic Response of a Rigid Footing Bonded to an Elastic Half Space

Abstract

The problem of determining the response of a rigid strip footing bonded to an elastic half plane is considered. The footing is subjected to vertical, shear, and moment forces with harmonic time-dependence; the bond to the half plane is complete. Using the theory of singular integral equations the problem is reduced to the numerical solution of two Fredholm integral equations. The results presented permit the evaluation of approximate footing models where assumptions are made about the interface conditions.

Simplified Model for Coupled Vibration of Adjacent Strip Footings

“…Luco and Westmann [4] solved the forced oscillations of a massless rigid strip footing with width L on half-space by using the mixed boundary-value approach. There are considerable difficulties in solving the integral equations numerically or analytically, therefore only a special case for Poisson's ratio v=0.5 was studied rigorously.…”

“…Warburton et al [3] provided an approximate method based on the relaxed contact assumption to study the dynamic response of two rigid circular footings on soil medium. More rigorous solutions for the impedance of footing can be obtained as a mixed boundary-value problem formulated in terms of dual integral equations [4,5]. However, as the solutions of dual integral equations cannot be expressed by elementary functions, there are limitations to obtain the contact stress functions for a DCI problem.…”

Impedance Functions of Adjacent Strip Foundations

“…Luco and Westmann (1972) studied the coupled horizontal rocking response of a surface strip foundation under the assumption of welded soil contact. Such response arises when the superstructure is subjected to lateral forces (e.g.…”

Finite Element Modeling of Shallow Foundations on Nonlinear Soil Medium

“…Its dynamic stiffness can be obtained analytically [2,3]. Under a harmonic motion, the reacting forces are related to displacements by the general form shown below: Finite element method is used in this study to conduct the dynamic analyses of strip foundation under harmonic displacement excitation in vertical and horizontal directions respectively.…”

“…strip foundation on elastic half-space [2,3] and on visco-elastic soil layer [4,5], circular foundation on elastic halfspace [6,7] and on visco-elastic half-space [8], rectangular foundation on elastic halfspace or layered medium [9,10], and cylindrical and rectangular embedded foundations [11]. Gazetas [12] and Mylonakis et al [13] compiled an extensive set of graphs and tables for dynamic stiffness of foundations with a variety of geometries and linear soil conditions.…”