Horizontal vibration of a rigid strip footing on viscoelastic half‐space

Abstract

This paper presented an analytical method for determining the response of a rigid strip foundation resting on the surface of a viscoelastic half‐space to horizontal dynamic loads, and the associated transient soil displacements resulting from the vibration of the footing. This mixed boundary value problem was solved by means of Jacobi orthogonal polynomials, a more efficient method compared to transforming the dual integral equations resulting from the boundary conditions to Fredholm integral equations. Displacements and stresses of the soil‐footing system were accordingly obtained by applying the inverse Fourier transform. Finally, we used the proposed solution to investigate the effects of material damping and Poisson's ratio of soil on the dynamic response of the strip footing, and the resulting soil displacements.

An analytical solution for the horizontal vibration behavior of a cylindrical rigid foundation in poroelastic soil layer

“…The interactions of structure foundations with their surrounding soil play an important role in many practical applications, such as pile dynamics problem, design of bridge piers and sub‐structural method 1–3 . However, most of research objects are aimed at the flexible rod or beam subjected to harmonic external force 4–7 .…”

“…The interactions of structure foundations with their surrounding soil play an important role in many practical applications, such as pile dynamics problem, design of bridge piers and sub-structural method. [1][2][3] However, most of research objects are aimed at the flexible rod or beam subjected to harmonic external force. [4][5][6][7] Due to the importance of large size cylindrical foundations (mainly refer to the anchorage open caisson and large-span bridges), the dynamic characteristics of the embedded foundation should also be paid attention.…”

Frequency‐dependent response of a rigid disk on a transversely isotropic soil layer subjected to horizontal motion

“…In the context of applied mathematics and engineering mechanics, the foregoing category on this complicated topic is mainly relevant to the study of load‐displacement transfer relationship, failure modes and stress concentration effect associated with natural soil 8–10 . For instance, the soil response to various loading forms has been systematically studied by some investigators, where the displacements, strains and stresses expressions have been presented by use of elasticity theory and Green's functions 11–12 . On the other hand, the force acting the surface of elastic soil should be recognized as time‐dependent rather than static, such as moving traffic, earthquake and machine vibration, etc 13–15 .…”

“…[8][9][10] For instance, the soil response to various loading forms has been systematically studied by some investigators, where the displacements, strains and stresses expressions have been presented by use of elasticity theory and Green's functions. [11][12] On the other hand, the force acting the surface of elastic soil should be recognized as time-dependent rather than static, such as moving traffic, earthquake and machine vibration, etc. [13][14][15] Similar assumptions have been also considered when investigating the corresponding soil-structure interaction problems for steady-state case, and this kind is a classical example for understanding the dynamic behavior of foundations.…”