Vertical and rocking motions of a flexible strip foundation placed on a layered transversely isotropic poroelastic half‐space

Abstract

An analytical method for vertical and rocking motions of a flexible strip foundation on a layered transversely isotropic proelastic half‐space is presented in this paper. The dynamic soil‐structure interactions are simultaneously restricted by the boundary conditions for the underlying media and the flexible strip foundation. For the underlying media, the plain strain dynamic responses of the layered poroelastic half‐space are obtained by the extended precise integration method. For the strip foundation, the deflection due to the vertical motion and the rocking motion are obtained by analytically solving the dynamic equilibrium of the thin plate. Then, the mixed boundary conditions for the dynamic interactions are degenerated into a set of linear equations by assuming Bessel series expansions for the contact stress. The series solutions for these linear equations can be utilized to yield the compliance functions and the dynamic responses for the underlying media. Finally, a calculation program is compiled to verify the presented theory and discuss the effects of the stratifications, the dynamic permeability, and the foundation flexibility.

Vertical vibration of a rigid disc over a transversely isotropic and layered poroelastic half-space

“…In the above literatures, the soil is assumed to be homogeneous and isotropic medium. However, soil subgrade commonly takes on a layered structure and its mechanical property shows anisotropy in nature [7].…”

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

“…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 . 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 16–17 . Accordingly, solving the forced vibration of rigid disk in the time and frequency domain is the main concern of the present work.…”

“…[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. [16][17] Accordingly, solving the forced vibration of rigid disk in the time and frequency domain is the main concern of the present work.…”