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

Abstract

The large size embedded foundation is widely used in the engineering, but the finite thickness of soil layer underlying this foundation is usually neglected in design, which leads to the non‐negligible error of calculation. By virtue of Biot's elastodynamic theory, this paper proposes a simple method to discuss the horizontal dynamic response of the cylindrical rigid foundation partially embedded in a poroelastic soil layer. First, based on the Novak plane strain model, the shaft resistance from the surrounding soil is simulated and solved. Second, the foundation end soil is assumed as a continuous medium of finite thickness, whose initial mechanism is derived from the dynamic interaction between the rigid disk and soil. Finally, the horizontal dynamic response factor is calculated by adopting newton's second law. Several cases are set to verify the rationality of the presented solution and to develop the analysis of key parameters. The numerical results suggest that the soil layer thickness has a significant influence on the dynamic vibration of the embedded foundation, and its effect is consistent with that of poroelastic half‐space when the thickness exceeds certain value.

Horizontal motions of a rigid disk placed on a poroelastic soil layer of finite thickness

“…According to the study of Kassir et al, 36 Pak and Saphores, 16 Yang et al, 37 and Zheng et al, 31 the horizontal dynamic impedance coefficient for the disk can be defined as the reciprocal value to C hh (i.e., the ratio of the contact stress on the surface of poroelastic subsoil to the horizontal displacement), and we obtain…”

“…According to the study of Kassir et al., 36 Pak and Saphores, 16 Yang et al., 37 and Zheng et al., 31 the horizontal dynamic impedance coefficient for the disk can be defined as the reciprocal value to C hh (i.e., the ratio of the contact stress on the surface of poroelastic subsoil to the horizontal displacement), and we obtain $$$$\begin{equation}{K}_{hh} = \frac{{2 - {\nu }_s}}{{ - {l}_1}}\int_{0}^{1}{{{\Phi }_1\left( t \right)}}dt = {k}_{hh} + {\rm{i}}{a}_0{c}_{hh}\end{equation}$$$$where, k hh is the stiffness coefficient that represented the ability of the rigid disk to resist deformation in the horizontal direction; c hh is the damping coefficient that reflected the dissipated energy.…”

The poroelastic layer with an axisymmetric cylindrical hole under different types of loading

“…The acoustic response of a rigidly backed poroelastic layer with a periodic set of elastic cylindrical inclusions embedded was studied in [17] by a semi-analytical approach, based on Biot's theory to account for the deformation of the skeleton, coupling mode matching technique, Bloch wave representation, and multiple scattering theory. A simple method to discuss the horizontal dynamic response of the cylindrical rigid foundation partially embedded in a poroelastic soil layer was proposed in [18] by virtue of Biot's elastodynamic model. It was based on the Novak plane strain model, the assumption of foundation end soil as a continuous medium of finite thickness, and adopting Newton's second law.…”

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

“…Wave propagation in soil due to external loads of complex environment has been a subject of great interests to many researchers and engineers in civil engineering, geophysics and allied fields over the last century. [1][2][3] In recognition that the circular geometry is most common in the foundation design, the interaction of a forced rigid disk with an elastic isotropic half-space or soil layer of finite thickness in both dynamic and static cases has attracted considerable attention, and their corresponding theories have also been useful as the basis for the analyses of piles, gravity foundations and anchor cables. [4][5][6][7] 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.…”