Vertical vibrations of rigid foundations of arbitrary shape in a multi-layered poroelastic medium

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

“…For the plane strain problem in a Cartesian coordinate system, the constitutive equations for the transversely isotropic poroelastic medium can be listed as bellow 13 $$\begin{equation}{\sigma }_x = {c}_{11}\frac{{\partial {u}_x}}{{\partial x}} + {c}_{13}\frac{{\partial {u}_z}}{{\partial z}} - {\alpha }_hp\end{equation}$$ $$\begin{equation}{\sigma }_z = {c}_{13}\frac{{\partial {u}_x}}{{\partial x}} + {c}_{33}\frac{{\partial {u}_z}}{{\partial z}} - {\alpha }_vp\end{equation}$$ $$\begin{equation} {\tau}_{\textit{xz}}={c}_{44}\left(\frac{\partial {u}_{x}}{\partial z}+\frac{\partial {u}_{z}}{\partial x}\right) \end{equation}$$ $$\begin{equation}p = - {M}_f \left({\alpha }_h\frac{{\partial {u}_x}}{{\partial x}} + {\alpha }_v\frac{{\partial {u}_z}}{{\partial z}} + \frac{{\partial {w}_x}}{{\partial x}} + \frac{{\partial {w}_z}}{{\partial z}}\right)\end{equation}$$Where …”

“…For the plane strain problem in a Cartesian coordinate system, the constitutive equations for the transversely isotropic poroelastic medium can be listed as bellow 13 𝜎 𝑥 = 𝑐 44 . Also, the expression for fluid discharge 𝑄 𝑓 is defined 13 :…”

“…Many existing studies on dynamic soil‐structure interaction (SSI) problem are mainly restricted to the investigations on the rigid base resting on the surface of a half‐space, 8–16 i.e., the deformation mode of foundation is considered as a rigid body. This assumption largely relies on the fact that the elastic modulus of the real foundation is usually larger than that of underlying media.…”

“…With the rapid development of society and population in coastal cities, more considerations in seismic design for modern constructions should be taken into account, and the need of urban resilience and off-shore industries impel researchers to reasonably consider the foundation flexibility and complex media. Many existing studies on dynamic soil-structure interaction (SSI) problem are mainly restricted to the investigations on the rigid base resting on the surface of a half-space, [8][9][10][11][12][13][14][15][16] i.e., the deformation mode of foundation is considered as a rigid body. This assumption largely relies on the fact that the elastic modulus of the real foundation is usually larger than that of underlying media.…”

Dynamic interaction between elastic plate and transversely isotropic poroelastic medium

“…Thereafter, Biot's poroelastodynamics theory has been employed by many researchers to study dynamic interaction problems between foundations and fluidsaturated porous media due to its close relevance to various practical problems in civil engineering. For example, the dynamic responses of rigid foundations under vertical loading were investigated by Kassir and Xu [2] for rigid strips, Jin and Liu [3], Zeng and Rajapakse [4] and Ai et al [5] for rigid circular plates, and Halpern and Christiano [6], Senjuntichai et al [7][8] and Keawsawasvong and Senjuntichai [9] for rigid rectangular plates. In addition, the influence of the flexibility of foundations on dynamic interaction between foundations and supporting poroelastic media was also investigated by Senjuntichai and Kaewjuea [10] for multiple flexible strips and Senjuntichai and Sapsathiarn [11] for a flexible circular plate.…”