Faculty of Engineering

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Elastodynamic Fundamental Solutions of a Transversely Isotropic Unsaturated Half-Space Subjected to Axisymmetric Buried Vertical and Fluid Loading
(Springer Science and Business Media B.V., 2025-06-17) Yoonirundorn K; Senjuntichai T; Keawsawasvong S.; Rajapakse R.K.N.D
This paper presents solutions for a transversely isotropic unsaturated half-space subjected to axisymmetric time-harmonic vertical and fluid pressure loading. The Biot’s coupled poroelastodynamic equations are modified to include the unsaturated case by adding the air phase into the balance equations. The resulting fully coupled field equations of the three-phase medium are analytically solved to obtain the frequency-domain general solutions by using Hankel integral transforms in the radial direction. A boundary value problem is then formulated to obtain explicit expressions for the solutions of a half-space subjected to internally applied time-harmonic vertical loading and applied fluid pressure. To validate the accuracy of the proposed formulation, a comparison is made with existing solutions for surface loading on an unsaturated half-space. Numerical results are presented to illustrate the influence of the degree of saturation and the frequency of excitation on the dynamic response of the unsaturated half-space under internal excitations. The analysis reveals significant differences in profiles of displacement, stress, and pore pressure for the unsaturated soils compared to fully saturated cases, highlighting the importance of incorporating partial saturation in dynamic poroelastic modelling for geotechnical and earthquake engineering applications.
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Vertical vibrations of an elastic foundation with arbitrary embedment within a transversely isotropic, layered soil
(Elsevier, 2014) Labaki, J; Mesquita, E; Rajapakse, R. K. N. D
Analytical methods based on linear elasticity have been used to model the dynamic response of foundations. These solutions commonly assume that soils are isotropic and elastic. Incorporation of anisotropy and the twophased nature of soils (solid skeleton with pores filled with water) is important in the study of dynamic response of foundations. This paper presents the explicit analytical solutions for a transversely isotropic poroelastic soil half-space under a buried time-harmonic vertical load and a time-harmonic pore pressure discontinuity. These versatile fundamental solutions are derived by using Hankel integral transforms. They can be used to analyze a variety of dynamic problems in geomechanics. The fundamental solutions are then applied to solve the timeharmonic vertical vibration of a flexible circular foundation by using variational methods. Selected numerical results are presented to demonstrate the influence of soil anisotropy, poroelasticity, foundation flexibility, depth of embedment and frequency of excitation on the vertical dynamic response of foundation and the force transmitted to soil.
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Vertical vibration of a circular foundation in a transversely isotropic poroelastic soil
(Elsevier, 2020-05-01) Senjuntichai, T; Keawsawasvong, S; Rajapakse, R. K. N. D
Analytical methods based on linear elasticity have been used to model the dynamic response of foundations. These solutions commonly assume that soils are isotropic and elastic. Incorporation of anisotropy and the two-phased nature of soils (solid skeleton with pores filled with water) is important in the study of dynamic response of foundations. This paper presents the explicit analytical solutions for a transversely isotropic poroelastic soil half-space under a buried time-harmonic vertical load and a time-harmonic pore pressure discontinuity. These versatile fundamental solutions are derived by using Hankel integral transforms. They can be used to analyze a variety of dynamic problems in geomechanics. The fundamental solutions are then applied to solve the time-harmonic vertical vibration of a flexible circular foundation by using variational methods. Selected numerical results are presented to demonstrate the influence of soil anisotropy, poroelasticity, foundation flexibility, depth of embedment and frequency of excitation on the vertical dynamic response of foundation and the force transmitted to soil.
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Dynamic Green's functions of homogeneous poroelastic half-plane
(American Society of Civil Engineers, 1994-11) Rajapakse, R. K. N. D; Senjuntichai, T
This paper presents a comprehensive analytical and numerical treatment of two‐dimensional dynamic response of a dissipative poroelastic half‐plane under time‐harmonic internal loads and fluid sources. General solutions for poroelastodynamic equations corresponding to Biot's theory are obtained by using Fourier integral transforms in the x‐direction. These general solutions are used to solve boundary‐value problems corresponding to vertical and horizontal loads, and fluid sources applied at a finite depth below the surface of a poroelastic half‐plane. Explicit analytical solutions corresponding to above‐boundary‐value problems are presented. The solutions for poroelastic fields of a half‐plane subjected to internal excitations are expressed in terms of semiinfinite Fourier type integrals that can only be evaluated by numerical quadrature. The integration path is free from any singularities due to the dissipative nature of the elastic waves propagating in a poroelastic medium, and the Fourier integrals are evaluated by using an adaptive version of the trapezoidal rule. The accuracy of present numerical solutions are confirmed by comparison with existing solutions for ideal elasticity and poroelasticity. Selected numerical results are presented to portray the influence of the frequency of excitation, poroelastic material properties and types of loadings on the dynamic response of a poroelastic half‐plane. Green's functions presented in this paper can be used to solve a variety of elastodynamic boundary‐value problems and as the kernel functions in the boundary integral equation method.

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