Faculty of Engineering
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Publication Open Access Vertical vibrations of a rigid disk embedded in a poroelastic medium(John Wiley & Sons, Ltd., 1999-12-25) Zeng, X; Rajapakse, R. K. N. Dhis paper considers the steady-state vertical vibrations of a rigid circular disk embedded at a finite depth below the free surface of a poroelastic medium. Biot's elastodynamic theory for porous media is used in the analysis. General solutions for axisymmetric poroelastic fields are obtained by using Hankel integral transforms. Analytical solutions for influence functions corresponding to four types of buried axisymmetric excitations are derived. The embedded disk problem is fomulated in terms of a set of coupled integral equations for unknown traction and pore pressure jumps across the disk. The kernel functions of the integral equations are the influence functions corresponding to buried vertical, radial and pore pressure ring loads. The system of integral equations is solved numerically by discretizing the disk into several concentric annular rings. Selected numerical solutions for displacements, vertical stress and pore pressure due to a buried fully flexible disk (uniform pressure) are also presented. The vertical compliances of a rigid disk are examined for different depths of embedment, poroelastic materials and hydraulic boundary conditions. Solutions for traction and pore pressure jumps are also examined. The present results are useful in the study of dynamic response of embedded foundations and anchors in poroelastic soils.Publication Embargo Exact stiffness method for quasi-statics of a multi-layered poroelastic medium(Pergamon, 1995-06-01) Senjuntichai, T; Rajapakse, R. K. N. DA method is presented to study the three-dimensional quasi-static response of a multi-layered poroelastic half-space with compressible constituents. The system under consideration consists of N layers of different thickness and material properties overlying a homogeneous half-space. Fourier expansion, Laplace transforms and Hankel transforms with respect to the circumferential, time and radial coordinates, respectively, are used in the formulation. Laplace-Hankel transforms of displacements and pore pressure at layer interfaces are considered as the basic unknowns. Exact stiffness matrices describing the relationship between generalized displacement and force vectors of a finite layer and a half-space are derived explicitly in the transform space. The global stiffness matrix of a layered system is assembled by considering the continuity of tractions and fluid flow at layer interfaces. The time histories of displacements, stresses and pore pressure are obtained by solving the stiffness equation system for discrete values of Laplace and Hankel transform parameters, and using numerical quadrature schemes for Laplace and Hankel transform inversions. Selected numerical results for different layered systems are presented to portray the influence of layering and poroelastic material properties. The advantage of the present method is that for an N-layered system, it yields a numerically stable symmetric stiffness matrix of order 4N × 4N when compared to the unsymmetric and numerically unstable coefficient matrix of order 8N × 8N associated with the conventional method based on the determination of layer arbitrary coefficients.Publication Embargo Transient response of a circular cavity in a poroelastic medium(John Wiley & Sons, Ltd, 1993-06) Rajapakse, R. K. N. D; Senjuntichai, TThis paper considers the transient response of a pressurized long cylindrical cavity in an infinite poroelastic medium. To obtain transient solutions, Biot's equations for poroelastodynamics are specialized for this problem. A set of exact general solutions for radial displacement, stresses, pore pressure and discharge are derived in the Laplace transform space by using analytical techniques. Solutions are presented for three different types of prescribed transient radial pressures acting on the surface of a permeable as well as an impermeable cavity surface. Time domain solutions are obtained by inverting Laplace domain solutions using a reliable numerical scheme. A detailed parametric study is presented to illustrate the influence of poroelastic material parameters and hydraulic boundary conditions on the response of the medium. Comparisons are also presented with the corresponding ideal elastic solutions to portray the poroelastic effects. It is noted that the maximum radial displacement and hoop stress at the cavity surface are substantially higher than the classical static solutions and differ considerably from the transient elastic solutions. Time histories and radial variations of displacement, hoop stress, pore pressure and fluid discharge corresponding to a cavity in two representative poroelastic materials are also presented.Publication Embargo Dynamic response of a multi‐layered poroelastic medium(John Wiley & Sons, Ltd, 1995-05) Rajapakse, R. K. N. D; Senjuntichai, TAn exact stiffness matrix method is presented to evaluate the dynamic response of a multi-layered poroelastic medium due to time-harmonic loads and fluid sources applied in the interior of the layered medium. The system under consideration consists of N layers of different properties and thickness overlying a homogeneous half-plane or a rigid base. Fourier integral transform is used with respect to the x-co-ordinate and the formulation is presented in the frequency domain. Fourier transforms of average displacements of the solid matrix and pore pressure at layer interfaces are considered as the basic unknowns. Exact stiffness (impedance) matrices describing the relationship between generalized displacement and force vectors of a layer of finite thickness and a half-plane are derived explicitly in the Fourier-frequency space by using rigorous analytical solutions for Biot's elastodynamic theory for porous media. The global stiffness matrix and the force vector of a layered system is assembled by considering the continuity of tractions and fluid flow at layer interfaces. The numerical solution of the global equation system for discrete values of Fourier transform parameter together with the application of numerical quadrature to evaluate inverse Fourier transform integrals yield the solutions for poroelastic fields. Numerical results for displacements and stresses of a few layered systems and vertical impedance of a rigid strip bonded to layered poroelastic media are presented. The advantages of the present method when compared to existing approximate stiffness methods and other methods based on the determination of layer arbitrary coefficients are discussed.