Research Papers - Department of Civil Engineering
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Publication Embargo Elastodynamic Green's functions of orthotropic half plane(American Society of Civil Engineers, 1991-03-01) Rajapakse, R.K.N.D; Wang, Y.The dynamic response of an orthotropic elastic half plane subjected to a set of time‐harmonic buried loadings is investigated. The governing differential equations are established in terms of displacements and a general solution is derived using Fourier integral transforms with respect to the x‐coordinate. The boundary‐value problems corresponding to time‐harmonic vertical and horizontal loads acting in the interior of the half plane are solved. Explicit analytical solutions are presented for displacements and stresses due to buried uniformly distributed and concentrated loadings. Some characteristics of the analytical solution are investigated, and its numerical evaluation is also discussed. Selected numerical results for displacements and stresses of isotropic, ice, layered soil, and cadmium half‐plane regions are presented. A discussion of these numerical solutions is presented to investigate the influence of the degree of material anisotropy, frequency of excitation, and the type of loading on the response of the elastic half plane.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 A coupled thermoporoelastic model with thermo-osmosis and thermal-filtration(Pergamon, 1998-12-01) Rajapakse, R. K. N. D; Zhou, Y; Graham, JA coupled thermoporoelastic model accounting for compressibility and thermal expansion of constituents, convective heat flow and changing porosity and related properties of a saturated soil is presented. The model also considers thermodynamically coupled water and heat flow (thermal-filtration and thermo-osmosis that are analogous to Sorêt and Dufour effects in solutions) . These coupling effects are reported to be significant in the case of semi-impermeable clay barriers used in waste repositories. The governing equations derived in terms of displacements, temperature and pore water pressure are non-linear. A mixed finite element formulation is presented to obtain numerical solutions. An exact analytical solution for a 1-D soil column is presented for a simplified linear case that includes thermodynamic coupling. Selected numerical solutions for soil columns and radially symmetric plane strain problems are presented to demonstrate the principle features of the coupled model and the significance of thermodynamic coupling.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 Green's functions of homogeneous poroelastic half-plane(American Society of Civil Engineers, 1994-11) Rajapakse, R. K. N. D; Senjuntichai, TThis 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.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.Publication Embargo Green's functions for transversely isotropic elastic half space(American Society of Civil Engineers, 1993-09) Rajapakse, R. K. N. D; Wang, YThis paper presents a comprehensive analytical treatment of the three‐dimensional response of a transversely isotropic elastic half space subjected to time‐harmonic excitations. General solutions for equations of equilibrium expressed in terms of displacements are derived by applying Fourier expansion with respect to the circumferential coordinate and Hankel integral transforms with respect to the radial coordinate. The general solutions are used to derive the explicit solutions for Green's functions (displacements and stresses) corresponding to a set of time‐harmonic circular ring loads acting inside a half space. The circumferential variation of the ring loads are assumed to be cosmθ for loadings in the vertical and radial directions and sinmθ for the loading in the circumferential direction. These Green's functions can be used as the kernel functions of the boundary‐integral‐equation method and in the development of solutions for a variety of elastodynamic boundary value problems. Comparisons with existing numerical solutions for an isotropic half space are presented to confirm the accuracy of the present solutions. Selected numerical results for displacements and stresses are presented to portray the dependence of the response of the half space on the frequency of excitation and the degree of anisotropy of the medium.Publication Open Access Dynamic axial load transfer from elastic bar to poroelastic medium(American Society of Civil Engineers, 1999-09) Rajapakse, R. K. N. D; Zeng, X.I.The time-harmonic response of a cylindrical elastic bar (pile) partially embedded in a homogeneous poroelastic medium and subjected to a vertical load is considered. The bar is modeled using 1D elastic theory valid for long bars in the low-frequency range, and the porous medium using Biot's 3D elastodynamic theory. The bar is bonded to the surrounding medium along the contact surface. The problem is formulated by decomposing the bar/porous medium system into a fictitious bar and an extended porous medium. A Fredholm's integral equation of the second kind governs the distribution of axial force in the fictitious bar. The integral equation involves kernels that are displacement and strain influence functions of a poroelastic half-space subjected to a buried, uniform vertical patch load. The governing integral equation is solved by applying numerical quadrature. The solutions for axial displacement and axial force of the bar, and the pore pressure are also derived. Selected numerical results for vertical impedance, axial force, and pore pressure profiles are presented to portray the influence of bar stiffness and length/radius ratio, frequency of excitation, and poroelastic properties.Publication Embargo Dynamic response of a pile in a multi-layered soil to transient torsional and axial loading(Thomas Telford Ltd, 1999-02-01) Rajapakse, R. K. N. D; Militano, G.The dynamic response of an elastic pile subjected to transient torsional and axial loading is considered. The pile is embedded in a multi-layered elastic soil. The stress field in a soil is simplified by following the existing solutions for a pile subjected to static torsional and axial loading. The dynamic equilibrium equation of soil is solved in the Laplace domain by using analytical techniques. The soil resistance is coupled into a one-dimensional governing equation of a pile segment and an analytical solution is presented. An impedance matrix can then be derived for a pile segment relating end stress resultants to the displacements. Non-homogeneous initial conditions of the pile are considered. The impedance matrices of pile segments are assembled by following the concepts of finite element method to analyse a pile embedded in a multi-layered soil. The treatment of soil base response is also discussed. Time domain solutions are obtained by using a numerical Laplace inversion procedure. The extension of the analysis to linear viscoelastic soils using the correspondence principle in the theory of viscoelasticity is discussed. Selected numerical solutions for a pile embedded in a homogeneous soil and a &squo;Gibson’ soil are presented to portray the influence of pile moduli and slenderness ratios, loading history and soil non-homogeneity on the dynamic response of an elastic pile. Nous étudions la réponse dynamique d’un pilot élastique soumis à une charge de torsion et axiale transitoire. Le pilot est enfoui dans un sol élastique constittué de plusieurs couches. Nous simplifions le champ de contrainte dans un sol en appliquant les solutions existantes pour un pilot soumis à une charge de torsion et axiale statique. L’équation de 1’équilibre dynamique du sol est résolue dans le domaine de Laplace en utilisant des techniques analytiques. Nous couplons la résistance du sol en une équation standard unidimensionnelle pour un segment de pilot et nous présentons une solution analytique. Une matrice d’impédance pent alors être dérivée pour un segment de pilot en liant les résultantes de contrainte en bout aux déplacements. Nous examinons les conditions initiales non homogènes du pilot. Pour analyser un pilot enfoui dans un sol constitué de plusieurs couches, nous assemblons les matrices d’impédance des segments de pilot en suivant les concepts de la méthode d’éléments finis. Nous discutons aussi du traitement de la réponse de base du sol. Les solutions du domaine de temporisation sont obtenues en utilisant une procédure d’inversion numérique de Laplace. Nous discutons de l’extension de l’analyse aux sols à viscoèlasticit´e;aire en utilisant le principe de correspondance dans la théorie de viscoélasdcité. Nous présentons de solutions numériques choisies pour un pilot enfoui dans un sol homogène et un sol &squo;Gibson’ pour décrire l’influence des modules de pilot et des coefficients de gracilité, des comportements aux charges et de la non homégénéité du sol sur la réponse dynamique d’un pilot élastique.