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In this paper, a complete elastodynamic solution for axisymmetric problems under axial body-forces in terms of two retarded potential functions in transversely isotropic media is extended to the case of general torsionless axisymmetry. Allowing for both axial and radial distributed internal loads through the use of an extra potential, the new solution retains its completeness via the theory of repeated wave equations. By virtue of its analytical design, the formulation can be reduced to the corresponding elastostatic case by simply suppressing the time-dependence of its potentials as well as the case of isotropy. In the limiting case of the latter material condition, the proposed representation for elastostatic problem degenerates to a recent extension of Love's potential function. [DOI: 10.1115/1.3130866] Keywords: potential method, mechanics, transversely isotropy, elastodynamics, elastostatics, axisymmetric, body-force, displacements, stresses, completeness

This paper describes a fundamental experimental study on the vertical, horizontal, and rocking dynamic behavior of single pile foundations in granular soils. Aimed at generating an extensive experimental database with sufficient parametric variations to clarify a number of issues, multiple series of canonical small-strain forced-vibration centrifuge tests were performed on two model piles using the technique of random vibration and impact loading. Correlated well with vertical-and horizontal-centric dynamic tests within the experimental program, a novel hybrid-mode test method by means of eccentric excitation is validated and employed for the characterization of the foundation responses in general planar motion. A large set of experimental data for different length scales were generated and synthesized in the frequency domain in the form of directional force-response transfer functions. By virtue of the physical measurements, the validity and limitations of two fundamental elastodynamic pile solutions pertaining to the physical dynamic soil-foundation problem are also evaluated. DOI: 10.1061/(ASCE)GT.1943-5606.0000038 CE Database subject headings: Piles; Vibration; Soil-structure interaction; Centrifuge models; Dynamic tests; Soil dynamics.

By virtue of a complete representation using two displacement potentials, an analytical derivation of the elastodynamic Green's functions for a transversely isotropic layer underlain by a transversely isotropic half-space is presented. Three-dimensional point-load and patch-load Green's functions for stresses and displacements are given in the complex-plane line-integral representations. The formulation includes a complete set of transformed stress-potential and displacement-potential relations in the framework of Fourier expansions and Hankel integral transforms, that is useful in a variety of elastodynamic as well as elastostatic problems. For the numerical computation of the integrals, a robust and effective methodology is laid out. Comparisons with the existing numerical solutions for a two-layered transversely isotropic half-space under static surface load, and a homogeneous transversely isotropic half-space subjected to buried time-harmonic load are made to confirm the accuracy of the present solutions. Selected numerical results for displacement and stress Green's functions are presented to portray the dependence of the response of the two-layered half-space on the frequency of excitation and the role of the upper layer. DOI: 10.1061/(ASCE)0733-9399(2008) 134:9(777) CE Database subject headings: Greens function; Layered systems; Wave propagation; Elasticity; Anisotropy; Boundaries; Asymmetry; Half space.

A theoretical formulation is presented for the determination of the displacements, strains, and stresses in a three-dimensional transversely isotropic linearly elastic medium. By means of a complete representation using two displacement potentials, it is shown that the governing equations of motion for this class of problems can be uncoupled into a fourth-order and a second-order partial differential equation in terms of the spatial and time coordinate under general conditions. Compatible with Fourier expansions and Hankel transforms in a cylindrical coordinate system, the formulation includes a complete set of transformed displacement-potential, strain-potential, and stress-potential relations that can be useful in a variety of elastodynamic as well as elastostatic problems. As an illustration of the application of the method, the solution for a half-space under the action of arbitrarily distributed, time-harmonic surface traction is derived, including its specialization to uniform patch loads and point forces. To confirm the accuracy of the numerical evaluation of the integrals involved, numerical results are also included for cases of different degree of the material anisotropy, frequency of excitation, and compared with existing solutions. DOI: 10.1061/(ASCE)0733-9399(2007)133:10(1134) CE Database subject headings: Wave propagation; Half space; Elasticity; Isotropy; Displacement; Boundary element method.

For tackling high-gradient, localized, or singular boundary value problems, the concept of an adaptive-gradient (AG) element family is introduced to advance the utility of discretization methods. Capable of encompassing regular and singular elements as special cases, a basic but versatile family of AG elements for multidimensional applications is derived whose gradient and singularity can be controlled parametrically to handle a wide variety of functional behavior with standard mesh configurations. As illustrations, examples of usage and performance in a set of linear and nonlinear mixed-boundary value problems are presented. DOI: 10.1061/(ASCE)0733-9399(2007)133:1(87) CE Database subject headings: Continuum mechanics; Boundary element method; Finite elements; Localization; Discontinuities; Distribution functions; Elasticity; Gradient; Interpolation; Numerical analysis.

A rigorous mathematical formulation is presented for a flexible tubular pile of finite length embedded in a semi-infinite soil medium under lateral loading. In the framework of three-dimensional elastostatics and classical beam theory, the complicated structure-medium interaction problem is shown to be reducible to three coupled Fredholm integral equations. Through an analysis of the associated Cauchy singular kernels, the intrinsic singular characteristics of the radial, angular, and vertical interracial load transfers are rendered explicit and incorporated into a rigorous numerical procedure. Detailed results on the three-dimensional load-transfer process, as well as their resultant one-dimensional analogs, am also provided for benchmark comparison and practical applications. CE Database subject headings: Pile foundations; Soil-structure interaction; Load transfer; Embedment: Elasticity: Stiffness; Flexure: Lateral loads.

To advance the mathematical and computational treatments of mixed boundary value problems involving multilayered media, a new derivation of the fundamental Green's functions for the elastodynamic problem is presented. By virtue of a method of displacement potentials, it is shown that there is an elegant mathematical structure underlying this class of three-dimensional elastodynamic problems which warrant further attention. Constituted by proper algebraic factorizations, a set of generalized transmission-reflection matrices and internal source fields that are free of any numerically unstable exponential terms common in past solution formats are proposed for effective computations of the potential solution. To encompass both elastic and viscoelastic cases, point-load Green's functions for stresses and displacements are generalized into complex-plane line-integral representations. An accompanying rigorous treatment of the singularity of the fundamental solution for arbitrary source-receiver locations via an asymptotic decomposition of the transmission-reflection matrices is also highlighted. DOI: 10.1061/(ASCE)0733-9399(2002)128:4(449) CE Database keywords: Green's function; Layered systems; Wave propagation; Elasticity; Viscoelasticity; Displacement; Boundary element method.

By means of scaled modeling on a geotechnical centrifuge, a systematic experimental investigation was conducted to examine the vertical dynamic response of surface foundations on granular soils. From the results of more than 100 tests, it was found that the dynamic characteristics of such foundations can be well represented in the frequency domain by the homogeneous half-space analytical solution despite the gravity- and load-induced spatial variations of the soil's modulus. However, it was also revealed that the foundation response has a significant nonlinear dependence on the soil bearing pressure and footing dimension. To capture such aspects, a set of equivalent-homogeneous elastic parameters was determined from the physical measurements for a wide range of soil-foundation configurations. Through an analytical synthesis, it was found that the equivalent-homogeneous Poisson's ratio of the soil can be taken as 0.25 while the equivalent-homogeneous shear modulus of the soil can be related through a power law to the soil's void ratio, footing radius, and average foundation bearing pressure. The practical relevance and potential applications of the resulting semiempirical formula for the dynamic foundation compliance are discussed.

A method for solving the finite-displacement problem of a curved elastic beam with axial, shear, and flexural deformation subject to distributed and point loads is presented. Within the context of the kinematic assumptions of the Timoshenko theory, a Lagrangian formulation of the problem is developed. In terms of three cross-sectional stress resultants, three Euler equations of equilibrium for the beam are derived with the aid of a variational principle fo finite deformation. Upon linearization to small strains and the adoption of a linear elastic constitutive relation between the stress and strain tensors, it is shown that the problem is reducible to a single second-order nonlinear ordinary differential equation. Subject to appropriate boundary conditions, the resulting two-point boundary-value problem is solved by a finite-element method By virtue of a continuation algorithm, accurate solutions of the system of nonlinear equations can be obtained for a variety of bifurcation and buckling problems. Comprehensive results are presented for two cantilever beams as illustrations.

In the framework of three-dimensional elastostatics and a higher-order structural mechanics theory, an exact formulation is presented for the torsionless axisymmetric load-transfer problem of a thin-walled cylindrical pile of finite length embedded in a semi-infinite medium. By virtue of a set of integral representations for the responses of the pile and the half-space under arbitrary interfacial loads, the tangential and radial conditions of contact in the soil-structure interaction problem are shown to be reducible to a system of Fredholm integral equations. Through an auxiliary analysis, the orders of the singularities of the contact load distributions can be determined mathematically. The results are incorporated into a numerical procedure for the solution of the Fredholm integral equations. Typical solutions for the contact load transfers, the internal axial force variation, and the displacement response as a function of various material and geometric parameters are included to illustrate the fundamental characteristics of the mechanical-interaction problem.

Presents information on a study which investigated the seismic behavior of cantilever retaining walls supporting liquefiable backfills. Details on the centrifuge test program; Set of experimental measurements and interpretations; Effect of flexural stiffness.