Jian-Fei Lu

Dynamic response of pile groups embedded in a poroelastic medium

Abstract The dynamic response of pile groups embedded in a homogeneous poroelastic medium and subjected to vertical loading is considered. The piles are represented by compressible beam-column elements and the porous medium uses Biots three-dimensional elastodynamic theory. The dynamic impedance of pile groups can be computed directly by using pile–soil–pile dynamic interaction factors. The axial forces and pore pressures along the length of pile groups are computed by superposition method, which greatly reduces the computational time for the direct analysis of pile groups. Parametric studies are conducted for various conditions of pile groups. The superposition method is proposed for the dynamic response analysis of pile groups that is computationally feasible for practical applications.

Transient foundation solution of saturated soil to impulsive concentrated loading

Abstract The transient dynamic response of saturated soil under suddenly applied normal and horizontal concentrated loading is studied in this paper. The behavior of saturated soil is governed by Biots consolidation theory. The general solutions for Biot equations of equilibrium are derived in terms of displacements and variations of fluid volume, using Laplace–Hankel integral transforms. The solutions in the time domain can be evaluated by numerical inverse Laplace–Hankel transforms. Selected numerical results for displacements, stresses, and pore pressures are presented. Comparisons with existing closed-form solutions for the elastic half-space are made to confirm the accuracy of the present solutions. The solutions can be used to study a variety of transient wave propagation problems and dynamical interactions between saturated soil and structures.

A Coupled BEM Model for the Dynamic Analysis of a Pile Embedded in a Half-space Soil Covered by a Water Layer

Dynamic analysis of a pile embedded in a half-space soil covered by a water layer is crucial for the designs of the pile foundations for bridges, docks and offshore platforms etc. In this paper, a coupled boundary element method (BEM) model is developed to evaluate the dynamic response of the pile. In the proposed model, the pile and half-space soil are treated as elastic media, while the water layer is considered as an acoustic medium. Three BEM formulations are established for the pile, half-space soil and water layer by means of the boundary element method (BEM), respectively. Using the three BEM formulations as well as the continuity conditions at the interfaces between three regions, a coupled BEM model for the pile-soil-water system is established. To validate the proposed model, results due to our model are compared with existing results. With the coupled BEM model for the pile-soil-water system, dynamic response of the pile is investigated. Presented numerical results show that when the pile is subjected to an axial load and torque, resonance phenomena is not obvious. However, when the pile is subjected to a horizontal load and moment, resonance phenomena is pronounced and the pile-soil modulus and density ratios have a considerable influences on resonant frequencies.

Analysis of the Wave Localization in a Disordered Periodic Bridge with Pile–Soil–Water–Structure Coupling

In this study, the wave localization in a disordered periodic bridge (DPB) with the pile–soil–water–structure (PSWS) coupling is investigated For simplicity, each span of the bridge is assumed to be composed of a pile foundation, a pier, two composite beams and three linking springs. To determine the compliances of the pile foundations, the pile–soil–water (PSW) interaction is simulated by the boundary element method (BEM). In terms of the compliances of the piles and the transfer matrices of the piers and beams, the transfer matrices of the spans of the periodic bridge are derived, by which the wave transfer matrices of the spans are obtained. Using Wolfs algorithm and the wave transfer matrices obtained, the localization factor characterizing the wave localization in the DPB is determined. With the proposed model, the effect of the beam-length disorder on wave localization is examined. Moreover, based on the wave transfer matrix method, the wave mode of a DPB segment and the wave conversion and power flow in the DPB segment are investigated. Numerical results show that due to the energy transmission from the superstructure of the bridge to the half-space soil via the pile foundations, the power flow associated with a complexband wave along the open DPB is usually nonzero and the power flow of a pseudo passband wave along the spans of the open DPB is no longer a constant.

Scattering of antiplane shear wave by a kinked crack

In this paper the scattering of antiplane shear waves by a kinked crack for a linearly elastic medium is considered. In order to solve the proposed problem, at first the broken crack problem is reduced to two coupled single cracks. Fourier integral transform method is employed to calculate the scattered field of a single crack. In order to derive the Cauchy type integral equations of a broken crack and analyze the singular stresses at the breakpoint, the scattered field of a single crack is separated into a singular part and a bounded part. The single crack solution is applied to derive the generalized Cauchy type integral equations of a broken crack. The singular stress and singular stress order are analyzed in the paper and the dynamic stress intensity factor (DSIF) at breakpoint is defined. Numerical solution of the obtained Cauchy type integral equations gives the DSIF at the crack tips and at the breakpoint. Comparison of the present results in some special cases with the known results confirms the proposed method. Some typical numerical results and corresponding analysis are presented at the end of the paper.

Dynamic Response of a Defected Periodic Viaduct to a Moving Point Load

A defected periodic viaduct (DPV) is an infinite viaduct consisting of a left and a right semi-infinite ordered periodic viaducts (OPV) and one or several in-between defected spans different from the standard span of the OPV. Currently, no methodology is available in the literature for assessing the dynamic response of a DPV to a moving load, as the presence of the defected spans breaks the periodicity of the OPV. In this study, a new FEM model for estimating the dynamic response of a DPV with one defected span to a moving load is proposed. To establish the model, the time-space domain (TSD) moving load is decomposed into the sum of its constituent frequency wavenumber domain (FWD) load components first. For the DPV subjected to the FWD load component, the response of the left and right semi-infinite OPVs of the DPV can be divided into two parts, namely, the free wave field and the scattered wave field. To determine the free wave field of the left and right semi-infinite OPVs of the DPV, the FEM equations for an individual span of the viaduct are established and applied to the two OPVs. The scattered wave field in the two semi-infinite OPVs consists of the characteristic waves of the OPV and can be determined using the FEM eigenvalue equations for the OPV free of external loads. Applying the span FEM equations to the defected span and using the expressions for the free wave field and the scattered wave field yield the FWD response of the DPV. The time-space domain response of the DPV can then be retrieved by superposing all the FWD responses of the DPV. Numerical simulations are conducted to investigate the influence of the defected span on the dynamic response of the DPV. For the DPV, there are two kinds of the resonant frequencies, namely, the resonant frequencies common to the corresponding OPV and the additional resonant frequencies due to the presence of the defected span. In some cases, the magnitudes of the responses at the additional resonant frequencies may be larger than those at the common resonance frequencies. Therefore, when conducting the design for a periodic viaduct, it is important to account for the influence of the defected span on the dynamic response of the periodic viaduct.

Free Vibration Analysis of a Periodic Viaduct Supported by Pile Foundations

In this study, a numerical model is developed for the analysis of the free vibration of an open-type periodic structure, namely, a periodic viaduct supported by pile foundations. The viaduct is supposed to be composed of infinite spans, with each span consisting of a pile foundation, a pier, two longitudinal beams (left and right beams), and three linking springs. The boundary-element method (BEM) is used to solve the pile-soil interaction problem first. Based on the developed BEM model for the pile-soil system, the compliances of the pile foundation are obtained. By using the compliances of the pile foundation, the joint conditions at the beam-beam-pier (BBP) junction and the transfer matrix method, the eigenvalue equation for the periodic viaduct is established. Numerical results for the energy bands of the viaduct show that there are three kinds of characteristic waves propagating in the periodic viaduct. The first and second kinds of waves are highly decaying. The third characteristic wave can propagate in pseudopassbands with a small attenuation. Also, it is found that, unlike a closed periodic structure, because of the energy transmission from the viaduct to the half-space soil, all energy bands for the open viaduct considered in this study are complex bands with nonzero imaginary wave numbers.

A Semi-Analytical Model for the Simulation of the Isolation of the Vibration Due to a Harmonic Load Using Pile Rows Embedded in a Saturated Half-Space~!2009-06-25~!2009-12-17~!2010-03-30~!

The isolation of the vibration due to a harmonic vertical load using pile rows embedded in a saturated poroelas- tic half-space is investigated in this study. Using the fundamental solution for a circular patch load and Mukis method, the second kind of Fredholm integral equations describing the dynamical interaction between the pile rows and the satu- rated poroelastic half-space are obtained. Numerical solution of the integral equations yields the dynamic response of the pile-half-space system. The vibration isolation effect of the pile rows is investigated via the proposed semi-analytical model. Numerical results indicate that stiffer piles have better isolation vibration effect than flexible piles. Moreover, the pile length and the spacing between neighboring piles in one pile row have significant influence on the isolation vibration effect of pile rows, while the influence of the spacing between neighboring pile rows is relatively smaller.

Vibration Analysis of a Circular Tunnel With Jointed Liners Embedded in an Elastic Medium Subjected to Seismic Waves

This paper presents a frequency domain analysis of a circular tunnel with piecewise liners subjected to seismic waves. In our model, the surrounding medium of the tunnel is considered as a linear elastic medium and described by the dynamic elasticity theory, while piecewise liners and connecting joints are treated as curved beams and described by a curved beam theory. Scattered wave field in the surrounding elastic medium are obtained by the wave function expansion approach. The governing equations for vibrations of a curved beam are discretized by the general differential quadrature method. We use domain decomposition methods to establish the global discrete dynamic equations for piecewise liners. Boundary least squares collocation methods, based on the continuity conditions of stresses and displacements between surrounding soil and the piecewise liners, are used to determine the response of the liners and the surrounding medium. Numerical results conclude that the presence of the joints significantly changes the distributions of the tunnel internal force, and dramatically increase shear forces and moment of the tunnel liners around joints.

A Model for the Wave Localization in a Disordered Periodic Elevated Railway Undergoing In-Plane Vibration

In this study, a model for the analysis of the wave localization in a special kind of simply-supported beam bridge, namely, the periodic elevated railway (PER), is developed. For simplicity, each span of the PER is supposed to be composed of two longitudinal beams, a pier, and three linking springs. The standard linear solid model is employed to describe the damping of the materials of the piers and beams. Transfer matrix for each span of the PER undergoing in-plane vibration is derived, whereby the wave transfer matrix for each span is obtained. By means of the Wolfs algorithm and using the aforementioned wave transfer matrices, the localization factors accounting for wave localization in the PER are determined. With the proposed model, the influence of the disorder of the beam lengths on the wave localization in the PER is examined. Also, the interactive effect of the damping and the beam-length disorder on the wave localization in the PER is investigated. As a special case, the wave localization in a PER with rigid beam-beam-pier (BBP) junctions is also discussed in this study. Moreover, by the wave transfer matrix method, the wave localization and conversion phenomena in a finite disordered PER segment are investigated. Finally, the relation between the response of a finite disordered PER segment to external loadings and the degrees of the disorder of the PER segment is examined.