Analytical Layer-element Method Research Articles

ALEM-FEM-BEM coupling for response analysis of pile group in laminated fluid-saturated geomaterials induced by tunnel excavation

This paper proposes a two-stage analytical methodology for predicting the response of pile groups in layered fluid-saturated soils induced by tunnel excavation. The Loganathan analytical approach is adopted for estimating the free-field response induced by tunneling. At the second phase, the solution to the surrounding soil of pile groups is employed as the kernel function based on the analytical layer-element method (ALEM). Subsequently, the analysis of soil-structure interaction is presented using the boundary element method (BEM). The Timoshenko-beam model is utilized to simulate each monopile combined with finite element method (FEM). Finally, the responses of adjacent pile groups are derived by the coordination conditions and coupling of BEM and FEM. Comparisons are made between the presented analytical solutions and existing experimental and numerical results. Parametric analyses are performed to evaluate the influence of soil permeability, material stratification, tunnel-pile distance, tunnel buried depth, and pile slenderness ratio on the mechanical behavior of grouped piles. The results show that the pile group in hard top and soft bottom saturated soils demonstrates better load-bearing capacity than that in soft upper and hard lower soils. Then, with the increment of tunnel-pile distance, the displacement and bending moment are reduced by 22.2 %-50 % and 41.2 %-66.7 %, respectively, and the increased rate of mechanical response over time slows down. Moreover, increasing the burial depth reduces the displacement by 8.6 %-33.3 % and the bending moment by 33.4 %-50 %, respectively, and the locations of peak responses increase from 0.6 times the pile length to 0.8 times the pile length.

Time-dependent transient response of piles partially embedded in layered viscoelastic saturated cross-anisotropic soils using a fractional-order Merchant model

A 3D analytical method is proposed for the lateral time-dependent response of monopiles partially embedded in stratified saturated viscoelastic cross-anisotropic soils under horizontal transient loads. Nevertheless, previous studies on ocean engineering have rarely considered the rheological properties of seabed materials. In this study, depending upon Biot's dynamical formulation, the linear elastic solution of the layered cross-anisotropic saturated soils due to lateral transient and vertical loads is solved using the analytical layer-element method (ALEM). The fractional-order Merchant model is adopted to describe the rheological deformation of the seabed, and the viscoelastic solution of the laminar cross-anisotropic saturated soils is derived by combining the elastic-viscoelastic transformation theory. Using the consolidation solution of the seabed as the kernel function, the pile-soil boundary problem is analyzed by the boundary element method (BEM) to obtain the BE equation of the viscoelastic saturated soils. The Timoshenko beam is employed to simulate the monopile, and based on the finite element method (FEM), the monopile is discretized into pile units to derive the FE matrix equation. Finally, the dynamic response formulation of the partially embedded offshore monopile is obtained by coupling the BE and FE equations through the coordination conditions of close contact between the Timoshenko beam and the seabed. The accuracy of the methodology is verified by comparing with the existing solutions and the numerical results from ABAQUS. And the effects of the transient load type, seabed viscosity, and pile properties on the horizontal response of partially embedded monopiles are explored.

A 3D coupled ALEM-BEM method for assessing pile mitigation performance to moving-harmonic-load induced vibrations in cross-anisotropic porous saturated media

The present investigation aims at proposing a three-dimensional ALEM-BEM coupling analytical approach to evaluate the isolation effectiveness of pile barriers in stratified cross-anisotropic porous saturated media under moving harmonic loads. The governing equations of Biot’s porous elastic theory are decoupled through an analytical layer-element method (ALEM). The pile-soil boundary equation is derived using BEM combined with a two-stage theory. Two-node beam cells are adopted to discretize the piles based on Timoshenko beam theory. The pile barrier mitigation effectiveness is obtained depending upon a vibration screening theory. After carefully validating the presented solutions by various reduced instances, the impacts of two-phase compressibility, geomaterial cross anisotropy, and load frequency on the mitigation effectiveness are analyzed. Results illustrate that the isolation effectiveness is more sensitive to the velocity in the medium with high two-phase compressibility or low cross-anisotropic coefficient. The pile screening effectiveness influenced by a high-speed load is more sensitive to the frequency.

Scour effects on the vertical dynamic response of single piles in transversely isotropic soils

Pile foundations in ocean engineering are often simultaneously subjected to dynamic loads and scour activity. A coupled finite element method (FEM) - analytical layer element method (ALEM) is provided in this paper for investigating the vertical dynamic impedances of piles in layered soils under scour conditions. The pile modeled as a one-dimensional vibration bar is solved using the FEM. The dynamic responses for a layered soil are derived from the ALEM. Based on the force equilibrium and the displacement compatibility at the pile-soil interface, the pile-soil interaction equations under scour conditions are established and solved. Finally, several numerical examples are performed to verify the correctness of the proposed method, and to explore the effects of scour type, scour depth and slenderness ratio on the vertical impedances of single piles, which show that these factors significantly affect the vertical pile-head impedances, and the optimal pile slenderness ratio is mainly associated with the excitation frequency.

Analytical layer-element solution for layered transversely isotropic saturated media subjected to rectangular moving loads

The analytical layer element method for multilayered transversely isotropic saturated soils due to rectangular moving loads is developed in this paper. The partial differential equations in the fixed Cartesian coordinate system are converted into those in the moving coordinate system. Applying the double Fourier transform, the ordinary differential equations are derived. Considering the continuity conditions at the layer interfaces and the boundary conditions, the transformed domain solutions for the displacement and the stress are deduced by the analytical layer element method. The solutions in the physical domain are obtained by performing the inverse Fourier transform. Several numerical examples are presented to examine the influences of the soils’ transverse isotropy, stratification characteristics, the thickness of the soft soil layer, and the load moving speed on the dynamic behaviors.

Analytical solution for the vertical vibration of a pipe pile embedded in poroelastic soil

This paper presents an analytical method to investigate the vertical vibration of a pipe pile in layered poroelastic soils due to a harmonic load. The relationship of general displacement and stress is obtained through a stiffness matrix which is derived by applying analytical layer element method. The pipe pile with a thick wall is governed by vibration theory of a one-dimensional bar. By considering the compatible conditions at the inner-surface and outer-surface of a pipe pile and soil, the vertical vibration performance is obtained. The proposed method is proved correct by comparing with the existing solutions. Parametric studies are carried out to illustrate the influences of wall thickness of the pipe pile, soil permeability and pile-soil stiffness ratio on the vibration characteristics of the pipe pile.

Dynamic response of pile group in two-layered soils under scour condition by FEM-ALEM approach

Pile groups for the bridge and jacket foundations in the marine or traffic geotechnical engineering are significantly influenced by the current scour in service. Under the effects of scour and dynamic load, the capability of the pile foundations to resist deformation is reduced and thus causes structural failure. This paper presents a FEM-ALEM coupling approach to study the dynamic interaction between a pile group and layered soils under scour condition. Behaviors of the pile group are analyzed by applying the finite element method. Fundamental solutions of the layered soils under scour condition are obtained by adopting the analytical layer element method. Comparisons with existing solutions are performed to confirm the correctness of the present approach, and numerical examples are provided to discuss the effects of the scour type, scour depth, scour width and layered property of soil on the dynamic behaviors of the pile group. The present coupling approach can be used to evaluate the responses of a pile group embedded in layered saturated soils under scour due to a vertical dynamic load.

A simplified method for evaluating temperature effect on the behavior of layered soil with a time-varying cylindrical heat source

The engineering application of cylindrical heat source usually influences the characteristics of the surrounding soil and induces significant coupling responses of temperature, seepage and stress fields. This paper presents a numerical investigation into the thermo-hydraulic-mechanical (THM) coupling behavior of layered soils surrounding a cylindrical heat source by combining the analytical layer element method (ALEM) and the finite element method (FEM). The FEM is utilized to analyze the soil-cylindrical heat source interaction and the ALEM is used to obtain the fundamental solution of the layered soil. Then the THM coupling solution between the heat source and the soil is obtained by the simplified FEM-ALEM coupling method. Detailed validation against experimental result, and verifications against semi-analytical solution and numerical results by Comsol Multiphysics are performed to confirm the robustness of the present method, followed by extensive parametric studies to examine the effects of decaying half-life and type of the time-varying heat source, and the soil layered characteristics on the behavior of soils. It’s evident that the present method is accessible and can be implemented via common programming language, e.g. Fortran.

Vertical response of a pile embedded in highly-saturated soil with compressible pore fluid and anisotropic permeability

For highly-saturated soils, the effect of air bubbles on the consolidation of soil is mainly reflected by the compressibility of pore fluid. In this paper, the effect of compressible pore fluid and anisotropic permeability on the soil mechanism is investigated based on the Biot’s consolidation theory and analytical layer element method (ALEM). The response of pile in highly-saturated soils is further investigated by employing the finite element method and theory of one-dimensional bar. The effects of compressibility of pore fluid and anisotropic parameter are investigated by means of numerical computation. The results show that the compressibility of pore fluid has a significant effect on the pile’s initial deformation while has less influence on the final displacement. The peak value of pore pressure in a highly-saturated soil with a larger compressibility is smaller and appears later. It takes less time for the pore water to completely dissipate in highly-saturated soil with a larger horizontal permeability coefficient.

On the consolidation and creep behaviour of layered viscoelastic gassy sediments

Gassy sediments are frequently encountered in engineering geology and geotechnical engineering. Gas bubbles contained in these sediments significantly change the engineering properties, and further influence the consolidation and creep process. The long term behaviour of gassy sediment is drastically different from that of saturated and unsaturated soils. This study presents an analytical solution for exploring such behaviour within layered viscoelastic gassy sediments under different type of load. An Analytical layer element method together with a Laplace-Hankel transform are employed to solve the governing equations, and the viscoelastic solution is then captured with the aid of the elastic-viscoelastic correspondence principle. Comparisons of the present solution with published semianalytical solutions and experimental results, for a single and double layered soils, are provided. Extensive parametric analyses were carried out to explore the effects of the soil skeleton model, fractional order, type of load, saturation degree and stratification characteristics on consolidation and creep processes. In the present model, the permeability is saturation degree- and porosity-dependent and the modulus of elasticity is time-dependent, which can simulate the long term behaviours of gassy sediments reasonably.

Thermo-mechanical behaviour of multi-layered media based on the Lord-Shulman model

The relaxation time model is introduced to analyse the thermo-mechanical problem for multi-layered media in this paper. The Fourier heat conduction equation is extended by introducing a relaxation time based on the Lord-Shulman model. For multi-layered media, the analytical layer-element method is employed to establish the global stiffness matrix equations by assembling the correlative layer-elements in the Laplace-Hankel domain. Then, solutions for displacement and temperature in the time domain are obtained by solving the global matrix equations and implementing a numerical inversion procedure. For numerical implementations, computational overflows are avoided by eliminations of positive exponentials in the stiffness matrix, and numerical instabilities in special cases due to singularity are removed by replacing singular layer-elements with well-conditioned ones. Comparisons with the existing solutions and the FEM analysis demonstrate the accuracy and efficiency of the proposed method. Finally, a series of numerical examples are presented to discuss the effects of transient load type, stratification, relaxation time and the surface heat transfer coefficient.

A simplified method for assessing the dynamic behaviour of a pile in layered saturated soils that considers current scour

Piles are commonly used in wharfs and offshore platform foundations. The coupled effects of current scour and dynamic load can reduce the non-deformability of a pile-soil system and ultimately lead to structural instability of structures. This paper develops a simplified method to study the dynamic interaction of layered saturated soils and piles under current scour conditions. Fundamental solutions for the dynamic consolidation of layered soil are obtained by the analytical layer element method (ALEM). The pile is modelled as a one-dimensional bar and solved by the finite element method (FEM). By coupling the ALEM and the FEM, solutions for the dynamic behaviour of the pile in soils are obtained while considering current scour. A flexibility matrix that is assembled by fundamental solutions is modified and expanded to match the stiffness matrix of the pile by the simplified method. This approach can solve pile-soil dynamic interaction problems under varied scouring conditions. The influences of scour type, scour depth, excitation frequency and layered property are examined, and the results show that the dynamic behaviour of the pile can be accurately simulated using the simplified method.

Dual integral equation solution of eccentricly loaded rectangular rigid foundation embedded in layered transversely isotropic soils

This paper investigates the static interaction between an eccentricly loaded rectangular rigid foundation and layered transversely isotropic soils. Firstly, the solution of the layered transversely isotropic soils is derived using the analytical layer element method. After decomposing the deformation forms of the rigid rectangular foundation under eccentric loads, we establish the dual integral equations through mixed boundary conditions. Then, the Jacobi orthogonal polynomial and the Bessel function are employed to solve the above dual integral equations, and the static response solution of the rigid rectangular foundation subjected to eccentric loads is obtained through superposition. The results of this study are compared with those obtained from ABAQUS simulation to verify the presented method. Finally, numerical examples are designed to further elucidate the influence of transverse isotropy and stratification of the soils as well as the embedded depth and aspect ratio of foundation on the static response of a rigid rectangular foundation due to eccentric loads.

3D dynamic analysis of a pavement plate resting on a transversely isotropic multilayered foundation due to a moving load

A method is proposed for the 3D dynamic analysis of a pavement plate resting on transversely isotropic multilayered foundation due to a moving load. The composite laminated plate theory and the analytical layer-element method are utilized to solve the dynamic plate-foundation interaction problem. The governing equations of motion of the pavement plate in the moving system are derived with a combination of the thin plate theory and laminated plate theory, while the solutions for the transversely isotropic multilayered foundation under dynamic loadings are achieved with the use of the analytical layer-element method. Then, based on the continuity conditions at the plate-foundation interface, the dynamic behavior of the pavement plate undergoing a moving load is achieved. Finally, several examples are given to confirm the accuracy of the proposed method and to illustrate the influences of the location of rebar, the velocity of moving load, the reinforcement ratio and the elastic modulus of concrete on the dynamic behavior of pavement plates.

Vertical dynamic analysis of a rigid disk embedded in layered saturated soils with compressible fluid

This paper introduces an approach for modelling the dynamic behavior of a vertically loaded rigid disk embedded in layered soils by coupling the analytical layer element method (ALEM) and boundary element method (BEM). The general solutions for dynamic behavior of layered saturated soils with compressible fluid are derived via ALEM. The disk-soil interface is divided into many elements according to the disk segments by utilizing BEM. The solutions for dynamic soil-disk interaction problem are obtained by coupling BEM and ALEM, where the ALEM solution is treated as the kernel function of BEM. The effectiveness of the present method is confirmed by the comparison with existing ones. Selected examples are performed to explore the effects of excitation frequency, embedded depth of the rigid disk, compressibility of pore fluid, permeability and the stratification characteristic on the dynamic responses.

General solutions of transversely isotropic multilayered media subjected to rectangular time-harmonic or moving loads

This paper presents the general solutions of three-dimensional transversely isotropic multilayered media subjected to a vertical or horizontal rectangular dynamic load by utilizing the analytical layer-element method, and the solutions can be used for both time-harmonic loads and moving ones. Based on the governing equations and constitutive equations of a transversely isotropic elastic body, the analytical layer-element solutions of a single medium layer are derived in the Fourier transformed domain by utilizing the double Fourier integral transform. Taking the continuity conditions between adjacent layer and boundary conditions into account, the global stiffness matrix can be obtained by assembling the interrelated layer elements. The final solutions in the frequency domain are recovered by the inversion of double Fourier integral transform. Numerical examples are given to study the influence of the transversely isotropic character, frequency of load excitation, stratification and the first layer's thickness when the media are subjected to a time-harmonic load, and the influence of the load speed as well as the load depth when the media are subjected to a moving constant load, respectively.

Transient dynamic response of multilayered saturated media subjected to impulsive loadings

SummaryThis paper presents a stable and efficient method for calculating the transient solution of layered saturated media subjected to impulsive loadings by means of the analytical layer element method. Starting with the field equations based on Biot's linear theory for porous, fluid‐saturated media, and the seepage continuity equation, an analytical layer element for a single layer is established by applying Laplace‐Hankel integral transform. The global stiffness matrix in the transform domain for a layered saturated half‐space subjected to a transient circular patch loading is obtained by assembling the layer elements of each layer. The displacements in the time domain are derived by Laplace‐Hankel inverse transform of the global stiffness matrix. Numerical examples are conducted to verify the accuracy of the method and to demonstrate the influences of type of transient loading, buried depth of loading, permeability, and stratification of materials on the transient response of the multilayered saturated poroelastic media.

Vibration isolation of row of piles embedded in transverse isotropic multi-layered soils

The analytical layer-element method is used to solve the transverse isotropic multi-layered soils, and the finite element method is used for the piles. Considering the displacement coordination and the equilibrium of the contact force along the pile-soil contact face, the dynamic response equations of the single row of piles under an external circular time-harmonic surface vertical load are achieved. Then, the displacements at the observation point with and without the effect of piles are obtained, respectively. The influences of the soils’ transverse isotropy, stratification characteristics and pile spacing on the isolation effect of the single row of piles are investigated.

Vibration of a pre-stressed plate on a transversely isotropic multilayered half-plane due to a moving load

• The pre-stressed plate is governed by the Kirchhoff plate theory. • The transversely isotropic multilayered half-plane is solved by the analytical layer-element method. • The contact stress and the deflection of plate are derived by considering compatibility conditions. • Influence of load speed, the rigidity of plate and the axial force applied on the plate are investigated. This paper presents an analytical research on the dynamic interaction problem between a pre-stressed plate and a transversely isotropic multilayered half-plane subjected to a moving load. The pre-stressed plate is governed by the Kirchhoff plate theory, and the transversely isotropic multilayered half-plane is solved by the analytical layer-element method. Combining the frictionless contact and displacement compatibility conditions between the plate and the soil, the contact stress and the deflection of plate in the Fourier transform domain are derived. With the aid of the inverse Fourier transform, the actual solutions can be further achieved. Numerical examples are given to illustrate the influence of load speed, the rigidity of plate, the axial force applied on the plate and the stratified character of the soil.

Behavior of a multilayered transversely isotropic half space due to horizontal transient loadings

Soils and the related structures are deeply influenced by horizontal transient loadings, such as the wind loads and the seismic forces on tall buildings, and the wave forces on offshore structures. So the stresses and displacements caused by horizontal transient loadings are worthy of study. This paper investigates the behavior of a multilayered transversely isotropic half space due to horizontal transient loadings over a circular area by using the analytical layer-element method. Numerical examples are given to make comparisons with ABAQUS and to expound the effect of transient loading characteristic, material anisotropy and loading depth on the behavior of media.