Finite Soil Layer Research Articles

Horizontal motions of a rigid disk placed on a poroelastic soil layer of finite thickness

AbstractIn the previous studies of rigid disk–soil dynamics, the soil under the foundation is usually treated as a poroelastic half‐space medium. However, the waves due to the vibration of rigid disk can reflect and refract back and forth between the finite soil layer and rigid bedrock, which would significantly influence the soil deformation and flow of the rigid disk–soil system. In order to overcome the shortcoming, this paper presents an analytical solution to determine the response of the rigid disk subjected to harmonic horizontal loads resting on poroelastic soil layer overlying rigid bedrock. The displacements and stresses field of the disk and soil are obtained by virtue of the Hankel transform method, dual integral equations method. Furthermore, the rationality and accuracy of the developed solution are confirmed in comparison with the previous studies. Based on the obtained solutions, numerical examples are performed to the effects of the thickness and permeability of poroelastic soil layer on the dynamic response of the rigid disk–soil system in the physical domain.

Elastodynamic Solutions of a Finite Soil Layer under Interior Distributed Actions

Through a method of displacement potentials, Fourier series, and Hankel integral transformation, the generalized solutions of an elastic layer resting on a rigid base under arbitrary, distributed, buried, and time-harmonic loads are developed in this study. With the proposed solution, the specific results for two kinds of uniform distributions as a kind of fundamental solutions in the interaction analysis of media and inclusions by the method of boundary integral equations are included as illustrations. Finally, numerical examples involving surface and buried patch loads are presented to validate the solutions and examine the effects of the thickness of the elastic layer. The results show that the proposed solution can cover the classical half-space solution by taking enough large thickness of the elastic layer (e.g., the ratio of the layer thickness beneath the load to the load radius ≥ 50 ) and the surface load solution by setting the load depth to zero; the underlying rigid base has significant and complex influence on the dynamic response of the thin layer due to wave reflections, which needs to be considered in the design and practice of related engineering.

An analytical model for the interaction between two dissimilar piles in a finite soil layer

AbstractAn analytical method is developed for the interaction between two dissimilar piles subjected to vertical loadings in a finite soil layer with a rigid base. A fictitious soil column is assumed for the corresponding shaft and the moduli of the soil–pile rod are expressed as a Heaviside step function of the modulus. The vertical soil displacements and the shaft resistances are calculated as the combined contributions by the two dissimilar piles in terms of the respective local coordinate systems. The displacements and stresses in two different local coordinates are transferred from one to the other using Graf's addition theorem. The boundary value problem for the soil layer is solved using the method of separation of variables with a series of undetermined constants. The unknown constants can be determined by considering the compatibility along the interfaces of the two soil–pile rods and the surrounding soil. A parametric study is performed to investigate the effects of the properties of the soil–pile system on the interaction between the two piles. Numerical results show that, for the dissimilar piles in the stiff soil, the effects of the difference of the pile lengths on the interaction factor are negligible. Also, the interaction factor of the dissimilar piles in the soft soil depends heavily on the difference in lengths.

Semi-Analytical Solutions for Two-Dimensional Transport and Transformation of Contaminants in Soil Medias Associated with Large-Strain Deformation

For the understanding of contaminant transport and transformation through landfill liner soils, most models are proposed with one-dimensional solutions. However, for large-scale contamination analysis, the one-dimensional analytical equations are not valid owing to the restriction of contaminants moving in horizontal direction. Thus, semi-analytical solutions for two-dimensional transport and transformation of contaminants through soil media with the consideration of large-strain deformation have been developed. To achieve this, Gibson’s large-strain consolidation theory is applied to capture the deformation of soil media under loading, with self-weight effects being taken into account. Transport and transformation of dissolved or sorbed contaminates in fully saturated finite soil medias are captured by extending a well-developed advection-dispersion model in two-dimensional space. The proposed analytical solutions are validated through simulating the process of coupled transport-transformation process of contaminants and consolidation of a finite soil layer. Profiles of contaminant concentration for different cases have been compared and discussed. The resulting simulation shows that large-strain deformation would restrict the transport and transformation of contaminants significantly, in both horizontal and vertical directions. Parameter studies also indicate that, with the increasing depth of soil layer, the breakthrough time for contaminants increases dramatically; diffusion coefficients affect the two-dimensional distributions of contaminant concentration and fate of contaminant in layered soil significantly. The numerical findings of this study can provide proper suggestions for the design of landfill liners.

Effect of Resonance in Soil-Structure Interaction for Finite Soil Layers

In case of seismic design the deformability of the soil should be considered, which can be performed in several ways. Most of the methods do not take into account the finite dimensions of the soil, which results significantly different behavior than the spring-dashpot systems. For an infinite medium, which is used in many cases, there are no eigenmodes, however in practical applications the soft soil is always bounded by rocks. For these cases the soil has eigenmodes and the resonance may influence considerably the response of the system. This question was investigated numerically by FE calculations, and it was found that in certain cases the resonance, which is neglected in the common design process, may significantly enhance the earthquake loads. In this paper this phenomenon is investigated and the parameter range is defined when this effect must be taken into account.

Soil and topographic effects on ground motion of a surficially inhomogeneous semi-cylindrical canyon under oblique incident SH waves

To elucidate the ground motion amplification due to combined soil and topographic effects, an analytical formulation in the framework of classical elastodynamics is derived for the scattering of oblique incident plane SH waves by a semi-cylindrical canyon covered by a local inhomogeneous soil layer with a radially-varying modulus. Allowing the shear modulus of the finite soil layer covering the circular surface of the canyon as a power of the radial distance, the governing equation of motion for the anti-plane shear problem is derived and solved analytically by the method of wave function expansion. The ground motions for both of the homogeneous and inhomogeneous canyons under oblique incident waves can be computed efficiently and a comprehensive set of numerical examples are presented as illustrations. The degree of inhomogeneity of the soil layer and its thickness are found to affect the magnitude and the pattern of ground motion amplification of the cylindrical canyon surface depending on the frequency content, the irregular topography and obliquity of the wave incidence.

Torsional dynamic response of a pile embedded in layered soil based on the fictitious soil pile model

The torsional dynamic response of a pile embedded in layered soil is investigated while considering the influence of the pile end soil. The finite soil layers under the end of the pile are modeled as a fictitious soil pile that has the same cross-sectional area as the pile and is in perfect contact with the pile end. To allow for variations of the modulus or cross-sectional area of the pile and soil, the soil surrounding and below the pile is vertically decomposed into finite layers. Using the Laplace transform and impedance function transfer method, the analytical solution for the dynamic response of the pile head in the frequency domain is then obtained, and the relevant semi-analytical solution in the time domain is derived using the inverse Fourier transform and convolution theorem. The rationality and accuracy of the solution is verified by comparing the torsional dynamic behavior of the pile calculated with the fictitious soil pile with those based on a rigid support model and a viscoelastic support model. Finally, a parametric study is conducted to investigate the influence of the properties and thickness of the pile end soil on the torsional dynamic response of the pile.

Vertical dynamic impedance of pile considering the dynamic stress diffusion effect of pile end soil

ABSTRACTA new analytical model is presented to analyze the dynamic stress diffusion effect of pile end soil on the vertical dynamic impedance of the pile. The surrounding soil of the pile is modeled by using the plane strain model and the pile is simulated by using one-dimensional elastic theory. Finite soil layers below the pile end are modeled as conical fictitious soil pile with stress diffusion angle which reflects the dynamic stress diffusion effect of pile end soil. By means of the Laplace transform and impedance function transfer method, the analytical solution of the vertical dynamic impedance at the pile head in frequency domain is yielded. Then, a comparison with other models is performed to verify the conical fictitious soil pile model. Finally, based on the proposed solution, the selected numerical results are compared to analyze the influence of dynamic stress diffusion effect for different design parameters of the soil-pile system on the vertical dynamic impedance at the pile head.

An alternative BE–FE formulation for a raft resting on a finite soil layer

This work presents a numerical tool for simulating the interaction of a raft with the soil, which can be a half space or a finite layer supported by a rigid base. The soil is modelled using the boundary element method (BEM) with Kelvin fundamental solutions. Infinite boundary elements (IBEs) are employed for the far field simulation, allowing computational cost reduction without compromising the accuracy. The IBE formulation is based on a triangular boundary element with linear shape functions instead of the commonly used quadrilateral IBEs. Displacements are restrained at the rigid base, when it exists. The raft is modeled with the finite element method (FEM) using a triangular element, which is obtained by combining bending effects and membrane effects. For the FEM–BEM coupling, the BEM tractions are considered as nodal reactions in the FEM formulation. The coupling is established using equilibrium and compatibility conditions, obtaining a system of equations that represents the complete problem.

A novel semi-analytical approach for non-uniform vegetated flows

In this paper a semi-analytical approach is proposed to understand the mechanism by which a non-uniform vegetated flowpasses over a finite thick soil layer covered with grass. The flow region is divided into three layers: a homogenous water layer, a mixed water-grass layer, and a finite thick soil layer (hereafter referred to as the water layer, the grass layer, and the soil layer). The flow of the water layer is governed by the Navier–Stokes equations. Both the grass and soil layers are regarded as porous media and the Biot’s theory of poroelasticity is applied to the porous medium flow. The semi-closed solutions are then obtained by the Runge–Kutta method. The drag force induced by the flow through the grass layer and the flow profiles of three patterns: submerged grass, emergent grass and mixed type are also discussed.

A new approach for time effect analysis of settlement for single pile based on virtual soil-pile model

A new approach is proposed to analyze the settlement behavior for single pile embedded in layered soils. Firstly, soil layers surrounding pile shaft are simulated by using distributed Voigt model, and finite soil layers under the pile end are assumed to be virtual soil-pile whose cross-section area is the same as that of the pile shaft. Then, by means of Laplace transform and impedance function transfer method to solve the static equilibrium equation of pile, the analytical solution of the displacement impedance function at the pile head is derived. Furthermore, the analytical solution of the settlement at the head of single pile is theoretically derived by virtue of convolution theorem. Based on these solutions, the influences of parameters of soil-pile system on the settlement behavior for single pile are analyzed. Also, comparison of the load-settlement response for two well-instrumented field tests in multilayered soils is given to demonstrate the effectiveness and accuracy of the proposed approach. It can be noted that the presented solution can be used to calculate the settlement of single pile for the preliminary design of pile foundation.

Longitudinal dynamic response of pile in layered soil based on virtual soil pile model

Taking the effect of finite soil layers below pile end into account, the longitudinal dynamic response of pile undergoing dynamic loading in layered soil was theoretically investigated. Firstly, finite soil layers below pile end are modeled as virtual soil pile whose cross-section area is the same as that of the pile and the soil layers surrounding the pile are described by the plane strain model. Then, by virtue of Laplace transform and impedance function transfer method, the analytical solution of longitudinal dynamic response at the pile head in frequency domain is yielded. Also, the semi-analytical solution in time domain undergoing half-cycle sine pulse at the pile head is obtained by means of inverse Laplace transform. Based on these solutions, a parametric study is conducted to analyze emphatically the effects of parameters of soil below pile end on velocity admittance and reflected wave signals at the pile head. Additionally, a comparison with other models with different supporting conditions from soil below pile end is performed to verify the model presented.

Guided wave propagation in single and double layer hollow cylinders embedded in infinite media

Millions of miles of pipes are being used for the transportation, distribution, and local use of petroleum products, gas, water, and chemicals. Most of the pipes are buried in soil, leading to the significance of the study on the subject of guided wave propagation in pipes with soil influence. Previous investigations of ultrasonic guided wave propagation in an elastic hollow cylinder and in an elastic hollow cylinder coated with a viscoelastic material have led to the development of inspection techniques for bare and coated pipes. However, the lack of investigation on guided wave propagation in hollow cylinders embedded in infinite media like soil has hindered the development of pipe inspection methods. Therefore the influence of infinite media on wave propagation is explored in this paper. Dispersion curves and wave structures of both axisymmetric and nonaxisymmetric wave modes are developed. Due to the importance of the convergence of numerical calculations, the requirements of thickness and element number of the finite soil layer between hollow cylinder and infinite element layer are discussed, and an optimal combination is obtained in this paper. Wave structures are used for the mode identification in the non-monotonic region caused by the viscoelastic properties of coating and infinite media.

Plane strain consolidation of soil layer with anisotropic permeability

This paper presents an alternative analytical technique to study a plane strain consolidation of a poroelastic soil by taking into account the anisotropy of permeability. From the governing equations of a saturated poroelastic soil, the relationship of basic variables for a point of a soil layer is established between the ground surface (z = 0) and the depth z in the Laplace-Fourier transform domain. Combined with the boundary conditions, an exact solution is derived for plane strain Biot’s consolidation of a finite soil layer with anisotropic permeability in the transform domain. Numerical inversions of the Laplace transform and the Fourier transform are adopted to obtain the actual solution in the physical domain. Numerical results of plane strain Biot’s consolidation for a single soil layer show that the anisotropic of permeability has a great influence on the consolidation behavior of the soils.

Transfer matrix solutions to plane-strain and three-dimensional Biot’s consolidation of multi-layered soils

Starting from the governing equations of a saturated poro-elastic soil in the Cartesian system, and introducing the displacement functions, the transfer matrix relationship of displacements, stresses, excess pore water pressure, and flux between the ground surface ( z = 0) and an arbitrary depth z of a finite soil layer is established in the Laplace-Fourier transforms domain. Based on this relationship and transfer matrix concept and by considering the continuity conditions between adjacent layers and the boundary conditions of the layered soil system, the solutions for plane-strain and three-dimensional Biot’s consolidation problems of a multi-layered soil system in the transformed domain are derived, respectively. The actual solutions in the physical domain can be acquired by the inversion of the Laplace-Fourier transforms. The numerical results for plane-strain and three-dimensional Biot’s consolidation problems of a single layer and multi-layered soil system are performed, and the feasibility and accuracy of the proposed solutions in this study are proved by comparing with some existing results.

A new analytical solution to axisymmetric Biot’s consolidation of a finite soil layer

A new analytical method is presented to study the axisymmetric Biot’s consolidation of a finite soil layer. Starting from the governing equations of axisymmetric Biot’s consolidation, and based on the property of Laplace transform, the relation of basic variables for a point of a finite soil layer is established between the ground surface (z= 0) and the depth z in the Laplace and Hankel transform domains. Combined with the boundary conditions of the finite soil layer, the analytical solution of any point in the transform domain can be obtained. The actual solution in the physical domain can be obtained by inverse Laplace and Hankel transforms. A numerical analysis for the axisymmetric consolidation of a finite soil layer is carried out.

A new method for solving Biot’s consolidation of a finite soil layer in the cylindrical coordinate system

A new method is developed to solve Biot’s consolidation of a finite soil layer in the cylindrical coordinate system. Based on the governing equations of Biot’s consolidation and the technique of Laplace transform, Fourier expansions and Hankel transform with respect to time t, coordinate θ and coordinate r, respectively, a relationship of displacements, stresses, excess pore water pressure and flux is established between the ground surface (z = 0) and an arbitrary depth z in the Laplace and Hankel transform domain. By referring to proper boundary conditions of the finite soil layer, the solutions for displacements, stresses, excess pore water pressure and flux of any point in the transform domain can be obtained. The actual solutions in the physical domain can be acquired by inverting the Laplace and the Hankel transforms.

Transfer matrix solutions for three-dimensional consolidation of a multi-layered soil with compressible constituents

In this paper, transfer matrix solutions for three-dimensional consolidation of a multi-layered soil considering the compressibility of pore fluid are presented. The derivation of the solutions starts with the fundamental differential equations of Biot’s three-dimensional consolidation theory, takes into account the compressibility of pore fluid in the Cartesian coordinate system, and introduces the extended displacement functions. The relationship of displacements, stresses, excess pore water pressure, and flux between the ground surface ( z = 0) and an arbitrary depth z is established for Biot’s three-dimensional consolidation problem of a finite soil layer with compressible pore fluid by taking the Laplace transform with respect to t and the double Fourier transform with respect to x and y, respectively. Based on this relationship of the transfer matrix, the continuity between layers, and the boundary conditions, the solutions for Biot’s three-dimensional consolidation problem of a multi-layered soil with compressible constituents in a Laplace–Fourier transform domain is obtained. The final solutions in the physical domain are obtained by inverting the Laplace–Fourier transforms. Numerical analysis is carried out by using a corresponding program based on the solutions developed in this study. This analysis demonstrates that the compressibility of pore fluid has a remarkable effect on the process of consolidation.

Determination of Initial Unconditional Solution of Heat Conductivity Equation for Evaluation of Temperature Variance in Finite Soil Layer

Determination of Initial Unconditional Solution of Heat Conductivity Equation for Evaluation of Temperature Variance in Finite Soil Layer

Effect of Presence of Rigid Base within the Soil on the Dynamic Response of Rigid Surface Foundation

Abstract The present experimental investigations study the effect of presence of rigid base at any depth within the soil mass on the dynamic response of foundation under vertical mode of vibration. Model block vibration tests on rigid surface footing are conducted on a different soil layer of finite thicknesses underlain by a rigid base. A concrete block of size 400 × 400 × 100 mm is used as the model block, and a Lazan type mechanical oscillator is used for inducing vibration in vertical direction. The finite soil layers of different thicknesses are prepared in a pit at the bottom of which a massive concrete layer of 300 mm thick was cast to represent it as a rigid base. In the investigation two different soils, namely, local in situ soil and sand are used. In total 72 tests are conducted in different loading combinations and soil types, and several important observations are reported. Two different methods are proposed to analyze the dynamic response of a foundation resting on a finite layer underlain by a rigid layer. Finally, the experimental results are compared with the results that were obtained by the proposed method. A Mass-Spring-Dashpot (MSD) model with proper consideration of damping factor is found to provide reasonably accurate results. Elastic Half Space Theory (EHST) with equivalent soil properties is found to underestimate the displacement amplitude.