Poroelastic Soil Research Articles

Dynamic response of an eccentrically lined circular tunnel in poroelastic soil under seismic excitation

An exact analysis for two-dimensional dynamic interaction of monochromatic progressive plane compressional and shear seismic waves with a permeable circular tunnel lining of circumferentially varying wall thickness buried in a boundless porous elastic fluid-saturated formation is presented. The novel features of Biot dynamic theory of poroelasticity in conjunction with the translational addition theorems for cylindrical wave functions, along with the appropriate wave field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in form of infinite series. The analytical results are illustrated with numerical examples in which an air-filled and water-saturated permeable tunnel lining of variable wall thickness, embedded within water-saturated surrounding formations of distinct frame properties (soft, stiff, and stiff viscoelastic soil), is insonified by fast compressional or shear waves at selected angles of incidence. The effects of liner eccentricity, interface permeability, formation material type, incident wave frequency, and angle of incidence on the hoop stress amplitude are evaluated and discussed for representative values of the parameters characterizing the system. Limiting cases are considered and good agreements with the solutions available in the literature are obtained.

On the seismic response of a flexible wall retaining a viscous poroelastic soil

A simple and reliable method is presented for the seismic analysis of a flexible wall retaining a layer of fluid-saturated viscous and poroelastic soil. A viscous version of the linear poroelastic Biot model is adopted for the description of the soil dissipative behavior. The effects of the wall flexibility and the mechanical properties of the soil on the amplitude and distribution of the pressures and the associated forces acting on the wall under harmonic loadings are firstly analyzed. The pseudostatic response is then recovered as a particular case for a vanishing small frequency of excitation. Finally, the response of the soil–wall system to generic seismic excitation is obtained using the Discrete Fourier Transform (FFT) method through the superposition of the contribution of each harmonic component of the ground acceleration spectrum. The analysis of the dynamic response obtained for different geometries of the wall and mechanical soil behavior allowed the relative importance of the various parameters involved in the seismic response of the system to be assessed.

Drained and undrained pullout capacity of a stiff inclusion in a saturated poroelastic matrix

AbstractShear‐lag analysis is used to obtain closed‐form solutions for the problem of a stiff inclusion embedded in a poroelastic soil matrix. The following assumptions are made: the soil matrix and the inclusion are elastic; plane strain conditions apply; and shear stresses at the soil‐inclusion interface follow Coulomb's friction law. Two solutions are obtained, the first one for drained conditions where no excess pore pressures are generated, and the second one for undrained conditions where excess pore pressures are produced and the soil does not change volume during pullout. The solutions are verified by comparing analytical predictions with numerical results obtained using a finite element method. Predictions from the analytical solutions are also compared with results from experiments conducted in a large‐scale pullout box. Both comparisons show good agreement. The analytical solution shows that the pullout capacity in drained and undrained conditions is overall independent of the relative stiffness of the soil and the inclusion. The most important factor controlling the pullout capacity is the coefficient of friction between the soil and the inclusion. Both drained and undrained pullout capacities increase with the coefficient of friction; although the drained capacity shows a proportional increase, it is not so for the undrained capacity. The ratio of undrained to drained pullout capacity is about 0.9 for friction coefficients smaller than 0.2, but can be as small as 0.6 for a coefficient of friction of 1.0. Copyright © 2006 John Wiley & Sons, Ltd.

Hydraulic Damping of Saturated Poroelastic Soils During Steady-State Vibration

A theoretical study of the steady-state response of a saturated poroelastic soil column during compressional and rotational harmonic vibrations is presented. Hydraulic damping due to Biot flow is evaluated for top-drained and double-drained boundary conditions and for compressional and rotational motions using the theory of a damped single-degree-of-freedom system. For compressional motions, the dynamic response of gravels and sands is highly influenced by the compressibility of the pore fluid. More hydraulic damping occurs as soil hydraulic conductivity increases and as the column boundary conditions change from top drained to double drained. On the other hand, hydraulic damping for rotational motions is significantly less than that for compressional motions and is dependent on a dimensionless hydraulic conductivity parameter Ks . For Ks within the range of 10−3 –100 , hydraulic damping may have an important contribution to total soil damping, especially at small strain levels.

Application of Biot's poroelasticity to some soil dynamics problems in civil engineering

This review type of paper shows how the poroelastodynamic theory of Biot can be applied to some soil dynamics problems encountered in transportation engineering, which have been solved by the present authors. These problems involve rigid walls retaining poroelastic soil and subjected to harmonic seismic waves and moving loads on poroelastic soil. Both classes of problems involve a soil layer over bedrock, are of the plane strain type and are solved analytically by two methods: a direct (almost exact and exact for the above two classes of problems) method and an approximate method. The effects of shear modulus, porosity, permeability and hysteretic damping of the soil medium as well as the seismic frequency for retaining walls and velocity for moving loads on the dynamic response are numerically evaluated in order to assess their relative importance on that response.

Plain strain soil–structure interaction model for a building supported by a circular foundation embedded in a poroelastic half-space

A simple theoretical model for soil–structure interaction in water saturated poroelastic soils is presented, developed to explore if the apparent building–foundation–soil system frequency changes due to water saturation. The model consists of a shear wall supported by a rigid circular foundation embedded in a homogenous, isotropic poroelastic half-space, fully saturated by a compressible and inviscid fluid, and excited by in-plane wave motion. The motion in the soil is governed by Biot's theory of wave propagation in fluid saturated porous media. Helmholtz decomposition and wave function expansion of the two P-wave and the S-wave potentials is used to represent the motion in the soil. The boundary conditions along the contact surface between the soil and the foundation are perfect bond (i.e. welded contact) for the skeleton, and either drained or undrained hydraulic condition for the fluid (i.e. pervious or impervious foundation). For the purpose of this exploratory analysis, the zero stress condition at the free surface is relaxed in the derivation of the foundation stiffness matrix, which enables a closed form solution. The implications of this assumption are discussed, based on published comparisons for the elastic case. Also, a closed form representation is derived for the foundation driving forces for incident plane (fast) P-wave or SV wave. Numerical results and comparison with the full-scale measurements are presented in the companion paper, published in this issue.

Vertical vibration of an embedded rigid foundation in a poroelastic soil

This paper considers time-harmonic vertical vibration of an axisymmetric rigid foundation embedded in a homogeneous poroelastic soil. The soil domain is represented by a homogeneous poroelastic half space that is governed by Biot's theory of poroelastodynamics. The foundation is subjected to a time-harmonic vertical load and is perfectly bonded to the surrounding half space. The contact surface can be either fully permeable or impermeable. The dynamic interaction problem is solved by employing an indirect boundary integral equation method. The kernel functions of the integral equation are the influence functions corresponding to vertical and radial ring loads, and a ring fluid source applied in the interior of a homogeneous poroelastic half space. Analytical techniques are used to derive the solution for influence functions. The indirect boundary integral equation is solved by using numerical quadrature. Selected numerical results for vertical impedance of rigid foundations are presented to demonstrate the influence of poroelastic effect, foundation geometry, hydraulic boundary condition along the contact surface and frequency of excitation.

Green’s functions for uniformly distributed loads acting on an inclined line in a poroelastic layered site

Based on one type of practical Biot’s equation and the dynamic-stiffness matrices of a poroelastic soil layer and half-space, Green’s functions were derived for uniformly distributed loads acting on an inclined line in a poroelastic layered site. This analysis overcomes significant problems in wave scattering due to local soil conditions and dynamic soil-structure interaction. The Green’s functions can be reduced to the case of an elastic layered site developed by Wolf in 1985. Parametric studies are then carried out through two example problems.

Dynamic stress concentration around elliptic cavities in saturated poroelastic soil under harmonic plane waves

Potential function and complex function in the elliptic coordinate system are employed to solve the problem of scattering harmonic plane waves by multiple elliptic cavities in water saturated soil medium. The steady state Biot’s dynamic equations of poroelasticity are uncoupled into Helmholtz equations via given potentials. The stresses and pore water pressures are obtained by using complex functions in elliptic coordinates with certain boundary conditions. Finally, the dynamic stresses for the case of two interacting elliptic cavities are obtained and discussed in details via a numerical example.

Dynamic impedances of piles and groups of piles in saturated soils

A three-dimensional boundary element model is presented for the computation of time-harmonic dynamic stiffness coefficients of piles and pile groups embedded in two-phase poroelastic soils. Piles are modelled as continuum elastic solids and soil as a fluid-filled poroelastic half-space governed by Biot’s theory. Piles are bonded to the surrounding medium along the contact surface where rigorous pile–soil interaction conditions are imposed. The technique has been applied to the calculation of vertical and horizontal dynamic impedance functions of piles and 2 × 2 pile groups. Selected numerical results are presented to portray the influence of excitation frequency, pile stiffness, porous medium properties and kind of pile–soil contact conditions.

Dynamic stiffness matrix of a poroelastic multi-layered site and its Green’s functions

Few studies of wave propagation in layered saturated soils have been reported in the literature. In this paper, a general solution of the equation of wave motion in saturated soils, based on one kind of practical Biot’s equation, was deduced by introducing wave potentials. Then exact dynamic-stiffness matrices for a poroelastic soil layer and halfspace were derived, which extended Wolfs theory for an elastic layered site to the case of poroelasticity, thus resolving a fundamental problem in the field of wave propagation and soil-structure interaction in a poroelastic layered soil site. By using the integral transform method, Green’s functions of horizontal and vertical uniformly distributed loads in a poroelastic layered soil site were given. Finally, the theory was verified by numerical examples and dynamic responses by comparing three different soil sites. This study has the following advantages: all parameters in the dynamic-stiffness matrices have explicitly physical meanings and the thickness of the sub-layers does not affect the precision of the calculation which is very convenient for engineering applications. The present theory can degenerate into Wolfs theory and yields numerical results approaching those for an ideal elastic layered site when porosity tends to zero.

Dynamic effects of moving load on a poroelastic soil medium by an approximate method

The problem of the dynamic response of a fully saturated poroelastic soil stratum on bedrock subjected to a moving load is studied by using the theory of Mei and Foda under conditions of plane strain. The applied load is considered to be the sum of a large number of harmonics with varying frequency in the form of a Fourier expansion. The method of solution considers the total field to be approximated by the superposition of an elastodynamic problem with modified elastic constants and mass density for the whole domain and a diffusion problem for the pore fluid pressure confined to a boundary layer near the free surface of the medium. Both problems are solved analytically in the frequency domain. The effects of the shear modulus, permeability and porosity of the soil medium and the velocity of the moving load on the dynamic response of the soil layer are numerically evaluated and compared with those obtained by the exact solution of the problem. It is concluded that for fine poroelastic materials, the accuracy of the present method against the exact one is excellent.

Stresses and excess pore pressure induced in saturated poroelastic halfspace by moving line load

This paper examines stresses and excess pore fluid pressure that are induced in a saturated poroelastic soil of halfspace extent by a concentrated line load. The line load is moving at a constant velocity along the surface of the poroelastic halfspace. The governing equations for the proposed analysis are based on the Biot's theory of dynamics in saturated poroelastic soils. The governing partial differential equations are solved using Fourier transforms. The solutions for the stresses and excess pore pressure are expressed in the forms of inverse Fourier transforms. The numerical results are obtained by performing the numerical inversion of the transform integrals. A parametric study is presented to illustrate the influences of the velocity of moving load and the poroelastic material parameters on the stresses and excess pore pressure. At a high velocity, the maximum values of the stresses in a poroelastic halfspace are smaller than those in an elastic solid, whilst at a low velocity the stresses in a poroelastic halfspace are larger than those in an elastic halfspace. The potential of diffusivity has an important influence on the stresses and excess pore pressure.

Dynamic response of a soft soil layer to flow and periodical disturbance

AbstractThe dynamic response of a soft soil layer of finite thickness under the mutual effects of flow and periodical disturbance at the free surface is discussed in this work. The homogeneous water is governed by potential theory and the soil layer obeys Biot's theory of poroelasticity. The boundary‐value problem is solved by an analytical algorithm, in which the wave number is found first. Secondly, the closed form solutions are found by a two‐parameter perturbation method with the boundary‐layer correction. The results are also compared with those of the poroelastic soil layer of infinite thickness to show the impermeable rigid boundary effect. Copyright © 2003 John Wiley & Sons, Ltd.

Dynamic pressures on a pair of rigid walls experiencing base rotation and retaining poroelastic soil

The dynamic response of a pair of rigid retaining walls to horizontal harmonic ground shaking is studied analytically. The two walls are elastically constrained against rotation at their base. The retained material is idealized as a uniform, fully saturated poroelastic layer of soil of constant thickness obeying Biot’s dynamic poroelastic theory. In the analysis, emphasis is given to the calculation of the wall rotation angle. The parameters examined include mainly the rotational flexibility of the wall constraint, the properties of the retained medium and the distance between the walls. The response quantities considered include the displacement of the wall, the wall pressures, and the associated forces. It is shown that, for a system experiencing base rotation, the maximum wall forces are much lower than those obtained for fixed-based rigid walls for any combination of the soil permeability and porosity and any distance between the walls.

Dynamic pressures on a pair of rigid walls retaining poroelastic soil

This work deals with the evaluation of the dynamic pressures and the associated forces on a pair of rigid vertical cantilever walls retaining a uniform, fully saturated poroelastic layer of soil. Hysteretic damping in the soil skeleton may also be present. Wall pressures and forces are induced by horizontal ground shaking harmonically varying with time and spatially invariant. The problem is solved analytically under conditions of plane strain. The governing partial differential equations of motion, after separation of variables and the simplifying assumptions of zero vertical normal stresses and zero horizontal variation of vertical displacements, reduce to a system of two ordinary differential equations for the amplitudes of the solid skeleton horizontal displacement and the pore water pressure, which are easily solved. The parameters examined include the ratio of the distance between walls to the height of the retained soil material and the soil material properties such as porosity, permeability and damping. The comprehensive numerical data presented indicate that the displacements, wall pressures and resultant forces are highly dependent on the distance between the walls for any values of porosity and permeability.

2D dynamic response of unlined and lined tunnels in poroelastic soil to harmonic body waves

AbstractThe problem of harmonic wave diffraction by tunnels in an infinite poroelastic saturated soil obeying Biot's theory is studied numerically under conditions of plane strain and the effect of poroelasticity on the response is assessed through some parametric studies. The method is based on the theory of Mei and Foda, which considers the total field to be approximated by the superposition of an elastodynamic problem with modified elastic constants and mass density for the whole domain and a diffusion problem for the pore fluid pressure confined to a boundary layer at the free boundaries. Both problems are solved numerically by the boundary element method in the frequency domain. Results dealing with the response of a circular tunnel with and without an elastic concrete liner in an infinite poroelastic medium to incident harmonic P and SV plane waves are provided and compared against analytical ones as well as to those corresponding to linear elastic soil behaviour. Copyright © 2002 John Wiley & Sons, Ltd.

Unsteady Oscillations of a Liquid-Saturated Poroelastic Soil Layer

Unsteady Oscillations of a Liquid-Saturated Poroelastic Soil Layer

Harmonic response of a rigid wall retaining poroelastic soil by direct approach

The problem of the determination of the dynamic pressures and the associated forces on a rigid, vertical cantilever wall retaining a semi-infinite, uniform, fullysaturated poroelastic layer of soil is solved analytically under conditions of plane strain. Hysteretic damping in the soil skeleton may also be present. The rigid wall and the base of the soil layer are both excited by an acceleration harmonically varying with time and spatially invariant. The governing partial differential equations of motion, after separation of variables and the simplifying assumption of zero vertical normal stresses, reduce to a system of two ordinary differential equations for the amplitudes of the horizontal solid skeleton displacement and the pore water pressure, which are easily solved. Soil displacements and stresses, wall pressures and resultant forces as well as the pore water pressure are explicitly expressed. Their variation with frequency, hysteretic damping, porosity and permeability is numerically computed in order to assess the relative importance of the various parameters on the response.

Dynamic pressures on rigid cantilever walls retaining poroelastic soil media. Part I. First method of solution

The problem of the determination of dynamic pressures and the associated forces on a rigid, vertical cantilever wall retaining a semi-infinite, uniform, fully-saturated poroelastic layer of soil is solved analytically under conditions of plane strain. Hysteretic damping in the soil skeleton may also be present. The rigid wall and the base of the soil layer are both excited by an acceleration harmonically varying with time and spatially invariant. The governing partial differential equations of motion, after separation of variables and the simplifying assumption of zero vertical normal stresses, reduce to a system of two ordinary differential equations for the amplitudes of the horizontal solid skeleton displacement and the pore water pressure, which are easily solved. Soil displacements and stresses, wall pressures and resultant forces as well as the pore water pressure are explicitly expressed. Their variation with frequency, hysteretic damping, porosity and permeability is numerically computed in order to assess the relative importance of the various parameters on the response.