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1.
By virtue of a pair of scalar potentials for the displacement of the solid skeleton and the pore fluid pressure field of a saturated poroelastic medium, an alternative solution method to the Helmholtz decomposition is developed for the wave propagation problems in the framework of Biot's theory. As an application, a comprehensive solution for three‐dimensional response of an isotropic poroelastic half‐space with a partially permeable hydraulic free surface under an arbitrarily distributed time‐harmonic internal force field and fluid sources is developed. The Green's functions for the poroelastic fields, corresponding to point, ring, and disk loads, are reduced to semi‐infinite complex‐valued integrals that can be evaluated numerically by an appropriate quadrature scheme. Analytical and numerical comparisons are made with existing elastic and poroelastic solutions to illustrate the quality and features of the solution. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

2.
An exact steady‐state closed‐form solution is presented for coupled flow and deformation of an axisymmetric isotropic homogeneous fluid‐saturated poroelastic layer with a finite radius due to a point sink. The hydromechanical behavior of the poroelastic layer is governed by Biot's consolidation theory. Boundary conditions on the lateral surface are specifically chosen to match the appropriate finite Hankel transforms and simplify the transforms of the governing equations. Ordinary differential equations in the transformed domain are solved, and then the analytical solutions in the physical space for the pore pressure and the displacements are finally obtained by using finite Hankel inversions. The analytical solutions at some special locations such as the top and bottom surfaces, lateral surface, and the symmetrical axis are given and analyzed. And a case study for the consolidation of a water‐saturated soft clay layer due to pumping is conducted. The analytical solution is verified against the finite element solution. Meanwhile, an analysis of coupled hydromechanical behavior is carried out herein. The presented analytical solution is an exact solution to the practical poroelastic problem within an axisymmetric finite layer. It can provide us a better understanding of the poroelastic behavior of the finite layer due to fluid extraction. Besides, it can be applied to calibrate numerical schemes of axisymmetric poroelasticity within finite domains. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

3.
In this paper, frequency domain dynamic response of a pile embedded in a half‐space porous medium and subjected to P, SV seismic waves is investigated. According to the fictitious pile methodology, the problem is decomposed into an extended poroelastic half‐space and a fictitious pile. The extended porous half‐space is described by Biot's theory, while the fictitious pile is treated as a bar and a beam and described by the conventional 1‐D structure vibration theory. Using the Hankel transformation method, the fundamental solutions for a half‐space porous medium subjected to a vertical or a horizontal circular patch load are established. Based on the obtained fundamental solutions and free wave fields, the second kind of Fredholm integral equations describing the vertical and the horizontal interaction between the pile and the poroelastic half‐space are established. Solution of the integral equations yields the dynamic response of the pile to plane P, SV waves. Numerical results show the parameters of the porous medium, the pile and incident waves have direct influences on the dynamic response of the pile–half‐space system. Significant differences between conventional single‐phase elastic model and the poroelastic model for the surrounding medium of the pile are found. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

4.
A single pile embedded in a layered poroelastic half‐space subjected to a harmonic lateral load is investigated in this study. Based on Biot's theory, the frequency domain fundamental solution for a horizontal circular patch load applied in the layered poroelastic half‐space is derived via the transmission and reflection matrices method. Utilizing Muki and Sternberg's method, the second kind of Fredholm integral equation describing the dynamic interaction between the layered half‐space and the pile subjected to a top harmonic lateral load is constructed. The proposed methodology is validated by comparing results of this paper with some existing results. Numerical results show that for a two‐layered half‐space, the thickness of the upper softer layer has pronounced influences on the dynamic response of the pile and the half‐space. For a three‐layered half‐space, the presence of a softer middle layer in the layered half‐space will enhance the compliance for the pile significantly, while a stiffer middle layer will diminish the dynamic compliance of the pile considerably. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

5.
Based on the Biot's poroelastic theory and using scalar potential functions both the ring load and point load displacement Green's functions for a transversely isotropic saturated porous full‐space composed of an upper half‐space, a finite thickness middle layer and a lower half‐space is analytically presented for the first time. It is assumed that each region consists of a different transversely isotropic material. The equations of poroelastodymanics in terms of the solid displacements and the pore fluid pressure are uncoupled with the help of two scalar potential functions, so that the governing equations for the potential functions are either a second order wave equation or a repeated wave‐heat transfer equation of sixth order. With the aid of Fourier expansion with respect to circumferential direction and Hankel integral transforms with respect to the radial direction in cylindrical coordinate system, the response is determined in the form of line integrals in the real space, followed by theorem of inverse Hankel integral transforms. The solutions degenerate to a single phase elastic material, and the results are compared with previous studies, where an excellent agreement may be observed with the results provided in the literature. Some examples of displacement Green's functions are finally given to illustrate the solution. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

6.
The vibrations of railway tracks on a poroelastic half‐space generated by moving trains are investigated through a vehicle–track–ground coupling model. The theoretical model incorporates a vehicle, a track, and a fully saturated poroelastic half‐space soil medium. The source of vibration excitation is divided into two components: the quasi‐static loads and the dynamic loads. The quasi‐static loads are related to the static component of the axle loads, whereas the dynamic loads are due to the dynamic wheel–rail interaction. A linear Hertizian contact spring is introduced between each wheelset and the rail to consider the dynamic loads. Biot's dynamic theory is used to characterize the poroelastic half‐space soil medium. Using the Fourier transform, the governing equations for the track–ground system are solved and the numerical results are presented for a single axle vehicle model. The different dynamic characteristics of the elastic soil medium and the saturated poroelastic medium are investigated. In addition, the different roles of the moving axle loads and the roughness‐induced dynamic loads are identified. It is concluded that the vibration level of the free field off the track predicted by the poroelastic soil medium is smaller than that predicted by the elastic soil medium for vehicle speed below the Rayleigh wave speed of the poroelastic half‐space, whereas it is larger for vehicle speed above the Rayleigh wave speed. The dynamic loads play an important role in the dynamic responses of the track–ground system. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

7.
This paper presents an analytical solution for the lateral dynamic response of a pipe pile in a saturated soil layer. The wave propagations in the saturated soil and the pipe pile are simulated by Biot's three‐dimensional poroelastic theory and one‐dimensional elastic theory, respectively. The governing equations of soil are solved directly without introducing potential functions. The displacement response and dynamic impedances of the pipe pile are obtained based on the continuous conditions between the pipe pile and both the outer and inner soil. A comparison with an existing solution is performed to verify the proposed solution. Selected numerical results for the lateral dynamic responses and impedances of the pipe pile are presented to reveal the lateral vibration characteristics of the pile‐soil system. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

8.
This paper presents an analysis of the rocking vibrations of a rigid cylindrical foundation embedded in poroelastic soil. The foundation is subjected to time‐harmonic rocking excitation and is perfectly bonded to the surrounding soil. The soil underlying the foundation base is represented by a homogeneous poroelastic half‐space, whereas the soil along the side of the foundation is modeled as an independent poroelastic stratum composed of a series of infinitesimally thin layers. The behavior of the soil is governed by Biot's poroelastodynamic theory. The contact surface between the foundation base and the poroelastic soil is assumed to be smooth and either fully permeable or impermeable. The dynamic interaction problem is solved by employing a simplified analytical method. Some numerical results for the nondimensional rocking dynamic impedance and nondimensional angular displacement amplitude of the foundation are presented to show the effect of nondimensional frequency of excitation, poroelastic material parameters, hydraulic boundary condition, depth ratio and mass ratio of the foundation. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

9.
A row of rigid piles is addressed as the countermeasures for isolating Rayleigh waves in a poroelastic half‐space. The complex characteristic equations for Rayleigh waves are derived via Biot's theory and their existence conditions are given. The piles are modeled as Euler–Bernoulli beams with longitudinal displacements and the diffracted field by each pile is constructed only with Rayleigh waves. Six infinite linear systems of algebraic equations are obtained in terms of the equilibrium of forces and continuity of displacements at the pile–soil interfaces. The systems are subsequently solved in the complex least‐squares sense. The influence of certain pile and soil characteristics such as the permeability of poroelastic soil, spacing between the piles and length of the piles on the isolating performance of a pile barrier is investigated. Computed results show that the permeability of poroelastic soil displays a significant effect on the vertical amplitude reduction of Rayleigh waves. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

10.
The problem of the dynamic responses of a semi‐infinite unsaturated poroelastic medium subjected to a moving rectangular load is investigated analytical/numerically. The dynamic governing equations are obtained with consideration of the compressibility of solid grain and pore fluid, inertial coupling, and viscous drag as well as capillary pressure in the unsaturated soil, and they can be easily degraded to the complete Biot's theory. Using the Fourier transform, the general solution for the equations is derived in the transformed domain, and then a corresponding boundary value problem is formulated. By introducing fast Fourier transform algorithm, the unsaturated soil vertical displacements, effective stresses, and pore pressures induced by moving load are computed, and some of the calculated results are compared with those for the degenerated solution of saturated soils and confirmed. The influences of the saturation, the load speed, and excitation frequency on the response of the unsaturated half‐space soil are investigated. The numerical results reveal that the effects of these parameters on the dynamic response of the unsaturated soil are significant.  相似文献   

11.
This work addresses in‐plane pressure P and vertically polarized shear SV seismic wave propagation in a finite, laterally inhomogeneous, multilayered poroelastic geological region resting on the homogeneous elastic half‐space. The particular approach followed here is based on a combination of the (i) viscoelastic approximation (isomorphism) to Biot's equations of dynamic poroelasticity and on the (ii) boundary integral equation method (BIEM) using frequency‐dependent fundamental solutions of the governing wave equations. The problem is formulated under plane strain conditions and time‐harmonic motions are assumed. Validation of the viscoelastic isomorphism and verification of the BIEM is done by solution of benchmark examples. These simulation studies reveal that the proposed methodology is able to depict a sensitivity of the seismic signals recovered to the following parameters: (i) poroelastic properties of fluid saturated layers; (ii) lateral geological inhomogeneity; (iii) surface topography and (iv) frequency content and direction of the incident wave. It is concluded that the combination of viscoelastic isomorphism with BIEM software provides an effective numerical tool for evaluating site‐effect phenomena in multilayered, fluid saturated geological regions with complex geometry. The numerical results obtained demonstrate that dynamic poroelasticity interacting with other physical peculiarities of the Earth's surface layers, such as lateral heterogeneity, material properties along the wave path, local geological profile and type of elastic wave, gives rise to complex seismic signals on the free surface at the site of interest. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

12.
This paper is dedicated to study the dynamic response of a thin‐plate resting on a layered poroelastic half‐space under a moving traffic load. Based on the dynamic poroelastic theory of Biot, the general solutions of the homogeneous poroelastic foundation are obtained by Fourier translation. By using the transmission and reflection matrices method in the frequency domain, the equivalent stiffness of the layered poroelastic half‐space is presented. Kirchhoff's hypotheses are applied to obtain the vertical displacement of the thin plate. By using the inverse Fourier transform, the time domain solution is obtained. As an example of three layers, the influences of the load velocity, the material properties of poroelastic layers, and the flexural rigidity of the plate on the response of the pavement system are examined. Analyses show that a soft intermediate layer results in the significant increase of vertical displacement of road pavement. Comparison with the existing work validates the present model. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

13.
This 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.  相似文献   

14.
徐满清 《岩土力学》2010,31(12):3997-4005
利用Muki和Sternberg的虚拟桩法,研究了饱和土体地基中排桩对移动荷载引起振动的被动隔振效果。隔振桩作为一维杆,饱和土体满足Biot理论。利用已有的移动荷载作用下的饱和土体的自由波场解及饱和土体内部受竖向圆形分布荷载作用下的基本解,建立了频域内土-桩的第2类Fredholm积分方程。通过Fourier逆变换得到时间域内评价隔振效果的振幅比。与已知文献结果相比较,验证了方法的正确性。数值结果表明,荷载速度对排桩的隔振效果有一定影响,即在相同隔振系统情况下,单排桩对低速荷载引起振动的隔振效果比高速移动荷载效果好。同时,较高速时的最佳桩长比低速时要短。  相似文献   

15.
This paper presents a novel analytical solution to the transient, z‐dependent, and asymmetric problem of an infinite wellbore drilled into a fluid‐saturated porous medium. The formulations are based on Biot's linear theory of poroelasticity, in which the dependency of poroelastic field variables to spatial coordinates as well as time domain is considered in the most general form. This gives flexibility to the solution in cases that cannot be analyzed using the conventional plane strain or symmetric models. One such case is when calculating the stress variations around an inclined wellbore where the far‐field stresses are acting over a finite vertical section. The results of our solution to this case with a three‐dimensional state of far‐field stress are used to analyze the stability of inclined wellbores passing through abnormally stressed formations. The presented solution is capable of finding expressions for fundamental solutions with stress or flow boundary conditions at the wellbore. These solutions are here adopted to analyze the pressure disturbances generated by multiprobe formation tester, a standard wireline device that is designed for downhole fluid sampling as well as estimating the directional permeabilities of subsurface earth formations. A comparison with the conventional solution for the relevant pressure diffusion equation indicates that the poroelastic effect is relatively significant in relation to the transient response of the pore pressure. Further, it is shown that the finite dimensions of sink probe would, to a great extent, contribute to the formation's pore pressure variations at its immediate proximity. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

16.
This paper considers the steady-state vertical vibrations of a rigid circular disk embedded at a finite depth below the free surface of a poroelastic medium. Biot's elastodynamic theory for porous media is used in the analysis. General solutions for axisymmetric poroelastic fields are obtained by using Hankel integral transforms. Analytical solutions for influence functions corresponding to four types of buried axisymmetric excitations are derived. The embedded disk problem is fomulated in terms of a set of coupled integral equations for unknown traction and pore pressure jumps across the disk. The kernel functions of the integral equations are the influence functions corresponding to buried vertical, radial and pore pressure ring loads. The system of integral equations is solved numerically by discretizing the disk into several concentric annular rings. Selected numerical solutions for displacements, vertical stress and pore pressure due to a buried fully flexible disk (uniform pressure) are also presented. The vertical compliances of a rigid disk are examined for different depths of embedment, poroelastic materials and hydraulic boundary conditions. Solutions for traction and pore pressure jumps are also examined. The present results are useful in the study of dynamic response of embedded foundations and anchors in poroelastic soils. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

17.
The dynamic responses of an anisotropic poroelastic half-space under an internal point load and fluid source are investigated in the frequency domain in this paper. By virtue of Fourier transform and Stroh formalism, the three-dimensional (3D) general solutions of the anisotropic Biot's coupling dynamics equations are derived in the frequency domain. Considering the two surface conditions, permeable and impermeable, the analytical solutions for displacement fields and pore pressure in half-space under a point source (point load or a fluid source) are obtained. When the material properties are isotropic, the numerical results of the poroelastic half-space are in excellent agreement with the existing analytical solutions. For anisotropic half-space cases, numerical results show the strong dependence of the dynamic Green's functions on the material properties.  相似文献   

18.
Two formulations for calculating dynamic response of a cylindrical cavity in cross‐anisotropic porous media based on complex functions theory are presented. The basis of the method is the solution of Biot's consolidation equations in the complex plane. Employing two groups of potential functions for solid skeleton and pore fluid (each group includes three functions), the u–w formulation of Biot's equations are solved. Difference of these two solutions refers to use of two various potential functions. Equations for calculating stress, displacement and pore pressure fields of the medium are mentioned based on each two formulations. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

19.
A simplified analytical method is presented for the vertical dynamic analysis of a rigid, massive, cylindrical foundation embedded in a poroelastic soil layer. The foundation is subjected to a time‐harmonic vertical loading and is perfectly bonded to the surrounding soil in the vertical direction. The soil underlying the foundation base is represented by a single‐layered poroelastic soil based on rigid bedrock while the soil at the side of the foundation is modeled as an independent poroelastic layer composed of a series of infinitesimally thin layers. The behavior of the soil is governed by Biot's poroelastodynamic theory and its governing equations are solved by the use of Hankel integral transform. The contact surface between the foundation base and the soil is smooth and fully permeable. The dynamic interaction problem is solved following standard numerical procedures. The accuracy of the present solution is verified by comparisons with the well‐known solutions obtained from other approaches for both the elastodynamic interaction problem and poroelastodynamic interaction problem. Numerical results for the vertical dynamic impedance and response factor of the foundation are presented to demonstrate the influence of nondimensional frequency of excitation, soil layer thickness, poroelastic material parameters, depth ratio and mass ratio on the dynamic response of a rigid foundation embedded in a poroelastic soil layer. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

20.
The paper presents a three‐dimensional study on the steady‐state response of a track system and layered half‐space soil medium subjected to the load induced by the passages of a moving train with the substructure method. Practically, due to the ground water table being several meters beneath the ground surface, the soil profile can be divided into two layers: the upper layer modeled by an elastic medium and the lower layer by a fully saturated poroelastic medium governed by Biot's theory. In the meanwhile, the rails are regarded as an infinitely long Euler beam, and the sleepers are represented by a continuous mass. The effect of the ballast is accounted for by introducing the Cosserat model for granular medium, and the train is described by a series of moving axle point loads, depending on the geometry of the train. The influences of the thickness, the mass and the rigidity of the elastic layer and the mass of the ballast on rail's displacement responses are carefully investigated. Numerical results show that the influences of these parameters are significant for high train velocity, while vanishes for low velocity. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

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