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1.
This paper proposes a coupled fluid layer–foundation–poroelastic half-space vibration model to study how still water affects foundations operating underwater. As an example, we consider the problem of the vertical vibration of a rigid disk on a poroelastic half-space covered by a fluid layer having a finite depth. The solution of the disk vibration problem is obtained using the boundary conditions at the free surface of the fluid layer and the boundary conditions at the fluid layer–poroelastic medium interface. The solution is expressed in terms of dual integral equations that are converted into Fredholm integral equations of the second kind and solved numerically. Selected numerical results for the vertical dynamic impedance coefficient are examined based on different water depths, poroelastic materials, disk permeabilities and frequencies of excitation. Based on the numerical results, it is proposed that the hydrodynamic pressure caused by the foundation vibration is the intrinsic reason that the existence of a fluid layer has such a great effect on the dynamic characteristics of the foundation. In many cases, the hydrodynamic pressure caused by the foundation vibration cannot be ignored when designing dynamic underwater foundations. These results are helpful in understanding the dynamic response of foundations under still water without water waves, such as foundations in pools, lakes and reservoirs. 相似文献
2.
This paper considers the vertical dynamic response of a disk on a saturated poroelastic half-space. Firstly the pressure-solid displacement form of the harmonic equations of motion for a poroelastic solid are developed from the form of the equations originally presented by Biot. These equations are solved by a new method. Then the mixed boundary value problem for the vertical harmonic vibration of a disk on a poroelastic half-space is studied. The two types of drainage conditions at the surface of the poroelastic half-space are considered: (a) the surface of the poroelastic half-space is assumed to be completely pervious both within and exterior to the plate; (b) The interface between the plate and the poroelastic half-space is assumed to be impervious and the exterior region is assumed to be pervious. By using the Hankel transform techniques, the paper develops the governing dual integral equations. These governing integral equations are further reduced to systems of standard Fredholm integral equations of the second kind by Abel transform. 相似文献
3.
This paper addresses the horizontal vibration of a rigid disk embedded in a poroelastic half-space in contact with a fluid half-space using the poroelastic theory of potentials. The solution of this problem is expressed in terms of dual integral equations that are converted into Fredholm integral equations of the second kind and solved numerically. Selected numerical results for the horizontal dynamic impedance coefficient are examined based on different poroelastic materials, embedment depths, and excitation frequencies; furthermore, the results are analyzed for the cases in which there is and is no fluid overlying the poroelastic medium to examine the effect of fluid. The results of this study are helpful for designing a foundation embedded in the seabed due to dynamic horizontal forces. 相似文献
4.
Morteza Eskandari-Ghadi Azizollah Ardeshir-Behrestaghi 《Soil Dynamics and Earthquake Engineering》2010
This paper is concerned with the investigation of the vertical vibration of a rigid circular disc buried at an arbitrary depth in a transversely isotropic half space in such a way the axis of material symmetry of the half space is normal to the surface of it and parallel to the vibration direction. By using the Hankel integral transforms, the mixed boundary-value problem is transformed to a pair of integral equations called dual integral equations, which generally can be reduced to a Fredholm integral equation of the second kind. With the aid of complex variable or contour integration, the governing integral equation is numerically solved in the general dynamic case. Two degenerated cases (i) the disc is buried in a transversely isotropic full space, and (ii) rigid circular disc is attached on the surface of the half space are discussed. The reduced static case of the dual integral equations is solved analytically and the vertical displacement, the contact pressure and the static impedance/compliance function are explicitly found. It is shown that the vertical pressure and the compliance function reduced for isotropic half space are identical to the previous solutions reported in the literature. The dynamic contact pressure under the disc and the impedance function are numerically evaluated in general dynamic case and graphically shown that the singularity exists in the contact pressure at the edge of the disc is the same as the static case. In addition, the impedance functions evaluated here for the isotropic domain are collapsed on the solution given by Luco and Mita. To show the effect of different material anisotropy, the numerical evaluations are given for some different transversely isotropic materials and compared. 相似文献
5.
This paper analytically examines the horizontal vibration of a rigid disk on a saturated poroelastic half-space. The pressure-solid displacement form of the harmonic equations of motion for asymmetric dynamic problem are developed from the form of the equations originally presented by Biot. Making use of a new method the solution of the above equations is obtained. According to the mixed boundary -value conditions, the dual integral equations of the horizontal vibration of a rigid disk on a saturated poroelastic half-space are established. By appropriate transforms, it is shown that the dual integral equations can be reduced to a pair of Fredholm integral equations of the second kind, whose solutions are then computed. Numerical results for the horizontal dynamic compliance coefficient are given at the end of this paper. 相似文献
6.
T. Senjuntichai S. Mani R.K.N.D. Rajapakse 《Soil Dynamics and Earthquake Engineering》2006,26(6-7):626-636
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. 相似文献
7.
An analytical approach is developed to study the dynamic response of a flexible plate on single-layered saturated soil. The analysis is based on Biot's two-phased theory of poroelasticity and also on the classical thin-plate theory. First, the governing differential equations for saturated soil are solved by the use of Hankel transform. The general solutions of the skeleton displacements, stresses, and pore pressures, derived in the transformed domain, are subsequently incorporated into the imposed boundary conditions, which leads to a set of dual integral equations describing the corresponding mixed boundary value problem. These governing integral equations are finally reduced to the Fredholm integral equations of the second kind and solved by standard numerical procedures. The accuracy of the present solution is validated via comparisons with existing solutions for an ideal elastic half-space. Furthermore, some numerical results are presented to show the influences of the layer depth, the plate flexibility, and the soil porosity on the dynamic compliances. 相似文献
8.
The closed form three-dimensional Green׳s function of a semi-infinite unsaturated poroelastic medium subjected to an arbitrary internal harmonic loading is derived, with consideration of capillary pressure and dynamic shear modulus varying with saturation. By applying the Fourier expansion techniques and Hankel integral transforms to the circumferential and radial coordinates, respectively, the general solution for the governing partial differential equations is obtained in the transformed domain. A corresponding boundary value problem is formulated. The integral solutions for the induced displacements, pore pressure and net stress are then determined considering the continuity conditions. The formulas are compared with the degenerated solution of saturated soils and confirmed. Numerical results reveal that the response of the unsaturated half-space depends significantly on the saturation by altering dynamic shear modulus to account for the effects of matric suction on soil stiffness. Slight differences between the results occur if only the saturation is taken into account. Moreover, a large source-depth results in a pronounced contribution to the reduction of surface displacement amplitudes. The analytical solutions concluded in the study offer a broader application to dynamic response associated with axi-symmetric and asymmetric conditions. 相似文献
9.
A half-space containing horizontally multilayered regions of different transversely isotropic elastic materials as well as a homogeneous half-space as the lowest layer is considered such that the axes of material symmetries of different layers and the lowest half-space to be as depth-wise. A rigid circular disc rested on the free surface of the whole half-space is considered to be under a forced either vertical or horizontal vibration of constant amplitudes. Because of the involved integral transforms, the mixed boundary value problems due to mixed condition at the surface of the half-space are changed to some dual integral equations, which are reduced to Fredholm integral equations of second kind. With the help of contour integration, the governing Fredholm integral equations are numerically solved. Some numerical evaluations are given for different combinations of transversely isotropic layers to show the effect of degree of anisotropy of different layers on the response of the inhomogeneous half-space. 相似文献
10.
The time-harmonic response of a pile in a poroelastic half space and under lateral loadings is studied. By treating the pile as a one-dimensional structure and the half-space as a three-dimensional poroelastic continuum, the dynamic interaction between a pile and a poroelastic medium is formulated as a Fredholm integral equation of the second kind. Green's functions for a distributed lateral force field acting inside a poroelastic half space is an important ingredient of this paper. Numerical results for lateral dynamic compliance functions are presented to illustrate the dynamic characteristics of a pile in a poroelastic half space. 相似文献
11.
The dynamic response of a tunnel buried in a two-dimensional poroelastic soil layer subjected to a moving point load was investigated theoretically. The tunnel was simplified as an infinite long Euler–Bernoulli beam, which was placed parallel to the traction-free ground surface. The saturated layer was governed by Biot’s theory. Combined with the specified boundary conditions along the beam and saturated poroelastic layer, the coupled equations of the system were solved analytically in the frequency–wavenumber domain based on Fourier transform. The time domain responses were obtained by the fast inverse Fourier transform. The critical velocity of the considered structure was determined from the dispersion curves. The different dynamic characteristics of the elastic soil medium and the saturated poroelastic medium subjected to the underground moving load were investigated. It is concluded that, for coarse materials or fine materials subjected to the high-velocity loading, models ignoring the coupling effects between the pore fluid and the soil skeleton may cause errors. The shear modulus and the permeability coefficients of the saturated soil as well as the load moving velocity had significant influence on the displacement and pore pressure responses. 相似文献
12.
基于孔隙介质的Biot理论,首先利用Laplace变换,给出圆柱坐标系下横观各向同性饱和弹性多孔介质在变换域上的波动方程;将波动方程解耦后,根据方位角的Fourier展开和径向Hankel变换,求解了Biot波动方程,得到以土骨架位移、孔隙水压力和土介质总应力分量的积分形式的一般解;借助一般解,建立了有限厚度饱和土层和饱和半空间的精确动力刚度矩阵,并由土层的层间界面连续条件建立三维非轴对称层状饱和地基的总刚度方程;在此基础上,系统研究了横观各向同性饱和半空间体在内部集中荷载激励下的动力响应,并给出了问题的瞬态解答.该研究为运用边界元法求解饱和地基动力响应奠定了理论基础. 相似文献
13.
Rocking vibrations of rigid disk on saturated poroelastic medium 总被引：2，自引：0，他引：2
The dynamic response of a rigid disk on a saturated poroelastic half space and subjected to harmonic rocking excitation is studied. The mixed boundary-value problem for the case of relaxed contact condition between the disk and the poroelastic half space is reduced to a Fredholm integral equation of the second kind, which is solved numerically. The dynamic compliance coefficient for the rocking vibration of a rigid disk on a poroelastic half space is presented. 相似文献
14.
Stresses and excess pore pressure induced in saturated poroelastic halfspace by moving line load 总被引：2，自引：0，他引：2
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. 相似文献
15.
Using reciprocal theorems for dynamic and static boundary value problems, boundary integral equations are presented for wave propagation in elastic, isotropic media and compressible, inviscid fluids in the time domain as well as in the frequency domain. For the analysis of fluid–soil and fluid–structure systems, suitable coupling conditions are prescribed along the interfaces. The numerical treatment of the boundary integral equations consists of a point collocation and of a discretization of the boundary, in which constant and linear approximation functions are assumed. Step-by-step integration is applied to the time-dependent equations, where again the states are taken to be linear and constant over each time interval. These boundary element procedures are used to analyse the response of dams due to horizontal and vertical ground motions considering dam–water interaction and absorption of hydrodynamic pressure waves at the reservoir bottom or at the far end into the soil medium. Both the frequency response and the impulse generated transient response are investigated. 相似文献
16.
An exact stiffness matrix method is presented to evaluate the dynamic response of a multi-layered poroelastic medium due to time-harmonic loads and fluid sources applied in the interior of the layered medium. The system under consideration consists of N layers of different properties and thickness overlying a homogeneous half-plane or a rigid base. Fourier integral transform is used with respect to the x-co-ordinate and the formulation is presented in the frequency domain. Fourier transforms of average displacements of the solid matrix and pore pressure at layer interfaces are considered as the basic unknowns. Exact stiffness (impedance) matrices describing the relationship between generalized displacement and force vectors of a layer of finite thickness and a half-plane are derived explicitly in the Fourier-frequency space by using rigorous analytical solutions for Biot's elastodynamic theory for porous media. The global stiffness matrix and the force vector of a layered system is assembled by considering the continuity of tractions and fluid flow at layer interfaces. The numerical solution of the global equation system for discrete values of Fourier transform parameter together with the application of numerical quadrature to evaluate inverse Fourier transform integrals yield the solutions for poroelastic fields. Numerical results for displacements and stresses of a few layered systems and vertical impedance of a rigid strip bonded to layered poroelastic media are presented. The advantages of the present method when compared to existing approximate stiffness methods and other methods based on the determination of layer arbitrary coefficients are discussed. 相似文献
17.
Decoupling of the coupled poroelastic equations for quasistatic flow in deformable porous media containing two immiscible fluids 总被引：1，自引：0，他引：1
The study of the poroelastic behavior of sedimentary materials containing two immiscible fluids in response to either applied stress or pore pressure change in a quasistatic limit, i.e., negligible second time-derivatives, is of great importance to many hydrogelogical problems, e.g., land subsidence caused by withdrawal of subsurface fluids. The poroelasticity models developed for analyzing these problems feature partial differential equations that are coupled in the terms describing viscous damping and strain field. To determine closed-form analytical solutions for induced volumetric strain (dilatation) of the solid framework and its interaction with fluid flows, the choice of normal coordinates whose transformation can be performed to decouple these poroelastic equations is highly desirable. In this paper, we show that normal coordinates for decoupling these equations are real-valued and equal to three different linear combinations of the dilatations of the solid and the fluids (or equivalently, three different linear combinations of two individual fluid pressures and solid dilatation). In contrast to fully saturated porous media, it is found that the viscous damping effect must be represented in normal coordinates in the presence of the second fluid. The resulting decoupled equations representing independent motional modes are a Laplace equation and two diffusion equations, which can be solved analytically under a variety of initial and boundary conditions. Thus, after inverse transformation of normal coordinates is performed, the closed-form analytical solutions for induced solid volumetric strain and excess pore fluid pressures can be obtained simultaneously from our decoupled partial differential equations. 相似文献
18.
By using integral transform methods, the Green's functions ofhorizontal harmonic force applied at the interior of the saturated half-space soil are obtained in the paper. The general solutions of the Biot dynamic equations in frequency domain are established through the use of Hankel integral transforms technique. Utilizing the above- mentioned general solutions, and the boundary conditions of the surface of the half-space and the continuous con-ditions at the plane of the horizontal force, the solutions of the boundary value problem can be determined. By the numerical inverse Hankel transforms method, the Green's functions of the harmonic horizontal force are obtainable. The degenerate case of the results deduced from this paper agrees well with the known results. Two numerical examples are given in the paper. 相似文献
19.
IntroductionThe wave propagation problems in saturated soil are very important for the civil engineering, geophysics and seismology. Biot (1956,1962) established the theory of wave propagation in saturated soil firstly, and hereafter many researchers have used Biot theory to study wave propagation problems in saturated soil. By using integral transform and potential function method, Philippacopoulos (1988) studied the Lamb(s problem of a vertical point force applied to the surface of saturate… 相似文献
20.
D. D. Theodorakopoulos A. P. Chassiakos D. E. Beskos 《Soil Dynamics and Earthquake Engineering》2001,21(4)
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. 相似文献