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1.
Eigenvalue approach, following Laplace and Fourier transforms, has been employed to find the general solution to the field
equations in an anisotropic liquid-saturated porous medium, in the transformed domain. The results of isotropic liquid-saturated
porous medium can be derived as a special case. A numerical inversion technique has been applied to get the solutions in the
physical domain. To illustrate the utility of the approach, an application of infinite space with impulsive force at the origin
has been considered. The results in the form of displacement and stress components have been obtained and discussed graphically
for a particular model. 相似文献
2.
Traditionally, most formulations of dynamic halfspace problems have represented the material as either an elastic or a viscoelastic solid. Herein the counterpart of Lamb's elastodynamic problem is reformulated and solved for a liquid-saturated poroelastic halfspace using Biot's theory of poroelasticity. The responses of the solid and fluid phases are evaluated due to steady-state harmonic concentrated loads applied to each phase at the surface. The solutions are presented over a broad range of permeabilities and are compared to solutions to Lamb's problem for equivalent drained and undrained solids. Methodology is then introduced by which these results are treated as Green functions for the solution of a mixed boundary-value problem. namely, the response of the poroelastic halfspace to steady-state harmonic vertical motion of a rigid. massless plate. It is observed that small differences exist among overall compliance functions for a drained solid, an undrained solid, and a liquid-saturated porous, halfspace. However, use of the poroelastic model permits the distribution between effective skeletal normal stresses and fluid stresses to be determined. 相似文献
3.
The dynamic problem in micropolar viscoelastic medium has been investigated by employing eigen value approach after applying
Laplace and Fourier transformations. An example of infinite space with concentrated force at the origin has been presented
to illustrate the application of the approach. The integral transforms have been inverted by using a numerical technique to
obtain the displacement components, force stresses, couple stress and microrotation in the physical domain. The results for
these quantities are given and illustrated graphically. 相似文献
4.
Solutions are presented for the problem of isothermal dessiccation shrinkage in a double‐layer porous partially saturated medium. The rheological model taken into account is linear poroelastic. Hence the analysis is mainly focused on hydromechanical coupling effects and contrasts of mechanical and hydraulic properties between two materials: a low thickness skin comprised between the outer boundary and the reference porous material. Three one‐dimensional ideal structures are taken into account: a wall of finite thickness (cartesian geometry), a thick cylinder and a thick sphere. The solution of the time‐dependent problem is arrived at by applying Laplace transforms to the field variables. Exact solutions are obtained in Laplace transform space using Mathematica© to solve the field equations whilst taking into account the continuity equations at the interface and the boundary conditions. The Talbot's modified algorithm has been performed to invert the Laplace transform solutions. A bibliographical and numerical study shows that this method is remarkably precise, stable and close to the analytical inversion. Results are presented using poroelastic data representative of a concrete material and involve a strong coupling effect between hydraulical and mechanical behaviours. A first approach elastic modelling of degradation process have been presented using a thin outer layer. Apart from emphasising the semi‐explicit solution utility due to accurate speed calculation, this paper deals with more complex problems than those which can be solved using purely analytical solutions. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
5.
层状地基中单桩负摩擦问题积分方程解法 总被引：9，自引：1，他引：8
利用Biot固结理论和积分方程方法研究了表面有堆载的层状地基中单桩负摩擦问题。根据层状饱和土的圆形载荷基本解得出了单桩在圆形均布载荷作用下在时间域内的第二类Fredholm积分方程组。运用Laplace变换对上述积分方程组进行简化。再结合传递和刚度矩阵传递到各个层中去,对变换域内的积分方程采用Schapery 逆变换方法得到时域内单桩的近似积分方程。求解积分方程组并进行相应的数值逆变换,就可得出层状地基中的单桩在表面圆形均布载荷作用下的位移、轴力、孔压和桩侧摩阻力随时间的变化情况。计算结果表明,桩侧剪力和孔压分层明显。 相似文献
6.
M D Sharma 《Journal of Earth System Science》2018,127(1):7
Propagation of surface waves is discussed in a cylindrical borehole through a liquid-saturated porous solid of infinite extent. The porous medium is assumed to be a continuum consisting of a solid skeletal with connected void space occupied by a mixture of two immiscible inviscid fluids. This model also represents the partial saturation when liquid fills only a part of the pore space and gas bubbles span the remaining void space. In this isotropic medium, potential functions identify the existence of three dilatational waves coupled with a shear wave. For propagation of plane harmonic waves along the axially-symmetric borehole, these potentials decay into the porous medium. Boundary conditions are chosen to disallow the discharge of liquid into the borehole through its impervious porous walls. A dispersion equation is derived for the propagation of surface waves along the curved walls of no-liquid (all gas) borehole. A numerical example is studied to explore the existence of cylindrical waves in a particular model of the porous sandstone. True surface waves do not propagate along the walls of borehole when the supporting medium is partially saturated. Such waves propagate only beyond a certain frequency when the medium is fully-saturated porous or an elastic one. Dispersion in the velocity of pseudo surface waves is analysed through the changes in consolidation, saturation degree, capillary pressure or porosity. 相似文献
7.
M. D. Sharma 《Journal of Earth System Science》2008,117(6):951-958
Biot’s theory for wave propagation in saturated porous solid is modified to study the propagation of thermoelastic waves in
poroelastic medium. Propagation of plane harmonic waves is considered in isotropic poroelastic medium. Relations are derived
among the wave-induced temperature in the medium and the displacements of fluid and solid particles. Christoffel equations
obtained are modified with the thermal as well as thermoelastic coupling parameters. These equations explain the existence
and propagation of four waves in the medium. Three of the waves are attenuating longitudinal waves and one is a non-attenuating
transverse wave. Thermal properties of the medium have no effect on the transverse wave. The velocities and attenuation of
the longitudinal waves are computed for a numerical model of liquid-saturated sandstone. Their variations with thermal as
well as poroelastic parameters are exhibited through numerical examples. 相似文献
8.
The decrease of density contrast with depth in sedimentary basins is approximated by an exponential function. The anomaly
equation, in frequency domain, of a prismatic model with an exponential density function is derived. The method has been extended
to derive the Fourier transforms of the gravity anomalies of the sedimentary basin, wherein the basin is viewed as vertical
prisms placed in juxtaposition. The gravity anomalies of the sedimentary basin are obtained by taking the inverse Fourier
transforms. Filon’s method has been extended for calculating accurate inverse Fourier transforms. The accuracy of the method
has been tested using a synthetic example. A combination of space and frequency domain methods have been developed for inversion
of gravity anomalies over the sedimentary basin. The method has been applied to interpret one synthetic profile and one field
profile over the Godavari basin. The method developed in this paper to calculate the inverse Fourier transforms yields continuous
spectrum with accurate values. The maximum depth deduced from the gravity anomalies is of the same order as the depth encountered
to the basement at the Aswaraopeta borewell. 相似文献
9.
The quasi-static development of the force, pore pressure and displacement is obtained in the system of a circular elastic pile partially embedded in a saturated porous elastic soil, and loaded axially on the top. The porous elastic soil is governed by Biot's theory. The problem is decomposed into two systems, namely, an extended porous elastic half-space in the absence of the pile characterized by the material constants of the medium, and a fictitious pile represented by a Young's modulus equal to the difference between the Young's moduli of the real pile and the medium. The problem is found to be governed by a Fredholm integral equation of the second kind. Laplace transforms are applied to time functions involved, and Hankel transforms to the radial coordinate of which the origin is at the centre of the pile. Numerical solutions are obtained for final and initial solutions for various practical values of the parameters involved. 相似文献
10.
The present paper is concerned with the problem of an orthotropic micropolar half-space subjected to concentrated and distributed
loads. The disturbance due to normal and tangential loads are investigated by employing eigen-value approach. The integral
transforms have been inverted by using a numerical technique to obtain the normal displacement, normal force stress and tangential
couple stress in the physical domain. The results of these quantities are given and illustrated graphically. 相似文献
11.
多孔介质渗透系数的空间尺度效应研究进展 总被引：6，自引：1，他引：5
多孔介质渗透系数的空间尺度问题是一个与地下流体运动和溶质运移的数值模拟密切相关的应用性课题,广泛的应用需求和新的计算方法使其成为近年的热门课题之一。它涉及到相互联系的两个方面：①非均质介质场渗透系数空间尺度行为的分析与模拟;②将局部测量尺度下的试验参数转化为数值模拟网格尺度下的参数输入值的升尺度（ｕｐｓｃａｌｉｎｇ）方法和计算模型。首先介绍了该课题在概念上的拓展及其物理含义,进而以方法为主线,对这一领域具有代表性的研究成果进行了分类和评述,讨论了该课题的研究对地下水流和溶质运移的模拟分析乃至整个多孔介质流体运动研究的意义。 相似文献
12.
Solutions are presented for the behaviour of a layered porous space which contains a decaying heat source. Such a problem arises when high-level nuclear waste is placed in deep underground depositories in deep clayey formations of sedimentary basins. The geometry of the problem is one dimensional and the porous space is constituted by two layers: a deep low permeability layer which contains the nuclear waste disposal and a superficial layer. The solution is used to examine the effects of contrasts of permeability, thermal conductivity and specific heat capacities between the two layers on the large-scale behaviour of the porous space. Results are presented, using realistic data, for the pore pressure and temperature evolution at the heat source centre, and for the vertical displacement of the ground level. The superficial layer has no significant effects on pore pressure, temperature and stress evolution near the heat source centre. The vertical displacement of the ground level is mainly due to the thermal dilatation of the pore water, so it decreases with an increasing of permeability of the superficial layer. The solution of the time-dependent problem is carried out by applying Laplace transforms to the field variables, obtaining solutions and then using numerical methods to invert the transformed solutions. Comparisons with numerical simulations taking into account the non-linear and non-reversible behaviour of the rock mass are presented. © 1998 John Wiley & Sons, Ltd. 相似文献
13.
Mansour A. Al-Garni 《Arabian Journal of Geosciences》2018,11(6):138
Gravity anomalies caused by a thin infinite sheet are interpreted quantitatively based on an integral transform approach which is elegant and simple. The proposed technique depends on the modified Hilbert transform which is called “Sundararajan transform.” The amplitudes of the well-known Hilbert transform and Sundararajan transform are exactly the same but with a phase difference of 270° between them. The interpretation of gravity anomalies due to a thin infinite sheet has been implemented using the Sundararajan transform rather than the well-known Hilbert transform, yielding a straightforward solution. Parameters such as the depth to the top of the sheet (z), the inclination angle (θ), and the amplitude coefficient (K) have been analytically determined using simple mathematical equations. The origin of the causative target can be determined by the intersection point between Hilbert and Sundararajan transforms as well as the intersection point of the amplitudes of the analytic signal of the two transforms. The proposed technique has been first applied to synthetic data where the procedures are clearly illustrated. The effect of noise on the interpretation procedures of the proposed technique has been investigated, showing in general satisfactory results especially depth estimation. However, the most sensitive parameter to noise is the dipping angle, which can be misleading in high level of noise, whereas the least sensitive parameter is the depth. Strictly speaking, the noise does not significantly distort the depth estimation obtained with this proposed technique. Finally, the interpretation of the gravity anomaly across the Mobrun ore body, Noranda, Quebec, Canada, has been carried out using the proposed technique where the parameters are estimated and compared to the results that have been published in literatures using different techniques. 相似文献
14.
15.
根据饱和多孔介质中考虑释放效应的一维渗透作用的可溶性污染物的迁移控制方程,通过Laplace变换和Fourier变换及其逆变换求得相应的通解形式。根据半无限体表面可溶性污染物点源注入情形下的基本解,通过积分方法得到半无限体表面圆形区域上作用循环浓度污染物后,在多孔介质内部污染物迁移过程的求解方法。作为一个典型算例,对渗透作用下循环浓度污染源引起的多孔介质中的迁移过程进行分析。算例表明,当污染源浓度为周期变化时,多孔介质内部污染物的浓度随时间增长由不稳定的周期变化过程逐渐过渡到稳定的循环过程,而某一深度处污染物浓度的相位则相应滞后。此时,稳定后的污染物浓度周期与污染源浓度周期相同。实际上,随多孔介质表面污染源浓度的周期变化,在靠近多孔介质表面一定深度范围内的污染物浓度在深度方向也呈增大或减小的交替变化过程。另一方面,在污染源循环变化过程中污染物不断向深处推进,而最终其影响范围限定在某一深度内。 相似文献
16.
在考虑横观各向同性含液饱和多孔介质固体骨架和流体可压缩性以及固体骨架的黏弹性特征下,基于横观各向同性含液饱和多孔介质u-w形式的三维动力控制方程,以固相位移u、液相相对位移w为基本未知量,综合运用Laplace变换、双重Fourier变换等方法,在直角坐标系下通过引入中间变量,将六元2阶动力控制方程组化为两组各含4个未知变量的常微分方程组,给出了直角坐标系下横观各向同性含液饱和多孔介质三维黏弹性动力反应的积分形式一般解;作为理论推导的验证,通过引入初始条件和边界条件,对横观各向同性含液饱和多孔介质半空间黏弹性瞬态反应问题进行了求解。解答的退化验证表明,所推导的理论解是正确的。 相似文献
17.
The leakage effect in porous fissured media has been considered in a general sense by introducing a new expression of the leakage term in this paper. The double porosity concept is employed and the related expressions are formulated using the upwind finite element approach. Considering the infinite extension of the problem domain, a mapped transient infinite element has been presented to simulate the far field of the infinite medium. Since the mass transfer function of the present mapped transient infinite element is dependent on both space and time variables, the mechanism of transient contaminant migration problems in infinite porous fractured media can be rigorously simulated because the property matrices of the element are evaluated at any time of interest. By comparing the current numerical results with the analytical ones, the accuracy, correctness and effectiveness of the present method have been established. Three different time discretization schemes were examined and it was found that either the central difference or the backward difference approximation is suitable for the upwind finite element simulation of transient contaminant migration problems. 相似文献
18.
Incised-valley shale systems are renowned as the fruitful exploration domains. However, the stratigraphic heterogeneity is significant, and thus, identifying the porous compartments within the thin-bedded and fractured shale system is one of the unconventional stratigraphic challenges. We present an innovative scheme for the exploration of the porous unconventional resources within the south Indus basin, Pakistan. The continuous wavelet transforms (CWT) exclusively detects the porous shales within the complete fractured system as compared to the full spectrum seismic data interpretation tool. The seismic amplitude, instantaneous frequency, and reflection strength tools show some tuning effects due to lithology and fluids. However, the tuning block of 28 Hz envelope sub-bands in conjunction with instantaneous phase tool accurately mark out the shale-plugged pinch out reservoirs. The synthetic wedge model based on the conventional seismic wavelet resolves the shale bed (incised-valley shale-filled lens) of about 23 m thickness, but shows limited imaging capability due to frequency band limitation for the porous shale locale. The acoustic impedance based on instantaneous spectral porosity modeling using the tuning volume of 28 Hz CWT has spectacularly resolved the thin-beds (gas shows) within the porosity range of 20 to 30%, which may have implications for future exploration of unconventional stratigraphic plays. 相似文献
19.
Frictionless contact formulation for dynamic analysis of nonlinear saturated porous media based on the mortar method 
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下载免费PDF全文 A finite element algorithm for frictionless contact problems in a two‐phase saturated porous medium, considering finite deformation and inertia effects, has been formulated and implemented in a finite element programme. The mechanical behaviour of the saturated porous medium is predicted using mixture theory, which models the dynamic advection of fluids through a fully saturated porous solid matrix. The resulting mixed formulation predicts all field variables including the solid displacement, pore fluid pressure and Darcy velocity of the pore fluid. The contact constraints arising from the requirement for continuity of the contact traction, as well as the fluid flow across the contact interface, are enforced using a penalty approach that is regularised with an augmented Lagrangian method. The contact formulation is based on a mortar segment‐to‐segment scheme that allows the interpolation functions of the contact elements to be of order N. The main thrust of this paper is therefore how to deal with contact interfaces in problems that involve both dynamics and consolidation and possibly large deformations of porous media. The numerical algorithm is first verified using several illustrative examples. This algorithm is then employed to solve a pipe‐seabed interaction problem, involving large deformations and dynamic effects, and the results of the analysis are also compared with those obtained using a node‐to‐segment contact algorithm. The results of this study indicate that the proposed method is able to solve the highly nonlinear problem of dynamic soil–structure interaction when coupled with pore water pressures and Darcy velocity. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
20.
A formulation has been derived for the flow of non-Newtonian (power-law) fluids in deformable, fractured porous media. The formulation is enhanced with a subgrid scale model to accurately represent the flow of the power-law fluids inside the cracks. The resulting equations have been discretised using standard (Lagrangian) finite element shape functions and with non-uniform rational B-splines (NURBS), which have been cast into a standard finite element datastructure using Bézier extraction. The effect of the power-law index on the velocity inside the fracture and on the total fluid flow through the porous medium has been analysed for a typical boundary-value problem. It is shown that large differences between non-Newtonian and linearised Newtonian fluids can occur for the fluid velocity inside the fracture. This can significantly influence the total fluid transport through the domain. A mesh sensitivity study has been carried out as well and shows that markedly smaller element sizes are required in order to obtain accurate results for the local flow inside the fracture, compared with the element sizes necessary for obtaining accurate results inside the porous medium away from the fracture. Moreover, a comparison has been made between the results obtained using standard Lagrange polynomials and those obtained using NURBS. It is shown that while both discretisation methods are able to accurately simulate the deformations and pressures in the porous medium, the higher interelement continuity of NURBS is mandatory for obtaining correct values of the fluid velocities inside the fracture, especially near the tips. 相似文献