共查询到20条相似文献，搜索用时 593 毫秒
1.
The strong coupling of applied stress and pore fluid pressure, known as poroelasticity, is relevant to a number of applied problems arising in hydrogeology and reservoir engineering. The standard theory of poroelastic behavior in a homogeneous, isotropic, elastic porous medium saturated by a viscous, compressible fluid is due to Biot, who derived a pair of coupled partial differential equations that accurately predict the existence of two independent dilatational (compressional) wave motions, corresponding to in-phase and out-of-phase displacements of the solid and fluid phases, respectively. The Biot equations can be decoupled exactly after Fourier transformation to the frequency domain, but the resulting pair of Helmholtz equations cannot be converted to partial differential equations in the time domain and, therefore, closed-form analytical solutions of these equations in space and time variables cannot be obtained. In this paper we show that the decoupled Helmholtz equations can in fact be transformed to two independent partial differential equations in the time domain if the wave excitation frequency is very small as compared to a critical frequency equal to the kinematic viscosity of the pore fluid divided by the permeability of the porous medium. The partial differential equations found are a propagating wave equation and a dissipative wave equation, for which closed-form solutions are known under a variety of initial and boundary conditions. Numerical calculations indicate that the magnitude of the critical frequency for representative sedimentary materials containing either water or a nonaqueous phase liquid is in the kHz–MHz range, which is generally above the seismic band of frequencies. Therefore, the two partial differential equations obtained should be accurate for modeling elastic wave phenomena in fluid-saturated porous media under typical low-frequency conditions applicable to hydrogeological problems. 相似文献
2.
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
3.
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. 相似文献
4.
《Advances in water resources》2002,25(8-12):1105-1117
Macroscopic differential equations of mass and momentum balance for two immiscible fluids in a deformable porous medium are derived in an Eulerian framework using the continuum theory of mixtures. After inclusion of constitutive relationships, the resulting momentum balance equations feature terms characterizing the coupling among the fluid phases and the solid matrix caused by their relative accelerations. These terms, which imply a number of interesting phenomena, do not appear in current hydrologic models of subsurface multiphase flow. Our equations of momentum balance are shown to reduce to the Berryman–Thigpen–Chen model of bulk elastic wave propagation through unsaturated porous media after simplification (e.g., isothermal conditions, neglect of gravity, etc.) and under the assumption of constant volume fractions and material densities. When specialized to the case of a porous medium containing a single fluid and an elastic solid, our momentum balance equations reduce to the well-known Biot model of poroelasticity. We also show that mass balance alone is sufficient to derive the Biot model stress–strain relations, provided that a closure condition for porosity change suggested by de la Cruz and Spanos is invoked. Finally, a relation between elastic parameters and inertial coupling coefficients is derived that permits the partial differential equations of the Biot model to be decoupled into a telegraph equation and a wave equation whose respective dependent variables are two different linear combinations of the dilatations of the solid and the fluid. 相似文献
5.
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
6.
本文应用包括地壳破裂发震过程中具有激发及衰减的非线性Rayleigh阻尼,用Voigt粘弹性模型表示地壳,它能更全面地反映地壳介质分子之间的内摩擦造成的粘滞性阻尼,在数学方法上,用解非线性问题解析法的摄动理论结合动坐标的富氏级数,把问题的非线性控制方程组化为各阶线性化的控制方程组后,再简化为标准的Mathieu方程构成的耦连方程组,再用WKBJ方法,给出其在稳定区域的近似解,从而得出了问题的解析解。 相似文献
7.
Numerical simulations of dilatational waves in an elastic porous medium containing two immiscible viscous compressible fluids indicate that three types of wave occur, but the modes of dilatory motion corresponding to the three waves remain uncharacterized as functions of relative saturation. In the present paper, we address this problem by deriving normal coordinates for the three dilatational waves based on the general poroelasticity equations of Lo et al. 2005 [13]. The normal coordinates provide a theoretical foundation with which to characterize the motional modes in terms of six connecting coefficients that depend in a well defined way on inertial drag, viscous drag, and elasticity properties. Using numerical calculations of the connecting coefficients in the seismic frequency range for an unconsolidated sand containing water and air as a representative example relevant to hydrologic applications, we confirm that the dilatational wave whose speed is greatest corresponds to the motional mode in which the solid framework and the two pore fluids always move in phase, regardless of water saturation, in agreement with the classic Biot theory of the fast compressional wave in a water-saturated porous medium. For the wave which propagates second fastest, we show, apparently for the first time, that the solid framework moves in phase with water, but out of phase with air [Mode (III)], if the water saturation is below about 0.8, whereas the solid framework moves out of phase with both pore fluids [Mode (IV)] above this water saturation. The transition from Mode (III) to Mode (IV) corresponds to that between the capillarity-dominated region of the water retention curve and the region reflecting air-entry conditions near full water saturation. The second of the two modes corresponds exactly to the slow compressional wave in classic Biot theory, whereas the first mode is possible only in a two-fluid system undergoing capillary pressure fluctuations. For the wave which has the smallest speed, the dilatational mode is dominated by the motions of the two pore fluids, which are always out of phase, a result that is consistent with the proposition that this wave is caused by capillary pressure fluctuations. 相似文献
8.
本文在小扰动条件下,从粘性可压缩流体的运动方程、状态方程以及连续性方程导出了它的波动方程,从而表明粘性可压缩流体中能够存在有耗损的纵波与横波。文中还针对自由界面、刚性界面、粘性流体内部分界面、粘性流体与弹性固体分界面等,求出了平面波的反射系数和透射系数。 相似文献
9.
An analytical model for describing the propagation and attenuation of Rayleigh waves along the free surface of an elastic porous medium containing two immiscible, viscous, compressible fluids is developed in the present study based on the poroelastic equations formulated by Lo et al. [Lo WC, Sposito G, Majer E. Wave propagation through elastic porous media containing two immiscible fluids. Water Resour Res 2005;41:W02025]. The dispersion equation obtained is complex-valued due to viscous dissipation resulting from the relative motion of the solid to the pore fluids. As an excitation frequency is stipulated, the dispersion equation that is a cubic polynomial is numerically solved to determine the phase speed and attenuation coefficient of Rayleigh waves in Columbia fine sandy loam permeated by an air–water mixture. Our numerical results show that, corresponding to three dilatational waves, there is also the existence of three different modes of Rayleigh wave in an unsaturated porous medium, which are designated as the R1, R2, and R3 waves in descending order of phase speed, respectively. The phase speed of the R1 wave is non-dispersive (frequency-independent) in the frequency range we examined (10 Hz–10 kHz) and decreases as water saturation increases, whose magnitude ranges from 20% to 49% of that of the first dilatational wave with respect to water content. However, it is revealed numerically that the R2 and R3 waves are functions of excitation frequency. Given the same water saturation and excitation frequency, the phase speeds of the R2 and R3 waves are found to be approximately 90% of those of the second and third dilatational waves, respectively. The R1 wave has the lowest attenuation coefficient whereas the R3 wave attenuates highest. 相似文献
10.
Beatriz Quintal Eva Caspari Klaus Holliger Holger Steeb 《Geophysical Prospecting》2019,67(8):2196-2212
In interconnected microcracks, or in microcracks connected to spherical pores, the deformation associated with the passage of mechanical waves can induce fluid flow parallel to the crack walls, which is known as squirt flow. This phenomenon can also occur at larger scales in hydraulically interconnected mesoscopic cracks or fractures. The associated viscous friction causes the waves to experience attenuation and velocity dispersion. We present a simple hydromechanical numerical scheme, based on the interface-coupled Lamé–Navier and Navier–Stokes equations, to simulate squirt flow in the frequency domain. The linearized, quasi-static Navier–Stokes equations describe the laminar flow of a compressible viscous fluid in conduits embedded in a linear elastic solid background described by the quasi-static Lamé–Navier equations. Assuming that the heterogeneous model behaves effectively like a homogeneous viscoelastic medium at a larger spatial scale, the resulting attenuation and stiffness modulus dispersion are computed from spatial averages of the complex-valued, frequency-dependent stress and strain fields. An energy-based approach is implemented to calculate the local contributions to attenuation that, when integrated over the entire model, yield results that are identical to those based on the viscoelastic assumption. In addition to thus validating this assumption, the energy-based approach allows for analyses of the spatial dissipation patterns in squirt flow models. We perform simulations for a series of numerical models to illustrate the viability and versatility of the proposed method. For a 3D model consisting of a spherical crack embedded in a solid background, the characteristic frequency of the resulting P-wave attenuation agrees with that of a corresponding analytical solution, indicating that the dissipative viscous flow problem is appropriately handled in our numerical solution of the linearized, quasi-static Navier–Stokes equations. For 2D models containing either interconnected cracks or cracks connected to a circular pore, the results are compared with those based on Biot's poroelastic equations of consolidation, which are solved through an equivalent approach. Overall, our numerical simulations and the associated analyses demonstrate the suitability of the coupled Lamé–Navier and Navier–Stokes equations and of Biot's equations for quantifying attenuation and dispersion for a range of squirt flow scenarios. These analyses also allow for delineating numerical and physical limitations associated with each set of equations. 相似文献
11.
Time harmonic point load and dynamic contact problem of contacting fluid and poroelastic half-spaces
The dynamic response of contacting fluid and fluid-saturated poroelastic half- spaces to a time-harmonic vertical point force or a point pore pressure is investigated. The solutions are formulated using the boundary conditions at the fluid-porous medium interface. The point load solutions are then used to solve the dynamic problem of the vertical vibration of a rigid disc (both permeable and impermeable discs are included) on the surface of the poroelastic half-space. The contact problems are solved by integrating the point force and point pore pressure solutions over the contact area with unknown discontinuous force and pore pressure distributions, which are determined from the boundary conditions. The solutions are expressed in terms of dual integral equations, which are converted to Fredholm integral equations of the second kind and solved numerically. Selected numerical results for the vertical dynamic compliance coefficient for the cases with or without fluid overlying the poroelastic half-space are presented to show the effects of the fluid. The influence of the permeability condition of the disc on the compliance of the poroelastic half-space is investigated. The displacement, vertical stress, pore pressure in the poroelastic half-space and water pressure in the fluid half-space are also examined for different poroelastic materials and frequencies of excitation. The present results are helpful in the study of the dynamic response of foundations on the seabed under seawater. 相似文献
12.
13.
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
14.
地下岩石由岩石骨架和孔隙流体组成,通常流体含黏性.地震波在地下介质中传播时受岩石骨架和黏性流体的影响会呈现出复杂的变化.本文将流、固体位移和应力连续作为边界条件,推导出含黏性流体孔隙介质分界面上反透射系数方程;通过建立上层为饱油、下层为饱盐水的砂岩孔隙介质模型,开展反透射系数特征研究,分别分析不同频率、不同黏滞系数条件下,含黏性流体孔隙介质分界面上反透射系数随入射角的变化.研究表明,孔隙介质分界面上和等效介质分界面上的反透射系数分别随入射角的变化趋势基本一致,说明方程推导和数值计算的正确性;快纵波反透射系数受频率、流体黏性的影响较小,而快横波反透射系数在一定入射角范围内受频率、流体黏性的影响比较大;由于黏性孔隙流体的作用,慢纵波和慢横波的反透射系数受入射角、频率及流体黏性的影响都很大. 相似文献
15.
We have modeled the effect of a direct current (DC) electric field on the propagation of seismic waves by the pseudospectral
time domain (PSTD) method, based on a set of governing equations for the poroelastic media. This study belongs to the more
general term of the seismoelectric coupling effect. The set of physical equations consists of the poroelastodynamic equations
for the seismic waves and the Maxwell's equations for the electromagnetic waves; the magnitude of the seismoelectric coupling
effect is characterized by the charge density, the electric conductivity, the Onsager coefficient, a function of the dielectric
permittivity, the fluid viscosity, and the zeta potential. The poroelastodynamic vibration of a solid matrix generates an
electric oscillation with the form of streaming current via the fluctuation of pore pressure. Meanwhile, fluctuating pore
pressure also causes oscillatory variation of the electric resistivity of the solid matrix. The simulated poroelastic wave
propagation and electric field variation with an existing background DC electric field are compared with the results of a
physical experiment carried out in an oilfield. The results show that the DC electric field can significantly affect the propagating
elastic energy through the seismoelectric coupling in a wide range of the seismic frequency band. 相似文献
16.
The equations of motion of a structure in undamped modal coordinates may have non-zero off-diagonal terms in the damping matrix. Although these terms are commonly neglected, studies have shown that they may have a significant influence on the response to dynamic loads. In this paper, two independent criteria are developed to determine when these damping terms will affect the structure's modal properties and response. It is found that even small off-diagonal damping values can be significant if the structure has closely spaced natural frequencies. To quantify and understand the influence of these damping terms, closed-form analytical expressions are derived for the modal properties and harmonic and stochastic response of structures with closely spaced natural frequencies. One conclusion is that off-diagonal damping terms will decrease a modal damping ratio for each pair of closely spaced modes. This is significant, since a response analysis performed by neglecting these off-diagonal terms will underestimate the true response. 相似文献
17.
Diffraction of plane SV waves by a shallow circular-arc canyon in a saturated poroelastic half-space 总被引：7，自引：0，他引：7
Jianwen Liang Zhenning Ba Vincent W. Lee 《Soil Dynamics and Earthquake Engineering》2006,26(6-7):582-610
An analytical solution for the scattering and diffraction of incident plane SV waves by a shallow circular-arc canyon in a saturated poroelastic half-space is derived by the wave function expansion method. The solution is utilized to analyze the dependence of the computed surface motions on the incident frequencies, incident angles, porosity, boundary drainage and Poisson's ratio. It is shown that, depending on the incident angles, the surface displacement amplitudes around a canyon in a dry poroelastic half-space and saturated poroelastic half-space can be very different. The surface displacement amplitudes of an undrained saturated poroelastic half-space are close to those of a drained saturated poroelastic half-space. For low porosity, the surface displacement amplitudes of a saturated poroelastic half-space are almost identical to those of a dry poroelastic half-space, and drainage condition has little influence on the surface displacement amplitudes. But for high porosity, the effect of drainage condition becomes significant, and for the same porosity, the displacement amplitudes of an undrained saturated half-space will be larger than those of a drained saturated half-space. Poisson's ratio is also an important factor affecting the surface displacement amplitudes around the canyon, both in drained and undrained conditions, but leads to larger effects for an undrained saturated half-space than for a drained saturated half-space. Large pore pressures are found around the canyon and their amplitudes depend on the incident angles and frequencies. Below the surface, the amplitudes of pore pressures are less than they are at the surface, especially for high frequencies. 相似文献
18.
Qazi Adnan Ahmad Guochen Wu Zong Zhaoyun Wu Jianlu Li Kun Du Tianwei Nasir Khan 《Geophysical Prospecting》2020,68(2):657-677
In exploration geophysics, the efforts to extract subsurface information from wave characteristics exceedingly depend on the construction of suitable rock physics model. Analysis of different rock physics models reveals that the strength and magnitude of attenuation and dispersion of propagating wave exceedingly depend on wave-induced fluid flow at multiple scales. In current work, a comprehensive analysis of wave attenuation and velocity dispersion is carried out at broad frequency range. Our methodology is based on Biot's poroelastic relations, by which variations in wave characteristics associated with wave-induced fluid flow due to the coexistence of three fluid phases in the pore volume is estimated. In contrast to the results of previous research, our results indicate the occurrence of two-time pore pressure relaxation phenomenon at the interface between fluids of disparate nature, that is, different bulk modulus, viscosity and density. Also, the obtained results are compatible with numerical results for the same 1D model which are accounted using Biot's poroelastic and quasi-static equation in frequency domain. Moreover, the effects of change in saturation of three-phase fluids were also computed which is the key task for geophysicist. The outcomes of our research reveal that pore pressure relaxation phenomenon significantly depends on the saturation of distinct fluids and the order of saturating fluids. It is also concluded that the change in the saturation of three-phase fluid significantly influences the characteristics of the seismic wave. The analysis of obtained results indicates that our proposed approach is a useful tool for quantification, identification and discrimination of different fluid phases. Moreover, our proposed approach improves the accuracy to predict dispersive behaviour of propagating wave at sub-seismic and seismic frequencies. 相似文献
19.
《Advances in water resources》1999,22(6):633-644
Large deformations that accompany longwall mining result in complex spatial and temporal distributions of changes in undrained pore fluid pressures around the advancing face. These seemingly anomalous changes are recorded in the rapid water level response of undermined and adjacent wells, and may be explained in the short-term as a undrained poroelastic effect. A three-dimensional finite element model is applied to define anticipated pore fluid response both around the advancing mining face, at depth, and in the near surface region. The results are carefully verified against the response recorded at three well-instrumented longwall sites. Pore pressure changes are indexed directly to volumetric strains defining zones of significant depressurization in the caving zone and in zones of extension adjacent to the subsidence trough on the ground surface. Overpressurization occurs in the abutment region, at panel depth, and in the surface compressive zone immediately inside the angle-of-draw. These results are confirmed with available, short-term water level response data, defining the strongly heterogeneous spatial response and the significance of well depth on anticipated water level response. 相似文献
20.
Knowledge of pore pressure using seismic data will help in planning the drilling process to control potentially dangerous abnormal pressures. Various physical processes cause anomalous pressures on an underground fluid. Non-equilibrium compaction is a significant process of overpressure generation. This occurs when the sedimentation rate is so rapid that the pore fluids do not have a chance to 'escape' from the pore space.
The model assumes a closed system and that the pore space is filled with water and hydrocarbon in a liquid state. Balancing mass and volume fractions yields the fluid pressure versus time of deposition and depth of burial. Thermal effects are taken into account. The pore pressure, together with the confining pressure, determines the effective pressure which, in turn, determines the bulk moduli of the rock matrix.
We assume a sandstone saturated with hydrocarbons and water, for which calibration of the model with experimental data is possible. The seismic velocities and attenuation factors are computed by using Biot's theory of dynamic poroelasticity and the generalized linear solid. The example shows that the formation can be overpressured or underpressured depending on the properties of the saturating fluid. Wave velocities and quality factors decrease with decreasing differential pressure. The effect is important below approximately 20 MPa. The model is in good agreement with experimental data for Berea sandstone and provides a tool for predicting pore pressure from seismic attributes. 相似文献
The model assumes a closed system and that the pore space is filled with water and hydrocarbon in a liquid state. Balancing mass and volume fractions yields the fluid pressure versus time of deposition and depth of burial. Thermal effects are taken into account. The pore pressure, together with the confining pressure, determines the effective pressure which, in turn, determines the bulk moduli of the rock matrix.
We assume a sandstone saturated with hydrocarbons and water, for which calibration of the model with experimental data is possible. The seismic velocities and attenuation factors are computed by using Biot's theory of dynamic poroelasticity and the generalized linear solid. The example shows that the formation can be overpressured or underpressured depending on the properties of the saturating fluid. Wave velocities and quality factors decrease with decreasing differential pressure. The effect is important below approximately 20 MPa. The model is in good agreement with experimental data for Berea sandstone and provides a tool for predicting pore pressure from seismic attributes. 相似文献