On the stresses produced in a liquid-saturated porous solid by normal and tangential forces on a moving strip of finite width

Summary This paper deals with the stresses produced in a semi-infinite liquid-saturated porous solid of the type considered byBiot [1]²), by moving normal and tangential forces acting simultaneously on a moving strip of finite width on the free surface. It has been found that the stresses can be obtained in a closed form. It has also been found that if the velocity of the strip exceeds a certain value, the nature of the stresses changes, and there are discontinuities of stress along certain lines. The results have been applied to study the changes in the stresses produced by moving normal and tangential forces with depth and distance.     

On formation compaction and energy balance law for liquid-saturated porous media reservoirs

In most treatments of liquid flow through porous media, it is assumed that the pore fluid and formation motions are decoupled except that porosity φ is taken to be a function of fluid pressure. This article examines the conditions under which such a decoupling is valid. More specifically, it is shown that the usual statements of the energy balance law ignore the work performed by the overburden as the formation compaction progresses. This work term is shown to be negligibly small in practical cases.     

Steady-state harmonic response of a rigid plate bearing on a liquid-saturated poroelastic halfspace

Soil–structure interaction problems are typically modelled by assuming subgrade behaviour to be either elastic or viscoelastic. Herein, compliance functions that may be used to solve soil–structure interaction problems are evaluated by treating the subgrade as a liquid-saturated poroelastic material whose behaviour is governed by Biot's theory. The compliances are evaluated for the harmonic rocking and vertical motions of rigid permeable and impermeable plates bearing on a poroelastic halfspace. Comparisons are made with elastic solutions which assume the subgrade to be either completely drained or undrained. Also, solid and fluid contact stresses are reported for the poroelastic case and compared to the solid contact stresses for the elastic cases.     

Pseudo Rayleigh wave in a partially saturated non-dissipative porous solid

Propagation of surface waves is studied at the pervious boundary of a porous solid saturated with a mixture of two immiscible fluids. An approach, based on continuum mixture theory, is used to derive a secular equation for the propagation of harmonic waves at the stress-free plane surface of this non-dissipative medium. Numerical analysis shows that this secular equation may not represent the propagation of true surface wave in the porous aggregate. Then, this equation is solved numerically for the propagation of pseudo Rayleigh wave or the leaky surface waves. To ensure the existence of pseudo Rayleigh wave, capillary effect between two (wetting and non-wetting) pore-fluids is related to the partial saturation. Effects of porosity and partial saturation coupled with capillary effect are observed on the phase velocity of pseudo Rayleigh waves in sandstone saturated with water-CO₂ mixture.     

Seismic wave propagation in a viscoelastic porous solid saturated by viscous liquid

A general solution is deduced of the differential equations describing the propagation of elastic waves in a dissipative liquid-filled viscoelastic porous solid. The velocities of three existing waves have been expressed in convenient form using the moduli of the solid phase and by introducing the frequency-dependent equivalent mass densities. The solution is then used to examine some of the phenomena which arise when each of the three-body waves, in turn, are incident on a traction-free plane boundary. Analytic expressions for the reflection coefficients are obtained. Numerical calculations have been made, for a particular model, in case of incidentP _I wave. Effect of viscoelasticity and viscosity on the reflection coefficients has also been exhibited.     

含黏滞流体各向异性孔隙介质中弹性波的频散和衰减

基于Biot理论,考虑液相的黏弹性变形和固液相接触面上的相对扭转,提出了含黏滞流体VTI孔隙介质模型.从理论上推导出,在该模型中除存在快P波、慢P波、SV波、SH波以外,还将存在两种新横波－慢SV波和慢SH波.数值模拟分析了6种弹性波的相速度、衰减、液固相振幅比随孔隙度、频率的变化规律以及快P波、快SV波的衰减随流体性质、渗透率、入射角的变化规律.结果表明慢SV波和慢SH波主要在液相中传播,高频高孔隙度时,速度较高;大角度入射时,快P波衰减表现出明显的各向异性,而快SV波的衰减则基本不变;储层纵向和横向渗透率存在差异时,快SV波衰减大的方向渗透率高.     

Stresses produced by a load moving over the rough boundary of a semi-infinite transversely isotropic solid

Summary Stresses produced due to a moving load over the plane surface (supposed to be rough) of a semi-infinite transversely isotropic medium have been calculated in this paper.     

Reflection and transmission of inhomogeneous waves in a composite porous solid saturated by two immiscible fluids

This paper is concerned with reflection and transmission of a plane, elastic, and inhomogeneous wave striking obliquely at some discontinuity inside a porous medium composed of two distinct solids and saturated by two immiscible fluids. It is found that four P‐ and two SV‐waves are reflected, whereas four P‐ and two SV‐waves are transmitted at the interface. All reflected and transmitted waves are inhomogeneous in nature and specified with different directions of propagation and attenuation vectors. An expression for the Umov–Poynting energy flux vector is derived for the system. Continuity of energy flux along normal to the interface gives 12 required boundary conditions. Expressions of amplitude and energy ratios of various reflected and transmitted waves are derived. Variations in amplitude and energy coefficients of reflected and transmitted waves with angle of incidence are numerically studied for a porous matrix composed of shaley sandstone and clay, saturated with water and oil. The effects of change in oil saturation and volume fraction of clay are also observed on amplitude ratios. Numerical simulation reveals that the change in sign in the difference of capillary pressure across the interface causes jump in the values of amplitude ratios of all waves.     

On the displacements produced in a porous elastic half-space by an impulsive line load. (Non-dissipative case)

Summary On the basis of Biot's dynamical theory of poroelasticity the disturbance produced by an impulsive line load in a porous elastic half-space is studied. Using the Laplace-Fourier transform we have solved for the displacement potentials in terms of which the displacements and stresses in the transformed space are expressible. The expressions for the solid displacements in the interior as well as on the surface of the half-space are obtained by Cagniard's technique. The displacements are expressed in terms of six algebraic terms — three of which are identified as the disturbance due to specific wave fronts and the others represent the head wave contributions. When specialized our results agree with those for the common elastic half-space.     

Reflection and refraction of plane harmonic waves at an interface between elastic solid and porous solid saturated by viscous liquid

A general solution of Biot's field equations governing small motions of a porous solid saturated by viscous liquid is employed to study the reflection and refraction at the interface between an elastic solid and a liquid-saturated porous solid. The incident wave is assumed to be plane and homogeneous, propagating through the isotropic elastic solid. The poroelastic solid is considered to be a dissipative one. Amplitude and energy ratios are computed numerically for a particular model. With first-order corrections for the porosity of solid and viscosity of liquid, the limiting cases of low and high frequencies are computed.     

Reflection and transmission ofSH waves in an initially stressed medium consisting of a sandy layer lying over a fluid-saturated porous solid

Biot's theory is employed to study the reflection and transmission ofSH waves in a sandy layer lying over a fluid-saturated porous solid half-space. The entire medium is considered under constant initial stress. Effects of sandiness, initial stress, anelasticity and viscosity of the interstitial fluid on the partitioning of energy are studied. In the presence of initial stress the incident wave starts attenuating when incider beyond a certain angle (depending upon the amount of initial stress), even if the medium is perfectly clastic. Anelasticity of the solid layer results in the dissipation of energy during transmission. The direction of attenuation vector of incident wave affects the dissipation energy to a large extent. Effect on partitioning of energy reverse at incidence after the critical angle. A complete account of energy returmed back to the underlying half-space and that which is dissipated in the overlying layer has been discussed analytically as well as numerically.     

Plate on viscoelastic foundation under a moving load

Summary In this note the deflection of a simply supported rectangular elastic plate on viscoelastic foundation has been obtained due to a moving load.     

Surface wave propagation in a transversely isotropic elastic layer overlying a liquid saturated porous solid half-space and lying under the uniform layer of liquid

Dispersion of Rayleigh-type surface wave is studied in a homogeneous transversely isotropic elastic layer overlying a nondissipative liquid-saturated porous solid half-space and lying under a uniform layer of homogeneous liquid. The frequency equation in the form of ninth-order determinant is obtained.Special cases have been deduced by reducing the depth of the layers to zero and by changing the transverse isotropic layer to an isotropic layer. Dispersion curves for the phase velocity have been plotted for a particular model.     

The Terrain Correction in a Moving Tangent Space

Conventionally the terrain/topographic reduction is based on the Bouguer Plate, which is flat and extends in the local tangent plane/horizontal plane to infinity. Here we aim at an error estimate of such a planar approximation of the Newton integral of the type of a disturbing potential and gravitational disturbance as linearized forms of the gravitational potential and the modulus of gravitational field intensity. To effect this quality control of the conventional terrain reduction, we first transform the spherical Newton functional from an equatorial frame of reference to an oblique meta-equatorial frame of reference with the evaluation point as a meta-North pole, and then by means of an oblique equiareal map projection of the azimuthal type to a tangent plane which moves at the evaluation point. The first term of these transformed Newton functionals is the planar approximation. The difference between the exact Newton kernels and their planar approximation are plotted and tabulated in Tables 1-3. Three configurations are studied in detail: for points at radius r = 10 km around the evaluation point the systematic error varies from 0.26% for a spherical height difference of the order of H – H* = 5 km, more than 0.80% for a spherical height difference of the order of H – H* = 1 km, and more than 1.60% for a spherical height difference of H – H* = 500 m. In contrast, the systematic error for spherical height difference H – H* = 1 km at a distance of r = 1000 km from the evaluation point increases to 44%. Indeed, the newly derived exact Newton kernels which are of the convolution type and are represented in the tangent space moving with the evaluation point can be preferably used with little extra computational effort.     

Heat dispersion effect on thermal convection in a porous medium layer

Thermal convection resulting from vertical temperature gradients in porous media is analyzed. The effect of heat dispersion is taken into account. It is found that heat dispersion increases the thermal stability of the flow field and may inhibit the appearance of convection currents, which would appear if dispersion effects are omitted.The longitudinal as well as the lateral dispersivities affect the thermal stability and the dimensions of the convection cells. As a result of the convection currents the horizontal streamlines in the steady state are distorted. The thermal convection exhibits internal waves in the field.     

高层建筑动态和静态风荷载的确定

简单介绍了利用高频天平测量高层建筑风荷载的原理和试验方法，讨论了高层建筑风响应的计算，提出了一种动态风荷载和静态风荷载沿高度分布的计算方法。结果分析指出：提出的求沿高层建筑高度分布的等效静态风荷载的方法适用于顺风向风力，应用于横风向风力有理论误差。     

基于Kelvin-Voigt黏弹性骨架的含非饱和流体孔隙介质BISQ模型(英文)

本文综合考虑了在波传播过程中孔隙介质的三种重要力学机制——"Biot流动机制一squirt流动机制-固体骨架黏弹性机制",借鉴等效介质思想,将含水饱和度引入波动力学控制方程,并考虑了不同波频率下孔隙流体分布模式对其等效体积模量的影响,给出了能处理含粘滞性非饱和流体孔隙介质中波传播问题的黏弹性Biot/squirt(BISQ)模型。推导了时间-空间域的波动力学方程组,由一组平面谐波解假设,给出频率-波数域黏弹性BISQ模型的相速度和衰减系数表达式。基于数值算例分析了含水饱和度、渗透率与频率对纵波速度和衰减的影响,并结合致密砂岩和碳酸盐岩的实测数据,对非饱和情况下的储层纵波速度进行了外推,碳酸盐岩储层中纵波速度对含气饱和度的敏感性明显低于砂岩储层。     

Electric conductivities of a cracked solid

Calculations on the basis of the self-consistent approximation are used to study the effects of randomly distributed elliptical cracks and of non-randomly distributed circular cracks, either dry or saturated by a highly conductive material phase, on the electric conductivities of a cracked body. Analytic and numeric results are given for two special non-random distributions. In the first, the cracks are assumed randomly distributed in planes parallel to a given plane. In the second, the crack normals are randomly distributed in parallel planes. The results of the theoretical calculations indicate that the magnitudes of the crack induced variations of the dry cracked rock depend upon a crack density parameter ? rather than upon the crack porosity. Here, ? is defined as $$\varepsilon = \frac{{2N}}{\pi }< \frac{{A^2 }}{P} > $$ whereN is the average number of cracks per unit volume, andA andP are the crack area and perimeter respectively. (For circular cracks of radiusa, ?=N〈a³〉.) Although a straightforward relationship does connect ? with the porosity, it may be more meaningful for laboratory experiments to concentrate upon measuring crack-induced variations as functions of crack density rather than of porosity. For saturated cracked rocks, the results of the calculations indicate that, in addition to ?, variations in conductivity depend also upon a saturation parameter Ω, which relates crack aspect ratio α to matrix and fluid conductivities σ and σ_F $$\Omega = \frac{{{\sigma \mathord{\left/ {\vphantom {\sigma {\sigma _F }}} \right. \kern-\nulldelimiterspace} {\sigma _F }}}}{\alpha }.$$