Theoretical investigation of convective instability in inclined and fluid-saturated three-dimensional fault zones

The convective instability of pore-fluid flow in inclined and fluid-saturated three-dimensional fault zones has been theoretically investigated in this paper. Due to the consideration of the inclined three-dimensional fault zone with any values of the inclined angle, it is impossible to use the conventional linear stability analysis method for deriving the critical condition (i.e., the critical Rayleigh number) which can be used to investigate the convective instability of the pore-fluid flow in an inclined three-dimensional fault zone system. To overcome this mathematical difficulty, a combination of the variable separation method and the integration elimination method has been used to derive the characteristic equation, which depends on the Rayleigh number and the inclined angle of the inclined three-dimensional fault zone. Using this characteristic equation, the critical Rayleigh number of the system can be numerically found as a function of the inclined angle of the three-dimensional fault zone. For a vertically oriented three-dimensional fault zone system, the critical Rayleigh number of the system can be explicitly derived from the characteristic equation. Comparison of the resulting critical Rayleigh number of the system with that previously derived in a vertically oriented one has demonstrated that the characteristic equation of the Rayleigh number is correct and useful for investigating the convective instability of pore-fluid flow in the inclined three-dimensional fault zone system. The related numerical results from this investigation have indicated that: (1) the convective pore-fluid flow may take place in the inclined three-dimensional fault zone; (2) if the height of the fault zone is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone stabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; (3) if the thickness of the stratum is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone destabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; and that (4) the shape of the inclined three-dimensional fault zone may affect the convective instability of pore-fluid flow in the system.     

Double Diffusion-Driven Convective Instability of Three-Dimensional Fluid-Saturated Geological Fault Zones Heated from Below

We conduct a theoretical analysis to investigate the double diffusion-driven convective instability of three-dimensional fluid-saturated geological fault zones when they are heated uniformly from below. The fault zone is assumed to be more permeable than its surrounding rocks. In particular, we have derived exact analytical solutions to the total critical Rayleigh numbers of the double diffusion-driven convective flow. Using the corresponding total critical Rayleigh numbers, the double diffusion-driven convective instability of a fluid-saturated three-dimensional geological fault zone system has been investigated. The related theoretical analysis demonstrates that: (1) The relative higher concentration of the chemical species at the top of the three-dimensional geological fault zone system can destabilize the convective flow of the system, while the relative lower concentration of the chemical species at the top of the three-dimensional geological fault zone system can stabilize the convective flow of the system. (2) The double diffusion-driven convective flow modes of the three-dimensional geological fault zone system are very close each other and therefore, the system may have the similar chance to pick up different double diffusion-driven convective flow modes, especially in the case of the fault thickness to height ratio approaching 0. (3) The significant influence of the chemical species diffusion on the convective instability of the three-dimensional geological fault zone system implies that the seawater intrusion into the surface of the Earth is a potential mechanism to trigger the convective flow in the shallow three-dimensional geological fault zone system.     

基于不同方向模量损失率的含瓦斯煤各向异性渗透模型

煤是自然界中一种常见的沉积岩,它具有显著的各向异性特征。然而目前针对煤体渗透特性研究,多数学者为了简化问题,多假设煤体为各向同性材料,提出了相应的各向同性渗透模型。这类模型并不能完全反映含瓦斯煤气-固耦合真实工程和室内试验的实际情况。假设煤体为横观各向同性,推导出以不同方向模量损失率为关键参数的煤体各向异性渗透模型,在此基础上,推导出含瓦斯煤的气-固耦合控制方程,并植入Comsol计算平台,系统研究煤体各向异性对气体扩散和渗透的影响。理论和数值研究结果表明：不同方向的模量损失率 反映出煤体结构各向异性变化程度,若 不同,其煤体各方向渗透特性也不相同;煤体渗透率的改变主要受解吸附效应和有效应力作用双重影响, 反映了这两种效应对于渗透率的影响程度;单轴应变或位移控制边界条件下,水平方向的模量损失率 对于垂直方向的煤体渗透率改变量 的影响程度大于对水平方向的煤体渗透率改变量 的影响程度,垂直方向模量损失率 对 的影响则弱于对于 的影响。     

Theoretical and numerical analyses of convective instability in porous media with upward throughflow

Exact analytical solutions have been obtained for a hydrothermal system consisting of a horizontal porous layer with upward throughflow. The boundary conditions considered are constant temperature, constant pressure at the top, and constant vertical temperature gradient, constant Darcy velocity at the bottom of the layer. After deriving the exact analytical solutions, we examine the stability of the solutions using linear stability theory and the Galerkin method. It has been found that the exact solutions for such a hydrothermal system become unstable when the Rayleigh number of the system is equal to or greater than the corresponding critical Rayleigh number. For small and moderate Peclet numbers (Pe ⩽ 6), an increase in upward throughflow destabilizes the convective flow in the horizontal layer. To confirm these findings, the finite element method with the progressive asymptotic approach procedure is used to compute the convective cells in such a hydrothermal system. Copyright © 1999 John Wiley & Sons, Ltd.     

The influence of faults in basin-fill deposits on land subsidence,Las Vegas Valley,Nevada, USA

The role of horizontal deformation caused by pumping of confined-aquifer systems is recognized as contributing to the development of earth fissures in semiarid regions, including Las Vegas Valley, Nevada. In spite of stabilizing water levels, new earth fissures continue to develop while existing ones continue to lengthen and widen near basin-fill faults. A three-dimensional granular displacement model based on Biot's consolidation theory (Biot, MA, 1941, General theory of three-dimensional consolidation. Jour. Applied Physics 12:155–164) has been used to evaluate the nature of displacement in the vicinity of two vertical faults. The fault was simulated as (1) a low-permeability barrier to horizontal flow, (2) a gap or structural break in the medium, but where groundwater flow is not obstructed, and (3) a combination of conditions (1) and (2). Results indicate that the low-permeability barrier greatly enhances horizontal displacement. The fault plane also represents a location of significant differential vertical subsidence. Large computed strains in the vicinity of the fault may suggest high potential for failure and the development of earth fissures when the fault is assumed to have low permeability. Results using a combination of the two boundaries suggest that potential fissure development may be great at or near the fault plane and that horizontal deformation is likely to play a key role in this development. Electronic Publication     

平行层状岩体的自重应力场

将平行层状复合岩体视为等效的模观各向同性体，推导出自重荷载下地应力的理论解，并分析了两个水平主应力受岩层倾角和岩体弹性参数的影响，结果表明，与各向同性岩体相比，水平主应力的变化范围增大了，并且两上水平主应力可能不再相等，而岩层倾角对水平主应力之比影响显著，当倾角从0－90度变化时，两个水平主应力能从相等到相差内倍，这也说明在地应力研究中，考察岩体的各向异性是十分必要的，所导出的自重应力场解答对地下工程问题具有一定的实用价值。     

The potential for convection and implications for geothermal energy in the Perth Basin, Western Australia

Convection of groundwater in aquifers can create areas of anomalously high temperature at shallow depths which could be exploited for geothermal energy. Temperature measurements in the Perth Basin (Western Australia) reveal thermal patterns that are consistent with convection in the Yarragadee Aquifer. This observation is supported by Rayleigh number calculations, which show that convection is possible within the range of aquifer thickness, geothermal gradient, salinity gradient and permeability encountered in the Yarragadee Aquifer, assuming that the aquifer can be treated as a homogeneous anisotropic layer. Numerical simulations of convection in a simplified model of the Yarragadee Aquifer show that: (1) the spacing of convective upwellings can be predicted from aquifer thickness and permeability anisotropy; (2) convective upwellings may be circular or elongate in plan view; (3) convective upwellings create significant temperature enhancements relative to the conductive profile; (4) convective flow rates are similar to regional groundwater flow rates; and (5) convection homogenises salinity within the aquifer. Further work is required to constrain the average horizontal and vertical permeability of the Yarragadee Aquifer, to assess the validity of treating the aquifer as a homogeneous anisotropic layer, and to determine the impact of realistic aquifer geometry and advection on convection.     

武汉长江Ⅰ级阶地含水层水文地质参数研究及工程应用

武汉地区长江Ⅰ级阶地含水层在水流等沉积动力的分选作用和上覆土层压力的固结作用下,其渗透系数必然存在各向异性。因此,基于含水层渗透系数的各向同性和以单井稳定流抽水试验得到的含水层水文地质参数所完成的基坑降水设计亦必然与工程实际存在差异。通过现场分层抽水试验、群井抽水试验,结合三维数值模拟反演计算,得出了武汉长江Ⅰ级阶地各含水层水文地质参数的基本规律和特性,即：各含水层渗透系数自上而下逐渐增加且表现为各向异性,其水平渗透系数大于垂直渗透系数,其比值介于1.6～2.6之间。工程实例表明,采用各向异性的水文地质参数和三维渗流分析进行的超深基坑降水设计,结果更接近于实际,且有利于降低工程造价和基坑周边环境损伤,亦有利于节约宝贵的地下水资源。     

Numerical simulation of groundwater flowing to horizontal seepage wells under a river

A horizontal seepage well, consisting of an interconnected vertical well, galleries, chambers and small-diameter radiating bores, is used to acquire relatively clean water that has been filtered through natural alluvial deposits in a riverbed. It has wide application, especially in arid and semi-arid areas. The lack of calculation formulae or models for horizontal seepage wells, up until now, has resulted in several false applications. Based on the analysis of groundwater flow characteristics, it has been concluded that several flow regimes coexist and hydraulic head loss exists in the horizontal seepage well. To avoid the difficulty of confirming the flux or head distribution in such a complex system, the model boundary of the whole horizontal seepage well has been moved to that of just the vertical well, and the well-aquifer system was treated as a heterogeneous medium, where the horizontal seepage well itself is a highly permeability medium. A mathematical model has been developed, based on the coupled seepage-pipe flow, by the introduction of equivalent hydraulic conductivity according to different flow regimes. Then a three-dimensional finite difference numerical model, based on the mathematical model, was developed and applied to a horizontal seepage well in China. The numerical model verified the groundwater flow characteristics of the horizontal seepage well. An erratum to this article can be found at     

晚更新世黄土渗透性的各向异性及其机制研究

非饱和黄土的渗透性是非饱和黄土性质的重要组成部分。研究黄土不同方向的渗透性对确定其湿陷范围和由于水的渗透引起的黄土滑坡具有很重要的理论意义。研究了黄土渗透性的各向异性特征及其机制。以具有明显各向异性的西安Q3原状黄土为研究对象,用TEN型张力计测量了黄土试样不同方向的、不同含水率下的吸力;用变水头渗透试验测量了黄土竖直和水平方向的饱和渗透系数。结果表明,当体积含水率在23%～41%时,张力计沿不同方向插入土样所测吸力相差不大;竖直方向的饱和渗透系数是水平方向的4.02倍。在吸力测量的基础上,根据土-水特征曲线,确定了竖直和水平方向的非饱和黄土的渗透系数。得出在黄土不同方向,随着吸力的增大或减小,渗透系数减小或增大;竖直方向的渗透系数普遍地大于水平方向的渗透系数;当吸力小于57 kPa时,随着吸力的增大,竖向渗透系数与水平向渗透系数的差值减小。通过观测黄土的结构,得出黄土结构对其渗透性有重要影响。     

干密度及冻融循环对黄土渗透性的各向异性影响

黄土作为特殊土之一广泛分布于我国中西部季节性冻土地区,以具有明显各向异性的西安Q3原状黄土为研究对象,采用GDS三轴渗透仪测量不同干密度原状黄土竖直向及水平向渗透系数。结果表明,原状黄土水平向渗透系数大于竖直向渗透系数,水平向渗透系数和竖直向渗透系数均随干密度增大而减小;原状黄土渗透各向异性随干密度增大而增强。在封闭系统下用冻融循环箱对干密度相同而初始含水率不同的原状黄土进行冻融试验,结果表明冻融后试样水平向及竖直向渗透系数均随冻融时试样初始含水率的增大而增大;冻融后黄土渗透各向异性随冻融时试样初始含水率的增大而减弱。随着冻融次数增加,黄土水平向及竖直向渗透系数先增大然后趋于稳定;黄土渗透各向异性随冻融次数增加而显著改变,表现在黄土的水平向渗透系数与竖直向渗透系数比值随着冻融循环次数的增加而减小。最后通过观测黄土的微观结构分析了其对黄土渗透性的重要影响。     

The helicity of the velocity field for cellular convection in a rotating layer

The helicity of a cellular convective flow in a horizontal layer of a compressible fluid (gas) heated from below and rotating about the vertical axis is studied using finite-difference numerical simulations. The medium is assumed to be polytropically stratified. A thermal perturbation that produces a system of Bénard-type hexagonal convection cells is introduced at the initial time. Next, the cells are deformed by the action of the Coriolis force; however, at some stage of the evolution, the flow is nearly steady (at later times, the cells break down). For given Rayleigh and Prandtl numbers, the velocity-field helicity for this stage averaged over the layer increases with decreasing polytrope index (i.e., with increasing the curvature of the static entropy profile) and has a maximum at a certain rotational velocity of the layer. Numerical simulations of such quasi-ordered convective flows should reduce the uncertainties in estimates of the helicity, a quantity important for the operation of MHD dynamos.     

基于等效塑性应变的三维边坡滑面搜索

边坡三维临界滑面的定位问题是边坡稳定性分析中尚未得以很好解决的一个重要问题。注意到临界滑面是由沿深部方向上的等效塑性应变的极大点所组成这一现象,在利用强度折减法将边坡带入临界平衡状态后,通过在水平面上设置一系列的垂直直线,并找出每条直线上的等效塑性应变最大值的位置,就得到了三维边坡滑面上离散点的分布。最后,采用被称为薄板光顺样条（thin-plate smoothing spline）函数的插值方法对滑面上的离散点进行了插值光顺处理,在不指定边坡滑动模式和滑面形状的前提下就可以得到三维边坡的临界滑面。通过在三维凸型边坡中的应用,体现了该方法在确定三维边坡临界滑面上的优越性。     

Elastic solutions for a transversely isotropic half-space subjected to a point load

We rederive and present the complete closed-form solutions of the displacements and stresses subjected to a point load in a transversely isotropic elastic half-space. The half-space is bounded by a horizontal surface, and the plane of transverse isotropy of the medium is parallel to the horizontal surface. The solutions are obtained by superposing the solutions of two infinite spaces, one acting a point load in its interior and the other being free loading. The Fourier and Hankel transforms in a cylindrical co-ordinate system are employed for deriving the analytical solutions. These solutions are identical with the Mindlin and Boussinesq solutions if the half-space is homogeneous, linear elastic, and isotropic. Also, the Lekhnitskii solution for a transversely isotropic half-space subjected to a vertical point load on its horizontal surface is one of these solutions. Furthermore, an illustrative example is given to show the effect of degree of rock anisotropy on the vertical surface displacement and vertical stress that are induced by a single vertical concentrated force acting on the surface. The results indicate that the displacement and stress accounted for rock anisotropy are quite different for the displacement and stress calculated from isotropic solutions. © 1998 John Wiley & Sons, Ltd.     

考虑剪应力作用时横观各向同性岩体中圆形巷道位移反分析的惟一性

推导了考虑剪应力作用时横观各向同性岩体中圆形巷道的位移解析解,利用参数可辨识条件对考虑剪应力作用时横观各向同性岩体中圆形巷道位移反分析的惟一性进行了探讨。结果表明,无论布置多少个测点也不能惟一地反分析出所有7个参数,必须至少已知3个参数,才有可能惟一地反分析出其他参数;水平与竖直地应力分量是否为 0 对反分析惟一性有一定影响;3个地应力分量的可辨识性最好,各向同性面上的弹性模量和泊松比次之,垂直于各向同性面方向的弹性模量和泊松比最差。与不考虑剪应力时位移反分析惟一性结果相比,考虑剪应力时参数的可辨识性顺序不变,但是条件惟一的比例降低,不惟一和绝对惟一的比例增加,说明考虑剪应力能够提高位移反分析的惟一性。工程实例计算表明,推导的位移解析解和反分析惟一性探讨结果能够很好地指导岩体参数反演计算。     

三维加筋边坡地震稳定性上限分析

基于极限分析上限定理,考虑均匀加筋和三角形加筋两种加筋模式,采用拟静力分析方法推导了一定边坡高度条件下的三维加筋边坡临界加筋强度的计算公式。通过与已有文献结果的对比,验证了所提方法的正确性,并讨论了边坡宽高比、水平和竖向地震力系数对三维边坡稳定性的影响。结果表明:地震力作用下边坡临界加筋强度随边坡宽高比的增大而增加,但其变化速率逐渐减小,当边坡宽高比大于10时,三维边坡加筋强度与二维情况相近;随着水平地震作用的增大,三维边坡临界加筋强度呈非线性增大;随着竖向地震作用的增大,临界加筋强度大致呈线性增加,且随着坡角的增大,竖向地震作用对临界加筋强度的影响更加显著;两种加筋模式下的边坡临界加筋强度值变化规律一致,且三角形加筋模式所需的加筋强度较小,效果较优。最后,针对实际工程提出了一些工程建议。     

沧东断裂(天津段)特征及导水导热性质分析

沦东断裂是华北平原区一条规模较大的隐伏断裂,经历了中、新生代两个裂陷旋回,一直为地热地质工作者所关注.人工地震表明:沧东断裂是一空间构造形态上陡下缓、走向北东、北部边界已沿至蓟运河断裂附近的大型拆离断裂.以水文地质理论为基础,对沧东断裂附近地热流体的水化学场、温度场特征的研究表明:沧东断裂在下部并不具备控制天津地热热源的构造条件,但断裂上部却具有明显的将深部高位热能以热对流形式向浅部传导的特征;在水力传导方面,除局部地段稍弱外,总体上沧东断裂带在水平和垂直方向上有较强的导水能力.     

Moving load response of an axially loaded Timoshenko beam on a multilayered transversely isotropic half-space comprising different media

This paper investigates the dynamic response of an axially loaded Timoshenko beam coupled with a multilayered transversely isotropic (TI) half-space subjected to a moving load. An axial force induced by the thermal expansion is taken into account in the Timoshenko beam. The half-space considers the alternate distribution of an arbitrary number of TI elastic and poroelastic layers to model foundation soils with different properties and moisture conditions. To solve the governing equations, Fourier transform is adopted. The stratified foundation is formulated by extending an “adapted stiffness matrix method” to a more general scenario with an arbitrary number of layers. The beam is then coupled with the foundation to derive solutions to the system in the frequency-wavenumber domain. The final results in the time-spatial domain are recovered by the inverse Fourier transform. After confirming the accuracy of the method in this study, the influences of the pore water existence, the transverse isotropy of different parameters, and the axial force are investigated. It can be observed that the effect of pore water existence on the maximum beam deflection can reach 22% in this study. The transverse isotropy of the elastic and shear moduli influences the critical speed of the beam deflection by altering the phase velocity of the first wave propagation mode of the beam-foundation system. The vertical permeability coefficient is more important than the horizontal one in determining the excess pore pressure. The rise of the beam temperature (axial force) decreases the critical speed and magnifies the vibrations.     

东构造结墨脱关键区域地应力场特征及其构造稳定性分析

为获取东构造结关键构造部位地应力特征、分析其构造稳定性,采用水压致裂法开展了墨脱断裂带西让段1个地应力孔、11个测试段的原位地应力测量工作。结果表明：61.43~121.34 m测试段最大、最小水平主应力值（SH、Sh）分别为3.05～14.50 MPa和2.16～9.87 MPa,垂向主应力值（Sv）为1.63~3.31 MPa,即SH>Sh>Sv;测点处应力场以水平挤压作用为主,均处于逆断层应力状态,且其主应力值随深度增加而逐渐增大,测点的最大水平主应力优势方位为北东东向;在整个地应力测量深度范围内,侧压系数值（Kav）为1.39~4.38,最大水平应力系数值（KHv）均大于1,且比值随深度的增加而增大,该关键部位区域应力场以水平应力为主导,方向性较强,所有测试段水平应力系数值（KHh）为1.23~1.66,与林芝−通麦段地应力特征参数计算结果基本相似;测点位置98 m以浅地层水平构造应力作用程度较小,应力积累水平较低,保持断层稳定所需的摩擦系数值小于实际断层的临界摩擦系数值,构造环境相对稳定,超过98 m深度地层由于水平构造应力起主要作用,保持断层稳定所需的摩擦系数值接近于实际断层的临界摩擦系数值,存在小概率发生断层失稳滑动的风险;区域强震在墨脱断裂带断层面上造成的左旋走滑方向上及逆冲方向上的库仑应力变化值的叠加量均为负值,抑制了断层的滑动,未能增加墨脱关键区域断层活动的危险性。     

The study of reflection/transmission phenomena in a corrugated interface between two magnetoelastic transversely isotropic media

In this paper, an integrated approach has been carried out with an intent to study the reflection and transmission phenomena of plane SH-type wave on a corrugated interface separating two magnetoelastic transversely isotropic half-space. Closed form expressions for reflection and transmission coefficients have been derived for both plane and corrugated surface. Rayleigh’s method of approximation have been incorporated to deduce equations for the first- and second-order approximation of corrugation. Analytical solutions for both the half-spaces have been worked out. All possible cases have been apprehended specially for anisotropic and an isotropic medium. The effects of magnetoelastic coupling parameter, angle at which the wave crosses the magnetic field, corrugation amplitude, frequency factor and wave number have been explained by collaborating with graphical analysis.