Inversely-Mapped Analytical Solutions for Flow Patterns around and within Inclined Elliptic Inclusions in Fluid-Saturated Rocks

In this paper, an inverse mapping is used to transform the previously-derived analytical solutions from a local elliptical coordinate system into a conventional Cartesian coordinate system. This enables a complete set of exact analytical solutions to be derived rigorously for the pore-fluid velocity, stream function, and excess pore-fluid pressure around and within buried inclined elliptic inclusions in pore-fluid-saturated porous rocks. To maximize the application range of the derived analytical solutions, the focal distance of an ellipse is used to represent the size of the ellipse, while the length ratio of the long axis to the short one is used to represent the geometrical shape of the ellipse. Since the present analytical solutions are expressed in a conventional Cartesian coordinate system, it is convenient to investigate, both qualitatively and quantitatively, the distribution patterns of the pore-fluid flow and excess pressure around and within many different families of buried inclined elliptic inclusions. The major advantage in using the present analytical solution is that they can be conveniently computed in a global Cartesian coordinate system, which is widely used in many scientific and engineering computations. As an application example, the present analytical solutions have been used to investigate how the dip angle of an inclined elliptic inclusion affects the distribution patterns of the pore-fluid flow and excess pore-fluid pressure when the permeability ratio of the elliptic inclusion is of finite but nonzero values.     

Theoretical and numerical analyses of pore-fluid flow focused heat transfer around geological faults and large cracks

In this paper, theoretical and numerical methods are used to investigate pore-fluid flow focused temperature distribution patterns around geological faults and cracks of any length-scales in hydrothermal systems. If the far field inflow is uniform and the long axis of an elliptical fault of any length-scale is parallel to the far field inflow direction, a complete set of analytical solutions has been presented for the pore-fluid velocity, stream function and excess pore-fluid pressure around the elliptical fault embedded in fluid-saturated porous media. Because the analytical solutions are explicitly expressed in the conventional Cartesian coordinate system, not only can they be used to gain a theoretical insight into the pore-fluid flow patterns around geological faults and large cracks, but also they can be used as valuable benchmark solutions for validating any numerical methods. After a finite element computational model is validated by comparing the numerical solutions with the present analytical solutions, it is used to investigate pore-fluid flow focused heat transfer around geological faults in hydrothermal systems. Some interesting conclusions in relation to the effects of geological faults on pore-fluid flow focused heat transfer have been made through both the theoretical and the numerical analyses.     

Deformation of two welded elastic half-spaces due to a long inclined tensile fault

The calculation of the deformation caused by shear and tensile faults is necessary for the investigation of seismic and volcanic sources. The solution of the two-dimensional problem of a long inclined shear fault in two welded half-spaces is well known. The purpose of this note is to present the corresponding solution for a tensile fault. Closed-form analytical expressions for the Airy stress function for a tensile line source in two welded half-spaces are first obtained. These expressions are then integrated analytically to derive the Airy stress function for a long tensile fault of arbitrary dip and finite width. Closed-form analytical expressions for the displacements and stresses follow immediately from the Airy stress function. These expressions are suitable for computing the displacement and stress fields around a long inclined tensile fault near an internal boundary.     

倾斜断层Vzz、Vzzz的联合反问题解

本文利用两个上延高度的V_zz极值距和其中之一高度的V_zzz的零值点获得了倾斜断层的位置、埋深、断距、倾向、倾角以及断层正逆性质等的反问题解。     

Flow Study in a Double Porosity Medium Containing Ellipsoidal Occluded Macro-voids

This paper presents an analytical study of fluid flow in a porous medium presenting pores of two different length scales: at the smallest or microscopic scale, the presence of connected voids confers a porous medium structure to the material investigated, while at the upper or mesoscopic scale, macro-pores are present. This microstructure is employed to represent the progressive opening of inter-aggregate pore spaces observed in natural compacted montmorillonites polluted by heavy metal ions. Three-dimensional analytical expressions are rigorously derived for pore fluid velocity and excess pore fluid pressure within the porous matrix, around an occluded ellipsoidal inter-aggregate void. The eccentricity ratio is employed to characterize the geometrical shape of the ellipsoidal void, while its orientation with respect to the inflow in the far field is determined by the dip angle θ. As an application, we investigate the flow focusing effect for varying eccentricity ratios and dip angles.     

Flow Study in a Double Porosity Medium Containing Low Concentrations of Ellipsoidal Occluded Macro-voids

This paper presents an analytical study of fluid flow in a porous medium presenting pores of two different length scales: at the smallest or microscopic scale, the presence of connected voids confers a porous medium structure to the material investigated, while at the upper or mesoscopic scale, macro-pores are present. This microstructure is employed to represent the progressive opening of inter-aggregate pore spaces observed in natural compacted montmorillonites polluted by heavy metal ions. Three-dimensional analytical expressions are rigorously derived for pore fluid velocity and excess pore fluid pressure within the porous matrix, around an occluded ellipsoidal inter-aggregate void. The eccentricity ratio is employed to characterize the geometrical shape of the ellipsoidal void, while its orientation with respect to the inflow in the far field is determined by the dip angle θ. As an application, we investigate the flow focusing effect for varying eccentricity ratios and dip angles.     

2-D deformation of two welded half-spaces due to a blind dip-slip fault

The solution of two-dimensional problem of an interface breaking long inclined dip-slip fault in two welded half-spaces is well known. The purpose of this note is to obtain the corresponding solution for a blind fault. The solution is valid for arbitrary values of the fault-depth and the dip angle. Graphs showing the variation of the displacement field with the distance from the fault, for different values of fault depth and dip angle are presented. Contour maps showing the stress field around a long dip-slip fault are also obtained     

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.     

垂直界面附近椭圆形夹杂对SH波的散射与地震动研究

利用复变函数法和Green函数法给出了SH波对垂直界面附近椭圆形夹杂散射问题的解析解答。首先,将待求的半空间模型沿垂直边界分割为区域Ⅰ和区域Ⅱ两个直角域。通过保角映射的方法将区域Ⅰ内椭圆形夹杂的外域映射为单位圆外域,并利用镜像方法构造出两个区域内满足直角域边界条件的散射波场及适用的Green函数;其次,利用界面契合思想,通过在界面处添加附加力系的方法建立起满足界面处位移和应力连续条件的无穷代数方程组,并截断有限项求解;最后,给出了求解地表位移幅值的具体算例。结果表明,入射波数、入射角度、夹杂位置、垂直界面以及材料参数都对地表位移幅值的分布有影响。     

渗流应力耦合作用下顺倾向层状边坡各向异性渗流特征数值模拟

渗流场与应力场耦合作用下边坡渗流规律对研究边坡稳定性至关重要,应用基于等效连续介质模型和Louis经验公式建立的各向异性岩体渗流应力耦合模型,对顺倾向层状边坡的各向异性渗流规律进行了模拟分析。研究表明：顺倾向层状边坡中水位降深随结构面倾角θ的增大先升高、后降低,呈现两头低、中间高的形态,且越靠近溢出点,结构面倾角对水位降深影响越大;θ约为42°时水位降深最大,潜水面最低,同时渗透各向异性系数达到最大值;顺倾向边坡岩层产状一定时,随着埋深的增加,岩体渗透各向异性系数逐渐减小,裂隙控渗特征由显著到逐渐变弱,表现出向各向同性渗流过渡的趋势。     

Brittle tectonics and pore-fluid conditions in the evolution of the Great Boundary Fault around Chittaurgarh,Northwestern India

This paper aims at reconstructing paleostress history and deciphering the pore-fluid pressure conditions during the reactivation of a regional-scale fault. Paleostress analyses of the mesoscopic structures suggest that three successive events of reactivation on the Great Boundary Fault occurred in thrust-type, strike-slip type and thrust-type tectonic-settings, respectively. Whereas the pore-fluid pressure was supralithostatic during the first and third events of reactivation, it was sublithostatic during the second event. Each event of reactivation induced a fluid pressure gradient, which resulted in the focused and enhanced flow of syntectonic fluids within the high permeability locales, primarily fractures and faults.Fluid inclusion study on strike-slip veins reveals that the syntectonic fluids were highly dense, Na–Ca–Cl brines of formational water origin. Stratigraphic evidence in favour of a 2-km-thick column of overburden above Kaimur sandstone beds implies that the strike-slip faulting occurred at 160–202 °C temperature and 53 MPa pressure. Variation in homogenization temperature reflects fluctuation in pore-fluid pressure during entrapment of syntectonic fluids and points to seismic pumping as a possible mechanism of fluid flow during faulting. High paleogeothermal gradient, obtained by fluid inclusion data, is ascribed to the high heat flow due to crustal stretching during the Proterozoic rifting, the basal and intermittent volcanism in the basin, and occurrence of Berach granite as the basement.     

浅埋管道水平横向作用下砂土极限承载力研究

断层、滑坡、液化等地质灾害引起的场地大变形对埋地管道结构安全产生严重的威胁。开展了中密砂中埋地管道−砂土水平横向相互作用的系列三维数值模拟,根据数值模拟的结果探讨了不同深径比下管−砂土横向相互作用时土体的破坏模式,研究了深径比对砂土极限承载力的影响。基于管周土体的破坏模式建立了简化计算模型,根据极限平衡理论推导了管道水平横向运动时砂土极限承载力计算公式。研究结果表明：极限状态下,浅埋管道周围土体形成延伸到地表的破裂面,轮廓线近似对数螺线;砂土的极限承载力随着深径比增加,最终在临界深径比处达到稳定;随着深径比的增加,土体发生剪切滑动破坏所需的管道位移也逐渐增大;由于横向承载力系数取值依据不同,国内外规范计算所得土体极限承载力差异较大;得到的解析解能够较好地预测中密砂土中浅埋管道水平横向运动时土体的极限承载力。     

A porosity-gradient replacement approach for computational simulation of chemical-dissolution front propagation in fluid-saturated porous media including pore-fluid compressibility

In dealing with chemical-dissolution-front propagation problems in fluid-saturated porous media, the chemical dissolution front represented by the porosity of the medium may have a very steep slope (i.e., a very large porosity gradient) at the dissolution front, depending on the mineral dissolution ratio that is defined as the equilibrium concentration of the dissolved minerals in the pore-fluid to the solid molar density of the dissolvable minerals in the solid matrix. When the mineral dissolution ratio approaches zero, the theoretical value of the porosity gradient tends to infinity at the chemical dissolution front. Even for a very small value of the mineral dissolution ratio, which is very common in geochemical systems, the porosity gradient can be large enough to cause the solution hard to converge when the conventional finite element method is used to solve a chemical dissolution problem in a fluid-saturated porous medium where the pore-fluid is compressible. To improve the convergent speed of solution, a porosity-gradient replacement approach, in which the term involving porosity-gradient computation is replaced by a new term consisting of pore-fluid density-gradient and pressure-gradient computation, is first proposed and then incorporated into the finite element method in this study. Through comparing the numerical results obtained from the proposed approach with the theoretical solutions for a benchmark problem, it has been demonstrated that not only can the solution divergence be avoid, but also the accurate simulation results can be obtained when the proposed porosity-gradient replacement approach is used to solve chemical-dissolution-front propagation problems in fluid-saturated porous media including pore-fluid compressibility.     

Finite element analysis of steady-state natural convection problems in fluid-saturated porous media heated from below

In this paper, a progressive asymptotic approach procedure is presented for solving the steady-state Horton–Rogers–Lapwood problem in a fluid-saturated porous medium. The Horton–Rogers–Lapwood problem possesses a bifurcation and, therefore, makes the direct use of conventional finite element methods difficult. Even if the Rayleigh number is high enough to drive the occurrence of natural convection in a fluid-saturated porous medium, the conventional methods will often produce a trivial non-convective solution. This difficulty can be overcome using the progressive asymptotic approach procedure associated with the finite element method. The method considers a series of modified Horton–Rogers–Lapwood problems in which gravity is assumed to tilt a small angle away from vertical. The main idea behind the progressive asymptotic approach procedure is that through solving a sequence of such modified problems with decreasing tilt, an accurate non-zero velocity solution to the Horton–Rogers–Lapwood problem can be obtained. This solution provides a very good initial prediction for the solution to the original Horton–Rogers–Lapwood problem so that the non-zero velocity solution can be successfully obtained when the tilted angle is set to zero. Comparison of numerical solutions with analytical ones to a benchmark problem of any rectangular geometry has demonstrated the usefulness of the present progressive asymptotic approach procedure. Finally, the procedure has been used to investigate the effect of basin shapes on natural convection of pore-fluid in a porous medium. © 1997 by John Wiley & Sons, Ltd.     

2-D deformation analysis of a half-space due to a long dip-slip fault at finite depth

Closed form analytical expressions of stresses and displacements at any field point due to a very long dip-slip fault of finite width buried in a homogeneous, isotropic elastic half-space, are presented. Airy stress function is used to derive the expressions of stresses and displacements which depend on the dip angle and depth of the upper edge of the fault. The effect of dip angle and depth of the upper edge of the fault on stresses and displacements is studied numerically and the results obtained are presented graphically. Contour maps for stresses and displacements are also presented. The results of Rani and Singh (1992b) and Freund and Barnett (1976) have been reproduced.     

小角度成层倾斜场地动力响应分析的大型振动台试验研究

基于大型振动台试验,研究小角度成层倾斜场地在倾向、走向、垂向、坡面方向、坡面垂直方向上的地震动响应特征,以及地层倾角对场地反应谱的影响规律。试验结果表明：在倾向方向,随着地层倾角的增大,倾斜场地的放大效应增大;在走向方向,当地层倾角小于12.5°时,放大效应强于水平成层场地;在倾向、走向方向,当地层倾角达到12.5°时,场地对反应谱短周期T≤0.1 s部分具有放大作用,对T＞0.1 s的部分具有削弱作用;在垂向方向,随着地层倾角的增加,倾斜场地的放大效应强于水平成层场地;在坡面方向,倾斜场地的放大效应弱于水平成层场地;在坡面垂向方向,倾斜场地的放大效应强于水平成层场地。该研究成果对小角度成层倾斜场地上的建筑物抗震设计具有一定的参考意义。     

Arterial faults and their role in mineralizing systems

In quartzo-feldspathic continental crust with moderate-to-high heat flow,seismic activity extends to depths of 10-20 km,bounded by isotherms in the 350-450 C range.Fluid overpressuring above hydrostatic in seismogenic crust,is heterogeneous but tends to develop in the lower seismogenic zone(basal seismogenic zone reservoir=b.s.z.reservoir) where the transition between hydrostatically pressured and overpressured crust is likely an irregular,time-dependent.3-D interface with overpressuring concentrated around active faults and their ductile shear zone roots.The term Arterial Fault is applied to fault structures that root in portions of the crust where pore fluids are overpressured(i.e.at hydrostatic pressure) and serve as feeders for such fluids and their contained solutes into overlying parts of the crust.While arterial flow may occur on any type of fault,it is most likely to be associated with reverse faults in areas of horizontal compression where fluid overpressuring is most easily sustained.Frictional stability and flow permeability of faults are both affected by the state of stress on the fault(shear stress,τ;normal stress,σ_n),the level of pore-fluid pressure,P_f,and episodes of fault slip,allowing for a complex interplay between fault movement and fluid flow.For seismically active faults the time dependence of permeability is critical,leading to fault-valve behaviour whereby overpressures accumulate at depth during interseismic intervals with fluid discharged along enhanced fault-fracture permeability following each rupture event.Patterns of mineralization also suggest that flow along faults is non-uniform,concentrating along tortuous pathways within the fault surface.Equivalent hydrostatic head above ground level for near-lithostatic overpressures at depth(1.65×depth of zone) provides a measure of arterial potential.Settings for arterial faults include fault systems developed in compacting sedimentary basins,faults penetrating zones of active plutonic intrusion that encounter overpressured fluids exsolved from magma,together with those derived from contact metamorphism of fluid-rich wallrocks,and/or from regional devolatilisation accompanying prograde metamorphism.Specially significant are active faults within accretionary prisms rooted into overpressured subduction interfaces,and steep reverse faults activated by high overpressures from b.s.z.reservoirs during compressional inversion.     

Displacement and stress distributions under a uniform inclined rectangular load on a cross‐anisotropic geomaterial

In practical engineering, an applied rectangular area load is not often horizontally or vertically distributed but is frequently inclined at a certain angle with respect to the horizontal and vertical axes. Thus, the solutions of displacements and stresses due to such a load are essential to the design of foundations. This article yields the analytical solutions of displacements and stresses subjected to a uniform rectangular load that inclines with respect to the horizontal and vertical axes, resting on the surface of a cross‐anisotropic geomaterial. The planes of cross‐anisotropy are assumed to be parallel to the horizontal ground surface. The procedures to derive the solutions can be integrated the modified point load solutions, which are represented by several displacement and stresses elementary functions. Then, upon integrations, the displacement and stress integral functions resulting from a uniform inclined rectangular load for (1) the displacements at any depth, (2) the surface displacements, (3) the average displacements in a given layer, (4) the stresses at any depth, and (5) the average stresses in a given layer are yielded. The proposed solutions are clear and concise, and they can be employed to construct a series of calculation charts. In addition, the present solutions clarify the load inclinations, the dimensions of a loaded rectangle, and the analyzed depths, and the type and degree of geomaterial anisotropy profoundly affect the displacements and stresses in a cross‐anisotropic medium. Parametric results show that the load inclination factor should be considered when an inclined rectangular load uniformly distributed on the cross‐anisotropic material. Copyright © 2008 John Wiley & Sons, Ltd.     

基于多因素椭圆堆叠的岩土细观建模方法

天然岩土体具有复杂的细观结构和组成特征,现有细观建模方法难以解决任意粒径、长短轴比、倾角以及平面分布特征的多因素岩土体细观建模问题。为此基于椭圆的4段圆弧等效,结合改进的分组波前堆叠法,实现了任意粒径、长短轴比、倾角以及平面分布的快速高体积率椭圆堆叠,并以此建立了与堆叠椭圆粒径、长短轴比、倾角以及平面分布一致的凸多边形结构。与现有的椭圆堆叠ALA法和圆盘堆叠ODR方法相比,提出的方法具有更高的椭圆堆叠体积率和堆叠效率,MATLAB环境下椭圆堆叠效率为500～600个/s。与现有仅能考虑颗粒粒径分布的岩土细观建模GBM法相比,提出的方法可以同时考虑颗粒的粒径、长轴、倾角,以及平面分布4个因素,快速生成任意粒径、长短轴比、倾角以及平面分布的颗粒堆积,并建立与椭圆分布一致的岩石细观结构。通过两个岩土体细观建模案例分析表明,所提方法可以提高岩土体模型的细观建模精度与生成效率。     

采动影响下逆断层活化规律的数值模拟

煤矿开采过程中断层活化时有发生,是矿井灾害防治研究的热点问题。为了揭示不同断层倾角条件下煤层开采对断层活化的影响,以淮南新集二矿地质采矿条件为例,采用FLAC3D进行数值模拟,系统研究逆断层下煤层开采过程中断层的动态活化规律,阐明了断层活化位置与工作面推进距离、断层倾角之间的关系。研究表明,断层活化可分为累积期、形成期、破坏期3个发育阶段;当工作面回采至工作面推进距离的一半时,断层开始活化,至开采结束,断层滑移量最大;倾角越小的断层面越早开始活化,倾角越大的断层面滑移量越大。研究成果为断层发育区煤炭资源安全开采提供了理论依据和技术参考。