Analytical solutions of linear finite‐ and small‐strain one‐dimensional consolidation

Analytical solutions are presented for linear finite‐strain one‐dimensional consolidation of initially unconsolidated soil layers with surcharge loading for both one‐ and two‐way drainage. These solutions complement earlier solutions for initially unconsolidated soil layers without surcharge and initially normally consolidated soil layers with surcharge. Small‐strain solutions for the consolidation of initially unconsolidated soil layers with surcharge loading are also presented, and the relationship between the earlier solutions for initially unconsolidated soil without surcharge and the corresponding small‐strain solutions, which was not addressed in the earlier work, is clarified. The new solutions for initially unconsolidated soil with surcharge loading can be applied to the analysis of low stress consolidation tests and to the partial validation of numerical solutions of non‐linear finite‐strain consolidation. They also clarify a formerly perplexing aspect of finite‐strain solution charts first noted in numerical solutions. Copyright © 2004 John Wiley & Sons, Ltd.     

Solubility of minerals of metamorphic and metasomatic rocks in hydrothermal solutions of varying acidity: Thermodynamic modeling at 400–800°C and 1–5 kbar

The character of solubility of 61 metamorphic and metasomatic minerals in an aqueous fluid was analyzed as a function of temperature, pressure, and fluid acidity by means of computer simulation of mineralfluid equilibria. Depending on the behavior of minerals in solutions of varying acidity, six main types of solubility diagrams were distinguished. The solubility of the majority of minerals is controlled mainly by fluid acidity rather than by P–T conditions. The analysis of model results provided insight into the mobility of chemical elements composing the minerals. The highest mobility in solutions of any acidity was established for Si, K, and Na. Ca and Mg are mobile in acidic solutions and inert in neutral and alkaline solutions. Fe(II) and Mn(II) are mobile in acidic and alkaline solutions but inert in neutral solutions. Fe(III) is mobile only in strongly acidic solutions and practically immobile in solutions of other compositions, which suggests that ferrous iron species must prevail in solutions. Al is mobile in alkaline and ultra-acidic solutions but inert in neutral and slightly acidic solutions. Correspondingly, a change in acidity must lead to the migration of some component into the solution and precipitation of other components. These conclusions are in agreement with the sequences of element mobility deduced from the experimental investigation of metasomatism. Most metamorphic fluids must be rich in silica and alkalis, which may result in the appearance of aggressive silica-alkali fluids responsible for regional metasomatism and granitization. In general, the solubility of Fe-, Mg-, Mn-, and Ca-bearing minerals in alkaline solutions is low compared with acidic solutions. Therefore, only acidic initial solutions could produce fluids enriched in these elements at the expense of leaching from metamorphic rocks during fluid migration. Fluids enriched mainly in Fe could initially be both acidic and alkaline.     

不排水双层粘性土地基极限承载力的数值分析

采用弹塑性有限元分析了条形基础作用下不排水条件的双层粘性土地基极限承载力性状。采用修正的地基承载力系数表征,并将不同的几何与土层参数条件下的数值解与上下限解和经典的经验解进行比较。表明弹塑性位移有限元法可以很好地求解地基的极限承载力问题,其求解得到的修正地基承载力系数与基于下限原理的有限元解很接近,而上限解高估了地基的极限荷载值,传统的经验解在某些条件下却偏小。     

Analytical solutions to 1-D horizontal and vertical water infiltration in saturated/unsaturated soils considering time-varying rainfall

Analytical solutions to 1-D horizontal and vertical water infiltration in saturated/unsaturated soils are developed that can consider the variation of rainfall with time. In this model, water content and the permeability coefficient are assumed to be exponential functions of the pressure head, and diffusivity is constant. By means of Fourier integral transformation, the analytical solutions are expressed as infinite series. The steady-state solutions for horizontal and vertical infiltration in unsaturated soils are then derived. The solutions can consider both flux and pressure head boundaries. The solutions are easy to implement compared with numerical solutions, although the restricted assumptions may limit their applicability in some ways. The analytical solutions provide a reliable tool for checking the accuracy of various numerical methods under the condition of constant diffusivity. Finally, the analysis carried out in a case study indicates that the pressure head differences caused by the transient infiltration in both the horizontal and vertical directions can be estimated using the steady-state solutions, and the effect of gravity on water infiltration mainly depends on the boundary conditions.     

The significance of ion exchange to interstitial solutions in clayey sediments

The ion population in interstitial solutions in clayey sediments is distributed by Donnan chemical potential forces between inner and outer (micellar and intermicellar respectively) solutions around clay-mineral particles. Extraction procedures which involve a single dilution step disturb the ion distribution between inner and outer solutions. The relationship of solutions extracted by squeezing to Donnan equilibrium remains relatively untested. A little-used method that may distinguish the in situ inner and outer solutions in the laboratory is suggested. It involves multiple dilution extractions from several aliquots of a single sediment sample. Each aliquot has a different sediment/water ratio and the line of best fit to the ion activities of extracted solutions may be extrapolated to the in situ sediment/water ratio. Efforts to distinguish inner and outer solutions in marine clayey sediments ought to be made because their existence is a fact of nature which may have importance to the study of the chemical evolution of such sediments.     

结构性土一维非线性大应变固结半解析解

以结构性较强的天然饱和软黏土为研究对象,考虑了沉积作用对其自重应力的影响,以及压缩性和渗透性的非线性变化,推导了任意加载条件下结构性土一维大应变固结控制方程,并采用半解析的方法对方程进行求解计算。再将其退化为无结构性的饱和软黏土固结解,与已有的大应变固结解进行了对比,验证了该解的正确性。最后将该半解析解计算结果与小应变固结理论解、不考虑结构性的固结理论解计算结果进行对比分析。结果表明：大应变固结理论的沉降计算值大于小应变固结理论的计算值,且二者的差值随着荷载的增加而增加;当考虑土体的结构性时,地表沉降计算值小于不考虑土体结构性的沉降计算值。     

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.     

Vertical stress distributions around batter piles driven in cross‐anisotropic media

This work presents analytical solutions to compute the vertical stresses for a cross‐anisotropic half‐space due to various loading types by batter piles. The loading types are an embedded point load for an end‐bearing pile, uniform skin friction, and linear variation of skin friction for a friction pile. The cross‐anisotropic planes are parallel to the horizontal ground surface. The proposed solutions can be obtained by utilizing Wang and Liao's solutions for a horizontal and vertical point load acting in the interior of a cross‐anisotropic medium. The derived cross‐anisotropic solutions using a limiting approach are in perfect agreement with the isotropic solutions of Ramiah and Chickanagappa with the consideration of pile inclination. Additionally, the present solutions are identical to the cross‐anisotropic solutions by Wang for the batter angle equals to 0. The influential factors in yielded solutions include the type and degree of geomaterial anisotropy, pile inclination, and distinct loading types. An example is illustrated to clarify the effect of aforementioned factors on the vertical stresses. The parametric results reveal that the stresses considering the geomaterial anisotropy and pile batter differ from those of previous isotropic and cross‐anisotropic solutions. Hence, it is imperative to take the pile inclination into account when piles are required to transmit both the axial and lateral loads in the cross‐anisotropic media. Copyright © 2008 John Wiley & Sons, Ltd.     

Two types of multiple solutions for microseismic source location based on arrival-time-difference approach

The arrival-time-difference approach is the dominant source location approach used in the microseismic source location area. Multiple solutions problem is one of the major concerns in microseismic source location, which is closely related to the microseismic network. This paper categorizes the multiple solutions into two types based on the origin times when using the arrival-time-difference approach. Type I multiple solutions are those which have the same origin time; type II multiple solutions are those with different origin times. The sufficient and necessary conditions to produce type I multiple solutions are that all sensors are located in a straight line for two-dimensional cases and on a plane for three-dimensional cases. The sufficient and necessary conditions to produce type II multiple solutions are that all sensors are located on a hyperbola for two-dimensional cases and on a hyperboloid for three-dimensional cases. Furthermore, the proofs indicate that type I multiple solutions are preventable, while a microseismic network consisting of the minimum number of sensors can never be free of type II multiple solutions. It means, besides the minimum number of sensors, at least one more sensor which is not on this hyperbola or hyperboloid is needed to uniquely determine a source. The results from field tests and applications indicate that when the sensors of a network lie on a hyperbola, the type II multiple solutions may not be the necessary outcome under the influence of errors in real data. However, the accuracy of the microseismic source location is affected significantly by this kind of networks. The results also show that not only the multiple solutions problem can be avoided effectively, but more importantly, the accuracy of the source location will be greatly improved by the optimization of network based on the characteristics of the microseismic network and field conditions.     

Transient response of a circular cavity in a poroelastic medium

This paper considers the transient response of a pressurized long cylindrical cavity in an infinite poroelastic medium. To obtain transient solutions, Biot's equations for poroelastodynamics are specialized for this problem. A set of exact general solutions for radial displacement, stresses, pore pressure and discharge are derived in the Laplace transform space by using analytical techniques. Solutions are presented for three different types of prescribed transient radial pressures acting on the surface of a permeable as well as an impermeable cavity surface. Time domain solutions are obtained by inverting Laplace domain solutions using a reliable numerical scheme. A detailed parametric study is presented to illustrate the influence of poroelastic material parameters and hydraulic boundary conditions on the response of the medium. Comparisons are also presented with the corresponding ideal elastic solutions to portray the poroelastic effects. It is noted that the maximum radial displacement and hoop stress at the cavity surface are substantially higher than the classical static solutions and differ considerably from the transient elastic solutions. Time histories and radial variations of displacement, hoop stress, pore pressure and fluid discharge corresponding to a cavity in two representative poroelastic materials are also presented.     

热水溶液地球化学

概述了热水溶液地球化学的主要研究内容和近年来在实验和理论研究方面的进展，包括高温高压下水的热力学性质、状态方程式、介电常数、电导率和电离平衡；ＮａＣｌ－ＣＯ２－Ｈ２Ｏ体系及其边界体系（ＮａＣｌ－Ｈ２Ｏ和ＣＯ２－Ｈ２Ｏ）的相关系、热力学性质和状态方程式，特别是利用人工流体包裹体技术和分子动力学模拟取得的新成果；高温高压电解质稀水溶液的电导测定；以ＨＫＦ模型为基础，热水溶液中不同物种的标准偏摩尔热力学性质和高温高压有关物理化学参数的估算；热水溶液中的物种形成（热液流体中的矿物溶解度测定、电势测量和谱学研究）；水和热水溶液结构的红外和拉曼谱学研究；水和热水溶液的传输性质（粘度和导热系数）。     

直-增-稳剖面设计问题的解析解

使用无量纲化方法对设计方程组进行了改写,新的无量纲化设计方程组有利于充分利用三角函数公式求解析解,所得到的解析解计算公式具有简洁的数学形式。将设计方程组求解问题分成两类,对于已知最大井斜角的第Ⅰ类问题,使用线性代数解方程组的克莱默法则直接就可以得出解析解。最大井斜角为未知数的第Ⅱ类问题,使用三角函数公式进行化简,得到形式简单、统一的解析解公式,避免了使用半角公式所带来的解析解计算公式的复杂性。所使用无量纲化方法具有一定的普适性,可以用于解决其他类型的二维剖面设计问题。     

On Garg's solution of Biot's equations for wave propagation in a one-dimensional fluid-saturated elastic porous solid

Garg's approximate analytical solutions of Biot's equations for wave propagation in a fluid-saturated elastic porous solid of infinite extent subjected to a velocity boundary condition of a Heaviside function at one end are examined for small and large drag. Garg's approximations were apparently introduced to facilitate exact inversion of Laplace transforms of certain quantities. The approximate solutions are compared with carefully evaluated numerical inverses of the Laplace transform solutions for different soils with widely varying properties. It is seen that for most soils (clays, silts and, sands) the error in Garg's approximate solutions in insignificant, and the solutions can be used as benchmarks for verifying numerical analysis procedures such as finite element codes.     

Scaling laws for hydraulic fractures driven by a power-law fluid in homogeneous anisotropic rocks

This study investigates parametric space of solutions for a planar hydraulic fracture propagating in a homogeneous anisotropic rock. It is assumed that the fracture has an elliptical shape and is driven by a power-law fluid. The purpose of this study is to investigate the influence of anisotropy and power-law fluid rheology on the parametric space of solutions. Rock anisotropy is represented by having two values of fracture toughness, one in the vertical direction and another one in the horizontal direction. Similarly, the effect of elastic anisotropy is approximated by using two different effective elastic moduli in the vertical and horizontal directions. In contrast to the isotropic case, for which there are four limiting solutions, the problem for anisotropic rocks features six different limiting cases. These cases represent competition between toughness and viscosity in the vertical and horizontal directions and competition between fluid storage inside the fracture and fluid leak-off into formation. Approximate expressions for the limiting solutions are obtained using global volume balance and tip asymptotic solutions. Despite the developed solutions rely on a series of approximations, they precisely capture all the scaling laws associated with the problem. Zones of applicability of these limiting solutions are calculated, and their dependence on the problem parameters is investigated.     

近靶纠偏轨道设计问题的解析解

在钻井监测过程中,当前井底接近目标点时,纠偏轨道一般采用“线段-圆弧”形式来设计。建立了近靶轨道设计的数学模型,对4种求解组合给出了数学模型的解析解。阐述了解析解的一个应用：绘制解析解曲线图能够帮助计算机软件使用者做出更加合理的纠偏轨道设计。实际算例表明,解析解能够准确、快速地给出近靶纠偏轨道的设计方案,对于指导钻井监测工作有一定的指导意义。     

饱和土表面在水平集中荷载作用下的瞬态反应

分析了水平集中荷载作用在半空间饱和土表面时的瞬态问题。利用Laplace-Hankel变换对非轴对称Biot固结方程进行解耦，利用Laplace-Hankel数值逆变换得到半空间饱和土在时域内的数值解。退化到线弹性中的解与文献中的结果进行比较，验证了文中结果的正确性和数值逆变换的可靠性.可以用于研究地震工程中地震波的传播以及饱和土与结构之间相互作用等问题。     

淡水文石珍珠可溶性有机质对CaCO3结晶的影响

以浙江诸暨淡水文石珍珠为实验原料,提取文石珍珠中的两种基质蛋白--酸可溶蛋白(ASM)和水可溶有蛋白(WSM),并分别将其制备成一系列不同浓度的基质蛋白溶液.利用上述两种不同浓度的可溶性有机基质溶液采用扩散法开展了碳酸钙的体外模拟矿化实验,探讨两种可溶性有机质的浓度在控制CaCO3结晶方面的作用.通过扫描电子显微镜及显微共聚焦拉曼光谱等方法对体外模拟矿化结果进行了观察和分析.结果表明,酸可溶蛋白对碳酸钙晶体的形貌和尺寸具有明显的调控作用,而对晶型无影响,不同浓度的酸可溶蛋白对碳酸钙晶体形貌影响差别不大,对尺寸的影响略有不同;水可溶蛋白对碳酸钙晶体的晶型、形貌及尺寸均有显著影响.不同浓度的水可溶蛋白对碳酸钙晶体的形貌和尺寸影响较大,对晶型有一定的调控作用.     

Sorption of silica by clay minerals

Clay minerals were reacted with silica-spiked solutions of unbuffered distilled water; water buffered at pH 5.5, 8 and 10; alkali chloride solutions; natural and artificial sea water to assess the influence of pH, silica and cation activities. The data are plotted as silica produced by dissolution or sorption of silica by clay surface as a function of initial silica concentration at a given pH and solution composition. This allows the determination of the dissolved silica value at which the clay mineral surface neither dissolves nor sorbs silica. The values of the various activities in different solutions are used to infer the phase equilibria between solution, clay mineral and the surface phase produced either by dissolution or sorption. Most intensively investigated were sorption reactions of kaolinite in sea water and other ionic solutions to form silica-rich, cation-rich surface phases in cationic solutions and silica-rich phases in cation-free solutions.Inferred equilibrium constants imply that silicate reconstitution is doubtful as a mechanism for partial control of silica and cation composition of sea water but is reasonable in silica-rich interstitial waters.     

On thermodynamic models for real solutions

The thermodynamic consistency of modern models of nonideal aqueous solutions is evaluated. It was shown that the models of concentrated aqueous solutions used in current studies are thermodynamically incorrect. Criteria were proposed for the thermodynamic consistency of physicochemical models of the nonideality of real solutions. An example is given for the correct extension of the Debye-Hueckel equation.