Thermodynamics of sodium feldspar I: Order parameter treatment and strain induced coupling effects

The thermodynamic behaviour of Na-rich feld-spars is derived from a Landau-type free energy expression which contains two order parameters. One order parameter describes the structural distortion during the displacive phase transition between monalbite and analbite, the other the Al, Si order. The structural phase transition \(C2/m - C\bar 1\) in sodium feldspar under thermal equilibrium is due to both order parameters and is accompanied by a crossover between a thermal regime with low Al, Si order (high-albite) and a thermal regime with high Al, Si order (low-albite). The crossover is a smooth function of temperature. Simple formulae are given for the calculation of thermodynamic potentials for thermal equilibrium and for metastable phases with temperature independent Al, Si order.     

Potassium and sodium self-diffusion in alkali feldspar

The rate of potassium self-diffusion in pure microcline was measured between 600° and 800° C using K⁴⁰ as a tracer. Transport of K⁴⁰ by processes other than volume diffusion was insignificant or minimal. Isotropic diffusion coefficients were calculated assuming spherical grains. The data are well fit by the Arrhenius relation and yield a pre-exponential factor (D₀) of 133.8 cm²/sec and an activation energy (Q) of 70 kcal/mole. Similar experiments on the self-diffusion of Na²² in a pure low-albite (exchanged microcline) yield D₀ of 2.31×10^–6 cm²/sec and Q of approximately 19 kcal/mole for the temperature interval from 200° to 600° C. The large difference in these activation energies suggests that the atomic mechanisms for sodium and potassium diffusion are different.     

地下圆形衬砌隧道对沿线地震动的影响(II):数值结果

利用地下圆形衬砌隧道对入射平面P波和SV波散射级数解答，定量分析了入射波长、入射角度、隧道直径、衬砌刚度等因素对沿线地表位移放大作用的影响。计算结果表明，当入射频率较低时，地下隧道的存在对地表位移幅值影响不大；而当入射频率较高时，地表位移幅值可以达到无隧道情况的4．5倍以上；衬砌情况下地表位移幅值可以高出非衬砌情况的87．8％。建议在地铁的规划设计中考虑地下隧道的建设对隧道沿线设计地震动的影响。     

Mechanism of feldspar weathering—I. Experimental studies

It has been widely accepted that a chemically altered, protective surface layer regulates the dissolution, and hence the weathering, of plagioclase feldspars under Earth's surface conditions. In this study, we examine this hypothesis in detail with the aid of scanning electron microscopy (SEM) and X-ray photoelectron spectroscopy (XPS). Using these techniques, we have been unable to find any direct evidence suggesting the presence of a chemically altered coating on feldspar surfaces which have been weathered in the lab. Instead, our results suggest that the mechanism controlling feldspar weathering is a surface controlled reaction.Based on SEM observations and measurements of rate of release of silica, we postulate that the process of feldspar dissolution proceeds in two stages in the lab. Initially, one observes the dissolution of ultrafine (? 1 μm diameter) particles which are produced during grinding of the sample, and which adhere tenaciously to the surfaces of larger grains. This is the stage which results in the non-linear rates of dissolution which are commonly observed in the lab (parabolic kinetics). Secondly, the dissolution occurs at sites of excess surface energy such as at dislocations or similar crystal defects. This process yields linear rates of dissolution, and it dominates the weathering of feldspars in the field.     

Fully coupled generalised hybrid-mixed finite element approximation of two-phase two-component flow in porous media. Part II: numerical scheme and numerical results

We consider the modeling and simulation of compositional two-phase flow in a porous medium, where one phase is allowed to vanish or appear. The modeling of Marchand et al. (in review) leads to a nonlinear system of two conservation equations. Each conservation equation contains several nonlinear diffusion terms, which in general cannot be written as a function of the gradients of the two principal unknowns. Also the diffusion coefficients are not necessarily explicit local functions of them. For the generalised mixed finite elements approximation, Lagrange multipliers associated to each principal unknown are introduced, the sum of the diffusive fluxes of each component is explicitly eliminated and the static condensation leads to a “global” nonlinear system of equations only in the Lagrange multipliers also including complementarity conditions to cope with vanishing or appearing phases. After time discretisation, this system can be solved at each time step using a semi-smooth Newton method. The static condensation involves “local” nonlinear systems of equations associated to each element, solved also by a semismooth Newton method. The algorithm is successfully applied to 1D and 2D examples of water–hydrogen flow involving gas phase appearance and disappearance.     

On the mechanical response of saturated cemented materials—part II: Experimental investigation and numerical simulations

Results of experimental investigation and numerical simulations of the mechanical response of the saturated cemented materials are reported. Saturated as well as dry samples cored from commercially available fire bricks are used. The samples were tested in a triaxial rock cell at different initial confining pressures. The tests have been simulated using the constitutive framework proposed in Part I of this paper. The results both experimental and numerical, provide the evidence in support of the proposed stress decomposition, thereby questioning the validity of Terzaghi's principle for the considered class of materials.     

秦－沈铁路列车运行引起的地面振动实测与分析

秦皇岛－沈阳铁路是国内一条快速客运专线, 2002年由铁道部组织了第2次综合试验,对垂直线路不同距离、不同行车速度下的地面振动进行了现场测试。首先分析了实测地面竖向振动加速度特征,重点讨论列车编组及行车速度对地面振动的影响。将轨道作为弹性地基上的梁,考虑轨枕的离散作用,建立了运行车辆-轨道-地面振动模型。基于薄层法原理,推导了柱坐标系下的二次形函数薄层法,求得分层土体的稳态响应,首次对秦皇岛－沈阳快速客运专线产生的地面振动进行了分析。结果表明：移动轴重作用率对加速度频谱起控制作用;因列车速度远小于地基的瑞利波速,故未出现地面振动放大现象;振动加速度与轮轴荷载呈线性增加趋势。     

Intergrowths of nepheline-potassium feldspar and kalsilite-potassium feldspar: A re-examination of the ‘pseudo-leucite problem’

The alkalic ultramafic Batbjerg intrusion of East Greenland contains rocks in which nepheline and leucite are important constituents. In addition, there are vermicular, finger print intergrowths of nepheline with potassium feldspar, and patchy to micrographic intergrowths of kalsilite with potassium feldspar. The history of the pseudoleucite problem is reviewed, and it is suggested that the term pseudoleucite be restricted to intergrowths of nepheline with alkali feldspar that appear to be pseudomorphs with the crystal morphology of leucite. It is further suggested that flame-like or feather-like finger print intergrowths of nepheline with alkali feldspar, that are either interstitial to the other minerals of the rock or have grown perpendicularly on relative large and often euhedral nepheline grains are an entirely different problem and are best explained by late-stage magmatic crystallization within the system NaAlSiO₄-KAlSiO₄-SiO₂-H₂O.In the Batbjerg intrusion the early crystallization of nepheline was followed by the co-crystallization of nepheline with leucite, or in some cases by nepheline and a silica-rich leucite. Although the magma was essentially dry, as indicated by the dominantly pyroxenitic character of the rocks, water pressure rose toward the late stages of crystallization as indicated by the presence of phlogopite and occasionally both amphibole and zeolite. Shrinkage of the leucite stability field attendant upon this rise in left the liquid that was crystallizing nepheline and leucite stranded on the nepheline-alkali feldspar cotectic. Shrinkage occurred too rapidly for the liquid to remain at the reaction point of the system, and leucite, therefore, was not resorbed. The remaining liquid crystallized rapidly as flames of vermicular intergrowth of nepheline with potassium feldspar (composition Ne 24.0, Ks 45.9, Qz 30.1), a texture that might be attributable to supercooling. Silica-rich leucite compositions (Ks 68.8, Qz 31.2) decomposed to intergrowths of kalsilite with potassium feldspar but reaction kinetics, or possibly variations in throughout the intrusion, prevented the breakdown of leucite.     

Mechanism of feldspar weathering—II. Observations of feldspars from soils

Examination of the surface morphology (via scanning electron microscopy) and surface composition (via X-ray photoelectron spectroscopy) of sodic plagioclase and potash feldspar grains taken from four different soils, provides little or no evidence for the existence of a tightly adhering protective surface layer of altered composition on the feldspar surface. Grains, from which all adhering clay has been removed by ultrasonic cleaning, exhibit the same chemical composition in the outermost few tens of angstroms as the underlying feldspar. Aluminum-rich ‘clay’ coatings which continue to adhere to the grains after ultrasonic treatment are patchy, highly hydrous, and unlikely to act as major diffusion-limiting, and thus protective, barriers. Attack by dissolution of the feldspar surface is non-uniform and follows a definite etching sequence characterized by the development and growth of distinctive etch pits. This dissolution sequence can be reproduced by treating fresh feldspars in the laboratory with strong HF-H₂SO₄^? solutions and, thus, the sequence is unaffected by the composition of the attacking solution. All of our results suggest that the dissolution of feldspar during weathering is controlled by selective chemical reaction at the feldspar-solution interface and not by uniform diffusion through a protective surface layer.     

Thermodynamics of multicomponent pyroxenes: II. Phase relations in the quadrilateral

The model for the thermodynamic properties of multicomponent pyroxenes (Part I) is calibrated for ortho- and clinopyroxenes in the quadrilateral subsystem defined by the end-member components Mg₂Si₂O₆, CaMgSi₂O₆, CaFeSi₂O₆, and Fe₂Si₂O₆. This calibration accounts for: (1) Fe-Mg partitioning relations between orthopyroxenes and augites, and between pigeonites and augites, (2) miscibility gap features along the constituent binary joins CaMgSi₂O₆-Mg₂Si₂O₆ and CaFeSi₂O₆-Fe₂Si₂O₆, (3) calorimetric data for CaMgSi₂O₆-Mg₂Si₂O₆ pyroxenes, and (4) the P-T-X systematics of both the reaction pigeonite=orthopyroxene+augite, and miscibility gap featurs, over the temperature and pressure ranges 800–1500°C and 0–30 kbar. The calibration is achieved with the simplifying assumption that all regular-solution-type parameters are constants independent of temperature. It is predicated on the assumptions that: (1) the Ca-Mg substitution is more nonideal in Pbca pyroxenes than in C2/c pyroxenes, and (2) entropies of about 3 and 6.5 J/K-mol are associated with the change of Ca from 6- to 8-fold coordination in the M2 site in magnesian and iron C2/c pyroxenes, respectively. The model predicts that Fe²⁺-Mg²⁺ M1-M2 site preferences in C2/c pyroxenes are highly dependent on Ca and Mg contents, with Fe²⁺ more strongly preferring M2 sites both in Ca-rich C2/c pyroxenes with a given Fe/(Fe+Mg) ratio, and in magnesian C2/c pyroxenes with intermediate Ca/(Ca+Fe+Mg) ratios.The proposed model is internally consistent with our previous analyses of the solution properties of spinels, rhombohedral oxides, and Fe-Mg olivines and orthpyroxenes. Results of our calibration extend an existing database to include estimates for the thermodynamic properties of the C2/c and Pbca pyroxene end-members clinoenstatite, clinoferrosilite, hedenbergite, orthodiopside, and orthohedenbergite. Phase relations within the quadrilateral and its constitutent subsystems are calculated for temperatures and pressures over the range 800–1700°C and 0–50 kbar and compare favorably with experimental constraints.     

Metamorphism of metapelites: calculations of equilibrium assemblages and numerical simulations of the crystallization of garnet

Abstract This work uses a simplified model of equilibrium to predict the assemblage sequence and compositional zoning in garnet that should result from prograde metamorphism of common bulk compositions of pelitic rocks. An internally-consistent set of model thermodynamic data are derived for natural mineral compositions from natural assemblages. Equilibrium assemblages can be calculated for pelitic compositions with excess quartz and either muscovite or K-feldspar at any pressure and water pressure. The compositions and abundances of phases in equilibrium assemblages can be calculated where the elements Mg, Fe and Mn are exchanged among phases. The prograde metamorphic assemblage sequences and the effects of pressure on assemblages, predicted by the simulation method presented here, are similar enough to natural observations to suggest that the simulations can be used to analyse natural equilibrium and growth processes. The calculated phase diagrams at moderate and high crustal pressures explain the mineral assemblage sequence produced by prograde metamorphism in common pelitic compositions. Garnet appears by continuous reaction of biotite and chlorite as the garnet-biotite-chlorite divariant field migrates toward higher Mg/Fe ratios over the bulk composition. Staurolite appears in common bulk compositions when garnet and chlorite become incompatible. An aluminum silicate phase can appear when staurolite and chlorite react. Staurolite breaks down at an extremum point to produce garnet. Continuous reaction of biotite and sillimanite causes growth of abundant garnet. The reaction sequence involving garnet, staurolite and aluminum silicates is probably different at low pressure, but the main reason that staurolite and garnet are rare is the restricted compositional range over which their assemblages exist. Andalusite appears by the divariant reaction of chlorite and cordierite appears at low temperature in low pressure assemblages for common bulk compositions by the extremumpoint breakdown reaction of chlorite. Compositional zoning of garnet and the systematic variation of biotite composition in metamorphic sequences indicate that garnet is probably fractionated during growth. Fractionation of garnet causes garnet-consuming, univariant reactions to become multivariant. The metastable persistence of garnet should reduce the abundance and stability range of staurolite. Fractionation of even small quantities of garnet should deplete the equilibrating bulk composition of Mn, but have little effect otherwise. The simulations show that the prograde assemblage sequence in pelitic rocks can be complex in detail, with some assemblages lasting over temperature intervals of only a few degrees. The major prograde reactions that release water are the breakdown of chlorite to form garnet at low grade and the breakdown of muscovite at high grade. The volume of water released by formation of garnet at high grade is also important. These reactions have the capacity to buffer water pressure. The density of anhydrous pelitic rock increases markedly when chlorite breaks down and by the continuous reaction forming garnet at high grade. The heat content is controlled principally by heat capacity and continuous reactions. Discontinuous reactions have little thermal buffering capacity. Simulations of garnet fractionation show that commonly-observed garnet zoning profiles can be formed by garnet growth in the assemblage garnet-biotite-chlorite in common bulk compositions. A reversal of Fe-zoning in garnet can occur when garnet resumes growth above staurolite grade in the assemblage garnetbiotite-sillimanite. Discontinuities in zoning profiles can be caused only by disequilibrium. The disequilibrium can be due to either metastable persistence during a hiatus in growth or to growth by irreversible reaction. Because the appearance of garnet is controlled by a continuous rather than a discontinuous reaction, the appearance of garnet is very sensitive to bulk composition. The early development of garnet is also sensitive to the pressure and water pressure of metamorphism. As a consequence the first garnet isograd is of limited thermometric value. Metastable persistence of kyanite and manite at high grades could reduce the abundance of garnet and allow biotite to persist. Metastable persistence would also limit the of cordierite formation.     

Electrons in feldspar II: a consideration of the influence of conduction band-tail states on luminescence processes

 Most natural feldspars contain many charged impurities, and display a range of bond angles, distributed about the ideal. These effects can lead to complications in the structure of the conduction band, giving rise to a tail of energy states (below the high-mobility conduction band) through which electrons can travel, but with reduced mobility: transport through these states is expected to be thermally activated. The purpose of this article is twofold. Firstly, we consider what kind of lattice perturbations could give rise to both localized and extended conduction band-tail states. Secondly, we consider what influence the band tails have on the luminescence properties of feldspar, where electrons travel through the sample prior to recombination. The work highlights the dominant role that 0.04–0.05-eV phonons play in both the luminescence excitation and emission processes of these materials. It also has relevance in the dating of feldspar sediments at elevated temperatures. Received: 11 May 2001 / Accepted: 6 September 2001     

Rate control in feldspar dissolution—II. The protective effect of precipitates

The ability of precipitates formed during incongruent dissolution of feldspars in aqueous solutions to act as barriers to mass transfer between the feldspar and the bulk solution is examined using the available textural evidence on such precipitates.

The propensity of precipitates for forming compact coatings on the dissolving grains is measured by a characteristic distance of diffusion of the precipitating component, a function of the diffusion coefficient of the component in solution and of the rate constant for its precipitation. The available evidence on precipitates formed during dissolution of feldspars, complemented by the evidence on similar precipitates produced from comparable solutions in the absence of feldspars, is sufficient for evaluating the protective effect of precipitates under laboratory conditions, and for setting limits to the conditions under which such an effect could be important during weathering and diagenesis.

Feldspar dissolution in the reported kinetic experiments at room temperature and 3 pH 10 could not have been controlled by diffusion through the precipitate, and changes in the rate of release of alkalies after the first couple of days in Lagache's experiments at 200°C also could not have been controlled by diffusion through the precipitate. Other things being equal, characteristic distances of diffusion of components reprecipitated during incongruent dissolution of silicates decrease with increasing temperature, and coating of dissolving grains by compact precipitate layers should be more common at metamorphic temperatures than in the temperature range of weathering and diagenesis.     

Experimental determination of partition coefficients for Rb,Sr and Ba between alkali feldspar and silicate liquid

Partitioning of Rb, Sr and Ba between alkali feldspar and a synthetic granitic melt has been determined at 8 kb and 720 to 780°C for a single quaternary granite composition. The results suggest that Henry's law is obeyed by Rb up to ~0.8 wt.% Rb₂O in both the liquid and in the alkali feldspar. The measured D values for Rb range from 0.77 to 1.1. For Ba, Henry's Law is obeyed up to ~0.6 wt.% BaO in the liquid and ~5 wt.% BaO in the alkali feldspar. D values for Ba range from 6.4 to 14. For Sr there is only a crude relationship between concentration in the liquid and concentration in the alkali feldspar at concentrations greater than ~0.6 wt.% SrO in the liquid and ~0.4 wt.% SrO in the alkali feldspar. D values for Sr range from 1.2 to 5.0. Partitioning of Sr is apparently sensitive to the concentration of Ba in the system and this partly explains the failure of Sr to obey Henry's Law.Linear least-squares fits to the partitioning data as a function of temperature suggest inverse correlation between temperature and D values. Rb shows only a slight temperature effect whereas Ba and Sr appear to be rather strongly affected by temperature, but the temperature range examined here is small compared to the scatter in the data making these trends relatively uncertain. Other factors that appear to affect partitioning, especially of Sr, are growth rate, development of sector zoning and Or content of the alkali feldspar. These factors severely limit the use of partitioning of these elements in alkali feldspar as geothermometers.The technique for measuring growth rates utilized here combined with measurement of trace element depletion in diffusion boundary layers adjacent to the alkali feldspar crystals makes it possible to estimate diffusivities for Ba and Sr. These estimates suggest a difference of 2 orders of magnitude between diffusivities for Ba and Sr in a vapor-saturated melt and those measured by HOFMANN and MAGARITZ (1976) for a dry obsidian glass.     

Study of the comprehensive risk analysis of dam-break flooding based on the numerical simulation of flood routing. Part II: Model application and results

The present model and methodology described in Part I of this work are applied to perform a comprehensive risk analysis of the dam-break flood of five reservoirs in the Haihe River Basin, China. The results indicate that the three-dimensional numerical simulation considering complex terrain can reflect the characteristics of flood routing and the three-dimensional phenomena. Based on the simulation results, it can be concluded that the risk grades of the consequences induced by a gradual or instantaneous dam break of the Dongwushi reservoir are extremely serious, as determined through the attribute synthetic approach. The results obtained from ranking the risk by the technique for order performance by similarity to ideal solution method are that the Dongwushi reservoir has the most serious consequences when the dam breaks followed by the Lincheng reservoir, the Miaogong reservoir and the Yunzhou reservoir, and the Youyi reservoir has the least severe consequences. Though the ranking of the relatively comprehensive risk coincides with that of the consequences, the dam safety measured by the dam failure probability plays an important role in ranking the risk. A sensitivity analysis is performed by individually increasing the weight of each criterion by 20 %, and the ranking order is not changed, suggesting that the evaluation model is reasonable, stable and reliable.     

Experimental and numerical studies of rock salt strain hardening

The work presented in this paper comes as part of a research program dealing with the thermomechanical behaviour of rock salt. It aims to study laboratory and in-situ long-term behaviour by means of creep tests with deviator and temperature changes. The laboratory results, using a triaxial multi-stages creep tests, highlighted the strain hardening character of rock salt. Furthermore, the in-situ results, using a borehole dilatometer multi-step creep test, have shown that the drilling is carried out in a weakly stressed pillar. The interpretation of the laboratory results, using the J.LEMAITRE law, did not indicate full agreement with all the test results. As a result a ‘double’ J.LEMAITRE model, which takes into account a double strain hardening variable, has been put forward. The validation of this model on the laboratory creep tests is very satisfactory. Furthermore, the activation energy seems satisfactory to represent the influence of the temperature. The in-situ behaviour modelling is clearly more complex than the modelization based on laboratory tests. In fact, it seems that if the rock salt behaviour is maintained by J.LEMAITRE law, it is necessary to vary with the stress, at least, one of the parameters assumed constant in the basic law.     

大陆深俯冲的最大深度——来自数值模拟实验的结果

采用粘弹性材料8块体有限元模型并设定温度场后进行的大陆深俯冲二维数值模拟表明,在组合载荷（负浮力、洋中脊推力从上到下10～30MPa和地幔对流拖曳力100MPa）作用下,陆壳俯冲实际垂向位移可达117km,最终俯冲深度达到147km,而洋壳实际垂向位移约162km,最终俯冲深度达到231km;在洋壳、陆壳俯冲到一定深度以前,它们的俯冲速度基本保持不变,表现为洋壳、陆壳底端的位移一时间曲线近似为直线;当俯冲时间超过9Ma,洋壳、陆壳分别达到167km、96km深度后,俯冲速度会越来越慢。     

Evolution of fluid chemistry in quartz compaction systems: Experimental investigations and numerical modeling

The evolution of fluid chemistry in compacting rock is controlled by coupled chemical processes and rock deformation. In order to characterize this evolution, we conducted water-rock interaction experiments using quartz aggregates at 150 °C and effective pressure of 34.5 MPa. A coupled fluid flow, chemical reaction, and creep compaction model is developed, in which both free-surface reaction and grain-contact dissolution are considered as system volume and porosity evolve.The direct experimental measurement and numerical modeling indicate that effective pressure has significant effects on pore-fluid chemistry. At the early stages of compaction, pore fluids are supersaturated with respect to bulk quartz. With increasing compaction and time, solute concentrations gradually decrease to saturated conditions. Supersaturation is caused mainly by dissolution of ultrafines and high-energy, unstable surfaces which are produced by stress concentrations at grain contacts during the very early stages of compaction. Grain-contact dissolution also contributes to the solute increase in pore fluid in the early stage of compaction, but the effect is small compared to that of ultrafines and unstable surfaces and only slight supersaturation can be produced by it. The gradual decrease in pore-fluid concentration is related to the mechanical removal of ultrafines by pore-fluid flow and the dissolution of ultrafines and unstable surfaces. It also results from the lessening of grain-contact dissolution.Pore fluids in compacting sedimentary basins of quartz sandstone are nearly saturated throughout most of diagenetic processes. Ultrafines and unstable surfaces produced by stress appear not to be the major sources of quartz cement.     

Reinforcing mechanism of anchors in slopes: a numerical comparison of results of LEM and FEM

This paper reports the limitation of the conventional Bishop's simplified method to calculate the safety factor of slopes stabilized with anchors, and proposes a new approach to considering the reinforcing effect of anchors on the safety factor. The reinforcing effect of anchors can be explained using an additional shearing resistance on the slip surface. A three‐dimensional shear strength reduction finite element method (SSRFEM), where soil–anchor interactions were simulated by three‐dimensional zero‐thickness elasto‐plastic interface elements, was used to calculate the safety factor of slopes stabilized with anchors to verify the reinforcing mechanism of anchors. The results of SSRFEM were compared with those of the conventional and proposed approaches for Bishop's simplified method for various orientations, positions, and spacings of anchors, and shear strengths of soil–grouted body interfaces. For the safety factor, the proposed approach compared better with SSRFEM than the conventional approach. The additional shearing resistance can explain the influence of the orientation, position, and spacing of anchors, and the shear strength of soil–grouted body interfaces on the safety factor of slopes stabilized with anchors. Copyright © 2003 John Wiley & Sons, Ltd.     

Efficiency of heavy mass technology in traffic vibration reduction: Experimental and numerical investigation

Vibrations induced by traffic and construction activities cause serious environmental problems. The reduction of the impact of these vibrations on the nearby environment constitutes an important challenge, mainly in urban area. This paper presents both experimental investigation and 3D numerical modeling of the performance of heavy masses technology for scattering the ground vibrations. The efficiency of this method is compared to that of the trench barriers, largely studied in the literature. Analyses show that the heavy mass constitutes an efficient technology for the attenuation of the traffic induced vibrations. The performance of this method depends mainly on the mass weight. An amplitude reduction ratio up to 70% can be reached using this technology.