An analytical method to estimate groundwater depletion from a confining layer

An analytical method was proposed to estimate depletion of groundwater in the confining layers through their entire exploitation history and also for limited periods, especially when data on the drawdown history of the pumped aquifer were sparse. The method was based on the solution for drawdown distribution in the confining layer under the condition that the water level was not under equilibrium conditions but resulted from the delayed drainage phenomenon at the outset. First, the method was used on a hypothetical confined regional aquifer system. It suggested that the calculation error of depletion was generally small and that the cumulative released water from the confining layer can be calculated as being closer to the actual total depletion (2.88 km³) than an existing method. Then, the method was applied to estimate the groundwater quantity released from confining layers in the Su-Xi-Chang region of China, where there is a paucity of groundwater level data. The depletion of groundwater in confining layers represented approximately 54 to 82 % of total withdrawals (9.2 km³) from 1965 to 2000. Therefore, the confining layers are the main consolidation layers in Su-Xi-Chang area. Uncertainty in the properties of the confining layers made the depletion calculation subject to error.     

地应力测量的误差处理及精度评定

本文从地应力测量数据误差处理的角度阐述了地应力计算的最小二乘法,对地应力测量精度评定方法进行了改进。采用协方差传播律进行误差计算,使精度评定的结果更加准确。利用应力的坐标变换关系,推导出应力与应力分量之间的微分关系,使主应力的精度计算更加简便。提出了主应力的偏用误差概念及其计算方法,使主应力方向的精度评定更加真实客观。     

An analysis of uncertainty in non-equilibrium and equilibrium geothermobarometry

In statistically optimised P–T estimation, the contributions to overall uncertainty from different sources are represented by ellipses. One source, for a diffusion‐controlled reaction at non‐equilibrium, is diffusion modelling of the reaction texture. This modelling is used to estimate ratios, Q, between free‐energy differences, ΔG, of reactions among mineral end‐members, to replace the equilibrium condition ΔG = 0. The associated uncertainty is compared with those already inherent in the equilibrium case (from end‐member data, activity models and mineral compositions). A compact matrix formulation is introduced for activity coefficients, and their partial derivatives governing error propagation. The non‐equilibrium example studied is a corona reaction with the assemblage Grt–Opx–Cpx–Pl–Qtz. Two garnet compositions are used, from opposite sides of the corona. In one of them, affected by post‐reaction Fe, Mg exchange with pyroxene, the problem of reconstructing the original composition is overcome by direct use of ratios between chemical‐potential differences, given by the diffusion modelling. The number of geothermobarometers in the optimisation is limited by near‐degeneracies. Their weightings are affected by strong correlations among Q ratios. Uncertainty from diffusion modelling is not large in comparison with other sources. Overall precision is limited mainly by uncertainties in activity models. Hypothetical equilibrium P–T are also estimated for both garnet compositions. By this approach, departure from equilibrium can be measured, with statistical uncertainties. For the example, the result for difference from equilibrium pressure is 1.2 ± 0.7 kbar.     

地球化学平衡的理论和计算

本文系统地回顾了多相组分化学平衡的理论基础和计算方法，重点分析了当今流行的平衡常数法和自由能量小法的异同，证明了这些方法在原则上的同一性同时也证明了反应平衡常数和物种自由能之间的可互换怀，并指出了互换的方法。     

岩土介质三维快速拉格朗日数值分析方法研究

研究了FLAC3D（fast lagrangian analysis of continua in 3 dimensions）的特点,并与有限单元法作了比较。FLAC3D方法以结点运动方程为支配方程,追踪了介质从受荷到达到平衡状态的过程,而有限元法是根据介质力学平衡方程直接求解,这是二者主要区别。FLAC3D没有采用介质真实的阻尼特性和结点质量,给出的不是介质所经历的真实过程,不能正确反映过程的影响,因此给出的介质应力和变形计算结果的物理意义是不甚明确的。求解过程中的介质振动,是一种噪音,可引起弹塑性介质计算结果误差,而弹性介质的计算结果几乎不受影响。研究指出了FLAC3D方法的优缺点。还通过算例作了四个方面的研究：(1) Drucker-Prager屈服准则与Mohr-Coulomb屈服准则比较;(2) 膨胀角取值对计算结果的影响;(3) 大变形与小变形对计算结果的影响;(4) 精度设置对计算结果的影响。研究表明,Drucker-Prager准则与Mohr-Coulomb准则结果差异颇大;膨胀角取值对结果的影响是敏感和显著的;一般情况下,取小变形模式是合适的,计算精度取10-5是足够的。     

Generalized numerical error analysis with applications to geochronology and thermodynamics

A general numerical error propagation procedure is developed to calculate the error in a quantity derived from measurements which are subject to errors. It is an alternative to computer intensive techniques such as Monte Carlo and can be applied to quite complex analytical problems where correlation among the measurement errors and among the final errors in results are present. Previous formulations have usually ignored correlated errors. Some of the assumptions involved in error propagation can also be checked numerically. This is an advantage over analytical formulations which cannot assess the validity of the calculated errors. Formulation as computer subroutines permits the analysis to be added to existing programs. Examples from the fields of geochronology and thermodynamics are used to highlight the advantages and the flexibility of the method.     

Fluorine-hydroxyl exchange in apatite and biotite: A potential igneous geothermometer

The free energy data for the simple fluorides, chlorides and hydroxides have been used to predict the distribution of these anions in hydrous minerals. The calculated partition of fluorine in phlogopite agrees well with published results; the distribution of fluorine and hydroxyl between apatite and phlogopite is temperature dependent and has been calculated. The temperatures deduced from analyses of natural apatite-biotite pairs frequently show discrepancies as compared with independent temperature estimates; these probably arise from late-stage exchange of the fluorine in phlogopite with an aqueous fluid, for which independent evidence is available.The fugacity of phosphorus in equilibrium with apatite, a ubiquitous hydrous mineral, has been calculated for various mineral assemblages. The estimates, which are subject to considerable error, are lower for basanites and alkali-basalts than for tholeiites and range from approximately 10^–14 at 1000° C to 10^–16 bars at 750° C for fayalitic rhyolites.     

复式河槽正常水深计算方法比较

明渠恒定均匀流正常水深在水力计算中十分重要。而对于复式河槽,当洪水漫滩后,直接运用曼宁方程推求正常水深,将带来很大误差。系统地总结了计算正常水深的各种方法,用二分法求解,并运用英国科学工程研究协会洪水水槽设施(SERC-FCF)的大量系列水槽实验成果加以比较。比较发现,精度由高到低依次为COHM方法、刘沛清法、断面倾斜分割法、动量传递法、谢汉祥法、断面叠加法。通过对各种方法详细分析,建议在计算天然复式河槽正常水深时,COHM方法是值得推广的一种好方法。     

Determining the amount of overstepping required to nucleate garnet during Barrovian regional metamorphism,Connecticut Valley Synclinorium

The novel method of inclusion barometry coupled with the calculation of the required affinity for garnet nucleation is applied to three samples from the previously well‐characterized Connecticut Valley Synclinorium in central Vermont. Raman shifts for quartz inclusions record a range of maximum peak shifts of the quartz 464 cm^?1 peak from 2.4 to 3.0 cm^?1. Temperature of garnet nucleation was constrained by calculating mineral assemblage diagrams in the MnNCKFMASHT system and plotting the intersection of quartz inclusion in garnet barometry (QuiG, quartz‐in‐garnet) with Zr‐in‐rutile thermometry. Utilizing the intersection of Zr‐in‐rutile thermometry with QuiG barometry, garnet nucleation is inferred to have occurred within a P–T range of ~8.6–9.5 kbar and ~560–575°C. These P–T conditions for garnet nucleation are significantly higher than calculated equilibrium garnet‐in isograds for the three samples. Affinities for garnet nucleation were calculated as the difference between the free energy of a fictive garnet composition based on the matrix assemblage and the free energy of the nucleated garnet. The calculated nucleation affinity varied from 300 to 600 kJ/mol O for St–Ky grade samples. These results suggest that the assumption that metamorphism proceeds as a sequence of near‐equilibrium conditions cannot, in general, be made for regional metamorphic terranes. This body of work agrees with numerous recent studies showing that garnet‐producing reactions must be overstepped in order to for garnet to nucleate.     

有限元强度折减系数法在北门沟坡滑坡稳定性评价中的应用

利用有限元强度折减系数法求得的滑坡安全稳定性系数进行北门沟滑坡稳定性评价。通过强度折减,当滑坡达到不稳定状态时,有限元计算不再收敛,此时的折减系数就是滑坡的安全稳定性系数。经计算,可以得到滑坡体破坏形式和破坏扩张趋势,有助于对滑体破坏机制的理解。计算表明,有限元强度折减法与传统刚体极限平衡法计算的稳定性系数很接近,这为滑坡稳定性评价提供了另一条途径。     

The prediction of mineral solubilities in natural waters: the NaKMgCaClSO4H2O system from zero to high concentration at 25° C

A chemical model of the seawater system, NaKMgCaClSO₄H₂O, is developed for predicting mineral solubilities in brines from zero to high ionic strengths. The calculated solubilities are shown to be in agreement with the experimental data from gypsum saturation (I < 0.06 m) to bischofite saturation (I > 20 m). The model utilizes activity coefficient expressions recently developed by Pitzer and co-workers and an algorithm for rapidly identifying the coexisting phases and their composition at equilibrium. The activity coefficient expressions are parameterized using binary and ternary system solubility and osmotic data. The results indicate that a free energy model defined by binary and ternary system data will accurately predict solubilities in more complex systems. The algorithm for solving the general chemical equilibrium problem is briefly discussed. The method can be used to model systems with an arbitrary number of possible non-ideal solution phases. The iterative procedure is guaranteed to converge and has been found to be efficient and easy to implement.Calculated phase diagrams associated with the seawater system are compared to experimental data. Our calculations are within experimental accuracy whereas the prediction of other seawater models are in substantial disagreement with the data even at low concentration. The calculation of evaporation sequences is also briefly discussed and qualitatively compared to field data. The mineral assemblages predicted by this method are in substantially better agreement with core samples than the sequences predicted by phase diagram methods (Braitsch, 1971), which do not explicitly include the Ca component.     

The calculation of mineral compositions and modes of olivine-two pyroxene-spinel assemblages

Duhem's theorem states that the equilibrium position of a system of known bulk composition and size is completely determined by two independent variables. Given these data all other equilibrium parameters can be calculated. The method of calculation is set down in detail for olivine-two pyroxene-spinel assemblages which may serve as models for portions of the upper mantle. To make the calculations, equations for the Gibbs energy of the constituent minerals, olivine, spinel, orthopyroxene and clinopyroxene are formulated. The olivine is treated as an ideal, binary, cationic solid solution. The spinel is treated as a ternary, reciprocal solution between the four end members MgAl₂O₄, MgCr₂O₄, FeAl₂O₄ and FeCr₂O₄. The pyroxenes are treated as seven-component, simplified reciprocal systems. The eight oxides SiO₂, TiO₂, Al₂O₃, Cr₂O₃, FeO, MgO, CaO and Na₂O are thought sufficient for expressing the composition of the model mantle.The paucity and inconsistency of the required thermodynamic data preclude accurate calculations. To illustrate the calculation and to arrive at some highly tentative results, the required free energy data are estimated by combining analytical data from Iherzolite xenoliths with interpretations of experimental data.It seems likely that the Al content of pyroxenes cannot be used as a geobarometer without considering the bulk composition of the assemblage or, equivalently, the composition of the associated spinel phase. Temperature estimates based on the Ca to Ca+Mg ratio in Ca-rich pyroxenes may be approximately correct in the restricted composition range of mantle derived xenoliths.     

A thermodynamic model for multicomponent melts,with application to the system CaO-Al2O3-SiO2

A thermodynamic model is proposed for calculation of liquidus relations in multicomponent systems of geologic interest. In this formulation of mineral-melt equilibria, reactions are written in terms of the liquid oxide components, and balanced on the stoichiometry of liquidus phases. In order to account for non-ideality in the liquid, a ‘Margules solution’ is derived in a generalized form which can be extended to systems of any number of components and for polynomials of any degree. Equations are presented for calculation of both the excess Gibbs free energy of a solution and the component activity coefficients.Application to the system CaO-Al₂O₃-SiO₂ at one atmosphere pressure is achieved using linear programming. Thermodynamic properties of liquidus minerals and the melt are determined which are consistent with adopted error brackets for available calorimetric and phase equilibrium data. Constraints are derived from liquidus relations, the CaO-SiO₂ binary liquid immiscibility gap, solid-solid $\text{P-T}$ reactions, and measured standard state entropies, enthalpies, and volumes of minerals in this system.Binary and ternary liquidus diagrams are recalculated by computer programs which trace cotectic boundaries and isothermal sections while checking each point on a curve for metastability. The maximum differences between calculated and experimentally determined invariant points involving stoichiometric minerals are 17°C and 1.5 oxide weight per cent. Because no solid solution models have been incorporated, deviations are larger for invariant points which involve non-stoichiometric minerals.Calculated heats of fusion, silica activities in the melt, and heats of mixing of liquids compare favorably with experimental data, and suggest that this model can be used to supplement the limited amount of available data on melt properties.     

The Gibbs free energy of mixing of natural silicate liquids; an expanded regular solution approximation for the calculation of magmatic intensive variables

The compositions of liquids coexisting with experimentally grown crystals of olivine, plagioclase, clinopyroxene, orthopyroxene, leucite, spinel, rhombohedral oxide, melilite and potassium feldspar are used to define, through mass action expressions of liquid/solid equilibrium, compositional derivatives of the Gibbs free energy of mixing of naturally occuring silicate liquids as a function of temperature, pressure and the fugacity of oxygen. The available experimental data describe these derivatives over a range of compositions which includes basic magmas. Therefore, for silicate liquids in this composition range, the topology of the Gibbs free energy of mixing can be approximated from experimental determinations of its derivatives. The majority of the existing thermodynamic data on the liquid phase is consistent with the application of regular solution theory to model the free energy of mixing. Strictly symmetric, temperature and pressure independent, regular solution interaction parameters are calibrated from this phase equilibrium data using regression techniques which have their basis in inverse theory. These techniques generate numerically stable interaction parameters which incorporate inter-variable correlation and account for experimental uncertainty. The regular solution model fits the available data on anhydrous silicate liquids to within the accuracy of the thermodynamic database +/?550 cals). Extensions to regular solution theory allow water solubility in more silica rich liquids to be modelled somewhat less accurately (+/?750 cals). The topology of the excess free energy of mixing surface is strongly asymmetric, possessing a single multicomponent saddle point which defines a spinodal locus. Given this prediction of a multicomponent spinode, a mathematical procedure based upon minimisation of the Gibbs free energy of mixing is developed for the calculation of the compositions of coexisting immiscible liquids. Predicted binodal compositions substantially agree with elemental liquid/liquid partitioning trends observed in lavas. Calculations suggest that an immiscible dome, in temperature-composition space, intersects the liquidus field of the magma type tholeiite. Immiscible phenomena are predicted at sub-liquidus temperatures for the bulk compositions of more basic or alkalic lavas, but are absent in more siliceous rock types for temperatures of the metastable liquid down to 900 K. The regular solution model is used in four petrological applications. The first concerns a prediction of the binary olivine-liquid phase diagram. The calculated geometry exhibits a minimum near Fa₇₅, which, though not in accord with experimental results on the pseudobinary system, compares quite favorably with olivine-liquid phase equilibria interpreted from rhyolites, namely that the olivine phenocrysts of rhyolites are more iron rich than their coexisting liquids. The second petrological example concerns estimating the depth of the source regions of several basic lavas whose compositions cover a range from ugandite to basaltic andesite. The third application is a calculation of the saturation temperatures and compositions of plagioclase and olivine in four experimental basaltic liquids and a prediction of the liquidus temperatures and first phenocryst compositions of the Thingmuli lava series of Eastern Iceland. Lastly, enthalpies of fusion are computed for a variety of stoichiometric compounds of geologic interest. These demonstrate good agreement with calorimetrically measured quantities     

页岩I型断裂韧性的分形计算方法与应用

水平井分段体积压裂是页岩气商业规模开发的重要工艺措施,如何评价页岩储层可压性是该工艺成功的关键。页岩断裂韧性是可压性评价的重要支撑参数,从I型断裂裂纹（裂缝）微观形态入手,结合断裂力学理论和分形理论,建立了页岩I型断裂韧性分形计算方法;借助晶体劈裂功法计算页岩表面能,采用密度、声波时差2种参数获取计算结果,对比分析新的分形方法计算数据、传统方法预测数据与试验测试数据,新的分形方法计算平均误差为3.63%,传统预测方法平均误差为 %,验证了方法的准确性;参考实例水平井测井解释数据,计算了水平段I型断裂韧性指数的全井筒连续性剖面,结合可压性级别与较大储层改造体积概率关系,优选可压性级别为III级及II级改造。建立的页岩I型断裂韧性分形计算方法对定量评价页岩储层可压性具有重要意义。     

挡土墙库仑土压力的遗传算法求解分析

在对破裂面上滑动土体静力极限平衡分析的基础上,建立了基于优化方法求解无黏性土、黏性土库仑土压力的自变量取值区间和目标函数模型,并采用遗传进化方法进行了实例求解分析。研究结果表明,遗传算法在计算挡土墙库仑主动土压力的过程中,收敛速度快、用时短,并具有较高的计算精度。算例1中5组无黏性土挡土墙的主动土压力的计算结果与经典库仑解析解非常接近,平均误差为1.748 %,平均进化代数为15代。算例2中8组黏性土挡土墙的主动土压力计算结果与文献的解答非常吻合,平均误差仅为0.017 %,平均进化代数为17.125代。遗传算法具有良好的适应性和强大的搜索性能,非常适合求解岩土工程优化问题。     

矿物在超临界溶液中的溶解度理论计算

本文概述了矿物在超临界溶液中的溶解度理论计算。讨论了平衡常数法和自由能法的热力学原理和计算机方法。两种方法都需要热力学数据,所不同的是平衡常数法需要的是反应平衡常数,而自由能法需要物种自由能数据。方法确定以后这些数据具备与否及其精度是这项研究的关键。此外当溶液中离子强度较大时,寻求一种适当的活度系数算法对溶解度理论计算也至关重要。     

岩土工程最小勘探数据量确定方法

准确地确定岩土设计参数统计特征值诸如均值、标准差是岩土工程可靠度分析与设计的重要前提。在满足岩土设计参数统计特征值计算精度条件下,文中提出了岩土工程最小勘探数据量的确定方法,定义了相对误差和相对变异性指标衡量岩土设计参数统计特征值计算准确性。系统地分析了静力触探试验数据量对砂土有效内摩擦角统计特征值计算精度的影响,并且根据相对误差和相对变异性指标确定了静力触探最小勘探数据量。研究结果表明,由静力触探试验间接估计砂土有效内摩擦角时均值相对误差较低,砂土有效内摩擦角相对变异性指标随静力触探试验数据量的增加而降低,即由认知不足引起的不确定性占总变异性的比值随静力触探试验数据量的增加而减小;当砂土有效内摩擦角容许相对变异性指标小于0.2时砂土有效内摩擦角在最大变异（COV=20%）与最小变异性（COV=5%）范围内,满足预定要求所需的最小静力触探试验数据量为10～100;若容许相对变异性指标小于0.3,所需的最小静力触探试验数据量为5～43。此外,间接估计岩土设计参数时经验回归模型不确定性对最小勘探数据量有显著影响。静力触探试验最小勘探数据量随经验回归模型不确定性的增大而增加,在确定岩土设计参数统计特征值时应尽量广泛收集勘探数据并选择精度较高的计算模型。     

起伏地表二维瑞雷面波正演模拟及波场分析

采用高精度交错网格有限差分法,建立了在起伏地表条件下瑞雷面波数值模拟的自由边界条件,通过对倾斜二层模型模拟的结果与解析解对比,二者完全一致,由此证明了起伏地表下瑞雷面波数值模拟的正确性。在此基础之上,模拟并分析了小凸起与小凹陷模型条件下,瑞雷面波的波场传播特征。通过分析得出瑞雷面波在这二种地形传播时,都存在反射、波型转换,以及能量再分配。因此,在起伏地表条件下,利用瑞雷面波进行勘探时要考虑起伏地表对瑞雷面波波场的影响。     

Energies and interactions in binary (Pbnm) orthosilicates: A Born parametrization

A structure-energy model valid for ionic orthosilfcates with orthorhombic symmetry is presented. The structure simulation is achieved with a distance-least-square modelling (DLS; Baerlocheret al., 1977) of cell edges and spacial coordinates in the asymmetric unit. The input parameters are based on multiple regressions of the mean effective radii of cations occupying the M1 and M2 positions. The cohesive energy is then evaluated as the sum of coulombic + repulsive + dispersive terms. The parametrization of the repulsive energy is achieved with the Huggins-Mayer form (cf. Tosi, 1964). The enthalpy at 298.15° K, 1 bar is then calculated with the Born-Haber-Fayans thermochemical cycle. Gibbs free energy values at different T conditions are then evaluated for various states of intracrystalline disorder and the stable configuration is selected, based on the principle of minimization of the Gibbs free energy of the system at equilibrium. The model is applied to 7 binary joins on which experimental data are available, to ascertain its consistency.The depicted solid solution properties, the calculated Gibbs free energy and the site occupancy predictions are in satisfactory agreement with experimental observations.