Analytical solutions for advective–dispersive solute transport in double‐layered finite porous media

Analytical solutions for advection and dispersion of a conservative solute in a one‐dimensional double‐layered finite porous media are presented. The solutions are applicable to five scenarios that have various combinations of fixed concentration, fixed flux and zero concentration gradient conditions at the inlet and outlet boundaries that provide a wide number of options. Arbitrary initial solute concentration distributions throughout the media can be considered via explicit formulations or numerical integration. The analytical solutions presented have been verified against numerical solutions from a finite‐element‐based approach and an existing closed‐form solution for double‐layered media with an excellent correlation being found in both cases. A practical application pertaining to advective transport induced by consolidation of underlying sediment layers on contaminant movement within a capped contaminated sediment system is presented. Comparison of the calculated concentrations and fluxes with alternative approaches clearly illustrates the need to consider advection processes. Consideration of the different features of contaminant transport due to varying pore‐water velocity fields in primary consolidation and secondary consolidation stages is achieved via the use of non‐uniform initial concentration distributions within the proposed analytical solutions. Copyright © 2010 John Wiley & Sons, Ltd.     

An analytical study on three‐dimensional versus two‐dimensional water table‐induced flow patterns in a Tóthian basin

Although it has been increasingly acknowledged that groundwater flow pattern is complicated in the three‐dimensional (3‐D) domain, two‐dimensional (2‐D) water table‐induced flow models are still widely used to delineate basin‐scale groundwater circulation. However, the validity of 2‐D cross‐sectional flow field induced by water table has been seldom examined. Here, we derive the analytical solution of 3‐D water table‐induced hydraulic head in a Tóthian basin and then examine the validity of 2‐D cross‐sectional models by comparing the flow fields of selected cross sections calculated by the 2‐D cross‐sectional model with those by the 3‐D model, which represents the “true” cases. For cross sections in the recharge or discharge area of the 3‐D basin, even if head difference is not significant, the 2‐D cross‐sectional models result in flow patterns absolutely different from the true ones. For the cross section following the principal direction of groundwater flow, although 2‐D cross‐sectional models would overestimate the penetrating depth of local flow systems and underestimate the recharge/discharge flux, the flow pattern from the cross‐sectional model is similar to the true one and could be close enough to the true one by adjusting the decay exponent and anisotropy ratio of permeability. Consequently, to determine whether a 2‐D cross‐sectional model is applicable, a comparison of hydraulic head difference between 2‐D and 3‐D solutions is not enough. Instead, the similarity of flow pattern should be considered to determine whether a cross‐sectional model is applicable. This study improves understanding of groundwater flow induced by more natural water table undulations in the 3‐D domain and the limitations of 2‐D models accounting for cross‐sectional water table undulation only.     

Recent advances in (soil moisture) triple collocation analysis

To date, triple collocation (TC) analysis is one of the most important methods for the global-scale evaluation of remotely sensed soil moisture data sets. In this study we review existing implementations of soil moisture TC analysis as well as investigations of the assumptions underlying the method. Different notations that are used to formulate the TC problem are shown to be mathematically identical. While many studies have investigated issues related to possible violations of the underlying assumptions, only few TC modifications have been proposed to mitigate the impact of these violations. Moreover, assumptions, which are often understood as a limitation that is unique to TC analysis are shown to be common also to other conventional performance metrics. Noteworthy advances in TC analysis have been made in the way error estimates are being presented by moving from the investigation of absolute error variance estimates to the investigation of signal-to-noise ratio (SNR) metrics. Here we review existing error presentations and propose the combined investigation of the SNR (expressed in logarithmic units), the unscaled error variances, and the soil moisture sensitivities of the data sets as an optimal strategy for the evaluation of remotely-sensed soil moisture data sets.     

Discussion on applying an analytical method to optimize the anti-freeze design parameters for underground water pipelines in seasonally frozen areas

Adopting the quasi-three-dimensional (Quasi-3D) numerical method to optimize the anti-freeze design parameters of an underground pipeline usually involves heavy numerical calculations. Here, the fitting formulae between the safe conveyance distance (SCD) of a water pipeline and six influencing factors are established based on the lowest water temperature (LWT) along the pipeline axis direction. With reference to the current widely used anti-freeze design approaches for underground pipelines in seasonally frozen areas, this paper first analyzes the feasibility of applying the maximum frozen penetration (MFP) instead of the mean annual ground surface temperature (MAGST) and soil water content (SWC) to calculate the SCD. The results show that the SCD depends on the buried depth if the MFP is fixed and the variation of the MAGST and SWC combination does not significantly change the SCD. A comprehensive formula for the SCD is established based on the relationships between the SCD and several primary influencing factors and the interaction among them. This formula involves five easy-to-access parameters: the MFP, buried depth, pipeline diameter, flow velocity, and inlet water temperature. A comparison between the analytical method and the numerical results based on the Quasi-3D method indicates that the two methods are in good agreement overall. The analytic method can be used to optimize the anti-freeze design parameters of underground water pipelines in seasonally frozen areas under the condition of a 1.5 safety coefficient.     

An Analytical Solution for Dynamic Response of the Plate with Different Impedances Subjected to Underwater Explosion

In this paper, the transmitted part of the incident wave is considered to revise Taylor’s solution, which is used to extend its application for analytical models to predict the response of the plate with different material properties. The influence of the material properties and the boundary condition of the plate on fluid and structural dynamics is systematically investigated. The analytical results are compared with those of detailed dynamic FE simulations and the two are in good agreement. The results indicate that the analytical method is valid and suitable for the plates with different material properties subjected to underwater explosion. It is found that Taylor’s results of the plate with small impedance are invalid, which indicates a potential application field for the analytical method.     

Effect of Groundwater Fluctuations on Pore Pressures and Earth Pressures on Coastal Excavation Retaining Walls

Pore water and earth pressures acting on retaining structures are investigated using an efficient coastal double-layered excavation model to determine offshore excavation responses to groundwater fluctuations outside foundation pits. Total pore water pressure includes excess pore water pressure (due to groundwater fluctuations) and steady pore water pressure (due to steady seepage) determined using one-dimensional consolidation theory of double-layered soil and one-dimensional steady-state flow theory, respectively. Rankine's active and passive earth pressures are obtained from pore water pressure. This method is applicable to arbitrary groundwater fluctuation conditions. How physical parameters affect pore water pressure is numerically investigated using examples, demonstrating the method's practicality for calculating pore water and earth pressures.     

钙同位素地球化学研究新进展及其在碳酸岩-共生硅酸盐研究中的应用

作为"非传统稳定同位素"家族成员,钙同位素正受到国际地学界日益广泛的关注.钙是主要的造岩元素,也是生物必需的元素.钙在地球各圈层广泛分布,研究钙同位素的地球化学行为将有助于提高我们对各种生物过程和地质过程的认识.钙同位素测定主要采用热电离质谱仪(TIMS)和多接收电感耦合等离子体质谱仪(MC-ICP-MS),分别表示为δ44/40 Ca和δ44/42Ca.目前自然界可观测到的δ44/40Ca变化范围为-2.0‰～6.75‰,约8.7‰.本文系统介绍了近年来钙同位素分析中样品溶解、化学分离、质谱测定以及高温地质过程中的钙同位素分馏及其地质应用等方面的研究成果,尤其对钙同位素在碳酸岩-共生硅酸盐岩研究中的意义、钙同位素组成以及取得的主要认识作了较为全面的介绍.阐述了放射成因40 Ca、部分熔融作用/分离结晶作用、地壳同化作用、古俯冲碳酸盐循环、热液蚀变作用、岩浆起源深度等对碳酸岩、硅酸盐岩的钙同位素组成造成的影响.最后,通过系统对比碳酸岩-共生硅酸盐岩的锂、镁、钙同位素研究成果,认为应该开展多元同位素体系的联合示踪.由于不同同位素体系存在相似性和差异性,而多元同位索体系相结合能有效地加强优势互补,将是同位素地球化学研究发展的一种必然趋势.     

成层软土地基预固结处理后桩基水平承载力估算方法

目前通过对软土地基预加固处理来提高桩基水平承载力已被工程界认可,但如何在工程前期设计过程中估算软土地基预处理后桩基水平承载力提高值仍是技术难点。基于此,参考Bowles[1]的地基土水平抗力计算式,同时考虑成层软土地基预排水固结处理影响,通过数学推导,推求出根据原状软土室内土工试验抗剪强度指标及预加固处理时间,估算软土地基预处理后桩基水平承载力提高值的实用计算方法。考虑桩侧土弹塑性屈服影响,推导出成层软土中水平受荷桩弹塑性解析解及塑性区深度的计算式,给出了桩顶水平位移、桩身最大弯矩的无量纲计算式及相关计算源代码。依托于浙江省某水闸桩基工程案例,根据提出的计算方法对桩基水平承载力、桩顶水平位移及桩身最大弯矩等性状进行预估计算,并与地基预处理前、后现场试桩检测值进行验证对比,认为桩基水平承载力、桩顶水平位移及桩身最大弯矩等预估计算成果与工程现场试桩的检测值较接近,对类似工程设计具有较好的参考价值。     

酸溶法测定硫铁矿中的全硫

在野外地质队实验室仪器少的条件下,用酸溶的方法分析硫铁矿中全硫,简单、快速、易操作,取得良好的结果。     

Moritz解析延拓解与Bjerhammar虚拟球面解的等价性

利用调和函数的性质以及球谐函数展开理论,并根据实数域上函数的幂级数展开式证明了Moritz解析延拓解与Bjerhammar虚拟球面解的等价性,同时分析了两种解的内在区别。