Dynamic stochastic estimation of physical variables

A fundamental problem facing the physical sciences today is analysis of natural variations and mapping of spatiotemporal processes. Detailed maps describing the space/time distribution of groundwater contaminants, atmospheric pollutant deposition processes, rainfall intensity variables, external intermittency functions, etc. are tools whose importance in practical applications cannot be overestimated. Such maps are valuable inputs for numerous applications including, for example, solute transport, storm modeling, turbulent-nonturbulent flow characterization, weather prediction, and human exposure to hazardous substances. The approach considered here uses the spatiotemporal random field theory to study natural space/time variations and derive dynamic stochastic estimates of physical variables. The random field model is constructed in a space/time continuum that explicitly involves both spatial and temporal aspects and provides a rigorous representation of spatiotemporal variabilities and uncertainties. This has considerable advantages as regards analytical investigations of natural processes. The model is used to study natural space/time variations of springwater calcium ion data from the Dyle River catchment area, Belgium. This dataset is characterized by a spatially nonhomogeneous and temporally nonstationary variability that is quantified by random field parameters, such as orders of space/time continuity and random field increments. A rich class of covariance models is determined from the properties of the random field increments. The analysis leads to maps of continuity orders and covariances reflecting space/time calcium ion correlations and trends. Calcium ion estimates and the associated statistical errors are calculated at unmeasured locations/instants over the Dyle region using a space/time kriging algorithm. In practice, the interpretation of the results of the dynamic stochastic analysis should take into consideration the scale effects.     

Dissolved carbon in pore waters from the carbonate barrier reef of Tahiti (French Polynesia) and its basalt basement

This paper deals with dissolved inorganic carbon (DIC) and organic carbon (DOC) in pore waters from a 150 m deep hole drilled through the carbonate barrier reef of Tahiti and its underlying basalt basement. Alkalinity-pH measurements were used to calculate the DIC species concentration, and DOC was analysed according to the high temperature catalytic oxidation technique. Salinity was used as a conservative tracer to help identify water origin and mixing within the hole. Water mixing, calcium carbonate dissolution and mineralization of organic carbon combined to form three distinct groups of pore water. In the deeper basalt layers, pore water with alkalinity of 1.4 meq kg^–1 pH of 7.6 and p(CO₂) of 1.2 mAtm was undersaturated with respect to both aragonite and calcite. In the intermediate carbonate layer, pore water with alkalinity of more than 2.0 meq kg^–1, pH of 7.70 and p(CO₂) of 1.4 mAtm was supersaturated with respect to both aragonite and calcite. The transition zone between those two groups extended between 80 and 100 m depth. The shift from aragonite undersaturation to supersaturation was mainly attributed to the mixing of undersaturated pore waters from the basalt basement with supersaturated pore waters from the overlaying limestone. In the top of the reef, inputs from a brackish water lens further increased p(CO₂) up to 5.6 times the atmospheric P(CO₂).     

Geostatistical regionalization of glacial aquitard thickness in northwestern Germany, based on fuzzy kriging

In many instances hydrogeological parameters obtained by conventional methods for selected localities within an aquifer or an aquitard are not sufficient for adequate regionalization at the scale of the entire layer. Here, we demonstrate an application of the fuzzy kriging method in regionalization of hydrogeological data, in which the set of conventional, crisp values is supplemented by imprecise information subjectively estimated by an expert. It is believed that such an approach eventually may reflect the real-world conditions more closely than a traditional crisp-value approach, because the former does not impose exactness artificially on phenomena which are diffuse by their nature. Spatial interpolation was done for the thickness of one of the major aquitards (till and glaciolacustrine clay) in northwestern Germany. The dataset consists of 329 crisp values from boreholes supplemented by 172 imprecise values defined as fuzzy numbers. It is demonstrated that the reliability of regionalization was higher, compared to regionalization performed with the crisp dataset only. Fuzzy kriging was performed with FUZZEKS (Fuzzy Evaluation and Kriging System) developed at the Ecosystem Research Center at the University of Kiel.     

Transport in a 2-D saturated porous medium: A new method for particle tracking

A new method for solving the transport equation based on the management of a large numbe of particles in a discretized 2-D domain is presented. The method uses numerical variables to represent the number of particles in a given mesh and is more complex than the 1-D problem. The first part of the paper focuses on the specific management of particles in a 2-D problem. The method also would be valid for three dimensions as long as the medium can be modeled similar to a layered system. As the particles are no longer tracked individually, the algorithm is fast and does not depend on the number of particles present. The numerical tests show that the method is nearly numerical dispersion free and permits accurate calculations even for simulations of low-concentration transport. Because each mesh is considered as a closed system between two successive time steps, it is easy to add adsorption phenomenon without any problem of numerical stability. The model is tested under conditions that are extremely demanding for its operating mode and gives a good fit to analytical solutions. The conditions in which it can be used to best advantage are discussed.     

A note on thermomechanical anisotropy of clays

Deep clays exhibit a pronounced strain anisotropy both during mechanical loading as well as during heating and cooling at constant stress in drained isotropic conditions. During mechanical loading vertical strain is larger than the horizontal one. During heating the vertical strain is larger than the horizontal one within the elastic range; the opposite is observed in the elasto-plastic range. The above described response can be interpreted adopting a consistent rotational, kinematic hardening thermo-elasto-plastic constitutive law.     

Overview of in-situ thermomechanical experiments in clay: Concept, results and interpretation

The HADES project (High Activity Disposal Experimental Site) aims at demonstrating the technical feasibility and the long-term safety of geological disposal of reprocessed HLW (High-Level Wastes) radioactive wastes. This disposal could be realised in the Tertiary Boom clay formation below the Mol/Dessel nuclear site. Previous studies in the 80's on the geomechanical behaviour of Boom clay, at host rock temperature (15°C), have demonstrated the mining capabilities of this clay. European partners have collaborated to increase the number of in-situ tests to be developed and operated from the Underground Research Facility (URF). Integrated large-scale experiments have been developed during the last four years, within the framework of the Commission of the European Communities (CEC) research contracts, in order to gain more insight into the thermal influence of heat-emiting wastes on the clay behaviour in the near field.

This paper summarizes the knowledge gained from the in-situ hydro-thermo-mechanical experiments realised from the URF. The objectives and main issues of the tests are described. Information regarding selection of parameters and representativeness of their measurements is discussed. Despite their different aims and designs, three hydro-thermo-mechanical experiments are compared in order to emphasize similarities in the general behaviour of the clay massif submitted to a thermal load. It is observed that its behaviour is qualitatively similar to the reaction upon a constant total stress increase. With the information now available, it is not obvious to draw conclusions with respect to the irreversibility of some phenomena.

Simple in-house analytical codes are able to simulate with a good accuracy the hydro-thermo-mechanical behaviour of clay. Nevertheless, these codes are not sufficient to describe the complexity of the phenomena that are involved in hydro-thermo-mechanical processes as pointed out by field data. In order to validate more complex models, the possibilities to improve the representativeness of the measurements are investigated.     

Thermomechanical properties of deep argillaceous formations

A difficulty in the interpretation of mechanical and thermo-mechanical tests on specimens drawn from large argillaceous formations is the strong inhomogeneity of void ratio, clay minerals and carbonates content.

In this paper a relationship is developed to link strength and the maximum preconsolidation stress to the initial void ratio and carbonate content. Compressibility is also correlated to carbonates.

Thermal strains in drained and undrained conditions for a Spanish, a belgian and an Italian natural clay are compared. In the elastic state strains are comparable, while in the plastic range thermal strains are highest for the Belgian clay, lower in the Spanish cemented clay and lowest in the Italian clay, very stiff and cemented.     

青藏高原东北地区现代降水中δD与δ^18O的关系研究

根据对取自青藏高原东北地区部分降水样中氢氧稳定同位素比率的分析，得到沱沱河站的大气水线（ＭＷＬ）为：δＤ＝８．２５δ＾１８Ｏ＋９．２２‰，与全球平均ＭＷＬ的差别较小；德令哈、西宁站的ＭＷＬ分别为：δＤ＝５．８６δ＾１８Ｏ－２７．２８‰和δＤ＝６．９６δ＾１８Ｏ－３０．１９‰，均与全球平均ＭＷＬ差别较大。这主要归因于水汽源地的非平衡蒸发和凝结物在非饱和大气中降落时的非平衡蒸发。上述地区的过量氘Ｅｘｄ