A coupling of mixed and discontinuous Galerkin finite-element methods for poroelasticity

In this paper, we formulate a finite-element procedure for approximating the coupled fluid and mechanics in Biot’s consolidation model of poroelasticity. We approximate the flow variables by a mixed finite-element space and the displacement by a family of discontinuous Galerkin methods. Theoretical convergence error estimates are derived and, in particular, are shown to be independent of the constrained specific storage coefficient, c _o . This suggests that our proposed algorithm is a potentially effective way to combat locking, or the nonphysical pressure oscillations, which sometimes arise in numerical algorithms for poroelasticity.     

A coupling of mixed and continuous Galerkin finite element methods for poroelasticity II: the discrete-in-time case

In this paper, we formulate a finite element procedure for approximating the coupled fluid and mechanics in Biot’s consolidation model of poroelasticity. Here, we approximate the pressure by a mixed finite element method and the displacements by a Galerkin method. Theoretical convergence error estimates are derived in a discrete-in-time setting. Of particular interest is the case when the lowest-order Raviart–Thomas approximating space or cell-centered finite differences are used in the mixed formulation and continuous piecewise linear approximations are used for displacements. This approach appears to be the one most frequently applied to existing reservoir engineering simulators.     

A coupling of mixed and continuous Galerkin finite element methods for poroelasticity I: the continuous in time case

In this paper, we formulate a finite element procedure for approximating the coupled fluid and mechanics in Biot’s consolidation model of poroelasticity. Here, we approximate the pressure by a mixed finite element method and the displacements by a Galerkin method. Theoretical convergence error estimates are derived in a continuous in-time setting for a strictly positive constrained specific storage coefficient. Of particular interest is the case when the lowest-order Raviart–Thomas approximating space or cell-centered finite differences are used in the mixed formulation, and continuous piecewise linear approximations are used for displacements. This approach appears to be the one most frequently applied to existing reservoir engineering simulators.     

Analysis of undrained cavity expansion in elasto‐plastic soils with non‐linear elasticity

A large strain analysis of undrained expansion of a spherical/cylindrical cavity in a soil modelled as non‐linear elastic modified Cam clay material is presented. The stress–strain response of the soil is assumed to obey non‐linear elasticity until yielding. A power‐law characteristic or a hyperbolic stress–strain curve is used to describe the gradual reduction of soil stiffness with shear strain. It is assumed that, after yielding, the elasto‐plastic behaviour of the soil can be described by the modified Cam clay model. Based on a closed‐form stress–strain response in undrained condition, a numerical solution is obtained with the aid of simple numerical integration technique. The results show that the stresses and the pore pressure in the soil around an expanded cavity are significantly affected by the non‐linear elasticity, especially if the soil is overconsolidated. The difference between large strain and small strain solutions in the elastic zone is not significant. The stresses and the pore pressure at the cavity wall can be expressed as an approximate closed‐form solution. Copyright © 2001 John Wiley & Sons, Ltd.     

Plastic deformation of wadsleyite: III. Interpretation of dislocations and slip systems

 Linear anisotropic elasticity has been applied to interpret the dislocation stability and ease of slip in wadsleyite. It is shown that wadsleyite is very isotropic from the elastic point of view. The influence of crystal chemistry and bonding on the choice of the slip plane is discussed. It is shown that slip is predominantly achieved on planes that do not shear Si–O bonds. It is suggested that dissociation of dislocations is essential in determining the ease of slip among the various slip systems. Received: 15 July 2002 / Accepted: 14 February 2003 Acknowledgements High-pressure experiments were performed at the Bayerisches Geoinstitut under the EU IHP – Access to Research Infrastructures Programme (Contract no. HPRI-1999-CT-00004 to D.C. Rubie). Enlightening discussions with A. Coujou and J. Rabier are gratefully acknowledged.     

Overcoming problems of density and thickness measurements in FTIR volatile determinations: a spectroscopic approach

The Beer–Lambert law is traditionally used to determine water and carbon concentrations in glasses from their infrared (IR) spectra. In practice, this method requires estimation of the thickness and density of the glass as well as the calibration of the molecular absorptivities of the species concerned. All of these parameters can be sources of practical difficulties and analytical uncertainty. These weaknesses in the application of the Beer–Lambert law have been overcome by an empirical analysis of the infrared spectra. Using a set of 292 spectra obtained on 113 natural and experimental tholeiitic glasses (SiO₂ 48.5–51 wt%; water contents 0–4000 ppm H₂O), it can be shown that the thickness–density (ρ d) product of a glass sample can be directly and reliably inferred from its IR spectrum. This allows the Beer–Lambert law to be rewritten. The new form no longer requires thickness or density estimations to determine volatile contents. Moreover, if needed, the thickness of the glass slab can also be accurately determined from the IR spectra. This new method is developed for quantitative determination of water concentrations in MORB glasses but can also be applied to any minor species (carbon, sulfur, etc.) provided it is active in the IR domain and that a suitable independent frequency of IR absorption can be identified. Precision is about 60 ppm H₂O on O–H⁻ contents. This method, tested on natural and experimental MORB-type glasses, can be applied to any chemical composition provided a set of reference spectra is available. Received: 16 September 1999 / Accepted: 18 February 2000     

Anisotropy of rock elasticity behavior and of gas migration in a Variscan Carboniferous rock mass in the South Limburg, The Netherlands

Investigations of the engineering geological, physical and rock mechanical properties have been carried out on Carboniferous core samples of the research wells Geverik, Kastanjelaan and Heugem in South Limburg, The Netherlands over a total length of 2687 m. On the basis of a mathematical modeling of the deformation and anisotropy of the Variscan-folded Carboniferous, the following parameters were determined: density, porosity, water resumption and specific permeability for gas.

Dynamic, static and uniaxial compression tests were performed in order to obtain direction-dependent data like dynamic elasticity modulus, static elasticity modulus (Young's modulus), shear modulus and the Poisson's ratios. Additionally, the stress–strain behaviors were determined by uniaxial strength, tensile strength and shear strength tests. For the evaluation of the anisotropy of the rock mass caused by tectonic movements, ultrasonic measurements were of greatest importance. The results show that the ultrasonic velocities of p- and s-waves are dependent on the rock type, the tectonic configuration and the degree of saturation.

The stress–strain behavior of mud, sand and marly limestones shows an orthogonal anisotropy, while limestones and siliceous limestones are quasi-isotropic. The anisotropy is related and parallel to the main tectonic axis and also to the rock texture.     

Two-dimensional numerical approach for the vibration isolation analysis of thin walled wave barriers in poroelastic soils

This paper is concerned with the vibration isolation efficiency analysis of total or partially buried thin walled wave barriers in poroelastic soils. A two-dimensional time harmonic model that treats soils and structures in a direct way by combining appropriately the conventional Boundary Element Method (BEM), the Dual BEM (DBEM) and the Finite Element Method (FEM) is developed to this aim. The wave barriers are impinged by Rayleigh waves obtained from Biot’s poroelasticity equations assuming a permeable free-surface. The suitability of the proposed model is justified by comparison with available previous results. The vibration isolation efficiency of three kinds of wave barriers (open trench, simple wall, open trench-wall) in poroelastic soils is studied by varying their geometry, the soil properties and the frequency. It is found that the efficiency of these wave barriers behaves similarly to these in elastic soils, except for high porosities and small dissipation coefficients. The efficiency of open trench-wall barriers can be evaluated neglecting their walls if they are typical sheet piles. This does not happen with walls of bigger cross-sections, leading in general to efficiency losses. Likewise, increasing the burial depth to trench depth ratio has a negative impact on the efficiency.     

Artificial neural networks and nonlinear regression techniques to assess the influence of slake durability cycles on the prediction of uniaxial compressive strength and modulus of elasticity for carbonate rocks

Understanding rock material characterizations and solving relevant problems are quite difficult tasks because of their complex behavior, which sometimes cannot be identified without intelligent, numerical, and analytical approaches. Because of that, some prediction techniques, like artificial neural networks (ANN) and nonlinear regression techniques, can be utilized to solve those problems. The purpose of this study is to examine the effects of the cycling integer of slake durability index test on intact rock behavior and estimate some rock properties, such as uniaxial compressive strength (UCS) and modulus of elasticity (E) from known rock index parameters using ANN and various regression techniques. Further, new performance index (PI) and degree of consistency (Cd) are introduced to examine the accuracy of generated models. For these purposes, intact rock dataset is established by performing rock tests including uniaxial compressive strength, modulus of elasticity, Schmidt hammer, effective porosity, dry unit weight, p‐wave velocity, and slake durability index tests on selected carbonate rocks. Afterward, the models are developed using ANN and nonlinear regression techniques. The concluding remark given is that four‐cycle slake durability index (I_d4) provides more accurate results to evaluate material characterization of carbonate rocks, and it is one of the reliable input variables to estimate UCS and E of carbonate rocks; introduced performance indices, both PI and Cd, may be accepted as good indicators to assess the accuracy of the complex models, and further, the ANN models have more prediction capability than the regression techniques to estimate relevant rock properties. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical analysis of frost effects in porous media. Benefits and limits of the finite element poroelasticity formulation

The aim of this paper is to analyse the performance of a finite element formulation usable for predicting the mechanical consequences of frost effects on porous media. It considers the characteristics of porous media and how the frost action can be assessed. The problem is then separated into two parts: thermal and poromechanical calculations. The constitutive equations developed in the framework of poromechanics are presented and the implementation in a usual finite element poroelasticity formulation based on Zuber's method is adopted. An analysis of the time‐step influence on the convergence rate is given and leads us to propose a simple method in order to obtain objectivity of the finite element response and avoid over‐long calculations. Frost effect simulations are carried out on real porous media (two fired clays) as a case study. Although the experimental behaviour of the porous media subjected to frost action is in accordance with some observations, the calculated strains appear to be overestimated compared with measurements. The problem could be largely attributable to the difficulty of assessing permeability evolution during frost development. Copyright © 2011 John Wiley & Sons, Ltd.     

Self-sealing isolation and immobilization: a geochemical approach to solve the environmental problem of waste acidic jarosite

Mimicking geochemical processes to solve environmental problems was implemented in dealing with waste acidic jarosite and alkaline coal fly ash. By placing these two chemically different materials adjacent to one another, a self-sealing layer was formed at the interface between both wastes, isolating and immobilizing chemical constituents in the process. A series of leaching experiments were performed on each material separately to study the release behavior of the principal constituents. Radiotracer experiments were conducted to explore diffusion and reaction of constituents such as Fe³⁺ in a combined jarosite/fly ash system. A model has been developed to simulate the coupled processes of diffusion and precipitation taking into account porosity change due to pore filling by precipitates. The formation of a self-sealing isolation layer in a hypothetical jarosite/fly ash disposal site was modelled. Leaching results indicate that the release of elements from jarosite is much larger than that from fly ash, and that the highly pH dependent release of Fe, Al, and Zn was controlled by the solubility of their hydroxides. Leaching results also suggest that precipitation reactions can be expected to occur at the interface between jarosite and alkaline coal fly ash where a large pH gradient exists. Radiotracer experiments showed that accumulation of constituents occurred at the interface. Modeled Fe³⁺ profiles in layered jarosite/fly ash were well validated by experiments. Modeling results also showed that with the accumulation of constituents at the interface, a new layer with low porosity was formed. Application of this model suggests that there is a potential use to form a self-sealing layer in jarosite/fly ash co-disposal sites.     

Construction of three-phase data to model multiphase flow in porous media: Comparing an optimization approach to the finite element approach

Multiphase flow modelling is a major issue in the assessment of groundwater pollution. Three-phase flows are commonly governed by mathematical models that associate a pressure equation with two saturation equations. These equations involve a number of secondary variables that reflect the fluid behaviour in a porous medium. To improve the computational efficiency of multiphase flow simulators, several simplified reformulations of three-phase flow equations have been proposed. However, they require the construction of new secondary variables adapted to the reformulated flow equations. In this article, two different approaches are compared to quantify these variables. A numerical example is given for a typical fine sand.     

某机场高填方地基的地下水问题探讨

文章首先简要介绍了某机场高填方修建前工程区的水文、水文地质条件，然后根据施工中和工后较长时间内高填方体内的孔隙水压力、钻孔水位及坡脚部位盲沟出水量的观测成果，综合分析了高填方体内地下水分布情况，进而就因坡脚部位地下水引起的工程问题(主要为沉降变形和坡体稳定性)进行了分析评价。最后认为坡脚部位高出原地面12m，相对稳定的地下水位将对工程造成非常不利的影响。     

Origin of oceanic phonolites by crystal fractionation and the problem of the Daly gap: an example from Rarotonga

Felsic alkalic rocks are a minor component of many ocean island volcanic suites, and include trachyte and phonolite as well as various types of alkaline and peralkaline rhyolite. However, there is considerable debate on the nature of their formation; for example, are they formed by partial melting of anomalous mantle or the final products of fractional crystallization of mafic magmas. The phonolites and foidal phonolites on Rarotonga were formed by low pressure crystal fractionation of two chemically distinct parental magmas. Low silica and high silica mafic magmas produced a basanite-foidal phonolite series and an alkali basalt-phonolite series, respectively. The foidal phonolite composition evolved from the low silica mafic magmas by approximately 60% fractionation of titanaugite + leucite + nepheline + magnetite + apatite. Fractionation continued with the crystallization of aegirine-augite + nepheline + kaersutite + magnetite + apatite. The phonolites formed from the alkali basalts by approximately 40% fractionation of kaersutite + titanaugite + Fe-Ti oxide + plagioclase + apatite and continued to evolve further by fractionation of anorthoclase + nepheline + aegerine-augite + Fe-Ti oxides. As the magmas fractionated in both suites, their overall viscosities (solid + liquid) increased until a point was reached whereby viscosity inhibited the eruption of magmas with compositions intermediate between the mafic rocks and the felsic rocks. However, the magmas continued to fractionate under static conditions with the residual fluid becoming foidal phonolitic in the low silica suite or phonolitic in the high silica suite. These phonolitic liquids, as a result of an increase in volatiles and enrichment of alkalis over aluminum, would actually have a lower viscosity than the intermediate liquids. This decrease in viscosity and the switch from a magma chamber being predominantly a liquid with suspended solids to a solid crystalline network with an interstitial liquid enabled phonolitic liquids to migrate, pool, and eventually erupt on the surface.     

Characterisation of primary and secondary carbonates in hypabyssal kimberlites: an integrated compositional and Sr-isotopic approach

Carbonates in fresh hypabyssal kimberlites worldwide have been studied to understand their origin [i.e. primary magmatic (high T) versus deuteric (‘low T’) versus hydrothermal/alteration (‘low T’)] and identify optimal strategies for petrogenetic studies of kimberlitic carbonates. The approach presented here integrates detailed textural characterisation, cathodoluminescence (CL) imaging, in situ major- and trace-element analysis, as well as in situ Sr-isotope analysis. The results reveal a wide textural diversity. Calcite occurs as fine-grained groundmass, larger laths, segregations, veins or as a late crystallising phase, replacing olivine or early carbonates. Different generations of carbonates commonly coexist in the same kimberlite, each one defined by a characteristic texture, CL response and composition (e.g., variable Sr and Ba concentrations). In situ Sr isotope analysis revealed a magmatic signature for most of the carbonates, based on comparable ⁸⁷Sr/⁸⁶Sr values between these carbonates and the coexisting perovskite, a robust magmatic phase. However, this study also shows that in situ Sr isotope analysis not always allow distinction between primary (i.e., magmatic) and texturally secondary carbonates within the same sample. Carbonates with a clear secondary origin (e.g., late-stage veins) occasionally show the same moderately depleted ⁸⁷Sr/⁸⁶Sr ratios of primary carbonates and coexisting perovskite (e.g., calcite laths-shaped crystals with ⁸⁷Sr/⁸⁶Sr values identical within uncertainty to those of vein calcite in the De Beers kimberlite). This complexity emphasises the necessity of integrating detailed petrography, geochemical and in situ Sr isotopic analyses for an accurate interpretation of carbonate petrogenesis in kimberlites. Therefore, the complex petrogenesis of carbonates demonstrated here not only highlights the compositional variability of kimberlites, but also raises concerns about the use of bulk-carbonate C-O isotope studies to characterise the parental melt compositions. Conversely, our integrated textural and in situ study successfully identifies the most appropriate (i.e. primary) carbonates for providing constraints on the isotopic parameters of parental kimberlite magmas.

     

Delineation and interpretation of spatial coseismic response of groundwater levels in shallow and deep parts of an alluvial plain to different earthquakes: A case study of the Kumamoto City area,southwest Japan

Coseismic changes in groundwater levels have been investigated throughout the world, but most studies have focused on the effects of one large earthquake. The aim of this study was to elucidate the spatial patterns of level changes in response to several earthquakes, and the relationship of the patterns to shallow and deep groundwater in the same area. We selected the Kumamoto City area in southwest Japan, a region with one of the richest groundwater resources in Japan, as our study site. Data from hourly measurements of groundwater levels in 54 wells were used to characterize the coseismic responses to four earthquakes that occurred in 2000, 2001, 2005, and 2008. Although the distance to the hypocenter (12–2573 km), and seismic energy (M_w = 5.0–8.0) of these earthquakes varied, systematic groundwater level changes were observed in the range of 0.01–0.67 m. Spatial patters of the level changes were clarified by interpolating the point data by a spline method. The zones where coseismic rises were observed were generally wider for deep groundwater than for shallow groundwater, probably as a result of an increase in compressive stress. General trends in the changes in groundwater levels, and calculated pressure changes, were clarified to be consistent in the deep groundwater, but the coseismic increases or decreases in compressive stress in the shallow groundwater were variable, depending on the distance to the earthquake epicenter. We developed a conceptual model of the mechanism underlying this phenomenon by assuming permeability enhancement induced by elastic strain and pore-pressure change over the depth range. In addition, the importance of local geology was identified, because levels in the area of Togawa lava (a porous andesite) tended to change more in magnitude, and more quickly, with a shorter recovery time, than levels measured in the area outside the lava.     

Design of tabular excavations in foliated rock: an integrated numerical modelling approach

Summary This paper presents a rock mechanics design methodology applicable to steeply dipping orebodies typical of many underground hardrock mines. The first stage in the design process is the characterization of the rock mass using bothin situ and laboratory data. The effects of anisotropy on rock mass behaviour are discussed with reference to laboratory and field observations. The second stage involves the use of a number of selected numerical modelling techniques to investigate ground response in the near-field rock mass surrounding the mining excavations. This study shows that the use of several numerical methods in conjunction, allowing for the advantages of each method to be maximized, provides a more comprehensive analysis of the different facets of stope design. This approach differs from those in the literature which seek to compare the different numerical methods in order to select just one method best suited for a problem. The design methodology employed emphasizes the importance of developing an understanding of ground deformation mechanisms as opposed to predicting absolute behaviour.