Modelling of chloride ingress into concrete through a single‐ion approach. Application to an idealized surface crack pattern

The paper examines ion (chloride) transport equations in porous media (concrete) integrated over a representative elementary volume, that is to say, averaging over the macroscopic level the phenomena that occur really at the pore scale. There are three basic variables to be used: chloride concentration, moisture and temperature. The diffusion process is examined, in addition to other phenomena such as convection (the motion of dissolved substances caused by flow of water in a pore solution of partially saturated media) or chloride binding (the capacity of free chloride of being chemically bound, particularly with C₃A to form Friedel salts). Contrary to other approaches, such effects are not considered by means of apparent diffusion coefficients but by developing the complete set of time‐dependent equations for both the chloride concentration within the pore solution and the moisture content within the pore space. Once the general model is described, the system of equations can be solved numerically by means of a two‐dimensional finite element formulation. The main objective is to reproduce results of experimental tests by means of a priori parameter estimation, according to the characteristics of materials and external environment conditions, thereby superseding the well‐known best fit a posteriori through Fick's second equation. While the introduction of hygrometric conditions and convection phenomena appears to be of high significance, other factors like temperature, surface concentration, chloride binding or equivalent hydration time are analysed too. The proposed model can reproduce bidimensional complex geometries, for example, cracked concrete cover, as well as variable surface condition. An application case is developed through a realistic model of the geometry of a crack. Copyright © 2014 John Wiley & Sons, Ltd.     

Effect of iron and carbonation on the diffusion of iodine and rhenium in waste encasement concrete and soil fill material under hydraulically unsaturated conditions

Assessing long-term performance of Category 3 cement wasteforms and accurate prediction for radionuclide encasement requires knowledge of the radionuclide–cement interactions and mechanisms of retention (i.e. sorption or precipitation). A set of sediment-concrete half-cell diffusion experiments was conducted under unsaturated conditions (4% and 7% by weight moisture content) using carbonated and non-carbonated concrete–soil half cells. Results indicate the behavior of Re and I release was comparable within a given half-cell test. Diffusivity in soil is a function of moisture content; a 3% increase in moisture content affords a one to two order of magnitude increase in diffusivity. Release of I and Re was 1–3 orders of magnitude less from non-carbonated, relative to carbonated, concrete monoliths. Inclusion of Fe in non-carbonate monoliths resulted in the lowest concrete diffusivity values for both I and Re. This suggests that in the presence of Fe, I and Re are converted to reduced species, which are less soluble and better retained within the concrete monolith. The release of I and Re was greatest from Fe-bearing, carbonated concrete monoliths, suggesting carbonation negates the effect of Fe on the retention of I and Re within concrete monoliths. This is likely due to enhanced formation of microcracks in the presence of Fe, which provide preferential paths for contaminant migration. Although the release of I and Re were greatest from carbonated concrete monoliths containing Fe, the migration of I and Re within a given half cell is dependent on the moisture content, soil diffusivity, and diffusing species.     

低煤阶煤中甲烷扩散性能分析

甲烷在煤基质中的扩散性能是影响煤层气产出的重要储层参数。采用云南东南部地区新近系中新统小龙潭组褐煤样品,开展了低煤阶煤中甲烷等温吸附实验。基于等温吸附实验获得的吸附量与时间的关系数据,应用一元孔隙结构气体非稳态扩散模型,计算了煤中甲烷气体扩散系数,揭示了煤中甲烷扩散规律和控制机理。研究结果表明,低煤阶煤中气体扩散规律服从Langmuir方程,煤中甲烷有效扩散系数和扩散系数随着压力的增高而增大;吸附时间常数随着压力的增高而减小,服从负指数函数规律。4个实验煤样Langmuir有效扩散系数和扩散系数分别是（1.71~5.46）×10-4 s-1和（2.17~6.91）×10-12 m2/s,Langmuir压力为0.63~1.97 MPa。在相同温度和压力条件下,干燥煤样的有效扩散系数和扩散系数大于平衡水分煤样,随着温度的增高,其有效扩散系数和扩散系数增加,煤中气体扩散性能增强。      

Measurement of flow properties of expansive clays

The paper deals with the determination of the flow properties of expansive and unsaturated clays under different conditions of stress. By choosing the moisture content as the dependent variable, the well known non-linear diffusin equation is derived. Numerical solutions using a finite element program are presented, assuming a linear relationship between the moisture diffusivity and the concentration (the relative moisture content). These solutions are interpreted and a procedure is proposed to derive the flow properties of the clay from the sorption curves. Results of tests are presented and used to illustrate the procedure. It is found that the lower the stress applied, the smaller the initial moisture diffusivity and the stronger the dependence of the moisture diffusivity upon the concentration.     

Numerical upper bounds to the ultimate load bearing capacity of three-dimensional reinforced concrete structures

This contribution is addressing the ultimate limit state design of massive three-dimensional reinforced concrete structures based on a finite-element implementation of yield design theory. The strength properties of plain concrete are modeled either by means of a tension cutoff Mohr Coulomb or a Rankine condition, while the contribution of the reinforcing bars is taken into account by means of a homogenization method. This homogenization method can either represent regions of uniformly distributed steel rebars smeared into the concrete domain, but it can also be extended to model single rebars diluted into a larger region, thereby simplifying mesh generation and mesh size requirements in this region. The present paper is mainly focused on the implementation of the upper bound kinematic approach formulated as a convex minimization problem. The retained strength condition for the plain concrete and homogenized reinforced regions are both amenable to a formulation involving positive semidefinite constraints. The resulting semidefinite programming problems can, therefore, be solved using state-of-the-art dedicated solvers. The whole computational procedure is applied to some illustrative examples, where the implementation of both static and kinematic methods produces a relatively accurate bracketing of the exact failure load for this kind of structures.     

Hydrogen diffusion in spinel grain boundaries and consequences for chemical homogenization in hydrous peridotite

Hydrogen can be stored in the structure of nominally anhydrous minerals as point defects, and these impurities substantially modify many physical properties of Earth’s mantle minerals. However, mantle rocks are composed of mineral grains separated by grain boundaries and interphase grains boundaries. Therefore, as a potential hydrogen reservoir, grain boundaries should be given proper attention. Here, I report an experimental investigation into hydrogen diffusion through grain boundaries in polycrystalline aggregates. Sintering and diffusion experiments were performed using a gas-medium high-pressure vessel at under pressure of 300 MPa and over a temperature range of 900–1,250°C. The diffusion assembly consisted of a polycrystalline cylinder of aluminous spinel + olivine crystals with a talc cylinder as the main hydrogen source. A Ni capsule was used to buffer the oxygen fugacity at Ni–NiO. Experimental durations varied from 5 min to 5 h. The presence of hydrogen in the crystals was measured by Fourier-transform infrared spectroscopy. The calculation of the diffusion coefficients was based on the estimation of the characteristic distance. The absence or presence of hydrogen recorded by the ‘hydrogen sensor’ olivines embedded in the aggregate allows the estimation of bounds on this characteristic distance. Results presented here suggest that hydrogen effective diffusion coefficients are only one order of magnitude faster (~10⁻⁹ m²s⁻¹ at 1,000°C) than in an olivine single crystal along the [100] axis. Resulting diffusion coefficients for hydrogen in grain boundary are four orders of magnitude faster than in a single crystal, but this diffusivity is not fast enough to affect hydrogen mobility in mantle rocks with grain sizes greater than ~1 mm. Thus, very limited chemical homogenization would occur using grain boundaries diffusion in mantle hydrous peridotite for incompatible and volatile element, such as hydrogen.     

Time homogenization for clays subjected to large numbers of cycles

This paper discusses the reliability and the efficiency of a time homogenization method employed to reduce the computational time during cyclic loading for two common geotechnical tests and two elastoplastic models for clays. The method of homogenization is based upon splitting time into two separate scales. The first time scale relates to the period of cyclic loading and the second to the characteristic time of the fatigue phenomenon. The time homogenization method is applied to simulate an undrained triaxial test (homogeneous stress state) and a pressuremeter test (nonhomogeneous stress state) under one‐way cyclic loading on normally consolidated clay. This method is coupled with two elastoplastic models dedicated to cyclic behavior of clay (a bounding surface plasticity model and a bubble model). Both linear and nonlinear elasticities are considered. The difficulty encountered when applying this method to models introducing nonlinear elasticity and kinematic hardening is pointed out. The performance of time homogenization related to the main parameters is numerically investigated by comparison with conventional finite element simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

Solution of the unsaturated soil moisture equation using repeated transforms

An alternative method of solution for the linearized ‘theta‐based’ form of the Richards equation of unsaturated flow is developed in two spatial dimensions. The Laplace and Fourier transformations are employed to reduce the Richards equation to an ordinary differential equation in terms of a transformed moisture content and the transform variables, s and ξ. Separate analytic solutions to the transformed equation are developed for initial states which are either in equilibrium or dis‐equilibrium. The solutions are assembled into a finite layer formulation satisfying continuity of soil suction, thereby facilitating the analysis of horizontally stratified soil profiles. Solution techniques are outlined for various boundary conditions including prescribed constant moisture content, prescribed constant flux and flux as a function of moisture change. Example solutions are compared with linearized finite element solutions. The agreement is found to be good. An adaptation of the method for treating the quasilinearized Richards equation with variable diffusivity is also described. Comparisons of quasilinear solutions with some earlier semi‐analytical, finite element and finite difference results are also favourable. Copyright © 2001 John Wiley & Sons, Ltd.     

Homogenization of granular material modeled by a three-dimensional discrete element method

A homogenization strategy for granular materials is presented and applied to a three-dimensional discrete element method (DEM), that uses superellipsoids as particles. Macroscopic quantities are derived from the microscopic quantities resulting from a DEM simulation by averaging over representative volume elements (RVEs). The implementation of an RVE is described in detail regarding the definition and discretization of the RVE boundary. The homogenization strategy is validated by DEM simulations of compression and shear tests of cohesionless granular assemblies. Finally, an elasto-plastic material model is fitted to the resulting stress–strain curves.     

Computational homogenization of uncoupled consolidation in micro‐heterogeneous porous media

Variationally consistent homogenization is exploited for the analysis of transient uncoupled consolidation in micro‐heterogeneous porous solids, whereby the classical approach of first‐order homogenization for stationary problems is extended to transient problems. Homogenization is then carried out in the spatial domain on representative volume elements (RVE), which are introduced in quadrature points in standard fashion. Along with the classical averages, a higher‐order conservation quantity is obtained. An iterative FE²‐algorithm is devised for the case of nonlinear permeability and storage coefficients, and it is applied to pore pressure changes in asphalt‐concrete (particle composite). Various parametric studies are carried out, in particular, with respect to the influence of the ‘substructure length scale’ that is represented by the size of the RVE's. Copyright © 2009 John Wiley & Sons, Ltd.     

Variability of soil moisture and its relationship with surface albedo and soil thermal diffusivity at Astronomical Observatory,Thiruvananthapuram, south Kerala

Continuous observation data collected over the year 2008 at Astronomical Observatory, Thiruvananthapuram in south Kerala (76°59′E longitude and 8°30′N latitude) are used to study the diurnal, monthly and seasonal soil moisture variations. The effect of rainfall on diurnal and seasonal soil moisture is discussed. We have investigated relationships of soil moisture with surface albedo and soil thermal diffusivity. The diurnal variation of surface albedo appears as a U-shaped curve on sunny days. Surface albedo decreases with the increase of solar elevation angle, and it tends to be a constant when solar elevation angle is greater than 40°. So the daily average surface albedo was calculated using the data when solar elevation angle is greater than 40°. The results indicate that the mean daily surface albedo decreases with increases in soil moisture content, showing a typical exponential relation between the surface albedo and the soil moisture. Soil thermal diffusivity increases firstly and then decreases with the increase of soil moisture.     

Influence of soil moisture content on surface albedo and soil thermal parameters at a tropical station

Half hourly data of soil moisture content, soil temperature, solar irradiance, and reflectance are measured during April 2010 to March 2011 at a tropical station, viz., Astronomical Observatory, Thiruvananthapuram, Kerala, India (76°59’E longitude and 8°29’N latitude). The monthly, seasonal and seasonal mean diurnal variation of soil moisture content is analyzed in detail and is correlated with the rainfall measured at the same site during the period of study. The large variability in the soil moisture content is attributed to the rainfall during all the seasons and also to the evaporation/movement of water to deeper layers. The relationship of surface albedo on soil moisture content on different time scales are studied and the influence of solar elevation angle and cloud cover are also investigated. Surface albedo is found to fall exponentially with increase in soil moisture content. Soil thermal diffusivity and soil thermal conductivity are also estimated from the subsoil temperature profile. Log normal dependence of thermal diffusivity and power law dependence of thermal conductivity on soil moisture content are confirmed.     

地下结构混凝土渗透特性试验研究

根据地下结构承受水压及构件存在裂缝的情况,采用自制混凝土试块模具、自制可控开裂混凝土装置、自制可控压力水头装置、裂缝测宽仪组成的试验系统,在不同水压、氯离子浓度、裂缝宽度以及浸泡时间等工况下进行了开裂混凝土渗透特性试验。试验结果表明：当其他试验条件相同时,压力水头下与自然浸泡状态下的氯离子运移规律有明显的差异,压力水头作用下混凝土各层自由氯离子含量均有明显的提高;存在控制氯离子浸泡溶液运移的裂缝宽度阈值,且该阈值不受水头压力大小的影响。该试验方法可作为同类研究的借鉴和参考。     

Modeling concrete exposed to high temperature: Impact of dehydration and retention curves on moisture migration

High‐performance concrete is a widely used building material for tunnels, high‐rise buildings, nuclear plants etc. When these structures are exposed to fire, high‐performance concrete is prone to spalling. Moisture migration is believed to be one of the processes directly related to this phenomenon. In this paper, moisture profiles measured experimentally from neutron radiography on heated concrete are compared with results from a numerical model implemented in the finite element code Cast3M. The water loss measured experimentally, and the numerical results suggest that the commonly used constitutive laws for dehydration and water retention curves need to be reconsidered. The influence of these constitutive laws on the moisture migration is investigated. The dehydration constitutive law plays an important role on the dehydration front but has negligible effect on the moisture accumulation behind this front. By contrast, the water retention curves do not influence the dehydration front but affect the quantity and location of water condensation. The role of the permeability is also discussed.     

多尺度有限单元法求解非均质多孔介质中的三维地下水流问题

应用多尺度有限单元法模拟非均质多孔介质中的三维地下水流问题。与传统有限单元法相比，多尺度有限单元法的基函数具有能反映单元内参数变化的优点，所以这种方法能在大尺度上抓住解的小尺度特征获得较精确的解。在介绍多尺度有限单元法求解非均质多孔介质中三维地下水流问题的基本原理之后，对参数水平方向渐变垂直方向突变的非均质多孔介质中的三维地下水流和Borden实验场的三维地下水流分别用多尺度有限单元法和传统等参有限单元法进行了计算，结果表明在模拟高度非均质多孔介质中的三维地下水流问题时，多尺度有限单元法比传统有限单元法有效，既节省计算量又有较高的精度；在模拟非均质性弱的多孔介质中的三维地下水流问题时，多尺度有限单元法虽然也能在大尺度上获得较为精确的解，但效果不明显。     

ParCYCLIC: finite element modelling of earthquake liquefaction response on parallel computers

This paper presents the computational procedures and solution strategy employed in ParCYCLIC, a parallel non‐linear finite element program developed based on an existing serial code CYCLIC for the analysis of cyclic seismically‐induced liquefaction problems. In ParCYCLIC, finite elements are employed within an incremental plasticity, coupled solid–fluid formulation. A constitutive model developed for simulating liquefaction‐induced deformations is a main component of this analysis framework. The elements of the computational strategy, designed for distributed‐memory message‐passing parallel computer systems, include: (a) an automatic domain decomposer to partition the finite element mesh; (b) nodal ordering strategies to minimize storage space for the matrix coefficients; (c) an efficient scheme for the allocation of sparse matrix coefficients among the processors; and (d) a parallel sparse direct solver. Application of ParCYCLIC to simulate 3‐D geotechnical experimental models is demonstrated. The computational results show excellent parallel performance and scalability of ParCYCLIC on parallel computers with a large number of processors. Copyright © 2004 John Wiley & Sons, Ltd.     

Theoretical study and simulation of moisture transport in unsaturated porous media by periodic homogenization

In this work, the macroscopic Richards equation for moisture transport is established in unsaturated porous media using periodic homogenization. By performing dimensional analysis on microscopic equations of moisture transfer, dimensional numbers characterizing moisture transport appear. The application of the asymptotic homogenization leads to the classical Richards equation, which is justified rigorously this way. Moreover, we obtain an accurate definition of the homogenized diffusion tensor of moisture involving the geometric properties of the microstructure and known transport properties of the material. A different behavior for the transport of water vapor between hygroscopic and super‐hygroscopic region is revealed. Finally, a simple 2D example where an analytical solution exists is addressed. Copyright © 2014 John Wiley & Sons, Ltd.     

Investigating soil thermodynamic parameters of the active layer on the northern Qinghai-Tibetan Plateau

The soil thermodynamic parameters, including thermal conductivity, diffusivity and volumetric capacity within the active layer on the northern Tibetan Plateau, were calculated using the measured data of soil temperature gradient, heat flux, and moisture at four stations from October 2003 to September 2004. The results showed that the soil thermodynamic parameters exhibited clear seasonal fluctuation. The thermal conductivity and diffusivity in summer and autumn at Beiluhe, Kexinling, and Tongtianhe were larger than those in winter. The volumetric thermal capacity causes an opposite change; it was larger in autumn and winter than in summer. In spring, the soil thermal conductivity at the Kekexili station was larger than that in summer. Generally, fine-grained soils and lower saturation degrees in the topsoil might be a reason for the lower soil thermal conductivity in winter. For a given soil, soil moisture was the main factor influencing the thermodynamic parameters. The unfrozen water content that existed in frozen soils greatly affected the soil thermal conductivity, whose contribution rate was estimated to be 55 %. The thermodynamic parameters of frozen soils could be expressed as a function of soil temperature, volumetric ice content and soil salinity, while for the unfrozen ground the soil moisture content is the dominant factor for those thermal parameters. As for the soil thermal diffusivity, there exists a critical value of soil moisture content. When the soil moisture content becomes less than a critical value, the soil thermal diffusivity increases as the soil moisture content rises.     

Numerical estimation of effective diffusion coefficients for charged porous materials based on micro-scale analyses

In order to describe diffusive transport of solutes through a porous material, estimation of effective diffusion coefficients is required. It has been shown theoretically that in the case of uncharged porous materials the effective diffusion coefficient of solutes is a function of the pore morphology of the material and can be described by the tortuosity (tensor) (Bear, 1988 [1]). Given detailed information of the pore geometry at the micro-scale the tortuosity of different materials can be accurately estimated using homogenization procedures. However, many engineering materials (e.g., clays and shales) are characterized by electrical surface charges on particles of the porous material which strongly affect the (diffusive) transport properties of ions. For these type of materials, estimation of effective diffusion coefficients have been mostly based on phenomenological equations with no link to underlying micro-scale properties of these charged materials although a few recent studies have used alternative methods to obtain the diffusion parameters (Jougnot et al., 2009; Pivonka et al., 2009; Revil and Linde, 2006 2, 3 and 4). In this paper we employ a recently proposed up-scaled Poisson–Nernst–Planck type of equation (PNP) and its micro-scale counterpart to estimate effective ion diffusion coefficients in thin charged membranes. We investigate a variety of different pore geometries together with different surface charges on particles. Here, we show that independent of the charges on particles, a (generalized) tortuosity factor can be identified as function of the pore morphology only using the new PNP model. On the other hand, all electro-static interactions of ions and charges on particles can consistently be captured by the ratio of average concentration to effective intrinsic concentration in the macroscopic PNP equations. Using this formulation allows to consistently take into account electrochemical interactions of ions and charges on particles and so excludes any ambiguity generally encountered in phenomenological equations.