Kinematic models for non‐coaxial granular materials. Part I: theory

The purpose of this paper is to present a physically based plasticity model for non‐coaxial granular materials. The model, which we shall call the double slip and rotation rate model (DSR² model), is a pair of kinematic equations governing the velocity field. The model is based on a discrete micro‐analysis of the kinematics of particles in contact, and is formulated by introducing a quantity called the averaged micro‐pure rotation rate (APR) into the unified plasticity model which was proposed by one of the authors. Our macro–micro mechanical analysis shows that the APR is a non‐linear function of, among other quantities, the macro‐rotation rate of the major principal axis of stress taken in the opposite sense. The requirement of energy dissipation used in the double‐sliding free‐rotating model appears to be unduly restrictive as a constitutive assumption in continuum models. In the DSR² model the APR tensor and the spin tensor are directly linked with non‐coaxiality of the stress and deformation rate tensors. We also propose a simplified plasticity model based on the DSR² model for a class of dilatant materials, and analyse its material stability. Copyright © 2005 John Wiley & Sons, Ltd.     

Micromechanical viscoelasto‐plastic models and finite element implementation for rate‐independent and rate‐dependent permanent deformation of stone‐based materials

This paper presents parallel and serial viscoelasto‐plastic models to simulate the rate‐independent and the rate‐dependent permanent deformation of stone‐based materials, respectively. The generalized Maxwell viscoelastic and Chaboche's plastic models were employed to formulate the proposed parallel and serial viscoelasto‐plastic constitutive laws. The finite element (FE) implementation of the parallel model used a displacement‐based incremental formulation for the viscoelastic part and an elastic predictor—plastic corrector scheme for the elastoplastic component. The FE framework of the serial viscoelasto‐plastic model employed a viscoelastic predictor—plastic corrector algorithm. The stone‐based materials are consisted of irregular aggregates, matrix and air voids. This study used asphalt mixtures as an example. A digital sample was generated with imaging analysis from an optically scanned surface image of an asphalt mixture specimen. The modeling scheme employed continuum elements to mesh the effective matrix, and rigid bodies for aggregates. The ABAQUS user material subroutines defined with the proposed viscoelasto‐plastic matrix models were employed. The micromechanical FE simulations were conducted on the digital mixture sample with the viscoelasto‐plastic matrix models. The simulation results showed that the serial viscoelasto‐plastic matrix model generated more permanent deformation than the parallel one by using the identical material parameters and displacement loadings. The effect of loading rates on the material viscoelastic and viscoelasto‐plastic mixture behaviors was investigated. Permanent deformations under cyclic loadings were determined with FE simulations. The comparison studies showed that the simulation results correctly predicted the rate‐independent and rate‐dependent viscoelasto‐plastic constitutive properties of the proposed matrix models. Overall, these studies indicated that the developed micromechanical FE models have the abilities to predict the global viscoelasto‐plastic behaviors of the stone‐based materials. Copyright © 2009 John Wiley & Sons, Ltd.     

Happy Jack Uraninite: A New Reference Material for High Spatial Resolution Analysis of U‐Rich Matrices

There is currently a lack of well‐characterised matrix‐matched reference materials (RMs) for forensic analysis of U‐rich materials at high spatial resolution. This study reports a detailed characterisation of uraninite (nominally UO_2+x) from the Happy Jack Mine (UT, USA). The Happy Jack uraninite can be used as a RM for the determination of rare earth element (REE) mass fractions in nuclear materials, which provide critical information for source attribution purposes. This investigation includes powder X‐ray diffraction (pXRD) data, as well as major, minor and trace element abundances determined using a variety of micro‐analytical techniques. The chemical signature of the uraninite was investigated at the macro (cm)‐scale with micro‐X‐ray fluorescence (µXRF) mapping and at high spatial resolution (tens of micrometre scale) using electron probe microanalysis (EPMA) and laser ablation‐inductively coupled plasma‐mass spectrometry (LA‐ICP‐MS) analyses. Based on EPMA results, the uraninite is characterised by homogeneous UO₂ and CaO contents of 91.57 ± 1.49% m/m (2s uncertainty) and 2.70 ± 0.38% m/m (2s), respectively. Therefore, CaO abundances were used as the internal standard when conducting LA‐ICP‐MS analyses. Overall, the major element and REE compositions are homogeneous at both the centimetre and micrometre scales, allowing this material to be used as a RM for high spatial resolution analysis of U‐rich samples.     

Determination of Platinum‐Group Elements and Gold in Ferromanganese Nodule Reference Samples

A measurement procedure for determining of Ru, Pd, Ir, Pt and Au mass fractions in ferromanganese deposits by inductively coupled plasma‐mass spectrometry after acid digestion and anion exchange preconcentration is presented. To eliminate incomplete recovery after sorption preconcentration of the platinum‐group elements (PGE) and Au, a standard addition method was used. Detection limits ranged from 0.02 ng (Pd, Ir) to 0.19 ng (Ru). The measurement results for ferromanganese nodule reference material NOD‐A‐1 and NOD‐P‐1 agree with earlier reported values. Intermediate precision of PGE concentration data for nodule reference materials in this work was 5–24% (1s) and could reflect sample heterogeneity.     

Incrementalization of a single hardening constitutive model for frictional materials

The governing equations for an elasto‐plastic constitutive model for frictional materials such as soil, rock, and concrete are presented, and the incremental form is indicated in preparation for implementation of the model in a user‐defined module for finite element calculations. This isotropic, work‐hardening and ‐softening model employs a single yield surface, it incorporates non‐associated plastic flow, and its capability of capturing the behaviour of different types of frictional materials under various three‐dimensional conditions has been demonstrated by comparison with measured behaviour, as presented in the literature. The incrementalization procedure is indicated and the resulting equations for the single hardening model are presented together with parameters for a dense sand. Following the implementation of the model, these parameters are used for evaluation of different integration schemes as presented in a companion paper by Jakobsen and Lade (Int. J. Numer. Anal. Meth. Geomech. 2002; 26 :661). Copyright © 2002 John Wiley & Sons, Ltd.     

Community‐Derived Standards for LA‐ICP‐MS U‐(Th‐)Pb Geochronology – Uncertainty Propagation,Age Interpretation and Data Reporting

The LA‐ICP‐MS U‐(Th‐)Pb geochronology international community has defined new standards for the determination of U‐(Th‐)Pb ages. A new workflow defines the appropriate propagation of uncertainties for these data, identifying random and systematic components. Only data with uncertainties relating to random error should be used in weighted mean calculations of population ages; uncertainty components for systematic errors are propagated after this stage, preventing their erroneous reduction. Following this improved uncertainty propagation protocol, data can be compared at different uncertainty levels to better resolve age differences. New reference values for commonly used zircon, monazite and titanite reference materials are defined (based on ID‐TIMS) after removing corrections for common lead and the effects of excess ²³⁰Th. These values more accurately reflect the material sampled during the determination of calibration factors by LA‐ICP‐MS analysis. Recommendations are made to graphically represent data only with uncertainty ellipses at 2s and to submit or cite validation data with sample data when submitting data for publication. New data‐reporting standards are defined to help improve the peer‐review process. With these improvements, LA‐ICP‐MS U‐(Th‐)Pb data can be considered more robust, accurate, better documented and quantified, directly contributing to their improved scientific interpretation.     

A bounding surface elasto‐viscoplastic constitutive model for non‐isothermal cyclic analysis of asphaltic materials

An elasto‐viscoplastic constitutive model for asphaltic materials is presented within the context of bounding surface plasticity theory, taking into account the effects of the stress state, void binder degree of saturation, temperature and strain rate on the material behaviour. A stress state dependent non‐linear elasticity model is introduced to represent time‐independent recoverable portion of the deformation. The consistent visco‐plasticity framework is utilised to capture the rate‐dependent, non‐recoverable strain components. The material parameters introduced in the model are identified, and their determination from conventional laboratory tests is discussed. The capability of the model to reproduce experimentally observed response of asphaltic materials is demonstrated through numerical simulations of several laboratory test data from the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

A coupled chemo‐thermo‐hygro‐mechanical model of concrete at high temperature and failure analysis

A hierarchical mathematical model for analyses of coupled chemo‐thermo‐hygro‐mechanical behaviour in concretes at high temperature is presented. The concretes are modelled as unsaturated deforming reactive porous media filled with two immiscible pore fluids, i.e. the gas mixture and the liquid mixture, in immiscible–miscible levels. The thermo‐induced desalination process is particularly integrated into the model. The chemical effects of both the desalination and the dehydration processes on the material damage and the degradation of the material strength are taken into account. The mathematical model consists of a set of coupled, partial differential equations governing the mass balance of the dry air, the mass balance of the water species, the mass balance of the matrix components dissolved in the liquid phases, the enthalpy (energy) balance and momentum balance of the whole medium mixture. The governing equations, the state equations for the model and the constitutive laws used in the model are given. A mixed weak form for the finite element solution procedure is formulated for the numerical simulation of chemo‐thermo‐hygro‐mechanical behaviours. Special considerations are given to spatial discretization of hyperbolic equation with non‐self‐adjoint operator nature. Numerical results demonstrate the performance and the effectiveness of the proposed model and its numerical procedure in reproducing coupled chemo‐thermo‐hygro‐mechanical behaviour in concretes subjected to fire and thermal radiation. Copyright © 2005 John Wiley & Sons, Ltd.     

Assessment of Nanosecond Laser Ablation Multi‐Collector Inductively Coupled Plasma‐Mass Spectrometry for Pb and Sr Isotopic Determination in Archaeological Glass: Mass Bias Correction Strategies and Results for Corning Glass Reference Materials

This work presents an evaluation of various methods for in situ high‐precision Sr and Pb isotopic determination in archaeological glass (containing 100–500 μg g^?1 target element) by nanosecond laser ablation multi‐collector‐inductively coupled plasma‐mass spectrometry (ns‐LA‐MC‐ICP‐MS). A set of four soda‐lime silicate glasses, Corning A–D, mimicking the composition of archaeological glass and produced by the Corning Museum of Glass (Corning, New York, USA), were investigated as candidates for matrix‐matched reference materials for use in the analysis of archaeological glass. Common geological reference materials with known isotopic compositions (USGS basalt glasses BHVO‐2G, GSE‐1G and NKT‐1G, soda‐lime silicate glass NIST SRM 610 and several archaeological glass samples with known Sr isotopic composition) were used to evaluate the ns‐LA‐MC‐ICP‐MS analytical procedures. When available, ns‐LA‐MC‐ICP‐MS results for the Corning glasses are reported. These were found to be in good agreement with results obtained via pneumatic nebulisation (pn) MC‐ICP‐MS after digestion of the glass matrix and target element isolation. The presence of potential spectral interference from doubly charged rare earth element (REE) ions affecting Sr isotopic determination was investigated by admixing Er and Yb aerosols by means of pneumatic nebulisation into the gas flow from the laser ablation system. It was shown that doubly charged REE ions affect the Sr isotope ratios, but that this could be circumvented by operating the instrument at higher mass resolution. Multiple strategies to correct for instrumental mass discrimination in ns‐LA‐MC‐ICP‐MS and the effects of relevant interferences were evaluated. Application of common glass reference materials with basaltic matrices for correction of ns‐LA‐MC‐ICP‐MS isotope data of archaeological glasses results in inaccurate Pb isotope ratios, rendering application of matrix‐matched reference materials indispensable. Correction for instrumental mass discrimination using the exponential law, with the application of Tl as an internal isotopic standard element introduced by pneumatic nebulisation and Corning D as bracketing isotopic calibrator, provided the most accurate results for Pb isotope ratio measurements in archaeological glass. Mass bias correction relying on the power law, combined with intra‐element internal correction, assuming a constant ⁸⁸Sr/⁸⁶Sr ratio, yielded the most accurate results for ⁸⁷Sr/⁸⁶Sr determination in archaeological glasses     

Separation and Precise Measurement of Lithium Isotopes in Three Reference Materials Using Multi Collector‐Inductively Coupled Plasma Mass Spectrometry

Lithium separation technique for three reference materials has been established together with precise determination of lithium isotope using a Neptune multi collector-inductively coupled plasma mass spectrometry (MC-ICP-MS). The solutions of lithium element standard reference materials, potassium, calcium, sodium, magnesium and iron single element, were used to evaluate analytical methods applied. Three separate stages of ion-exchange chromatography were carried out using organic cation-exchange resin (AG 50W-X8). Lithium was enriched for the three stages using different eluants, which are 2.8 M HCl, 0.15 M HCl and 0.5 M HCl in 30% ethanol, respectively. The columns for the first and second stages are made of polypropylene, and those for the third stage are made of quartz. Total reagent volume for the entire chemical process was 35 mL for three reference materials. The recovery yielded for the three stages is 98.9–101.2% with an average of 100.0%, 97.6–101.9% with an average of 99.9%, and 99.8–103.3% with an average of 100.6%, respectively. The precision of this technique is conservatively estimated to be ±0.72–1.04‰ (2σ population), which is similar to the precision obtained by different authors in different laboratories with MC-ICP-MS. The δ7Li values (7Li/6Li relative to the IRMM-016 standard) determined for andesite (AGV-2) and basalt (BHVO-2) are 5.68‰ (n=18), 4.33‰ (n=18), respectively. The δ7Li value (7Li/6Li relative to the L-SVEC standard) determined for IRMM-016 is –0.01‰ (n=15). All these analytical results are in good agreement with those previously reported. In addition, the results for the same kinds of samples analyzed at the MLR Key Laboratory of Metallogeny and Mineral Assessment, Institute of Mineral Resources, Chinese Academy of Geological Sciences, are consistent with those obtained at the Plasma Laboratory, University of Maryland, within analytical uncertainty. According to these experiment results, it is concluded that this proposed procedure is a suitable method for determining the lithium isotopic composition of natural samples.     

A constitutive model for the dynamic and high‐pressure behaviour of a propellant‐like material: Part I: Experimental background and general structure of the model

This paper is the first part of a work that aims at developing a mechanical model for the behaviour of propellant‐like materials under high confining pressure and strain rate. The behaviour of a typical material is investigated experimentally. Several microstructural deformation processes are identified and correlated with loading conditions. The resulting behaviour is complex, non‐linear, and characterized by multiple couplings. The general structure of a relevant model is sought using a thermodynamic framework. A viscoelastic‐viscoplastic‐compaction model structure is derived under suitable simplifying assumptions, in the framework of finite, though moderate, strains. Model development, identification and numerical applications are given in the companion paper. Copyright © 2001 John Wiley & Sons, Ltd.     

Ground response curves for rock masses exhibiting strain‐softening behaviour

A literature review has shown that there exist adequate techniques to obtain ground reaction curves for tunnels excavated in elastic‐brittle and perfectly plastic materials. However, for strain‐softening materials it seems that the problem has not been sufficiently analysed. In this paper, a one‐dimensional numerical solution to obtain the ground reaction curve (GRC) for circular tunnels excavated in strain‐softening materials is presented. The problem is formulated in a very general form and leads to a system of ordinary differential equations. By adequately defining a fictitious ‘time’ variable and re‐scaling some variables the problem is converted into an initial value one, which can be solved numerically by a Runge–Kutta–Fehlberg method, which is implemented in MATLAB environment. The method has been developed for various common particular behaviour models including Tresca, Mohr–Coulomb and Hoek–Brown failure criteria, in all cases with non‐associative flow rules and two‐segment piecewise linear functions related to a principal strain‐dependent plastic parameter to model the transition between peak and residual failure criteria. Some particular examples for the different failure criteria have been run, which agree well with closed‐form solutions—if existing—or with FDM‐based code results. Parametric studies and specific charts are created to highlight the influence of different parameters. The proposed methodology intends to be a wider and general numerical basis where standard and newly featured behaviour modes focusing on obtaining GRC for tunnels excavated in strain‐softening materials can be implemented. This way of solving such problems has proved to be more efficient and less time consuming than using FEM‐ or FDM‐based numerical 2D codes. Copyright © 2003 John Wiley & Sons, Ltd.     

Cavity expansion analyses of crushable granular materials with state‐dependent dilatancy

Crushability is one of the important behaviors of granular materials particularly under high stress states, and affects both the deformability and strength of the materials that are in essence associated with state‐dependent dilatancy. In this presentation, first, a new critical state model is proposed to take into account the three different modes of compressive deformation of crushable granular materials, i.e. particle rearrangement, particle crushing and pseudo‐elastic deformation. Second, the governing equations for cavity expansion in crushable granulates are introduced, in which the state‐dependent dilatancy as well as the bounding surface plasticity model are used. Then, the procedure to obtain semi‐analytical solutions to cavity expansion in the material is described in detail, in which a commercial differential equation solver is employed. Finally, cavity expansion analyses are carried out on Toyoura sand, a well‐documented granular material, to demonstrate the effects of crushability and state‐dependent dilatancy. The study shows that particle crushing does occur at both high stress and critical states and affects the stress fields and the deformation behavior of the material surrounding the cavity in association with state‐dependent dilatancy. This leads to conclusion that particle crushing and state‐dependent dilatancy have to be taken into account when cavity expansion theory is used to interpret cone penetration tests and pressuremeter tests. Copyright © 2011 John Wiley & Sons, Ltd.     

Determination of Platinum‐Group Elements and Re‐Os Isotopes using ID‐ICP‐MS and N‐TIMS from a Single Digestion after Two‐Stage Column Separation

We report an improved procedure for the determination of the platinum‐group elements (PGE) and Re, and Os isotopes from a single sample aliquot by isotope dilution (ID) using inductively coupled plasma‐mass spectrometry (ICP‐MS) and negative thermal ionisation mass spectrometry (N‐TIMS), respectively. A two‐stage column method was used to purify PGE‐Re from their sample matrix and interfering elements (e.g., Mo, Zr and Hf) after Os had been separated by CCl₄ solvent extraction. The first column separation step used cation exchange resin (AG50W‐X8) to concentrate PGE‐Re and some potential interfering elements (e.g., Mo, Zr and Hf). In the second step, N‐benzoyl‐N‐phenylhydroxylamine (BPHA) extraction resin was used to separate PGE‐Re from the remaining interfering elements, which all remained strongly absorbed to the resin. The method was used to determine the PGE and rhenium, and Os isotope ratios in a range of geochemical reference materials (TDB‐1, WGB‐1, BHVO‐2 and UB‐N). The obtained results agree well with those previously published. This new method enables PGE‐Re abundances and Os isotopic ratios to be determined on the same sample digestion, and circumvents the problems created by sample heterogeneity when comparing PGE and Re‐Os isotope data.     

‘Box‐Profile’ Ion Implants as Geochemical Reference Materials for Electron Probe Microanalysis and Secondary Ion Mass Spectrometry

Although electron probe microanalysis and secondary ion mass spectrometry are widely used analytical techniques for geochemical and mineralogical applications, metrologically rigorous quantification remains a major challenge for these methods. Secondary ion mass spectrometry (SIMS) in particular is a matrix‐sensitive method, and the use of matrix‐matched reference materials (RMs) is essential to avoid significant analytical bias. A major problem is that the number of available RMs for SIMS is extremely small compared with the needs of analysts. One approach for the production of matrix‐specific RMs is the use of high‐energy ion implantation that introduces a known amount of a selected isotope into a material. We chose the more elaborate way of implanting a so‐called ‘box‐profile’ to generate a quasi‐homogeneous concentration of the implanted isotope in three dimensions, which allows RMs not only to be used for ion beam analysis but also makes them suitable for EPMA. For proof of concept, we used the thoroughly studied mineralogically and chemically ‘simple’ SiO₂ system. We implanted either ⁴⁷Ti or ⁴⁸Ti into synthetic, ultra‐high‐purity silica glass. Several ‘box‐profiles’ with mass fractions between 10 and 1000 μg g^?1 Ti and maximum depths of homogeneous Ti distribution between 200 nm and 3 μm were produced at the Institute of Ion Beam Physics and Materials Research of Helmholtz‐Zentrum Dresden‐Rossendorf. Multiple implantation steps using varying ion energies and ion doses were simulated with Stopping and Range of Ions in Matter (SRIM) software, optimising for the target concentrations, implantation depths and technical limits of the implanter. We characterised several implant test samples having different concentrations and maximum implantation depths by means of SIMS and other analytical techniques. The results show that the implant samples are suitable for use as reference materials for SIMS measurements. The multi‐energy ion implantation technique also appears to be a promising procedure for the production of EPMA‐suitable reference materials.     

A numerical method for the study of shear band propagation in soft rocks

This paper investigates the possibility of interpreting progressive shear failure in hard soils and soft rocks as the result of shear propagation of a pre‐existing natural defect. This is done through the application of the principles of fracture mechanics, a slip‐weakening model (SWM) being used to simulate the non‐linear zone at the tips of the discontinuity. A numerical implementation of the SWM in a computation method based on the boundary element technique of the displacement discontinuity method (DDM) is presented. The crack and the non‐linear zone at the advancing tip are represented through a set of elements, where the displacement discontinuity (DD) in the tangential direction is determined on the basis of a friction law. A residual friction angle is assumed on the crack elements. Shear resistance decreases on elements in the non‐linear zone from a peak value at the tip, which is characteristic of intact material, to the residual value. The simulation of a uniaxial compressive test in plane strain conditions is carried out to exemplify the numerical methodology. The results emphasize the role played by the critical DD on the mechanical behaviour of the specimen. A validation of the model is shown through the back analysis of some experimental observations. The results of this back analysis show that a non‐linear fracture mechanics approach seems very promising to simulate experimental results, in particular with regards to the shear band evolution pattern. Copyright © 2009 John Wiley & Sons, Ltd.     

Rapid Determination of Trace Element Compositions in Peridotites by LA‐ICP‐MS Using an Albite Fusion Method

A rapid sample preparation procedure is described to determine trace element compositions of peridotites using LA‐ICP‐MS. Peridotite powders were fused with albite in a molybdenum–graphite assembly to obtain homogeneous glasses. Best conditions for the fusion procedure (heating at 1500–1550 °C for 10–15 min with a sample‐to‐flux ratio of 1:2) were constrained with melting experiments on two USGS reference materials, PCC‐1 and DTS‐2B. Mass fractions of first series transition elements, Ba and Pb, in quenched glasses of PCC‐1 and DTS‐2B are consistent with published data within 10% RSD. Three spinel peridotite xenoliths from eastern China were analysed following both our method and conventional solution ICP‐MS. Compared with solution ICP‐MS, the relative deviations of our method for most elements were within 10%, while for the REE, Ta, Pb, Th and U, the relative deviations were within 20%. In particular, volatile elements (e.g., Pb and Zn) are retained in the glass. Compared with conventional wet chemistry digestion, our method is faster. Additional advantages are complete sample fusion, especially useful for samples with acid‐resistant minerals (spinel and rutile), and long‐term conservation of glasses allowing unlimited repeated measurements with microbeam techniques. The same approach can be used for analyses of other mantle rocks, such as eclogites and pyroxenites.     

Granite rock fragmentation at percussive drilling – experimental and numerical investigation

The aim of this study is to numerically model the fracture system at percussive drilling. Because of the complex behavior of rock materials, a continuum approach is employed relying upon a plasticity model with yield surface locus as a quadratic function of the mean pressure in the principal stress space coupled with an anisotropic damage model. In particular, Bohus granite rock is investigated, and the material parameters are defined based on previous experiments. This includes different tests such as direct tension and compression, three‐point bending, and quasi‐oedometric tests to investigate the material behavior at both tension and confined compression stress states. The equation of motion is discretized using a finite element approach, and the explicit time integration method is employed. Edge‐on impact tests are performed, and the results are used to validate the numerical model. The percussive drilling problem is then modeled in 3D, and the bit‐rock interaction is considered using contact mechanics. The fracture mechanism in the rock and the bit penetration‐ resisting force response are realistically captured by the numerical model. Copyright © 2013 John Wiley & Sons, Ltd.     

A superposition scheme to obtain fundamental boundary element solutions in multi‐layered elastic media

A superposition scheme is proposed to obtain a fundamental solution for boundary elements in multi‐layered elastic media. A three‐layered elastic region is obtained by superposing two sets of bonded half‐planes and subtracting one infinite plane. Therefore, the solution for an element in a layered media can be expressed in terms of bonded half‐plane solutions and an infinite‐plane solution. The major advantages of this superposition scheme are: (1) it is unnecessary to introduce elements at the interface, (2) it can be extended to higher‐order element, and (3) it may be applicable to three dimensions easily. The accuracy and performance of the developed model is illustrated by two examples. For the problem of a pressurized two‐dimensional crack within a three‐layered system, the comparison with other numerical results shows the model is quite accurate and efficient. The model is also used for a study of a practical two‐dimensional mining problem in South Africa, i.e. stoping through a dyke with material properties different from the host rock. Copyright © 2000 John Wiley & Sons, Ltd.     

Two‐scale modeling of solute dispersion in unsaturated double‐porosity media: Homogenization and experimental validation

A two‐scale modeling of solute transport in double‐porosity (DP) media under unsaturated water flow conditions is presented. The macroscopic model was developed by applying the asymptotic homogenization method. It is based on theoretical and empirical considerations dealing with the orders of magnitude of characteristic quantities involved in the process. For this purpose a physical model that mimics the behavior of DP medium was built. The resulting two‐equation model relies on a coupling exchange term between micro‐ and macro‐porosity subdomains associated with local non‐equilibrium solute concentrations. The model was numerically implemented (Comsol Multiphysics^®) to simulate the macroscopic one‐dimensional physical process taking place into the porous medium of 3D periodic microstructure. A series of dispersion experiments of NaCl solution under unsaturated steady‐state flow conditions were performed. The experimental results were used first to calibrate the dispersion coefficient of the model, and second to validate it through two other independent experiments. The excellent agreement between the numerical simulations and the measurements of the time evolution of the non‐symmetrical breakthrough curves provides a proof of predictive capacity of the developed model. Copyright © 2010 John Wiley & Sons, Ltd.