Analysis of the FEBEX multi‐barrier system including thermoplasticity of unsaturated bentonite

Deep geological repository involving a multibarrier system constitutes one of the most promising options for isolating high‐level radioactive waste from the human environment. To certify the efficiency of waste isolation, it is essential to understand the behaviour of confining geomaterial under a variety of environmental conditions. To this end, results from a near‐to‐real experiment, the full‐scale engineered barriers in situ experiment, are studied by means of a thermo–hydro–mechanical finite element approach, including a consistent thermoplastic constitutive model for unsaturated soils. Laboratory tests are simulated to calibrate model parameters. The results of the numerical simulations are compared with sensor measurements and show the ability of the model to reproduce the main behavioural features of the system. The influence of the hysteretic and temperature‐dependent retention of water on the mechanical response is exhibited. Finally, those results are interpreted in the light of thermoplasticity of unsaturated soils, which reveals the highly coupled and non‐linear characters of the processes encountered. Copyright © 2011 John Wiley & Sons, Ltd.     

CASM: a unified state parameter model for clay and sand

The purpose of this paper is to present a simple, unified critical state constitutive model for both clay and sand. The model, called CASM (Clay And Sand Model), is formulated in terms of the state parameter that is defined as the vertical distance between current state (v, p′) and the critical state line in v–ln p′ space. The paper first shows that the standard Cam-clay models (i.e. the original and modified Cam-clay models) can be reformulated in terms of the state parameter. Although the standard Cam-clay models prove to be successful in modelling normally consolidated clays, it is well known that they cannot predict many important features of the behavior of sands and overconsolidated clays. By adopting a general stress ratio-state parameter relation to describe the state boundary surface of soils, it is shown that a simple, unified constitutive model (CASM) can be developed for both clay and sand. It is also demonstrated that the standard Cam-clay yield surfaces can be either recovered or approximated as special cases of the yield locus assumed in CASM. The main feature of the proposed model is that a single set of yield and plastic potential functions has been used to model the behaviour of clay and sand under both drained and undrained loading conditions. In addition, it is shown that the behaviour of overconsolidated clays can also be satisfactorily modelled. Simplicity is a major advantage of the present state parameter model, as only two new material constants need to be introduced when compared with the standard Cam-clay models. © 1998 John Wiley & Sons, Ltd.     

A water retention model accounting for void ratio changes in double porosity clays

This paper presents a constitutive model that predicts the water retention behaviour of compacted clays with evolving bimodal pore size distributions. In line with previous research, the model differentiates between the water present inside the saturated pores of the clay aggregates (the microstructure) and the water present inside the pores between clay aggregates (the macrostructure). A new formulation is then introduced to account for the effect of the macrostructural porosity changes on the retention behaviour of the soil, which results in a consistent evolution of the air-entry value of suction with volumetric deformations. Data from wetting tests on three different active clays (i.e. MX-80 bentonite, FEBEX bentonite, and Boom clay), subjected to distinct mechanical restraints, were used to formulate, calibrate, and validate the proposed model. Results from free swelling tests were also modelled by using both the proposed double porosity model and a published single porosity model, which confirmed the improvement in the predictions of degree of saturation by the present approach. The proposed retention model might be applied, for example, to the simulation of the hydromechanical behaviour of engineered bentonite barriers in underground nuclear waste repositories, where compacted active clays are subjected to changes of both suction and porosity structure under restrained volume conditions.

     

Modelling chemo‐hydro‐mechanical behaviour of unsaturated clays: a feasibility study

Effective capabilities of combined chemo‐elasto‐plastic and unsaturated soil models to simulate chemo‐hydro‐mechanical (CHM) behaviour of clays are examined in numerical simulations through selected boundary value problems. The objective is to investigate the feasibility of approaching such complex material behaviour numerically by combining two existing models. The chemo‐mechanical effects are described using the concept of chemical softening consisting of reduction of the pre‐consolidation pressure proposed originally by Hueckel (Can. Geotech. J. 1992; 29 :1071–1086; Int. J. Numer. Anal. Methods Geomech. 1997; 21 :43–72). An additional chemical softening mechanism is considered, consisting in a decrease of cohesion with an increase in contaminant concentration. The influence of partial saturation on the constitutive behaviour is modelled following Barcelona basic model (BBM) formulation (Géotech. 1990; 40 (3):405–430; Can. Geotech. J. 1992; 29 :1013–1032). The equilibrium equations combined with the CHM constitutive relations, and the governing equations for flow of fluids and contaminant transport, are solved numerically using finite element. The emphasis is laid on understanding the role that the individual chemical effects such as chemo‐elastic swelling, or chemo‐plastic consolidation, or finally, chemical loss of cohesion have in the overall response of the soil mass. The numerical problems analysed concern the chemical effects in response to wetting of a clay specimen with an organic liquid in rigid wall consolidometer, during biaxial loading up to failure, and in response to fresh water influx during tunnel excavation in swelling clay. Copyright © 2005 John Wiley & Sons, Ltd.     

Assessment of using borehole-closure data to determine the constitutive behavior of salt

Borehole closure data have often been used to determine the constitutive behaviour of rock salt. This is an inverse problem and analysis of the data is confused by the fact that borehole closure is a structural response that does not uniquely determine constitutive behaviour since both the stress and deformation depend on the constitutive behaviour. This application brief assesses the conclusion of a recent study that the transient power law, ? = K τ^mtⁿ, which includes no term to account for steady-state deformation, is a better constitutive model for salt than are models that account for steady-state straining, and that an empirical model developed from the borehole closure data could be extrapolated to give conservative predictions of long-term closure of single or widely spaced openings.     

Effect of suction on the mechanical behaviour of iron ore rock

The effect of suction on the behaviour of iron ore has been studied from both physical and mechanical points of view. The porosity and the suction phenomena have been analysed using different experimental techniques. Uniaxial compressive tests on partially saturated samples have shown that the suction is responsible for strength and cohesion improvement. Considering the theory of partially saturated porous soils of Coussy and Dangla (Mécanique des sols non saturés (2002 edn). Hermès Science: 2002; 390), we have proposed a constitutive law for partially saturated iron ore. The real increase in the apparent cohesion due to the capillary attraction forces is overestimated if the yield function is written in terms of effective stresses. The effect of the capillary cohesion has been modelled with a function in the expression of the apparent cohesion of the yield function. The effect of suction on the mechanical behaviour has been represented in the effective stresses space and in the total stresses space like the Alonso model (Géotechnique 1990; 40 :405–430). Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical modelling of lumpy clay landfill

Two trial motorway embankments built on a landfill consisting of clayey lumps were monitored over the period of 3 and 5 years, respectively. The subsoil of the embankment was instrumented by hydrostatic levelling profiles, pore pressure transducers and depth reference points installed in boreholes. An advanced constitutive model for clays (hypoplastic model for clays with meta‐stable structure) was used for numerical modelling of both case histories. Basic hypoplastic model for clays was calibrated using isotropic compression tests and triaxial compression tests on reconstituted clay. Three additional model parameters describing the effects of lumpy structure were calibrated using oedometer tests on specimens prepared from scaled‐down lumpy material (material with smaller size of clay lumps). The performance of the model was evaluated by comparison with the results of the centrifuge model of self‐weight consolidated landfill. Finally, the hypoplastic model was used for simulation of both trial embankments and the results were compared with in situ measurements. The degradation of the lumpy structure of the upper layer of the in situ landfill due to weathering was back analysed using monitoring data. Copyright © 2010 John Wiley & Sons, Ltd.     

On incremental non‐linearity in granular media: phenomenological and multi‐scale views (Part I)

On the basis of fundamental constitutive laws such as elasticity, perfect plasticity, and pure viscosity, many elasto‐viscoplastic constitutive relations have been developed since the 1970s through phenomenological approaches. In addition, a few more recent micro‐mechanical models based on multi‐scale approaches are now able to describe the main macroscopic features of the mechanical behaviour of granular media. The purpose of this paper is to compare a phenomenological constitutive relation and a micro‐mechanical model with respect to a basic issue regularly raised about granular assemblies: the incrementally non‐linear character of their behaviour. It is shown that both phenomenological and micro‐mechanical models exhibit an incremental non‐linearity. In addition, the multi‐scale approach reveals that the macroscopic incremental non‐linearity could stem from the change in the regime of local contacts between particles (from plastic regime to elastic regime) in terms of the incremental macroscopic loading direction. Copyright © 2005 John Wiley & Sons, Ltd.     

Simulation of cement-improved clay structures with a bonded elasto-plastic model: A practical approach

Engineering practice has usually dealt with the treated soil bodies using simplistic constitutive models (e.g. elastic perfectly-plastic Mohr–Coulomb). In this paper, a more refined bonded elasto-plastic model is here applied, with emphasis on the ease of calibration. Empirical studies have identified the ratio of cement content to the cured mixture void ratio as a controlling variable for mechanical response. This observation is elaborated upon to show that measuring porosity and unconfined compressive strength is enough to initialize the state variables of a bonded elasto-plastic model. Data from cement-improved Bangkok clay is employed to illustrate and validate the calibration procedure proposed. The structure-scale consequences of the constitutive model choice for the soil–cement are explored through the parametric analysis of an idealized excavation problem. A treated soil–cement slab is characterized by increasing cement contents in the clay–cement mixture. Two sets of parametric analysis are run characterizing the clay–cement either with a linear elastic-perfectly plastic model or with the bonded elasto-plastic model. The same values of unconfined compressions strength (UCS) are specified for the two models to make comparisons meaningful. Results from both series of analysis are compared highlighting the differences in predicted behaviour of the retaining wall and the excavation stability.     

Stress-path dependent behavior of a weathered clay crust

Triaxial compression and oedometer consolidation tests are commonly performed to evaluate the strength and deformation behavior of soils. However, in the field, the stress paths imposed by various engineering works may deviate from the stress paths conventionally used in laboratory tests. Moreover, the stress-paths followed by different soil elements under a foundation are different. To obtain representative soil parameters, the laboratory stress path should be similar to that followed in the field. In this study, a significant number of stress-path triaxial tests, with stress probes in various directions, have been conducted to study the stress-path dependent behavior of an overconsolidated weathered crust of Champlain clay in Eastern Ontario. Both undrained and drained tests have been conducted for samples isotropically consolidated to the in situ vertical stress and anisotropically consolidated to in situ state of stress. The yield locus of the clay crust has been defined. It has been observed that the strength-deformation and yielding behavior of this weathered clay crust highly depends on the stress-path as well as on the in situ stress history.     

Experimental study and constitutive modelling of elasto‐plastic damage in heat‐treated mortar

This study investigates the effect of a heat‐treatment upon the thermo‐mechanical behaviour of a model cement‐based material, i.e. a normalized mortar, with a (w/c) ratio of 0.5. First, a whole set of varied experimental results is provided, in order to either identify or validate a thermo‐mechanical constitutive model, presented in the second paper part. Experimental responses of both hydraulic and mechanical behaviour are given after different heating/cooling cycling levels (105, 200, 300, 400^°C). The reference state, used for comparison purposes, is taken after mass stabilization at 60^°C. Typical uniaxial compression tests are provided, and original triaxial deviatoric compressive test responses are also given. Hydraulic behaviour is identified simultaneously to triaxial deviatoric compressive loading through gas permeability K_gas assessment. K_gas is well correlated with volumetric strain evolution: gas permeability increases hugely when ε_v testifies of a dilatant material behaviour, instead of contractile from the test start. Finally, the thermo‐mechanical model, based on a thermodynamics approach, is identified using the experimental results on uniaxial and triaxial deviatoric compression. It is also positively validated at residual state for triaxial deviatoric compression, but also by using a different stress path in lateral extension, which is at the origin of noticeable plasticity. Copyright © 2009 John Wiley & Sons, Ltd.     

Modelling the behaviour of an embankment on soft clay with different constitutive models

The paper investigates the effect of constitutive models on the predicted response of a simplified benchmark problem, an embankment on soft soil. The soft soil is assumed to have the properties of POKO clay from Finland and five different constitutive models are used to model the deposit. Two of the models are isotropic models, i.e. the Modified Cam Clay model and the Soft‐Soil model. The other models are recently proposed constitutive models that account for plastic anisotropy. The S‐CLAY1 and S‐CLAY1S models are embedded in a standard elasto‐plastic framework and account for anisotropy via a rotational hardening law. In addition, the S‐CLAY1S model accounts for bonding and destructuration. In contrast, the Multilaminate Model for Clay (MMC) accounts for plastic anisotropy by utilizing so‐called multilaminate framework. The results of numerical simulations show that accounting for anisotropy results in notable differences in the predicted settlements and horizontal movements compared to the predictions using the isotropic models. There are also significant differences in the K₀ predictions by the different constitutive models and this has a significant impact on the results. Copyright © 2006 John Wiley & Sons, Ltd.     

F. E. analysis of field consolidation curves obtained with the modified borehole shear device (BHSD)

A modified version of the bore hole sheat device (BHSD) was used to obtain field consolidation curves in a soft sensitive clay. The Porewater pressure dissipation was monitored at the centre of one of the shear plates. This paper describes briefly the in situ device employed and demonstrates the basic features of the linearelastic F. E. program ‘SOL’. A detailed study is made to simulate the field behaviour with the finite element approach. Comparisons are made between the field and analytical consolidation behaviour. Difficulties in predicting the value of the coefficient of consolidation of a sensitive clay using the BHSD consolidation curves are discussed.     

Finite element analysis of consolidation of layered clay soils using an elastic visco-plastic model

This paper presents a general one-dimensional (1-D) finite element (FE) procedure for a highly non-linear 1-D elastic visco-plastic (1-D EVP) model proposed by Yin and Graham for consolidation analysis of layered clay soils. In formulating the 1-D FE procedure, a trapezoidal formula is used to avoid the unsymmetry of the stiffness matrix for a Newton (modified Newton) iteration scheme. Unlike many other 1-D FE approaches in which the initial in situ stresses (or stress/strain states) are considered indirectly or even not considered, the initial in situ stress/strain states are taken into account directly in this paper. The proposed FE procedure is used for analysis of 1-D consolidation of a clay with published test results in the literature. The FE modelling results are in good agreement with the measured results. The FE model and procedure is then used to analyse the consolidation of a multi-layered clay soils with a parametric study on the effects of the variations of creep parameters in Yin and Graham's 1-D EVP model. It is found that the creep parameters ψ/V and t₀ have significant influence on the compression and porewater pressure dissipation. For some boundary conditions, changes of parameters in one layer will have some effects on the consolidation behaviour of another layer due to the different consolidation rates. Finally, the importance of initial stress/strain states is illustrated and discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

THM analysis of a large‐scale heating test incorporating material fabric changes

Engineered barriers are basic elements in the design of repositories for the isolation of high‐level radioactive waste. This paper presents the thermo‐hydro‐mechanical (THM) analysis of a clay barrier subjected to heating and hydration. The study focuses on an ongoing large‐scale heating test, at almost full scale, which is being carried out at the CIEMAT laboratory under well‐controlled boundary conditions. The test is intensely instrumented and it has provided the opportunity to study in detail the evolution of the main THM variables over a long period of time. Comprehensive laboratory tests carried out in the context of the FEBEX and NF‐PRO projects have allowed the identification of the model parameters to describe the THM behaviour of the compacted expansive clay. A conventional THM approach that assumes the swelling clay as a single porosity medium has been initially adopted to analyse the evolution of the test. The model was able to predict correctly the global THM behaviour of the clay barrier in the short term (i.e. for times shorter than three years), but some model limitations were detected concerning the prediction of the long‐term hydration rate. An additional analysis of the test has been carried out using a double structure model to describe the actual behaviour of expansive clays. The double structure model explicitly considers the two dominant pore levels that actually exist in the FEBEX bentonite and it is able to account for the evolution of the material fabric. The simulation of the experiment using this enhanced model provides a more satisfactory reproduction of the long‐term experimental results. It also contributes to a better understanding of the observed test behaviour and it provides a physically based explanation for the very slow hydration of the barrier. Copyright © 2011 John Wiley & Sons, Ltd.     

Theoretical investigation of the effects of consolidation on contaminant transport through clay barriers

Consolidation of clayey contaminant barriers such as landfill liners has been postulated as a cause of early breakthrough of contaminants. In this paper we theoretically investigate this proposition. For this purpose a sophisticated one‐dimensional, large‐deformation model of coupled mechanical consolidation and solute transport is employed. This new model is a generalization of existing coupled consolidation and solute transport models described in the literature. It takes into account both non‐linearities in geometry as well as constitutive relations. The latter relate the compressibility, hydraulic conductivity and coefficient of effective diffusivity to the deformation of the soil. The model is applied to a case study of a clay liner and geomembrane system. Results obtained from numerical solution of the model equations are compared with those from various simplified models, including a ‘diffusion only’ (i.e. a rigid soil) model traditionally used in contaminant barrier design. For barriers incorporating low compressibility soils (as for many well compacted clays), there is little difference between contaminant transit (i.e. breakthrough) times predicted by the two models. However, for contaminant barriers incorporating more compressible soils, consolidation is shown to significantly accelerate transport. These results indicate the potential importance of accounting for the effects of soil consolidation and highlight the limitations of existing models when modelling solute transport through composite barriers utilizing soft soils. Based on these limited results, we suggest a possible way of taking into account soil consolidation using simplified models. Copyright © 2008 John Wiley & Sons, Ltd.     

Critical issues in modelling the long-term hydro-thermomechanical performance of natural clay barriers

Performance assessment of deep repositories for heat-generating radioactive waste requires the capability of predicting reliably the evolution of the system during a time period commensurate with the hazardous life of the waste. In many repository designs clay barriers represent important elements of the waste isolation system.

In order to provide reasonable assurance that clay barriers will ensure long-term waste isolation, it is essential to understand their behaviour under a variety of conditions. Due to the variability of argillaceous materials, to the complexity of the phenomena that might take place in a waste repository and to the longevity of the required isolation, an adequate understanding of the behaviour and the capability to model the evolution of the clay barriers are not easy tasks. The factors that need to be understood and modelled include stress evolution, long-term strain or creep, thermal effects on solid skeleton, on interstitial fluids and on mineralogy. The difficulty of the task is increased by the facts that many effects are coupled, that their rates must be extremely low, in order to be realistic, and that the time period to be modelled defies the possibility of direct experimental observation. Several critical issues are identified and discussed briefly, such as: constitutive law to describe the thermo-mechanical behaviour of the clay skeleton, modelling of the fluid phase in clays and its response to heating, thermal fracturing and healing. Strategies are suggested for a rational approach to the experimental investigation of some relevant processes. The study of suitable natural analogues, for example the thermo-metamorphic halo occurring at Orciatico in Tuscany, could provide valuable insights in the thermal effects of heating clay barriers. It is conceivable that models describing a variety of relevant phenomena, such as dehydration, fracturing and permeability changes could be tested through the study of the Orciatico analogue.

In the end performance assessments of clay barriers would benefit through improvements in modelling: this would involve progress in understanding the basic phenomena and their coupled nature, improved conceptual and mathematical models and increased reliability for their calibration/validation. The improved understanding of phenomena requires additional experimental activities on various levels: molecular, microscopic, macroscopic, medium scale and in situ.     

On overestimation of displacements in numerical calculation of zoned dams

Overestimation of displacements in numerical calculations can occur if some requirements are not met by the constitutive relations. Along with consideration for small strain behaviour of soils¹ the stiffening effects of unloading in shear should be taken into account. The latter problem is analysed in the paper using embankment dams as a typical example. Strain and stress paths in their cores and shells were derived from field measurement results and frequent path direction changes during seemingly monotonic loading process were discovered. Proportional loading test results of isotropically and anisotropically consolidated sand allowed interpretation of the in situ paths by the incremental theory of plasticity and distinction between the sections where unloading and reloading in shear develop. Furthermore, the analysis of these tests showed a marked stiffening of the soil due to unloading as well as neutral loading in shear. The strain redistribution due to material inhomogeneity, either inherent or introduced by the loading process, was identified as a common reason for the frequent occurrence of this phenomenon. Consequently, overestimations in displacement calculations can be brought about by neglecting this important effect by the constitutive model used. Accordingly, the unit response envelopes of some typical constitutive laws have been checked from this special point of view, and the models properly describing this phenomenon selected.     

Cavity expansion in unsaturated soils exhibiting hydraulic hysteresis considering three drainage conditions

Cavity expansion theory assists in the interpretation of in situ tests including the cone penetration test and pressuremeter test. In this paper, a cavity expansion analysis is presented for unsaturated silty sand exhibiting hydraulic hysteresis. The similarity technique is used in the analysis. The soil stress–strain behaviour is described by a bounding surface plasticity model. Results of oedometric compression tests, isotropic compression tests and triaxial shear tests for both saturated and unsaturated states are used to calibrate the model. The void ratio, suction, degree of saturation and effective stress are fully coupled in the analysis. The influence of where the initial hydraulic state is located on the soil–water characteristic curve on the cavity wall pressure is investigated and found to be significant. Also, the effects of three different drainage conditions (constant suction, constant moisture content and constant contribution of suction to the effective stress) on cavity wall pressure are studied. It is found that the drainage condition in which the contribution of suction to the effective stress is constant offers a good approximation to the other two. This may simplify interpretation of in situ tests. When testing occurs quickly, meaning a constant moisture content condition prevails, a constant contribution of suction condition can be assumed without loss of significant accuracy. The contribution of suction assumed in the interpretation can be taken as being equal to the in situ value, although this discovery may not be applicable to all soil types, constitutive models and soil–water characteristic curves. Copyright © 2015 John Wiley & Sons, Ltd.