Tomasz Hueckel

Uniqueness and localization—I. Associative and non-associative elastoplasticity

Abstract Localization of deformation into a planar band in the incremental response of elasto-plastic material is studied in the case of small strains and rotations. The critical hardening modulus for localization is given in an explicit form (uncoupled from the band normal) for an arbitrary rate independent non-associative plasticity. Loss of uniqueness of the response is investigated in terms of positiveness of the second order work density. Criteria for loss of second order work positiveness and localization are compared for plane stress and plane strain. In these cases, for the associative flow rule, the threshold for the second order work positiveness coincides with the threshold for shear band formation. This coincidence may not, however, occur if localization into splitting mode is attained.

Nonassociated and coupled flow rules of elastoplasticity for rock-like materials☆

Incremental elastoplastic stress-strain relations are studied which allow for non association of plastic strain rates with the (smooth) current yield surface (non-normality), and/or changing elastic moduli because of plastic deformations (elastoplastic coupling). These circumstances, often accompanied by strain/softening, are significant in various geotechnical media, particularly rocks. On the basis of a suitable description of the rate relations, various ranges of the hardening modulus are established and their distinct behavioural characteristics, such as rate response uniqueness and material stability (or lack thereof) are systematically studied and interpreted in mechanical terms. Specialization to the standard compression tests and for particular forms of constitutive laws is made. Similarities to and differences from the traditional associated flow rules of elastoplasticity are pointed out. (a) /TRRL/

An Improved Volume Measurement for Determining Soil Water Retention Curves

The complete determination of soil water retention curves requires the sample volume to be measured in order to calculate its void ratio and degree of saturation. During drying in the pressure plate apparatus, cracks often appear in the sample altering its deformation and evaporation patterns. Consequently, this causes a significant scatter in the volume measurement when using the volume displacement method. This paper proposes a simple method to avoid cracking, by limiting friction and adhesion boundary effects, to allow for unrestrained shrinkage of the sample. Such modification of the technique decreases the measurement error by a factor of three.

Chemo-mechanical coupling in saturated porous media: elastic-plastic behaviour of homoionic expansive clays

Chemically active saturated homoionic clays are considered in a two-phase framework. The solid phase contains the clay particles, absorbed water and salt. The fluid phase, or pore water, contains free water and salt. Water, and possibly salt, can transfer between the two phases. In addition free water may diffuse through the porous medium. A global understanding of the phenomena involved, namely deformation, transfer and diffusion, is proposed. Emphasis is laid on the chemo-mechanical constitutive equations in an elastic–plastic setting. Elastic chemo-mechanical coupling is introduced through a potential, in such a way that the tangent poro-elasticity matrix remains symmetric. Material parameters needed to quantify the coupling are calibrated from specific experiments available in the recent literature. The elasto-plastic behaviour aims at reproducing qualitatively and quantitatively the typical experimental responses observed on almost pure Na-Montmorillonite clays during chemical and mixed chemo-mechanical loadings. Increase of the salinity of pore water at a constant confinement stress leads to a volume decrease, so-called chemical consolidation. Subsequent exposure to a distilled water solution produces swelling: however, the latter is smaller than the chemical consolidation so that the chemical loading cycle results in a net contractancy, the amount of which increases with the confinement. In fact, plastic yielding takes place at low salinities of pore water, and when it stops, chemical preconsolidation is generated. Natural clays which contain cations of different species are considered in a companion paper, Gajo et al. [Int. J. Solids Struct., this issue], as they require to account for electro-chemo-mechanical couplings. � 2002 Published by Elsevier Science Ltd.

CHEMO-PLASTICITY OF CLAYS SUBJECTED TO STRESS AND FLOW OF A SINGLE CONTAMINANT

SUMMARY Isothermal chemo-elasto-plasticity of clays is discussed, to describe strains induced in clay by permeation of it with a low dielectric constant organic contaminant, in the presence of stress. The strain is crucial in controlling permeability changes in chemically a⁄ected clay barriers of landfills and impoundments. The theory encompasses chemical softening or yield surface reduction, coeƒcient of chemical reversible expansion or contraction due to mass concentration increase, as well as chemical sensitivity of bulk plastic modulus. The experiments on chemistry and stress dependent permeability of Sarnia clay performed by Fernandez and Quigley (1985, 1991) are interpreted using this model. The numerical representations of the chemo-plastic softening function and the chemo-elastic strain function, as well as plastic bulk modulus sensitivity to concentration are evaluated for dioxane and ethanol. Specific requirements for the tests for chemo-plastic behavior of clays are discussed.

INCREMENTAL BOUNDARY VALUE PROBLEMS IN THE PRESENCE OF COUPLING OF ELASTIC AND PLASTIC DEFORMATIONS: A ROCK MECHANICS ORIENTED THEORY

Abstract In some elastoplastic systems (typically rocklike media) the elastic properties are affected by plastic yielding. This “coupling” phenomenon is dealt with in this paper in the context of the incremental theory of plasticity with nonassociated (lacking normality) flow laws. Some extremum properties and uniqueness conditions are given for solution of the rate problem. Stability conditions are established. The results achieved are equally applicable to media with nonassociative flow rules without coupling, with or without worksoftening, and are believed to be novel in this more traditional area. The results are cast into algebraic formulations for finite element models, in view of their practical applications.

Thermomechanical properties of deep argillaceous formations

Abstract A difficulty in the interpretation of mechanical and thermo-mechanical tests on specimens drawn from large argillaceous formations is the strong inhomogeneity of void ratio, clay minerals and carbonates content. In this paper a relationship is developed to link strength and the maximum preconsolidation stress to the initial void ratio and carbonate content. Compressibility is also correlated to carbonates. Thermal strains in drained and undrained conditions for a Spanish, a belgian and an Italian natural clay are compared. In the elastic state strains are comparable, while in the plastic range thermal strains are highest for the Belgian clay, lower in the Spanish cemented clay and lowest in the Italian clay, very stiff and cemented.

Chemo-Mechanical Consolidation of Clays: Analytical Solutions for a Linearized One-Dimensional Problem

Consolidation (and swelling) of clayey soils caused by change in chemistry of pore fluid is addressed. Such phenomena are caused by changes in the concentration of various species in the solution and result primarily from a stress-independent deformation of individual clusters, and from a mechanical weakening or strengthening of the clay solid matrix in the presence of stress. Second, transport of chemicals that involves concentration gradients induces additional driving forces of osmotic consolidation due to semipermeable membrane nature of clay. In this paper an extension of Terzaghis model of the mechanical consolidation to incorporate chemical loading of soil is proposed. A linearized model is used to solve analytically two one-dimensional problems of consolidation of a homogeneous layer simulating a landfill liner with drained or undrained boundaries. The numerical results show a strong dependence of distribution of pore pressure on the chemical load and chemically induced settlements of soil to be comparable to the mechanical ones.

Electro-chemo-mechanical couplings in saturated porous media: elastic-plastic behaviour of heteroionic expansive clays

Chemically active saturated clays containing several cations are considered in a two-phase framework. The solid phase contains the negatively charged clay particles, absorbed water and ions. The fluid phase, or pore water, contains free water and ions. Electroneutrality is ensured in both phases, which gives rise to electrical fields. Water and ions can transfer between the two phases. In addition, a part of free water diffuses through the porous medium. A global understanding of all phenomena, deformation, transfer, diffusion and electroneutrality, is provided. Emphasis is laid on the electro-chemo-mechanical constitutive equations in an elastic–plastic setting. Elastic chemo-mechanical coupling is introduced through a potential, in such a way that the tangent elastic stiffness is symmetric. Material parameters needed to estimate the coupling are calibrated from specific experiments available in the recent literature. The elastic–plastic behaviour aims at reproducing qualitatively and quantitatively typical experimental phenomena observed on natural clays during chemical and mixed chemo-mechanical loadings, including chemical consolidation and swelling already described in Int. J. Solids Structures (39 (10), 2773–2806) in the simpler context of Na-Montmorillonite clays. Crucially, the successive exposure of a clay to pore solutions with chemical content dominated by a cation already present in the clay or quasi-absent leads to dramatically different volume changes, in agreement with experimental data. � 2002 Elsevier Science Ltd. All rights reserved.

Desiccation cracking of soils

ABSTRACT The scope of this paper is to present the global mechanisms of soil desiccation, including drying shrinkage and cracking. The paper first reviews the basic processes that are beneath the word “desiccation”. Then the results of an experimental study of desiccation are presented, in which strains, suction, water content, degree of saturation and crack geometry are investigated. The results show that cracking initiates close to the onset of de-saturation. Insights into the micro-scale are proposed to explain this observation. A scenario for the processes leading to crack initiation is further established in terms of the macroscopic variables: an assessment of the stress building up is proposed, until a critical point at which the tensile strength is met. Desiccation crack pattern formation is finally discussed.