Implicit integration under mixed controls of a breakage model for unsaturated crushable soils

This paper discusses a series of stress point algorithms for a breakage model for unsaturated granular soils. Such model is characterized by highly nonlinear coupling terms introduced by breakage‐dependent hydro‐mechanical energy potentials. To integrate accurately and efficiently its constitutive equations, specific algorithms have been formulated using a backward Euler scheme. In particular, because implementation and verification of unsaturated soil models often require the use of mixed controls, the incorporation of various hydro‐mechanical conditions has been tackled. First, it is shown that the degree of saturation can be replaced with suction in the constitutive equations through a partial Legendre transformation of the energy potentials, thus changing the thermomechanical state variables and enabling a straightforward implementation of a different control mode. Then, to accommodate more complex control scenarios without redefining the energy potentials, a hybrid strategy has been used, combining the return mapping scheme with linearized constraints. It is shown that this linearization strategy guarantees similar levels of accuracy compared with a conventional strain–suction‐controlled implicit integration. In addition, it is shown that the use of linearized constraints offers the possibility to use the same framework to integrate a variety of control conditions (e.g., net stress and/or water‐content control). The convergence profiles indicate that both schemes preserve the advantages of implicit integration, that is, asymptotic quadratic convergence and unconditional stability. Finally, the performance of the two implicit schemes has been compared with that of an explicit algorithm with automatic sub‐stepping and error control, showing that for the selected breakage model, implicit integration leads to a significant reduction of the computational cost. Such features support the use of the proposed hybrid scheme also in other modeling contexts, especially when strongly nonlinear models have to be implemented and/or validated by using non‐standard hydro‐mechanical control conditions. Copyright © 2015 John Wiley & Sons, Ltd.     

Genealogy of hypoplasticity and barodesy

This article is an attempt at providing an insight into the development of hypoplasticity (including barodesy, which is a recent development of hypoplasticity) as a theory elaborated since 1977, when the first version was published by the first author, until present. The multiplicity of the many versions published since then is hard to overlook. This article presents a review and insight into the evolution of a theory and the struggle to formulate a satisfactory constitutive law. Among the many proposed versions, we focus on those ones that can be seen as changes of paradigm. Copyright © 2016 John Wiley & Sons, Ltd.     

A new bounding surface model for thermal cyclic behaviour

To accurately predict soil volume changes under thermal cycles is of great importance for analysing the performance of many earth structures such as the energy pile and energy storage system. Most of the existing thermo‐mechanical models focus on soil behaviour under monotonic thermal loading only, and they are not able to capture soil volume changes under thermal cycles. In this study, a constitutive model is proposed to simulate volume changes of saturated soil subjected to cyclic heating and cooling. Two surfaces are defined and used: a bounding surface and a memory surface. The bounding surface and memory surface are mainly controlled by the preconsolidation pressure (a function of plastic volumetric strain) and the maximum stress experienced by the soil, respectively. Under thermal cycles, the distance of the two surfaces and plastic modulus increase with an accumulation of plastic strain. By adopting the double surface concept, a new elastoplastic model is derived from an existing single bounding surface thermo‐mechanical model. Comparisons between model predictions and experimental results reveal that the proposed model is able to capture soil volume changes under thermal cycles well. The plastic strain accumulates under thermal cycles, but at a decreasing rate, until stabilization. Copyright © 2017 John Wiley & Sons, Ltd.     

Constitutive and numerical framework for modeling joints and faults in rock

A three‐dimensional constitutive model for joints is described that incorporates nonlinear elasticity based on volumetric elastic strain, and plasticity for both compaction and shear with emphasis on compaction. The formulation is general in the sense that alternative specific functional forms and evolution equations can be easily incorporated. A corresponding numerical structure based on finite elements is provided so that a joint width can vary from a fraction of an element size to a width that occupies several elements. The latter case is particularly appropriate for modeling a fault, which is considered simply to be a joint with large width. For small joint widths, the requisite equilibrium and kinematic requirements within an element are satisfied numerically. The result is that if the constitutive equation for either the joint or the rock is changed, the numerical framework remains unchanged. A unique aspect of the general formulation is the capability to handle either pre‐existing gaps or the formation of gaps. Representative stress–strain plots are given to illustrate both the features of the model and the effects of changes in values of material parameters. Copyright © 2015 John Wiley & Sons, Ltd.     

Generalized plasticity state parameter‐based model for saturated and unsaturated soils. Part 1: Saturated state

The behavior of granular materials is known to depend on its loose or dense nature, which in turns depends both on density and confining pressure. Many models developed in the past require the use of different sets of constitutive parameters for the same material under different confining pressures. The purpose of this paper is to extend a basic generalized plasticity model for sands proposed by Pastor, Zienkiewicz and Chan by modifying the main ingredients of the model flow—rule, loading–unloading discriminating direction and plastic modulus—to include a dependency on the state parameter. The proposed model is tested against the available experimental data on three different sands, using for each of them a single set of material parameters, finding a reasonably good agreement between experiments and predictions. Copyright © 2010 John Wiley & Sons, Ltd.     

Chemo‐mechanics of cemented granular solids subjected to precipitation and dissolution of mineral species

This paper studies the chemo‐mechanics of cemented granular solids in the context of continuum thermodynamics for fluid‐saturated porous media. For this purpose, an existing constitutive model formulated in the frame of the Breakage Mechanics theory is augmented to cope with reactive processes. Chemical state variables accounting for the reactions between the solid constituents and the solutes in the pore fluid are introduced to enrich the interactions among the microstructural units simulated by the model (i.e., grains and cement bonds). Two different reactive processes are studied (i.e., grain dissolution and cement precipitation), using the chemical variables to describe the progression of the reactions and track changes in the size of grains and bonds. Finally, a homogenization strategy is used to derive the energy potentials of the solid mixture, adopting probability density functions that depend on both mechanical and chemical indices. It is shown that the connection between the statistics of the micro‐scale attributes and the continuum properties of the solid enables the mathematical capture of numerous mechanical effects of lithification and chemical deterioration, such as changes in stiffness, expansion/contraction of the elastic domain, and development of inelastic strains during reaction. In particular, the model offers an interpretation of the plastic strains generated by aggressive environments, which are here interpreted as an outcome of chemically driven debonding and comminution. As a result, the model explains widely observed macroscopic signatures of geomaterial degradation by reconciling the energetics of the deformation/reaction processes with the evolving geometry of the microstructural attributes. Copyright © 2015 John Wiley & Sons, Ltd.     

Limitations of suction‐controlled triaxial tests in the characterization of unsaturated soils

Behavior of unsaturated soils is influenced by many factors, and the influences of these factors are usually coupled together. Suction‐controlled triaxial (SCTX) tests are considered to allow researchers to investigate influences of individual variables on unsaturated soils under specified stress path with controls of stresses, pore water, and air pressures. In the past 50 years, SCTX testing method has been established as a standard approach to characterize constitutive behavior of unsaturated soils. Most important concepts for modern unsaturated soil mechanics were developed upon results from the SCTX tests. Among these, one of the most important contributions in the constitutive modeling of elasto‐plastic behavior for unsaturated soils is the Barcelona basic model (BBM) proposed by Alonso et al. in 1990. The BBM successfully explained many features of unsaturated soils and received extensive acceptance. However, the SCTX tests are designed based upon the divide‐and‐conquer approach in which an implicit assumption is used: soil behavior is stress‐path independent. However, it is well‐established that unsaturated soil behavior is elasto‐plastic and stress‐path dependent. It is found that the SCTX tests in fact cannot control the stress path of an unsaturated soil during loading. This incapability, in combination with complicated loading/collapse behavior of unsaturated soils, makes the SCTX tests for characterizing unsaturated soil questionable. This paper discusses the limitations of the SCTX tests in the characterization of unsaturated soils. A possible solution to the problem was proposed based on a newly developed modified state surface approach. The discussions are limited for isotropic conditions. Copyright © 2015 John Wiley & Sons, Ltd.     

Elastoplastic model with loading memory surfaces (LMS) for monotonic and cyclic behaviour of geomaterials

A new elastoplastic model called loading memory surface based on the critical state concept and the multi‐surface framework is proposed for geomaterials. The model uses a hypoelastic formulation and two plastic mechanisms. The formulations of the model are made in three‐dimensional stress–strain space and work under both monotonic and cyclic loadings. A newly introduced formalism makes it possible to obtain the cyclic response directly from the monotonic loading one. This formalism gives a three‐dimensional generalization of the well‐known Masing rule. The model has been validated against test results of Hostun sand under several conditions: monotonic and cyclic, drained and undrained, tests in compression and in extension, and at different confining pressures and different densities. Copyright © 2014 John Wiley & Sons, Ltd.     

A numerical study of mechanical behavior of a cement paste under mechanical loading and chemical leaching

Based on relevant experimental data of a petroleum cement paste under mechanical loading and chemical leaching, an elastic‐plastic model is first proposed by taking into account plastic shearing and pore collapse. The degradation of mechanical properties induced by the chemical leaching is characterized by a chemical damage variable which is defined as the increase of porosity. Both elastic and plastic properties of the cement paste are affected by the chemical damage. The proposed model is calibrated from and applied to describe mechanical responses in triaxial compression tests respectively on sound and fully leached samples. In the second part, a phenomenological chemical model is defined to establish the relationship between porosity change and calcium dissolution process. The dissolution kinetics is governed by a diffusion law taking into account the variation of diffusion coefficient with calcium concentration. The chemical model is coupled with the mechanical model, and both are applied to describe mechanical response of cement paste samples subjected to progressive chemical leaching and compressive stresses. Comparisons between experimental data and numerical results are presented.     

Dynamic analysis of strain localization in water‐saturated clay using a cyclic elasto‐viscoplastic model

A computational framework is presented for dynamic strain localization and deformation analyses of water‐saturated clay by using a cyclic elasto‐viscoplastic constitutive model. In the model, the nonlinear kinematic hardening rule and softening due to the structural degradation of soil particles are considered. In order to appropriately simulate the large deformation phenomenon in strain localization analysis, the dynamic finite element formulation for a two‐phase mixture is derived in the updated Lagrangian framework. The shear band development is shown through the distributions of viscoplastic shear strain, the axial strain, the mean effective stress, and the pore water pressure in a normally consolidated clay specimen. From the local stress–strain relations, more brittleness is found inside the shear bands than outside of them. The effects of partially drained conditions and mesh‐size dependency on the shear banding are also investigated. The effect of a partially drained boundary is found to be insignificant on the dynamic shear band propagation because of the rapid rate of applied loading and low permeability of the clay. Using the finer mesh results in slightly narrower shear bands; nonetheless, the results manifest convergency through the mesh refinement in terms of the overall shape of shear banding and stress–strain relations. Copyright © 2013 John Wiley & Sons, Ltd.