Ahmad Pouya

Elastoplastic deformation of porous media applied to the modelling of compaction at basin scale

Abstract For simulation and modelling of coupled phenomena occurring during basin evolution, the mechanical aspects of rock deformation are generally restricted to vertical compaction characterized by a simple relation between the effective vertical stress and the rock porosity. Elasto-plasticity leads to a more general formulation which, in principle, allows for the calculation of horizontal deformation and stress field. Various aspects of this application of continuum mechanics to the compaction of sedimentary rocks at basin scale are presented. Firstly, the problems of mechanical deformation and of fluid flow—or pressure evolution—are shown to be intimately coupled through the effective stress concept. The elasto-plastic Cam-Clay rheology is recalled as a satisfactory approach of the stress-strain relationship for fine-grained sediments. This gives the complete bases for numerical modelling of the hydro-mechanical problems related to sedimentary basin evolution. Secondly, two numerical codes which are of standard use in civil engineering problems are tentatively applied to basin modelling. The first code (CESAR) is a finite element one which fully takes into account the hydro-mechanical couplings. The slow sedimentation process, whereby the geological structure is progressively built, can be accounted for by incremental deposition of layers. In practice the computation is so time-consuming that only restricted simulation on existing sedimentary structure can be seriously considered. A second computer code (FLAC) based on finite difference method is then applied. Some special development makes it possible to account for the geometrical evolution (build-up) of a basin and some cases studies are presented to show the importance of lateral deformation during the development of a margin-type basin. However these possibilities were obtained at the expense of a fixed fluid pressure field and we did not succeed in coupling the hydraulical and mechanical computations. Thirdly, a simple incremental mechanical model is proposed for completely solving the coupled hydro-mechanical problem in the case of progressive sedimentation. A numerical solution is obtained in the 1-D case and gives results which are consistent with some published ones. Since it is 1-D, this solution offers only a few advantageous features at present. However generalization to several dimensions can be imagined.

Numerical Modelling of Steady-State Flow in 2D Cracked Anisotropic Porous Media by Singular Integral Equations Method

The equations governing plane steady-state flow in heterogeneous porous media containing curved-line intersecting cracks (Pouya and Ghabezloo in Transp Porous Media 84:511–532, 2010) and the potential solution obtained for these equations are considered here. The theoretical results are first completed for the mass balance at crack intersections points. Then, a numerical procedure based on a singular integral equations method is described concretely to derive this solution for cracked materials. Closed-form expressions of elementary integrals for special choice of collocation points lead to a very quick and easy numerical method. It is shown that this method can be applied efficiently to the study of the steady-state flow in cracked materials with anisotropic matrix permeability and a dense distribution of curved-line intersecting cracks. Some applications of this method to the permeability of cracked materials are given.

Mechanical behaviour of fine grained sediments: experimental compaction and three-dimensional constitutive model

Abstract The usual undimensional description of deformations of sediments, based on a phenomenological relationship between porosity and the vertical effective stress, does not give information about the horizontal stress and, moreover, is irrelevant for sedimentary structures in which deformation process is not only vertical. Modelling three-dimensional deformation processes in sedimentary basins requires a three-dimensional mechanical constitutive model for sediments. A special œdometric cell was conceived in G.3S. This cell allows the measurement of the lateral stress during œdometric compaction and so enables us to elaborate a three-dimensional model of mechanical behaviour. Four varieties of fine-grained sediments were studied by this cell in a large scale of strain and stresses. The modified Cam-Clay model was used for fitting the experimental data and it was shown that this model can reproduce the mechanical compaction of sediments up to 50 MPa of vertical effective stress (about 3 km burial depth), if its parameters are deduced from œdometric (zero lateral strain) data.

Microscale insight into the influence of humidity on the mechanical behavior of mudstones

The mechanical behavior of mudstones strongly depends on humidity. In this paper, we present some microstructural insights into this phenomenon gained from a microscale investigation using a novel experimental method. The experimental method consists of combined hydric and mechanical loading tests in environmental scanning electron microscopy, as well as full-field strain measurement by digital image correlation techniques. The sample is subjected to a stepwise wetting (21%, 80%, and 99% relative humidity); for each equilibrium moisture state, a uniaxial compression test is performed. The microscale observation reveals that humidity-induced changes in the mechanical behavior of mudstones are controlled by the deformation and microcracking upon wetting. With increasing relative humidity, expansion of pores causes the clay matrix to be softer. In addition, because of the reduction in shear modulus and the lessening of capillary effect, shear bands are prone to appear at a high humidity state. The microcracking upon wetting, which results in predamage of the material, also affects the mechanical behavior. Finally, the sample with more moisture exhibits a more ductile behavior that involves more pronounced microcracking at failure.

Micro-macro approach for the rock salt behaviour

Abstract Rock salt is considered as a pure aggregate of halite (mineral NaCl) crystals and its behaviour is investigated by a micro–macro approach. The behaviour of the polycrystalline aggregate is deduced from the properties of the constituent halite crystals. A model for the elastoplastic behaviour of halite crystal has been deduced from experimental data available in the literature. The basic equations of the micro–macro model for the polycrystalline medium and the calculation method are then presented and the elastoplastic behaviour of rock salt is investigated by this method. The hardening effects obtained for the polycrystal are found to be very different from those obtained for FCC metal polycrystals. The differences are explained as a consequence of differences of families of glide systems in these crystals. Finally, the internal stresses in the polycrystal are studied in order to elucidate the origin of cracking and damage of the rock salt.

Micro-Macro Analysis and Phenomenological Modelling of Salt Viscous Damage and Application to Salt Caverns

AbstractThis paper aims to gain fundamental understanding of the microscopic mechanisms that control the transition between secondary and tertiary creep around salt caverns in typical geological storage conditions. We use a self-consistent inclusion-matrix model to homogenize the viscoplastic deformation of halite polycrystals and predict the number of broken grains in a Representative Elementary Volume of salt. We use this micro-macro modeling framework to simulate creep tests under various axial stresses, which gives us the critical viscoplastic strain at which grain breakage (i.e., tertiary creep) is expected to occur. The comparison of simulation results for short-term and long-term creep indicates that the initiation of tertiary creep depends on the stress and the viscoplastic strain. We use the critical viscoplastic deformation as a yield criterion to control the transition between secondary and tertiary creep in a phenomenological viscoplastic model, which we implement into the Finite Element Method program POROFIS. We model a 850-m-deep salt cavern of irregular shape, in axis-symmetric conditions. Simulations of cavern depressurization indicate that a strain-dependent damage evolution law is more suitable than a stress-dependent damage evolution law, because it avoids high damage concentrations and allows capturing the formation of a damaged zone around the cavity. The modeling framework explained in this paper is expected to provide new insights to link grain breakage to phenomenological damage variables used in Continuum Damage Mechanics.

Simulation of the Unsaturated Excavation Damage Zone Around a Tunnel Using A Fully Coupled Damage-Plasticity Model

During tunnel excavation, stress redistribution produces plastic deformation and damage around the opening. Moreover, the surrounding soil can be either saturated or unsaturated. Suction has a significant influence on the mechanical behaviour of geomaterials. Depending on their stress state and on their moisture content, clay-based materials can exhibit either a ductile or a brittle behaviour. Plasticity leads to permanent strains and damage causes the deterioration of the soil elastic and hydraulic properties. The damage-plasticity model proposed in this work is formulated in terms of a damaged constitutive stress, defined from the principle of Bishops hydro-mechanical stress (for unsaturated conditions), and from the principle of damaged effective stress used in Continuum Damage Mechanics. The evolution laws are obtained by using the principle of strain equivalence. This hydro-mechanical damage-plasticity model was implemented in a Finite Element code. The excavation of a tunnel is simulated at different constant suctions. The results obtained illustrate the influence of suction on the development of plastic and damaged zones.

Determination of an equivalent continuum mechanical model for the fractured EDZ around underground galleries by homogenization

An equivalent continuum model (ECM) is proposed in order to represent the hydromechanical behaviour of the fractured excavation-damaged zone (EDZ) around deep underground galleries excavated in claystone. The fractures observed in these galleries show a regular trend that makes a possible elaboration of the ECM based on theoretical homogenization methods. The ECM that is first established for plane fracture surfaces is then extended to curved, conical shape fracture surfaces based on some simplification assumptions. Stress and displacement fields have been compared around the EDZ by using the ECM in a numerical simulation or by introducing the fractures individually as discontinuities in the model. The results show that although the size of the EDZ is too small compared with that of the representative elementary volume considered in homogenization approaches, the ECM obtained in this way seems to reproduce a well fractured EDZ behaviour.

Self-consistent micromechanical approach for damage accommodation in rock-like polycrystalline materials

In quasi-brittle polycrystalline materials, damage by cracking or cleavage dominates plastic and viscous deformation. This paper proposes a micromechanical model for rock-like materials, incorporating the elastic-damage accommodation of the material matrix, and presents an original method to solve the system of implicit equations involved in the formulation. A self-consistent micromechanical approach is used to predict the anisotropic behavior of a polycrystal in which grain inclusions undergo intragranular damage. Crack propagation along planes of weakness with various orientation distributions at the mineral scale is modeled by a softening damage law and results in mechanical anisotropy at the macroscopic scale. One original aspect of the formulated inclusion–matrix model is the use of an explicit expression of Hill’s tensor to account for matrix ellipsoidal anisotropy. To illustrate the model capabilities, a uniaxial compression test was simulated for a variety of polycrystals made of two types of mineral inclusions with each containing only one plane of weakness. Damage always occurred in only one mineral type: the damaging mineral was that with a smaller shear modulus (respectively higher bulk modulus) when bulk modulus (respectively shear modulus) was the same. For two minerals with the same shear moduli but different bulk moduli, the maximum damage in the polycrystal under a given load was obtained at equal mineral fractions. However, for two minerals with different shear moduli, the macroscopic damage was not always maximum when the volume fraction of two minerals was the same. When the weakness planes’ orientations in the damaging mineral laid within a narrow interval close to the loading direction, the macroscopic damage behavior was more brittle than when the orientations were distributed over a wider interval. Parametric studies show that upon proper calibration, the proposed model can be extended to understand and predict the micro–macro behavior of different types of quasi-brittle materials.

On Elastoplastic Damage Modelling in Unsaturated Geomaterials

In the context of nuclearwaste disposal, the modelling of the behaviour of host rocks and soils still needs improvement.Unsaturated porous geomaterials exhibit particular behaviourwhen exposed to suction. Their non-linear behaviour may result fromtwo different processes, plasticity which induces irreversible strains and damage which causes a deterioration of their elastic properties. Many elasto-plastic models are now available for unsaturated soils, most of them based on the Barcelona Basic Model (Alonso et al., 1990). They take into consideration a certain number of issues linkedwith the nature of unsatured soils.Models coupling damage and plasticity have also been proposed for continuous media. Since very few works have attempted to connect these two distinct fields, unsaturated soil mechanics and continuum damage mechanics, thiswork focuses on themain issues related to the development of amodel coupling elasto-plasticity and damage for unsaturated porous media.