Fluid driven transition from damage to fracture in anisotropic porous media - a multiscale XFEM approach

Copyright © 2019 SpringerIn this paper, a numerical method is proposed to simulate multiscale fracture propagation driven by fluid injection in transversely isotropic porous media. Intrinsic anisotropy is accounted for at the continuum scale, by using a damage model in which two equivalent strains are defined to distinguish mechanical behavior in the direction parallel and perpendicular to the layer. Nonlocal equivalent strains are calculated by integration, and are directly introduced in the damage evolution law. When the weighted damage exceeds a certain threshold, the transition from continuum damage to cohesive fracture is performed by dynamically inserting cohesive segments. Diffusion equations are used to model fluid flow inside the porous matrix and within the macro fracture, in which conductivity is obtained by Darcy's law and the cubic law, respectively. In the fractured elements, the displacement and pore pressure fields are discretized by using the XFEM technique. Interpolation on fracture elements is enriched with jump functions for displacements, and with level-set-based distance functions for fluid pressure, which ensures that displacements are discontinuous across the fracture, but that the pressure field remains continuous. After spatial and temporal discretization, the model is implemented in a Matlab code. Simulations are carried out in plane strain. The results validate the formulation and implementation of the proposed model, and further demonstrate that it can account for material and stress anisotropy

Transportation networks inspired by leaf venation algorithms

Copyright IoP publishingBiological systems have adapted to environmental constraints and limited resource availability. In the present study, we evaluate the algorithm underlying leaf venation (LV) deployment using graph theory. We compare the traffic balance, travel and cost efficiency of simply-connected LV networks to those of the fan tree and of the spanning tree. We use a Pareto front to show that the total length of leaf venations is close to optimal. Then we apply the LV algorithm to design transportation networks in the city of Atlanta. Results show that leaf-inspired models can perform similarly or better than computer-intensive optimization algorithms in terms of network cost and service performance, which could facilitate the design of engineering transportation networks

Retention and permeability properties of damaged porous rocks

International audienceThe objective of this research work is to model the influence of deformation and damage on the permeability and retention properties of cracked porous media. This is achieved thanks to the introduction of microscale information into a macroscopic damage model. To this end, the Pore Size Distribution (PSD) of the material is coupled to the mechanical behaviour of the rock. Changes to this distribution due to deformation and damage are modelled and then used to capture induced changes to the retention and permeability properties of partially saturated materials. Rock microstructure is characterized by the size distributions of natural pores and cracks, which are used to update intrinsic permeability with Hagen-Poiseuille flow equation and Darcy's law. The void space occupied by water is computed by integrating the pore size distributions of natural pores and cracks up to the capillary pore radius (r(sat)). Laplace equation is used to relate r(sat) to the capillary pressure. The paper explains how to update PSD parameters with the macroscopic variables (such as deformation and damage), and then how to update permeability and retention properties with the PSD parameters. Conventional triaxial compression tests are simulated under controlled capillary pressure and under controlled water content. The proposed model captures well the intrinsic permeability decrease associated to the elastic compression of the natural pores, followed by the permeability jump due to crack opening. The modeling framework can be adapted to any rock constitutive model, including thermo-hydro-chemo-mechanical couplings. Applications may be found in energy production, ore exploitation and waste management

Using a geo-mechanical damage model to assess permeability in cracked porous media: internal length parameter issues

Copyright © 2012 Begell House, Inc.DOI: dx.doi.org/10.1615/SpecialTopicsRevPorousMedia.v3.i1.60The THHMD model is a thermo-hydro-mechanical damage model dedicated to unsaturated rocks. The present article questions one of the postulates of the model's formulation, namely using the same Representative Elementary Volume (REV) to define the crack density tensor and to compute the damaged permeability. In this study a drained triaxial compression test is simulated by considering that the REV's dimension (noted b) is a flow internal length. We show that the length b can be used to scale the influence of damage on permeability. Secondly, a nuclear waste repository is modeled. Multiphase flow is studied in fractured porous bedrock subjected to heating. It is demonstrated that (1) the THHMD model is mesh-independent, (2) b can be considered as the homogenization scale necessary to define the damage field, and (3) the model can be improved by adding one internal length parameter in the formulation

DEM modelling of sequential fragmentation of zeolite granules under oedometric compression based on XCT observations

Copyright © 2019 Elsevier B.V.The objective of our research is to define a new Discrete Element Method (DEM) that can describe the processes involved in particle breakage and the resulting macroscopic behaviour of the particulate assembly, by directly observing and characterizing breakage mechanisms. To this aim, an oedometer compression test is performed on a dry granular assembly of zeolite, while acquiring 3D images of the specimen at several strain levels with an x-ray computed tomography device. We construct a DEM model that reproduces experimental observations, mainly: axial splitting is the main breakage mode; fragments are subjected to further breakage; very few fragments pass through the breakage plane. A fragment size limit is defined to reduce the computational cost associated with large numbers of breakage generations. We simulate the oedometer test for the same initial microstructure as in the lab test and with realistic particle mechanical properties, and compare the re-ults to the 3D images. The numerical results show that our proposed model can capture the size evolution, shape change and mechanical response of the tested specimens

A fully coupled damage-plasticity model for unsaturated geomaterials accounting for the ductile-brittle transition in drying clayey soils

International audienceThis paper presents a hydro-mechanical constitutive model for clayey soils accounting for damage-plasticity couplings. Specific features of unsaturated clays such as confining pressure and suction effects on elastic domain and plastic strains are accounted for. A double effective stress incorporating both the effect of suction and damage is defined based on thermodynamical considerations, which results in a unique stress variable being thermodynamically conjugated to elastic strain. Coupling between damage and plasticity phenomena is achieved by following the principle of strain equivalence and incorporating the double effective stress into plasticity equations. Two distinct criteria are defined for damage and plasticity, which can be activated either independently or simultaneously. Their formulation in terms of effective stress and suction allows them to evolve in the total stress space with suction and damage changes. This leads to a direct coupling between damage and plasticity and allows the model to capture the ductile/brittle behaviour transition occurring when clays are drying. Model predictions are compared with experimental data on Boom Clay, and the flexibility of the model is illustrated by presenting results of simulations in which either damage or plasticity dominates the coupled behaviour

Fabric-enriched Modeling of Anisotropic Healing induced by Diffusion in Granular Salt

This study aims to model anisotropic damage (i.e. increase of porosity and loss of stiffness) and healing (i.e. recovery of stiffness) in salt rock subject to microcrack initiation, propagation, and rebonding. We introduce enriched fabric tensors in a Continuum Damage Mechanics model to link micro-crack evolution with macroscopic deformation rates. We carry out creep tests on granular salt assemblies to infer the form of fabric descriptors. We use moments of probability of fabric descriptors to find relationships between microstructural and phenomenological variables. Creep processes in salt include glide, cross-slip, diffusion, and dynamic recrystallization. We assume that healing is predominantly governed by diffusive mass transfer. We model the corresponding crack cusp propagation on grain faces by means of a two-dimensional diffusion equation. We calibrate this grainscale healing model against experimental measures of crack cusp propagation distance. We simulate the opening, closure and rebonding of three orthogonal families of micro-cracks during a compression-tension loading cycle. Multi-scale model predictions illustrate the evolution of stiffness, deformation, and crack geometry during the anisotropic damage and healing process, and highlight the increased healing efficiency with time. We expect that the proposed modeling approach will provide more precise and reliable performance assessments on geological storage facilities in salt rock

Thermo-Hydro-Mechanical Modeling of Damage in Unsaturated Porous Media: Theoretical Framework and Numerical Study of the EDZ

Copyright © 2011 John Wiley & Sons, Ltd.DOI: dx.doi.org/10.1002/nag.1005The damage model presented in this article (named ‘THHMD’ model) is dedicated to non-isothermal unsaturated porous media. It is formulated by means of three independent strain state variables, which are the thermodynamic conjugates of net stress, suction and thermal stress. The damage variable is a second-order tensor. Stress/strain relationships are derived from Helmholtz free energy, which is assumed to be the sum of damaged elastic potentials and ‘crack-closure energies’. Damage is assumed to grow with tensile strains due to net stress, with pore shrinkage due to suction and with thermal dilatation. Specific conductivities are introduced to account for the effects of cracking on the intensification and on the orientation of liquid water and vapor flows. These conductivities depend on damage and internal length parameters. The mechanical aspects of the THHMD model are validated by comparing the results of a triaxial compression test with experimental measurements found in the literature. Parametric studies of damage are performed on three different heating problems related to nuclear waste disposals. Several types of loading and boundary conditions are investigated. The thermal damage potential is thoroughly studied. The THHMD model is expected to be a useful tool in the assessment of the Excavation Damaged Zone, especially in the vicinity of nuclear waste repositories