XFEM,strong discontinuities and second-order work in shear band modeling of saturated porous media

We investigate shear band initiation and propagation in fully saturated porous media by means of a combination of strong discontinuities (discontinuities in the displacement field) and XFEM. As a constitutive behavior of the solid phase, a Drucker–Prager model is used within a framework of non-associated plasticity to account for dilation of the sample. Strong discontinuities circumvent the difficulties which appear when trying to model shear band formation in the context of classical nonlinear continuum mechanics and when trying to resolve them with classical numerical methods like the finite element method. XFEM, on the other hand, is well suited to deal with problems where a discontinuity propagates, without the need of remeshing. The numerical results are confirmed by the application of Hill’s second-order work criterion which allows to evaluate the material point instability not only locally but also for the whole domain.     

A finite element algorithm for parameter identification of material models for fluid saturated porous media

In this contribution an algorithm for parameter identification of geometrically linear Terzaghi–Biot‐type fluid‐saturated porous media is proposed, in which non‐uniform distributions of the state variables such as stresses, strains and fluid pore pressure are taken into account. To this end a least‐squares functional consisting of experimental data and simulated data is minimized, whereby the latter are obtained with the finite element method. This strategy allows parameter identification based on in situ experiments. In order to improve the efficiency of the minimization process, a gradient‐based optimization algorithm is applied, and therefore the corresponding sensitivity analysis for the coupled two‐phase problem is described in a systematic manner. For illustrative purpose, the performance of the algorithm is demonstrated for a slope stability problem, in which a quadratic Drucker–Prager plasticity model for the solid and a linear Darcy law for the fluid are combined. Copyright © 2001 John Wiley & Sons, Ltd.     

Cracking risk of partially saturated porous media—Part I: Microporoelasticity model

Drying of deformable porous media results in their shrinkage, and it may cause cracking provided that shrinkage deformations are hindered by kinematic constraints. This is the motivation to develop a thermodynamics‐based microporoelasticity model for the assessment of cracking risk in partially saturated porous geomaterials. The study refers to 3D representative volume elements of porous media, including a two‐scale double‐porosity material with a pore network comprising (at the mesoscale) 3D mesocracks in the form of oblate spheroids, and (at the microscale) spherical micropores of different sizes. Surface tensions prevailing in all interfaces between solid, liquid, and gaseous matters are taken into account. To establish a thermodynamics‐based crack propagation criterion for a two‐scale double‐porosity material, the potential energy of the solid is derived, accounting—in particular—for mesocrack geometry changes (main original contribution) and for effective micropore pressures, which depend (due to surface tensions) on the pore radius. Differentiating the potential energy with respect to crack density parameter yields the thermodynamical driving force for crack propagation, which is shown to be governed by an effective macrostrain. It is found that drying‐related stresses in partially saturated mesocracks reduce the cracking risk. The drying‐related effective underpressures in spherical micropores, in turn, result in a tensile eigenstress of the matrix in which the mesocracks are embedded. This way, micropores increase the mesocracking risk. Model application to the assessment of cracking risk during drying of argillite is the topic of the companion paper (Part II). Copyright © 2009 John Wiley & Sons, Ltd.     

Composite damage constitutive model of jointed rock mass considering crack propagation length and joint friction effect

In order to study the damage constitutive model of rock mass with non-persistent joints in engineering practice, the assumption that the rock mesoscopic elements strength obeys the Weibull distribution function of random, the Drucker–Prager criterion is used as a representation method to describe the strength of the mesoscopic elements, and mesoscopic damage variable is deduced. Combined with the energy principle and the fracture damage theory, the macroscopic damage variable formula is deduced considering the crack propagation length and the friction effect of joint closure in the rock mass. Finally, based on the strain equivalent hypothesis of Lemaitre and considering the coupling of macro and micro defects, the composite damage variables are derived. A macro–meso composite damage constitutive model of rock mass with non-persistent joints is established based on the Drucker–Prager criterion. The theoretical constitutive curves of the model are in good agreement with the experimental constitutive curves of the non-persistent jointed rock masses. The considering effects of crack propagation length and joint closure friction effect are compared with those without considering the crack propagation length and joint closure friction effect, which finds that the former is superior to the latter, and the rationality and validity of the model is verified.     

Instability of wave propagation in saturated poroelastoplastic media

In the present work, stationary discontinuities and fluttery instabilities of wave propagation in saturated poro‐elastoplastic media are analysed in the frame of Biot theory. The generalized Biot formulations are particularly employed for simulating non‐linear coupled hydro‐mechanical behaviour of the media. Inertial coupling effect between the solid and the fluid phases of the media is also taken into account. The non‐associated Drucker–Prager criterion to describe non‐linear constitutive behaviour of pressure dependent elasto‐plasticity for the solid skeleton of the media is particularly considered. With omission of compressibility of solid grains and the pore fluid, the critical conditions of stationary discontinuities and flutter instabilities occurring in wave propagation are given in explicit forms. It is shown that when the stationary discontinuity is triggered at the surface of discontinuity there still may exist real wave speeds. The wave speeds across the stationary discontinuity surface entirely cease to be real only in non‐associated plasticity, certain ranges of value of Poisson's ratio and when compression stress normal to the surface of discontinuity dominates the stress state at the surface. It is also indicated that the fluttery instabilities, under which some wave speeds cease to be real even in strain hardening stage, may occur prior to stationary discontinuities only for non‐associated plasticity under certain conditions. These conditions are: (1) both the porosity and the Poisson's ratio possess relatively low values and (2) the deviatoric part of the effective stress normal to the surface of discontinuity is compressive. A region in the porosity–Poisson's ratio plot, in which fluttery instabilities are possible to occur, is given. Copyright © 2002 John Wiley & Sons, Ltd.     

Effect of plastic deformation on hydraulic fracturing with extended element method

The propagation of hydraulic fracture in elastic rocks has widely been investigated. In the paper, we shall focus on numerical modeling of hydraulic fracturing in a class of porous rocks exhibiting plastic deformation. The plastic strain of porous rocks is described by a non-associated plastic model based on Drucker–Prager criterion. The plastic deformation is coupled with fluid pressure evolution described by the lubrication theory. An extended finite element method is used for modeling the propagation of fracture. The fracture propagation criterion is based on the J-integral. The proposed numerical model is validated by comparisons with numerical and analytical results. The influence of plastic deformation on fracture propagation process is investigated.

     

A micromechanical modeling of ductile behavior of a porous chalk: Formulation,identification, and validation

Porosity strongly affects the overall ductile behavior of cohesive geomaterials undergoing plastic deformation. In the present paper, we proposed an original micromechanical approach that suitably couples Drucker–Prager‐type plasticity, evolving porosity under general triaxial loadings. The resulting model has the advantage to be based on a single macroscopic yield function, which also plays the role of plastic potential. It is shown that this yield function is particularly appropriate to account for the pore collapse and plastic shearing mechanisms that govern the mechanical behavior of the studied Lixhe chalk. Finally, the new model is implemented and validated by comparison to triaxial tests data, covering a wide range of confining pressures. Copyright © 2011 John Wiley & Sons, Ltd.     

Poroplastic modelling of the excavation and ventilation of a deep cavity

A plastic deviatoric model with hardening is developed on the basis of geomechanical tests performed in the saturated case on low permeable porous material such as argillite. This model is a generalized Mohr–Coulomb plastic criterion combined with a Drucker–Prager plastic potential and the hardening parameter is the plastic distortion. Three different hardening functions have been introduced on the basis of triaxial tests: an increase of friction angle, a decrease of cohesion after a threshold and a contractancy to dilatancy transition for volumetric plastic strain. This plastic model has been adapted to the partially saturated case. The effective stress is expressed thanks to the equivalent interstitial pressure π. Numerical results are presented for the excavation and monotonous ventilation of a deep cylindrical cavity. A first plastification due to excavation is followed by a second one due to desaturation. The extent of the non-saturated zone provokes an extent of a plastic zone in the rock mass. Analysis shows that the origin of the plastification can be found in the deviatoric stresses because mean effective stresses are compressive during drying. Copyright © 2004 John Wiley & Sons, Ltd.     

Weak discontinuity in porous media: an enriched EFG method for fully coupled layered porous media

In this paper, a series of multimaterial benchmark problems in saturated and partially saturated two‐phase and three‐phase deforming porous media are addressed. To solve the process of fluid flow in partially saturated porous media, a fully coupled three‐phase formulation is developed on the basis of available experimental relations for updating saturation and permeabilities during the analysis. The well‐known element free Galerkin mesh‐free method is adopted. The partition of unity property of MLS shape functions allows for the field variables to be extrinsically enriched by appropriate functions that introduce existing discontinuities in the solution field. Enrichment of the main unknowns including solid displacement, water phase pressure, and gas phase pressure are accounted for, and a suitable enrichment strategy for different discontinuity types are discussed. In the case of weak discontinuity, the enrichment technique previously used by Krongauz and Belytschko [Int. J. Numer. Meth. Engng., 1998; 41:1215–1233] is selected. As these functions possess discontinuity in their first derivatives, they can be used for modeling material interfaces, generating only minor oscillations in derivative fields (strain and pressure gradients for multiphase porous media), as opposed to unenriched and constrained mesh‐free methods. Different problems of multimaterial poro‐elasticity including fully saturated, partially saturated one, and two‐phase flows under the assumption of fully coupled extended formulation of Biot are examined. As a further development, problems involved with both material interface and impermeable discontinuities, where no fluid exchange is permitted across the discontinuity, are considered and numerically discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

A three‐phase soil model for simulating stress wave propagation due to blast loading

A three‐phase soil model is proposed to simulate stress wave propagation in soil mass to blast loading. The soil is modelled as a three‐phase mass that includes the solid particles, water and air. It is considered as a structure that the solid particles form a skeleton and their voids are filled with water and air. The equation of state (EOS) of the soil is derived. The elastic–plastic theory is adopted to model the constitutive relation of the soil skeleton. The damage of the soil skeleton is also modelled. The Drucker–Prager strength model including the strain rate effect is used to describe the strength of the soil skeleton. The model is implemented into a hydrocode Autodyn. The recorded results obtained by explosion tests in soil are used to validate the proposed model. Copyright © 2004 John Wiley & Sons, Ltd.     

Frictionless contact formulation for dynamic analysis of nonlinear saturated porous media based on the mortar method

A finite element algorithm for frictionless contact problems in a two‐phase saturated porous medium, considering finite deformation and inertia effects, has been formulated and implemented in a finite element programme. The mechanical behaviour of the saturated porous medium is predicted using mixture theory, which models the dynamic advection of fluids through a fully saturated porous solid matrix. The resulting mixed formulation predicts all field variables including the solid displacement, pore fluid pressure and Darcy velocity of the pore fluid. The contact constraints arising from the requirement for continuity of the contact traction, as well as the fluid flow across the contact interface, are enforced using a penalty approach that is regularised with an augmented Lagrangian method. The contact formulation is based on a mortar segment‐to‐segment scheme that allows the interpolation functions of the contact elements to be of order N. The main thrust of this paper is therefore how to deal with contact interfaces in problems that involve both dynamics and consolidation and possibly large deformations of porous media. The numerical algorithm is first verified using several illustrative examples. This algorithm is then employed to solve a pipe‐seabed interaction problem, involving large deformations and dynamic effects, and the results of the analysis are also compared with those obtained using a node‐to‐segment contact algorithm. The results of this study indicate that the proposed method is able to solve the highly nonlinear problem of dynamic soil–structure interaction when coupled with pore water pressures and Darcy velocity. Copyright © 2015 John Wiley & Sons, Ltd.     

Theoretical analyses of nonaqueous phase liquid dissolution‐induced instability in two‐dimensional fluid‐saturated porous media

This paper deals with the theoretical aspects of nonaqueous phase liquid (NAPL)‐dissolution‐induced instability in two‐dimensional fluid‐saturated porous media including solute dispersion effects.After some weaknesses associated with the previous work are analyzed and overcome, a comprehensive dimensionless number, known as the Zhao number, is proposed to represent the main driving force and three controlling mechanisms of an NAPL‐dissolution system that has a finite domain. The linear stability analysis is carried out to derive the critical value of the comprehensive dimensionless number of the NAPL‐dissolution system in a limit case as the ratio of the equilibrium concentration to the density of the NAPL approaches zero. As a result, a theoretical criterion that can be used to assess the instability of planar NAPL‐dissolution fronts in two‐dimensional fluid‐saturated porous media of finite domains has been established. Not only can the present theoretical results be used for the theoretical understanding of the effect of solute dispersion on the instability of an NAPL‐dissolution front in the fluid‐saturated porous medium of either a finite domain or an infinite domain, but also they can be used as benchmark solutions for verifying numerical methods employed to simulate detailed morphological evolution processes of NAPL‐dissolution fronts in two‐dimensional fluid‐saturated porous media. Copyright © 2009 John Wiley & Sons, Ltd.     

A multiscale homogenization model for strength predictions of fully and partially frozen soils

Soil freezing is often used to provide temporary support of soft soils in geotechnical interventions. During the freezing process, the strength properties of the soil–water–ice mixture change from the original properties of the water-saturated soil to the properties of fully frozen soils. In the paper, a multiscale homogenization model for the upscaling of the macroscopic strength of freezing soil based upon information on three individual material phases—the solid particle phase (S), the crystal ice phase (C) and the liquid water phase (L)—is proposed. The homogenization procedure for the partially frozen soil–water–ice composite is based upon an extension of the linear comparison composite (LCC) method for a two-phase matrix–inclusion composite, using a two-step homogenization procedure. In each step, the LCC methodology is implemented by estimating the strength criterion of a two-phase nonlinear matrix–inclusion composite in terms of an optimally chosen linear elastic comparison composite with a similar underlying microstructure. The solid particle phase (S) and the crystal ice phase (C) are assumed to be characterized by two different Drucker–Prager strength criteria, and the liquid water phase (L) is assumed to have zero strength capacity under drained conditions. For the validation of the proposed upscaling strategy, the predicted strength properties for fully and partially frozen fine sands are compared with experimental results, focussing on the investigation of the influence of the porosity and the degree of ice saturation on the predicted failure envelope.     

Macroscopic criteria for Green type porous materials with spheroidal voids: application to double porous materials

Combined effects of matrix plastic compressibility and void shape are investigated for ductile porous materials. To this end, a spheroidal volume containing a confocal spheroidal (prolate or oblate) void subjected to uniform strain rate boundary conditions has been first studied. A Green type matrix is chosen as a prototype for investigating effects of plastic compressibility. This is carried out by using a kinematics limit analysis theory from which a closed‐form expression of the macroscopic criterion is established for the considered class of materials. These results are then extended to ductile porous materials made up of a green matrix containing randomly oriented spheroidal voids. In the framework of a two‐step homogenization procedure, the obtained results are implemented to describe the macroscopic behavior of double porous materials involving spherical voids at the microscale and randomly oriented and distributed spheroidal voids at the mesoscale. For validation purpose, the new derived criteria are assessed and validated by comparing their predictions to available upper bounds and numerical data from literature. Copyright © 2017 John Wiley & Sons, Ltd.     

Peridynamics simulations of geomaterial fragmentation by impulse loads

In this work, we have developed nonlinear peridynamics models of drained and saturated geomaterials, and applied them to simulations of dynamic fragmentation and ejecta formation due to impulse loads. First, we have re‐phrased and re‐interpreted the non‐local state‐based peridynamics formulation to connect the non‐local integral operator with the local differential operator. Second, we have implemented the Drucker–Prager plasticity model in state‐based peridynamics at finite strain. A peridynamics version of the Hughes and Winget algorithm is derived for the constitutive update. Third, we have developed a peridynamics U‐p formulation for saturated geomaterials. Fourth, numerical simulations have been carried out to verify the proposed peridynamics formulations in the simulation of geomaterial fragmentation induced by impulse loads. Comparisons of analytical and numerical results indicate that the peridynamics model has the ability to both match traditional continuum compression examples, as well as simulate complex geomaterial fragmentation processes resulting from impulse loads. Copyright © 2015 John Wiley & Sons, Ltd.     

Localized failure of fibre‐reinforced elastic–plastic materials subjected to plane strain loading

We consider discontinuous bifurcations as the indicator of a localized failure for a class of composites that are characterized by elastic fibres reinforcing an elastic–plastic matrix. A macroscopic tangent stiffness tensor for the fibre‐reinforced composite is developed by consistently homogenizing the contribution of fibres in a spherical representative volume element. Analytical solutions are derived for the critical hardening modulus and corresponding bifurcation directions for the case of plane strain loading. Properties of the solutions are further illustrated on the example of the non‐associated Drucker–Prager model at onset of yielding. Results show that presence of fibres decreases the critical hardening modulus, thus inhibiting the onset of strain localization. The rate of decrease in the critical hardening modulus is the highest for pure shear, followed by uniaxial tension, uniaxial compression, biaxial tension and biaxial compression. The main fibre parameters that control the onset of strain localization are their volumetric content and their stiffness modulus whereby very stiff fibres can produce the most significant decrease in the critical hardening modulus, especially for the state of biaxial tension. The critical hardening modulus for the non‐associated Drucker–Prager model exhibits a full range of localization modes including compaction bands, dilation bands, and transition in the form of shear bands regardless of the presence of fibres. Presence of fibres affects bifurcation directions, except in the case when Poisson's ratio of the matrix is equal to 0.25. The results demonstrate stabilizing effects of fibres by which they provide the control against the onset of strain localization. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical study of two‐phase fluid distributions in fractured porous media

Two‐phase fluid distributions in fractured porous media were studied using a single‐component multiphase (SCMP) lattice Boltzmann method (LBM), which was selected among three commonly used numerical approaches through a comparison against the available results of micro X‐ray computed tomography. The influence of the initial configuration and the periodic boundary conditions in the SCMP LBM for the fluid distribution analysis were investigated as well. It was revealed that regular porous media are sensitive to the initial distribution, whereas irregular porous media are insensitive. Moreover, to eliminate the influence of boundaries, the model's buffer size of an SCMP LBM simulation was suggested to be taken as approximately 12.5 times the average particle size. Then, the two‐phase fluid distribution of a porous medium was numerically studied using the SCMP LBM. Both detailed distribution patterns and macroscopic morphology parameters were reasonably well captured. Finally, the two‐phase fluid distributions in a fractured porous media were investigated. The influence of the degree of saturation, fracture length, and fracture width on the fluid distributions and migration was explored. Copyright © 2015 John Wiley & Sons, Ltd.     

Micromechanics of saturated and unsaturated porous media

The homogenization method is used to determine the formulation of the behaviour of both saturated and unsaturated porous media. This approach makes it possible to assess the validity of the effective stress concept as a function of the properties of the porous media at the microscopic scale. Furthermore, the influence of the morphologies of the solid and fluid phases on the macroscopic behaviour is studied. The strain induced by drying is examined as a function of the morphological properties. Copyright © 2002 John Wiley & Sons, Ltd.     

Comparison of continuous and discontinuous constitutive models to simulate concrete behaviour under mixed‐mode failure conditions

The paper presents detailed FE simulation results of concrete elements under mixed‐mode failure conditions according to the so‐called shear‐tension test by Nooru‐Mohamed, characterized by curved cracks. A continuous and discontinuous numerical two‐dimensional approach was used. In order to describe the concrete's behaviour within continuum mechanics, two different constitutive models were used. First, an elasto‐plastic model with isotropic hardening and softening was assumed. In a compression regime, a Drucker–Prager criterion with a non‐associated flow rule was used. In turn, in a tensile regime, a Rankine criterion with an associated flow rule was adopted. Second, an isotropic damage constitutive model was applied with a single scalar damage parameter and different definitions of the equivalent strain. Both constitutive laws were enriched by a characteristic length of micro‐structure to capture properly strain localization. As an alternative approach, the extended finite element method was used. Our results were compared with the experimental ones and with results of other FE simulations reported in the literature. Copyright © 2015 John Wiley & Sons, Ltd.