A multiscale work-analysis approach for geotechnical structures

This paper presents a second-order work analysis in application to geotechnical problems by using a novel effective multiscale approach. To abandon complicated equations involved in conventional phenomenological models, this multiscale approach employs a micromechanically-based formulation, in which only four parameters are involved. The multiscale approach makes it possible a coupling of the finite element method (FEM) and the micromechanically-based model. The FEM is used to solve the boundary value problem (BVP) while the micromechanically-based model is utilized at the Gauss point of the FEM. Then, the multiscale approach is used to simulate a three-dimensional triaxial test and a plain-strain footing. On the basis of the simulations, material instabilities are analyzed at both mesoscale and global scale. The second-order work criterion is then used to analyze the numerical results. It opens a road to interpret and understand the micromechanisms hiding behind the occurrence of failure in geotechnical issues.     

Micromechanical approach to effective viscoelastic properties of micro‐fractured geomaterials

The aim of this paper is to formulate a micromechanics‐based approach to non‐aging viscoelastic behavior of materials with randomly distributed micro‐fractures. Unlike cracks, fractures are discontinuities that are able to transfer stresses and can therefore be regarded from a mechanical viewpoint as interfaces endowed with a specific behavior under normal and shear loading. Making use of the elastic‐viscoelastic correspondence principle together with a Mori‐Tanka homogenization scheme, the effective viscoelastic behavior is assessed from properties of the material constituents and damage parameters related to density and size of fractures. It is notably shown that the homogenized behavior thus formulated can be described in most cases by means of a generalized Maxwell rheological model. For practical implementation in structural analyses, an approximate model for the isotropic homogenized fractured medium is formulated within the class of Burger models. Although the approximation is basically developed for short‐term and long‐term behaviors, numerical applications indicate that the approximate Burger model accurately reproduce the homogenized viscoelastic behavior also in the transient conditions.     

A probabilistic approach for computing water retention of particulate systems from statistics of grain size and tessellated pore network

The paper offers an analytical determination of the hydraulic properties of an unsaturated soil with reference to its retention curve, which describes the relationship between the volumetric water content and capillarity through matric suction. The analysis combines a particulate approach focused on the physics at the pore scale, including microstructural aspects, with a probabilistic approach where the void space and grain size are considered as random variables. In the end, the soil water characteristic curve of an unsaturated granular medium along a drying path can be derived analytically based on the sole information of particle size distribution. The analysis hinges on the tessellation of a wet granular system into an assemblage of tetrahedral unit cells revealing a pore network upon which capillary physics are computed with respect to pore throat invasion by a non-wetting fluid with evolving pendular capillary bridges. The crux of the paper is to pass from particle size probability distribution to a matching void space distribution to eventually reveal key information such as void cell and solid volume statistics. Making reasonable statistically based assumptions to render calculations tractable, the water retention curve can be readily constructed. Model predictions compare quite favourably with experimental data available for actual soils, especially in the high saturation range. Having a sound scientific basis, the model can be made amenable to address a variety of soils with a wider range of particle sizes.     

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.     

Homogenization‐based analysis of anisotropic damage in brittle materials with unilateral effect and interactions between microcracks

This paper is devoted to micromechanical modeling of induced anisotropic damage in brittle geomaterials. The formulation of the model is based on a proper homogenization procedure by taking into account unilateral effects and interactions between microcracks. The homogenization procedure is developed in the framework of Eshelby's inclusion solution and Ponte‐Castaneda and Willis (J. Mech. Phys. Solids 1995; 43 :1919–1951) estimate. The homogenization technique is combined with the thermodynamics framework at microscopic level for the determination of damage evolution law. A rigorous crack opening–closure transition condition is established and an energy‐release‐rate‐based damage criterion is proposed. Computational aspects on the implementation of micromechanical model are also discussed. The proposed model is evaluated by comparing numerical predictions with experimental data for various laboratory tests on concrete. Parametric studies on unilateral effects and influences of microcracks interactions are finally performed and analyzed. Copyright © 2008 John Wiley & Sons, Ltd.     

A PACKING GENERATION SCHEME FOR THE GRANULAR ASSEMBLIES WITH PLANAR ELLIPTICAL PARTICLES

In this paper, a new generator algorithm and a computer program PG2D is introduced for 2D numerical simulation of packing configuration in a granular material composed of elliptical particles of different a/b aspect ratios. Each elliptical particle is approximated by four connected arcs. The centre co-ordinates and radius of each arc and co-ordinates of connecting points can be determined from the formulae derived by entering the major axis length, 2a, and the eccentricity. The domain to be filled with particles can be a polygon of any shape. Given the size of the packing domain, geometrical information and numbers of particles to be generated, the packing location of each particle and the co-ordinates of contact points along with contact normal rose diagram can be generated as outputs. Simulation results show that this new algorithm can provide quite a reasonable packing model in accordance with the initial input required for the analysis of the mechanics of granular material. This generation scheme has the potential to cover packing generation and behaviour analysis of 3D sphere or ellipsoidal shaped granular materials. © 1997 by John Wiley & Sons, Ltd.     

Micromechanics approach to poroelastic behavior of a jointed rock

The formulation of macroscopic poroelastic behavior of a jointed rock is investigated within the framework of a micro–macro approach. The joints are modeled as interfaces, and their behavior is modeled by means of generalized poroelastic state equations. Starting from Hill's lemma extended for a jointed medium and extending the concept of strain concentration to relate the joint displacement jump to macroscopic strain, the overall poroelastic constitutive equations for the jointed rock are formulated. The analysis emphasizes the main differences and similarities of the resulting behavior with respect to that characterizing ordinary porous media. It is shown that, unlike ordinary porous media, conditions on the poroelastic parameters of joints are required for the macroscopic drained stiffness to entirely define the poroelastic behavior. This is achieved, for instance, if the joint network is characterized by a unique Biot coefficient. Extension of the analysis to non‐linear poroelasticity is also outlined. Finally, the theoretical formulation is applied to two particular cases of jointed rock for which explicit expressions of the overall poroelastic parameters are derived. Copyright © 2011 John Wiley & Sons, Ltd.     

The intrinsic permeability of microcracks in porous solids: Analytical models and Lattice Boltzmann simulations

The paper presents a synthesis of analytical modeling and computational simulations of the intrinsic permeability of microcracks, embedded in porous materials taking into account the interaction of the fluid flow in the microcrack with the surrounding porous material. In the first part of the paper, using the DARCY , STOKES , BRINKMAN , and the BEAVERS–JOSEPH approximations, we derive the intrinsic permeability of a plain non‐rough microcrack in terms of the microcrack geometry and the permeability of the porous material surrounding the microcrack. In the second part of the paper, the intrinsic permeability of a microcrack is determined by means of computational simulations using the framework of the lattice Boltzmann method with partial bounceback conditions. The comparison of predictions from the analytical model and the numerical simulations show an excellent agreement. Copyright © 2017 John Wiley & Sons, Ltd.