A micromechanical finite element model for linear and damage‐coupled viscoelastic behaviour of asphalt mixture

This study presents a finite element (FE) micromechanical modelling approach for the simulation of linear and damage‐coupled viscoelastic behaviour of asphalt mixture. Asphalt mixture is a composite material of graded aggregates bound with mastic (asphalt and fine aggregates). The microstructural model of asphalt mixture incorporates an equivalent lattice network structure whereby intergranular load transfer is simulated through an effective asphalt mastic zone. The finite element model integrates the ABAQUS user material subroutine with continuum elements for the effective asphalt mastic and rigid body elements for each aggregate. A unified approach is proposed using Schapery non‐linear viscoelastic model for the rate‐independent and rate‐dependent damage behaviour. A finite element incremental algorithm with a recursive relationship for three‐dimensional (3D) linear and damage‐coupled viscoelastic behaviour is developed. This algorithm is used in a 3D user‐defined material model for the asphalt mastic to predict global linear and damage‐coupled viscoelastic behaviour of asphalt mixture. For linear viscoelastic study, the creep stiffnesses of mastic and asphalt mixture at different temperatures are measured in laboratory. A regression‐fitting method is employed to calibrate generalized Maxwell models with Prony series and generate master stiffness curves for mastic and asphalt mixture. A computational model is developed with image analysis of sectioned surface of a test specimen. The viscoelastic prediction of mixture creep stiffness with the calibrated mastic material parameters is compared with mixture master stiffness curve over a reduced time period. In regard to damage‐coupled viscoelastic behaviour, cyclic loading responses of linear and rate‐independent damage‐coupled viscoelastic materials are compared. Effects of particular microstructure parameters on the rate‐independent damage‐coupled viscoelastic behaviour are also investigated with finite element simulations of asphalt numerical samples. Further study describes loading rate effects on the asphalt viscoelastic properties and rate‐dependent damage behaviour. Copyright © 2006 John Wiley & Sons, Ltd.     

Micromechanical modeling for rate‐dependent behavior of salt rock under cyclic loading

The dependence of rock behavior on the deformation rate is still not well understood. In salt rock, the fundamental mechanisms that drive the accumulation of irreversible deformation, the reduction of stiffness, and the development of hysteresis during cyclic loading are usually attributed to intracrystalline plasticity and diffusion. We hypothesize that at low pressure and low temperature, the rate‐dependent behavior of salt rock is governed by water‐assisted diffusion along grain boundaries. Accordingly, a chemo‐mechanical homogenization framework is proposed in which the representative elementary volume (REV) is viewed as a homogeneous polycrystalline matrix that contains sliding grain‐boundary cracks. The slip is related to the mass of salt ions that diffuse along the crack surface. The relationship between fluid inclusion‐scale and REV‐scale stresses and strains is established by using the Mori–Tanaka homogenization scheme. It is noted from the model that a lower strain rate and a larger number of sliding cracks enhance stiffness reduction and hysteresis. Thinner sliding cracks (i.e., thinner brine films) promote stiffness reduction and accelerate stress redistributions. The larger the volume fraction of the crack inclusions, the larger the REV deformation and the larger the hysteresis. Results presented in this study shed light on the mechanical behavior of salt rock that is pertinent to the design of geological storage facilities that undergo cyclic unloading, which could help optimize the energy production cycle with low carbon emissions.     

Discontinuous deformation analysis with second‐order finite element meshed block

The discontinuous deformation analysis (DDA) with second‐order displacement functions was derived based on six‐node triangular mesh in order to satisfy the requirement for the accurate calculations in practical applications. The matrices of equilibrium equations for the second‐order DDA were given in detail for program coding. By close comparison with widely used finite element method and closed form solutions, the advantages of the modified DDA were illustrated. The program coding was carried out in C++ environment and the new code applied to three examples with known analytical solutions. A very good agreement was achieved between the analytical and numerical results produced by the modified DDA code. Copyright © 2006 John Wiley & Sons, Ltd.     

Unsaturated slope stability analysis with steady infiltration or evaporation using elasto‐plastic finite elements

The paper presents results of unsaturated slope stability analyses using elasto‐plastic finite elements in conjunction with a novel analytical formulation for the suction stress above the water table. The suction stress formula requires four parameters, three for the soil type and one for the steady infiltration (or evaporation) due to environmental effects. The suction stress approach enables the analysis to proceed in the context of classical effective stress, while maintaining the advantages of a general non‐linear finite element approach in which no advance assumptions need to be made about the shape or location of the critical failure surface. The results show the extent to which suctions above the water table can increase the factor of safety of a slope for a variety of different soil types and infiltration rates. All stability analyses that include the effects of suction stresses are contrasted with more traditional approaches in which water pressures above the water table are ignored. Copyright © 2005 John Wiley & Sons, Ltd.     

Spectral analysis of nonlocal regularization in two‐dimensional finite element models

Strain‐softening in geomaterials often leads to ill‐posed boundary‐valued problems (BVP), which cannot be solved with finite element methods without introducing some kind of regularization such as nonlocal plasticity. Hereafter we propose to apply spectral analysis for testing the performance of nonlocal plasticity in regularizing ill‐posed BVP and producing mesh‐independent solutions when local plasticity usually fails. The spectral analysis consists of examining the eigenvalues and eigenvectors of the global tangential stiffness matrix of the incremental equilibrium equations. Based on spectral analysis, we propose a criterion for passing or failing the test of constitutive regularization in the context of BVP. If the eigenvalues of the tangential operator are all positive then the regularization succeeds, otherwise it fails and may not prevent artificial mesh‐dependent solutions from appearing. The approach is illustrated in the particular case of a biaxial compression with strain‐softening plasticity. In this particular case, local softening plasticity is found to produce negative eigenvalues in the tangential stiffness matrix, which indicates ill‐posed BVP. In contrast, nonlocal softening plasticity always produces positive eigenvalues, which regularizes ill‐posed BVP. The dominant eigenvectors, which generate localized deformation patterns, have a bandwidth independent of mesh size, provided that the mesh is fine enough to capture localization. These mesh‐independent eigenmodes explain why nonlocal plasticity produces numerical solutions that are mesh‐independent. Copyright © 2011 John Wiley & Sons, Ltd.     

Bearing capacity of non-associative coaxial granular materials by upper bound limit analysis and finite elements

In this paper, an upper bound estimate of the limit load on non-associative coaxial granular materials is presented. The kinematic approach of the upper bound limit analysis has been utilised. The failure mechanism is assumed to coincide with the direction of the shear bands at every point throughout the body. The shear band orientation in non-associative coaxial materials, i.e. those with the same major principal stress and major principal strain increment directions, can be found based on the angle of dilation and the major principal stress direction. Therefore, having known the stress field at limiting equilibrium, the orientation of the shear bands and hence, the failure mechanism can be obtained. In this study, the stress field is first determined by the method of stress characteristics. Then, the finite element interpolation technique is used to interpolate the stress field and to find the orientation of the shear bands at every point within the field. Once the failure mechanism and the stress state at every point along velocity discontinuities have been found, the upper bound limit analysis has been performed to estimate the limit load.     

On finite volume method implementation of poro‐elasto‐plasticity soil model

Accurate prediction of the interactions between the nonlinear soil skeleton and the pore fluid under loading plays a vital role in many geotechnical applications. It is therefore important to develop a numerical method that can effectively capture this nonlinear soil‐pore fluid coupling effect. This paper presents the implementation of a new finite volume method code of poro‐elasto‐plasticity soil model. The model is formulated on the basis of Biot's consolidation theory and combined with a perfect plasticity Mohr‐Coulomb constitutive relation. The governing equation system is discretized in a segregated manner, namely, those conventional linear and uncoupled terms are treated implicitly, while those nonlinear and coupled terms are treated explicitly by using any available values from previous time or iteration step. The implicit–explicit discretization leads to a linearized and decoupled algebraic system, which is solved using the fixed‐point iteration method. Upon the convergence of the iterative method, fully nonlinear coupled solutions are obtained. Also explored in this paper is the special way of treating traction boundary in finite volume method compared with FEM. Finally, three numerical test cases are simulated to verify the implementation procedure. It is shown in the simulation results that the implemented solver is capable of and efficient at predicting reasonable soil responses with pore pressure coupling under different loading situations. Copyright © 2015 John Wiley & Sons, Ltd.     

Formulation of a three‐dimensional rate‐dependent constitutive model for chalk and porous rocks

Rate‐dependent behaviour of chalk and other porous rocks has undergone widespread study in geomechanics due to its implications on the performance of engineering structures. We present a rate‐dependent constitutive model for chalk and other porous rocks with several new features. The model formulation is based on a viscoplastic rate‐lines approach in which the axial strain rate depends on the proximity of the stress point to an elliptical reference surface. A non‐associated viscoplastic potential surface and an axial scaling algorithm are used to determine the viscoplastic strain components. The model predicts that axial yields stress varies as a power function of applied axial strain rate, as shown by published laboratory data. Comparisons with published experimental data indicate that the model is capable of reproducing observed rate‐dependent behaviour of chalk under a variety of loading conditions. Copyright © 2006 John Wiley & Sons, Ltd.     

An extended finite element framework for slow‐rate frictional faulting with bulk plasticity and variable friction

We present an extended finite element (FE) approach for the simulation of slow‐rate frictional faulting in geologic media incorporating bulk plasticity and variable friction. The method allows the fault to pass through the interior of FEs without remeshing. The extended FE algorithm for frictional faulting, advocated in two recent articles, emanates from a variational equation formulated in terms of the relative displacement on the fault. In the present paper we consider the combined effects of bulk plasticity and variable friction in a two‐dimensional plane strain setting. Bulk plasticity is localized to the fault tip and could potentially be used as a predictor for the initiation and propagation of new faults. We utilize a variable velocity‐ and state‐dependent friction, known as the Dieterich–Ruina or ‘slowness’ law, formulated in a slip‐weakening format. The slip‐weakening/variable friction model is then time‐integrated according to the generalized trapezoidal rule. We present numerical examples demonstrating the convergence properties of a global Newton‐based iterative scheme, as well as illustrate some interesting properties of the variable friction model. Copyright © 2009 John Wiley & Sons, Ltd.     

Implementation of the finite element method in the three‐dimensional discontinuous deformation analysis (3D‐DDA)

A modified three‐dimensional discontinuous deformation analysis (3D‐DDA) method is derived using four‐noded tetrahedral elements to improve the accuracy of current 3D‐DDA algorithm in practical applications. The analysis program for the modified 3D‐DDA method is developed in a C++ environment and its accuracy is illustrated through comparisons with several analytical solutions that are available for selected problems. The predicted solutions for these problems using the modified 3D‐DDA approach all show satisfactory agreement with the corresponding analytical results. Results presented in this paper demonstrate that the modified 3D‐DDA method with discontinuous modeling capabilities offers a useful computational tool to determine stresses and deformations in practical problems involving fissured elastic media with reasonable accuracy. Copyright © 2008 John Wiley & Sons, Ltd.     

Advanced programming methods and data structures for computational modelling using edge‐based finite volume methods

The generation of a numerical model must consider the separate issues of the governing equations, the numerical representation of those equations, the data structure that describes the model, the choice of programming language and finally the implementation and code management issues. These issues are considered as a whole in this paper and as a consequence, 10 golden rules for numerical modelling are proposed. By way of application, a saturated–unsaturated flow problem is modelled using the Richards equation and an innovative edge‐based finite volume method. The implementation uses a novel data structure. This is shown to have over 91% code re‐use and hence code written in this way is highly flexible and applicable to many different problems. By way of example, a compacted core earth filled dam problem has been solved. Finally, we conclude that this advanced programming method can significantly reduce code development time. Copyright © 2004 John Wiley & Sons, Ltd.     

A comparative study of the hypoplasticity and the fabric‐dependent dilatant double shearing models for granular materials

In this paper, we consider the mechanical response of granular materials and compare the predictions of a hypoplastic model with that of a recently developed dilatant double shearing model which includes the effects of fabric. We implement the constitutive relations of the dilatant double shearing model and the hypoplastic model in the finite element program ABACUS/Explicit and compare their predictions in the triaxial compression and cyclic shear loading tests. Although the origins and the constitutive relations of the double shearing model and the hypoplastic model are quite different, we find that both models are capable of capturing typical behaviours of granular materials. This is significant because while hypoplasticity is phenomenological in nature, the double shearing model is based on a kinematic hypothesis and microstructural considerations, and can easily be calibrated through standard tests. Copyright © 2006 John Wiley & Sons, Ltd.     

Thermodynamic‐based model for coupling temperature‐dependent viscoelastic,viscoplastic, and viscodamage constitutive behavior of asphalt mixtures

Based on the continuum damage mechanics, a general and comprehensive thermodynamic‐based framework for coupling the temperature‐dependent viscoelastic, viscoplastic, and viscodamage behaviors of bituminous materials is presented. This general framework derives systematically Schapery‐type nonlinear viscoelasticity, Perzyna‐type viscoplasticity, and a viscodamage model analogous to the Perzyna‐type viscoplasticity. The resulting constitutive equations are implemented in the well‐known finite element code Abaqus via the user material subroutine UMAT. A systematic procedure for identifying the model parameters is discussed. Finally, the model is validated by comparing the model predictions with a comprehensive set of experimental data on hot mix asphalt that include creep‐recovery, creep, uniaxial constant strain rate, and repeated creep‐recovery tests in both tension and compression over a range of temperatures, stress levels, and strain rates. Comparisons between model predictions and experimental measurements show that the presented constitutive model is capable of predicting the nonlinear behavior of asphaltic mixes under different loading conditions. Copyright © 2011 John Wiley & Sons, Ltd.     

A novel computational approach for large deformation and post‐failure analyses of segmental retaining wall systems

Segmental retaining wall (SRW) systems are commonly used in geotechnical practice to stabilize cut and fill slopes. Because of their flexibility, these systems can tolerate minor movements and settlements without incurring damage or crack. Despite these advantages, very few numerical studies of large deformations and post‐failure behavior of SRW systems are found in the current literature. Traditional numerical methods, such as the finite element method, suffer from mesh entanglement, thus are unable to simulate large deformations and flexible behavior of retaining wall blocks in SRW systems. To overcome the above limitations, a novel computational framework based on the smoothed particle hydrodynamics (SPH) method was developed to simulate large deformations and post‐failure behavior of soils and retaining wall blocks in SRW systems. The proposed numerical framework is a hybrid continuum/discontinuum approach that can model soil as an elasto‐plastic material and retaining wall blocks as independent rigid bodies associated with both translational and rotational degrees of freedom. A new contact model is proposed within the SPH framework to simulate the interaction between the soil and the blocks and between the blocks. As an application of the proposed numerical method, a two‐dimensional simulation of an SRW collapse was simulated and compared to experimental results conducted under the same conditions. The results showed that the proposed computational approach provided satisfactory agreement with the experiment. This suggests that the new framework is a promising numerical approach to model SRW systems. Copyright © 2014 John Wiley & Sons, Ltd.     

An elasto‐plastic three phase model for partially saturated soil for the finite element simulation of compressed air support in tunnelling

This paper presents a fully coupled finite element formulation for partially saturated soil as a triphasic porous material, which has been developed for the simulation of shield tunnelling with heading face support using compressed air. While for many numerical simulations in geotechnics use of a two‐phase soil model is sufficient, the simulation of compressed air support demands the use of a three‐phase model with the consideration of air as a separate phase. A multiphase model for soft soils is developed, in which the individual constituents of the soil—the soil skeleton, the fluid and the gaseous phase—and their interactions are considered. The triphasic model is formulated within the framework of the theory of porous media, based upon balance equations and constitutive relations for the soil constituents and their mixture. An elasto‐plastic, cam–clay type model is extended to partially saturated soil conditions by incorporating capillary pressure according to the Barcelona basic model. The hydraulic properties of the soil are described via DARCY 's law and the soil–water characteristic curve after VAN GENUCHTEN . Water is modelled as an incompressible and air as a compressible phase. The model is validated by means of selected benchmark problems. The applicability of the model to geotechnical problems is demonstrated by results from the simulation of a compressed air intervention in shield tunnelling. Copyright © 2009 John Wiley & Sons, Ltd.     

Review and enhancement of 3D concrete models for large‐scale numerical simulations of concrete structures

The present paper focuses on selected plasticity and damage‐plasticity models for describing the 3D material behavior of concrete. In particular, a plasticity model and a damage‐plasticity model are reviewed and evaluated. Based on the results of the evaluation, enhancements are proposed, aiming at improving the correspondence between predicted and observed material behavior and aiming at implementing a robust and efficient stress update algorithm in a finite element program for performing large‐scale 3D numerical simulations of concrete structures. The capabilities of the concrete models are demonstrated by 3D numerical simulations of benchmark tests with combined bending and torsional loading and combined compression and shear loading and by a large‐scale 3D finite element analysis of a model test of a concrete arch dam. Copyright © 2011 John Wiley & Sons, Ltd.     

An improved return‐map stress update algorithm for finite deformation analysis of general isotropic elastoplastic geomaterials

This paper develops a novel return mapping algorithm for the numerical integration of general isotropic finite strain elastoplastic constitutive models for geomaterials. The constitutive formulation is founded on multiplicative decomposition of the deformation gradient. The logarithmic strain measure as well as the exponential approximation of the plastic flow rule is utilized to restore the standard infinitesimal format return mapping algorithm. Central to the algorithm is the exploitation of a set of three mutually orthogonal unit base tensors for the representation of constitutive relations and the corresponding integration of the rate form of the constitutive equations. The base tensors constitute a local cylindrical coordinate system in the principal space, which allows to formulate the return mapping algorithm in the three‐dimensional space and reduce the dimension of the problem to be analyzed from six down to three. With the proposed approach, direct determination of the principal axes and the transformation procedure between the general space and the principal space, as required in traditional spectral decomposition, are avoided. Furthermore, the matrices that are involved in the inversion evaluation take simple forms, leading to extremely easy inverse computation. As a result, the consistent tangent operator can be streamlined into a form simpler and more compact than those by conventional integration methods. Following the formulation of the integration procedure, a numerical experiment is performed to assess the accuracy and efficiency of the proposed algorithm. Copyright © 2014 John Wiley & Sons, Ltd.     

Hybrid time integration and coupled solution methods for nonlinear finite element analysis of partially saturated deformable porous media at small strain

The goal of the paper is to determine the most efficient, yet accurate and stable, finite element nonlinear solution method for analysis of partially saturated deformable porous media at small strain. This involves a comparison between fully implicit, semi‐implicit, and explicit time integration schemes, with monolithically coupled and staggered‐coupled nonlinear solution methods and the hybrid combination thereof. The pore air pressure p_a is assumed atmospheric, that is, p_a=0 at reference pressure. The solid skeleton is assumed to be pressure‐sensitive nonlinear isotropic elastic. Coupled partially saturated ‘consolidation’ in the presence of surface infiltration and traction is simulated for a simple one‐dimensional uniaxial strain example and a more complicated plane strain slope example with gravity loading. Three mixed plane strain quadrilateral elements are considered: (i) Q4P4; (ii) stabilized Q4P4S; and (iii) Q9P4; “Q” refers to the number of solid skeleton displacement nodes, and “P” refers to the number of pore fluid pressure nodes. The verification of the implementation against an analytical solution for partially saturated pore water flow (no solid skeleton deformation) and comparison between the three time integration schemes (fully implicit, semi‐implicit, and explicit) are presented. It is observed that one of the staggered‐coupled semi‐implicit schemes (SIS(b)), combined with the fully implicit monolithically coupled scheme to resolve sharp transients, is the most efficient computationally. Copyright © 2015 John Wiley & Sons, Ltd.     

Coupled formulation and algorithms for the simulation of non‐planar three‐dimensional hydraulic fractures using the generalized finite element method

This paper presents a coupled hydro‐mechanical formulation for the simulation of non‐planar three‐dimensional hydraulic fractures. Deformation in the rock is modeled using linear elasticity, and the lubrication theory is adopted for the fluid flow in the fracture. The governing equations of the fluid flow and elasticity and the subsequent discretization are fully coupled. A Generalized/eXtended Finite Element Method (G/XFEM) is adopted for the discretization of the coupled system of equations. A Newton–Raphson method is used to solve the resulting system of nonlinear equations. A discretization strategy for the fluid flow problem on non‐planar three‐dimensional surfaces and a computationally efficient strategy for handling time integration combined with mesh adaptivity are also presented. Several three‐dimensional numerical verification examples are solved. The examples illustrate the generality and accuracy of the proposed coupled formulation and discretization strategies. Copyright © 2015 John Wiley & Sons, Ltd.     

Image‐based modelling and analysis of microstructures for two‐scale problems in geomechanics

This paper focuses on the geometry modelling and numerical analysis of microstructures of geomaterials employing the concept of image‐based engineering. The novel modelling and analysis techniques with digital images are incorporated with the mathematical homogenization method to study the interaction between individual phases, each of whose shape and spatial distribution are irregular. Owing to the distinctive features of these computational techniques, the evaluation of homogenized properties for geomaterials provides the reliable information about the micro‐ or macroscopic mechanical behaviours for engineering practice. It is, naturally, inevitable that engineers' demands on safety and efficient design place emphasis on quantitative estimates for these values. Thus, calibration accompanied with actual measurements comes within the scope of this study so that these properties would be realistic and practical from the engineering viewpoints. Copyright © 2002 John Wiley & Sons, Ltd.