Elasto‐plastic modelling of stress‐path‐dependent behaviour of interfaces

A single‐surface elasto‐plastic model developed by Desai and his coworkers is used to predict the behaviour of an interface between sand and a steel plate. The loading in the experiments and in their predictions followed various stress and displacement paths. The results of predictions of the two‐ and three‐dimensional behaviour of the interface under both constant normal stress and constant normal stiffness conditions are presented. The predictions are compared with their corresponding experimental results. The model parameters were determined on the basis of 2‐D conventional experiments under the condition of constant normal stress and they were used in the prediction of the interface behaviour in various stress paths. There is, in general, a good agreement between the predicted and experimental results. Copyright © 2000 John Wiley & Sons, Ltd.     

Monotonic and cyclic modeling of interface between geotextile and gravelly soil

This paper describes a modified elasto‐plasticity damage model to capture monotonic and cyclic behavior of the interface between a geotextile and gravelly soil. New damage variable and shear strength criterion are introduced on the basis of test observations. The formulations of the modified model are obtained by extending those of the original interface model. The model parameters with physical meaning are easily determined from a group of cyclic shear tests and a confining compression test. The model predictions are compared with the results of a series of direct shear tests and large‐scale pullout tests. The comparison results demonstrate that the model accurately describes the monotonic and cyclic stress–strain relationship of the interface between a geotextile and gravelly soil while capturing new characteristics: (1) the strength that is nonlinearly dependent on the normal stress; (2) significant shear strain‐softening; (3) the comprehensive volumetric strain response with dependency on the shear direction; and (4) the evolution of behavior associated with the changes in the physical state that includes the geotextile damage. This model is used in a finite element analysis of pullout tests, indicating that the tensile modulus of a geotextile has a significant effect on the response of the geotextile–gravel system. Copyright © 2009 John Wiley & Sons, Ltd.     

Finite element modelling of thick plates on two‐parameter elastic foundation

This paper is intended to give some information about how to build a model necessary for bending analysis of rectangular and circular plates resting on a two‐parameter elastic foundation, subjected to combined loading and permitting various types of boundary conditions. The formulation of the problem takes into account the shear deformation of the plate and the surrounding interaction effect outside the plate. The numerical model based on an 18‐node zero‐thickness isoparametric interface element interacting with a thick Reissner–Mindlin plate element with three degrees of freedom at each of the nine nodes, which enforce C⁰ continuity requirements for the displacements and rotations of the midsurface, is proposed. Stiffness matrices of a special interface element are superimposed on the global stiffness matrix to represent the stiffening elastic foundation under and beyond the plate. Some numerical examples are given to illustrate the advantages of the method presented. Copyright © 2001 John Wiley & Sons, Ltd.     

Homogenization of anisotropic elastoplastic behaviors of a porous polycrystal with interface effects

This paper is devoted to develop a theoretical framework to predict the macroscopic transversely isotropic elastoplastic behavior of clay‐like material, which is viewed as a porous polycrystal. We consider evolutions of two local plastic mechanisms of grains and interface simultaneously, for which a Schmid criterion is used for the strength of sheet‐like grains and a Tresca criterion for the strength of interfaces between particles. By adapting the standard incremental method, we propose firstly a classic self‐consistent model, which does not consider the effect of interface, then a generalized self‐consistent model in which the solid phase is represented by laminated (or isotropic) spherical grains surrounded by interfaces. Comparisons of numerical predictions between these two methods are performed and have demonstrated the validity of the generalized self‐consistent model taking account of interface effects. Numerical simulations of uniaxial compression tests have shown that the macroscopic elastoplastic behavior of polycrystalline (clay‐like) material can be successfully predicted by the way of considering the two local plastic mechanisms at microscopic scale. Copyright © 2013 John Wiley & Sons, Ltd.     

Constitutive description of interface behavior including cyclic loading and particle breakage within the framework of critical state soil mechanics

The cyclic behavior of soil–structure interface can be very important in dynamic problems. The cyclic behavior of soil–structure interface may be nonlinear, which includes hysteresis, hardening, degradation, and particle breakage. The breakage of granular soil particles during shearing of granular soil–structure interface is associated with cyclic degradation and can be critical to the dynamic behavior of soil–structure system. The critical state soil mechanics concept formerly used to simulate the nonlinear monotonic behavior of granular soil–structure interface was modified and extended to describe the cyclic behavior, especially soil‐particle breakage and degradation during cyclic shearing. Soil‐particle breakage was assumed to relate to the energy consumption during cyclic shearing and the critical state line of the soil–structure interface was assumed to translate with the consumption of shearing energy during cyclic shearing as the threshold value is attained. The model was formulated in the framework of generalized plasticity and is capable of describing the salient features of granular soil–structure interface under cyclic loading. Most of the model parameters have straightforward physical meanings and are calibrated using monotonic or cyclic interface test results. The proposed model was calibrated and validated against published test results. The dependency of interface behavior on stress path and cyclic degradation can be successfully described by the proposed model. Copyright © 2008 John Wiley & Sons, Ltd.     

A basal slip model for Lagrangian finite element simulations of 3D landslides

A Lagrangian numerical approach for the simulation of rapid landslide runouts is presented and discussed. The simulation approach is based on the so‐called Particle Finite Element Method. The moving soil mass is assumed to obey a rigid‐viscoplastic, non‐dilatant Drucker–Prager constitutive law, which is cast in the form of a regularized, pressure‐sensitive Bingham model. Unlike in classical formulations of computational fluid mechanics, where no‐slip boundary conditions are assumed, basal slip boundary conditions are introduced to account for the specific nature of the landslide‐basal surface interface. The basal slip conditions are formulated in the form of modified Navier boundary conditions, with a pressure‐sensitive threshold. A special mixed Eulerian–Lagrangian formulation is used for the elements on the basal interface to accommodate the new slip conditions into the Particle Finite Element Method framework. To avoid inconsistencies in the presence of complex shapes of the basal surface, the no‐flux condition through the basal surface is relaxed using a penalty approach. The proposed model is validated by simulating both laboratory tests and a real large‐scale problem, and the critical role of the basal slip is elucidated. Copyright © 2016 John Wiley & Sons, Ltd.     

Coupled HM analysis using zero‐thickness interface elements with double nodes. Part I: Theoretical model

In recent years, the authors have proposed a new double‐node zero‐thickness interface element for diffusion analysis via the finite element method (FEM) (Int. J. Numer. Anal. Meth. Geomech. 2004; 28 (9): 947–962). In the present paper, that formulation is combined with an existing mechanical formulation in order to obtain a fully coupled hydro‐mechanical (or HM) model applicable to fractured/fracturing geomaterials. Each element (continuum or interface) is formulated in terms of the displacements (u) and the fluid pressure (p) at the nodes. After assembly, a particular expression of the traditional ‘u–p’ system of coupled equations is obtained, which is highly non‐linear due to the strong dependence between the permeability and the aperture of discontinuities. The formulation is valid for both pre‐existing and developing discontinuities by using the appropriate constitutive model that relates effective stresses to relative displacements in the interface. The system of coupled equations is solved following two different numerical approaches: staggered and fully coupled. In the latter, the Newton–Raphson method is used, and it is shown that the Jacobian matrix becomes non‐symmetric due to the dependence of the discontinuity permeability on the aperture. In the part II companion paper (Int. J. Numer. Anal. Meth. Geomech. 2008; DOI: 10.1002/nag.730 ), the formulation proposed is verified and illustrated with some application examples. Copyright © 2008 John Wiley & Sons, Ltd.     

A theoretical and numerical framework for modeling gypsum cavity dissolution

In this paper, a large‐scale diffuse interface model is used to describe the evolution of a gypsum cavity formation induced by dissolution. The method is based upon the assumption of a pseudo‐component dissolving with a thermodynamic equilibrium boundary condition. A methodology is proposed based on numerical computations with fixed boundaries in order to choose suitable parameters for the diffuse interface model, and hence predict the correct dissolution fluxes and surface recession velocity. Additional simulations were performed to check which type of momentum balance equation should be used. The numerical results did not show a strong impact of this choice for the typical initial boundary value problems under consideration. Calculations with a variable density and Boussinesq approximation were also performed to evaluate the potential for natural convection. The results showed that the impact of density driven flows was negligible in the cases under investigation. The potential of the methodology is illustrated on two large‐scale configurations: one corresponding to a gypsum lens located strictly within a porous rock formation and the other to an isolated pillar in a flooded gypsum room and pillar quarry. Copyright © 2016 John Wiley & Sons, Ltd.     

Cyclic macro‐element for soil–structure interaction: material and geometrical non‐linearities

This paper presents a non‐linear soil–structure interaction (SSI) macro‐element for shallow foundation on cohesive soil. The element describes the behaviour in the near field of the foundation under cyclic loading, reproducing the material non‐linearities of the soil under the foundation (yielding) as well as the geometrical non‐linearities (uplift) at the soil–structure interface. The overall behaviour in the soil and at the interface is reduced to its action on the foundation. The macro‐element consists of a non‐linear joint element, expressed in generalised variables, i.e. in forces applied to the foundation and in the corresponding displacements. Failure is described by the interaction diagram of the ultimate bearing capacity of the foundation under combined loads. Mechanisms of yielding and uplift are modelled through a global, coupled plasticity–uplift model. The cyclic model is dedicated to modelling the dynamic response of structures subjected to seismic action. Thus, it is especially suited to combined loading developed during this kind of motion. Comparisons of cyclic results obtained from the macro‐element and from a FE modelization are shown in order to demonstrate the relevance of the proposed model and its predictive ability. Copyright © 2001 John Wiley & Sons, Ltd.     

Plane SH‐waves at a corrugated interface between two dissimilar perfectly conducting self‐reinforced elastic half‐spaces

In this paper, we have attempted a problem of reflection and refraction of plane harmonic SH‐wave at a corrugated interface between two different perfectly conducting self‐reinforced elastic half‐spaces. Rayleigh's method is employed to find out the expressions of reflection and refraction coefficients for first‐ and second‐order approximation of the corrugation. The expressions of these coefficients show that they depend on the properties of half‐spaces, angle of incidence, frequency of the incident wave and are strongly influenced by the corrugation of the interface. Numerical computations are performed for a particular model having special type of interface and the variation of these coefficients are depicted graphically against the angles of incidence, frequency parameter, corrugation parameter at different values of reinforcement parameters. Results of some earlier works are reduced as a particular case of this formulation. Copyright © 2005 John Wiley & Sons, Ltd.     

Three dimensional elasto‐plastic interface for embedded beam elements with interaction surface for the analysis of lateral loading of piles

This paper presents a numerical formulation for a three dimensional elasto‐plastic interface, which can be coupled with an embedded beam element in order to model its non‐linear interaction with the surrounding solid medium. The formulation is herein implemented for lateral loading of piles but is able to represent soil‐pile interaction phenomena in a general manner for different types of loading conditions or ground movements. The interface is formulated in order to capture localized material plasticity in the soil surrounding the pile within the range of small to moderate lateral displacements. The interface is formulated following two different approaches: (i) in terms of beam degrees of freedoms; and (ii) considering the displacement field of the solid domain. Each of these alternatives has its own advantages and shortcomings, which are discussed in this paper. The paper presents a comparison of the results obtained by means of the present formulation and by other well‐established analysis methods and test results published in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical modeling of three‐phase dissolution of underground cavities using a diffuse interface model

Natural evaporite dissolution in the subsurface can lead to cavities having critical dimensions in the sense of mechanical stability. Geomechanical effects may be significant for people and infrastructures because the underground dissolution may lead to subsidence or collapse (sinkholes). The knowledge of the cavity evolution in space and time is thus crucial in many cases. In this paper, we describe the use of a local nonequilibrium diffuse interface model for solving dissolution problems involving multimoving interfaces within three phases, that is, solid–liquid–gas as found in superficial aquifers and karsts. This paper generalizes developments achieved in the fluid–solid case, that is, the saturated case [1]. On one hand, a local nonequilibrium dissolution porous medium theory allows to describe the solid–liquid interface as a diffuse layer characterized by the evolution of a phase indicator (e.g., porosity). On the other hand, the liquid–gas interface evolution is computed using a classical porous medium two‐phase flow model involving a phase saturation, that is, generalized Darcy's laws. Such a diffuse interface model formulation is suitable for the implementation of a finite element or finite volume numerical model on a fixed grid without an explicit treatment of the interface movement. A numerical model has been implemented using a finite volume formulation with adaptive meshing (e.g., adaptive mesh refinement), which improves significantly the computational efficiency and accuracy because fine gridding may be attached to the dissolution front. Finally, some examples of three‐phase dissolution problems including density effects are also provided to illustrate the interest of the proposed theoretical and numerical framework. Copyright © 2014 John Wiley & Sons, Ltd.     

A macroelement formulation for shallow foundations on cohesive and frictional soils

The scope of this paper is to present a macroelement model for shallow foundations encompassing the majority of combinations of soil and foundation–soil interface conditions that are interesting for practical applications. The basic idea of the formulation is to raise the common assumption that the surface of ultimate loads of the foundation is identified as a yield surface in the space of force parameters which the footing is subjected to. Instead, each non‐linear mechanism participating in the global response of the system is modelled independently and the surface of ultimate loads is retrieved as the combined result of all active mechanisms. This allows formulating each mechanism by respecting its particular characteristics and offers the possibility of activating, modifying or deactivating each mechanism according to the context of application. The model comprises three non‐linear mechanisms: (a) the mechanism of sliding at the soil–footing interface, (b) the mechanism of soil yielding in the vicinity of the footing and (c) the mechanism of uplift as the footing may get detached from the soil. The first two are irreversible and dissipative and are combined within a multi‐mechanism plasticity formulation. The third mechanism is reversible and non‐dissipative. It is reproduced with a phenomenological non‐linear hyperelastic model. The model is validated with respect to the existing results for shallow foundations under quasi‐static loading tests. It is shown that although the ultimate surface of the foundation is not explicitly used in the formulation of the model, the obtained force states by the model are always contained within it. Copyright © 2010 John Wiley & Sons, Ltd.     

Modeling of dynamic cohesive fracture propagation in porous saturated media

In this paper, a mathematical model is presented for the analysis of dynamic fracture propagation in the saturated porous media. The solid behavior incorporates a discrete cohesive fracture model, coupled with the flow in porous media through the fracture network. The double‐nodded zero‐thickness cohesive interface element is employed for the mixed mode fracture behavior in tension and contact behavior in compression. The crack is automatically detected and propagated perpendicular to the maximum effective stress. The spatial discretization is continuously updated during the crack propagation. Numerical examples from the hydraulic fracturing test and the concrete gravity dam show the capability of the model to simulate dynamic fracture propagation. The comparison is performed between the quasi‐static and fully dynamic solutions, and the performance of two analyses is investigated on the values of crack length and crack mouth opening. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamic sliding of tetrahedral wedge: The role of interface friction

The role of interface friction is studied by slow direct shear tests and rapid shaking table experiments in the context of dynamic slope stability analysis in three dimensions. We propose an analytical solution for dynamic, single and double face sliding and use it to validate 3D‐DDA. Single face results are compared with Newmark's solution and double face results are compared with shaking table experiments performed on a concrete tetrahedral wedge model, the interface friction of which is determined by constant velocity and velocity stepping, direct shear tests. A very good agreement between Newmark's method on one hand and our 3D analytical solution and 3D‐DDA on the other is observed for single plane sliding with 3D‐DDA exhibiting high sensitivity to the choice of numerical penalty value. The results of constant and variable velocity direct shear tests reveal that the tested concrete interface exhibits velocity weakening. This is confirmed by shaking table experiments where friction degradation upon multiple cycles of shaking culminated in wedge run out. The measured shaking table results are fitted with our 3D analytical solution to obtain a remarkable linear logarithmic relationship between friction coefficient and sliding velocity that remains valid for five orders of magnitude of sliding velocity. We conclude that the velocity‐dependent friction across rock discontinuities should be integrated into dynamic rock slope analysis to obtain realistic results when strong ground motions are considered. Copyright © 2011 John Wiley & Sons, Ltd.     

Composite element model for the bonded anchorage head of stranded wire cable in tension

An elasto‐viscoplastic model is formulated using composite element technique for the bonded anchorage head of stranded wire cable in rock mass. This composite element contains sub‐elements corresponding to the rock material, the grout material, the stranded wire material, the rock/grout interface, and the grout/stranded wire interface, respectively. The displacement in each aforementioned sub‐element is interpolated from the corresponding nodal displacements of the composite element. In this manner, the mesh generation taking into account of tension cable anchors may be highly facilitated. By the application of the virtual work principle, the governing equation for solving the nodal displacements of the composite element is established. The proposed model has been incorporated into the conventional finite element algorithm and implemented in the program CORE3, in which the anchorage head is embedded within the composite elements. The comparative study concerning the pull‐out test has been carried out for the validation of the proposed model and algorithm. Copyright © 2015 John Wiley & Sons, Ltd.     

Frictional contact of laminated elastic half‐spaces allowing interface cavities. Part 1: Analytical treatment

The paper deals with the plane problem on frictional contact of stratified elastic half‐spaces provided discontinuity of their direct touch. Imperfectness of contact of the bodies is assumed to be caused by surface unevenness of their surface layers. The problem is formulated within the framework of the homogenized model with microlocal parameters. Using the method of complex potentials in combination with the method of interface gaps the problem is reduced to a singular integral equation on the function of interface gap height. Copyright © 2001 John Wiley & Sons, Ltd.     

Application of thermodynamics to the global modelling of shallow foundations on frictional material

Soil–shallow foundation interaction has been theoretically analysed within the framework of thermomechanics. The design of a global interaction model has been achieved with an original treatment of the Clausius–Duhem inequality. The role of the gravity volume forces is emphasized. The paper is focused on a strip footing based on dense sand and subjected to time‐independent plastic processes. The theoretical approach has confirmed that an associated global flow rule cannot be expected to hold true. The analysis of the sources of dissipation has led to the development of a soil–footing interface model and a complete interaction model accounting for the interface constraints and the intrinsic frictional properties of the soil. Finally, the abilities of the complete model are checked by comparisons with experimental results found in the literature. Copyright © 2001 John Wiley & Sons, Ltd.