Dynamic analysis of strain localization in water‐saturated clay using a cyclic elasto‐viscoplastic model

A computational framework is presented for dynamic strain localization and deformation analyses of water‐saturated clay by using a cyclic elasto‐viscoplastic constitutive model. In the model, the nonlinear kinematic hardening rule and softening due to the structural degradation of soil particles are considered. In order to appropriately simulate the large deformation phenomenon in strain localization analysis, the dynamic finite element formulation for a two‐phase mixture is derived in the updated Lagrangian framework. The shear band development is shown through the distributions of viscoplastic shear strain, the axial strain, the mean effective stress, and the pore water pressure in a normally consolidated clay specimen. From the local stress–strain relations, more brittleness is found inside the shear bands than outside of them. The effects of partially drained conditions and mesh‐size dependency on the shear banding are also investigated. The effect of a partially drained boundary is found to be insignificant on the dynamic shear band propagation because of the rapid rate of applied loading and low permeability of the clay. Using the finer mesh results in slightly narrower shear bands; nonetheless, the results manifest convergency through the mesh refinement in terms of the overall shape of shear banding and stress–strain relations. Copyright © 2013 John Wiley & Sons, Ltd.     

Description of deformation process in inherently anisotropic granular materials

The main focus in this work is on modeling of mechanical response of granular materials that display inherent anisotropy. Both the experimental and numerical investigations are described. First, the results of direct shear as well as drained/undrained triaxial tests that involve crushed limestone with elongated angular‐shaped particles are reviewed. Afterward, a mathematical framework is presented for modeling of elastic/ inelastic deformation that incorporates the multi‐laminate approach. The deformation is monitored on a set of randomly oriented planes, and the formulation incorporates the thickness of the shear band that is associated with sliding/separation process. A systematic procedure for identification of material functions/ parameters is outlined that is based on the results of direct shear tests, and the framework is later applied to simulate the behavior under triaxial conditions. The results of numerical simulations are compared with the experimental data. Copyright © 2011 John Wiley & Sons, Ltd.     

Kinematic modelling of shear band localization using discrete finite elements

Modelling shear band is an important problem in analysing failure of earth structures in soil mechanics. Shear banding is the result of localization of deformation in soil masses. Most finite element schemes are unable to model discrete shear band formation and propagation due to the difficulties in modelling strain and displacement discontinuities. In this paper, a framework to generate shear band elements automatically and continuously is developed. The propagating shear band is modelled using discrete shear band elements by splitting the original finite element mesh. The location or orientation of the shear band is not predetermined in the original finite element mesh. Based on the elasto‐perfect plasticity with an associated flow rule, empirical bifurcation and location criteria are proposed which make band propagation as realistic as possible. Using the Mohr–Coulomb material model, various results from numerical simulations of biaxial tests and passive earth pressure problems have shown that the proposed framework is able to display actual patterns of shear banding in geomaterials. In the numerical examples, the occurrence of multiple shear bands in biaxial test and in the passive earth pressure problem is confirmed by field and laboratory observations. The effects of mesh density and mesh alignment on the shear band patterns and limit loads are also investigated. Copyright © 2003 John Wiley & Sons, Ltd.     

Bearing capacity of shallow foundations in transversely isotropic granular media

The main focus in this work is on the assessment of bearing capacity of a shallow foundation in an inherently anisotropic particulate medium. Both the experimental and numerical investigations are carried out using a crushed limestone with elongated angular‐shaped aggregates. The experimental study involves small‐scale model tests aimed at examining the variation of bearing capacity as a function of the angle of deposition of the material. In addition, the results of a series of triaxial and direct shear tests are presented and later employed to identify the material functions/parameters. The numerical part of this work is associated with the development and implementation of a constitutive framework that describes the mechanical response of transversely isotropic frictional materials. The framework is based on the elastoplasticity and accounts for the effects of strain localization and inherent anisotropy of both the deformation and strength characteristics. The results of numerical simulations are compared withthe experimental data. A parametric study is also carried out aimed at examining the influence of various simplifications in the mathematical framework on its predictive abilities. Copyright © 2009 John Wiley & Sons, Ltd.     

Finite volume–based modeling of flow‐induced shear failure along fracture manifolds

In this paper, a numerical model to predict flow‐induced shear failure along pre‐existing fractures is presented. The framework is based on a discrete fracture representation embedded in a continuum describing the damaged matrix. A finite volume method is used to compute both flow and mechanical equilibrium, whereas specifically tailored basis functions are used to account for the physics at discontinuities. The failure criterion is based on a maximum shear strength limit, which changes with varying compressive stress on the fracture manifold. The displacements along fracture manifolds are obtained such that force balance is achieved under conditions, where shear stress of the failing fracture segment is constrained to the maximum shear strength at the segment. Simultaneously, the fluid pressure is computed independently of the shear slip. A relaxation model approach is used to obtain the maximum shear limit on the fracture manifold, which leads to grid convergence.     

Dilatancy of granular materials in a strain space multiple mechanism model

A granular material consists of an assemblage of particles with contacts newly formed or disappeared, changing the micromechanical structures during macroscopic deformation. These structures are idealized through a strain space multiple mechanism model as a twofold structure consisting of a multitude of virtual two‐dimensional mechanisms, each of which consists of a multitude of virtual simple shear mechanisms of one‐dimensional nature. In particular, a second‐order fabric tensor describes direct macroscopic stress–strain relationship, and a fourth‐order fabric tensor describes incremental relationship. In this framework of modeling, the mechanism of interlocking defined as the energy less component of macroscopic strain provides an appropriate bridge between micromechanical and macroscopic dilative component of dilatancy. Another bridge for contractive component of dilatancy is provided through an obvious hypothesis on micromechanical counterparts being associated with virtual simple shear strain. It is also postulated that the dilatancy along the stress path beyond a line slightly above the phase transformation line is only due to the mechanism of interlocking and increment in dilatancy due to this interlocking eventually vanishing for a large shear strain. These classic postulates form the basis for formulating the dilatancy in the strain space multiple mechanism model. The performance of the proposed model is demonstrated through simulation of undrained behavior of sand under monotonic and cyclic loading. Copyright © 2010 John Wiley & Sons, Ltd.     

Thermoplasticity and strain localization in transversely isotropic materials based on anisotropic critical state plasticity

Geomaterials such as soils and rocks are inherently anisotropic and sensitive to temperature changes caused by various internal and external processes. They are also susceptible to strain localization in the form of shear bands when subjected to critical loads. We present a thermoplastic framework for modeling coupled thermomechanical response and for predicting the inception of a shear band in a transversely isotropic material using the general framework of critical state plasticity and the specific framework of an anisotropic modified Cam–Clay model. The formulation incorporates anisotropy in both elastic and plastic responses under the assumption of infinitesimal deformation. The model is first calibrated using experimental data from triaxial tests to demonstrate its capability in capturing anisotropy in the mechanical response. Subsequently, stress‐point simulations of strain localization are carried out under two different conditions, namely, isothermal localization and adiabatic localization. The adiabatic formulation investigates the effect of temperature on localization via thermomechanical coupling. Numerical simulations are presented to demonstrate the important role of anisotropy, hardening, and thermal softening on strain localization inception and orientation. Copyright © 2016 John Wiley & Sons, Ltd.     

Non‐isothermal plasticity model for cyclic behaviour of soils

On the one hand, it has been observed that liquefaction‐induced shear deformation of soils accumulates in a cycle‐by‐cycle pattern. On the other hand, it is known that heating could induce plastic hardening. This study deals with the constitutive modelling of the effect that heat may have on the cyclic mechanical properties of cohesive soils, a relatively new area of interest in soil mechanics. In this paper, after a presentation of the thermo‐mechanical framework, a non‐isothermal plasticity cyclic model formulation is presented and discussed. The model calibration is described based on data from laboratory sample tests. It includes numerical simulations of triaxial shear tests at various constant temperatures. Then, the model predictions are compared with experimental results and discussed in the final section. Both drained and undrained loading conditions are considered. The proposed constitutive model shows good ability to capture the characteristic features of behaviour. Copyright © 2007 John Wiley & Sons, Ltd.     

Finite strain analysis of nonuniform deformation inside shear bands in sands

A methodology has been developed to extend the incremental (Eulerian) Digital Image Correlation (DIC) technique to enable a Lagrangian‐based large‐strain analysis framework to examine the nature of strain and kinematic nonuniformity within shear bands in sands. Plane strain compression tests are performed on dense sands in an apparatus that promotes unconstrained persistent shear band formation. DIC is used to capture incremental, grain‐scale displacements in and around shear bands. The performance of the developed accumulation algorithm is validated by comparing accumulated displacements with two sources of reference measurements. A comparison between large and infinitesimal rotation is performed, demonstrating the nature of straining within shear bands in sands and the necessity of using a finite strain formulation to characterize ensuing behavior. Volumetric strain variation along the shear band is analyzed throughout macroscopic postpeak deformation. During softening, volumetric activity within the shear band is purely dilative. During the global critical state, the shear band material is seen on the average to deform at zero volumetric strain; however, locally, the sand is seen to exhibit significant nonzero volumetric strain, putting into question the current definition of critical state. At the softening‐critical state transition, a spatially periodic pattern of alternating contraction and dilation along the shear band is evidenced, and a preliminary evaluation indicates that the periodicity appears to be a physical phenomenon dictated only in part by median grain size. Copyright © 2011 John Wiley & Sons, Ltd.     

Elasto‐plastic model for cement‐treated sand

This paper presents an elasto‐plastic model for non‐linear analyses of cement‐treated sand. Various laboratory tests were systematically carried out to investigate the pre‐peak and post‐peak behaviours of a cement‐treated sand. On the basis of these experimental results, the new model was built within the framework of a relatively simple elasto‐plastic theory. Two failure criteria are employed to express tensile and shear failure characteristics observed in the experimental results of the cement‐treated sand. The proposed model can describe strain‐hardening and strain‐softening responses under both failure modes. In the strain‐softening rules, the smeared crack concept is used, and a characteristic length is considered to avoid the issue of mesh‐size dependency. Since the failure criterion and strain‐hardening/softening rules are based on the experimental evidences, the model is relatively easy to understand and the parameters used in the model have clear physical meaning. The proposed model was applied to simulate the behaviour of cement‐treated sand in various laboratory tests, allowing for a reasonable comprehensive evaluation. It was demonstrated that the proposed model is suitable for describing both the tensile and shear failure behaviours of cement‐treated sand. Copyright © 2006 John Wiley & Sons, Ltd.     

Crustal reworking in a shear zone: transformation of metagranite to migmatite

This study uses field, microstructural and geochemical data to investigate the processes contributing to the petrological diversity that arises when granitic continental crust is reworked. The Kinawa migmatite formed when Archean TTG crust in the São Francisco Craton, Brazil was reworked by partial melting at ~730 °C and 5–6 kbar in a regional‐scale shear zone. As a result, a relatively uniform leucogranodiorite protolith produced compositionally and microstructurally diverse diatexites and leucosomes. All outcrops of migmatite display either a magmatic foliation, flow banding or transposed leucosomes and indicate strong, melt‐present shearing. There are three types of diatexite. Grey diatexites are interpreted to be residuum, although melt segregation was incomplete in some samples. Biotite stable, H₂O‐fluxed melting is inferred via the reaction Pl + Kfs + Qz + H₂O = melt and geochemical modelling indicates 0.35–0.40 partial melting. Schlieren diatexites are extremely heterogeneous; residuum‐rich domains alternate with leucocratic quartzofeldspathic domains. Homogeneous diatexites have the highest SiO₂ and K₂O contents and are coarse‐grained, leucocratic rocks. Homogeneous diatexites, quartzofeldspathic domains from the schlieren diatexites and the leucosomes contain both plagioclase‐dominated and K‐feldspar‐dominated feldspar framework microstructures and hence were melt‐derived rocks. Both types of feldspar frameworks show evidence of tectonic compaction. Modelling the crystallization of an initial anatectic melt shows plagioclase appears first; K‐feldspar appears after ~40% crystallization. In the active shear zone setting, shear‐enhanced compaction provided an essentially continuous driving force for segregation. Thus, Kinawa migmatites with plagioclase frameworks are interpreted to have formed by shear‐enhanced compaction early in the crystallization of anatectic melt, whereas those with K‐feldspar frameworks formed later from the expelled fractionated melt. Trace element abundances in some biotite and plagioclase from the fractionated melt‐derived rocks indicate that these entrained minerals were derived from the wall rocks. Results from the Kinawa migmatites indicate that the key factor in generating petrological diversity during crustal reworking is that shear‐enhanced compaction drove melt segregation throughout the period that melt was present in the rocks. Segregation of melt during melting produced residuum and anatectic melt and their mixtures, whereas segregation during crystallization resulted in crystal fractionation and generated diverse plagioclase‐rich rocks and fractionated melts.     

Transpressive Structures in the Ghadir Shear Belt,Eastern Desert,Egypt: Evidence for Partitioning of Oblique Convergence in the Arabian‐Nubian Shield during Gondwana Agglutination

Transpressional deformation has played an important role in the late Neoproterozoic evolution of the ArabianNubian Shield including the Central Eastern Desert of Egypt. The Ghadir Shear Belt is a 35 km-long, NW-oriented brittleductile shear zone that underwent overall sinistral transpression during the Late Neoproterozoic. Within this shear belt, strain is highly partitioned into shortening, oblique, extensional and strike-slip structures at multiple scales. Moreover, strain partitioning is heterogeneous along-strike giving rise to three distinct structural domains. In the East Ghadir and Ambaut shear belts, the strain is pure-shear dominated whereas the narrow sectors parallel to the shear walls in the West Ghadir Shear Zone are simple-shear dominated. These domains are comparable to splay-dominated and thrust-dominated strike-slip shear zones. The kinematic transition along the Ghadir shear belt is consistent with separate strike-slip and thrustsense shear zones. The earlier fabric(S1), is locally recognized in low strain areas and SW-ward thrusts. S2 is associated with a shallowly plunging stretching lineation(L2), and defines ～NW-SE major upright macroscopic folds in the East Ghadir shear belt. F2 folds are superimposed by ～NNW–SSE tight-minor and major F3 folds that are kinematically compatible with sinistral transpressional deformation along the West Ghadir Shear Zone and may represent strain partitioning during deformation. F2 and F3 folds are superimposed by ENE–WSW gentle F4 folds in the Ambaut shear belt. The sub-parallelism of F3 and F4 fold axes with the shear zones may have resulted from strain partitioning associated with simple shear deformation along narrow mylonite zones and pure shear-dominant deformation in fold zones. Dextral ENEstriking shear zones were subsequently active at ca. 595 Ma, coeval with sinistral shearing along NW-to NNW-striking shear zones. The occurrence of upright folds and folds with vertical axes suggests that transpression plays a significant role in the tectonic evolution of the Ghadir shear belt. Oblique convergence may have been provoked by the buckling of the Hafafit gneiss-cored domes and relative rotations between its segments. Upright folds, fold with vertical axes and sinistral strike-slip shear zones developed in response to strain partitioning. The West Ghadir Shear Zone contains thrusts and strikeslip shear zones that resulted from lateral escape tectonics associated with lateral imbrication and transpression in response to oblique squeezing of the Arabian-Nubian Shield during agglutination of East and West Gondwana.     

Exhumed lateral margins and increasing flow confinement of a submarine landslide complex

Submarine landslides, including the basal shear surfaces along which they fail, and their subsequent infill, are commonly observed in modern seabed and seismic reflection data sets; their resultant relief impacts sediment routing and storage patterns on continental margins. Here, three stacked submarine landslides are documented from the Permian Ecca Group, Laingsburg depocentre, Karoo Basin, South Africa, including two superimposed lateral margins. The stratigraphic framework includes measured sections and correlated surfaces along a 3 km long, 150 m high outcrop. Two stacked 2·0 to 4·5 km wide and 90 m and 60 m deep erosion surfaces are recognized, with lateral gradients of 8° and 4°, respectively. The aim of this study was to understand the evolution of a submarine landslide complex, including: evolution of basal shear surfaces/zones; variation of infill confinement; and location of the submarine landslides in the context of basin‐scale sedimentation and degradation rates. Three stages of formation are identified: (i) failure of submarine landslide 1, with deposition of unconfined remobilized deposits; (ii) failure of submarine landslide 2, forming basal shear surface/zone 1, with infill of remobilized deposits and weakly confined turbidites; and (iii) failure of submarine landslide 3, forming basal shear surface/zone 2, with infill of remobilized deposits and confined turbidites, transitioning stratigraphically to unconfined deposits. The expression of basal shear varies laterally, from metres thick zones in silt‐rich strata to sharp stepped surfaces in sand‐rich strata. Faulting and rotation of overlying bedding suggest that the shear surfaces/zones were dynamic. Stacking of landslides resulted from multi‐phase slope failure, increasing down‐dip topography and confinement of infilling deposits. The failure slope was probably a low supply tilted basin margin evidenced by megaclast entrainment from underlying basin‐floor successions and the lack of channel systems. This study develops a generic model of landslide infill, as a function of sedimentation and degradation rates, which can be applied globally.     

Using the Maximum Effective Moment Criterion to Interpret Quartz <c>‐Fabric Patterns

The Maximum Effective Moment (MEM) criterion predicts that the initial orientation of ductile shear zones and shear bands is ~55° relative to the maximum principal stress axis (σ1) and that the kinematic vorticity number (Wk) is ~0.94. These preferred orientations should be reflected in the pattern of quartz -fabrics in shear zones and shear bands. Common quartz -fabrics in plane strain can be divided into low-temperature (L) and high-temperature (H) fabrics, with each group showing three patterns. A steady flow with a constant value of Wk≈0.94 gives rise to L-1 and H-1 patterns, which are commonly characterized by a single axis girdle normal to the shear zone and a single -point maximum parallel to the shear zone.Once the conjugate set develops, L-1 and H-1 have opening angles of ~70° and ~110°, respectively. L-2 and H-2 are asymmetric patterns associated with variable deformation partitioning and vorticity values of 0< Wk<0.94. In contrast, L-3 and H-3 are symmetric patterns associated with 100% deformation partitioning and Wk=0. The opening angle in quartz -fabrics is implicitly linked to the temperature during deformation. The opening angle is ~70° at low temperature and ~110° at high temperature. However, a linear correction between the opening angle and the temperature cannot be established. During deformation partitioning, synthetic shear bands form earlier than antithetic bands and are more easily developed. This may result in opening angles of <70° for low-temperature fabrics and of >110° for high-temperature fabrics. The following criteria can be used to recognize reworked shear zones that have experienced multiple orogenic phases and changes in the stress state: 1) the initial Wk is larger or smaller than ~0.94; 2) the change in Wk is abrupt, rather than progressive; 3) inconsistent shear senses are inferred for the different phases of deformation; and 4) a negative value of Wk is found in reworked shear zones.     

Constitutive modelling of aggregate interlock in concrete

A model for formed cracks in concrete is presented. The model can be used in isolation for existing cracks or linked with other damage or plasticity models and applied once a crack has fully formed. It can be applied directly to interface finite elements or used to control the behaviour of crack planes in more general constitutive models that are applied to 2D and 3D continuum elements. The focus of the present development is on aggregate interlock and crack closing behaviour, which is examined from available experimental data. A contact function is derived and is used to differentiate between three contact states. These states are named open, where there is no contact, interlock, for which the stresses depend upon the nearest distance to the contact surface and closed, for which the stresses depend upon the relative displacements directly. The model is developed within an elasto‐plastic framework using effective stresses, which are related to the total stresses via a contact proportion function. The relationship between the effective normal and shear yield stresses is found to be parabolic and the yield shear stress to be dependent upon the opening and embedment displacements. The performance of the model is assessed against experimental data from shear‐normal tests and it is concluded that the model is able to represent the key characteristics of the behaviour of formed cracks in concrete. Copyright © 2002 John Wiley & Sons, Ltd.     

Elastoplastic multiphase model for simulating the response of piled raft foundations subject to combined loadings

A multiphase model and corresponding computational time‐saving finite element code is proposed in this paper for predicting the settlements experienced by a piled raft foundation when subject to the combined action of vertical and lateral loadings. This model, which is formulated in the framework of an elastoplastic behaviour for the soil and the reinforcing piles as well, explicitly accounts for the shear and flexural behaviour of the latter. Starting from a simple analytical example where all the concepts attached to this model are clearly illustrated, the main stages leading to its finite element implementation are then presented. The numerical tool thus elaborated, is applied to the simulation of a pile‐reinforced strip foundation submitted to a horizontally applied seismic load in addition to a permanent vertical load. One of the key results of such a simulation in terms of design recommendation, lies in the conclusion that, while the shear and flexural contributions of the reinforcement play quite a negligible role in the case of a vertical load (as compared with their axial resistance), they remain absolutely essential for withstanding the seismic lateral loading. Copyright © 2006 John Wiley & Sons, Ltd.     

Liquefaction and cyclic mobility model for saturated granular media

A new constitutive law for the behaviour of undrained sand subjected to dynamic loading is presented. The proposed model works for small and large strain ranges and incorporates contractive and dilative properties of the sand into the unified numerical scheme. These features allow to correctly predict liquefaction and cyclic mobility phenomena for different initial relative densities of the soil. The model has been calibrated as an element test, by using cyclic simple shear data reported in the literature. For the contractive sand behaviour a well‐known endochronic densification model has been used, whereas a plastic model with a new non‐associative flow rule is applied when the sand tends to dilate. Both dilatancy and flow rule are based on a new state parameter, associated to the stiffness degradation of the material as the shaking goes on. Also, the function that represents the rearrangement memory of the soil takes a zero value when the material dilates, in order to easily model the change in the internal structure. Proceeding along this kind of approach, liquefaction and cyclic mobility are modelled with the same constitutive law, within the framework of a bi‐dimensional FEM coupled algorithm developed in the paper. For calibration purposes, the behaviour of the soil in a cyclic simple shear test has been simulated, in order to estimate the influence of permeability, frequency of loading, and homogeneity of the shear stress field on the laboratory data. Copyright © 2006 John Wiley & Sons, Ltd.     

A model for stress and plastic strain induced nonlinear,hyperelastic anisotropy in soils

The experimental evidence that cohesive and granular soils possess an elastic range in which the elasticity is both nonlinear and anisotropic—with stiffness and directional characteristics strongly dependent on stress and plastic strain (the so‐called ‘stress history’)—is given a formulation based on hyperelasticity. This is accomplished within the framework of elastoplastic coupling, through a new proposal of elastic potentials and a combined use of a plastic‐strain‐dependent fabric tensor and nonlinear elasticity. When used within a simple elastoplastic framework, the proposed model is shown to yield very accurate simulations of the evolution of elastic properties from initial directional stiffening to final isotropic degradation. Within the proposed constitutive framework, it is shown that predictions of shear band formation and evolution become closer to the existing experimental results, when compared to modelling in which elasticity does not evolve. Copyright © 2007 John Wiley & Sons, Ltd.     

Effects of pore water pressure dissipation on rate dependency of shear strength in localised failure of soils

The paper presents analytical solutions for the evolution of excess pore pressures in the vicinity of a shear band in a rate‐dependent, strain‐softening permeable soil, with the aim to explore, both qualitatively and quantitatively, the potential variation of failure shear stress in the shear band. The solutions encompass both dissipation of a pre‐existing pore pressure regime within the main soil domain, and the effects of generation of additional pore pressure within the shear band itself. The simplified analytical solutions were checked by numerical inversion of exact solutions in Laplace transform space, confirming their high accuracy. The solutions show that it is possible for the failure shear stress to rise initially because of short‐term dissipation of the pre‐existing excess pore pressure at a faster rate than generation of new excess pore pressure within the shear band. This apparent strain hardening in a strain‐softening soil can be misleading in that it can temporarily slow down the sliding mass and create a false sense of stabilization of the slope. It can also result in additional temporary shear resistance for sliding foundations or pipelines on the seabed. Copyright © 2015 John Wiley & Sons, Ltd.