From solid to granular gases: the steady state for granular materials

This paper aims at extending the well‐known critical state concept, associated with quasi‐static conditions, by accounting for the role played by the strain rate when focusing on the steady, simple shear flow of a dry assembly of identical, inelastic, soft spheres. An additional state variable for the system, the granular temperature, is accounted for. The granular temperature is related to the particle velocity fluctuations and measures the agitation of the system. This state variable, as is in the context of kinetic theories of granular gases, is assumed to govern the response of the material at large strain rates and low concentrations. The stresses of the system are associated with enduring, frictional contacts among particles involved in force chains and nearly instantaneous collisions. When the first mechanism prevails, the material behaves like a solid, and constitutive models of soil mechanics hold, whereas when inelastic collisions dominate, the material flows like a granular gas, and kinetic theories apply. Considering a pressure‐imposed flow, at large values of the normal stress and small values of the shear rate, the theory predicts a nonmonotonic shear rate dependence of the stress ratio at the steady state, which is likely to govern the evolution of landslides. Copyright © 2013 John Wiley & Sons, Ltd.     

Theoretical investigation of the cavity expansion problem based on a hypoplasticity model

The problem of the symmetric quasi‐static large‐strain expansion of a cavity in an infinite granular body is studied. The body is assumed to be dry or fully drained so that the presence of the pore water can be disregarded. Both spherical and cylindrical cavities are considered. Numerical solutions to the boundary value problem are obtained with the use of the hypoplastic constitutive relation calibrated for a series of granular soils. As the radius of the cavity increases, the stresses and the density on the cavity surface asymptotically approach limit values corresponding to a so‐called critical state. For a given soil, the limit values depend on the initial stresses and the initial density. A comparison is made between the solutions for different initial states and different soils. Applications to geotechnical problems such as cone penetration test and pressuremeter test are discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

Stress–dilatancy based modelling of granular materials and extensions to soils with crushable grains

Stress–dilatancy relations have played a crucial role in the understanding of the mechanical behaviour of soils and in the development of realistic constitutive models for their response. Recent investigations on the mechanical behaviour of materials with crushable grains have called into question the validity of classical relations such as those used in critical state soil mechanics. In this paper, a method to construct thermodynamically consistent (isotropic, three‐invariant) elasto‐plastic models based on a given stress–dilatancy relation is discussed. Extensions to cover the case of granular materials with crushable grains are also presented, based on the interpretation of some classical model parameters (e.g. the stress ratio at critical state) as internal variables that evolve according to suitable hardening laws. Copyright © 2004 John Wiley & Sons, Ltd.     

Modeling of granular bed‐stone column‐improved soft soil

The present study pertains to the development of a mechanical model for predicting the behavior of granular bed‐stone column‐reinforced soft ground. The granular layer that has been placed over the stone column‐reinforced soft soil has been idealized by the Pasternak shear layer. The saturated soft soil has been idealized by the Kelvin–Voigt model to represent its time‐dependent behavior and the stone columns are idealized by stiffer Winkler springs. The nonlinear behavior of the granular fill has been incorporated in this study by assuming a hyperbolic variation of shear stress with shear strain as in one reported literature. Similarly, for soft soil it has also been assumed that load‐settlement variation is hyperbolic in nature. The effect of consolidation of the soft soil due to inclusion of the stone columns has also been included in the model. Plane‐strain conditions are considered for the loading and foundation soil system. The numerical solutions are obtained by a finite difference scheme and the results are presented in a non‐dimensional form. Parametric studies for a uniformly loaded strip footing have been carried out to show the effects of various parameters on the total as well as differential settlement and stress concentration ratio. It has been observed that the presence of granular bed on the top of the stone columns helps to transfer stress from soil to stone columns and reduces maximum as well as differential settlement. Copyright © 2007 John Wiley & Sons, Ltd.     

A multi‐mechanism constitutive model for plastic adaption under cyclic loading

As is well known, granular soils under cyclic loading dissipate a large amount of energy and accumulate large irreversible strains. Usually, with time, this second effect reduces and the accumulation rate decreases with the number of cycles until obtaining a sort of ideal stationary cyclic state at which ratcheting disappears. In this paper, only this ideal state is taken into consideration and simulated by means of a multi‐mechanism constitutive model for plastic adaptation. For this purpose, the concept of cycle is discussed, many different categories of cyclic stress/strain paths are considered and some theoretical issues concerning both the flow and the strain‐hardening rules are tackled. Even though the paper focuses on soil behaviour, the conclusions can be extended to all materials exhibiting ratcheting due to volumetric behaviour.Copyright © 2013 John Wiley & Sons, Ltd.     

A visco‐elasto‐plastic model for granular materials under simple shear conditions

The numerical simulation of rapid landslides is quite complex mainly because constitutive models capable of simulating the mechanical behaviour of granular materials in the pre‐collapse and post‐collapse regimes are still missing. The goal of this paper is to introduce a constitutive model capable of capturing the response of dry granular flows from quasi‐static to dynamic conditions, in particular when the material experiences a sort of solid‐to‐fluid phase transition. An ideal assembly of identical spheres under simple shear conditions is considered. In the constitutive model, void ratio and granular temperature have been chosen as state variables, and both shear and normal stresses are computed as the sum of two contributions: the quasi‐static one and the collisional one. The former is determined by using a perfect elasto‐plastic model including the critical state concept, while the latter is derived from the kinetic theory of granular gases. The evolution of the granular temperature, fundamentally governing the material phase transition, is obtained by imposing the kinetic fluctuating energy balance. The constitutive relationship has been integrated, under both constant pressure and constant volume conditions, and the influence of shear strain rate, initial void ratio and normal pressure on the mechanical response has been investigated. Copyright © 2015 John Wiley & Sons, Ltd.     

An enhanced constitutive model for crushable granular materials

Studies in the past have tried to reproduce the mechanical behaviour of granular materials by proposing constitutive relations based on a common assumption that model parameters and parameters describing the properties, including gradation of individual grains are inevitably linked. However successful these models have proved to be, they cannot account for the changes in granular assembly behaviour if the grains start to break during mechanical loading. This paper proposes to analyse the relation between grading change and the mechanical behaviour of granular assembly. A way to model the influence of grain breakage is to use a critical state‐based model. The influence of the amount of grain breakage during loading, depending on the individual grain strength and size distribution, can be introduced into constitutive relations by means of a new parameter that controls the evolution of critical state with changes in grain size distribution. Experimental data from a calcareous sand, a quartz sand, and a rockfill material were compared with numerical results and good‐quality simulations were obtained. The main consequences of grain breakage are increased compressibility and a gradual dilatancy disappearance in the granular material. The critical state concept is also enriched by considering its overall relation to the evolution of the granular material. Copyright © 2009 John Wiley & Sons, Ltd.     

初始组构各向异性对砂土力学特性及临界状态的影响

采用离散元方法,利用半径扩展法和重力沉积法分别生成具有初始各向同性和各向异性内结构的试样,并开展三轴不排水压缩和拉伸试验,研究不同制样方法产生的初始各向异性对砂土宏微观力学特性及其临界状态的影响。运用组构张量对砂土的各向异性进行量化,分析不同初始组构各向异性对组构张量演化的影响并确定了组构张量的临界值。试验结果表明：初始组构各向异性对试样的剪胀性有重要影响,由于受重力影响形成初始各向异性,其各向异性程度越大、组构方向与加载方向越一致,剪胀性越显著;初始组构各向异性对试样的临界状态没有影响,砂土的组构张量具有唯一的临界状态值。     

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.     

Discrete element modelling of deep penetration in granular soils

This paper presents a numerical study on deep penetration mechanisms in granular materials with the focus on the effect of soil–penetrometer interface friction. A two‐dimensional discrete element method has been used to carry out simulation of deep penetration tests on a granular ground that is under an amplified gravity with a K₀ lateral stress boundary. The numerical results show that the deep penetration makes the soil near the penetrometer move in a complex displacement path, undergo an evident loading and unloading process, and a rotation of principal stresses as large as 180°. In addition, the penetration leads to significant changes in displacement and velocity fields as well as the magnitude and direction of stresses. In general, during the whole penetration process, the granular ground undergoes several kinds of failure mechanisms in sequence, and the soil of large deformation may reach a stress state slightly over the strength envelope obtained from conventional compression tests. Soil–penetrometer interface friction has clear effects on the actual penetration mechanisms. Copyright © 2005 John Wiley & Sons, Ltd.     

Effects of periodic fluctuations of micro‐polar boundary conditions on shear localizations in granular soil–structure interaction

In this work, the interface behavior between an infinite extended narrow granular layer and a rough surface of rigid body is investigated numerically, using finite element method in the updated Lagrangian (UL) frame. In this regard, the elasto‐plastic micro‐polar (Cosserat) continuum approach is employed to remove the limitations caused by strain‐softening of materials in the classical continuum. The mechanical properties of cohesionless granular soil are described with Lade's model enhanced by polar terms, including Cosserat rotations, curvatures, and couple stresses. Furthermore, the mean grain diameter as the internal length is incorporated into the constitutive relations accordingly. Here, the evolution and location of shear band, within the granular layer in contact with the rigid body, are mainly focused. In this regard, particular attention is paid to the effects of homogeneous distribution and periodic fluctuation of micro‐polar boundary conditions, prescribed along the interface. Correspondingly, the effects of pressure level, mean grain diameter, and stratified soil are also considered. The finite element results demonstrate that the location and evolution of shear band in the granular soil layer are strongly affected by the non‐uniform micro‐polar boundary conditions, prescribed along the interface. It is found that the shear band is located closer to the boundary with less restriction of grain rotations. Furthermore, the predicted thickness of shear band is larger for higher rotation resistance of soil grains along the interface, larger mean grain diameter, and higher vertical pressure. Regarding the stratified soil, comprising a thin layer with slightly different initial void ratio, the shear band moves towards the layer with initially higher void ratio. Copyright © 2011 John Wiley & Sons, Ltd.     

水泥加固不同地区软土的试验研究

对不同地区软土经水泥加固后的强度形成特征进行了研究。进行直接剪切试验及无侧限抗压试验测定了水泥加固土的力学指标,发现不同地区的软土经水泥加固后力学性质存在很大差异,从试样的粒度成分、有机质含量及加固后试样的微观结构特征等方面对此进行解释。结果表明,试样的粒度成分及有机质含量会对加固效果产生很大影响,黏粒含量越大,有机质含量越高,对水泥加固土强度的形成越不利。为在用水泥进行不同性质的软土加固处理时采取合理的附加措施提供了理论依据。     

Analysis of soil‐structural interface behavior using three‐dimensional DEM simulations

The shear behavior at the interface between the soil and a structure is investigated at the macroscale and particle‐scale levels using a 3‐dimensional discrete element method (DEM). The macroscopic mechanical properties and microscopic quantities affected by the normalized interface roughness and the loading parameters are analyzed. The macro‐response shows that the shear strength of the interface increases as the normalized roughness of the interface increases, and stress softening and dilatancy of the soil material are observed in the tests that feature rough interfaces. The particle‐scale analysis illustrates that a localized band characterized by intense shear deformation emerges from the contact plane and gradually expands as shearing progresses before stabilizing at the residual stress state. The thickness of the localized band is affected by the normalized roughness of the interface and the normal stress, which ranges between 4 and 5 times that of the median grain diameter. A thicker localized band is formed when the soil has a rough shearing interface. After the localized band appears, the granular material structuralizes into 2 regions: the interface zone and the upper zone. The mechanical behavior in the interface zone is representative of the interface according to the local average stress analysis. Certain microscopic quantities in the interface zone are analyzed, including the coordination number and the material fabric. Shear at the interface creates an anisotropic material fabric and leads to the rotation of the major principal stress.     

Generalized plasticity state parameter‐based model for saturated and unsaturated soils. Part II: Unsaturated soil modeling

The aim of this paper is to extend the generalized plasticity state parameter‐based model presented in part 1 to reproduce the hydro‐mechanical behavior of unsaturated soils. The proposed model is based on two pairs of stress–strain variables and a suitable hardening law taking into account the bonding—debonding effect of suction and degree of saturation. A generalized state parameter for unsaturated state is proposed to reproduce soil behavior using a single set of material parameters. Generalized plasticity gives a suitable framework to reproduce not only monotonic stress path but also cyclic behavior. The hydraulic hysteresis during a drying—wetting cycle and the void ratio effect on the hydraulic behavior is introduced. Comparison between model simulations and a series of experimental data available, both cohesive and granular, are given to illustrate the accuracy of the enhanced generalized plasticity equation. Copyright © 2010 John Wiley & Sons, Ltd.     

An elastoplastic model based on the shakedown concept for flexible pavements unbound granular materials

Nowadays, the problem of rutting of flexible pavements linked to permanent deformations occurring in the unbound layers is taken into account only by mechanistic empirical formulas. Finite element modelling of realistic boundary value problems with incremental rheological models will lead to unrealistic calculation time for large cycle numbers. The objective of the authors is to present a simplified model which can be used to model the flexible pavements rutting with the finite elements framework. This method is based on the shakedown theory developed by Zarka which is usually associated to materials like steels. It has been adapted for granular materials by introducing a yield surface taking into account the mean stress influence on the mechanical behaviour and a dependency of the hardening modulus with the stress state. The Drucker–Prager yield surface has been used with a non‐associated flow rule. Comparisons with repeated load triaxial tests carried out on a subgrade soil have been done. These comparisons underline the capabilities of the model to take into account the cyclic behaviour of unbound materials for roads. Finally, a discussion, dealing with the use of the simplified method within a finite element modelling of a full‐scale experiment, is presented. Copyright © 2005 John Wiley & Sons, Ltd.     

ACMEG‐TS: A constitutive model for unsaturated soils under non‐isothermal conditions

This paper introduces an unconventional constitutive model for soils, which deals with a unified thermo‐mechanical modelling for unsaturated soils. The relevant temperature and suction effects are studied in light of elasto‐plasticity. A generalized effective stress framework is adopted, which includes a number of intrinsic thermo‐hydro‐mechanical connections, to represent the stress state in the soil. Two coupled constitutive aspects are used to fully describe the non‐isothermal behaviour. The mechanical constitutive part is built on the concepts of bounding surface theory and multi‐mechanism plasticity, whereas water retention characteristics are described using elasto‐plasticity to reproduce the hysteretic response and the effect of temperature and dry density on retention properties. The theoretical formulation is supported by comparisons with experimental results on two compacted clays. Copyright © 2008 John Wiley & Sons, Ltd.     

Micromechanical aspects of the shear strength of wet granular soils

This paper presents a micromechanical model for the analysis of wet granular soils at low saturation (below 30%). The discrete element method is employed to model the solid particles. The capillary water is assumed to be in a pendular state and thus exists in the form of liquid bridges at the particle‐to‐particle contacts. The resulting inter‐particle adhesion is accounted for using the toroidal approximation of the bridge. Hydraulic hysteresis is accounted for based on the possible mechanism of the formation and breakage of the liquid bridges during wetting and drying phases. Shear test computational simulations were conducted at different water contents under relatively low net normal stresses. The results of these simulations suggest that capillary‐induced attractive forces and hydraulic hysteresis play an important role in affecting the shear strength of the soil. These attractive forces produce a tensile stress that contributes to the apparent cohesion of the soil and increases its stiffness. During a drying phase, capillary‐induced tensile stresses, and hence shear strength, tend to be larger than those during a wetting phase. The proposed model appears to capture the macroscopic response of wet granular materials and revealed a number of salient micromechanical mechanisms and response patterns consistent with theoretical considerations. Copyright © 2008 John Wiley & Sons, Ltd.     

A micro‐mechanical study of peak strength and critical state

We present a micro‐mechanical analysis of macroscopic peak strength, critical state, and residual strength in two‐dimensional non‐cohesive granular media. Typical continuum constitutive quantities such as frictional strength and dilation angle are explicitly related to their corresponding grain‐scale counterparts (e.g., inter‐particle contact forces, fabric, particle displacements, and velocities), providing an across‐the‐scale basis for a better understanding and modeling of granular materials. These multi‐scale relations are derived in three steps. First, explicit relations between macroscopic stress and strain rate with the corresponding grain‐scale mechanics are established. Second, these relations are used in conjunction with the non‐associative Mohr–Coulomb criterion to explicitly connect internal friction and dilation angles to the micro‐mechanics. Third, the mentioned explicit connections are applied to investigate, understand, and derive micro‐mechanical conditions for peak strength, critical state, and residual strength. Copyright © 2015 John Wiley & Sons, Ltd.     

Geotechnical properties of 3D-printed transparent granular soil

This paper proposes a 3D-printed transparent granular soil technique based on the contour rotation interpolation method, 3D printing and transparent soil technologies. Laboratory tests, including one-dimensional compression, direct shear and triaxial compression tests, are assessed for mechanical properties of 3D-printed transparent granular soil. The results show that 3D-printed transparent granular soil can be used to consider the effect of shape on macromechanical soil properties, which is an advantage that cannot be achieved by the previously presented transparent soil techniques. Subsequently, a simple model test of rigid flat plate penetration into transparent granular soil is performed. The obtained soil displacements using the PIV technique are compared with the classical shallow strain path method solution. This comparison indicates that the proposed 3D-printed transparent granular soil can capture the soil deformation pattern, although the accuracy needs to be further improved. The proposed 3D-printed transparent granular soil technique could be used for model test that needs to consider the shape of sand particle.

     

Microstructural deformation mechanisms of unsaturated granular soils

A discrete model for unsaturated granular soils has been developed. Three discrete entities have been defined: particles, water menisci and pores. Local interaction forces and water transfer mechanisms have been integrated into a model through the appropriate equilibrium and balance equations. The results of several numerical tests using this model have been described and discussed. Simulations include wetting and drying under load tests, the application of suction cycles and the effect of a deviatoric stress ratio on wetting‐induced collapse. The model reacts just as true granular soil samples behave in laboratory tests. The model provides a new insight into the internal mechanisms leading to large‐scale features of behaviour such as wetting‐induced collapse or the increase in soil strength provided by suction. The paper also stresses that matric suction changes acting on a granular structure are capable of explaining most of the macroscopic features of stress–strain behaviour. Copyright © 2002 John Wiley & Sons, Ltd.