Normalizing Behavior of Unsaturated Granular Pavement Materials

One of the important components of a flexible pavement structure is granular material layers. Unsaturated granular pavement materials (UGPMs) in these layers influence stresses and strains throughout the pavement structure, and have a large effect on asphalt concrete fatigue and pavement rutting (two of the primary failure mechanisms for flexible pavements). The behavior of UGPMs is dependent on water content, but this effect has been traditionally difficult to quantify using either empirical or mechanistic methods. This paper presents a practical mechanistic framework for determining the behavior of UGPMs within the range of water contents, densities, and stress states likely to be encountered under field conditions. Both soil suction and generated pore pressures are determined and compared to confinement under typical field loading conditions. The framework utilizes a simple soil suction model that has three density-independent parameters, and can be determined using conventional triaxial equipment that is available in many pavement engineering laboratories.     

Evaluation of Two Homogenization Techniques for Modeling the Elastic Behavior of Granular Materials

This paper discusses the capabilities of two homogenization techniques to accurately represent the elastic behavior of granular materials considered as assemblies of randomly distributed particles. The stress-strain relationship for the assembly is determined by integrating the behavior of the interparticle contacts in all orientations, using two different homogenization methods, namely the kinematic method and the static method. The numerical predictions obtained by these two homogenization techniques are compared to results obtained during experimental studies on different granular materials. Relations between elastic constants of the assembly, interparticle properties, and fabric parameters are discussed, as well as the capabilities of the models to take into account inherent and stress-induced anisotropy for different stress conditions.     

Anisotropic Nonlinear Elastic Model for Particulate Materials

This paper presents the development of an elastic model for particulate materials based on micromechanics considerations. A particulate material is considered as an assembly of particles. The stress–strain relationship for an assembly can be determined by integrating the behavior of the interparticle contacts in all orientations and using a static hypothesis which relates the average stress of the granular assembly to a mean field of particle contact forces. Hypothesizing a Hertz–Mindlin law for the particle contacts leads to an elastic nonlinear behavior of the particulate material, we were able to determine the elastic constants of the granular assembly based on the properties of the particle contacts. The numerical predictions, compared to the results obtained during experimental studies on different granular materials, show that the model is capable of taking into account both the influence of the inherent anisotropy and the influence of the stress-induced anisotropy for different stress conditions.     

Critical State of Granular Materials Based on the Sliding-Rolling Theory

By representing the assembly by a simplified column model, a constitutive theory was recently developed for a two-dimensional assembly of rods. This theory, referred to as the sliding-rolling theory, is extended in this paper to represent the triaxial stress-strain behavior of granular materials. The sliding-rolling theory provides a dilatancy rule and an expression for the slope of the line of zero dilatancy in the stress space. These rules are then combined with triaxial observations to provide a microstructural interpretation of the critical state of granular materials. According to the theory, the slope of the critical state line in the stress space depends on the interparticle friction angle and the degree of contact normal anisotropy. To verify the basic ideas of the sliding-rolling theory, numerical experiments are conducted using the discrete-element method on three-dimensional assemblies of spheres.     

Micro-Macro Quantification of the Internal Structure of Granular Materials

We have attempted a multiscale quantification of the internal structure of granular materials. The internal structure of granular materials, i.e., the geometrical information on granular particles and their spatial arrangement, was described mathematically on the particle scale using Voronoi–Delaunay tessellations. These tessellations were further modified into two cell systems: a solid cell system and a void cell system, with the internal supporting structure properly reflected. By doing so, the two cell systems were geometrically and physically significant. Taking solid/void cells as the microscopic basic elements, the behavior of granular materials was expressed as the volumetric average of the microcell behavior. Macroscopically, the internal structure could be characterized by the statistical measures from the geometry of the microcells. Our approach was used to investigate the anisotropic behavior of granular materials. A study on the void cells explains how the spatial arrangement affects the strength and dilatancy of granular materials. A new anisotropic fabric tensor was defined based on the void cell anisotropy. The correlation between the anisotropic fabric tensor and the macro behavior of granular materials was verified with numerical simulations. The results showed that the new material anisotropic tensor is a more effective definition than the existing ones based on particle orientations and contact normals.     

Simple Nonlinear Model for Elastic Response of Cohesionless Granular Materials

A constitutive model based on hyperelasticity is proposed to capture the resilient (elastic) behavior of granular materials. Resilient behavior is a widely accepted idealization of the response of unbound granular layers of pavements, following shakedown. The coupling property of the proposed model accounts for shear dilatancy and pressure-dependent behavior of the granular materials. The model is calibrated using triaxial resilient test data obtained from the literature. A statistical comparison is made between the predictions of the proposed model and a few of the prominent models of resilient response. The proposed coupled hyperelastic model yields a significantly better fit to the experimental data. It also offers a computational efficiency when implemented in a classical nonlinear finite elemental framework.     

Sliding and Rolling Constitutive Theory for Granular Materials

By analyzing a microelement based on four spheres, equations governing the equilibrium of the microelement are developed. By examining these equations more closely, two primary mechanisms of failure of the microelements, one based on particle sliding and the other based on particle rolling, are identified. For each primary mechanism, two separate mechanisms, one based on collapse of the microelement in the vertical direction and the other based on collapse in the horizontal direction, are recognized. With the aid of these concepts, constitutive equations are developed for a two-dimensional assembly of granular particles. The assembly is considered to consist of four-sphere microelements. Taking the plastic strain to be a consequence of the collapse of some of the microelements, equations are developed for plastic strain. The formulation yields loading criteria and flow directions. With suitable hardening rules, it is shown that the microstructural model is capable of simulating most of the salient features of the stress-strain behavior of granular materials. In particular, the stress-dilatancy relation, taking into consideration phenomena of phase transformation, and critical state failure are simulated satisfactorily.     

Hysteresis of Capillary Stress in Unsaturated Granular Soil

Constitutive relationships among water content, matric suction, and capillary stress in unsaturated granular soils are modeled using a theoretical approach based on the changing geometry of interparticle pore water menisci. A series of equations is developed to describe the net force among particles attributable to the combined effects of negative pore water pressure and surface tension for spherical grains arranged in simple-cubic or tetrahedral packing order. The contact angle at the liquid–solid interface is considered as a variable to evaluate hysteretic behavior in the soil–water characteristic curve, the effective stress parameter χ, and capillary stress. Varying the contact angle from 0 to 40° to simulate drying and wetting processes, respectively, is shown to have an appreciable impact on hysteresis in the constitutive behavior of the modeled soils. A boundary between regimes of positive and negative pore water pressure is identified as a function of water content and contact angle. Results from the analysis are of practical importance in understanding the behavior of unsaturated soils undergoing natural wetting and drying processes, such as infiltration, drainage, and evaporation.     

Effect of Contact Force Models on Granular Flow Dynamics

The contact force model consisting of a linear spring dashpot with a frictional glider has been widely adapted to simulate granular flows. Real contact mechanics between two solid bodies is very complicated. Extensive theoretical and experimental studies exist for binary contacts. Very little work has been reported that addresses the effect of contact mechanics on the bulk behavior of granular materials. We first briefly summarize the difference of binary contacts between a linear spring–dashpot model and the Hertzian nonlinear spring with two nonlinear dashpot models. We then compare the constitutive behaviors of a granular material using a linear and a nonlinear model. The stress- and strain-rate relation in simple shear flow and the resulting coordination number are calculated using the discrete element method. It is found that although at the grain level binary contact between two particles depends on whether a linear or a nonlinear model is used, the bulk behavior of granular materials is qualitatively similar with either model.     

Coupled Continuum-Discrete Model for Saturated Granular Soils

A coupled hydromechanical model was used to analyze the mesoscale pore fluid flow and microscale solid phase deformation of saturated granular soils. The fluid motion was idealized using averaged Navier–Stokes equations, and the discrete element method was employed to model the assemblage of solid particles. The fluid–particle interactions were quantified using established semiempirical relationships. Simulations were conducted to investigate the three-dimensional response of sandy deposits when subjected to critical and overcritical upward pore fluid flow. These simulations revealed complex response patterns after the onset of quicksand conditions and provided valuable insight into the associated mechanisms. The employed model provides an effective tool to assess the microscale mechanisms and characteristics of the partially drained response of saturated granular media.     

Model for Granular Materials with Surface Energy Forces

In light of environmental differences (such as gravitational fields, surface temperatures, atmospheric pressures, etc.), the mechanical behavior of the subsurface soil on the Moon is expected to be different from that on the Earth. Before any construction on the Moon can be envisaged, a proper understanding of soil properties and its mechanical behavior in these different environmental conditions is essential. This paper investigates the possible effect of surface-energy forces on the shear strength of lunar soil. All materials, with or without a net surface charge, exhibit surface-energy forces, which act at a very short range. Although, these forces are negligible for usual sand or silty sand on Earth, they may be important for surface activated particles under extremely low lunar atmospheric pressure. This paper describes a constitutive modeling method for granular material considering particle level interactions. Comparisons of numerical simulations and experimental results on Hostun sand show that the model can accurately reproduce the overall mechanical behavior of soils under terrestrial conditions. The model is then extended to include surface-energy forces between particles in order to describe the possible behavior of lunar soil under extremely low atmospheric pressure conditions. Under these conditions, the model shows that soil has an increase of shear strength due to the effect of surface-energy forces. The magnitude of increased shear strength is in reasonable agreement with the observations of lunar soil made on the Moon’s surface.     

Mix-Mode Elastic Finite Element Formulation for Bonded Granular Material Considering Rotation of Particles

Rotation of particles in granular material is an important mechanism, which is responsible for the distinct feature of moment transfer within granular material. A couple-stress continuum is adopted to model such effect. The paper presents a mix-mode finite element formulation for the analysis of a couple stress continuum. A modified variational formulation is proposed to render unconditional convergence. The developed finite element method is validated by comparing the computed results with closed-form solutions. In order to verify whether the couple-stress continuum is appropriate for modeling granular media, finite element results for two different boundary value problems are performed and compared with that obtained from discrete analysis. Physical meaning of internal length, a new parameter of the material, is discussed. The suitability of the couple-stress continuum for modeling granular medium is evaluated.     

Modeling Liquefaction by a Multimechanism Model

An anisotropic constitutive model was recently presented for describing the stress–strain behavior of granular materials with considerations for the initial and induced anisotropy. The model was developed within the framework of a microstructural theory known as the sliding–rolling theory. The resulting model falls within the definition of multimechanism models. The model was shown to satisfactorily represent the drained and undrained behaviors under monotonic loading. The framework used in the model allows extension to describe the behavior under cyclic loading, which is the subject of the present paper. Specifically, the model is further developed for representing the undrained behavior of granular materials under one- and two-way cyclic loading, some of which cause liquefaction resulting in large strain accumulations and the others lead to limited pore pressure and strain accumulations. The validity of the model is verified using triaxial data on Nevada sand.     

Microscopic Evaluation of Strain Distribution in Granular Materials during Shear

The evolution of local strains during shear of particles of a granular material is presented in this paper. A cylindrical specimen composed of 6.5-mm spherical plastic particles was loaded under an axisymmetric triaxial loading condition. Computed tomography (CT) was used to acquire three-dimensional images of the specimen at three shearing stages. The high-resolution CT images were used to identify the 3D coordinates of 400 particles. Nine strain components (normal, shear, and rotation), rotation angles, and local dilatancy angles for particle groups were calculated, and their frequency distribution histograms are presented and discussed. It was found that there is no preferred shear direction, and the standard deviation values for shear strain components (εxy, εxz, and εyz) were almost equal for the specific test shearing stage. Shear strains as high as 25.6% were recorded for some particle groups. Furthermore, granular particle groups rotated in the 3D space with almost equal amounts of rotation strains when loaded under axisymmetric triaxial condition. Rotation strain values are very close to the corresponding shear strains. Compared to particle sliding, rotation plays a major role in the shearing resistance of granular materials. The cumulative vertical rotation angles can be as high as 38° and the horizontal rotation angles have values as high as 60°. The statistical distributions of the local dilatancy angle (ψ1) of particle groups were calculated and found to be increasing as shearing continues. The “global” dilatancy angle value is very close to the mean local ψ1 during the first stage of shearing (i.e, when global εz = ?7.3%)     

Micromechanical Analysis for Interparticle and Assembly Instability of Sand

Instability of granular material may lead to catastrophic events such as the gross collapse of earth structures, and thus it is an important topic in geotechnical engineering. In this paper, we adopt the micromechanics approach for constitutive modeling, in which the soil is considered an assembly of particles, and the stress-strain relationship for the assembly is determined by integrating the behavior of the interparticle contacts in all orientations. Although analyses regarding material instability have been extensively studied for a soil element at the constitutive level, it has not been considered at the interparticle contact level. Through an eigenvalue analysis, two modes of instability are identified at the local contact level: the singularity of tangential stiffness matrix and the loss of positiveness of second-order work. The constitutive model is applied to simulate drained and undrained triaxial tests on Toyoura sand of various densities under various confining pressures. The predictions are compared with experimentally measured instability at the assembly level. The modes of stability at the interparticle contact level and their relations to the overall instability of the assembly are also analyzed.     

Ultimate State of Samples of Ellipsoids under Different Stress Paths

The ultimate state of granular material was investigated by the discrete element method. This paper discusses a series of numerical triaxial tests on samples of two kinds of ellipsoids. Samples of three different densities were loaded along various stress paths. The ellipsoids were mixed in the proportions 50:50 by weight. The longer particles have an aspect ratio (major length/minor length) of 1.5 and the other particles have an aspect ratio of 1.2. The samples were generated by deposition under gravity to simulate the air-pluviation sample preparation technique. Then they were consolidated isotropically. Fourteen stress-path controlled triaxial tests were conducted numerically for each sample. They are sheared to the ultimate state to determine the friction angle and void ratio at the ultimate state. When samples of different densities were sheared along the same loading path, a unique ultimate state was observed. The initial density does not affect the ultimate state. However, when different loading paths are applied to the same numerical specimen, they do not always arrive at the same critical state in the void-mean stress space.     

Influence of Micromaterial Heterogeneity on Strain Localization in Granular Materials

Lade’s constitutive model was modified to incorporate the couple stress and the particle’s rotation within the framework of the Cosserat continuum. The finite element equations were implemented in the finite-element program (ABAQUS) to predict the strain localization (shear bands) in granular materials. Material spatial heterogeneity such as local void ratio, particle size, surface roughness and shape indices was mapped into the finite element mesh to account for the local heterogeneity of the material properties. The model was found to respond well to such spatial heterogeneities and the results compare well with experiments. The material spatial distributions were generated using scanning electron microscope and optical microscope images. The surface roughness and the shape indices were found to affect the shear band thickness; a parametric study was performed and such effects were found to be significant. The shear band thickness was found to increase as the surface roughness of the particles, particle size, and the particle angularity index increase while it tends to decrease as the particle sphericity, initial density and the confining pressure increase.     

Collapse Behavior of Compacted Silty Clay in Suction-Monitored Oedometer Apparatus

This paper presents a methodology to investigate the collapse behavior of unsaturated soils using suction-monitored oedometer tests. By incorporating independent suction measurement, the oedometer apparatus is capable of following the same stress paths as in double oedometer tests, while continuously monitoring the suction. The proposed method has been used to investigate the collapse behavior of a compacted silty clay and to confirm the uniqueness of the loading-collapse surface as identified from loading and wetting paths. A new mathematical form of the yield surface within an elastoplastic framework is proposed on the basis of test results over a wide range of suctions (0 to 30,000?kPa) and net stresses (up to 7,000?kPa). The fundamental assumptions of the newer type of elastoplastic framework, which incorporate the degree of saturation within their stress variables, are evaluated, and the limitations of such models are identified. The collapse behavior of samples with different fabrics induced by differing compaction characteristics is also investigated within an elastoplastic framework. The difference in fabric, which is observed through a petrological microscope, can be presented in a quantitative way with different model parameters.     

Elastoplastic Model for the Long-Term Behavior Modeling of Unbound Granular Materials in Flexible Pavements

The constitutive modeling of cyclic plasticity of soils has made great progress, especially in the area of sands liquefaction modeling. Nowadays, the problem of rutting of flexible pavements linked to permanent deformations occurring in the unbound layers is taken into account only by empirical formulas. This paper presents an elastoplastic model with both isotropic and kinematic hardening. The yield surface, plastic potential, and isotropic hardening are based on a model for sands, which takes into account the influence of the initial void ratio and of the mean stress on the mechanical behavior. A kinematic hardening has been added in order to take into account the mechanical behavior of the material for large cycle numbers. A complete model is then developed, simulations are presented, and comparisons with repeated load triaxial tests carried out on a subgrade soil (clayey sand), have been made. These comparisons underline the capabilities of the model to take into account the monotonic, cyclic, and ratchetting behavior of unbound materials for roads.