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.     

Small-Strain Behavior of Granular Soils. I: Model for Cemented and Uncemented Sands and Gravels

A simple formulation is presented that predicts the nonlinear small strain behavior of cemented and uncemented granular soils. Its performance is evaluated through the comparison of model predictions to results from laboratory tests. A companion paper evaluates the performance of this model implemented in a site response analysis code through comparison with the measured response at two sites. The formulation for the maximum shear modulus, Gmax, which is selected through the evaluation of existing formulations and data, is presented with the hysteretic model developed to describe the shear modulus reduction and damping increase with increasing strains. Few parameters are needed to predict the small strain response, and correlations between model parameters and index properties of granular materials are presented when possible. The model, SimSoil, is shown to capture the cyclic response for sands and gravels with varying densities over a wide range of pressures measured in laboratory tests, including cases when cementation is present.     

Effect of Design and Site Factors on the Long-Term Performance of Flexible Pavements

Results are presented from a study to evaluate the relative influence of design and site factors on the performance of in-service flexible pavements. The data are from the SPS-1 experiment of the Long-Term Pavement Performance program. This experiment was designed to investigate the effects of HMA surface layer thickness, base type, base thickness, and drainage on the performance of new flexible pavements constructed in different site conditions (subgrade type and climate). Base type was found to be the most critical design factor affecting fatigue cracking, roughness (IRI), and longitudinal cracking (wheel path). The best performance was shown by pavement sections with asphalt treated bases (ATB). This effect should be interpreted in light of the fact that an ATB effectively means a thicker HMA layer. Drainage and base type, when combined, also play an important role in improving performance, especially in terms of fatigue and longitudinal cracking. Base thickness has only secondary effects on performance, mainly in the case of roughness and rutting. In addition, climatic conditions were found to have a significant effect on flexible pavement performance. Wheel path longitudinal cracking and transverse cracking seem to be associated with a wet-freeze environment, while nonwheel path longitudinal cracking seems to be dominant in a freeze climate. In general, pavements built on fine-grained soils have shown the worst performance, especially in terms of roughness. Although most of the findings from this study support the existing understanding of pavement performance, they also provide an overview of the interactions between design and site factors and new insights for achieving better long-term pavement performance.     

New Stabilized Finite Element Method Embedded with a Cap Model for the Analysis of Granular Materials

Standard displacement-based finite element formulations show a tendency to lock in the modeling of nearly incompressible materials. This overly stiff response often leads to an overestimation of the collapse load for the system. In this paper we present a stabilized mixed displacement-pressure finite element method that can effectively model the nearly incompressible materials in their elastic and inelastic range. The stabilized formulation is free of volumetric locking effects and allows equal low-order interpolation for both the displacement and the pressure fields. The formulation is integrated with a three-surface elastoplastic cap model for the simulation and analysis of granular materials. The good performance of the method is demonstrated via numerical examples of the hydrostatic compression test for concrete and the bearing capacity and limit load analyses of flexible footings.     

Modeling Permanent Deformation of Unbound Granular Materials under Repeated Loads

Finite-element analysis on a pavement structure under traffic loads has been a viable option for researchers and designers in highway pavement design and analysis. Most of the constitutive drivers used were nonlinear elastic models defined by empirical resilient modulus equations. Few isotropic/kinematic hardening elastoplastic models were used but applying thousands of repeated load cycles became computationally expensive. In this paper, a cyclic plasticity model based on fuzzy plasticity theory is presented to model the long-term behavior of unbound granular materials under repeated loads. The discussion focuses on the model parameters that control long-term behavior such as elastic shakedown. The performance of the constitutive model is presented by comparing modeled and measured permanent strain at various numbers of load cycles. Calculated resilient modulus from the complete stress-strain curve is also discussed.     

Modeling Nonlinear Anisotropic Elastic Properties of Unbound Granular Bases Using Microstructure Distribution Tensors

The resilient properties of unbound aggregate bases are important parameters in the design of asphalt pavements. Previous studies have shown that these resilient properties exhibit nonlinear and transverse anisotropic characteristics. The paper in hand presents a micromechanics-based approach to model the nonlinear and anisotropic properties of unbound aggregate bases. The anisotropic behavior is captured using two microstructure parameters representing the preferred orientation of aggregate particles, and the ratio of the normal contact stiffness to shear contact stiffness among particles. The nonlinear response is modeled using a relationship that relates the shear modulus to particle packing, material properties, particle size, and confining pressure. The micromechanics model is used to represent the resilient properties for a total of 18 different combinations of material conditions with different aggregate types, moisture contents, and gradation characteristics. Anisotropic and nonlinear resilient properties were measured at ten different stress states for each of the material conditions. The results presented in this paper show that the micromechanics model is capable of successfully representing the experimental measurements.     

Degradation of a Granular Base under a Flexible Pavement: DEM Simulation

Flexible pavements are composed by an asphalt concrete layer, granular base and subbase layers, and a natural subgrade. The granular materials forming part of the granular layers are subjected to static and dynamic loads during their engineering life. As a result of these loads particle crushing may occur depending on the strength of the particles forming the granular layers. Particle crushing is important since it is associated with several detrimental effects such as settlements and a reduction in hydraulic conductivity. A computer simulation using the discrete element method (DEM) is presented in order to understand and visualize how crushing initiates and develops inside a simulated pavement structure.     

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.     

Modeling Cross Anisotropy in Granular Materials

A constitutive model has been developed to capture the behavior of cross-anisotropic frictional materials. The elastoplastic, single hardening model for isotropic materials serves as the basic framework. Based on the experimental results of cross-anisotropic sands in isotropic compression tests, the principal stress coordinate system is rotated such that the model operates isotropically within the rotated framework. Experimental plastic work contours on the octahedral plane are plotted for a series of true triaxial tests on dense Santa Monica Beach sand to study the effects of cross anisotropy on the evolution of yield surfaces. The amount of rotation of the yield and plastic potential surfaces decreases to zero (isotropic state) with loading. The model is constructed for cases where the principal stress and material symmetry axes are collinear and no significant rotation of principal stresses occur. The model incorporates fourteen parameters that can be determined from simple experiments, such as isotropic compression, drained triaxial compression, and triaxial extension tests. A series of true triaxial and isotropic compression tests on dense Santa Monica Beach sand are used as a basis for verification of the capabilities of the proposed model.     

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.     

Role of Learning Algorithm in Neural Network-Based Backcalculation of Flexible Pavements

Nondestructive testing (NDT) methods are widely used for the performance evaluation of flexible pavements. Falling weight deflectometer (FWD), which measures time-domain deflections resulting from applied impulse loads, is the most popular technique among all NDT methods. The evaluation of the FWD data requires the inversion of mechanical pavement properties using a backcalculation tool that includes both a forward pavement response model and an optimization algorithm. Neural networks (NNs) have also emerged as alternative tools that can be employed for pavement backcalculation problems relative to their real-time processing abilities. However, there have been no comprehensive analyses in previous studies that focus on the learning algorithm and the architecture of a NN model, which considerably affect backcalculation results. In this study, 284 different NN models were developed using synthetic training and testing databases obtained by layered elastic theory. Results indicated that both the learning algorithm and network architecture play important roles in the performance of the NN based backcalculation process.     

Stochastic Modeling of Load-Induced Settlement in Loose Granular Materials

The response of loose cohesionless granular material to surface applied loads is investigated from the viewpoint of probabilistic mechanics of particulate media. A model is proposed that is based on the combined propagation of intergranular forces and an excess volume of voids. In this regard, it provides a bridge between earlier theories developed independently for the diffusion of stresses and for the propagation of settlements. In its general formulation, the theory can model three-dimensional, transient effects. However, the model is believed to be limited to normally consolidated or noncompacted, fully drained or dry, granular materials that do not exhibit dilatancy effects. The derived numerical modeling of steady state deflection patterns under a rigid footing is found to be in good agreement with x-ray images of laboratory model tests using noncompacted silt. The proposed theory recognizes the discrete and inherently random nature of natural granular materials such as cohesionless soils and builds upon these fundamental characteristics to predict responses of such materials to boundary applied load. This is achieved by modeling intergranular force and excess pore volume propagation as Markovian diffusion-advection processes. This approach, which departs from traditional continuum mechanics models, seems to have potential for addressing some of the challenging aspects of granular material mechanics in lunar or Martian environments.     

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.     

Elastic Model for Partially Saturated Granular Materials

This paper presents the development of an elastic model for partially saturated granular materials based on micromechanical factor consideration. A granular material is considered as an assembly of particles. The stress-strain relationship for an assembly can be determined by integrating the behavior at all interparticle contacts and by using a static hypothesis, which relates the average stress of the granular assembly to a mean field of particle contact forces. As for the nonsaturated state, capillary forces at grain contacts are added to the contact forces created by an external load. These are then calculated as a function of the degree of saturation, depending on the grain size distribution and on the void ratio of the granular assembly. Hypothesizing a Hertz-Mindlin law for the grain contacts leads to an elastic nonlinear behavior of the particulate material. The prediction of the stress-strain model is compared to experimental results obtained from several different granular materials in dry, partially saturated and fully saturated states. The numerical predictions demonstrate that the model is capable of taking into account the influence of key parameters, such as degree of saturation, void ratio, and mean stress.     

Innovative Data Acquisition for Heavily Instrumented Flexible Pavements

A data acquisition program was written to allow independent triggering of multiple test sections of a thin flexible pavement. A total of 129 electronic sensors were installed in 17 test sections and subjected to 2,100 truck passes over several months immediately after construction. The measured strains were highly variable in the thin flexible pavement, but the program was still able to successfully trigger each section independently. The majority of signal processing was also performed within the program, which was written in Lab VIEW 7 Express. This approach significantly reduced the amount of postprocessing effort that would have otherwise been required. The quality of the triggering approach was compared to independently collected weigh in motion data. The majority of the test sections recorded within 0.5% of the number of vehicles recorded by the weigh in motion system. Key components of all major facets of the data acquisition and programming performed are discussed in detail.     

Wave Velocities in Granular Materials under Microgravity

Velocities of primary (P) and shear (S) waves in granular materials are highly dependent on confining stress. These wave velocities are related to mechanical properties of the materials such as stiffness, density, and stress history. Measurements of the wave velocities using piezoelectric sensors provide scientists and engineers a technique for nonintrusive characterization of those mechanical properties. For aerospace engineering, measuring the wave velocities under microgravity, which simulates low loading and stress conditions, has a number of potential applications. It can help the understanding of the soil mechanics and the development of appropriate materials handling technologies in extraterrestrial environments, which will be crucial to meeting NASA’s future space exploration goals. This paper presents the technique and results of experiments conducted at NASA Glenn Research Center using the 2.2?s drop tower. Velocities of P and S waves in three sizes of glass beads and one size of alumina beads were measured under initially dense or loose compaction states. It was found that under microgravity, the wave signals were significantly weaker and the velocities were much slower. The material that makes up the beads has a strong influence on the wave velocities as well. The initial compaction state also has some influence on the wave velocities.     

Disturbed State Model for Porous Saturated Materials

The widely used Terzaghi theory for deformation or consolidation in porous materials is based on the effective stress, a rather fictitious quantity, carried by the soil skeleton through the particle contact area, which is assumed to be negligible. This note presents a new generalized model based on the disturbed state concept, in which the average or weighted stress carried by the soil skeleton and fluid is defined on the basis of the change in contact area during deformation, that can be proportional to quantities such as the void ratio. A simple problem is solved in which the predictions from the proposed model and Terzaghi theory are compared. The proposed model has potential application as a general procedure for deformation in porous materials.     

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.     

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.