Pressure-Level Dependency and Densification Behavior of Sand Through Generalized Plasticity Model

Natural soil deposits and man-made earth structures exhibit complicated engineering behavior that is influenced by factors such as the stress level and drainage conditions. The stress conditions within a soil structure vary greatly, ranging from very low to very high values, due to the dead weight, loading and boundary conditions. Saturated sand deposits that exhibit drained conditions under static loading become undrained when subject to earthquake excitations. The Pastor–Zienkiewicz–Chan model has demonstrated considerable success in describing the inelastic behavior of soils under isotropic monotonic and cyclic loadings, including liquefaction and cyclic mobility. This study proposed modifications to the Pastor–Zienkiewicz–Chan model so that effects of stress level and densification behavior are simulated. The proposed model suggested that the angle of internal friction, elastic and plastic moduli are dependent on the pressure levels. Relevant modifications were made to incorporate a power term of mean effective stress on the loading plastic modulus so that a stress-level dependent volume change is obtained in combination with the stress-dilatancy relationship. To better simulate cyclic loading with reference to densification behavior, an exponential term of plastic volumetric strain is included for the unloading and reloading plastic moduli. A total of 11 parameters are needed for monotonic loading, whereas 15 parameters are needed in describing the cyclic behavior. The model simulations were compared with undrained and drained triaxial test results of several kinds of sand under dense and loose states. The predictive capability for monotonic and cyclic loading conditions was also demonstrated.     

Numerical Modeling of Nonhomogeneous Behavior of Structured Soils during Triaxial Tests

The nonhomogeneous behavior of structured soils during triaxial tests has been studied using a finite element model based on the Structured Cam Clay constitutive model with Biot-type consolidation. The effect of inhomogeneities caused by the end restraint is studied by simulating drained triaxial tests for samples with a height to diameter ratio of 2. It was discovered that with the increase in degree of soil structure with respect to the same soil at the reconstituted state, the inhomogeineities caused by the end restraint will increase. By loading the sample at different strain rates and assuming different hydraulic boundary conditions, inhomogeneities caused by partial drainage were investigated. It was found that if drainage is allowed from all faces of the specimen, fully drained tests can be carried out at strain rates about ten times higher than those required when the drainage is allowed only in the vertical direction at the top and bottom of the specimen, confirming the findings of previous studies. Both end restraint and partial drainage can cause bulging of the triaxial specimen around mid-height. Inhomogeneities due to partial drainage influence the stress–strain behavior during destructuring, a characteristic feature of a structured soil. With an increase in the strain rate, the change in voids ratio during destructuration reduces, but, in contrast, the mean effective stress at which destructuration commences was found to increase. It is shown that the stress–strain behavior of the soil calculated for a triaxial specimen with inhomogeneities, based on global measurements of the triaxial response, does not represent the true constitutive behavior of the soil inside the test specimen. For most soils analyzed, the deviatoric stress based on the global measurements is about 25% less than that for the soil inside the test specimen, when the applied axial strain is about 30%. Therefore it can be concluded that the conventional global measurements of the sample response may not accurately reflect the true stress–strain behavior of a structured soil. This finding has major implications for the interpretation of laboratory triaxial tests on structured soils.     

Numerical Analysis of a Tunnel in Residual Soils

This paper presents results of an elastoplastic finite element back analysis of a shallow tunnel through residual soils. The tunnel was constructed as part of the expansion of the underground transit system in the city of S?o Paulo, Brazil. A comprehensive laboratory testing program on undisturbed soil samples was performed in order to characterize the stress–strain–strength behavior of the residual soils. Results from this laboratory testing program were used to calibrate a nonassociated elastoplastic constitutive model utilized to reproduce the behavior of the residual soils under stress paths typical of underground excavation. A stress transfer method is proposed to simulate, using a two-dimensional finite element analysis, the response of the soil mass to the three-dimensional advancement of a tunnel excavation. Comparisons are presented between monitored displacements from an instrumented section of the Paraíso tunnel, empirical predictions, and the results of a finite element back analysis. Good agreement is achieved between the displacements obtained from field instrumentation data and the empirical and numerical results.     

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.     

Dynamic Analysis of Multilayered Soils to Water Waves and Flow

In nature, a soil profile generally consists of several heterogeneous layers. This study is aimed at discussing the interactive problem of oscillatory water waves and flow passing over multilayered soils. The soil behavior is considered as viscoelastic in the present mathematical model modified from Biot’s poroelastic theory. Employing this model, the dynamic response including the profiles of pore water pressure and effective stress in the multilayered soils is discussed. The results reveal that the perturbed pore pressure is different from that inside a single-layered soil where the thickness of the first soil layer is less than the water wavelength. The discrepancy of the vertical effective stresses between multilayered and single-layered soils is even much more apparent under the same conditions. Moreover, seepage force is examined and is found to be larger near the bed surface and the bottom of the first soil layer where soils are easily disturbed by external disturbance. The locations where soil failure might happen are found near the troughs of surface water waves.     

Numerical Study of Impact of Soil Anisotropy on Seismic Performance of Retaining Structure

Recent laboratory investigations indicate that the stress–strain–strength responses of granular soils are appreciably affected by the fabric orientation of the soil relative to the frame of principal stresses. Especially, a sand specimen exhibiting a dilative response during triaxial compression may show a contractive response during triaxial extension under otherwise identical conditions. This observation is of practical importance for applications concerning essentially undrained loading conditions, because the effective mean normal stress at failure, and consequently, the shear strength, associated with an undrained contractive path are considerably lower than those following a dilative path. This raises a question about the impact of soil anisotropy on seismic performance of retaining structures subjected to active and passive earth pressures, because the directions of principal stresses in retained soils for the two cases are very different. This note presents a set of fully coupled finite-element analyses incorporating an anisotropic sand model. The analyses reveal that the impact of fabric anisotropy could be significant when the retaining structure is under passive earth pressure conditions.     

Performance of a Three-Dimensional Hvorslev–Modified Cam Clay Model for Overconsolidated Clay

It is well established that critical state soil mechanics provides a useful theoretical framework for constitutive modeling of soil. Most of the critical state models, including the popular modified Cam clay (MCC) model, predict soil behavior in the subcritical region fairly well. However, the predictions for heavily overconsolidated soils, in the supercritical region, are not so satisfactory. Furthermore, the critical state models were developed from triaxial test data and extension of these models into three-dimensional (3D) stress space has not been investigated thoroughly. In the present work, experiments were carried out to obtain stress–strain behavior of overconsolidated soil in triaxial compression, extension, and plane strain conditions. A novel biaxial device has been developed to conduct the plane strain tests. The experimental results were used to formulate Hvorslev–MCC model which has MCC features in the subcritical region and Hvorslev surface in the supercritical region. The model was generalized to 3D stress space using the Mohr–Coulomb failure criterion. A comparison of the model predictions with test results has indicated that the Hvorslev–MCC model performs fairly well up to the peak supercritical point, during which deformations are fairly uniform and the specimens remain reasonably intact. Limitations of this simple model in predicting postpeak localization are also discussed. The model’s predictions for volumetric response in different shear modes seem to agree reasonably well with test results.     

Finite Strain, Anisotropic Modified Cam Clay Model with Plastic Spin.?II: Application to Piezocone Test

Micromechanical and anisotropic behavior of soils is analyzed using the plastic spin and anisotropic modified Cam clay model (AMCCM) in an updated Lagrangian reference frame. The micromechanical behavior of soils is especially important in large strain problems. The anisotropic behavior inherently exists in soils. This study uses AMCCM with the plastic spin to evaluate the pore pressure response in cone penetration tests. This test is a typical example for large strain problems. The analytical results indicate that the predicted pore pressure is closer to the measured one when the plastic spin is incorporated in AMCCM. It also shows that the micromechanical behavior is paramount in the vicinity of the cone tip where large strains and rotations occur.     

MicroROM: A Physics-Based Constitutive Model for Ni-Based Superalloys

In this article, a physics-based constitutive model is developed for representing the stress–plastic strain response of Ni-based superalloys by considering the hardening mechanisms that contribute to the macroscopic yield stress and the subsequent strain-hardening response in order to derive the entire tensile stress–strain curve. It is demonstrated that the log stress vs log plastic strain curves of Ni-based superalloys such as 702 Li and ME3 exhibit a bilinear behavior with a lower strain-hardening exponent in the low plastic strain regime and a much higher strain-hardening exponent in the high plastic strain regime. These two hardening regimes can be modeled on the basis of self-hardening of individual slip planes and latent hardening of five operative independent slip systems due to cross-slip from {111} planes to {001} planes, leading to the formation of incomplete and complete Kear-Wilsdorf locks. The proposed physics-based constitutive model, dubbed as MicroROM, exhibits a form that is similar to the Ramberg–Osgood (RO) constitutive model, which is widely used in structural analyses of engineering designs and components. MicroROM is applied to predict the tensile stress–strain curves of 720 Li and ME3 with either a subsolvus or supersolvus microstructure for temperatures ranging from 24 °C to 815 °C. The agreement is good between model predictions and experiment data from the literature. The sensitivity of the predicted stress–strain response to individual microstructural parameters is highlighted and the relation to individual hardening mechanisms is elucidated.     

Suction Stress Characteristic Curve for Unsaturated Soil

The concept of the suction stress characteristic curve (SSCC) for unsaturated soil is presented. Particle-scale equilibrium analyses are employed to distinguish three types of interparticle forces: (1) active forces transmitted through the soil grains; (2) active forces at or near interparticle contacts; and (3) passive, or counterbalancing, forces at or near interparticle contacts. It is proposed that the second type of force, which includes physicochemical forces, cementation forces, surface tension forces, and the force arising from negative pore-water pressure, may be conceptually combined into a macroscopic stress called suction stress. Suction stress characteristically depends on degree of saturation, water content, or matric suction through the SSCC, thus paralleling well-established concepts of the soil–water characteristic curve and hydraulic conductivity function for unsaturated soils. The existence and behavior of the SSCC are experimentally validated by considering unsaturated shear strength data for a variety of soil types in the literature. Its characteristic nature and a methodology for its determination are demonstrated. The experimental evidence shows that both Mohr–Coulomb failure and critical state failure can be well represented by the SSCC concept. The SSCC provides a potentially simple and practical way to describe the state of stress in unsaturated soil.     

Hardening Models and Their Predictions of Material Response

Several hardening models are investigated in this paper to examine how they predict material behavior under closed-loop loading paths. The linear Prager's kinematic hardening rule and a new kinematic hardening model proposed in a previous paper are first used to solve a thin-walled tube problem subjected to combined internal pressure and axial loads. Closed-form transient and steady-state solutions are achieved for closed-loop loading paths, and the corresponding yield center loci and plastic strain trajectories are illustrated. This paper then shows that Phillips's kinematic hardening rule and the two-surface plasticity theory all predict an unreasonable material response. A conclusion is finally reached that the newly proposed kinematic hardening model has more potential than the other models, and further theoretical and experimental investigations are suggested to probe the optimum form of the plastic modulus to make this new model qualitatively, and also quantitatively, describe well material behavior.     

General Formulation of Two Kinematic Hardening Constitutive Models with a Smooth Elastoplastic Transition

Two new constitutive models formulated within the framework of kinematic hardening plasticity are presented and their implementation into a finite-element program is described. The models are extensions of two existing constitutive models for reconstituted clays and introduce a number of kinematic surfaces within the modified CAM clay bounding surface. The new key feature of the models is a hardening modulus which results in a smooth variation of stiffness with strain, from the high elastic value, within the first kinematic surface, to the value on the bounding surface. Other features include a mathematical formulation of the models in general stress space to facilitate their implementation into a finite-element program, a variety of shapes of the yield and plastic potential surfaces in the deviatoric plane, and the novel concept of changing the active yield surface, which is necessary for the consistent formulation and implementation of the models into a finite-element code. The models are shown to have the ability to reproduce realistically the observed nonlinear prefailure behavior of overconsolidated clays in the small strain range.     

Seismic Earth Pressure on Retaining Structures

A simple kinematic method to predict the seismic earth pressure against retaining structures is developed. The fundamental solution to the free-field seismic response considering nonlinear, plastic behavior of soil is included in the retaining wall analysis for the first time. Perturbation to the free-field response caused by soil-structure interaction effects for different types of wall movement is considered. Results from this kinematic method are compared with those obtained from finite-element analysis and observed from laboratory shaking table tests performed on model retaining walls.     

Undrained Fragility of Clean Sands, Silty Sands, and Sandy Silts

In this paper, intergranular (ec) and interfine (ef) void ratios and confining stress are used as indices to characterize the stress–strain response of gap graded granular mixes. It was found that at the same global void ratio (e) and confining stress, the collapse potential (fragility) of silty sand increases with an increase in fines content (FC) due to a reduction in intergranular contact between the coarse grains. Beyond a certain threshold fines content (FCth), with further addition of fines, the interfine contact friction becomes significant. The fragility decreases and the soil becomes stronger. The value of FCth depends on e and the characteristics of fines and coarse grains. At FCFCth), fine grain friction plays a primary role and dispersed coarse grains provide a beneficial, secondary reinforcement effect. At the same ef, the collapse potential decreases with an increase in sand content. Beyond a certain limiting fines content, the soil behavior is controlled by ef only. An intergranular matrix diagram is presented that delineates zones of different behaviors of granular mixes as a guideline to determine the anticipated behavior of gap-graded granular mixes. New equivalent intergranular contact void ratios, (ec)eq and (ef)eq, are introduced to characterize the behavior of such soils, at FCFCth, respectively.     

Sydney Soil Model. II: Experimental Validation

This paper presents simulations of the mechanical behavior of reconstituted and natural soils using a new model presented in a companion paper and referred to as the “Sydney soil model.” It is demonstrated that the performance of the proposed model is essentially the same as that of modified Cam clay model when describing the behavior of clays in laboratory reconstituted states. The model has also been employed to simulate the drained and undrained behavior of structured clays and sands, including calcareous clay and sand. Five sets of conventional triaxial tests and one set of true triaxial tests have been considered. It is demonstrated that the new model provides satisfactory qualitative and quantitative modeling of many important features of the behavior of structured soils, particularly in capturing various patterns of the stress and strain behavior associated with soil type and structure. A general discussion of the model parameters is also included. It is concluded that the Sydney soil model is suitable for representing the behavior of many soils if their ultimate state during shearing can be defined by an intrinsic and constant stress ratio M* and a unique relationship between mean effective stress and voids ratio, i.e., a unique p′-e curve.     

Local and Global Stress–Strain Behaviors of Transformation-Induced Plasticity Steel Using the Combined Nanoindentation and Finite Element Analysis Method

Transformation-induced plasticity (TRIP) steels have excellent strain hardening exponents and resistibility against tensile necking using the strain-induced martensite formation that occurs as a result of the plastic deformation and strain on the retained austenite phase. Detailed studies on the microstructures and local mechanical properties, as well as global mechanical properties, are necessary in order to thoroughly understand the properties of TRIP steels with multiple phases of ferrite, bainite, retained austenite, and martensite. However, methods for investigating the local properties of the various phases of the TRIP steel are limited due to the very complicated and fine microstructures present in TRIP steel. In this study, the experimental and numerical methods, i.e., the experimental nanoindenting results and the theoretical finite element analyses, were combined in order to extract the local stress–strain curves of each phase. The local stress–strain curves were in good agreement with the values presented in the literature. In particular, the global plastic stress–strain behavior of the TRIP steel was predicted using the multiple phase unit cell finite element analysis, and this demonstrated the validity of the obtained properties of each local phase. The method of extracting the local stress–strain curves from the nanoindenting curves and predicting the global stress–strain behavior assists in clarifying the smart design of multi-phase steels.     

Single Hardening Elasto-Plastic Model for Kaolin Clay with Loading-History-Dependent Plastic Potential Function

The effect of principal stress rotation on the mechanical behavior of Kaolin clay is investigated using combined axial-torsional tests on hollow cylindrical specimens. The yielding behavior and failure criteria are found to be strongly dependent on the principal stress rotation angle (β) and plastic work. A unique plastic potential function determined solely by the current stress state is not sufficient to model the plastic flow observed in these experiments. Therefore, a single hardening elasto-plastic model that includes a loading-history-dependent plastic potential function is proposed for normally consolidated Kaolin clay subjected to principal stress rotation. A general methodology for incorporating history dependency in modeling complex elasto-plastic behavior of cohesive soils is presented along with comparisons of model predictions with experimental data.     

Unsaturated Constitutive Surfaces from Pressuremeter Tests

A methodology to identify the collapse potential of unsaturated soils is proposed in this paper on the basis of pressuremeter test results associated with independent measurements of the in situ matric suction. A solution combining the expansion of a cylindrical cavity to a modified Cam clay critical state model has been introduced and accommodated to the framework of unsaturated soil behavior. This accounts for changes in soil properties induced by suction changes. Interpretation of pressuremeter tests performed under unsaturated and soaked conditions links the amount of collapse to strength and stiffness changes and provides assessment to the constitutive soil parameters that are necessary to define the yield envelopes of the soil. A comprehensive site investigation program comprising field and laboratory tests carried out in two residual soil sites is discussed in order to validate the proposed methodology. Values of shear strength, in situ stress, and yield pressure derived from both field and laboratory data are used as input parameters of a constitutive model adopted for describing the yield envelopes of these unsaturated residual soil sites.     

Numerical Modeling of Seismic Response of Rigid Foundation on Soft Soil

A numerical model was developed to simulate the response of two instrumented, centrifuge model tests on soft clay and to investigate the factors that affect the seismic ground response. The centrifuge tests simulated the behavior of a rectangular building on 30?m uniform and layered soft soils. Each test model was subjected to several earthquakelike shaking events at a centrifugal acceleration level of 80g. The applied loading involved scaled versions of an artificial western Canada earthquake and the Port Island ground motion recorded during the 1995 Kobe Earthquake. The centrifuge model was simulated with the three-dimensional finite-difference-based fast Lagrangian analysis of continua program. The results predicted with the use of nonlinear elastic–plastic model for the soil are shown to be in good agreement with measured acceleration, soil response, and structural behavior. The validated model was used to study the effect of soil layering, depth, soil–structure interaction, and embedment effects on foundation motion.     

Modeling and Simulation of Porous Elastoviscoplastic Material

Many materials exhibit elasto–visco–plastic behavior when subjected to loadings with certain strain rate. Examples include natural materials such as metals, clays, and soils and manmade materials such as some biomimic materials. Some voids may exist or be introduced in these materials. The effects of the voids on the material response are important in predicting the strength, reliability, and service life of structural systems containing these materials. This paper presents the results of applying a statistical micromechanical approach to describe the macroscopic behavior of elasto–visco–plastic materials containing many randomly dispersed spherical voids. Most existing micromechanics based models are only applicable to monotonic proportional loadings. The limitation is removed by integrating the material model into the framework of continuum plasticity. With the discrete integration algorithm and local return mapping algorithm, the proposed computation method is applicable to any loading and unloading histories and is ready for implementing into finite element analysis.