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.     

Simple Plasticity Sand Model Accounting for Fabric Change Effects

A simple stress-ratio controlled, critical state compatible, sand plasticity model is presented, first in the triaxial and then in generalized stress space. The model builds upon previous work of the writers, albeit the presentation here is made with extreme simplicity in mind, and three novel aspects are introduced. The first is a fabric-dilatancy related quantity, scalar valued in the triaxial and tensor valued in generalized stress space, which is instrumental in modeling macroscopically the effect of fabric changes during the dilatant phase of deformation on the subsequent contractant response upon load increment reversals, and the ensuing realistic simulation of the sand behavior under undrained cyclic loading. The second aspect is the dependence of the plastic strain rate direction on a modified Lode angle in the multiaxial generalization, a feature necessary to produce realistic stress-strain simulations in nontriaxial conditions. The third aspect is a very systematic connection between the simple triaxial and the general multiaxial formulation, in order to use correctly the model parameters of the former in the implementation of the latter. The simulative ability of the model is illustrated by comparison with data over a very wide range of pressures and densities.     

Finite-Element Simulations of Full-Scale Modular-Block Reinforced Soil Retaining Walls under Earthquake Loading

A finite-element procedure was used to simulate the dynamic behavior of four full-scale reinforced soil retaining walls subjected to earthquake loading. The experiments were conducted at a maximum horizontal acceleration of over 0.8 g, with two walls subjected to only horizontal accelerations and two other walls under simultaneous horizontal and vertical accelerations. The analyzes were conducted using advanced soil and geosynthetic models that were capable of simulating behavior under both monotonic and cyclic loadings. The soil behavior was modeled using a unified general plasticity model, which was developed based on the critical state concept and that considered the stress level effects over a wide range of densities using a single set of parameters. The geosynthetic model was based on the bounding surface concept and it considered the S-shape load-strain behavior of polymeric geogrids. In this paper, the calibrations of the models and details of finite-element analysis are presented. The time response of horizontal and vertical accelerations obtained from the analyses, as well as wall deformations and tensile force in geogrids, were compared with the experimental results. The comparisons showed that the finite-element results rendered satisfactory agreement with the shake table test results.     

Modeling the Stress-Strain Relations of Sand in Cyclic Plane Strain Loading

A modeling procedure to simulate stress-strain relations of sand subjected to cyclic loading is proposed. Results from drained plane strain compression, extension, and cyclic loading tests on Toyoura sand are analyzed. The monotonic loading behavior is simulated by the generalized hyperbolic equation to use as the skeleton curves in the simulation of cyclic behavior. To construct hysteretic stress-strain curves based on the skeleton curves, the Masing’s rule is generalized to the proportional rule consisting of the internal and external rules. The drag rule is then introduced to simulate cyclic stress-strain behavior in which the stress amplitude increases at a decreasing rate during cyclic loading with a constant strain amplitude. It is assumed that any plastic shear strain increment taking place in a certain direction drags the whole skeleton curve for loading in the opposite direction towards the direction of the concerned shear strain increment. The measured cyclic stress-strain behavior is well simulated by the proposed method.     

Plasticity Model for Sand under Small and Large Cyclic Strains

A plasticity constitutive model for sands is proposed, which combines a bounding surface framework for large cyclic strains with a Ramberg-Osgood-type hysteretic formulation for relatively smaller strains. The distinction between small and large cyclic strains is based on the volumetric threshold cyclic shear strain γtv, a well-established geotechnical parameter. The state parameter ψ is used explicitly to interrelate the critical, peak, and dilatancy deviatoric stress ratios. The plastic modulus is expressed as a particular function of accumulated plastic volumetric strain, which simulates empirically the effect of fabric evolution during shearing. Extensive comparisons with experiments show accurate simulation of the basic aspects of cyclic behavior for a wide range of cyclic strain amplitudes, specifically, (1) the degradation of shear modulus and increase of hysteretic damping with cyclic shear strain amplitude; (2) the evolving rates of shear strain and excess pore pressure (or volumetric strain) accumulation with number of cycles; and (3) the resistance to liquefaction. The 14 model parameters are proven independent of initial and drainage conditions, as well as the cyclic shear strain amplitude. The simulation of monotonic shearing is equally accurate.     

Unified Elastoplastic–Viscoplastic Bounding Surface Model of Geosynthetics and Its Applications to Geosynthetic Reinforced Soil-Retaining Wall Analysis

The static and dynamic behaviors of reinforced soil structures are possibly subjected to the effects of creep or stress relaxation due to the time-dependent behavior of geosynthetic inclusions and backfill. To simulate the time-dependent monotonic and cyclic behavior of geosynthetics, an isothermal constitutive model is formulated within the framework of elastoplasticity–viscoplasticity. The concept of bounding surface plasticity is first utilized to formulate a time-independent cyclic model of geosynthetics. In order to capture the hardening stiffness of some polyester geosynthetics, an exponential bounding curve is used in simulating the primary loading. The time-independent version of the model was extended into an elastoplastic–viscoplastic model using overstress viscoplasticity with reference to available experimental data. The model was evaluated using creep, stress relaxation, monotonic, and cyclic loading test results obtained for different geosynthetics. It was then incorporated into a finite-element code and the static and dynamic behavior of a geosynthetic reinforced soil wall was analyzed. The analyzed results, with and without consideration to the time-dependent behavior of the reinforcements, were compared. It was demonstrated that although the end-of-construction behavior of the reinforced soil wall was less influenced by the time-dependent properties of geogrids, the long-term performance was considerably affected. The seismic response was also affected to some extent by the rate-dependent behavior of geogrids. The effects were more significant for short and/or large vertical spacing reinforcement layout.     

Sand Plasticity Model Accounting for Inherent Fabric Anisotropy

A sand plasticity constitutive model is presented herein, which accounts for the effect of inherent fabric anisotropy on the mechanical response. The anisotropy associated with particles’ orientation distribution, is represented by a second-order symmetric fabric tensor, and its effect is quantified via a scalar-valued anisotropic state variable, A. A is defined as the first joint isotropic invariant of the fabric tensor and a properly defined loading direction tensor, scaled by a function of a corresponding Lode angle. The hardening plastic modulus and the location of the critical state line in the void ratio?mean effective stress space, on which the dilatancy depends, are made functions of A. The incorporation of this dependence on A in a pre-existing stress-ratio driven, bounding surface plasticity constitutive model, achieves successful simulations of test results on sand for a wide variation of densities, pressures, loading manners, and directions. In particular, the drastic difference in material response observed experimentally for different directions of the principal stress axes with respect to the anisotropy axes, is well simulated by the model. The proposed definition and use of A has generic value, and can be incorporated in a large number of other constitutive models in order to account for inherent fabric anisotropy effects.     

Bounding Surface Model for Geosynthetic Reinforcements

Geosynthetic reinforcements are manufactured from polymers such as polyester, polypropylene, and high-density polyethylene. Compared to metals, they exhibit large plastic strains, and highly nonlinear and hysteretic behaviors under cyclic loading. Most geosynthetic reinforcements do not sustain compression load. Traditional cyclic models with the Masing rule fail to simulate such unique behavior. A 1D bounding surface concept is used to develop a model that considers these unique properties of geogrids. The unique features of the model include nonparallel bounding lines and different loading and unloading hardening parameters. The model was calibrated and compared with the experimental results of two geogrids under monotonic and cyclic loadings with different load amplitudes.     

Numerical Simulation of the Influence of Initial State of Sand on Element Tests and Micropile Performance

This paper presents a state-dependent constitutive model for sand formulated within the critical-state framework and its implementation into a numerical analysis (FLAC3D) program. The implemented model was verified by using drained triaxial results on sands. The proposed model is shown to capture the stress path dependent behavior of sand over a wide range of densities and confining pressures well based on a unique set of parameters. Numerical simulations of the behavior of a micropile under vertical loading shows that the side and tip resistance, and thus the total resistance of the pile, are functions of the “in situ state” of soil as defined by the state parameter ψ = e-ec in which e is the void ratio and ec the void ratio at the critical state.     

Modeling of Shallowly Embedded Offshore Pipelines in Calcareous Sand

The results of centrifuge modeling of pipe–soil interaction for shallowly embedded offshore pipelines are presented. A non-associated bounding surface model is constructed in vertical–horizontal (V–H) load space on the basis of test data and the theory of plasticity to simulate the response of a pipeline embedded in sandy soil under combined (vertical and horizontal) monotonic loading, taking into account possible pre-loading effects. The model needs nine parameters that can be back calculated from model or field tests and in some cases estimated theoretically. It provides a suitable basis for modeling the load-displacement response of shallowly embedded offshore pipelines. The model reproduces the key features of the load-displacement response of pipelines observed in centrifuge model tests. In particular, the adoption of bounding surface plasticity allows a gradual transition from elastic to plastic response to be simulated and the introduction of a non-associated flow rule allows the model to predict the strain-softening behavior of pipes under horizontal loading. The lateral breakout resistance predicted by the model agrees very well with experimental data.     

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.     

Constitutive Model for Static Liquefaction

A general, three-dimensional formulation of the elastoplastic refined Superior sand constitutive model is presented. The model is aimed at realistic simulation of liquefaction phenomena occurring in loose saturated granular materials under monotonic static loading. The isotropic hardening/softening is related to plastic deformation and distance to a reference yield surface. The nonassociated flow rule is used with the closed yield surface introduced previously in the Superior sand model. The refined model accounts for the different response of materials with different deposition densities. The model prediction of drained and undrained plane-strain compression is presented and compared with the response in triaxial compression/extension loading. Static and kinematic instability states also are discussed.     

Liquefaction, Cyclic Mobility, and Failure of Silt

It is known that the mechanical properties of low-plasticity silt are similar to those of sand, and yet silts are frequently used as coastal reclamation materials in many cities and industrial areas and will thus be susceptible to liquefaction. Samples of a low-plasticity silt have been tested under monotonic and cyclic loading under isotropic and anisotropic stress conditions to characterize liquefaction, cyclic failure, and to develop an empirical model describing its cyclic strength. A sedimentation technique produced samples that had the highest susceptibility to liquefaction. Contractive behavior of monotonically loaded samples was triggered when the stress path reached an initial phase transformation (IPT) in both compression and extension tests. The samples became dilative after reaching a phase transformation (PT) point. The cyclic shear behavior of the silt samples prepared using the sedimentation method and consolidated at various initial sustained deviator stress ratios was examined in terms of two different failure criteria: a double amplitude axial strain εa,DA = 5% for reversal conditions; or axial plastic strain εa,P = 5% for nonreversal. For isotropically consolidated samples the initial phase transformation determined from undrained monotonic extension tests was the boundary between stable and contractive behavior. For anisotropically consolidated samples failure was defined by a bounding surface formed by undrained monotonic compression tests. An empirical model was developed relating the number of cycles to failure under conditions of both liquefaction and cyclic mobility to the initial anisotropic sustained deviator stress and cyclic deviator stress ratio.     

Shear Strength and Stiffness of Sands Containing Plastic or Nonplastic Fines

This paper presents the results of a systematic laboratory investigation on the static behavior of silica sand containing various amounts of either plastic or nonplastic fines. Specimens were reconstituted using a new technique suitable for element testing of homogeneous specimens of sands containing fines deposited in water (e.g., alluvial deposits, hydraulic fills, tailings dams, and offshore deposits). The fabric of sands containing fines was examined using the environmental scanning electron microscope (ESEM). Static, monotonic, isotropically consolidated, drained triaxial compression tests were performed to evaluate the stress-strain-volumetric response of these soils. Piezoceramic bender element instrumentation was developed and integrated into a conventional triaxial apparatus; shear-wave velocity measurements were made to evaluate the small-strain stiffness of the sands tested at various states. The intrinsic parameters that characterize critical state, dilatancy, and small-strain stiffness of clean, silty, and clayey sands were determined. All aspects of the mechanical behavior investigated in this study (e.g., stress-strain-volumetric response, shear strength, and small-strain stiffness) are affected by both the amount and plasticity of the fines present in the sand. Microstructural evaluation using the ESEM highlighted the importance of soil fabric on the overall soil response.     

Two-Surface Plasticity Model for Cyclic Undrained Behavior of Clays

Based on a new type of kinematic hardening and the theory of critical state soil mechanics, a two-surface model is herein developed for predicting the undrained behavior of saturated cohesive soils under cyclic loads. The anisotropic hardening rule works in two steps: (1) introducing a new concept, memory center, to take into account the memory of particular loading history; and (2) regulating the movement of the bounding and loading surfaces according to the direction of loading paths in stress space. Conventional triaxial tests have been performed on reconstituted clay samples in the laboratory. The proposed model is verified with respect to the observed behavior of soil samples. It is shown that like a multisurface model, this model can realistically describe some important responses of clays subjected to both monotonic and cyclic loading, while incorporating the memory of particular loading events.     

Parametric Studies on the Behavior of Reinforced Soil Retaining Walls under Earthquake Loading

The finite element procedures are extremely useful in gaining insights into the behavior of reinforced soil retaining walls. In this study, a validated finite element procedure was used for conducting a series of parametric studies on the behavior of reinforced soil walls under construction and subject to earthquake loading. The procedure utilized a nonlinear numerical algorithms that incorporated a generalized plasticity soil model and a bounding surface geosynthetic model. The reinforcement layouts, soil properties under monotonic and cyclic loadings, block interaction properties, and earthquake motions were among major variables of investigation. The performance of the wall was presented for the facing deformation and crest surface settlement, lateral earth pressure, tensile force in the reinforcement layers, and acceleration amplification. The effects of soil properties, earthquake motions, and reinforcement layouts are issues of major design concern under earthquake loading. The deformation, reinforcement force, and earth pressure increased drastically under earthquake loading compared to end of construction.     

RC Slabs Strengthened with Prestressed and Gradually Anchored CFRP Strips under Monotonic and Cyclic Loading

This paper presents the test results of reinforced concrete slabs strengthened with prestressed and gradually anchored carbon fiber–reinforced polymer (CFRP) strips under monotonic and cyclic loading. To take full advantage of the externally bonded CFRP technique, it is beneficial to apply the laminates in a prestressed state, which relieves the stress in the steel reinforcement and reduces crack widths and deflection. The aim of the monotonic tests was to determine the strengthening efficiency of the new prestressing technique and to investigate serviceability and ultimate states. The cyclic tests were performed to identify the fatigue behavior of the strengthened slabs and to investigate the influence of long-term cyclic loading and elevated temperature on the bond properties of the prestressed CFRP laminates and the ductility and flexural strength of the strengthened slabs. A nonlinear analytical model of reinforced concrete members strengthened with passive and prestressed CFRP strips under static loading is proposed in the paper. A comparison of the experimental and predicted results reveals an excellent agreement in the full range of loading.     

Analyzing Dynamic Behavior of Geosynthetic-Reinforced Soil Retaining Walls

An advanced generalized plasticity soil model and bounding surface geosynthetic model, in conjunction with a dynamic finite element procedure, are used to analyze the behavior of geosynthetic-reinforced soil retaining walls. The construction behavior of a full-scale wall is first analyzed followed by a series of five shaking table tests conducted in a centrifuge. The parameters for the sandy backfill soils are calibrated through the results of monotonic and cyclic triaxial tests. The wall facing deformations, strains in the geogrid reinforcement layers, lateral earth pressures acting at the facing blocks, and vertical stresses at the foundation are presented. In the centrifugal shaking table tests, the response of the walls subject to 20 cycles of sinusoidal wave having a frequency of 2 Hz and of acceleration amplitude of 0.2g are compared with the results of analysis. The acceleration in the backfill, strain in the geogrid layers, and facing deformation are computed and compared to the test results. The results of analysis for both static and dynamic tests compared reasonably well with the experimental results.     

Cyclic hardening in copper described in terms of combined monotonic and cyclic stress-strain curves

Hardening of polycrystalline copper subjected to tension-compression loading cycles in the plastic region is discussed with reference to changes in flow stress determined from equations describing dislocation glide. It is suggested that hardening is as a result of the accumulation of strain on a monotonic stress-strain curve. On initial loading, the behaviour is monotonic. On stress reversal, a characteristic cyclic stress-strain curve is followed until the stress reaches a value in reverse loading corresponding to the maximum attained during the preceding half cycle. Thereafter, the monotonic path is followed until strain reversal occurs at completion of the half cycle. Repetition of the process results in cyclic hardening. Steady state cyclic behaviour is reached when a stress associated with the monotonic stress-strain curve is reached which is equal to the stress associated with the cyclic stress-strain curve corresponding to the imposed strain amplitude.     

Liquefaction Resistance of Sandy Soils under Partially Drained Condition

In order to simulate the effect of drainage on soils adjacent to gravel drains that are installed as countermeasure against liquefaction, several series of cyclic triaxial tests were performed on saturated sands under partially drained conditions. The condition of partial drainage under cyclic loading was simulated in the laboratory using triaxial testing equipment installed with a drainage control valve to precisely regulate the volume of water being drained from test specimens. Effects of both drainage conditions and loading frequencies on cyclic response were incorporated through the coefficient of drainage effect, α*. Experimental results showed that for sand exhibiting strain softening, the partially drained response was controlled by the critical effective stress ratio while for sand showing strain hardening behavior, the controlling factor was the phase transformation stress ratio. Moreover, test results indicated that the minimum liquefaction resistance under partially drained conditions can be used as a parameter to describe the liquefaction resistance of sands improved by the gravel drain method. From these results, a simplified procedure for designing gravel drains based on the factor of safety (FL) concept was proposed.