A two-surface plasticity model for stiff clay

This paper presents a constitutive model for describing some important features of the behavior of natural stiff clay evidenced experimentally such as the limited elastic zone, the presence of strain hardening and softening, and the smooth transition from elastic behavior to a plastic one. The model, namely ACC-2, is an adapted Modified Cam Clay model with two yield surfaces: similarly to bounding surface plasticity theory, an additional yield surface—namely Inner yield surface—was adopted to account for the plastic behavior inside the conventional yield surface. A progressive plastic hardening mechanism was introduced with a combined volumetric-deviatoric hardening law associated with the Inner yield surface, enabling the plastic modulus to vary smoothly during loading paths. The main feature of the proposed model is that its constitutive equations can be simply formulated based on the consistency condition for the Inner yield surface, so that it can be efficiently implemented in a finite element code using a stress integration scheme similar to that of the Modified Cam Clay model. Furthermore, it is proved to be an appropriate model for natural stiff clay: the simulations of a set of tests along different mechanical loading paths on natural Boom Clay show good agreement with the experimental results.     

An elastoplastic model with combined isotropic–kinematic hardening to predict the cyclic behavior of stiff clays

This paper presents a kinematic hardening model for describing some important features of natural stiff clays under cyclic loading conditions, such as closed hysteretic loops, smooth transition from the elastic behavior to the elastoplastic one and changes of the compression slope with loading/unloading loops. The model includes two yield surfaces, an inner surface and a bounding surface. A non-associated flow rule and a kinematic hardening law are proposed for the inner surface. The adopted hardening law enables the plastic modulus to vary smoothly when the kinematic yield surface approaches the bounding surface and ensures at the same time the non-intersection of the two yield surfaces. Furthermore, the first loading, unloading, and reloading stages are treated differently by applying distinct hardening parameters. The main feature of the model is that its constitutive equations can be simply formulated based on the consistency condition for the inner yield surface based on the proposed kinematic hardening law; thereby, this model can be easily implemented in a finite element code using a classic stress integration scheme as for the modified Cam Clay model. The simulation results on the Boom Clay, natural stiff clay, have revealed the relevance of the model: a good agreement has been obtained between simulations and the experimental results from the tests with different stress paths under cyclic loading conditions. In particular, the model can satisfactorily describe the complex case of oedometric conditions where the deviator stress is positive upon loading (compression) but can become negative upon unloading (extension).     

Kinematic hardening plasticity formulation of small strain behaviour of soils

An objective of this paper is to demonstrate that the small strain model developed by the authors can be incorporated into the conventional kinematic hardening plasticity framework to predict pre‐failure defor mations. The constitutive model described in this paper is constituted by three elliptical yield surfaces in triaxial stress space. Two inner surfaces are rotated ellipses of the same shape, representing the boundaries of the linear elastic and small strain regions, while the third surface is the modified Cam clay large‐scale yield surface. Within the linear elastic region, the soil behaviour is elastic with cross‐coupling between the shear and volumetric stress–strain components. Within the small strain region, the soil behaviour is elasto‐plastic, described by the kinematic hardening rule with an infinite number of loading surfaces defined by the incremental energy criterion. Within the large‐scale yield surface, the soil behaviour is elasto‐plastic, described by kinematic and isotropic hardening of the small strain region boundary. Since the yield surfaces have different shapes, the uniqueness of the plastic loading condition imposes a restriction on the ratio between their semi‐diameters. The model requires 12 parameters, which can be determined from a single consolidated undrained triaxial compression test. Copyright © 2000 John Wiley & Sons, Ltd.     

SANICLAY: simple anisotropic clay plasticity model

SANICLAY is a new simple anisotropic clay plasticity model that builds on a modification of an earlier model with an associated flow rule, in order to include simulations of softening response under undrained compression following K_o consolidation. Non‐associativity is introduced by adopting a yield surface different than the plastic potential surface. Besides, the isotropic hardening of the yield surface both surfaces evolve according to a combined distortional and rotational hardening rule, simulating the evolving anisotropy. Although built on the general premises of critical state soil mechanics, the model induces a critical state line in the void ratio–mean effective stress space, which is a function of anisotropy. To ease interpretation, the model formulation is presented firstly in the triaxial stress space and subsequently, its multiaxial generalization is developed systematically, in a form appropriate for implementation in numerical codes. The SANICLAY is shown to provide successful simulation of both undrained and drained rate‐independent behaviour of normally consolidated sensitive clays, and to a satisfactory degree of accuracy of overconsolidated clays. The new model requires merely three constants more than those of the modified Cam clay model, all of which are easily calibrated from well‐established laboratory tests following a meticulously presented procedure. Copyright © 2006 John Wiley & Sons, Ltd.     

A general modelling of expansive and non-expansive clays

This paper presents an elastoplastic model for saturated expansive and non-expansive clays. The original feature of this model is that a plastic mechanism is introduced during unloading to take into account the irreversible swelling of the macroporosities. These strains are induced by the repulsive stresses which are unbalanced at the scale of the microporosities. Thus two yield surfaces are activated: a classical contact yield surface (F_C) similar to an associated modified Cam-clay approach and a swelling yield surface (F_R−A) based on the non-associated plasticity. The formulation considers that for the normally consolidated stress states, the strains are mainly produced by an increase of the contact stresses. For the overconsolidated stress states, the repulsive stresses balance the external stresses. The rheological parameters are easily determined from the results of either triaxial or oedometer tests. The model is then used in a finite element program, using the classical concepts of plasticity, especially for the loading–unloading criterion based on the sign of the plasticity multiplier. Simulations of the convergence of a gallery (under an earth retaining structure) sunk at great depth in Boom clay are presented. The results are compared with those obtained with the Cam-clay model. Copyright © 1999 John Wiley & Sons, Ltd.     

The influence of the plastic potential on plane strain failure

The influence of the shape of the plastic potential in the deviatoric plane on plane strain collapse is investigated. The most commonly employed elastic‐perfect plastic models are considered, which adopt well‐known failure criteria for defining the yield and plastic potential surfaces, namely the von Mises, the Drucker–Prager, the Tresca, the Mohr–Coulomb and the Matsuoka–Nakai criteria. Finally, the conclusions are also extended to strain hardening/softening models. For simple constitutive models based on perfect plasticity, it is shown that the value of the Lode's angle at plastic collapse in plane strain conditions strongly depends on the specific failure surface adopted for reproducing the plastic potential surface. If the value of the Lode's angle at yield coincides with the failure value prescribed by the plastic potential, the stress–strain curves exhibit the typical perfect plastic behaviour with yield coinciding with failure, otherwise the stress changes after yield and the stress‐strain curves resemble those of strain hardening/softening models. The infinite strength which is in some situations exhibited by the Drucker–Prager model in plane strain condition is investigated and explained, and it is shown that this can also affect strain hardening/softening models. Copyright © 2013 John Wiley & Sons, Ltd.     

Implicit integration of a mixed isotropic–kinematic hardening plasticity model for structured clays

In recent years, a number of constitutive models have been proposed to describe mathematically the mechanical response of natural clays. Some of these models are characterized by complex formulations, often leading to non‐trivial problems in their numerical integration in finite elements codes. The paper describes a fully implicit stress‐point algorithm for the numerical integration of a single‐surface mixed isotropic–kinematic hardening plasticity model for structured clays. The formulation of the model stems from a compromise between its capability of reproducing the larger number of features characterizing the behaviour of structured clays and the possibility of developing a robust integration algorithm for its implementation in a finite elements code. The model is characterized by an ellipsoid‐shaped yield function, inside which a stress‐dependent reversible stiffness is accounted for by a non‐linear hyperelastic formulation. The isotropic part of the hardening law extends the standard Cam‐Clay one to include plastic strain‐driven softening due to bond degradation, while the kinematic hardening part controls the evolution of the position of the yield surface in the stress space. The proposed algorithm allows the consistent linearization of the constitutive equations guaranteeing the quadratic rate of asymptotic convergence in the global‐level Newton–Raphson iterative procedure. The accuracy and the convergence properties of the proposed algorithm are evaluated with reference to the numerical simulations of single element tests and the analysis of a typical geotechnical boundary value problem. Copyright © 2007 John Wiley & Sons, Ltd.     

A middle surface concept (MSC) model for saturated sands in general stress space

An elastoplastic constitutive model is proposed for saturated sands in general stress space using the middle surface concept (MSC). In MSC, different features of stress–strain response of a material are divided into different pseudo‐yield surfaces. The true‐yield surface representing the true response is established by using various links between the yield surfaces. In this MSC sand model, several well‐known features of sand response are represented by three different pseudo‐yield surfaces, which are developed in a simple and straightforward way. These features include the critical state behaviour, the effects of state parameter, unloading and reloading plastic deformation, the influence of fabric anisotropy, and phase transformation line related behaviour. Finally, the model predictions and test results are compared for two different types of sands under a variety of loading conditions and good comparisons are obtained. The application of MSC to saturated sand modelling shows the versatility of MSC as a general concept for modelling stress–strain response of materials. Copyright © 2006 John Wiley & Sons, Ltd.     

A two-surface thermomechanical plasticity model considering thermal cyclic behavior

In thermal-related engineering such as thermal energy structures and nuclear waste disposal, it is essential to well understand volume change and excess pore water pressure buildup of soils under thermal cycles. However, most existing thermo-mechanical models can merely simulate one heating–cooling cycle and fail in capturing accumulation phenomenon due to multiple thermal cycles. In this study, a two-surface elasto-plastic model considering thermal cyclic behavior is proposed. This model is based on the bounding surface plasticity and progressive plasticity by introducing two yield surfaces and two loading yield limits. A dependency law is proposed by linking two loading yield limits with a thermal accumulation parameter n_c, allowing the thermal cyclic behavior to be taken into account. Parameter n_c controls the evolution rate of the inner loading yield limit approaching the loading yield limit following a thermal loading path. By extending the thermo-hydro-mechanical equations into the elastic–plastic state, the excess pore water pressure buildup of soil due to thermal cycles is also accounted. Then, thermal cycle tests on four fine-grained soils (natural Boom clay, Geneva clay, Bonny silt, and reconstituted Pontida clay) under different OCRs and stresses are simulated and compared. The results show that the proposed model can well describe both strain accumulation phenomenon and excess pore water pressure buildup of fine-grained soils under the effect of thermal cycles.

     

A cap model for partially saturated soils

The present paper deals with the extension of a cap model in order to describe the material behavior of partially saturated soils, in particular, of partially saturated sands and silts. The soil model is formulated in terms of two stress state variables, using net stress and matric suction and, alternatively, the average soil skeleton stress and suction, the latter playing the role of a stress‐like plastic internal variable. The yield surface, consisting of a shear failure surface and a hardening cap surface, the plastic potentials for the non‐associated flow rule and the hardening law for the cap are extended by taking into account the effects of matric suction on the material behavior. Furthermore, the third invariant of the deviatoric stress tensor is taken into account in the formulation of the yield surfaces. The developed model is validated by the numerical simulation of an extensive series of suction controlled tests for a silty sand, which were conducted at different constant values of suction. Although both versions of the soil model yield identical results for stress paths at constant values of matric suction, differences are encountered for stress paths involving wetting. Copyright © 2007 John Wiley & Sons, Ltd.     

CASM: a unified state parameter model for clay and sand

The purpose of this paper is to present a simple, unified critical state constitutive model for both clay and sand. The model, called CASM (Clay And Sand Model), is formulated in terms of the state parameter that is defined as the vertical distance between current state (v, p′) and the critical state line in v–ln p′ space. The paper first shows that the standard Cam-clay models (i.e. the original and modified Cam-clay models) can be reformulated in terms of the state parameter. Although the standard Cam-clay models prove to be successful in modelling normally consolidated clays, it is well known that they cannot predict many important features of the behavior of sands and overconsolidated clays. By adopting a general stress ratio-state parameter relation to describe the state boundary surface of soils, it is shown that a simple, unified constitutive model (CASM) can be developed for both clay and sand. It is also demonstrated that the standard Cam-clay yield surfaces can be either recovered or approximated as special cases of the yield locus assumed in CASM. The main feature of the proposed model is that a single set of yield and plastic potential functions has been used to model the behaviour of clay and sand under both drained and undrained loading conditions. In addition, it is shown that the behaviour of overconsolidated clays can also be satisfactorily modelled. Simplicity is a major advantage of the present state parameter model, as only two new material constants need to be introduced when compared with the standard Cam-clay models. © 1998 John Wiley & Sons, Ltd.     

Delayed plastic model for time‐dependent behaviour of materials

A delayed plastic model, based on the theory of plasticity, is proposed to represent the time‐dependent behaviour of materials. It is assumed in this model that the stress can lie outside the yield surface and the conjugate stress called static stress is defined on the yield surface. The stress–strain relation is calculated based on the plastic theory embedding the static stress. Thus, the stress–strain relation of the model practically corresponds to that of the inviscid elastoplastic model under fairly low rate deformation. The delayed plastic model is coupled with the Cam‐clay model for normally consolidated clays. The performance of the model is then examined by comparing the model predictions with reported time‐dependent behaviour of clays under undrained triaxial conditions. It is shown that the model is capable of predicting the effect of strain rate during undrained shear and the undrained creep behaviour including creep rupture. Copyright © 2001 John Wiley & Sons, Ltd.     

A two-surface plasticity model for cyclic behavior of saturated clay

This paper presents a two-surface plasticity model for describing some important features of saturated clay under cyclic loading conditions, such as closed hysteresis loops, cyclic shakedown and degradation, and different stress–strain relations for two-way loading. The model, namely ACC-2-C, is based on the elastoplastic model ACC-2 (an adapted Modified Cam Clay model with two yield surfaces) developed by Hong et al. (Acta Geotech 11(4):871–885, 2015). The small-strain nonlinearity concept is adopted to achieve the nonlinear characteristics of clay during unloading–loading stage. The new hardening law related to accumulated deviatoric plastic strain is proposed for the inner surface to describe the cyclic shakedown and degradation. Following the advantages of the ACC-2 model, the constitutive equations are simply formulated based on the consistency condition for the inner yield surface. The model is conveniently implemented in a finite element code using a stress integration scheme similar to the Modified Cam Clay model. The simulation results are highly consistent with experimental data from drained and undrained isotropic cyclic triaxial tests in normally consolidated saturated clay under both one-way and two-way loadings.

     

Explicit solutions for the instantaneous undrained contraction of hollow cylinders and spheres in porous elastoplastic medium

In this article we present closed‐form solutions for the undrained variations in stress, pore pressure, deformation and displacement inside hollow cylinders and hollow spheres subjected to uniform mechanical pressure instantaneously applied to their external and internal boundary surfaces. The material is assumed to be a saturated porous medium obeying a Mohr–Coulomb model failure criterion, exhibiting dilatant plastic deformation according to a non‐associated flow rule which accounts for isotropically strain hardening or softening. The instantaneous response of a porous medium submitted to an instantaneous loading is undrained, i.e. without any fluid mass exchange. The short‐term equilibrium problem to be solved is now formally identical to a problem of elastoplasticity where the constitutive equations involve the undrained elastic moduli and particular equivalent plastic parameters. The response of the model is presented (i) for extension and compression undrained triaxial tests, and (ii) for unloading problems of hollow cylinders and spheres through the use of appropriately developed closed‐form solutions. Numerical results are presented for a plastic clay stone with strain hardening and an argilite with strain softening. The effects of plastic dilation, of the strain softening law and also of geometry of the cavity on the behaviour of the porous medium have been underlined. Analytical solutions provide valuable benchmarks enabling various numerical methods in undrained conditions with a finite boundary to be verified. Copyright © 2002 John Wiley & Sons, Ltd.     

Hydro‐mechanical response of collapsible soils under different infiltration events

The behavior of a partially saturated soil during surface‐water infiltration is analyzed by means of an elasto‐plastic constitutive model formulated in terms of effective stress and extended to unsaturated conditions. The model is calibrated considering laboratory‐scale experimental results under suction‐controlled conditions. The wetting process in two collapsing soils, initially loaded at in situ stresses, is simulated by imposing two different boundary conditions: surface ponding and water flow. The stress paths resulting from the imbibition process are analyzed at different points inside the layer. Copyright © 2015 John Wiley & Sons, Ltd.     

An anisotropic elastoplastic model for soft clays based on logarithmic contractancy

A new constitutive model for soft structured clays is developed based on an existing model called S‐CLAY1S, which is a Cam clay type model that accounts for anisotropy and destructuration. The new model (E‐SCLAY1S) uses the framework of logarithmic contractancy to introduce a new parameter that controls the shape of the yield surface as well as the plastic potential (as an assumed associated flow rule is applied). This new parameter can be used to fit the coefficient of earth pressure at rest, the undrained shear strength or the stiffness under shearing stress paths predicted by the model. The improvement to previous constitutive models that account for soil fabric and bonding is formulated within the contractancy framework such that the model predicts the uniqueness of the critical state line and its slope is independent of the contractancy parameter. Good agreement has been found between the model predictions and published laboratory results for triaxial compression tests. An important finding is that the contractancy parameter, and consequently the shape of the yield surface, seems to change with the degree of anisotropy; however, further study is required to investigate this response. From published data, the yield surface for isotropically consolidated clays seems ‘bullet’ or ‘almond’ shaped, similar to that of the Cam clay model; while for anisotropically consolidated clays, the yield surface is more elliptical, like a rotated and distorted modified Cam clay yield surface. © 2015 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons Ltd.     

Simulation of cyclic strength degradation of natural clays via bounding surface model with hybrid flow rule

Strength loss of natural clays subjected to seismic loading is a critical factor contributing to earthquake‐induced ground failure and associated hazards. This work proposes a bounding surface constitutive law to simulate cyclic strength degradation of natural clays resulting from the loss of structure and attendant accumulation of excess pore pressures. The proposed model employs an enhanced plastic flow rule that can simulate accurately the development of pore pressure and explicitly incorporates soil structure effects. The validation of the model with reference to the experimental evidence available for 3 structured clays shows that with a single set of parameters the proposed model can reasonably represent the mechanical behavior of natural clays under various loading conditions (1D compression, monotonic shearing in compression and extension, cyclic loading, and postcyclic shearing). Particularly, its satisfactory performance in terms of quantification of cyclic strength degradation encourages the use of the model in simulating boundary value problems related to the stability of geotechnical facilities under earthquakes.     

Implementation of DSC model and application for analysis of field pile tests under cyclic loading

The disturbed state concept (DSC) model, and a new and simplified procedure for unloading and reloading behavior are implemented in a nonlinear finite element procedure for dynamic analysis for coupled response of saturated porous materials. The DSC model is used to characterize the cyclic behavior of saturated clays and clay–steel interfaces. In the DSC, the relative intact (RI) behavior is characterized by using the hierarchical single surface (HISS) plasticity model; and the fully adjusted (FA) behavior is modeled by using the critical state concept. The DSC model is validated with respect to laboratory triaxial tests for clay and shear tests for clay‐steel interfaces. The computer procedure is used to predict field behavior of an instrumented pile subjected to cyclic loading. The predictions provide very good correlation with the field data. They also yield improved results compared to those from a HISS model with anisotropic hardening, partly because the DSC model allows for degradation or softening and interface response. Copyright © 2000 John Wiley & Sons, Ltd.