A hypoplastic model for clay and sand

The theory of hypoplasticity was developed initially for non-cohesive soils. However, sand and clay have many common properties; therefore arose the idea to extend the hypoplastic model to clay. The proposed model is able to describe the behaviour of cohesive soils with the incorporation of an appropriate structure tensor into the constitutive equation. This tensor is a stress-like internal parameter, also called back stress. This enables us to describe the behaviour of cohesive soils with the same material parameters for several states of consolidation and also to model barotropy and pycnotropy of sand. Numerical simulations of element tests are performed in order to check the performance of this hypoplastic model. Experimental data obtained with normally and overconsolidated clay and sand specimens with various densities are taken for comparison, and it is shown that the model is capable of describing the material behaviour of clay and sand. The determination of the material constants, the calibration method, is also presented in this paper.     

Performance of mixed and enhanced finite elements for strain localization in hypoplasticity

Displacement and mixed finite element formulations of shear localization in materials are presented. The formulations are based on hypoplastic constitutive laws for soils and the mixed enhanced treatment involving displacement, strain and stress rates as independently varied fields. Included in these formulations are the standard displacement method, the three‐field mixed formulation, the enhanced assumed strain method and the mixed enhanced strain method. Several numerical examples demonstrating the capability and performance of the different finite element formulations are presented. The numerical results are compared with available experimental data for Hostun RF sand and numerical results for Karlsruhe sand on biaxial tests. Copyright © 2011 John Wiley & Sons, Ltd.     

Quantitative prediction of discrete element models on complex loading paths

The ability of discrete element models to describe quantitatively (and not only qualitatively) the constitutive behaviour of a dense sand is assessed in this paper. Two kinds of 3D discrete models are considered. Both consider spheres as elementary particles. Nevertheless, the first model implements a contact law with rolling resistance whereas the second takes into account clumps made of two spheres. The discrete models are calibrated and validated from mechanical tests performed on a dense Hostun sand with a true triaxial apparatus. The calibration is carried out from axisymmetric drained compression tests, while the validation is discussed from monotonic and cyclic stress proportional loading paths and from a circular stress path in the deviatoric stress plane. The quality of the predictions of the discrete models are evaluated by comparison with the predictions given with advanced phenomenological constitutive relations, mainly an incrementally non-linear relation. Predictions given by the discrete models are remarkable, particularly when it is put in perspective with respect to the very few number of mechanical tests required for their calibration. However, these results and conclusions were reached in enabling conditions, and some limitations of such discrete models should be kept in mind.     

Analysis of liquefaction susceptibility of nearly saturated sands

A new constitutive formulation for simulating the behaviour of nearly saturated sands under seismic loads is presented. The formulation is based on combining the Henry's law for dissolution of gas in water, the ideal or perfect gas law and the law of conservation of mass. The effects of transient air dissolution in water on the compressibility of partially saturated soils are also taken into account. The model was calibrated based on numerical simulations of isotropically consolidated cyclic triaxial tests conducted on partially saturated samples of Toyoura sand. A multi‐yield plasticity soil constitutive model implemented in the finite element code DYNAFLOW was used for these numerical simulations. It is shown that the formulation proposed here is able to reasonably predict the soil cyclic undrained behaviour at various degrees of saturation (95% and higher). Copyright © 2006 John Wiley & Sons, Ltd.     

Selection of sand models and identification of parameters using an enhanced genetic algorithm

Numerous constitutive models of granular soils have been developed during the last few decades. As a consequence, how to select an appropriate model with the necessary features based on conventional tests and with an easy way of identifying parameters for geotechnical applications has become a major issue. This paper aims to discuss the selection of sand models and parameters identification by using genetic algorithm. A real‐coded genetic algorithm is enhanced for the optimization with high efficiency. Models with gradually varying features (elastic‐perfectly plastic modelling, nonlinear stress–strain hardening, critical state concept and two‐surface concept) are selected from numerous sand models as examples for optimization. Conventional triaxial tests on Hostun sand are selected as the objectives in the optimization. Four key points are then discussed in turn: (i) which features are necessary to be accounted for in constitutive modelling of sand; (ii) which type of tests (drained and/or undrained) should be selected for an optimal identification of parameters; (iii) what is the minimum number of tests that should be selected for parameter identification; and (iv) what is the suitable and least strain level of objective tests to obtain reliable and reasonable parameters. Finally, a useful guide, based on all comparisons, is provided at the end of the discussion. Copyright © 2015 John Wiley & Sons, Ltd.     

Significance of molecular-level behaviour incorporation in the constitutive models of expansive clays – a review

Expansive clays are widely prevalent all over the world as one of the most problematic soils. These soils undergo significant volume change with a change in the moisture regime, thereby posing problems to the stability of the structures founded on such strata. Efforts have been made to model the erratic behaviour of these soils at the macro, micro, and, to a lesser extent, nano levels. Micro and nano level fabrics, believed to have a central role in the overall behaviour of expansive clays, are only partially considered in the modelling concepts; natural clay fabrics with multiple clay minerals, silt and sand inclusions, micro fissures, cementation, overconsolidation, induration and other such features have never been considered. This paper covers a review of deficiencies in the existing constitutive models for the expansive characteristics of the natural clayey soils at macro, micro and nano levels. These shortcomings are discussed in the light of the understanding of the fundamentals including fabric and structure controlling the swelling mechanism of the expansive clayey soils at the molecular level. Finally, a framework based on authors’ work to incorporate molecular level behaviour in the constitutive modelling of expansive clays is presented.     

适用于砂土循环加载分析的边界面塑性模型

基于临界状态土力学框架,建立了一个适用于砂土排水循环加载的边界面塑性模型。采用了考虑虚拟峰值应力比的偏应变硬化准则,初始加载阶段应力点位于边界面上,反向加载阶段以历史最大屈服面作为边界面,同时实现了对密砂软化现象的模拟和对历史所受最大应力的记忆。边界面采用修正的椭圆形,引入考虑密度与应力水平的状态相关剪胀函数,采用非相关联流动法则和以应力反向点作为映射中心的径向映射准则。模型仅有10个参数,通过常规三轴试验即可确定,并且使用一套参数可以模拟不同围压、密度的单调和循环加载情况。分别对饱和砂土的单调、循环排水三轴试验进行模拟,结果表明,该模型能够合理地反映饱和砂土排水条件下的应力-应变特性。     

Predictive potential of Perzyna viscoplastic modelling for granular geomaterials

This paper reappraises Perzyna-type viscoplasticity for the constitutive modelling of granular geomaterials, with emphasis on the simulation of rate/time effects of different magnitude. An existing elasto-plastic model for sands is first recast into a Perzyna viscoplastic formulation and then calibrated/validated against laboratory test results on Hostun sand from the literature. Notable model features include (1) enhanced definition of the viscous nucleus function and (2) void ratio dependence of stiffness and viscous parameters, to model the pycnotropic behaviour of granular materials with a single set of parameters, uniquely identified against standard creep and triaxial test results. The comparison between experimental data and numerical simulations points out the predicative capability of the developed model and the complexity of defining a unique viscous nucleus function to capture sand behaviour under different loading/initial/boundary and drainage conditions. It is concluded that the unified viscoplastic simulation of both drained and undrained response is particularly challenging within Perzyna's framework and opens to future research in the area. The discussion presented is relevant, for instance, to the simulation of multiphase strain localisation phenomena, such as those associated to slope stability problems in variably saturated soils.     

Study on the swelling behaviour of blended clay–sand soils

Soils containing expansive clays undergo swelling that can be both detrimental and beneficial in various applications. In the Arabian Gulf coastal region, natural heterogeneous soils containing clay and sand (tills, shales, and clayey sands) support most of the civil infrastructure systems. Likewise, mixes of clay and sand are used for local earthwork construction such as roads and landfills. A clear understanding of the swelling behaviour of such soils is pivotal at the outset of all construction projects. The main objective of this paper was to understand the evolution of swelling with increasing clay content in local soils. A theoretical framework for clay–sand soils was developed using phase relationships. Laboratory investigations comprised of mineralogical composition and geotechnical index properties of the clay and sand and consistency limits, swelling potential, and morphology of clay–sand mixes. Results indicated that soil consistency of mixes of a local expansive clay and an engineered sand depends on the weighted average of the constituents. Mixes with 10% clay through 40% clay capture the transition from a sand-like behaviour to a clay-like behaviour. Influenced by the initial conditions and soil matrix, the swelling potential of the investigated mixes correlated well with soil plasticity (SP(%) = 0.16 (I _p)^1.188). The parameters sand void ratio and clay–water ratio were found to better explain the behaviour of blended clay–sand soils.     

Bifurcation and instability modelling by a multimechanism elasto‐plastic model

The bifurcation and instability conditions in geomechanics are closely related to the elasto‐plastic behaviour. In this paper the potential of a multimechanism elasto‐plastic model to predict various modes of failure is examined. First, a brief overview for the essential aspects of the constitutive model and the development of the elasto‐plastic constitutive matrix for this model are presented. Then, numerical simulations of different drained and undrained paths in the axisymmetric and plane‐strain conditions for the Hostun sand are illustrated. These examples confirm the capacity of the model to reproduce instability and strain localization phenomena. The obtained response is in agreement with experimental observations, theoretical developments and numerical analyses existing in the literature. Copyright © 2007 John Wiley & Sons, Ltd.     

Cyclic degradation and non-coaxiality of soft clay subjected to pure rotation of principal stress directions

Foundation soils are often under non-proportional cyclic loadings. The deformation behaviour and the mechanism of non-coaxiality under continuous pure principal stress rotation for clays are not clearly investigated up to now. In order to study the effect of pure principal stress rotation, a series of cyclic undrained tests on Shanghai soft clay subjected to cyclic rotation of principal stress directions keeping the deviatoric stress constant under the pure rotation condition were conducted using hollow cylinder apparatus. Based on this, the evolutions of excess pore pressure and strains during cyclic loading were investigated, together with the effects of the intermediate principal stress parameter and the deviatoric stress level on stress–strain stiffness and non-coaxiality. The result can provide an experimental basis for constitutive modelling of clays describing the behaviour under non-proportional loadings.     

Unified bounding surface model for monotonic and cyclic behaviour of clay and sand

Acta Geotechnica - This paper presents a constitutive model enabled to simulate monotonic and cyclic behaviour of clay and sand in a unified framework. The bounding surface concept has been...     

Development in modeling cyclic loading of sands based on kinematic hardening

In this paper, there is presented an elastoplastic constitutive model to predict sandy soils behavior under monotonic and cyclic loadings. This model is based on an existing model (Cambou‐Jafari‐Sidoroff) that takes into account deviatoric and isotropic mechanisms of plasticity. The flow rule used in the deviatoric mechanism is non‐associated and a mixed hardening law controls the evolution of the yield surface. In this research the critical state surface and history surface, which separates the virgin and cyclic states in stress space, are defined. Kinematic hardening modulus and stress–dilatancy law for monotonic and cyclic loadings are effectively modified. With taking hardening modulus as a function of deviatoric and volumetric plastic strain and with defining the history surface and stress reversal, the model has the ability to predict the sandy soils' behavior. All of the model parameters have clear physical meanings and can be determined from usual laboratory tests. In order to validate the model, the results of homogeneous tests on Hostun and Toyoura sands are used. The results of validation show a good capability of the proposed model. Copyright © 2009 John Wiley & Sons, Ltd.     

Bayesian model selection for sand with generalization ability evaluation

Current studies have focused on selecting constitutive models using optimization methods or selecting simple formulas or models using Bayesian methods. In contrast, this paper deals with the challenge to propose an effective Bayesian-based selection method for advanced soil models accounting for the soil uncertainty. Four representative critical state-based advanced sand models are chosen as database of constitutive model. Triaxial tests on Hostun sand are selected as training and testing data. The Bayesian method is enhanced based on transitional Markov chain Monte Carlo method, whereby the generalization ability for each model is simultaneously evaluated, for the model selection. The most plausible/suitable model in terms of predictive ability, generalization ability, and model complexity is selected using training data. The performance of the method is then validated by testing data. Finally, a series of drained triaxial tests on Karlsruhe sand is used for further evaluating the performance.     

An AI-based model for describing cyclic characteristics of granular materials

Modelling cyclic behaviour of granular soils under both drained and undrained conditions with a good performance is still a challenge. This study presents a new way of modelling the cyclic behaviour of granular materials using deep learning. To capture the continuous cyclic behaviour in time dimension, the long short-term memory (LSTM) neural network is adopted, which is characterised by the prediction of sequential data, meaning that it provides a novel means of predicting the continuous behaviour of soils under various loading paths. Synthetic datasets of cyclic loading under drained and undrained conditions generated by an advanced soil constitutive model are first employed to explore an appropriate framework for the LSTM-based model. Then the LSTM-based model is used to estimate the cyclic behaviour of real sands, ie, the Toyoura sand under the undrained condition and the Fontainebleau sand under both undrained and drained conditions. The estimates are compared with actual experimental results, which indicates that the LSTM-based model can simultaneously simulate the cyclic behaviour of sand under both drained and undrained conditions, ie, (a) the cyclic mobility mechanism, the degradation of effective stress and large deformation under the undrained condition, and (b) shear strain accumulation and densification under the drained condition.     

Predictions of a continuous hyperplasticity model for Bangkok clay

The performance of a new constitutive model called ‘kinematic hardening modified Cam clay’ (KHMCC) is presented. The model is described using the ‘continuous hyperplasticity’ framework. Essentially this involves an infinite number of yield surfaces, thus allowing a smooth transition between elasticity and plasticity. The framework allows soil models to be developed in a relatively succinct mathematical form, since the entire constitutive behaviour can be determined through the specification of two scalar potentials. An implementation of the continuous hyperplasticity model is also described. The model requires eight parameters plus a viscosity coefficient for rate-dependent analysis. The model is defined in terms of triaxial stress–strain variables for this study, and is used to model monotonic triaxial tests on Bangkok clay. Comparisons of the theoretical predictions with the results of cyclic undrained triaxial compression tests on Bangkok clay are also presented.     

Disturbed state model for sand–geosynthetic interfaces and application to pull-out tests

Successful numerical simulation of geosynthetic-reinforced earth structures depends on selecting proper constitutive models for soils, geosynthetics and soil–geosynthetic interfaces. Many constitutive models are available for modelling soils and geosynthetics. However, constitutive models for soil–geosynthetic interfaces which can capture most of the important characteristics of interface response are not readily available. In this paper, an elasto-plastic constitutive model based on the disturbed state concept (DSC) for geosynthetic–soil interfaces has been presented. The proposed model is capable of capturing most of the important characteristics of interface response, such as dilation, hardening and softening. The behaviour of interfaces under the direct shear test has been predicted by the model. The present model has been implemented in the finite element procedure in association with the thin-layer element. Five pull-out tests with two different geogrids have been simulated numerically using FEM. For the calibration of the constitutive models used in FEM, the standard laboratory tests used are: (1) triaxial tests for the sand, (2) direct shear tests for the interfaces and (3) axial tension tests for the geogrids. The results of the finite element simulations of pull-out tests agree well with the test data. The proposed model can be used for the stress-deformation study of geosynthetic-reinforced embankments through numerical simulation. Copyright © 1999 John Wiley & Sons, Ltd.     

Analytical definition of collapse surface in multiaxial space as a criterion for flow liquefaction occurrence

Prediction of flow liquefaction occurrence in multiaxial stress space is presented in this paper. The closed-form relation analytically attained by means of Dafalias-Manzari constitutive equations gives the flow stress ratio as a function of model parameters, state parameter, direction of undrained loading and especially initial condition of consolidation. These proposed flow condition can predict the occurrence of flow liquefaction initiated by any loadings whether the soil is consolidated isotropically or anisotropically. Suggested predictions are compared with the results of triaxial tests performed on Hostun RF sand. The results show that increasing consolidation stress ratio leads to flow stress ratio increase.     

Investigation of monotonic and cyclic behavior of sand using a bounding surface plasticity model

Developing the pore water pressures in loose to medium sands below the water table may lead to liquefaction during earthquakes. The simulation of liquefaction (cyclic mobility and flow liquefaction) in sandy soils is one of the major challenges in constitutive modeling of soils. This paper presents the simulation of sand behavior using a critical state bounding surface plasticity model (Dafalias and Manzari’s model, 2004) during monotonic and cyclic loading. The drained, undrained, and cyclic triaxial tests were simulated using Dafalias and Manzari’s model. The simulation results showed that the model predicts behavior of sand, reasonably well. Also, for CSR?<?0.2, number of cycles for liquefaction is significantly increased. The residual strength of Babolsar sand is produced when it is deformed to an axial strain of 20 to 25%.