Model For Unsaturated Soils Research Articles

A new constitutive model of unsaturated soils using bounding surface plasticity (BSP) and a non-associative flow rule

This paper presents a constitutive model for unsaturated soils, based on the non-associate bounding surface plasticity concept under a critical state framework. With a limited number of parameters, this model allows removing the sudden stiffness reduction at the on-set of plastic strains when the stress reaches the yield surface. It also enables to reproduce smooth transitions from pre-peak hardening to post-peak softening and from contractant to dilatant behavior, which are common short comings of more classic models. The performance of this model is highlighted by a comparison between its numerical results, those from other unsaturated elastic–plastic models and experimental data.

Shakedown modeling of unsaturated expansive soils subjected to wetting and drying cycles

It is important to model the behavior of unsaturated expansive soils subjected to wetting and drying cycles because they alter significantly their hydro-mechanical behavior and therefore cause a huge differential settlement on shallow foundations of the structure. A simplified model based on the shakedown theory (Zarka method) has been developed in this study for unsaturated expansive soils subjected to wetting and drying cycles. This method determines directly the stabilized limit state and consequently saves the calculation time. The parameters of the proposed shakedown-based model are calibrated by the suction-controlled oedometer tests obtained for an expansive soil compacted at loose and dense initial states, and then validated for the same soil compacted at intermediate initial state by comparing the model predictions with the experimental results. Finally, the finite element equations for the proposed shakedown model are developed and these equations are implemented in the finite element code CAST3M to carry out the full-scale calculations. A 2D geometry made up of the expansive soil compacted at the intermediate state is subjected to successive extremely dry and wet seasons for the different applied vertical loads. The results show the swelling plastic deformations for the lower vertical stresses and the shrinkage deformations for the higher vertical stresses.

The determination of model dimension for an embankment to study soil atmosphere interaction with Finite Element Method

In order to study the interaction between soil and atmosphere, Hericourt experimental embankment was instrumented with different equipments for collecting the meteorological data, runoff, soil temperature and volumetric water content, etc. The corresponding water flux and heat flux boundary conditions of the Hydro-thermal coupled model of unsaturated soil can be calculated based on the energy and mass balance. However, in Finite Element Method, a suitable model dimension of experimental embankment needs to be set in advance, which will diminish the effect of bottom and lateral boundaries. Therefore, in this paper, four different dimension models are calculated respectively and compared in two cases with different boundary conditions. For Case 1, top water flux boundary condition is set as infiltration and evaporation happening on the soil surface alternately. In Case 2, top heat flux boundary condition is assumed based on daily solar radiation value. Comparing the results of four model dimensions, temperature and volumetric water content distributions in four dimensions lead nearly consistent results. Therefore, with consideration of computational time and accuracy, dimension 2 or 3 is suggested for Hydro-thermal study of Hericourt embankment case.

Incorporating anisotropy in the Barcelona basic model

The paper presents an elasto-plastic model for unsaturated soils that extends the Barcelona basic model to introduce a dependency of mechanical behaviour on material anisotropy. The model builds upon a previous proposal by Al-Sharrad and Gallipoli [1] by linking material anisotropy to both the distortion and aspect ratio of the elliptical yield curve in the constant suction plane of deviator versus mean net stress. In order to take into account anisotropic behaviour, an additional constitutive equation is therefore proposed to uniquely relate the aspect ratio and the distortion of the yield ellipse. The new model is calibrated and validated against the experimental data by Al-Sharrad [2] via the simulation of triaxial tests conducted at various suctions on compacted kaolin samples. These simulations show that the new model predicts yield stresses and shear strains during anisotropic loading with greater accuracy compared to the model of Al-Sharrad and Gallipoli [1].

A finite strain elastoplastic constitutive model for unsaturated soils incorporating mechanisms of compaction and hydraulic collapse

Although the deformation of unsaturated soils has usually been described based on simple infinitesimal theory, simulation methods based on the rational framework of finite strain theory are attracting attention especially when solving geotechnical problems such as slope failure induced by heavy rain in which large a deformation is expected. The purpose of this study is to reformulate an existing constitutive model for unsaturated soils (Kikumoto et al., 2010) on the basis of finite strain theory. The proposed model is based on a critical state soil model, modified Cam-clay, implementing a hyperelastic model and a bilogarithmic lnv -lnP ’ (v , specific volume; P ’, effective mean Kirchhoff stress) relation for a finite strain. The model is incorporated with a soil water characteristic curve based on the van Genuchten model (1990) modified to be able to consider the effect of deformation of solid matrices. The key points of this model in describing the characteristics of unsaturated soils are as follows: (1) the movement of the normal consolidation line in lnv -lnP ’ resulted from the degree of saturation (Q , deviatoric Kirchhoff stress), and (2) the effect of specific volume on a water retention curve. Applicability of the model is shown through element simulations of compaction and successive soaking behavior.

A Constitutive Model for Unsaturated soils based on a Compressibility Framework dependent on Suction and Degree of Saturation

The Modified Cam Clay model is extended to account for the behaviour of unsaturated soils using Bishop’s stress. To describe the Loading – Collapse behaviour, the model incorporates a compressibility framework with suction and degree of saturation dependent compression lines. For simplicity, the present paper describes the model in the triaxial stress space with characteristic simulations of constant suction compression and triaxial tests, as well as wetting tests. The model reproduces an evolving post yield compressibility under constant suction compression, and thus, can adequately describe a maximum of collapse.

Fully undrained cyclic loading simulation on unsaturated soils using an elastoplastic model for unsaturated soils

Several researchers have reported that Bishop’s mean effective stress decreases in unsaturated soils under fully undrained cyclic loading conditions, and unsaturated soils are finally liquefied in a similar manner as saturated soils. This paper presents a series of simulations of such fully undrained cyclic loading on unsaturated soils using an elastoplastic model of the unsaturated soil. This model is formulated using the Bishop’s effective stress tensor incorporating the following concepts: the volumetric movement of the state boundary surface containing the normal consolidation line and the critical state line due to the variation in the degree of saturation, a soil water characteristic curve model considering the effect of specific volume and hysteresis, the subloading surface model, and Boyle’s law. Comparisons between the simulation results and the experimental ones show that the model agreed well with the unsaturated soil behavior under cyclic loading. Finally, the typical cyclic behavior of unsaturated soils under fully undrained conditions, such as the mechanism of liquefaction of unsaturated soils, the compression behavior, and an increase in the degree of saturation, are described through the proposed simulation results.

Relating shear strength of unsaturated soils with capillary water retention curve

This paper proposes a new water retention model for unsaturated soils, which takes into account capillary condensation of adsorbed water. In the proposed water retention model, the degree of saturation of a soil is separated into that based on capillary water and that based on adsorbed water. Through the analysis of a partially saturated two-cylinder system, a new shear strength criterion for unsaturated soils is proposed, in which only the degree of saturation based on capillary water contributes to the variation of shear strength with suction. The proposed shear strength criterion is justified against thermodynamic principles. The proposed strength criterion is compared against existing criteria in the literature, which shows that it provides a much improved prediction of the experimental data, for a wide range of suction values.

A coupled two‐phase fluid flow and elastoplastic deformation model for unsaturated soils: theory, implementation, and application

SummaryAlthough numerous numerical models have been proposed for simulating the coupled hydromechanical behaviors in unsaturated soils, few studies satisfactorily reproduced the soil–water–air three‐phase coupling processes. Particularly, the impacts of deformation dependence of water retention curve, bonding stress, and gas flow on the coupled processes were less examined within a coupled soil–water–air model. Based on our newly developed constitutive models (Hu et al., 2013, 2014, 2015) in which the soil–water–air couplings have been appropriately captured, this study develops a computer code named F2Mus3D to investigate the coupled processes with a focus on the above impacts. In the numerical implementation, the generalized‐α time integration scheme was adopted to solve the equations, and a return‐mapping implicit stress integration scheme was used to update the state variables. The numerical model was verified by two well‐designed laboratory tests and was applied for modeling the coupled elastoplastic deformation and two‐phase fluid flow processes in a homogenous soil slope induced by rainfall infiltration. The simulation results demonstrated that the numerical model well reproduces the initiation of a sheared zone at the toe of the slope and its propagation toward the crest as the rain infiltration proceeds, which manifests a typical mechanism for rainfall‐induced shallow landslides. The simulated plastic strain and deformation would be remarkably underestimated when the bonding stress and/or the deformation‐dependent nature of hydraulic properties are ignored in the coupled model. But on the contrary, the negligence of gas flow in the slope soil results in an overestimation of the rainfall‐induced deformation. Copyright © 2015 John Wiley & Sons, Ltd.

Implicit integration under mixed controls of a breakage model for unsaturated crushable soils

This paper discusses a series of stress point algorithms for a breakage model for unsaturated granular soils. Such model is characterized by highly nonlinear coupling terms introduced by breakage-dependent hydro-mechanical energy potentials. To integrate accurately and efficiently its constitutive equations, specific algorithms have been formulated using a backward Euler scheme. In particular, because implementation and verification of unsaturated soil models often require the use of mixed controls, the incorporation of various hydro-mechanical conditions has been tackled. First, it is shown that the degree of saturation can be replaced with suction in the constitutive equations through a partial Legendre transformation of the energy potentials, thus changing the thermomechanical state variables and enabling a straightforward implementation of a different control mode. Then, to accommodate more complex control scenarios without redefining the energy potentials, a hybrid strategy has been used, combining the return mapping scheme with linearized constraints. It is shown that this linearization strategy guarantees similar levels of accuracy compared with a conventional strain–suction-controlled implicit integration. In addition, it is shown that the use of linearized constraints offers the possibility to use the same framework to integrate a variety of control conditions (e.g., net stress and/or water-content control). The convergence profiles indicate that both schemes preserve the advantages of implicit integration, that is, asymptotic quadratic convergence and unconditional stability. Finally, the performance of the two implicit schemes has been compared with that of an explicit algorithm with automatic sub-stepping and error control, showing that for the selected breakage model, implicit integration leads to a significant reduction of the computational cost. Such features support the use of the proposed hybrid scheme also in other modeling contexts, especially when strongly nonlinear models have to be implemented and/or validated by using non-standard hydro-mechanical control conditions. Copyright © 2015 John Wiley & Sons, Ltd.

Explicit formulation of at-rest coefficient and its role in calibrating elasto-plastic models for unsaturated soils

Normally, suction-controlled triaxial tests are used to characterize soil behavior in constitutive modeling of unsaturated soils. However, this type of tests requires sophisticated equipment and is time-consuming. This has been one of the major obstacles to the implementation and dissemination of unsaturated soil mechanics beyond the research context.In contrast to suction-controlled triaxial tests, the suction-controlled oedometer test requires simpler equipment and a shorter testing period. Oedometer tests represent the at-rest earth pressure (K0) condition, which is an important stress state in any simulation. The major disadvantage of the oedometer test is that its lateral stress is controlled by the condition of zero lateral strain and remains unknown during the testing process. At present, no well-established, simple, and objective methods are available that take advantage of oedometer test results for constitutive modeling purposes.This paper derives an explicit formulation of the at-rest coefficient for unsaturated soils and develops an optimization approach for simple and objective identification of material parameters in elasto-plastic models for unsaturated soils using the results from suction-controlled oedometer tests. This is achieved by combining a modified state surface approach (MSSA), recently proposed to model the elasto-plastic behavior of unsaturated soils, with the quasi-Newton method to simultaneously calibrate all parameters governing virgin behavior in elasto-plastic models. The Barcelona Basic Model (BBM) is used to demonstrate the application of the proposed explicit formulation and calibration method. Results predicted using obtained parameters are compared with laboratory test results for the same stress paths in order to evaluate the simplicity and objectivity of the proposed method.

Laboratory Approach for Faster Determination of the Loading-Collapse Yield Curve of Compacted Soils

AbstractA shift in the preconsolidation pressure or yield limit with suction, referred to as the loading-collapse (LC) yield curve, is an important feature of elastoplastic models of unsaturated soils. The LC curve is typically defined in the matric suction versus mean stress plane to account for the effects of matric suction. Conventional methods to determine the LC yield curve rely on a series of isotropic compression tests on specimens with identical stress history. This paper presents an alternative method to determine the LC yield curve from isotropic compression test results of specimens without identical stress history restrictions. A series of equations is proposed, derived from elastoplastic theory and incorporated into conventional compression test results, for drawing the specific LC yield curve. The advantage of the proposed methodology is that the compression tests results need not be taken from identical stress history specimens, which leads to a shorter time frame in the laboratory. Moreove...

A constitutive model for unsaturated soil–structure interfaces

SummaryA constitutive model for simulation of the behavior of unsaturated interfaces is presented here. The model is an extension of an existing critical state compatible interface model for dry and saturated interfaces that was already proposed by one of the authors [Lashkari, A. 2013. Int. J. Numer. Anal. Meth. Geomech. 37(8): 904–931]. For a proper simulation of the behavior of partially saturated interfaces, the extended model is formulated in terms of two pairs of work conjugate stress–strain‐like variables. The modified model simulations are compared with the existing data of dry, unsaturated, and saturated interfaces. For each interface type, it is shown that the proposed model can capture the essential elements of the behavior using a unique set of parameters. Copyright © 2015 John Wiley & Sons, Ltd.

A thermo-hydro-mechanical model of unsaturated soils based on bounding surface plasticity

This paper presents a thermo-hydro-mechanical model of unsaturated soils based on effective stress concept and bounding surface plasticity. It is formulated in terms of effective saturation Se and temperature T unlike existing THM models, which use the suction and temperature to predict the behavior of unsaturated soils. An isotropic yield limit is defined in a 3D space p′-Se-T and subsequently generalized to the triaxial stress space. Regarding the hydraulic component, the non-isothermal water retention curves of deformable soils are combined with the present model. However, the part treating the flow of water and temperature is not covered. Finally, the proposed formulations are supported by comparisons with existing experimental results under isotopic and oedometric paths.

Coupled hydro-mechanical analysis of slope under rainfall using modified elasto-plastic model for unsaturated soils

Two modifications for the basic Barcelona model (BBM) are present. One is the replacement of the net stress by the average skeleton stress in unsaturated soil modeling, and the other is the adoption of an expression for the load−collapse (LC) yield surface that can match flexibly the normal compression lines at different suctions. The predictions of the modified BBM for the controlled-suction triaxial test on the unsaturated compacted clay are presented and compared with the experimental results. A good agreement between the predicted and experimental results demonstrates the reasonability of the modified BBM. On this basis, the coupled processes of groundwater flow and soil deformation in a homogeneous soil slope under a long heavy rainfall are simulated with the proposed elasto-plastic model. The numerical results reveal that the failure of a slope under rainfall infiltration is due to both the reduction of soil suction and the significant rise in groundwater table. The evolution of the displacements is greatly related to the change of suction. The maximum collapse deformation happens near the surface of slope where infiltrated rainwater can quickly reach. The results may provide a helpful reference for hazard assessment and control of rainfall-induced landslides.

Recent developments of generalized plasticity models for saturated and unsaturated soils

Soil undergoes both elastic and plastic deformations under different loading conditions. A relatively accurate constitutive model of soil behaviors should be capable of predicting the elastic and plastic deformations properly. Among a large number of elastoplastic constitutive models developed over the last several decades, constitutive models based on generalized plasticity have been successfully utilized in modeling the mechanical behavior of various soils. This paper attempts to present a review of the most recent developments of generalized plasticity models for geotechnical problems. After a brief review of generalized plasticity theories and constitutive models, limitations of the original Pastor-Zienkiewicz model in practical application are summarized. Afterwards, recent achievements in the generalized plasticity models for both saturated and unsaturated soils and their applicability are analyzed, and a general approach for modification of generalized plasticity models is highlighted.

Resilient modulus modelling of unsaturated subgrade soils: laboratory investigation of silty sand subgrade

In flexible pavement structures, stiffness of unbound granular layers and subgrade soil significantly contribute to the overall performance of the pavement system. The stiffness of pavement unbound materials is widely characterised by the resilient modulus, Mr, which is obtained from repeated load triaxial (RLT) tests. Although pavement unbound materials are usually in partially saturated conditions and experience seasonal moisture content and therefore suction variations in the field, their stiffness is conventionally characterised using the total stress approach in which the effect of soil suction is not taken into account. Thus, an enhanced approach in predicting the stiffness of subgrade soils has to account for the partially saturated conditions and incorporate soil suction (i.e. matric suction) in the Mr constitutive models. In this study, several Mr prediction models that take into account the effect of pore suction were investigated. The Mr data set from an experimental investigation of two silty sand subgrade soils that was conducted using a suction-controlled RLT testing apparatus was used to optimise the parameter of these models. The capability of the Mr predictive models in capturing the resilient modulus behaviour of the silty sand subgrade soils and its variation due to seasonal changes in the moisture content (soil suction) were evaluated. It was observed that the Mr models that combine the three fundamental stress state variables (confining stress, deviator stress and matric suction) performed better in capturing the resilient modulus behaviour of the subgrade materials.

Impact of Bioclogging on Peat vs. Sand Biofilters

Biological clogging of unsaturated soils is an important process that can lead to the development of a biomat and failure of biofilters used to treat various wastewater streams. Septic beds and peat filters used to treat septic tank effluent are important applications. Several conceptual models have been developed to simulate clogging in saturated soils; however, limited effort has been conducted to develop similar models for unsaturated soils. Different conceptual models have been proposed to simulate biological clogging in unsaturated systems. These models include the impacts of biomass growth on the relative permeability term for unsaturated flow, but limited experimental data have been used to validate these models. In this study, column experiments were conducted to study the clogging process in loose and dense peat, filter media sand, and septic bed sand. Experimental data indicated that the pore structure of the peat, in comparison to two commonly used sands for septic drainage fields, allowed the biomass to distribute itself over a greater depth within the peat biofilter and delayed the formation of a biomat at the surface and eventual clogging of the filter medium.

A smoothed cap model for variably saturated soils and its robust numerical implementation

Summary This paper deals with the numerical implementation of a cap model for unsaturated soils. It provides a brief review of existing cap model approaches, based on which an improved model formulated in terms of generalised effective stress and matric suction is derived and described in detail. Although the proposed model is a multisurface plasticity model, it can efficiently be implemented using only single-surface projections because of the smoothness of the model, which is obtained by construction. Numerical algorithms are provided for these single-surface stress projections, using a single-equation approach whenever possible. The robustness of the utilised single-equation approaches is enhanced by proposing problem-fitted start-up procedures based on investigations of the nonlinear projection equations. A comparison of the model response with extensive material test data is used to validate the model and to demonstrate the robust application of the approach to silty sands and low to medium plasticity clays. Copyright © 2015 John Wiley & Sons, Ltd.

A porous model to simulate the evolution of the soil–water characteristic curve with volumetric strains

Volumetric strains modify the soil–water retention curve. An easy way to take this phenomenon into account is by means of a percolation model based on the pore size distribution of the material. The model proposed herein is able to simulate the retention curves during wetting–drying cycles. As volumetric deformations modify the pore size distribution, its effect on the retention curves can be easily included in the model. The model is validated by comparing some numerical results with experimental results. This procedure represents an option to create fully coupled constitutive models for unsaturated soils.