Constitutive Model For Unsaturated Soils Research Articles

Modified State Surface Approach to Study Unsaturated Soil Hysteresis Behavior

Unsaturated soils are often used as a construction material in transportation infrastructures. In this situation, unsaturated soils are subjected to cyclic mechanical loading from traffic loads or wetting-drying cycles in seasonal climatic conditions. While mechanical hysteresis is a common feature of soils in general, hydraulic hysteresis is associated with unsaturated soils. Although several constitutive models for unsaturated soils have been proposed, the mechanical and hydraulic hysteresis behavior of unsaturated soils has been little studied. A modified state surface approach (MSSA) was first proposed for investigating the mechanical behavior of unsaturated soils. It was then extended to study the coupled hydro-mechanical behavior of unsaturated soils with a special focus on the consistency between different soil phases. However, hydraulic and mechanical hysteresis were neglected in MSSA formulations. In this paper, based on evidence from experimental results, the MSSA is extended further to study the coupled hydro-mechanical hysteresis behavior of unsaturated soils. The extended MSSA can reproduce several forms of mechanical and hydraulic behavior observed in experimental results that cannot be represented by existing constitutive models. To demonstrate the capabilities of the extended MSSA, typical behaviors are simulated and compared, qualitatively, with the characteristic trends of the behavior of unsaturated soils. Experimental results from the literature are then used to evaluate the model to predict, quantitatively, the observed behaviors. The agreement between measured and predicted results is considered satisfactory and confirms the possibility of the proposed approach to reproduce the hysteresis behavior of unsaturated soils.

Bounding surface constitutive model for unsaturated soils considering microscopic pore structure and bonding effect

This article presents a bounding surface model for unsaturated soils by using skeleton stress and bonding variable based on microcosmic pore structure as constitutive variables. A Hydraulic hysteresis soil-water characteristic curve model considering deformation and hydraulic hysteresis is combined to achieve hydraulic coupling. The proposed model can capture the change of the inter-particles bonding effect in the deformation process of unsaturated soils and accurately predict the hydraulic mechanical behavior of unsaturated soils under complicated loading paths and wetting-drying cycles. The validity of the proposed model is confirmed by the results of unsaturated isotropic compression tests, wetting-drying cycles tests and unsaturated triaxial shear tests reported in the literature.

Simulating Undrained Tests on Unsaturated Soils

AbstractA simple fully coupled constitutive model for unsaturated soils is presented and used to simulate the behavior of unsaturated soils subjected to undrained conditions. The mechanical model i...

A unified constitutive model for unsaturated soil under monotonic and cyclic loading

This study presents a sophisticated elastoplastic constitutive model for unsaturated soil using Bishop-type skeleton stress and degree of saturation as state variables in the framework of critical state soil mechanism. The model is proposed in order to describe the coupled hydromechanical behavior of unsaturated soil irrespective of what kind of the loadings or the drainage conditions may be. At the same time, a water retention characteristic curve considering the influence of deformation on degree of saturation is also proposed. In the model, the superloading and subloading concepts are introduced to consider the influences of overconsolidation and structure on deformation and strength of soils. The proposed model only employs nine parameters, among which five parameters are the same as those used in Cam-Clay model. The other four parameters have the clear physical meanings and can be easily determined by conventional soil tests. The capability and accuracy of the proposed model have been validated carefully through a series of laboratory tests such as isotropic loading tests and triaxial monotonic and cyclic compression tests under different mechanical and hydraulic conditions.

A hierarchical thermo‐hydro‐plastic constitutive model for unsaturated soils and its numerical implementation

SummaryUnsaturated soils are highly heterogeneous 3‐phase porous media. Variations of temperature, the degree of saturation, and density have dramatic impacts on the hydro‐mechanical behavior of unsaturated soils. To model all these features, we present a thermo‐hydro‐plastic model in which the hydro‐mechanical hardening and thermal softening are incorporated in a hierarchical fashion for unsaturated soils. This novel constitutive model can capture heterogeneities in density, suction, the degree of saturation, and temperature. Specifically, this constitutive model has 2 ingredients: (1) it has a “mesoscale” mechanical state variable—porosity and 3 environmental state variables—suction, the degree of saturation, and temperature; (2) both temperature and mechanical effects on water retention properties are taken into account. The return mapping algorithm is applied to implement this model at Gauss point assuming an infinitesimal strain. At each time step, the return mapping is conducted only in principal elastic strain space, assuming no return mapping in suction and temperature. The numerical results obtained by this constitutive model are compared with the experimental results. It shows that the proposed model can simulate the thermo‐hydro‐mechanical behavior of unsaturated soils with satisfaction. We also conduct shear band analysis of an unsaturated soil specimen under plane strain condition to demonstrate the impact of temperature variation on shear banding triggered by initial material heterogeneities.

Hydromechanical Constitutive Model for Unsaturated Soils with Different Overconsolidation Ratios

Hydromechanical Constitutive Model for Unsaturated Soils with Different Overconsolidation Ratios

Including degree of capillary saturation into constitutive modelling of unsaturated soils

The degree of saturation (S) of soil can be separated into two components: the degree of capillary saturation (S′) that is based on the capillary water and the degree of adsorptive saturation (S″) that is based on the adsorbed water. This paper discusses the role of the degree of capillary saturation (S′) in modelling the coupled hydro-mechanical behaviour of unsaturated soils and proposes a new constitutive model for unsaturated soils by using the degree of capillary saturation (S′) and the effective inter-particle stress (σij′). An enhanced hydraulic model is introduced to describe the hydraulic hysteresis and hydro-mechanical interaction in terms of the degree of capillary saturation (S′). In the proposed constitutive model, the shear strength, yield stress and deformation behaviour of unsaturated soils are governed directly by the above two constitutive variables, namely σij′ and S′. To be in line with the existing finite element frameworks for unsaturated soils, the proposed model is eventually generalised to constitutive functions consisting of only primary variables such as the net stress (σij), suction (s) and degree of saturation (S). The typical performance of the model for simulating the characteristic trends of unsaturated soil behaviour is discussed in several different scenarios. The model is then validated against a variety of experimental data in the literature, and the results show that a reasonable agreement can be obtained using this new constitutive model.

A stress integration scheme for elasto-plastic response of unsaturated soils subjected to large deformations

This paper proposes an algorithm for performing explicit integration of constitutive models for unsaturated soils in problems where consideration of stress rate objectivity becomes necessary due to large deformations. As many constitutive models for unsaturated soils incorporate suction forces, as well as stresses and strains, into the material description, an accurate integration procedure is more complicated than similar schemes proposed for saturated soils. The difficulties of integration are also coupled with the need to incorporate objectivity (frame independency) within the integration procedure. Application of the proposed method is limited to constitutive models that assume additive decomposition of the strains. A fully coupled finite deformation numerical model is considered with displacement, pore water pressure and suction as the nodal variables. Details of the implementation of the stress integration algorithm at each stage of an analysis are given. The algorithm is then applied to solve some large-scale geotechnical problems. Numerical examples are also provided to assess the performance of the algorithm under different loading conditions.

UNIAXIAL COMPRESSION TEST OF UNSATURATED MASADO UNDER CONSTANT DEGREE OF SATURATION CONDITION AND ITS MODELING

Soils in surface ground are usually unsaturated. Proper modeling of the characteristics ofunsaturated soil is therefore absolutely needed. However, due to its complicated mechanical behavior,establishing a constitutive model for unsaturated soil is far more difficult than that for saturated soil. In thisresearch, uniaxial compression tests were firstly conducted on unsaturated Masado (Decomposed granite)under constant degree of saturation condition to investigate the mechanical behavior of the soil at differentdegree of saturation. Then, based on the test data, the performances of previously proposed elastoplasticconstitutive model for unsaturated soil were checked carefully, taking the Bishop-type skeleton stress and thedegree of saturation as the state variables. It is found that the mechanical behavior of the unsaturated Masadocan be properly described by the proposed elastoplastic constitutive model that takes the skeleton stress andthe degree of saturation as the state variables.Keywords: Unsaturated Soil, Degree of Saturation, Constitutive Model, Uniaxial Compression Test

Effects of stress conditions on B-value measurement

The B-value, measured after setting up a specimen for triaxial testing, is used for evaluating the degree of saturation of a specimen. However, the stress conditions used when measuring the B-value have not been standardized. Although some experimental approaches have been pursued, no detailed analyses have evaluated the effects of the measurement conditions on the B-value results. In this study, the B-values of nearly saturated specimens under various stress conditions were investigated, using a smart triaxial test apparatus capable of elaborate stress control, and comparisons among measurement results were conducted. Moreover, by applying Henry׳s law, which governs the dissolution of the gas phase into the liquid phase, to an existing constitutive model for unsaturated soil, a new soil model was proposed. This new model accurately represents the behaviors of pore air even under nearly saturated conditions. In addition, the effects of the stress conditions on the B-values were investigated through numerical simulations of B-value measurements.

Numerical analysis on seepage failures of dike due to water level-up and rainfall using a water–soil-coupled smoothed particle hydrodynamics model

For seepage failures of dike due to water level-up and rainfall, surface infiltration and strength change induced by suction reduction are important factors; thus, numerical analysis should consider the coupling of water and soil, as well as the effect of saturation to obtain more precise failure mechanism. Based on the advanced smoothed particle hydrodynamics (SPH) method, this work proposed a two-phase-coupled SPH model in coordination with a novel constitutive model for unsaturated soils. Then, a triaxial compression test is simulated to check the applicability of the SPH method on the soil phase. After that, the failure test of a dike due to water level-up is discretized and simulated, from which the seepage process, the distribution of maximum shear strain, the slip surface, and pore water pressure are obtained. The two-phase-coupled SPH model is also applied to a slope failure test of heavy rainfall, and the results are compared to the model test. Finally, a dike failure test due to rainfall is analyzed using the proposed SPH model to reproduce the surface infiltration and suction reduction. The proposed SPH model provides several insights of seepage failures and can be a helpful tool for the analysis of dike failures induced by water level-up and rainfall.

Constitutive Model of Unsaturated Soils Considering the Effect of Intergranular Physicochemical Forces

AbstractA clayey soil is an electrically charged porous medium whose behavior is sensitive to the variations in the composition and concentration of pore water. Pronounced physicochemical interaction can occur between the solid particle and the pore water so that the clayey soil shows strong chemomechanical coupling effects and complex mechanical behaviors. If the degree of saturation varies the pore-water composition and concentration can also vary, resulting in intensive physicochemical effects in the soil. In this paper, a conceptual constitutive model for unsaturated soils is proposed to explain the influence of pore-fluid chemistry on the chemomechanical behavior of unsaturated clayey soils. A new intergranular stress which can effectively account for the physicochemical effects including osmosis, capillarity, and adsorption is introduced as the stress-state variable. The formulation of the proposed model can lead to a remarkable unification of the experimental results obtained under complex chemomec...

Dynamic Analysis of Unsaturated Soils Subjected to Large Deformations

This paper deals with the large deformation analysis of partially saturated soils subjected to dynamic loading. The so-called ‘mixture’ theory is employed to consider the hydro-mechanical coupling involved in this kind of problem. The finite element method is used to discretise the problem domain and the generalized-α algorithm is employed to integrate the governing equations over time. Some of the most challenging aspects of dynamic analysis of partially saturated soils will be discussed. One of the key challenges is selecting a consistent constitutive model within the theory of mixtures that can incorporate the pore suction forces into the description of stress. The necessity of such incorporation has frequently been reported in experimental studies of unsaturated soils. To tackle this problem, a unique strategy for integrating the constitutive model for unsaturated soils is adopted. Moreover, an absorbing boundary condition, which prevents wave reflection from rigid boundaries, is introduced and implemented into the numerical algorithm. Finally, a solution for the problem of dynamic compaction of soil in a partially saturated condition is presented.

Thermo-elastoplastic constitutive model for unsaturated soils

This study presents a simple approach to modelling the effect of temperature on the deformation and strength of unsaturated/saturated soils by using the average skeleton stress and degree of saturation. The concept of thermo-induced equivalent stress is introduced to consider the influence of temperature on the pre-consolidated stress. A skeleton stress–saturation framework is applied to enable the model to describe the thermo-elastoplastic behaviour of both unsaturated and saturated soils, as the skeleton stress can smoothly shift to Terzaghi’s effective stress if saturation changes from the unsaturated to the saturated condition. The new model only employs seven parameters, of which five parameters are the same as those used in the Cam-Clay model. The other two parameters can be easily determined by oedometer tests and simple thermo-mechanical tests. Numerical simulations of isotropic loading tests and triaxial shear tests under different conditions are conducted to illustrate the performance of the proposed model. By comparing with experimental temperature controlled oedometer tests and triaxial tests, it is confirmed that the proposed model is able to capture the thermo-mechanical behaviour of unsaturated/saturated normally and over-consolidated soils with a set of unified parameters.

Modeling the Dependency of Soil-Water Retention Curve on Volumetric Deformation

AbstractPorous models are built using the current pore-size distribution of the material and can reproduce the phenomenon of hysteresis during wetting–drying cycles. The term current pore-size distribution means that the size of the pores is being updated as the soil deforms. This type of model can be used advantageously for the development of fully coupled hydromechanical constitutive models for unsaturated soils. Also, because the volumetric deformation affects the pore-size distribution of the soil, the influence of the former on the retention curves can be easily assessed. This paper presents a porous-solid model that simulates the hydraulic hysteresis of soils and the influence of the volumetric deformation on the soil-water retention curves. The precision obtained in numerical and experimental comparisons shows the adequacy of the model.

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.

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.

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.

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.