Model For Unsaturated Soils Research Articles

Numerical Simulation of Geosynthetic Clay Liner Desiccation under High Thermal Gradients and Low Overburden Stress

A multiphase, thermohydro-mechanical model of unsaturated soils is presented to assess the risk of desiccation of a geosynthetic clay liner (GCL) in a composite lining system (i.e., a high-density polyethylene geomembrane over a geosynthetic clay liner) under conditions encountered in brine or solar ponds, where temperatures can reach up to 95°C and the geosynthetic clay liner is subject to low effective stress. The model considers void ratio and temperature-dependent soil–water characteristic curves (SWCCs) for needle-punched GCLs. The model was validated against results from experimental column studies.

A New Soil-Water Characteristic Curve Model for Unsaturated Loess Based on Wetting-Induced Pore Deformation

The soil-water characteristic curve (SWCC) is the basis for describing seepage, strength, and constitutive model of unsaturated soil. The existing SWCC models do not work accurately for evaluating loess, because they do not consider the pore deformation that is induced by wetting. The present study develops a new SWCC model for unsaturated loess. The model considers the effect of wetting-induced pore deformation (WIPD) on the SWCC. The new model includes 6 parameters, which could be confirmed by laboratory tests. The pore volume function (PVF) was described by the WIPD. The shift factor ξ1i and the compression factor ξ2i were introduced into the model. The relationship between the void ratio e and ξ1i and ξ2i was established using the average pore radius. The new SWCC model for saturated loess was improved based on the classical van Genuchten (V-G) model. If the WIPD had not been considered, the new model would regress into the classical V-G model. SWCC tests of unsaturated loess with different void ratios were carried out to verify the new model. The model parameters were calibrated in the original state, and the SWCCs of different void ratios were predicted by the new model and found to be in good agreement with the test results.

Modelling effects of recent suction history on small-strain stiffness of unsaturated soil

Recent suction history has been found to affect shear modulus of unsaturated soil at small strains (i.e., from 0.001% to 1%). In this study, a bubble model for unsaturated soil is developed within the framework of kinematic hardening and bounding surface plasticity. An elliptical elastic bubble is defined inside a modified Cam-clay bounding surface. Being a key feature of the proposed model, the size of the elastic bubble is modelled as a function of suction, degree of saturation, and plastic volumetric strain. Translation of the elastic bubble is governed by suction, degree of saturation, and stress increments. Moreover, hardening modulus depends on not only stress and void ratio, but also suction, degree of saturation, and relative position of the elastic bubble and the bounding surface. The proposed model is evaluated using suction-controlled constant-p shear tests on completely decomposed tuff (silt). It is evident that the new model is capable of capturing well the effects of recent suction history on nonlinear stress–strain relation and shear modulus degradation at small strains.

A fully coupled simple model for unsaturated soils

SummaryDifferent phenomena influence the strength and volumetric behavior of unsaturated soils. Among the most important are suction hardening, hydraulic hysteresis, and the influence of volumetric strain on the soil‐water retention curves. Fully coupled hydro‐mechanical models require including all three phenomena in their constitutive relationships. Among these phenomena, suction hardening is the most influencing as it determines the apparent preconsolidation stress, the position of the loading‐collapse yield surface, and the shift of both the isotropic consolidation and the critical state lines. In this paper, a fully coupled hydro mechanical model is presented. It is based on the modified Cam‐Clay model but includes a yield surface with anisotropic hardening that takes account of the shift of the critical state line with suction. For highly overconsolidated materials, the sub‐loading surface concept has been included in order to increase the precision of the model for these materials. The shift of the retention curves produced by volumetric strains is simulated using a hydraulic model based on the grain and current pore size distribution of the soil.

Calibration of a double structure constitutive model for unsaturated compacted soils

This paper describes a calibration procedure for the double structure constitutive model ICDSM (Imperial College Double Structure Model), developed for highly expansive clays, when the model is applied to MX-80 bentonite. Firstly, the model calibration process is discussed and organised in a number of hierarchical steps. These steps involve the estimation of the macrostructural parameters that can be derived from oedometer, isotropic and triaxial laboratory data. Estimation of the microstructural parameters is more challenging due to the limited knowledge of an expansive clay’s fabric and of the physico-chemical phenomena that control its evolution upon wetting. Nevertheless, this paper discusses the available sources of data and identifies the appropriate information that is needed to characterise the micro-structural behaviour of the bentonite. Finally, through the simulation of a swelling pressure test on a bentonite plug, the hydration of the material is studied as a hydro-mechanical coupled process. Particular attention is devoted to the evolution of the stress state of the sample, which is compared to the experimental measurements in order to demonstrate that the constitutive model accurately reproduces the expansive behaviour of MX-80 bentonite.

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.

Laboratory Study on Load Carrying Capacity of Pile Group in Unsaturated Clay

In this study, an attempt is made to investigate the load transfer in pile groups constructed in saturated and unsaturated soil using aluminum model piles of $$20\times 20$$ mm in cross section and 200 mm in length with six group configurations, single, $$2\times 1$$ , $$3\times 1$$ , $$2\times 2$$ , $$3\times 2$$ , and $$3\times 3$$ , groups in addition to pull-out test. The samples are prepared at three different soil properties: two models with the same degree of saturation and two with different dry unit weights and the third is unsaturated soil model with. A relationship between the soil suction and water content is introduced using a digital monitor, accompanied by eight suction probes planted in CBR molds. This relationship is used to predict the value of suction when conducting tests on models of the unsaturated soil. Further, the soil suction is measured using a filter paper method. Results of ultimate load capacity obtained from the load–displacement curves reveal an increase in the ultimate load with increasing the number of piles in the group for the same soil properties, and also an increase in the soil dry unit weight. Further, the results indicate an increase in pile capacity when the soil becomes in unsaturated state compared with saturated soil for the same pile group tested. On the other hand, the pull-out test gives a maximum load carrying capacity when the single pile tested was in saturated soil with high dry density, and minimum results are obtained when tested in unsaturated condition with the percentage of increase being about 463 and 34% for two saturated soils, compared with that for unsaturated soil.

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.

Numerical Investigation on Infiltration and Runoff in Unsaturated Soils with Unsteady Rainfall Intensity

Modeling infiltration into soil and runoff quantitative evaluations is very significant for hydrological applications. In this paper, a flow model of unsaturated soils was established. A computational process of soil water content and runoff prediction was presented that combines an analytical solution with numerical approaches. The solutions have good agreements with the experimental results and other infiltration solutions (Richards numerical solution and classical Green–Ampt solution). We analyzed the effects on cumulative infiltration and runoff under three conditions of rainfall intensity with same average magnitude. These rainfall conditions were (Case 1) decreasing rainfall, (Case 2) steady rainfall, and (Case 3) increasing rainfall, respectively. The results show that the cumulative infiltration in Case 1 is the highest among the three cases. The cumulative runoff under condition of Case 3 is smaller than that of decreasing rainfall at the initial stage, which then becomes larger at the later stage. The time of runoff under the conditions of Case 1 is earliest among the three rainfall conditions, which is about 50% earlier than Case 3. Therefore, project construction for urban flood control should pay more attention to urban flood defense in increasing rainfall weather than other rainfall intensities under the same average magnitude. The approaches presented can be utilized to easily and effectively evaluate infiltration and runoff as a theoretical foundation.

A pore-scale model for simulating water flow in unsaturated soil

Pore-scale simulation and tomography have been used in a combination over the past decade to study some fundamental physical and biogeochemical processes in soil that are difficult or impossible to measure, one of which is water flow in unsaturated soil. Considering that an important application of pore-scale simulation in soil is to elucidate how convective water flow distributes soluble nutrients through the heterogeneous pore space when water flow is in steady state, we propose an alternative model in this paper to simulate unsaturated water flow at pore scale. The model is quasi-static, consisting of two steps. The first one is to determine water distribution in the pore geometry using a morphological model; once the water distribution is known under a pressure, the water–air interface is fixed in space. The second step is to simulate water flow numerically by solving the Stokes equations in which the water–air interface is treated as a boundary. We test the water flow model against analytical solution of thin water film flow over a non-slip solid wall, and then combine it with the morphological model to simulate water flow in 3D soil structures acquired using X-ray tomography at resolution of 10 µm. As a validation, we compare the permeability calculated by the model under different saturations with those estimated by the van Genuchten formula using the saturated permeability and water retention parameters obtained from the morphological model. We also discuss the pros and cons of the model and its implications in unsaturated soil modelling.

The, K.M. A Study on the Relationship Between Matric Suction and the Void Ratio and Moisture Content of a Compacted Unsaturated Soil

The volumetric behaviour of compacted unsaturated soils is particularly complex due to the co-existence of three different phases: solid, liquid and air. Matric suction has been perceived as a significant influence on the volumetric behaviour of unsaturated soils and has been used as one of the constitutive variables for most the constitutive models of unsaturated soils in the literature. However, suction-controlled works are complex in practice since they generally require special test procedures and advanced equipment, and usually are very time-consuming. Thus, some researchers have tried to seek alternative frameworks that use the traditional choice of state variables to simulate the behaviour of unsaturated soils. Recently, Kodikara [1] proposed the MPK framework to interpret the behaviour of compacted unsaturated soil in the void ratio (e) – net stress (p) – moisture ratio (ew ) space. The distinct advantage of the model is that it is based on traditional constant moisture content compaction testing which is more common and simple than constant suction loading. The MPK framework has been shown to be capable of presenting the volumetric behaviour of compacted unsaturated soils. However, this framework is expected to use not only for compacted soil but for the behaviour of unsaturated soil in general. The incorporation of soil suction within the MPK framework can be helpful for creating a correlation with previous models which used matric suction as a constitutive variable. This paper presents the development of LWSBS for one clayey soil in Hungary within the MPK framework and then suction is incorporated, which is related to void ratio and moisture ratio through SWCC.

Theoretical and experimental investigations on the role of transient effects in the water retention behaviour of unsaturated granular soils

In the present study, an experimental setup is presented and employed to examine the influence of rate of change of saturation on the transient water retention curves of granular soils with a low suction range. The results are evaluated and compared to existing theoretical approaches to model the non-equilibrium soil–water retention behaviour as well as to experimental findings from other researchers. Furthermore, suction stress characteristic curves under non-equilibrium conditions are obtained. Finally, the importance and the application of the results in hydro-mechanical modelling of unsaturated soils are discussed.

A coupled hydro-mechanical constitutive model for unsaturated frictional and cohesive soil

The present study has developed a constitutive model for both saturated and unsaturated soils. The model considers the effect of mechanical and hydraulic loading on the soil behavior in critical state framework. The mechanical part has separate mechanisms, deviatoric mechanism taking advantage of multi-yield surface plasticity, and isotropic mechanism with classical plasticity formulation. The water retention part is based on the bounding surface concept. Comparison of experimental data and model predictions for saturated and unsaturated states in frictional and cohesive soils, validates the model performance considering soil behavior under different drainage and loading conditions by using one set parameters.

Numerical analysis of suction influence on the behaviour of unsaturated elasto-plastic soil medium

The paper presents a concept of numerical analysis of suction influence on behaviour of partially saturated soil medium. Behaviour of soil is described by elasto-plastic model of unsaturated soil [1]. A numerical procedure of stress path simulation in the triaxial test [2] is used for the analysis of one non-standard shear path (for 3 suction levels).

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.

Numerical modelling of rainfall-induced instability of vegetated slopes

Vegetation is known to play an important role in reducing landslide hazard. This paper presents a numerical model, which allows modelling of rainfall-induced instabilities of vegetated slopes. Both the mechanical reinforcement and the water uptake by plant roots are taken into account by considering a coupled mechanical–hydrological system. A modified Cam-Clay model for unsaturated soil is used. The mechanical reinforcement of roots is simulated by its contribution to the preconsolidation pressure. The water uptake is modelled by a sink term for variably saturated flow. The numerical model is implemented in two finite-element codes for two- and three-dimensional problems. The model performance is demonstrated by two numerical examples.

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.

Modeling the mechanical behavior of unsaturated expansive soils based on Bishop principle of effective stress

Modeling the mechanical behavior of expansive clays is of interest in understanding the performance of nuclear waste disposal designs that include clay materials as buffers around waste containers, backfill for underground openings, seals between adjacent openings, or as host-rock constituents. The buffers, backfill, and seals will be unsaturated during construction and will re-saturate at varying rates after cessation of disposal operations. The mechanical behavior of the clay materials during re-wetting could affect the pressure on waste containers, other engineered components, or the host rock and could influence fluid flow and radionuclide transport. The authors describe an approach to mechanical modeling of unsaturated soils using the moisture retention characteristic curve and the Bishop principle of effective stress to evaluate suction effects on stress. The approach incorporates swelling, thermal expansion, and soil hardening and stiffening due to suction or compaction and uses stress–strain relationships based on elastoplasticity. Suction contributions to soil stress, strength, and stiffness are evaluated using the same moisture retention characteristic curve that is a standard input for hydrological modeling. The model is illustrated through several numerical simulations of oedometer free-swell and confined-swell testing of a bentonite–sand mixture and a granular bentonite. Results are presented with and without the effect of physicochemical swelling to illustrate magnitude of the swelling influence on independent variables and different mechanical responses. The model prediction is highly dependent on the swelling/shrinkage behavior of bentonite, which could be a source of uncertainty in estimating potential pressure due to a bentonite buffer in a nuclear waste repository design.

Theoretical soil water characteristic curves for large graded soil

The present study is focused on a theoretical model of unsaturated soil based on elastic spherical particle arrangement, which can be considered to be a simplified DEM method. The model is presented with a large graded soil. This approach follows a new research method so that the physical phenomena are explained and the number of experimental parameters is limited. The theoretical model takes into account the different arrangements of soil particles so that the entire void ratio scale is covered. The wetting and drying paths are modelled. A comparison with the Brooks and Corey (1962) theory and the new theory is achieved on experimental results with a sample of glass micro-sphere and two natural soils, the Livet-Gavet sandy-loam and the Livet-Gavet loam. It shows that this new theory improves precision of the prediction using only simple physical parameters.