Constitutive modelling of unsaturated soils Research Papers (original) (raw)

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- Numerical Modeling, Unsaturated soil, Geotechnical Engineering, Genetic Algorithms

The Intergovernmental Panel on Climate Change (IPCC) provides convincing evidence of global warming as a result of increased greenhouse gas production. There has been a greater occurrence of extreme climate events in recent decades. We need to ensure that our buildings and infrastructure can cope with such events and possibly more extreme events in the future. A good grounding in unsaturated soil mechanics will be necessary to understand future changes involving the drying and desiccation of soils that will occur in dry seasons and the wetting and infiltration processes that prevail during wet seasons. To predict the impacts of climate change will require the use of robust numerical modelling of climate/soil interactions that can be used to model the effects of future climate regimes. To achieve this we need high quality field observations involving climate/soil interaction that can be used to validate the models. This paper reports on a study in the UK to acquire such data.

- by Domenico Gallipoli
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- Earth Sciences, Environmental Science, Geophysics, Remote Sensing

Spatial variability of material properties is inherent in both natural soil deposits and earth structures, yet it is often ignored during geotechnical design. With the objective of developing novel methods for assessing the effects of soil variability on groundwater flow, this study presents a stochastic finite element model of seepage through a flood defense embankment with randomly heterogeneous material properties. Stochastic modeling is undertaken by means of a Monte Carlo simulation which involves a large number of finite element analyses, each with randomly varied porosity at element level, which leads to a corresponding random variation of both permeability and water retention properties across the embankment domain. This provides a statistical distribution of responses, such as total flow rate and time to reach steady state, instead of a single deterministic result as in conventional studies of seepage through unsaturated heterogeneous soils. As the degree of heterogeneity increases, water tends to flow along the most permeable paths inside the soil mass, resulting in an irregular shape of the predicted wetting fronts and pore pressure contours. The mean and standard deviation of the computed quantities strongly depend on the statistics of the input porosity field. Simulations are also conducted to compare the statistical variation of flow rate with and without dependency of the water retention curve on porosity. With recent growth in computer speed, stochastic finite element models based on the Monte Carlo approach can become a powerful design tool, especially if a quantitative assessment of geotechnical risks is required. Copyright © 2011 John Wiley & Sons, Ltd.

- by Marcelo Sánchez and +1
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- Finite Element Methods, Numerical Modeling, Unsaturated soil, Geotechnical Engineering

The paper describes and evaluates an incremental plasticity constitutive model for unsaturated, anisotropic, nonexpansive soils (CMUA). It is based on the modified Cam‐Clay (MCC) model for saturated soils and enhances it by introducing anisotropy (via rotation of the MCC yield surface) and an unsaturated compressibility framework describing a double dependence of compressibility on suction and on the degree of saturation of macroporosity. As the anisotropic and unsaturated features can be activated independently, the model is downwards compatible with the MCC model. The CMUA model can simulate effectively: the dependence of compressibility on the level of developed anisotropy, uniqueness of critical state independent of the initial anisotropy, an evolving compressibility during constant suction compression, and a maximum of collapse. The model uses Bishop's average skeleton stress as its first constitutive variable, favouring its numerical implementation in commercial numerical analysis codes (eg, finite element codes) and a unified treatment of saturated and unsaturated material states.

Composite geotextiles with polyester yarn reinforcement have been commonly used in combination with unsaturated soils. Both unsaturated and saturated shear strength of the interfaces were investigated between a composite geotextile and three major types of materials: silty sand (SM), low-plasticity silt (ML) and highplasticity clay (CH) in a direct shear box. The interfaces were formed using two methods (A and B) to reﬂect the wide range of possible contact conditions in practice. Method A involved statically compacting the soil directly on top of the composite geotextile, while for Method B, the soil was statically compacted in a separate mold and later brought into contact with the composite geotextile. Type B interfaces required a larger displacement to mobilize the shear strength than Type A interfaces. The ultimate failure envelopes of SM and ML soils were similar to those oftheir interfaceshearing. Notably, the failureenvelopes for the clay-geotextile interfaceof both types were higher than that of clay alone. The unsaturated soil-only shearing had a higher peak strength and tended to dilate more than saturated soil-only shearing, while unsaturated soil-interface shearing appeared to be more contractant than saturated interface shearing. The strength variations with suction for all tested soils and interface shearing were clearly non-linear. A new model that takes account of the condition of soil-geotextile contact intimacy is proposed for predicting the variation of interface strength with suction, based on the variation of the soil's apparent cohesion with suction and the geotextile-water retention curve.

The paper gives a brief description of double wall cell triaxial equipment for testing soil samples under unsaturated conditions and presents results of some of the calibrations necessary to achieve accurate measurements of inner cell water volume, pore water volume, pressure, load and displacement. The calibration of the measurement devices showed linear relationships between the raw readings and applied values with the regression constants differ from 1 and 0. The result of apparent volume change calibrations showed significant correlation between cell water volume fluctuation and temperature fluctuation inside testing room. A correction to the measured volume was therefore required to reduce the effects of long-term temperature fluctuation on the measured volume. Investigation of the accuracy of volume change measurement with the double wall cell showed excellent matching between the inner cell volume change and pore water volume change under saturated conditions, indicating the high reliability of the double wall system for apparent volume change measurements.

Mounding often occurs beneath engineering structures designed to infiltrate reuse water. AQTESOLV software and a spreadsheet solution for Hantush, together with soil moisture water balance (SWAGMAN farm model), were used for quantitatively predicting the height and extent of groundwater mounding underground to assess the groundwater-flow simulations of infiltration from a hypothetical irrigation site. Horizontal and vertical permeability, aquifer thickness, specific yield, and basin geometry are among the aquifer and recharge properties inputs. For 2.2 ha sites, the maximum heights of the simulated groundwater mound ranges up to 0.29 m. The maximum areal extent of groundwater mounding measured from the edge of the infiltration basins of 0.24 m ranges from 0 to 75 m. Additionally, the simulated height and extent of the groundwater mounding associated with a hypothetical irrigation infiltration basin for 2.2 ha development may be applicable to sites of different sizes, using the recharge rate estimated from the SWAGMAN farm model. For example, for a 2.2 ha site with a 0.0002 m/day recharge rate, the irrigation infiltration basin design capacity (and associated groundwater mound) would be the same as for a 1.1 ha site with a 0.0004 m/day recharge rate if the physical characteristics of the aquifer are unchanged. The study claimed that the present modelling approach overcomes the complications of solving the Hantush equation for transient flow. The approach utilised in this study can be applied for other purposes such as measuring the feasibility of infiltrating water, attenuation zone, risk mitigation essential for decision-makers and planning regulators in terms of environmental effects and water use efficiency.

A new elasto-plastic model for unsaturated soils incorporating the effect of evolving fabric anisotropy is presented. The model is formulated in terms of mean net stress, deviator stress and suction and reduces to the Barcelona Basic Model for an isotropic material. Model simulations are performed and compared against experimentally observed behaviour from constant suction triaxial tests on isotropically and anisotropically compacted kaolin samples along a variety of stress paths. Simulations indicate an improvement in the prediction of the size and shape of the yield surface compared to the Barcelona Basic Model. In addition, the deformation generated during shearing are better predicted than in the Barcelona Basic Model, even though experimentally observed strains are still grossly over-estimated. Further refinement to model assumptions are required to improve predictions of experimental data and the reformulation of the model in terms of average skeleton stresses, instead of net stresses, might help in this respect as outlined in Al-Sharrad (2013).

The paper presents a mechanical model for non-isothermal behaviour of unsaturated soils. The model is based on an incrementally non-linear hypoplastic model for saturated clays and can therefore tackle the non-linear behaviour of overconsolidated soils. A hypoplastic model for non-isothermal behaviour of saturated soils was developed and combined with the existing hypoplastic model for unsaturated soils based on the effective stress principle. Features of the soil behaviour that are included into the model, and those that are not, are clearly distinguished. The number of model parameters is kept to a minimum, and they all have a clear physical interpretation, to facilitate the model usefulness for practical applications. The step-by-step procedure used for the parameter calibration is described. The model is finally evaluated using a comprehensive set of experimental data for the thermo-mechanical behaviour of an unsaturated compacted silt.

The thesis focuses on three different areas: development of constitutive models for unsaturated soils, improvement of the finite element code “Compass” for coupled flow-deformation analysis involving unsaturated soils and application of the improved code to the simulation of pressuremeter tests in unsaturated soils.
On the constitutive side, a unique relationship is proposed between degree of saturation, suction and specific volume by introducing dependency on specific volume in the simplified van Genuchten equation. This is a significant improvement over the common assumption of a state surface expression for degree of saturation. If combined with an elasto-plastic stress-strain model predicting the variation of specific volume, the proposed relationship is capable of reproducing irreversible changes of degree of saturation and changes of degree of saturation experimentally observed during shearing. Predictions show very good agreement with experimental results from tests on compacted Speswhite Kaolin published in the literature.
On the numerical side, a number of changes to the code “Compass” have been performed. The new relationship for degree of saturation is implemented in the code and the implementation is validated against three benchmark problems. Use of the new relationship for degree of saturation results in significantly different predictions to those obtained if a conventional state surface expression for degree of saturation is used (as present in the original code).
Implementation of the water and air continuity equations in “Compass” has been corrected by expressing these equations in terms of flux velocities relative to the soil skeleton. This is the form in which the equations should be expressed if they are to be combined with Darcy’s law for liquid and gas flows. The simulation of a notional laboratory test shows that the incorrect combination of Darcy’s law with absolute flux velocities, as present in the original code, causes significant errors.
The convergency algorithm at constitutive level employed in the code has been corrected by introducing residual flux terms in the two flow equations, analogous to residual forces in the equilibrium equation. These terms must be taken into account if a convergency algorithm for an elasto-plastic stress-strain model is used and the relationship assumed for variation of degree of saturation involves any dependency on net stresses. A numerical study of a notional laboratory test shows that omission of residual flux terms results in substantial errors and may cause failure to converge.
The plane_strain formulation of code “Compass” has been corrected by imposing the condition of nullity only on the out-of-plane component of the total strain rate vector instead of the out-of-plane component of each single contribution to the total strain rate, as was done in the original code. Such inconsistency, due to the history of development of finite element programs, also appears in other examples published in the literature. Numerical simulations of two types of bi-axial tests show that significantly different results are generally predicted by the correct and incorrect formulations, and also provide an explanation why this type of error was difficult to detect in codes implementing traditional models for saturated soils.
The potential of the enhanced version of code “Compass” for analysing boundary value problems is demonstrated by simulations of pressuremeter tests in unsaturated soil. This study also provides some initial insight into the interpretation of pressuremeter tests in unsaturated soil by simulating tests at different loading rates in a normally consolidated soil. The mechanical behaviour of the soil is represented by the elasto-plastic Barcelona Basic Model of Alonso, Gens and Josa (1990) while the variation of degree of saturation is modelled by the new relationship proposed in the thesis. The entire range of loading rates, from undrained to fully drained (with respect to liquid), is simulated. Relatively small changes of suction are predicted even in the fastest test and the computed cavity pressure-cavity strain relationships are all very similar regardless of loading rate. It may therefore be possible to model even rapid pressuremeter tests in unsaturated soils as a drained (constant suction) process. Further work is required to investigate the generality of this conclusion.

The paper presents a bounding surface model that describes the gradual yielding of unsaturated soils subjected to isotropic loads. The model originates from consideration of the capillary bonding between soil grains, which leads to the definition of a “unified normal compression line” that is valid in both saturated and unsaturated conditions. This line has the same slope and intercept of the saturated normal compression line but is formulated in terms of a “scaled stress” variable, which takes into account the mechanical effect of capillarity by factoring the average skeleton stress (also known as Bishop’s stress) with a power function of degree of saturation. The normal compression behaviour of unsaturated soils is therefore described by only one additional parameter, which is the exponent of the degree of saturation in the scaled stress expression. For over-consolidated soils, the occurrence of gradual yielding is introduced by assuming that, as the soil state moves towards the unified normal compression line, the slope of the loading curve tends towards the slope of the unified normal compression line according to an expression requiring only one extra parameter. Interestingly, this expression can be integrated in a closed form to provide a general equation for all loading paths in saturated and unsaturated conditions. Different loading curves are simply distinguished by the different values of the integration constants. Unloading paths are also simulated in a similar way. The proposed model requires a total of five parameters, which include the three standard parameters for saturated soils (i.e. the slope and intercept of the saturated normal compression line and the slope of the swelling line) plus one parameter to describe unsaturated behaviour and one parameter to describe the gradual yielding of over-consolidated soils subjected to loading.

- by Domenico Gallipoli
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- Civil Engineering, Soil Science, Unsaturated soil, Geotechnical Engineering

In the paper, we present newly developed hydro-mechanical hypoplastic model for partially saturated soils predicting small strain stiffness. Hysteretic void ratio dependent water retention model has been incorporated into the existing hypoplastic model. This required thorough revision of the model structure to allow for the hydro-mechanical coupling dependencies. The model is formulated in terms of degree of saturation, rather than of suction. Subsequently, the small strain stiffness effects were incorporated using the intergranular strain concept modified for unsaturated conditions. New features included degree of saturation-dependent size of the elastic range and an updated evolution equation for the intergranular strain. The model has been evaluated using two comprehensive data sets on completely decomposed tuff from Hong-Kong and Zenos Kaolin from Iran. It has been shown that the modified intergranular strain formulation coupled with the hysteretic water retention model correctly reproduces the effects of both the stress and suction histories on small strain stiffness evolution. The model can correctly predict also different other aspects of partially saturated soil behaviour, starting from the very small strain range up to the asymptotic large-strain response.

Rainfall is the most frequent triggering factor for landslides and the development of early warning systems has to take account of this. It is suggested that direct measurement of pore pressure gives the most reliable prediction of failure of a slope. The amount of rainfall can be only a crude indicator of failure as the processes that occur between rain falling on a slope and the resulting pore water pressure change are complex, highly non-linear and hysteretic. The paper describes high capacity tensiometers developed within the EU-funded MUSE Research Training Network that have been used for measuring suctions in slopes. High-capacity tensiometers are capable of direct measurement of pore water pressure down to −2 MPa and are also able to record positive pore water pressures. Two methods of field installation are discussed; one developed by ENPC in France uses a single tensiometer per hole, and the second technique, developed by Durham University in the UK, allows multiple tensiometers to be used at different depths within a single borehole. Continuous monitoring of pore water pressure has been carried out over several months and shows the responses to climatic events.

- by Domenico Gallipoli and +3
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- Numerical Modeling, Unsaturated soil, Geotechnical Engineering, Genetic Algorithms

The thesis focuses on three different areas: development of constitutive models for unsaturated soils, improvement of the finite element code "Compass" for coupled flow-deformation analysis involving unsaturated soils and application of the improved code to the simulation of pressuremeter tests in unsaturated soils. On the constitutive side, a unique relationship is proposed between degree of saturation, suction and specific volume, by introducing dependency on specific volume in the simplified van Genuchten [48] equation. This is a significant improvement over the common assumption of a state surface expression for degree of saturation. If combined with an elasto-plastic stress-strain model predicting the variation of specific volume, the proposed relationship is capable of reproducing irreversible changes of degree of saturation and changes of degree of saturation experimentally observed during shearing. Predictions show very good agreement with experimental results from...

This paper investigates the “initial” and “evolving” mechanical anisotropy of a compacted unsaturated soil. A wide campaign of triaxial compression and extension tests, involving different stress and suction paths, has been performed on both isotropically and anisotropically compacted samples of unsaturated Speswhite Kaolin. The first objective is the definition of the initial yield surface of the compacted soil after suction equalization and before any plastic loading/wetting path takes place. This is followed by the investigation of the evolution of the yield surface induced by plastic straining along different loading/wetting paths. Experimental results are interpreted by using two alternative stress variables, namely net stresses and Bishop’s stress. Constant suction cross-sections of the yield surface are represented as distorted ellipses not passing through the origin in the q:p plane of deviator stress versus mean net stress, and by distorted ellipses passing through the origin in the q:p* plane of deviator stress versus mean Bishop’s stress. The inclination of these distorted elliptical yield curves evolves with plastic straining but remains the same at all suction levels for a given level of plastic deformation. The critical state lines in the planes q:p and q:p*, or in the semi-logarithmic v:lnp and v:lnp* planes (v is the specific volume), are generally independent of initial anisotropy or stress history, suggesting that fabric memory tends to be erased at critical state.

- by Domenico Gallipoli and +1
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- Civil Engineering, Unsaturated soil, Geotechnical Engineering, Soil Mechanics

One of the most common mitigation methods for founding on expansive soils is the full or the partial removal of expansive soils and replacement with non-expansive soils. In case of partial removal of expansive soils (sand cushion), there are no definitive guidelines for estimating the depth and lateral extent of sand cushion. In practice, most engineers suggest some arbitrary thickness for the sand cushion without consideration to the depth of the zone of potential volume change which in itself is difficult to determine. A parametric study was performed using a two-dimensional finite element program to investigate the effect of sand cushion parameters on the swelling behavior of expansive soils under climate change conditions. The finite element program used is CRISP modified to include a nonlinear elastic constitutive soil model developed by Fredlund (1993). Soil considered in this analysis was Regina Clay. Sand cushion parameters considered include depth, lateral extension, and relative density.

A formalism for double structure hydromechanical coupled modelling of aggregated unsaturated soils has been developed. Independent coupled hydromechanical models are considered for each structural level, including independent measures of macromechanical and micromechanical effective stresses. The models are linked using a coupling function to obtain the global response. The individual components have been selected to represent the behaviour of compacted expansive clays. The macrostructural mechanical model is based on the existing hypoplastic model for unsaturated soils. Hydromechanical coupling at each structural level is efficiently achieved by linking the effective stress formulation with the water retention model. An essential component of the model is representation of microstructural swelling. It is demonstrated that its calibration on wetting induced expansion measured in oedometric (mechanical) tests leads to a correct global hydraulic response, providing a supporting argument for the adopted coupling approach. An interesting consequence of the model formulation is that it does not suffer from volumetric rachetting, which is often regarded as one of the main drawbacks of hypoplasticity. The proposed model has a small number of material parameters. Its predictive capabilities have been confirmed by simulation of comprehensive experimental data set on compacted Boom clay.

In the present study, a comprehensive elasto-plastic model with the critical state boundary level based on Barcelona Model for the prediction of behaviors of the unsaturated soil was provided and offered. This model was successful in the evaluation of the specific characteristics of behaviors of unsaturated soil and it explained the behaviors near the reality of this type of soil and it can be widely used. This model is located in a limited constitute code(Fortran) and is able to be carried out for the prediction of the behaviors of soil structures formed by the unsaturated soil. Using this model, a variety of problems with different boundary conditions can be analyzed. In this research, in order to generalize the possibility of a better prediction of different behaviors of unsaturated soil and to eliminate the inconsistency with the results provided in the laboratory, an modifid approach of Barcelona model was suggested. The laboratory results from a series of suction control tests in the real tri-axial apparatus on the sandy silt soil were achieved. Calibrating the model and drawing yield curve, the Non-compliance lab results and LC 1 curve is regarded as the deficiency of the identification model and is corrected by providing a coefficient in the correlation. The results of comparison for the constant suction (CS) and constant water content (CW) testing showed the operating improvement in the model.

The paper presents an approach to predicting variation of a degree of saturation in unsaturated soils with void ratio and suction. The approach is based on the effective stress principle for unsaturated soils and several underlying assumptions. It focuses on the main drying and wetting processes and does not incorporate the effects of hydraulic hysteresis. It leads to the dependency of water retention curve (WRC) on void ratio, which does not require any material parameters apart from the parameters specifying WRC for the reference void ratio. Its validity is demonstrated by comparing predictions with the experimental data on four different soils taken over from the literature. Good correlation between the measured and predicted behaviour indirectly supports applicability of the effective stress principle for unsaturated soils.

The paper presents the analytical solution for the steady-state infiltration from a buried point source into two types of heterogeneous cross-anisotropic unsaturated half-spaces. In the first case, the heterogeneity of the soil is modelled by an exponential relationship between the hydraulic conductivity and the soil depth. In the second case, the heterogeneous soil is represented by a multilayered half-space where each layer is homogeneous. The hydraulic conductivity varies exponentially with moisture potential and this leads to the linearization of the Richards equation governing unsaturated flow. The analytical solution is obtained by using the Hankel integral transform. For the multilayered case, the combination of a special forward and backward transfer matrix techniques makes the numerical evaluation of the solution very accurate and efficient. The correctness of both formulations is validated by comparison with alternative solutions for two different cases. The results from typical cases are presented to illustrate the influence on the flow field of the cross-anisotropic hydraulic conductivity, the soil heterogeneity and the depth of the source. Copyright © 2004 John Wiley & Sons, Ltd.

- by Domenico Gallipoli
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- Numerical Modeling, Unsaturated soil, Geotechnical Engineering, Irrigation

An analysis of results from published laboratory tests on Jossigny silt and Barcelona clayey silt is presented to confirm the existence of a unique capillary bonding function linking the quotient between unsaturated and saturated void ratio, at the same mean average skeleton stress, to a single capillary bonding scalar variable. The analysis confirms that the same capillary bonding function applies to both normally consolidated and critical stress states.The above two experimental sets with the addition of further published data for Speswhite Kaolin are also used to study the relationship between unsaturated critical shear strength, mean average skeleton stress and capillary bonding variable. The results of such analysis are assessed in the light of a similar modelling framework proposed in the literature.

- by Domenico Gallipoli and +1
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- Numerical Modeling, Unsaturated soil, Geotechnical Engineering, Genetic Algorithms

A thermo-mechanical constitutive model for unsaturated clays is constructed based on the existing
model for saturated clays originally proposed by the authors. The saturated clays model was formulated
in the framework of critical state soil mechanics and modified Cam-clay model. The existing model has
been generalized to simulate the experimentally observed behavior of unsaturated clays by introducing
Bishop’s stress and suction as independent stress parameters and modifying the hardening rule and yield
criterion to take into account the role of suction. Also, according to previous studies, an increase in
temperature causes a reduction in specific volume. A reduction in suction (wetting) for a given confining
stress may induce an irreversible volumetric compression (collapse). Thus an increase in suction (drying)
raises a specific volume i.e. the movement of normal consolidation line (NCL) to higher values of void
ratio. However, some experimental data confirm the assumption that this reduction is dependent on the
stress level of soil element. A generalized approach considering the effect of stress level on the
magnitude of clays thermal dependency in compression plane is proposed in this study. The number of
modeling parameters is kept to a minimum, and they all have clear physical interpretations, to facilitate
the usefulness of model for practical applications. A step-by-step procedure used for parameter calibration
is also described. The model is finally evaluated using a comprehensive set of experimental data
for the thermo-mechanical behavior of unsaturated soils.

- by Saeed Tourchi
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- Constitutive modelling of unsaturated soils

Compacted clay fills are generally placed at the optimum value of water content and, immediately after placement, they are unsaturated. Wetting might subsequently occur due, for example, to rainfall infiltration, which can cause volumetric deformation of the fill (either swell or collapse) with associated loss of shear strength and structural integrity. If swelling takes place under partially restrained deformation, due for example to the presence of a buried rigid structure or a retaining wall, additional stresses will develop in the soil and these can be detrimental to the stability walling elements and other building assets. Factors such as dry density, overburden pressure, compaction water content and type of clay are known to influence the development of stresses. This article investigates these factors by means of an advanced stress path testing program performed on four different clays with different mineralogy, index properties and geological histories.
Specimens of kaolin clay, London clay, Belfast clay and Ampthill clay were prepared at different initial states and subjected to “controlled” wetting whereby the suction was reduced gradually to zero under laterally restrained conditions (i.e. Ko conditions). The results have shown that the magnitude of the increase in horizontal stresses (and therefore the increase of Ko) is influenced by the overburden pressure, compaction water content, dry density at the time of compaction and mineralogy.

This paper presents a methodology for the identification of parameter values in the Barcelona Basic Model (BBM) by inverse analysis of the experimental cavity pressure–cavity strain curve from pressuremeter tests in unsaturated soils. This methodology involves a high-dimensional optimization process which is particularly challenging due to the existence of a large number of local minima caused by the nonlinearity of the BBM. A novel parallel modified particle swarm optimization algorithm is utilized to minimize the difference between measured and computed values on the cavity pressure–cavity strain curve. The computed cavity pressure–cavity strain curve is obtained by using a finite element model of an unsaturated soil whose mechanical behaviour is described by the BBM. An example is presented to validate the proposed methodology making use of artificial experimental results that had been calculated by a finite element simulation of pressuremeter tests. Finally, the application to a real case is presented by showing that the proposed methodology can safely identify the values of at least six BBM parameters via inverse analysis of pressuremeter tests at different suction levels.

The paper presents a collaborative piece of research undertaken by seven research teams from different universities within the ‘Mechanics of Unsaturated Soils for Engineering’ (MUSE) network. The objective is to benchmark different approaches to constitutive modelling of mechanical and water retention behaviour of unsaturated soils by comparing simulations of suction-controlled and constant water content laboratory tests. A set of 13 triaxial and oedometer laboratory tests, covering the mechanical and water retention behaviour of an unsaturated compacted silty soil under a variety of stress paths, has been provided by one of the seven participating teams. This data set has been used by the other six teams for calibrating a constitutive model of their choice, which has been subsequently employed for predicting strains and degree of saturation in three of the 13 tests used for calibration, as well as in one ‘blind’ test for which experimental results had not been previously disclosed. By comparing predictions from all teams among themselves and against experimental data, the work highlights the capability of some of the current modelling approaches to reproduce specific features of the mechanical and water retention behaviour of unsaturated soils helping to identify potential areas of weakness where future research should focus. It also demonstrates the dispersion of results to be expected when different constitutive models, independently calibrated by different teams of researchers, are used to predict soil behaviour along the same stress path.

- by Domenico Gallipoli and +3
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- Finite Element Methods, Numerical Modeling, Unsaturated soil, Geotechnical Engineering
- by Gabriela Medero and +1
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- Numerical Modeling, Unsaturated soil, Geotechnical Engineering, Genetic Algorithms
- by Carlos Pereira
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- Civil Engineering, Finite Element Methods, Numerical Modeling, Unsaturated soil

Experiments were conducted to investigate the odometric swell behavior of expansive soil specimens mixed independently with two different granular additives: silica sand and granulated tire rubber (GTR). All specimens were prepared with the same global water content. However, specimens that contained sand swelled less than did analogous specimens that contained GTR, regardless of the surcharge stress imposed before inundation. Phase relationship analyses based on " oversize correction " equations derived for mixtures with three solid phases indicate that the specimens possessed clay portions with different dry density and initial water content. Such differences are attributed mainly to the role of additive grain stiffness during specimen preparation. Results from complementary discrete element method simulations indicate that the stiffness of the additive grains may also play a role in mitigating the swell via contact force alterations upon swell.

- by M Rouainia
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- Civil Engineering, Unsaturated soil, Geotechnical Engineering, Soil Mechanics

A new constitutive model is developed for the mechanical behaviour of unsaturated soils based on the theory of hypoplasticity and the effective stress principle. The governing constitutive relations are presented and their application is demonstrated using several experimental data from the literature. Attention is given to the stiffening effect of suction on the mechanical response of unsaturated soils and the phenomenon of wetting-induced collapse. All model parameters have direct physical interpretation, procedures for their quantification from test data are highlighted. Quantitative predictions of the model are presented for wetting, drying and constant suction tests.

This paper presents a new method for selecting parameter values in elasto-plastic models for unsaturated soils under isotropic stress states. The proposed method is an improvement over more traditional calibration approaches as it explicitly takes into account experimental yielding behaviour when defining the unsaturated normal compression surface. This is achieved by “enriching” measured yield stresses with corresponding values of specific volume (estimated from the observed elastic and virgin responses), which generates experimental points that can be interpolated together with virgin compression data. The proposed methodology is general and independent of the chosen mathematical forms of normal compression surface, elastic law and constitutive variables. The validity of the method is demonstrated by calibrating a reference model from a set of constant suction isotropic compression tests. Both improved and traditional calibration approaches are employed to select model parameter values which are then used to predict yield curves in the mean net stress–suction plane. Because of the incorporation of yielding data in the interpolation of the normal compression surface, the improved calibration method produces a more accurate prediction of yield stresses at different suctions compared with the standard method. Due to its generality and limited subjectivity, the proposed method provides an unbiased tool to compare strengths and weaknesses of different constitutive models.

The popularity of the Barcelona Basic Model (BBM) has grown steadily since publication in 1990 due to its ability of capturing key aspects of unsaturated soil behaviour. Nevertheless, BBM is still rarely employed by practitioners partly because of the absence of simple and objective methods for selecting parameter values from laboratory tests. One difficulty is that, in BBM, individual aspects of the isotropic virgin behaviour are controlled by multiple parameters while, at the same time, a single parameter controls more than one aspect of soil behaviour. This has led to iterative procedures where parameter values are adjusted in turn to match experiments, which requires significant experience and can lead to the selection of widely different parameter values depending on the user. The proposed method streamlines parameter selection with a view to increasing the appeal of BBM for practitioners. The method adopts a “sequential” procedure where the five parameters governing isotropic virgin behaviour are matched to degrees of freedom in BBM, which are then fixed one at a time, in a specific order, without any assumption about other parameters. The simplicity and reduced subjectivity of the method in comparison with iterative procedures is demonstrated by selecting parameter values from laboratory tests.

The paper presents an elasto-plastic model for unsaturated soils that takes explicitly into account the mechanisms with which suction affects mechanical behaviour as well as their dependence on degree of saturation. The proposed model is formulated in terms of two constitutive variables directly related to these suction mechanisms: the average skeleton stress, which includes the average fluid pressure acting on the soil pores, and an additional scalar constitutive variable, 'csi', related to the magnitude of the bonding effect exerted by meniscus water at the inter-particle contacts. The formulation of the model in terms of variables closely related to specific behaviour mechanisms leads to a remarkable unification of experimental results of tests carried out with different suctions. The analysis of experimental isotropic compression data strongly suggests that the quotient between the void ratio, e, of an unsaturated soil and the void ratio es, corresponding to the saturated state at the same average soil skeleton stress, is a unique function of the bonding effect due to water menisci at the inter-particle contacts. The same result is obtained when examining critical states at different suctions. Based on these observations, an elastoplastic constitutive model is developed using a single yield surface the size of which is controlled by volumetric hardening. In spite of this simplicity, it is shown that the model reproduces correctly many important features of unsaturated soil behaviour. It is especially remarkable that, although only one yield surface is used in the formulation of the model, the irreversible behaviour in wetting–drying cycles is well captured. Because of the behaviour normalisation achieved by the model, the resulting constitutive law is economical in terms of the number of tests required for parameter determination.

- by Radhey Sharma and +2
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- Numerical Modeling, Unsaturated soil, Geotechnical Engineering, Genetic Algorithms

- by C. Mancuso
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- Civil Engineering, Finite Element Methods, Plasticity, Numerical Modeling

The present study utilizes a series of anisotropic consolidation tests followed by a decrease of the mean stress under constant axial load to define the yield locus of anisotropically consolidated soil samples and to evaluate the ability of different yield surface shapes in accommodating the observed behaviour. Nine different axial load tests are used, including three different water contents and three different consolidation stress obliquities. For each test, the “end of compression” and the “failure initiation” stress states are assumed to define the yield locus. Two isotropic and two anisotropic ellipsoids are used to describe the experimentally determined yield points. It proves that a distorted ellipsoid is superior in capturing the behaviour, provided that its aspect ratio is handled as an independent variable.

- by Panagiotis (Panos) Sitarenios and +1
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- Unsaturated soil, Constitutive Modeling, Constitutive modelling of unsaturated soils

This study was carried out to investigate the undrained behaviour of weakly bonded soil. Artificial specimens were used and were prepared from a mixture of sand and kaolin. The mixture was fired at 500°C for 5 h to create uniform strength of artificial weakly bonding between sand particles. Based on microscopic observation of the specimens revealed that the fired kaolin formed bridges between the sand particles and most of the sand particles were entirely coated by kaolin. It was observed that very few sand grains made a direct grain to grain contact. The occurrences of inter-particle voids either isolated or connected to form larger voids. Fissures found in between the bonding and the grains were due to high temperature firing. A series of consolidated undrained tests (CU) were performed using conventional triaxial compression test. The stress ratio curves for the bonded specimens showed a significant peak at early strain and the values of maximum stress ratios dropped with increasing applied confining stresses. For the destructured (or unbounded) specimens, no apparent peaks were observed and the stress values were slightly lower compared to that of bonded specimens. The bounding surface for the destructured specimens is represented by a straight line equivalent to stress ratio of 1.24. This line is equivalent to strength parameters of internal friction angle, φ’ and cohesion intercept, c’ of 31° and 21 kPa, respectively. Meanwhile, the bounding surface for the bonded specimens is indicated by some curvature at low stress (p′<150 kPa) and high stresses (p′>1100 kPa). The study clearly suggested the role of bonding on the engineering behaviour of residual soils in undrained conditions.

An improved relationship for the variation of degree of saturation in an unsaturated soil is presented, incorporating the influence of changes of void ratio. When combined with an elasto-plastic stress–strain model, this is able to represent irreversible changes of degree of saturation and changes of degree of saturation caused by shearing. Experimental data from tests on compacted Speswhite kaolin are used to demonstrate the success of the proposed new expression for degree of saturation. The experimental data involve a wide variety of stress paths, including wetting, isotropic loading and unloading under constant suction, constant suction shearing, and constant water content shearing. Improved representation of the variation of degree of saturation has important consequences for numerical modelling of coupled flow-deformation problems, where the expression used for the degree of saturation can influence significantly the suction generated within the soil and hence the predicted stress–strain behaviour.

- by Antonio Gens
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- Civil Engineering, Numerical Modeling, Unsaturated soil, Geotechnical Engineering

- by Guangjing Chen
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- Civil Engineering, Numerical Modeling, Geotechnical Engineering, Irrigation

A unique facility for engineering and biological research has been established with the aim of improving fundamental understanding of the effects of climate change on slopes. This paper describes the building and monitoring of a full-scale embankment representative of UK infrastructure, the planting and monitoring of representative vegetation, and the construction of a system of sprinklers and covers to control climate. A summary of the results of the first experiments simulating predicted future UK climate and the response of the embankment is also presented. The information that has begun to be gathered is providing data related to the failure modes anticipated as a result of climate change and hence on the sustainability of UK infrastructure slopes.

- by Domenico Gallipoli and +2
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- Numerical Modeling, Unsaturated soil, Geotechnical Engineering, Genetic Algorithms

The paper compares the accuracy and efficiency of explicit stress integration schemes for elasto-plastic unsaturated soil models with automatic error control. Numerical tests are performed with reference to the Barcelona Basic Model (BBM), one of the most popular elasto-plastic models for unsaturated soils, by using eight explicit Runge–Kutta algorithms of various order as well as a novel application of the extrapolation method described in the companion paper. Initially, the results obtained from the lowest order Runge–Kutta scheme (i.e. Modified Euler) as well as the extrapolation method are checked against accurate solutions of a number of BBM paths involving changes of strains and suction. Subsequently, the efficiency and accuracy of all algorithms are assessed for generic increments of strains and suction, while the difference between two alternative error control methods is also analysed. The results presented, although strictly valid for the Barcelona Basic Model, are expected to be general and relevant to other similar unsaturated elasto-plastic models formulated in terms of two independent stress variables such as net stress and suction.

The numerical integration of the stress–strain relationship is an important part of many finite element code used in geotechnical engineering. The integration of elasto-plastic models for unsaturated soils poses additional challenges associated to the presence of suction as an extra constitutive variable with respect to traditional saturated soil models. In this contribution, a range of explicit stress integration schemes are derived with specific reference to the Barcelona Basic Model (BBM), which is one of the best known elasto-plastic constitutive models for unsaturated soils. These schemes, however, do not address possible non-convexity of the loading collapse (LC) curve and neglect yielding on the suction increase (SI) line. The paper describes eight Runge–Kutta methods of various orders with adaptive substepping as well as a novel integration scheme based on Richardson extrapolation. The algorithms presented also incorporate two alternative error control methods to ensure accuracy of the numerical integration. Extensive validation and comparison of different schemes are presented in a companion paper. Although the algorithms presented were coded for the Barcelona Basic Model, they can be easily adapted to other unsaturated elasto-plastic models formulated in terms of two independent stress variables such as net stress and suction.

The net stress plus suction and the average skeleton stress plus modified suction are two alternative sets of energetically consistent stress variables for modelling the hydro-mechanical behaviour of unsaturated soils. When used in conjunction with their work-conjugate strains, both sets of stress variables correctly calculate the first-order term of the hydro-mechanical work input into a soil element subjected to infinitesimal changes of deformation and water content. They therefore also correctly calculate the increment of internal energy along a given stress-strain path, that is the integral of the first-order term of the infinitesimal work input. This paper shows, however, that the above two sets of stress variables lead to different values of the second-order term of the hydro-mechanical work input. They are therefore no longer equivalent with respect to other aspects of material behaviour governed by the second-order work such as the flow rule of elasto-plastic models. The flow rule assumes the normality between plastic strains and equipotential surfaces defined in the conjugate stress-strain space. This normality is however lost when an elasto-plastic model originally formulated in terms of net stress plus suction is recast in terms of average skeleton stress plus modified suction (or vice versa) by means of standard mapping relationships between stress variables. To restore normality in both stress spaces, it is necessary to impose specific forms of elastic and plastic behaviour.

- by Domenico Gallipoli and +1
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- Civil Engineering, Soil Science, Materials Science, Thermodynamics
- by Antonio Gens and +1
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- Civil Engineering, Numerical Modeling, Unsaturated soil, Geotechnical Engineering