Water Retention Model Research Articles

Numerical simulation of a water infiltration test on a proposed backfill material in nuclear waste repositories

A water infiltration test was numerically simulated using the finite element method. The modified Barcelona Basic Model and the double-structure water retention model was used for the numerical analysis. A methodology is presented for parameter identification and calibration purpose. The experimental results highlighted the porosity redistribution and hydration-induced heterogeneity along the hydration-path. The simulation results successfully captured the moisture migration in the soil sample. A comparison between the measured and predicted total stress values revealed the influence of interfacial friction between the soil sample and cell wall.

Analytical expressions for noncapillary soil water retention based on popular capillary retention models

AbstractRecently, Weber et al. proposed a new model for noncapillary retention of soil water without introducing new parameters. The model is based on the integral of any given saturation function for the capillary part in log space. In the original paper, the integration was carried out numerically. Here, we derive analytical solutions for the most popular soil water retention models (van Genuchten, Kosugi, and Brooks–Corey).

Comparison of soil hydraulic properties estimated from steady-state experiments and transient field observations through simulating soil moisture in regenerated Sphagnum moss

Growing Sphagnum moss for peatland restoration and fibre farming requires the proper moisture regime be maintained; thus, there is a desire to optimize growth by creating ideal hydrological conditions. However, it is uncertain which parameterization method is most suitable to describe field-scale processes and which soil water retention model and hydraulic conductivity curve (approach) is the most acceptable to use. Parameterizations of the van Genuchten – Mualem (VGM) equation were done using RETC, curve fitting to direct measurements of the water retention and unsaturated hydraulic conductivity curves; and Hydrus-1D, inverse modelling to field observations of soil moisture. The acceptability of each parameterization was tested by comparing soil moisture estimates based on forward simulations to observed soil moisture in two regenerated moss profiles, established in 1970 and 2006 cases, respectively. The transient field model simulated soil moisture well, and had an RMSE of 0.05 and 0.06 for 1970 and 2006, respectively. The most error occurred during the wettest and driest periods of the simulations. Simulated soil moisture was consistently drier than the observed soil moisture, in the steady-state laboratory simulation, and had markedly higher RMSE, 0.14 and 0.27 for the 1970 and 2006 profiles, respectively. The estimate of the VGM α parameter, an approximately the inverse of the air-entry pressure, fit to direct measurements of the retention and unsaturated hydraulic conductivity curves was an order of magnitude higher than that fit to field observation. The results of the simulation suggest that inverse modelling to field soil moisture should be used to estimate VGM parameters to more accurately represent field-scale soil moisture dynamics.

A modified physical-based water-retention model for continuous soil moisture estimation during infiltration: experiments on saline and non-saline soils

ABSTRACT Water infiltration is an issue of vital concern to farmland irrigation. Besides, a soil-water evaluation during infiltration benefits irrigation determination and salt leaching, which has still not been well revealed through a physical-based model regarding continuous soil-water estimation. We conducted one-dimensional infiltration on non-saline loam soil and saline sandy loam soil to propose a modified water-retention model which was expected to estimate continuous soil-water changes during infiltration. Results indicated that for the non-saline soil and the saline soil with different salinities, the modified water-retention model can be established based on the vertical one-dimensional algebraic model and the Kostiakov model. But different from the traditional vertical one-dimensional algebraic model, the new established model can be adopted for calculating and predicting continuous water content during infiltration at any duration, with higher accuracy than using HYDRUS, due to direct parameter acquisition from the observed infiltration data rather than indirect acquisition from soil water characteristic curve. The established potential relationship between soil moisture and cumulative infiltration promotes the development of precise agriculture.

A double-structure hydromechanical constitutive model for compacted bentonite

This paper presents a double-structure elastoplastic constitutive model that can describe the hydromechanical behavior of compacted bentonite. The model is formulated based on a new developed double-structure hydromechanical framework that consists of four key components, including the mechanical model and water retention model at the macrostructure scale and microstructure scale, respectively. Hydromechanical coupling at each structure scale is achieved by liking the effective stress with the corresponding water retention model. Independent coupled hydromechanical models are developed for each structure scale and the global response is obtained with an introduction of the structure parameter ξ. The elastoplastic deformation occurs at both the microstructure and macrostructure in the proposed model. Model responses under the different hydromechanical loading paths are finally discussed and the model performance is investigated and validated via simulations of comprehensive tests on FEBEX bentonite. The simulation results demonstrate that the proposed model is able to reproduce various swelling behavior of compacted bentonite, including the swelling deformation under different constant stresses and the swelling pressure under the constant volume. In particular, the dry density effects can also be reproduced.

Fully coupled elastoplastic hydro‐mechanical analysis of unsaturated porous media using a meshfree method

SummaryThis paper presents the first application of an advanced meshfree method, ie, the edge‐based smoothed point interpolation method (ESPIM), in simulation of the coupled hydro‐mechanical behaviour of unsaturated porous media. In the proposed technique, the problem domain is spatially discretised using a triangular background mesh, and the polynomial point interpolation method combined with a simple node selection scheme is adopted for creating nodal shape functions. Smoothing domains are formed on top of the background mesh, and a constant smoothed strain, created by applying the smoothing operation over the smoothing domains, is assigned to each smoothing domain. The deformation and flow models are developed based on the equilibrium equation of the mixture, and linear momentum and mass balance equations of the fluid phases, respectively. The effective stress approach is followed to account for the coupling between the flow and deformation models. Further coupling among the phases is captured through a hysteretic soil water retention model that evolves with changes in void ratio. An advanced elastoplastic constitutive model within the context of the bounding surface plasticity theory is employed for predicting the nonlinear behaviour of soil skeleton. Time discretisation is performed by adopting a three‐point discretisation method with growing time steps to avoid temporal instabilities. A modified Newton‐Raphson framework is designed for dealing with nonlinearities of the discretised system of equations. The performance of the numerical model is examined through a number of numerical examples. The state‐of‐the‐art computational scheme developed is useful for simulation of geotechnical engineering problems involving unsaturated soils.

Experimental and Modeling Study of Soil Water Retention Curves of Compacted Bentonite considering Salt Solution Effects

Due to its low hydraulic conductivity, high swelling capacity, and good adsorption properties, the Gaomiaozi (GMZ) bentonite has been selected as potential buffer/backfill materials for construction of engineered barriers in the deep geological repository for disposal of high-level nuclear waste (HLW) in China. Investigation of salt solution effects on the water retention properties of compacted bentonite is of great importance in the context of geological disposal of HLW based on the multibarrier concept. In this study, amended specimens were obtained through a spray of different concentrations of salt solutions to reach target salt contents, respectively. With employment of the vapor phase technique for suction control, water retention tests were conducted on densely compacted GMZ bentonite (1.7 Mg/m3) with different salt contents under confined conditions. Corresponding soil water retention curves (SWRCs) were obtained. Analysis indicates that, for a given suction, the measured water content of GMZ bentonite specimen increases as the salt content (or pore fluid concentration) increases. The influencing rate depends on suction. For lower suctions (lower than 38 MPa), the water retention capacity increases as the salt content increases, while for higher suctions (higher than 38 MPa), the influence can be negligible. Based on the Fredlund and Xing (1994) equation, a soil water retention model was proposed for simulation of the SWRCs of compacted GMZ bentonite with consideration of pore fluid chemistry. Parameters were analyzed and determined with consideration of influences of the pore fluid concentration. Verification indicates that the SWRCs simulated by the proposed model are well agreed with the measured ones.

Finite element implementation of a fully coupled hydro-mechanical model and unsaturated soil analysis under hydraulic and mechanical loads

The finite element implementation of a fully coupled hydro-mechanical constitutive model Zhou et al. (2012a, b) is presented here. An explicit integration scheme with four main steps is adopted to integrate the constitutive relation coupling with the soil water retention model. The finite element program can simulate complex hydro-mechanical processes with highlights on flow-deformation coupling and hydraulic hysteresis. The performance of the developed program is validated at both element level (against unsaturated triaxial test results) and small-scale model set-up level (against 1-d consolidation, sand column and loading/wetting test results). Several applications for unsaturated soils are analysed, including: (1) equilibrium processes after fast-drying/wetting (1-d); (2) slow-loading after different suction histories (1-d, compared with the finite element results by Sheng et al. (2003b); and (3) a flexible footing (2-d) affected by a leaking underground pipe.

A new water retention model that considers pore non-uniformity and evolution of pore size distribution

Pore size distribution (PSD), which is usually measured using mercury intrusion porosimetry (MIP) tests, is often used to predict the water retention curve (WRC) of unsaturated soil. Existing models generally predict the drying path of the WRC only because the intrusion of non-wetting mercury in MIP tests is equivalent to air entry during drying. Moreover, the PSD changes under hydro-mechanical loads, which has a significant effect on water retention behaviour. In this study, a new model is developed to predict both the main drying and wetting paths of WRCs. Based on a single PSD at reference stress and suction conditions, we quantified the influence of pore non-uniformity on MIP test results and the main drying and wetting paths of WRCs using the new model. From the reference PSD, we determined variation in the PSD with stress and suction and incorporated this variation into modelling of the WRC. The newly developed model was applied to simulate the PSD variation and the hysteretic WRC of different soils. Based on the results, it is evident that the new model is able to capture the evolution of the PSD during drying, wetting and compression. Moreover, the main drying and wetting paths of WRCs of unsaturated soil were closely predicted.

A simple model for local-scale sensible and latent heat advection contributions to snowmelt

Abstract. Local-scale advection of energy from warm snow-free surfaces to cold snow-covered surfaces is an important component of the energy balance during snow-cover depletion. Unfortunately, this process is difficult to quantify in one-dimensional snowmelt models. This paper proposes a simple sensible and latent heat advection model for snowmelt situations that can be readily coupled to one-dimensional energy balance snowmelt models. An existing advection parameterization was coupled to a conceptual frozen soil infiltration surface water retention model to estimate the areal average sensible and latent heat advection contributions to snowmelt. The proposed model compared well with observations of latent and sensible heat advection, providing confidence in the process parameterizations and the assumptions applied. Snow-covered area observations from unmanned aerial vehicle imagery were used to update and evaluate the scaling properties of snow patch area distribution and lengths. Model dynamics and snowmelt implications were explored within an idealized modelling experiment, by coupling to a one-dimensional energy balance snowmelt model. Dry, snow-free surfaces were associated with advection of dry air that compensated for positive sensible heat advection fluxes and so limited the net influence of advection on snowmelt. Latent and sensible heat advection fluxes both contributed positive fluxes to snow when snow-free surfaces were wet and enhanced net advection contributions to snowmelt. The increased net advection fluxes from wet surfaces typically develop towards the end of snowmelt and offset decreases in the one-dimensional areal average melt energy that declines with snow-covered area. The new model can be readily incorporated into existing one-dimensional snowmelt hydrology and land surface scheme models and will foster improvements in snowmelt understanding and predictions.

Soil Water Retention: Uni‐Modal Models of Pore‐Size Distribution Neglect Impacts of Soil Management

Core Ideas A uni‐ and a bi‐modal soil water retention model were evaluated. The bi‐modal double‐exponential model fitted better to soil pore‐size distribution. The uni‐modal model fit was affected by texture, soil organic C, and tillage. Uni‐modal models are not well suited for describing the pore‐size distribution. Most models describing soil water retention imply a uni‐modal pore‐size distribution (PSD). The uni‐modal model presented by van Genuchten (termed vanG) is widely used although double‐exponential models (termed Dex) implying a bi‐modal PSD may better reflect reality. We tested the ability of vanG and Dex models to represent water retention in sandy top‐ and subsoils with different texture, in soil with contrasting management (Highfield), and in soil exposed to different tillage (Flakkebjerg). Soils were subjected to matric potentials from –10 hPa to –1.5 MPa. For all soils, the bi‐modal Dex model showed a better fit to water retention data than the uni‐modal vanG model. Neither of the models worked well for highly sorted soils. The vanG model gave a poorer fit for topsoils than for subsoils because of a more pronounced bi‐modality of the PSD in topsoils caused by larger soil organic carbon (SOC) content and tillage. For Highfield soils, the root mean squared error (RMSE) of the vanG fit increased from long‐term bare fallow (low C content, intensive tillage) to permanent grass (high C content, no tillage) reflecting a more distinct bi‐modality of the PSD for well‐structured soils. We conclude that uni‐modal models should be used with great caution when describing effects of texture and management on PSD and that bi‐modal models may provide a better fit to PSD.

A High‐Resolution Global Map of Soil Hydraulic Properties Produced by a Hierarchical Parameterization of a Physically Based Water Retention Model

AbstractA correct quantification of mass and energy exchange processes among Earth's land surface, groundwater, and atmosphere requires an accurate parameterization of soil hydraulic properties. Pedotransfer functions (PTFs) are useful in this regard because they estimate these otherwise difficult to obtain characteristics using texture and other ubiquitous soil data. Most PTFs estimate parameters of empirical hydraulic functions with modest accuracy. In a continued pursuit of improving global‐scale PTF estimates, we evaluated whether improvements can be obtained when estimating parameters of hydraulic functions that make physically based assumptions. To this end, we developed a PTF that estimates the parameters of the Kosugi retention and hydraulic conductivity functions (Kosugi, 1994, https://doi.org/10.1029/93WR02931, 1996, https://doi.org/10.1029/96WR01776), which explicitly assume a lognormal pore size distribution and apply the Young‐Laplace equation to derive a corresponding pressure head distribution. Using a previously developed combination of machine learning and bootstrapping, the developed five hierarchical PTFs allow for estimates under practical data‐poor to data‐rich conditions. Using an independent global data set containing nearly 50,000 samples (118,000 retention points), we demonstrated that the new Kosugi‐based PTFs outperformed two van Genuchten‐based PTFs calibrated on the same data. The new PTFs were applied to a 1 × 1 km2 global map of texture and bulk density, thus producing maps of the parameters, field capacity, wilting point, plant available water, and associated uncertainties. Soil hydraulic parameters exhibit a much larger variability in the Northern Hemisphere than in the Southern Hemisphere, which is likely due to the geographical distribution of climate zones that affect weathering and sedimentation processes.

Estimating Soil Water Retention Curve by Inverse Modelling from Combination of In Situ Dynamic Soil Water Content and Soil Potential Data

Soil water retention curves (SWRCs) are crucial for characterizing soil moisture dynamics, and are particularly relevant in the context of irrigation management. Inverse modelling is one of the methods used to parameterize models representing these curves, which are closest to the field reality. The objective of this study is to estimate the soil hydraulic properties through inverse modelling using the HYDRUS-1D code based on soil moisture and potential data acquired in the field. The in situ SWRCs acquired every 30 min are based on simultaneous soil water content and soil water potential measurements with 10HS and MPS-2 sensors, respectively, in five experimental fields. The fields were planted with drip-irrigated lettuces from February to March 2016 in the Chrey Bak catchment located in the Tonlé Sap Lake region, Cambodia. After calibration of the van Genuchten soil water retention model parameters, we used them to evaluate the performance of HYDRUS-1D to predict soil moisture dynamics in the studied fields. Water flow was reasonably well reproduced in all sites covering a range of soil types (loamy sand and loamy soil) with root mean square errors ranging from 0.02 to 0.03 cm3 cm−3.

Tensile strength during drying of remoulded and compacted clay: The role of fabric and water retention

Abstract The paper presents an experimental investigation on the tensile strength of an unsaturated clay, both in remoulded and compacted states. To complete the experimental study, a new apparatus was designed with the purpose of determining direct tensile stress under controlled-displacement or controlled-force. The design exploits a direct shear test box, which was adapted to the scope of this investigation. Three different hydro-mechanical paths were followed before the tensile strength was determined: a) drying paths on remoulded samples; b) drying paths after compaction at different initial water contents; and c) dynamic compaction at different water contents, hence at different suctions and degrees of saturation. A microstructural investigation was also performed to better understand the experimental results and obtain the most relevant physical parameters. The preparation methods induced different initial fabrics, which dominated the water retention properties, as well as the tensile strength behaviour. A recent model for water retention, including the effects of multimodal fabric, was calibrated on available data and used to predict the suction of the samples along the drying paths, where direct information was not available. A simple model for tensile strength was proposed for its evolution, which included the role of multimodal fabric and their different water storage capabilities, the evolution of dry density and the initial water content (at the beginning of the tensile test path). For the compacted sample, typically showing a multimodal pore size distribution, the tensile strength was found to be a function of the state variables describing the macropore network. Dry density increases on drying appeared in all the cases to dominate the tensile response, Water exchange and suction increase were well correlated to the tensile response evolution.

Biochar In Situ Decreased Bulk Density and Improved Soil-Water Relations and Indicators in Southeastern US Coastal Plain Ultisols

Biochar may improve soil physical properties for crop growth, but multiyear, multicrop field studies are lacking. To determine the effects of biochar on soil physical properties, we applied 0, 10, 20, 40, and 80 Mg ha biochar with/without NPK fertilizer to the surface 15 cm of 1 × 1 m plots in a single association of fine-loamy, siliceous, subactive, thermic Oxyaquic and Aquic Paleudults under a 2-year corn-winter wheat–double-crop soybean rotation. After 3 years, we sampled soil to 7.6 cm, measured bulk density and water retention, and then derived pore-size distribution and related physical and water retention model parameters. Fertilizer had little to no effect. Among the statistically significant results, biochar increased structural porosity (3- to 59-μm effective pore diameter [EPD]) but neither matrix- (0.2- to 3-μm EPD) nor macro (EPD >59 μm) porosity. Biochar ≥40 Mg ha decreased bulk density 16%; 80 Mg ha increased total porosity 14%. However, it also increased water content at −1,500 kPa 22.5%. Biochar ≥40 Mg ha increased the drained upper limit (DUL) by 15%; relative field capacity, 3%; and total and structural plant-available water (PAW: held between the DUL and −1,500 kPa), 7 and 18%, respectively. Increases were greatest at −10 kPa and least at −33 kPa. At −10 kPa, 80 Mg ha biochar increased total PAW 4.0-mm equivalent depth compared with 5.7 mm for structural PAW, approximately 0.5-day demand for actively growing corn. Modeled saturated water content increased with total porosity. Biochar improved plant-soil-water relations, but required high rates.

A Comprehensive Model for Single Ring Infiltration II: Estimating Field‐Saturated Hydraulic Conductivity

Core Ideas Four approaches were tested to estimate Kfs from single ring infiltration data. Highest accuracy occurred when capillary length was appropriately constrained. Kfs estimates improved if capillary length was overestimated vs. underestimated. Assuming a universal capillary length can also be useful for determining Kfs. Kfs can be accurately estimated using both early‐time and steady‐state data. In this study, we explored four approaches to infer field‐saturated hydraulic conductivity (Kfs) from both early‐time and steady‐state infiltration measurements using an explicit expression for three‐dimensional flow. All approaches required an estimate of the soil capillary length, λ. Approach 1 estimated Kfs via optimization, in which all other infiltration parameters (9 in total) were known. The remaining approaches constrained λ through different interpretations of coefficients generated by linear regression between infiltration and time. Approach 2 utilized these coefficients plus estimated soil water content to simultaneously quantify both λ and Kfs. Approach 3 used an analytical expression in which λ was estimated based on water retention/unsaturated hydraulic conductivity parameters, while Approach 4 adopted a universal λ value of 15 cm. The accuracy of these four approaches were tested using numerical and laboratory infiltration data. Approach 1 had the highest accuracy but also required the most auxiliary data, making it most suitable for laboratory and numerical experiments. Approach 2 was the least consistent, providing negative estimates for λ and Kfs under certain conditions. Approach 3 also gave accurate predictions of Kfs, but may be inaccurate in instances where the water retention model parameters are uncertain or do not describe soil hydraulic behaviors well. Approach 4 provided reasonable estimates of Kfs (within a factor of three from the actual value in most cases), while not requiring additional observational data. The optimal approach for interpreting Kfs will thus vary depending on the type and quality of available auxiliary data.

Arbuscular Mycorrhiza Alleviates Restrictions to Substrate Water Flow and Delays Transpiration Limitation to Stronger Drought in Tomato.

Arbuscular mycorrhizal fungi (AMF) proliferate in soil pores, on the surface of soil particles and affect soil structure. Although modifications in substrate moisture retention depend on structure and could influence plant water extraction, mycorrhizal impacts on water retention and hydraulic conductivity were rarely quantified. Hence, we asked whether inoculation with AMF affects substrate water retention, water transport properties and at which drought intensity those factors become limiting for plant transpiration. Solanum lycopersicum plants were set up in the glasshouse, inoculated or not with Funneliformis mosseae, and grown for 35 days under ample water supply. After mycorrhizal establishment, we harvested three sets of plants, one before (36 days after inoculation) and the second (day 42) and third (day 47) within a sequential drying episode. Sampling cores were introduced into pots before planting. After harvest, moisture retention and substrate conductivity properties were assessed and water retention and hydraulic conductivity models were fitted. A root water uptake model was adopted in order to identify the critical substrate moisture that induces soil derived transpiration limitation. Neither substrate porosity nor saturated water contents were affected by inoculation, but both declined after substrates dried. Drying also caused a decline in pot water capacity and hydraulic conductivity. Plant available water contents under wet (pF 1.8–4.2) and dry (pF 2.5–4.2) conditions increased in mycorrhizal substrates and were conserved after drying. Substrate hydraulic conductivity was higher in mycorrhizal pots before and during drought exposure. After withholding water from pots, higher substrate drying rates and lower substrate water potentials were found in mycorrhizal substrates. Mycorrhiza neither affected leaf area nor root weight or length. Consistently with higher substrate drying rates, AMF restored the plant hydraulic status, and increased plant transpiration when soil moisture declined. The water potential at the root surface and the resistance to water flow in the rhizosphere were restored in mycorrhizal pots although the bulk substrate dried more. Finally, substrates colonized by AMF can be more desiccated before substrate water flux quantitatively limits transpiration. This is most pronounced under high transpiration demands and complies with a difference of over 1,000 hPa in substrate water potential.

Parametric soil water retention models: a critical evaluation of expressions for the full moisture range

Abstract. Few parametric expressions for the soil water retention curve are suitable for dry conditions. Furthermore, expressions for the soil hydraulic conductivity curves associated with parametric retention functions can behave unrealistically near saturation. We developed a general criterion for water retention parameterizations that ensures physically plausible conductivity curves. Only 3 of the 18 tested parameterizations met this criterion without restrictions on the parameters of a popular conductivity curve parameterization. A fourth required one parameter to be fixed. We estimated parameters by shuffled complex evolution (SCE) with the objective function tailored to various observation methods used to obtain retention curve data. We fitted the four parameterizations with physically plausible conductivities as well as the most widely used parameterization. The performance of the resulting 12 combinations of retention and conductivity curves was assessed in a numerical study with 751 days of semiarid atmospheric forcing applied to unvegetated, uniform, 1 m freely draining columns for four textures. Choosing different parameterizations had a minor effect on evaporation, but cumulative bottom fluxes varied by up to an order of magnitude between them. This highlights the need for a careful selection of the soil hydraulic parameterization that ideally does not only rely on goodness of fit to static soil water retention data but also on hydraulic conductivity measurements. Parameter fits for 21 soils showed that extrapolations into the dry range of the retention curve often became physically more realistic when the parameterization had a logarithmic dry branch, particularly in fine-textured soils where high residual water contents would otherwise be fitted.

Fractal-based models for the unsaturated soil hydraulic functions

Reliable estimates of the unsaturated soil hydraulic properties are needed in many research and engineering projects. Fractal based approaches have become popular for describing the hydraulic functions. New models based on fractal geometry are presented to describe the wetting phase relative permeability (unsaturated hydraulic conductivity) of porous media. Analytical expressions were derived using the fractal capillary pressure (water retention) model proposed by Alfaro Soto and Vilar (2006) and the statistical pore size distribution models of Mualem (1976a) and Burdine (1953) for the unsaturated hydraulic conductivity. The newly derived models provide predictions of the relative permeability to water, as well as of the fractal dimension for modeling the pore structure of a soil. Results are compared with previous formulations by Brooks and Corey (1964), van Genuchten (1980) and Kosugi (1996), as well as with experimental water retention and hydraulic conductivity data of four soils having widely different soil textures. The proposed models agreed closely with observed data. The analytical models may be attractive alternative for estimating the unsaturated hydraulic conductivity when no laboratory or field measurements are available.

Water retention model for compacted bentonites

The water retention behaviour of compacted bentonites is strongly affected by multi-physical and multi-scale processes taking place in these materials. Experimental data have evidenced major effects of the material dry density, the imposed volume constraints, and the soil fabric. This paper presents a new water retention model accounting for proper retention mechanisms in each structural level of compacted bentonites, namely adsorption in the intra-aggregate pores and capillarity in the inter-aggregate ones. The model is calibrated and validated against experimental data on different bentonite-based materials, showing good capabilities in capturing the main features of the behaviour. The model is able to reproduce experimental data on compacted bentonites over a wide range of suction values, within a unified framework, and using a limited number of parameters. Some of the parameters introduced are shown to take approximately the same value for several bentonites, providing a significant basis for preliminary design when dedicated experiments are missing.