Water Retention Model Research Articles

A numerical analysis of Thermo–Hydro–Mechanical behavior in the FE experiment at Mont Terri URL: Investigating capillary effects in bentonite on the disposal system

We investigated thermo–hydro–mechanical (T-H–M) coupled behavior observed during the full-scale heater emplacement experiment at the Mont-Terri underground research laboratory conducted in the Opalinus clay as part of the DECOVALEX-2023 Task C project. Utilizing the OGS-FLAC simulator, we created a three-dimensional model to simulate multiphase flow in the experiment, applying extended Philip and de Vries’ model and incorporating the anisotropic T–H–M properties of the Opalinus clay. The simulation, which included a ventilation process, spanned five years of heating experiments and successfully replicated the measured temperature, pore pressure, displacement, and relative humidity results in bentonite and host rock during the experiment. The analysis revealed that capillary pressure significantly influenced the pore pressure change in the host rock near the tunnel, while thermal pressurization became dominant with increasing distance. Consequently, we conducted a sensitivity analysis on a simplified model to evaluate the effect of capillary pressure on the disposal system. Capillarity is a dominant factor for the multiphase flow depending on the distance from the heat. Variations in capillary pressure were observed depending on the gas entry pressure and water retention model, indicating that the capillarity of unsaturated bentonite could inherently affect the T–H–M results within the disposal system.

A state-dependent bimodal soil water retention model considering evolutions of pore-scale soil–water interaction

Existing soil water retention models can capture the effects of void ratio and/or net mean stress on the changes in soil water retention curve (SWRC). However, most of them, especially those for bimodal soil that is composed of macro- and micro-pore systems, do not consider the simultaneous evolutions of pore structure and particle contacts, and neglected the drainage processes of bulk water and meniscus water when subjected to any external hydro-mechanical loading condition. This paper proposes a state-dependent bimodal SWRC model considering pore structure evolution and pore-scale water drainage. In this model, an elastoplastic relationship is introduced to describe the variations of void ratio with net mean stress and suction, whilst the corresponding changes in the pore structure are modelled by the shift and scaling of the pore-size distribution and the volumetric proportion between the macro- and micro-pore systems. By relating stress-induced changes in void ratio and coordination number to the mean pore radius and total meniscus water volume, respectively, the soil water content at different stages of water drainage can be determined. The model is validated against existing and new data, and can capture the effects of void ratio, isotropic stress, and K0 stress for unimodal and bimodal soils.

Influence of dry density and wetting–drying cycles on the soil–water retention curve of compacted loess: experimental data and modeling

AbstractIn this paper, the EC-5 water sensor and the MPS-6 water potential sensor were used to measure water content and suction, respectively, to investigate the evolution of soil–water retention properties of compacted loess samples prepared at different dry densities and subjected to different numbers of wetting–drying cycles. The water retention data were integrated with a detailed microstructural investigation, including morphological analysis (by scanning electron microscopy) and pore size distribution determination (by nuclear magnetic resonance). The microstructural information obtained shed light on the double porosity nature of compacted loess, allowing the identification of the effects of compaction dry density and wetting–drying cycles at both intra- and inter-aggregate levels. The information obtained at the microstructural scale was used to provide a solid physical basis for the development of a simplified version of the water retention model presented in Della Vecchia et al. (Int J Numer Anal Meth Geomech 39: 702–723, 2015). The model, adapted for engineering application to compacted loess, requires only five parameters to capture the water retention properties of samples characterized by different compaction dry densities and subjected to different numbers of wetting–drying cycles. The comparison between numerical simulations and experimental results, both original and from the literature, shows that only one set of parameters is needed to reproduce the effects of dry density variation, while the variation of only one parameter allows the reproduction of the effects of wetting and drying cycles. With respect to the approaches presented in the literature, where ad hoc calibrations are often used to fit density and wetting–drying cycle effects, the model presented here shows a good compromise between simplicity and predictive capabilities, making it suitable for practical engineering applications.

Data-driven discovery of interpretable water retention models for deformable porous media

The water retention behavior—a critical factor of unsaturated flow in porous media—can be strongly affected by deformation in the solid matrix. However, it remains challenging to model the water retention behavior with explicit consideration of its dependence on deformation. Here, we propose a data-driven approach that can automatically discover an interpretable model describing the water retention behavior of a deformable porous material, which can be as accurate as non-interpretable models obtained by other data-driven approaches. Specifically, we present a divide-and-conquer approach for discovering a mathematical expression that best fits a neural network trained with the data collected from a series of image-based drainage simulations at the pore-scale. We validate the predictive capability of the symbolically regressed counterpart of the trained neural network against unseen pore-scale simulations. Further, through incorporating the discovered symbolic function into a continuum-scale simulation, we showcase the inherent portability of the proposed approach: The discovered water retention model can provide results comparable to those from a hierarchical multi-scale model, while bypassing the need for sub-scale simulations at individual material points.

Performance of a Set of Soil Water Retention Models for Fitting Soil Water Retention Data Covering All Textural Classes

A clean environment is an essential component of sustainable development, which is based on a comprehensive understanding of the behavior of water, soil, and air. The soil water retention (SWR) curve is a crucial function that describes how soil retains water, playing a fundamental role in irrigation and drainage, soil conservation, as well as water and contaminant transport in the vadose zone. This study evaluates the accuracy, performance, and prediction capabilities of 15 SWR models. A total of 140 soil samples were collected from different sites, covering all textural classes. Standard suction tests, using both hanging column and ceramic pressure plate extractors, were conducted to compile the SWR databank. 15 SWR models were selected and fitted to the SWR data points. Soil texture, bulk density, and organic matter were used to determine their effect on the performance of the SWR models. The results indicate that the Tani and Russo models exhibit the lowest levels of accuracy and performance among the selected models. Based on the Akaike and Bayesian information criteria analysis, the van Genuchten model exhibits the lowest values among the selected models, with poor prediction capabilities in estimating the SWR curve. The significance test at the 0.05 level (95% confidence interval) shows that according to the calculated p-values for the Pearson correlation coefficient between RMSE and texture, the Brooks-Corey and van Genuchten models are poorly influenced by soil properties. The performance of the models is not significantly affected by the soil organic matter. Similarly, bulk density does not significantly affect model performance except for the Brooks–Corey, van Genuchten, Tani, and Russo models. Among the SWR models considered, the double exponential, Groenevelt and Grant, and Khlosi et al. models demonstrate superior accuracy and performance in predicting the SWR curve. This is supported by lower values for RMSE, Akaike, and Bayesian information criteria.

Probabilistic analysis of a sustainable landfill cover considering stress-dependent water retention model and copula-based random fields

Material properties, crucial design parameters in landfill cover systems, can exhibit spatial variability due to non-uniform particle size and uneven compaction, affecting cover performance. Additionally, cover thickness, another key design parameter, can induce stress variation and influence soil-water retention capability. Previous designs always ignored these uncertainties and stress effects, potentially leading to unreasonable design schemes. This study aims to provide design recommendations for a three-layer landfill cover system under heavy rainfall, considering these factors simultaneously by the random finite element method (RFEM). The stress effects are captured using a stress-dependent soil-water retention curve (SDSWRC) and the hysteresis in the SDSWRC is considered in probabilistic analyses. For practical applications, uncertainties in two easily controllable particle size parameters, D10 and D60, are depicted by copula-based cross-correlated random fields. Based on empirical equations, the spatial variability of SDSWRC and water permeability function (WPF) can be further characterised by D10 and D60 random fields. It is found that considering SDSWRC and its spatial variability (e.g., shape) can overestimate percolation by at least 1.7 times compared to deterministic analysis using SWRC. The spatial variability of SDSWRC shape has a more significant impact than spatially variable saturated water permeability on cover system performance. Among candidate copulas, the CClayton copula (survival copula of Clayton copula) yields the most conservative results due to its upper tail dependence. The particle size and thickness of the bottom layer influence the cover system performance more than the upper two layers. A bottom layer with D10≤ 0.009 mm and D60/D10≥ 7.54, and thickness ≥ 0.8 m is recommended to achieve a satisfactory performance level with a 100-year design life.

A graph-based approach for modeling the soil–water retention curve of granular soils across the entire suction range

This study investigates experimentally the water retention behavior of granular soils from saturation to oven-dry state. The soil–water retention curve (SWRC) tests were conducted on a well-graded sand with clay using tensiometer and chilled-mirror hygrometer techniques. The soil samples were statically compacted at various water contents to different initial densities. The results showed that individual linear segments in the log–log graph could characterize the desorption process of capillary and adsorption water. A novel water retention model in a simple mathematical form was developed by conceptualizing the total water content as the sum of the suction-dependent capillary and adsorption components. The model parameters possess an unambiguous physical meaning. They can be easily calibrated based on the graphical properties of the test data using simple linear regression, which is a significant advantage over conventional SWRC models. The model was validated using the water retention data of the tested soil in this study and the available data of granular soils in the literature. The reproduced curves agree well with the experimental results. This study also analyzed the influence of compaction water content, initial density, and clay content on the capillary and adsorption components of the water retention curve. Additionally, the proposed framework provides a quick approximation method for the adsorption capacity, which plays an essential role in assessing the effective stress and the simulation of liquid film flow in unsaturated granular soils.

Modelling of preferential gas flow in saturated bentonite using a bimodal, strain-dependent pore model

This paper presents a novel strain-dependent water retention model for improved predictive modelling of localized gas flow in bentonite. The proposed model uses fundamental material properties such as dry density and montmorillonite content to generate improved predictions of water retention under different strain conditions. The model was validated with the use of laboratory measurements of capillary pressure in MX-80 bentonite at different dry densities. An additional phenomenological test simulated microfracture induced gas flow in FEBEX bentonite, which showed strong local desaturation due to developing microfractures and a resulting decreasing gas entry pressure. The application of the approach provided first good results that can be relevant for modelling radioactive waste repositories.

A generalized water retention model in a wide suction range considering the initial void ratio and its verification

A generalized water retention curve (WRC) model in a wide suction range considering the initial void ratio is presented in this paper. Both capillary and adsorbed water in soil pores are considered. Based on the experimental results that the adsorbed water content wa is not dependent on the initial void ratio, a new degree of saturation equation of adsorbed water is established. Meanwhile, a new degree of saturation equation of capillary water at various initial void ratios is proposed with a void ratio-related expression of the air entry value. Compared to Lu’s model, only one parameter b is introduced in the established model, which can be easily calibrated using WRCs under two initial void ratios. The measured WRC results of 5 soils are used to verify the proposed model in comparison with the other 3 widely used WRC models. The soil used in the model validation covers a wide range of soil types from sandy soil to clay soil, including clayey silty sand, sandy clay till, clayey silt, expansive soil and lateritic soil. The proposed model is well verified for its ability to describe soil water retention characteristics in a wide suction range at various initial void ratios.

Exploring soil water retention hysteresis in the entire suction range and microstructure evolution of loess: The influence of sediment depths

Sediment depths can influence both soil structure and hydraulic processes, resulting in diverse soil-water retention properties. This study aimed to investigate the impact of sediment depths on soil-water retention hysteresis across the entire suction range, as well as the microstructure evolution of loess during the drying-wetting cycle. Laboratory tests were conducted to achieve this objective. The test results demonstrated that the water retention properties of the natural loess were significantly affected by sediment depths over the entire suction range. And the tested samples shrank considerably due to drying, while the swelling curves were almost linear induced by the wetting. Besides, the commonly used four water retention models were adopted to fit the test data, and Zhou's model showed the best-fitting performance. Furthermore, the local degree of hysteresis in the low suction range was generally larger than that in the high suction range for all samples, and the minimum local degree of hysteresis corresponded to the in-situ suction of tested samples. The average degree of hysteresis of JY-5 m, JY-15 m, and JY-30 m samples were 0.12, 0.14, and 0.13 respectively. Regarding microstructure change, the void ratios (which were smaller than the actual void ratios of soil samples) measured by the mercury intrusion porosimetry (MIP) tests became larger after undergoing the drying-wetting cycle, and most of the increased pores were primarily attributed to the formation of small mesopores in the vicinity of the main capillary pores. The results of this study contribute valuable insights into the dynamics of soil-water retention hysteresis and the associated microstructure evolution of loess.

Double porosity water retention model for bentonite-based clays with deformation considered

Double porosity water retention model for bentonite-based clays with deformation considered

Analytical solutions for steady vertical flux through unsaturated soils with generalized hydraulic properties

In this paper, analytical solutions for one-dimensional nonlinear steady-state vertical flux through unsaturated soils are presented. The analytical solutions are applicable for homogeneous soils for which the hydraulic conductivity function is a generalized form of the well-known Brooks-Corey and rational models. The adopted generalized soil–water retention model involves two additional parameters which reflect the curvature of hydraulic functions near saturation. The main advantage of the used generalized hydraulic conductivity function is that it fits better experimental data. The soil domain is a finite-depth medium overlying a fixed groundwater level. The derived analytical solutions are obtained using the Maclaurin series expansion technique. Analytical solutions for both infiltration and evaporation are developed. For evaporation from a fixed groundwater level, the derived solutions can be used to predict the existence of a vaporization plane below the soil surface. For this case, analytical expression of the position of drying front separating liquid and gas regions is derived. The analytical results are compared to numerical ones for various infiltration and evaporation examples and excellent agreements are obtained. The generalized model is also used to fit experimental data obtained for two soils. The results show that the use of the standard Brooks-Corey model may lead to an overestimation of the position of the drying front.

Modelling the viscoplastic behaviour of Callovo-Oxfordian claystone with consideration of damage effect

In order to evaluate the performance of deep geological disposal of radioactive waste, an underground research laboratory (URL) was constructed by Andra in the Callovo-Oxfordian (COx) claystone formation at the Meuse/Haute-Marne (MHM). The construction of URL induced the excavation damage of host formations, and the ventilation in the galleries desaturated the host formation close to the gallery wall. Moreover, it is expected that the mechanical behaviour of COx claystone is time-dependent. This study presents a constitutive model developed to describe the viscoplastic behaviour of unsaturated and damaged COx claystone. In this model, the unsaturation effect is considered by adopting the Bishop effective stress and the van Genuchten (VG) water retention model. In terms of the viscoplastic behaviour, the nonstationary flow surface (NSFS) theory for unsaturated soils is used with consideration of the coupled effects of strain rate and suction on the yield stress. A progressive hardening law is adopted. Meanwhile, a non-associated flow rule is used, which is similar to that in Barcelona basic model (BBM). In addition, to describe the damage effect induced by suction change and viscoplastic loading, a damage function is defined based on the crack volume proportion. This damage function contains two variables: unsaturated effective stress and viscoplastic volumetric strain, with the related parameters determined based on the mercury intrusion porosimetry (MIP) tests. For the model validation, different tests on COx claystone under different loading paths are simulated. Comparisons between experimental and simulated results indicated that the present model is able to well describe the viscoplastic behaviour of damaged COx claystone, including swelling/shrinkage, triaxial extension and compression, and triaxial creep.

A simple water retention model of dual-porosity soils based on self-similarity of bimodal pore size distribution

The bimodal characteristic of water retention curves of dual-porosity soils has been fully recognized, however, the excessive number of fitted parameters in the existing models limits their application. This study develops a simple water retention model for dual-porosity soils that considers the self-similar characteristics of the pore size distribution (PSD) between macropore and micropore regions. In the model, we simulate the macropore PSD by differential VG model, which is then shifted and scaled to capture micropore PSD. It is hypothesized that the bimodal PSD can be obtained by superimposing the PSDs of macropore and micropore regions to derive the bimodal water retention curve (BWRC). The mercury intrusion porosimetry (MIP) tests and water retention tests are conducted on Nanyang clay with three different dry densities to evaluate the proposed BWRC. The results show that the new parameter can be determined by the MIP dataset and then used to predict the water retention behavior of dual-porosity soils well. Finally, we also explore the application of the proposed BWRC in predicting the hydraulic conductivity of dual-porosity soils without adding any extra parameters.

Scale-Dependent Field Partition Based on Water Retention Functional Data

Functional data are being used increasingly in recent years and in many environmental sciences, such as hydrology applied to agriculture. This means that the output, instead of a scalar variable represented by a spatial map, is given by a function. Furthermore, in site-specific management, there is a need to delineate the field into management areas depending on the agricultural procedure and on the scale of application. In this paper, an approach based on multivariate geostatistics is illustrated that uses the parameters of Dexter’s water retention model and some soil properties to arrive at a multiscale delineation of an agricultural field in Iran. One hundred geo-referenced soil samples were taken and subjected to various measurements. The volumetric water contents at the different suctions were fitted to Dexter’s model. The estimated curve parameters plus the measurements of the soil variables were transformed into standardized Gaussian variables and the values transformed were subjected to geostatistical cokriging and factorial cokriging procedures. These results show that soil properties (organic carbon, bulk density, saturated hydraulic conductivity and tensile strength of soil aggregates) influence the parameters of Dexter’s model, although to different extents. The thematic maps of both soil properties and water retention curve parameters displayed a varying degree of spatial association that allowed the identification of homogeneous areas within the field. The first regionalized factors (F1) at the scales of 508 m and 3000 m made it possible to provide different delineations of the field into homogeneous areas as a function of scale, characterized by specific physical and hydraulic properties. F1 at a short and long distance could be interpreted as “porosity indicator” and “hydraulic indicator”, respectively. Such type of field delineation proves particularly useful in sustainable irrigation management. This paper emphasizes the importance of taking the spatial scale into account in precision agriculture.

A soil-brine retention model for wetting processes considering the hysteresis effects

Wetting hydrological processes are relevant to a considerable number of natural hazards, including landslides, dam breaks, surface runoff after floods, etc. The notable difference between wetting and drying soil–water retention curves (SWRC) has been attributed to the hysteresis phenomenon. Although recent studies confirm enhanced impurity levels of permeating fluid, most modeling approaches simply consider water retention along the drying path and neglect the impurity of pore water. Therefore, the main objective of this paper is to introduce a new water retention model along the wetting path by taking the osmotic potential into account, reflecting the influence of dissolved salts. The new model, referred to as the soil-brine retention curve (SBRC) was developed based on the 1980 van Genuchten model (VG). The results reveal the robustness of the model in predicting the experimental wetting retention data for different soil types exposed to both saline and distilled water. Statistical analysis confirms the capability of the new model with an average R2 of 0.97 and RMSE of 0.047. The wetting branch can be estimated based on an existing drying curve, assuming predefined values of entrapped air and air expulsion value. However, a more reliable prediction can be made if two extra parameters of entrapped air and air expulsion are calibrated for the pure water wetting curve. Furthermore, for the case of saline water, the wetting SBRC can be estimated using one more parameter than those used for pure water.

A hydro-mechanical constitutive model for unsaturated soils over a wide saturation range

A hydro-mechanical constitutive model for unsaturated soils is proposed to describe the hydraulic and mechanical behaviour over a wide saturation range. Bishop’s effective stress and the effective degree of saturation are taken as the basic constitutive variables. A simple and novel loading-collapse yield curve is constructed to capture the variation of the yield stress with the hydraulic state over a wide saturation range. A non-orthogonal plastic flow rule is adopted to obtain the direction of the plastic strain increment. A simple water retention model is developed to describe the hydraulic behaviour of unsaturated soils. The proposed constitutive relation is presented through the calculation of the total strain increment and the calculation of the increment of the effective degree of saturation. All material parameters can be determined through conventional laboratory tests. The performance of the proposed model is illustrated through numerical examples of three classical stress paths, i.e., the isotropic compression path with constant suction, the wetting path with constant net stress, and the triaxial shearing path with constant suction and mean net stress. The capability of the proposed model to capture the hydraulic and mechanical behaviour of unsaturated soils is validated by simulating the test results from the literature.

A Family of Soil Water Retention Models Based on Sigmoid Functions

AbstractThe soil water retention curve is the fundamental soil hydraulic property to characterize soil water movement and solute transport. Many efforts have been devoted in the past decades to developing models to describe soil water retention curves. However, most of them are empirical equations or assume that soil pore size distributions conform to a lognormal distribution. Yet, few effects have been undertaken to systematically propose and compare a series of possible alternative probability density functions to describe the sigmoid retention curves with parameters physically explainable. Here, we proposed a family of five soil water retention models based on sigmoid functions with parameters of clear physical implications coinciding with the statistical measures of soil pore size distribution. Compared with the widely used models (i.e., Brooks & Corey, 1964; Kosugi, 1996; van Genuchten, 1980), the proposed models have somewhat improved performances to characterize water retention data for a wide range of soil textures without introducing additional model parameters. Two of the proposed models are capable of characterizing the observed two local extrema in the moisture capacity curves. The associated unsaturated hydraulic conductivity models of the proposed soil water retention models are also derived, which show superior performance in characterizing the observed hydraulic conductivities compared with competing models, especially in macropore regimes. Additionally, we analyzed the parameter‐equivalent conversion between the proposed and the existing models, and a simple linear regression equation can be used to derive the parameters of the proposed models from the existing and other alternative different proposed models.

Numerical Investigation of Saturated-Unsaturated Flow and Stability Analysis of Tailings Dams Considering the Influence of Saline Solutions

A tailings dam is normally constructed through self-consolidation with minimum compaction effort. Accordingly, special attention to the ultimate limit design in assessing the tailings dam instability condition is of primary importance. Furthermore, the existence of pore fluid chemical contaminants with high concentrations makes soil hydraulic and shear resistance properties subject to considerable changes.Therefore, this study aims to investigate the stability of a tailing dam using saturated-unsaturated flow analysis under 0.2 and 0.6 M sodium chloride solutions and pure water as a benchmark. To make the analyses as realistic as possible, recently developed solute-dependent hydraulic conductivity and water retention models are embedded into the numerical software. The results show that the saline-based model has higher pore water pressure than the pure water model due to more rainfall penetration by increasing the pore fluid salt concentration. Furthermore, increasing salt solution concentration enhances the tailing dam's drainagecondition, which leads to an increase in the dam's shear strength and, consequently, the factor of safety. Therefore, the stability of the tailings dam is improved by the combined impact of salt on both the flow and strength.

Comparison of Five Models for Estimating the Water Retention Service of a Typical Alpine Wetland Region in the Qinghai–Tibetan Plateau

Model evaluation of water retention (WR) services has been commonly applied for national or global scientific assessment and decision making. However, evaluation results from different models are significantly uncertain, especially on a small regional scale. We compared the spatial–temporal variations and driving factors of the WR service by five models (i.e., the InVEST model (InVEST), precipitation storage model (PRS), water balance model I (WAB I), water balance model II (WAB II), and NPP-based surrogate model (NBS) based on partial correlation analysis and spatial statistics on the Ramsar international alpine wetland region of the Qinghai–Tibetan Plateau (QTP). The results showed that the wetland area continued to decrease, and built-up land increased from 2000 to 2015. The average WR volume ranged from 2.50 to 13.65 billion m3·yr−1, with the order from high to low being the PRS, WAB I, WAB II, and InVEST models, and the average total WR capacity was 2.21 × 109 by the NBS model. The WR service followed an increasing trend from north to south by the InVEST, PRS, WAB I, and WAB II models, while the NBS model presented a river network pattern of high values. The WR values were mainly reduced from 2000 to 2010 and increased from 2010 to 2015 in the PRS, WAB I, WAB II, and InVEST models, but the NBS model showed the opposite trend. Precipitation determined the spatial distribution of WR service in the InVEST, PRS, WAB I, and WAB II models. Still, the spatial variation was affected by climate factors, while the NPP data influenced the NBS model. In addition, the InVEST model in estimating WR values in wetlands and the PRS and WAB I models poorly estimate runoff, while the WAB II model might be the most accurate. These findings help clarify the applicability of the WR models in an alpine wetland region and provide a valuable background for improving the effectiveness of model evaluation.