Soil Water Retention Curve Model Research Articles

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

AbstractThis 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.

Investigation on strength and deformation properties of lateritic clay

Lateritic clay is often used as a construction material for roads in tropical and subtropical areas. However, these materials exhibit high compressibility, high rate of creep, and susceptibility to severe cracking due to swelling and shrinkage behavior. These traits are closely linked to its hydro-mechanical and deformation properties. In this study, firstly, a boundary line between the swelling and compression deformation zone was determined based on the results of wetting tests. This boundary line is crucial for identifying the specific deformation mechanisms observed in unsaturated lateritic clays under varying water conditions. Secondly, an analysis of the relationship between pore size distribution and the soil water retention curve (SWRC) were conducted. A simple bimodal SWRC model, using the normal distribution function, was proposed. Additionally, the strength characteristics of lateritic clay were investigated over a wide suction range. It was observed that the existing strength model significantly underestimated the tested values in the medium to high suction range. To address this, a segmented strength equation was introduced based on unsaturated effective stress analysis. This approach allows enables enhanced predictions of the strength properties of lateritic clay. Altogether, these findings have greatly contributed to a better understanding of the engineering properties of lateritic clay.

Soil–Water Retention Curve Prediction for Compacted London Clay Subjected to Moisture Cycles

The evolution of the hydraulic properties of London Clay when compacted at a range of initial conditions (density and water content) was investigated. The soil–water retention curve (SWRC) is observed to change as the soil is subjected to cycles of wetting and drying. A new method is presented for predicting these changes in the soil–water retention curves (SWRCs) based on the starting conditions for each cycle. The method is based on relationships between the degree of saturation before drying (Sr,i), which includes the effect of void ratio and soil fabric, and key parameters that characterize the shape of SWRCs (air-entry value and slope of the transition zone). The relationship between the Sr,i and the air-entry value (or yield point, YP), and the relationship between the YP and the slope of the transition zone of the SWRC were established for the large experimental data set of two types of London clay of high and very high plasticity. The fitting parameters of a bi-linear SWRC model were estimated and used to constrain the fitting parameters of the van Genuchten model. As the SWRC of compacted clay continuously changes with progressive moisture cycles, this model allows the prediction of this evolution for the modelling of earthworks over the years, when subject to changing climatic conditions, without the need for an extensive experimental program.

A simple method to determine soil–water retention curves of compacted active clays

Determining the Soil Water Retention Curve (SWRC) of an active clay constitutes a challenge due to the significant, and sometimes irreversible, volume changes that occur during wetting and drying cycles. A novel yet simple method of experimentally determining the evolution of the SWRCs with moisture cycles is presented based on the results of a rigorous experimental study. Its purpose is to support the modelling of water flux in earthworks exposed to weather cycles that cause deterioration. Firstly, three SWRC branches (the primary drying, a scanning drying, and a scanning wetting branch) are measured and used to fit the proposed generic SWRC semi-empirical model in terms of water ratio, that, in the adsorptive region, is independent of the compaction conditions (void ratio and water content at compaction). Soil Shrink-Swell Curves (SSSCs) in terms of water ratio versus void ratio, that are easy to measure, can be determined for different compaction conditions over several drying and wetting cycles. Finally, the SSSCs are combined with the generic SWRC model to determine the evolution of the SWRCs with moisture cycles for the compaction conditions of interest. This method is demonstrated for two London clays of high and very high plasticity. Samples were compacted in five different conditions, varying in gravimetric water content and dry density, and were cycled six times between 1 and 80 MPa of total suction. The generic SWRC model was fitted to the experimental data. The model was able to estimate the SWRC in terms of degree of saturation over the six drying-wetting cycles without propagation of error. The significance of the research is that SWRC can now be determined over a range of wetting and drying cycles quickly and simply and enable modelling of deterioration of clays fills due to the action of weather to be accurate.

Permanent deformation of unsaturated granular material under multiple drying and wetting cycles

Abstract This investigation proposes an empirical–analytical model for the soil–water retention curve (SWRC) as well as the permanent deformation prediction of unsaturated granular materials under multiple hydraulic cycles. To calibrate and verify the proposed approach, the normalized SWRC model was firstly applied to predict the normalized SWRCs of two unsaturated soils under multiple drying and wetting cycles. The predicted and experimental results showed a good correspondence of the model. The normalized permanent deformation model is subsequently used to estimate the final permanent deformations of two granular materials (clay-crushed tuff aggregates (CTAs) mixture and Missillac sand), with suction under multiple drying and wetting cycles. The results showed that the proposed approach can effectively evaluate the normalized SWRCs and the final permanent deformations of the studied granular materials.

Temperature effects on the hydraulic properties of unsaturated rooted soils

Soil temperature of vegetated landfill earthen covers varies with time during their service, due to heat released by the degradation of municipal solid waste. In this study, an experimental campaign to capture soil water-retention curve (SWRC) and hydraulic conductivity function (HCF) of unsaturated rooted soils was conducted at different temperatures (25, 45, and 60 °C). Simplified evaporation tests were conducted by subjecting soil specimens to a prolonged drying period at maintained temperature. Based on the responses of matric suction and water content, SWRC and HCF were determined by the instantaneous profile method. It was found that increasing temperature reduced water-retention capacity, due to root shrinkage, thermal expansion of liquid phase, and reduction in forces of capillarity and adsorption. Soil hydraulic conductivity was enhanced by the increase in soil temperature due to reduction of water viscosity and potential preferential flow at root channels induced by root shrinkage. Temperature effects on SWRC and HCF of rooted soils are suction-dependent. A new nonisothermal SWRC model was developed to capture the dual effects of roots and temperature. By using the same set of calibrated parameters, the model demonstrates its ability to predict SWRCs reasonably well within the range of temperature investigated.

Bayesian reliability-based prediction of the soil water retention curve using finite data

The soil water retention curve (SWRC) is a core concept of unsaturated soil mechanics. To date, while various SWRC prediction models have been developed, they require large datasets to generate accurate results. Most importantly, and uncoincidentally, obtaining large SWRC datasets from experimental procedures might prove costly, time-consuming, and sometimes rigorous; thus, making only limited data available for use. However, determining the inherent uncertainties in predictions when using finite data has been elusive. To address this problem, we propose a reliability-based approach using a Bayesian framework that is logical and rigorous for quantifying uncertainty in model parameters. The proposed Bayesian method is Hamiltonian Monte Carlo (HMC). The HMC is a Markov chain Monte Carlo (MCMC) method that applies the Hamiltonian dynamics to solve and update posterior distributions in Bayesian analysis. Different SWRC datasets and models were used to validate and test the efficacy and robustness of the model in making predictions. The results show that the method is so robust that even imperfect prior knowledge provides reliable SWRC prediction results comparable with other methods. Furthermore, computation time and cost are significantly reduced because of the small (MCMC) sample size required to complete numerical solutions.

Parameter estimation of soil water retention curve with Rao-1 algorithm

The soil water retention curve (SWRC) has a significant role in determining the unsaturated properties of soil. A stochastic optimization algorithm named Rao-1 algorithm is employed to estimate the parameters of the SWRC model in this paper. The Rao-1 algorithm is a simple heuristic search algorithm containing only addition and multiplication operations. This paper introduces the method and its application in the determination of soil water retention model parameters in detail. In this study, van Genuchten model is used to depict the SWRC for its good fitting capacity, and parameters of the van Genuchten model are determined using Rao-1 algorithm. The feasibility and efficiency of the method are validated via the experimental results of 24 soil samples of 12 soil textural classes. Besides, the performance of Rao-1 algorithm is compared with that of Particle Swarm Optimization algorithm, Differential Evolution algorithm, and RETC program. Through comparative analysis, Rao-1 algorithm outperforms other methods in determining SWRC parameters.

A novel unified model for volumetric hardening and water retention in unsaturated soils

This paper presents a novel unified model coupling soil volumetric hardening and water retention. The volumetric hardening law is formulated using the effective stress concept and can be applied to various soil types with unified formulations. This law also considers the influence of stress-induced anisotropy, and provides an enhanced prediction of soil response under elevated stress levels and loading–unloading cycles. Furthermore, this law is coupled with a new Soil Water Retention Curve (SWRC) model by considering the dependency of SWRC on the volume change. The new SWRC model captures the hysteretic nature of the water retention, and offers an improved prediction of the hydraulic path for high suction levels. The SWRC model also allows capturing the experimentally observed reduction in the degree of saturation which may occur during the early compression stage under constant suction. With the coupling of the volumetric hardening law and the SWRC model, the unified model is finally developed. The unified model is validated with reasonable accuracy against a wide range of experimental data reported in the literature on clay, silt and sand.

Soil-water retention curve model for fine-grained soils accounting for void ratio–dependent capillarity

This paper presents a soil-water retention curve (SWRC) model for fine-grained soils. Compared with existing studies, the proposed model accounts for the distinct roles of the volume change of soils on capillarity and adsorption mechanisms. The capillary water is described by a relation that includes the characteristics of the pore-size distributions as parameters, while the absorbed water is modeled by a novel proposition that both considers the phenomenon of capillary condensation and allows for the decoupling between the degree of capillary and adsorptive saturation. Based on this feature, the void ratio effects are considered in a way in which they only affect capillary water, i.e., consistent with how volume change influences soil microstructures. The relative contributions of void ratio effects and hydraulic hysteresis on the path- and history-dependence of a SWRC in Sr–s–e space, where Sr is degree of saturation, s is matric suction, e is void ratio, for deformable unsaturated soils are examined. The significance of discriminating the effects of volume change on capillary and adsorptive water is illustrated by applying the SWRC model to computing the shear strength of unsaturated soils with different void ratios. The model performance is assessed by comparing against test data reported for four types of fine-grained soils in the literature and those tested for natural loess in this work.

Modelling of soil-water retention curve considering the effects of existing salt solution in the pore fluid

Soil-water retention curve (SWRC) has a wide application in geoenvironmental engineering from the predication of unsaturated shear strength to transient two-phase flow and stability analyses. Although various SWRC models have been proposed to take into account some influencing factors, less attention has been given to consider the effects of pore fluid osmotic potential. Therefore, the key objective of this study is to extend van Genchten’s model so that osmotic potential is considered as an independent factor governing the SWRC behavior. The new model comprises only six variables, which can be calibrated through minimal experimental measurements. More importantly, most of the model parameters have physical meaning by correlating macroscopic volumetric behavior and general trends of SWRC to osmotic potential. The results of validation tests revealed that the new osmotic-dependent SWRC model can predict the retention data in terms of both total and matric suction for two different soils and various molar concentrations very good. The proposed modeling approach does not require any advanced mercury intrusion porosimetry (MIP) tests, yet it can deliver excellent predictions by calibrating only six parameters which are far less than those incorporated into similar models for saline water permeating through the pore structure.

Effect of Porosity on Soil-Water Retention Curves: Theoretical and Experimental Aspects

Porosity change is a common characteristic of natural soils in fluid-solid interaction problems, which can lead to an obvious change of the soil-water retention curve (SWRC). The influence of porosity on soil water retention phenomena is investigated by a theoretical model and an experimental test in this study. A model expressing the change in suction with porosity and effective saturation is put forward theoretically. The model is based on an idealization of three-phase porous materials, the pore structures of which are homogeneous and isotropic. It accounts for the porosity effect on soil water retention, using four parameters with clear physical meanings. The presented model can obtain the SWRC at any porosity, which will reduce the test number required in characterizing the hydraulic behavior of soil. A laboratory experiment for loamy sand with different porosities is performed. The test results show that suction has a significant variation with changes in porosity and decreases with the increase of porosity. The formulation is verified by both the test data and the literature data for FEBEX bentonite and Boom clay. The very good agreements between measured and predicted results show that the SWRC model is reliable and feasible for various soils.

ANÁLISE EXPERIMENTAL E VALIDAÇÃO DE CURVAS BIMODAIS DE RETENÇÃO DE ÁGUA NO SOLO PARA SOLOS ARENO-ARGILOSOS RESIDUAIS DA FORMAÇÃO ITAQUERI EM SÃO CARLOS – SP

Esse estudo experimental oferece parâmetros para validar e ajustar quatro modelos de curva de retenção da água no solo (CRA) presentes na literatura. O experimento foi realizado no solo do campus da Universidade Federal de São Carlos, Estado de São Paulo, utilizou-se tensiômetros para monitorar a sucção matricial do solo e o conteúdo de água em diferentes profundidades. Amostras de solo foram coletadas para construir as CRAs por meio de três técnicas de calibração de papel filtro Whatman n°42 e assim obter a relação sucção matricial por umidade do solo. Os modelos de CRA foram utilizados para ajustar os valores de teor de água segundo a proposta de CRA bimodais. O experimento foi validado em laboratório medindo-se a umidade das amostras em cada profundidade, obtidas em datas diferentes e então correlaciona-las com os respectivos valores de pressão de sucção obtidas no instante de cada amostragem. O modelo de CRA de Van Genuchten com restrição de Bourdine e calibração de papel filtro de Oliveira e Marinho foi o que obteve melhor ajuste na representação da dinâmica da água no perfil em termos dos coeficientes globais: R², Nash-Sutcliffe, EAPM e RMSE.

Assessing an efficient hybrid of Monte Carlo technique (GSA-GLUE) in Uncertainty and Sensitivity Analysis of vanGenuchten Soil Moisture Characteristics Curve

Studying model uncertainty and identifying the parameter uncertainty in the modeling of water flow through the soil is useful to improve water and soil management. This research aimed to assess the uncertainty of the parameters of soil water retention curve (SWRC) models using an efficient hybrid of the Monte Carlo technique e.g. generalized likelihood uncertainty estimation (GLUE). GLUE estimates the parameters of vanGenuchten, vanGenuchten-Mualem, and vanGenuchten-Burdine models for four soil classes. Also, to evaluate the relative importance of the model parameters, generalized sensitivity analysis (GSA) was performed. The results of the uncertainty analysis showed that among the studied models, the vanGenuchten-Mualem model with the indices of S = 0.05, T = 0.4, d-factor = 0.25 and, PCI = 100 was considered as the most accurate model with the least uncertainty. Also, the results of GSA were demonstrated that alpha and n parameters were sensitive parameters in the models. Consequently, identifying the uncertainty of the SWRC model structure and its parameters, relevant models with higher accuracy can be used in the study of soil water processes, and better water resource allocation.

Water retention models for soils mixed with waste residues: application of the modified van-Genuchten and Brooks-Corey models

Applying additives (e.g., biochar and rapeseed-oil residue) to soils is a common agronomic practice used to improve water-retaining capacity. An investigation of water availability and an applicability evaluation of traditional soil water retention curve (SWRC) are therefore necessary for the soil mixed with waste residues. We aimed to investigate the impact of additives on water retention and further to develop models for their prediction. Loam and sandy loam were mixed with different amounts of rapeseed-oil residue and biochar, respectively. And results show that the biochar and rapeseed-oil residue retain more water, with a minimum and maximum increase in soil moisture by approximately 26.2% and 92.7%, and 10.2% and 19.4%, respectively, relative to pure soil. Furthermore, based on the soil capillary theory, modified van–Genuchten (M-VG) and Brooks–Corey (M-BC) models were constructed and compared, which indicate that both the modified physics-based models (M-SWRC) have higher accuracy than the traditional SWRC models in soil moisture prediction; furthermore, the M-VG model outperforms the M-BC model, due to larger R2 and smaller MAPE and RMSE. For the field soils mixed with additives, the soil suction density function has potentials for SWRC model modification based on the soil capillary theory.

A generalized water retention model with soil fabric evolution

This paper introduces a novel soil–water retention curve model that considers two different mechanisms of water retention – namely capillarity and adsorption – and their evolution with soil fabric along a generalized stress path. The model is formulated based on a new developed framework, which is justified against experimental evidence and incorporates the following developments: (i) the characteristics of the capillary and adsorption water retention curves are identified, and an ad-hoc water retention model is developed for each mechanism; (ii) the capillary and adsorption water retention curves are related to the experimentally determinable water retention curve thanks to a newly defined parameter named “contribution factor”, which changes with the evolution of the fabric. The proposed model is an elastoplastic water retention model and it allows to describe satisfactorily the water retention capacity of different soils. All simulation results support the statement that the adsorptive mechanism plays a crucial rule in the high suction range while capillarity is important in the low suction range. Moreover, it is shown that the developed capillary water retention curve allows to easily compute, at any state of the soil, a suitable capillary degree of saturation; the latter, adopted within the generalized effective stress concept, makes it possible to interpret shear strength data under different saturation conditions properly.

Determining the Unsaturated Hydraulic Properties of Cohesionless Soils: An Integrated Experimental and Inverse Modeling Approach

Abstract A simple, inexpensive and quick method for measuring the van Genuchten soil water retention curve (SWRC) model parameters for cohesionless soil is presented. The proposed method is an integration of laboratory testing and numerical modeling. The experimental testing consists of multistage bottom-top water imbibition of a dry sand column while recording pore pressure at the inlet. The experiment is then simulated numerically using Hydrus 1D, and the van Genuchten SWRC model parameters are determined through inverse modeling to match the recorded pore pressures. The soil column flushing includes multiple flow stoppages and resumptions, all before permeating one pore volume of water. The flow stoppage results in a time-dependent redistribution of moisture near the waterfront that is controlled by the unsaturated hydraulic properties of the soil and is reflected by changes in the pore pressure measurements. The uniqueness of this method comes from the simple experimental setup and the multistage flushing that can reduce the testing time by a factor of 30 compared with other methods. The results from testing three different sands with different grain size distributions are presented. The new method generated consistent results from multiple specimens tested at a range of flow rates for the three sands. The hypothesis behind moisture redistribution during flow stoppage was confirmed through a combination of experimental and numerical observations. The van Genuchten SWRC parameters obtained from the new method were comparable to those obtained using the conventional hanging column test for Sands B and C and available data in the literature. Sand A could not be tested using the hanging column test because of its large particle size, which demonstrates the wide range of soils that can be tested using the new proposed method.

Probabilistic characterization of the soil-water retention curve and hydraulic conductivity and its application to slope reliability analysis

Abstract Soil-water retention curve (SWRC) and hydraulic conductivity are two indispensable inputs in unsaturated seepage analysis for analyzing water flow in unsaturated soils, which can be obtained through direct measurements. Generally, the test data of the SWRC and unsaturated hydraulic conductivity obtained from direct measurements are limited because such measurements are time-consuming and costly. Thus, it is hard to determine an SWRC and hydraulic conductivity with certainty from a probabilistic perspective. How to quantify the uncertainty in them remains an unresolved question. This paper aims to propose a Bayesian approach to characterize the SWRC and hydraulic conductivity. The proposed approach is illustrated through a slope example. Results show that the proposed Bayesian approach is not only able to quantify the uncertainty in the estimated SWRC and hydraulic conductivity, but also capable of predicting the SWRC and hydraulic conductivity with reasonable accuracy. This facilitates the determination of both the SWRC and hydraulic conductivity in geotechnical applications for engineers by making use of the available test data. Moreover, the proposed approach offers a viable way to provide a robust estimate of slope failure probability by virtue of Bayesian model averaging, allowing SWRC parameter uncertainty and model selection uncertainty to be considered simultaneously in reliability analysis. This addresses the dilemma of over-reliance on a single SWRC model in geotechnical reliability analysis involving unsaturated soils. It is worthy to note that among the four candidate models, three of them belong to one category which may have similar abilities, other parametric models in different categories need to be considered in future research.

A novel segmental model to describe the complete soil water retention curve from saturation to oven dryness

Traditional water retention models that use the residual water content parameter fail to accurately describe the dry end of the soil water retention curve (SWRC). We developed two- and three-segment smooth, continuous SWRC models, acknowledging the existence of three saturation states, for water contents ranging from saturation to oven-dryness. The equations near the oven dryness end in both models were obtained based on the assumption of proportionality between the soil water content and the logarithm of suction. The equations in the wet range for both models were modified from the van Genuchten model and/or Brook-Corey model(s) by removing the residual water content parameter. The continuity and smoothness conditions at the junction points reduced the fitting parameters of the three- and two- segment models from 9 to 4 and from 6 to 3, respectively. Both models were tested with water retention data from the Washington soil database and the Unsaturated Soil Hydraulic Database (UNSODA) over nearly the entire range. Both models were also compared with seven existing SWRC models and were evaluated on the basis of the adjusted coefficient of determination (adj R2), the root mean square error (RMSE) and the Kashyap information criteria (KIC). The testing results showed that the three-segment model performed better than the two-segment model at fitting the SWRC at the dry end. For the three-segment model, the adj R2 value was greater than 0.90, the RMSE was less than 0.02, and the mean KIC value was −67.0, and these values were superior to those of the other models. In addition, the three-segment model was robust and stable for extrapolation of values in the dry range when data near the dry end were unavailable.

An empirical soil water retention model based on probability laws for pore‐size distribution

ABSTRACTKnowledge of the soil water retention curve (SWRC) is critical to mathematical modeling of soil water dynamics in the vadose zone. Traditional SWRC models were developed based on bundles of cylindrical capillaries (BCCs) using a residual water content, which fail to accurately describe the dry end of the curve. This study improved and expanded on the traditional BCC models. Specifically, the total water retention was treated as a weighed superposition of capillary and adsorptive components. We proposed a mathematical continuous expression for water retention from saturation to oven dryness, which also allowed for a partition of capillary and adsorptive retention. We further evaluated six capillary retention functions using different probability laws for pore‐size distribution—namely, the log‐logistic, Weibull, lognormal, two‐parameter van Genuchten (VG), three‐parameter VG (or Dagum), and Fredlund–Xing (FX) distributions. Model testing against 144 experimental data showed better agreement of the proposed model with experimental observations than the traditional approaches that use the residual water content. The Dagum and FX distributions, which have one more degree of freedom, provided better agreement with experimental data than the other four distributions. The log‐logistic and lognormal distributions fitted the experimental data better than the Weibull and VG distribution for loam soils. In addition, the fitted weighting factor w using the log‐logistic and lognormal distributions better correlated to soil clay content than the other four distributions. Our study suggests that the log‐logistic and lognormal distributions are more suitable to model soils’ pore‐size distribution than other tested distributions.