Brooks-Corey Research Articles

Assessment of Two SWCC models for predicting the curve fitting parameters of lateritic soil: bentonite mixtures

This study compares the capabilities of soil water characteristic curve (SWCC) models by Brooks-Corey (BC) and van Genuchten (vG) in estimating the curve fitting parameters for lateritic soil—bentonite mixtures. The SWCCs of soil treated with 0–10% bentonite and compacted with British standard light (BSL) energy at compaction states representing dry of optimum, optimum, and wet of optimum conditions were measured by sequential desorption using pressure plate extractor. The fitting parameters of the two equations were determined by a non-linear fitting program. The fitting capabilities of the models on the measured data were compared by statistical indices namely the root mean square error (RMSE), linearity (R2) and index of agreement (d). Results revealed that volumetric water content increased as bentonite content increased with specimens containing 10% bentonite recording the highest and therefore has greater capacity to retain water/contaminants, while the air entry value (AEV) for the various soil mixtures also increased with higher bentonite content. The study also found that the estimated volumetric water contents approximated the measured values at all suctions with a high degree of accuracy with RMSE values that ranged from 0.0035 to 0.0150 for vG model which are somewhat lower than the values for BC equation. Similarly, R2 for the vG equation (≥ 0.99) are, on average, slightly higher than those of the BC fits. However, the d values associated with the BC model which varied between 0.788 and 0.971 are higher than those of the vG (0.784–0.968). Overall, the study established that the vG model proved marginally superior in respect of goodness of fit.

Estimating the Specific Yield and Groundwater Level of an Unconfined Aquifer Using Time-Lapse Electrical Resistivity Imaging in the Pingtung Plain, Taiwan

This study aims to apply geophysical methods to determine the Specific Yield (Sy) and Groundwater Level (GWL) in an unconfined aquifer of the Pingtung Plain in South Taiwan. Sy is an important hydraulic parameter for assessing groundwater potential. Obtaining specific yield for a large area is impractical due to the limited coverage and the high cost of the pumping test, which limits the potential evaluation of regional groundwater. Therefore, we used time-lapse Electrical Resistivity Imaging (ERI) to determine the Sy and GWL. Seasonal variations were considered when measuring time-lapse resistivity for five different months in 2019. We calculated the Sy and GWL from inverted resistivity data using empirical formulas and the soil–water characteristic curve (SWCC). We first used Archie’s law to calculate the relative saturation change with depth for each ERI profile, and then we used the Van Genuchten (VG) and Brooks–Corey (BC) empirical equations to estimate Sy and GWL. Finally, we compared the obtained GWL to the existing observation well to verify the findings of our study. The results showed that the VG and BC are able to predict Sy and GWL; however, the BC result is less consistent with the observation well result. In the study area, the dry season GWL ranged from 24.5 m to 35.2 m for the VG results and from 25.7 m to 35.5 m for the BC results. The wet season GWL ranged from 26.5 m to 38.9 m for the VG and from 26.4 m to 38.2 m for the BC results. The spatial distribution of the GWL shows a high gradient of GWL in the northeastern region, induced by significant proximal fan recharge. The determined spatial distribution of Sy varies from 0.15 to 0.21 for the VG and 0.14 to 0.20 for the BC results, indicating the study area has significant potential for groundwater resources. Therefore, nondestructive resistivity imaging can be used to aid in the determination of hydraulic parameters.

Properties governing flow of solution and air through crushed ore for heap leaching: Part II unsaturated dual-phase flow

Heap leaching of low-grade ores is often restricted by the hydrology of the bed, which limits the rate of dissolution of the target mineral. Although much research has been published on the flow of solution and air through sand, little has been published on the hydrology of coarser rocks. Physical and hydraulic testing of rocks and agglomerates is often incorporated as a part of heap leach design, however, much still relies on experiential rules. Over the past decade, the lead author has performed physical and hydraulic testing of a large number of ore samples considered for heap leaching. In reviewing the data, it was found that the hydraulic conductivity function (HCF), relating the hydraulic conductivity to the degree of saturation, can be modelled with traditional capillary models such as Brooks-Corey (BC) and van Genuchten-Mualem (VGM), but only at lower moisture contents. Furthermore, it was found that the HCF can be modelled as a discontinuous J-curve, with the hydraulic conductivity equal to the saturated hydraulic conductivity (Ks) above the air-entry point, rather than a continuous J-curve with a fitted Ks value, as recommended by other authors. Previous authors have also suggested that the discontinuity represents a transition between capillary- and gravity-controlled flow. However, the author(s) propose that the discontinuity is caused rather by the presence of “dead voids”, which fill up at higher moisture contents without generating additional flow channels. The point of discontinuity was found to correspond to the air-entry value obtained independently from the air conductivity curves. The experiential rule of a maximum void saturation of 65% for heap aeration appears to correspond on average with the experimental data.

Parameter identification of unsaturated seepage model of core rockfill dams using principal component analysis and multi-objective optimization

The seepage behavior of core walls is an important aspect of safety monitoring of core rockfill dams. The permeability coefficient of unsaturated soil of the core wall is a nonlinear function not a constant. Since there are many seepage monitoring points in the core wall, parameter identification of unsaturated seepage model of soil core wall based on the data of these points is a high-dimensional multi-objective optimization problem. In this paper, a parameter identification method of unsaturated seepage in the core wall is proposed, in which an unsaturated seepage model, principal component analysis (PCA), and elitist non-dominated sorting genetic algorithm (NSGA-II) are combined. The seepage monitoring sequence of measuring points in saturated and unsaturated regions of the core wall is synthesized to a few comprehensive variables by PCA respectively. The NSGA- II is adopted to optimize the objective functions established by these comprehensive variables to obtain the Pareto-optimal solutions. The efficiency, accuracy, and robustness to the error of the proposed method have been confirmed in a fictitious dam and an actual dam. The predicted seepage pressure with the Brooks-Corey (BC) model is in best agreement with the measured data, and the simulated seepage field is more in line with the actual situation.

Effect of Shelterbelt Construction on Soil Water Characteristic Curves in an Extreme Arid Shifting Desert

To explore the impact of artificial shelterbelt construction with saline irrigation on the soil water characteristic curve (SWCC) of shifting sandy soil in extreme arid desert areas, three treatments including under the shelterbelt (US), bare land in the shelterbelt (BL) and shifting sandy land (CK) in the hinterland of the Taklimakan Desert were selected. The age of the shelterbelt is 16, and the vegetation cover is mainly Calligonum mongolicum. The soils from different depths of 0–30 cm were taken keeping in view the objective of the study. The SWCCs were determined by the centrifugal method and fitting was performed using various models such as the Gardner (G) model, Brooks–Corey (BC) model and Van Genuchten (VG) model. Then, the most suitable SWCC model was selected. The results showed that electrical conductivity (EC) and organic matter content of BL and US decreased with the increasing soil depth, while the EC and organic matter content of CK increased with the soil depth. The changes in soil bulk density, EC and organic matter of 0–5 cm soil were mostly significant (p < 0.05) for different treatments, and the differences in SWCCs were also significant among different treatments. Moreover, the construction of an artificial shelterbelt improved soil water-holding capacity and had the most significant impacts on the surface soil. The increase in soil water-holding capacity decreased with increasing soil depth, and the available soil water existed in the form of readily available water. The BC model and VG model were found to be better than the G model in fitting results, and the BC model had the best fitting result on CK, while the VG Model had the best fitting result on BL with higher organic matter and salt contents. Comparing the fitting results of the three models, we concluded that although the fitting accuracy of the VG model tended to decrease with increasing organic matter and salinity, the VG model had the highest fitting accuracy when comparing with BC and G models for the BL treatment with high organic matter and salinity. Therefore, the influence of organic matter and salinity should be considered when establishing soil water transfer function.

A comparative study of soil-water characteristic curves for compacted lateritic soil – bacillus coagulans mixtures

A comparative study of soil-water characteristic curves (SWCCs) for compacted lateritic soil ̶ Bacillus coagulans (B. coagulans) mixtures for municipal solid waste (MSW) application was studied. Soil treatment was performed at approximately about one-third pore volume of the microbes (i.e., B. coagulans) for suspension densities of 0, 1.5×108, 6.0×108, 1.2×109, 1.8×109 and 2.4×109cells/ml, correspondingly. Soil specimens were prepared at optimum moisture content (OMC) of British Standard light (BSL) compaction energy. Cementation reagent was applied on the compacted soil and permitted to penetrate until partial saturation was achieved. A set-up of pressure plate extractor was employed to measure the volumetric water content, θ (VWC) in the laboratory for varying matric suctions with a minimum of 10 kPa up to a maximum of 1,500 kPa. The unsaturated hydraulic conductivity (UHC) and VWC were assessed using Brooks - Corey (BC) and Fredlund - Xing (FX) models. Largely, BC and FX models overrated the VWC. Also, the VWC decreased with higher matric suction for the two models considered and the laboratory measured values. The UHC predicted for matric suctions of 500 and 1,500 kPa initially decreased for B. coagulans suspension density up to 1.2×109 cells/ml for BC and FX models, with the exception of a few cases, but thereafter increased with increase in microbial density. For FX model at 1,500 kPa, UHC values of 2.42×10–9, 2.02×10–9, 9.31×10–10, 8.09×10–10 , 1.29×10–9 and 2.27×10–9m/s were recorded at 0, 1.5×108, 6.0×108, 1.2×109, 1.8×109 and 2.4×109cells/ml, respectively. In the case of BC model, values of 2.26×10–17, 1.41×10–14, 2.2×10–14, 4.6×10–19 , 3.25×10–17 and 2.45×10–14m/s were recorded at 0, 1.5×108, 6.0×108, 1.2×109, 1.8×109 and 2.4×109cells/ml, respectively. Thus, the FX model met the design maximum hydraulic conductivity value of 1 x 10–9 m/s requirement for MSW system when lateritic soil was treated with B. coagulans suspension density of 1.2×109 cells/ml, while the BC model satisfied the requirement for all the microbial densities considered and it is recommended for modelling of UHC of lateritic soil admixed with B. coagulans for MSW containment application.

Quantifying the hydraulic properties of some Egyptian soils using RETC code

Temporal and spatial soil variabilities reduce the accuracy of quantifying the hydraulic properties of the soil, leading to poor irrigation management. Modeling estimation and computer codes (e.g., RETC code) have been used to quantify and predict soil hydraulic properties. One hundred soil samples were collected to represent soil textural classes according to USDA textural triangle. Following the physical, chemical and hydraulic characterization of the soil samples collected, one soil sample was chosen to represent each texture class. The selected soil samples covered six USDA textural classes. Then, Brooks-Corey (B-C) (1964) and van Genuchten (vG) (1980) parametric models were used to describe the functional relationship between soil water tension and water content, i.e. the soil water retention curve, and the Mualem (1976) theoretical models of pore size distribution were used to predict the functions of unsaturated conductivity K (θ) and soil water diffusivity D (θ). The RETC (retention curve) code was used to obtain the parameters of vG and B-C models by simultaneously matching to the observed data. Output file of refining process showed the iteration levels to achieve minimum value of residual summed square (RSSQ).The values of determination coefficient (R2) of the fitted θ (h) as a power function increased after fitting the experimental data either in B-C or in vG models. The values of R2 of the fitted equation of θ (h) with both B-C and vG data increased after refining process through RETC code. The increments of R2 values after refining are more pronounced in coarse textured samples (Sand, Loamy sand, and Sandy loam).The values of determination coefficient (R2) of the fitted functions K (θ) and D (θ) as a power function are highly significant after fitting soil parameters either in B-C or in vG models. While using RETC code refined the obtained soil parameters of both K (θ) and D(θ) increasing R2 values of fitted power function and reducing residual summation square. RETC reduced the value of residual summed square (RSSQ) of the objective function O(b) under using both B-C and vG models. This reduction of RSSQ by using RETC fluctuated between 60.4% and 98.2% with B-C for six soil textural classes. While, the reduction of RSSQ by using RETC fluctuated between 90.4% and 98.6% with vG for the same six soil textural classes. In general, the RETC code is a good tool for obtaining accurate values of hydraulic properties in a variety of soil textures.

Estimating the water characteristic curve for soil containing residual plastic film based on an improved pore-size distribution

Although plastic-film mulching has played an important role in agriculture production in arid areas, the practice has resulted in the accumulation of large amounts of residual plastic film (RPF) in the soil. This intensely impedes the movement of the water and solutes in soil by seriously affecting the physical and hydraulic properties of soil, in particular the soil water characteristic curve (SWCC). Despite the severity of the problem, studies on how RPF affects soil properties and the SWCC remain scarce. This paper thus aims to achieve a better understanding of the influences of RPF on soil pores and SWCC. In this study, SWCCs were measured under five concentrations of RPF (0 kg·hm−2, 50 kg·hm−2, 100 kg·hm−2, 200 kg·hm−2 and 400 kg·hm−2) and three soil textures (sandy soil, sandy loam and loam soil) based on the pressure plate extractor test. A model for estimating SWCC for soil with residual plastic film (RPF-SWCC) based on an improved pore-size distribution is proposed, and its performance was evaluated and compared with those for existing models, including the van Genuchten (VG), Brooks-Corey (BC) and log normal distribution (LND) models. The results showed that there is a clear influence by the RPF in soil on the shape of the SWCC, and the order of the different soil types in regards to soil water holding capacity was loam soil > sandy loam > sandy soil, with or without RPF. The RPF-SWCC model accounted for the effects of water blocking by RPF, thereby achieving improved fitting accuracy compared to that by the VG, BC and LND models, especially for soil with high RPF concentration. The average Nash-Sutcliffe efficiency coefficient (NSE), mean absolute percentage error (MAPE) and symmetric mean absolute percentage error (SMAPE) for achieved for the RPF-SWCC model were 0.9943, 3.37% and 3.43%, respectively, which was an improvement on the 0.9938, 5.94% and 5.06% achieved for the VG model, 0.9926, 4.43% and 4.25% for the BC model and 0.9923, 15.00% and 7.53% for the LND model, respectively. In addition, the correlation between the parameters of the RPF-SWCC model and RPF concentration showed that the saturated soil water content and residual soil water content decreased and increased with increasing RPF concentration, respectively. In addition, soil RPF increased and decreased the proportion of macropores and soil water holding capacity, respectively. This study can provide a theoretical and technical basis for research into soil water movement and the efficient utilization of water and fertilizer in areas with high agricultural film residue.

A Novel Relative Permeability Model for Gas and Water Flow in Hydrate-Bearing Sediments With Laboratory and Field-Scale Application

In a producing gas hydrate reservoir the effective porosity available for fluid flow constantly changes with dissociation of gas hydrate. Therefore, accurate prediction of relative permeability using legacy models (e.g. Brooks-Corey (B-C), van Genuchten, etc.) that were developed for conventional oil and gas reservoirs would require empirical parameters to be calibrated at various Sh over its range of variation, but such calibrations are precluded because of lack of experimental relative permeability data. This study proposes a new relative permeability model for gas hydrate-bearing media that is a function of maximum capillary pressure, capillary entry pressure, pore size distribution index, residual saturations, hydrate saturation, and four other constants. The three novel features of the proposed model are: (i) requires fitting its six empirical parameters only once using experimental data from any single Sh, and the same set of empirical parameters predict relative permeability at all Sh, (ii) includes the effect of capillarity, and (iii) includes the effect of pore-size distribution. From practical standpoint, the model can be used to simulate multiphase flow in gas hydrate-bearing sediments where the proposed relative permeability can account for the evolving hydrate saturation. The proposed model is implemented in a numerical simulator and the wall time required to perform simulations using the proposed model is shown to be similar to the time it takes to run same simulations with the B-C model. The proposed model is a step forward towards achieving the goal of physically accurate modeling of multiphase flow for gas hydrate-bearing sediments that accounts for the effect of gas hydrate saturation change on relative permeability.

Comparison of the performance of 22 models describing soil water retention curves from saturation to oven dryness

AbstractSoil water retention curve (SWRC) is key hydraulic property for vadose zone hydrology. Selected 22 SWRC models with different structures were divided into four types: traditional, single‐segment, two‐segment, and three‐segment models. According to the accuracy and model selection criterion, these models were compared and evaluated using water retention data from saturation to oven dryness of 94 soil samples covering almost all soil types. Among the models, the EG model (exponential model combined with the Groenevelt–Grant model) shows the best performance, but the BC (Brooks–Corey) and VG (van Genuchten) models performed the worst. The relationship between model performance and complexity showed that traditional models with residual water content performed worse than segmental models from saturation to oven dryness, and the segmental models performed worse with an increase in the segment number. In general, models with more parameters perform better, but when the parameter number is greater than five, the model performance gradually worsens due to the equifinality of different parameters. The correlation analysis between soil properties on model performance showed that soil texture has a more significant effect on model performance than bulk density and organic matter content, because the models are primarily affected by their mathematical forms rather than the physical significance of the parameters. Each model picks its limitations and may apply to only one or particular group(s) of soil(s). Therefore, the complementarities of different models may be a great choice to improve SWRC fitting and simulation in arid soil.

An Experimental Study on the Hydromechanical Behaviours of the Evolution of Postearthquake Landslide Deposits

In this study, a series of experiments of the full-scale physical model was employed to investigate the hydromechanical behaviours of the postearthquake landslide evolution, in forms of rill erosion and shallow headward failure on the rill bank slopes under unsaturated conditions. Soil-water characteristic curves (SWCC) were established using the Brooks-Corey (BC) and van Genuchten (VG) models. The stability of the shallow failure was then analyzed via a one-dimensional and unsaturated stability analysis model of the infinite slope. This measurement revealed that the preferential flow and the matrix flow coexisted when infiltration occurred and the VG model performs better in fitting the SWCC than the BC model. Consistent feedback between stability calculations and experimental observations enables the analysis of mechanisms of rill erosion and slope failure of postseismic landslide under the impact of preferential flow. Furthermore, the seepage-induced internal erosion phenomenon was observed in the experiment. This work thus provides a new perspective on the triggering mechanisms of debris flow during the postseismic period.

Characterising the role of parametric functions in the van Genuchten empirical model on CO2 storage performance

In the application of two-phase flow in porous media within the context of CO2 sequestration, a non-wetting phase is used to displace a wetting phase residing in-situ to the maximum extent through a network of pore conduits. The storage performance of this physical process can be assessed through numerical simulations where transport properties are usually described using the Brooks & Corey (BC) or van Genuchten (vG) model. The empirical constant, namely the pore geometry index, is a primary parameter in both of these models and experimental evidence shows a variation in the value of this empirical constant. It is, therefore, essential to cast this empirical constant into a ternary diagram for all types of clastic porous media to demarcate the efficiency of two-phase flow processes in terms of the pore geometry index (PGI). In doing so, this approach can be used as a tool for designing more efficient processes, as well as for the normative characterisation of two-phase flow, taking into consideration the predominance of capillary pressure or relative permeability effects. This concept is based on the existence of a PGI estimation for clastic sediments, for which the value for 12 sediment mixtures fall between 1.01 and 3.00. Statistical data obtained from soil physics is used for developing and validating numerical models where a good match is observed in numerical simulations. In this context, a new methodology for the effective characterisation of PGI for different clastic rocks is proposed. This paper presents theoretical observations and continuum-scale numerical simulation results of a PGI characterisation for the prediction of the hydraulic properties of clastic reservoir rocks. The effect of key parameters in the vG empirical model, such as the pressure strength coefficient and the PGI, is incorporated into the simulation analysis. In particular, the model is used to investigate the effects of parameter representation on CO2 storage performance in a saline aquifer. Subsequent analysis shows that the PGI is a very important parameter for defining the flow characteristics of simulation models. It can also be flexibly changed for each rock type and this approach may thus be practical when simulating the evolution of CO2 plume in reservoirs with sedimentary heterogeneities, such as intra-aquifer aquitard layers or graded beds. The use of the realistic PGI boundaries promises a more precise description of the hydraulic behaviour in sandstones and shale when using either the BC or vG model.

Analytical Method to Determine Soil Hydraulic Properties from Vertical Infiltration Experiments

Core Ideas A new method was proposed to determine Brooks‐Corey (BC) model parameters. Only a vertical infiltration experiment and simple measurements were required. The new method has great potentials to be applied in situ on various scales. Soil hydraulic properties are basic inputs for simulating water and solute transport in the vadose zone. Many methods have been developed to directly measure or indirectly estimate soil hydraulic properties. However, low‐cost, simple and robust methods are still scarce even in a laboratory. Here we present a new analytical method, based on an approximate solution to the one‐dimensional vertical infiltration problem that can be used to determine Brooks–Corey model parameters. Measurements include cumulative infiltration, wetting front advance with time, and initial and final upper boundary water contents, during a one‐dimensional vertical infiltration experiment. Infiltration experiments with twelve disturbed soils were performed to test the new method. The results indicated that the estimated saturated hydraulic conductivities from transient infiltration processes were consistent with those measured with a constant‐head method. The estimated soil water retention curves (SWRCs) by the analytical method for the twelve soils were in agreement with those measured by a direct method in which soil water potentials were measured through tensiometers. The root mean square error (RMSE) of the estimated soil water contents by the new method were less than 0.045 cm3 cm–3 for the twelve soils. Compared to most direct methods, the new method is inexpensive, rapid and easy to use, and thus can be a substitute for direct methods in a laboratory. Although how to monitor representative wetting front remains unsolved, the new method has a potential for use in the future in determining in situ soil hydraulic properties where lateral flows are negligible.

Analytical Solution of a One‐Dimensional Horizontal‐Absorption Equation Based on the Brooks–Corey Model

Core Ideas Least‐action and variational principles were used to analyze soil water content distribution. An analytical solution of a one‐dimensional horizontal‐absorption equation was proposed. A new method to predict the distribution of SWC and estimate the Brooks–Corey model parameters. A simple and approximate analytical solution of a one‐dimensional horizontal‐absorption equation is of great importance for measuring soil hydraulic properties. Several methods for determining the parameters of the Brooks–Corey (BC) model are promising, but all are based on assumptions to some degree. We have developed a new analytical solution for one‐dimensional horizontal constant‐saturation absorption based on the least‐action and variational principles. The profiles of soil–water content (SWC) calculated by the new method were very agreeable with numerical solutions, especially for high water contents. A comparison with a numerical solution calculated by HYDRUS‐1D indicated that the analytical solution accurately estimated the BC model parameters for calculating the profile of SWC, cumulative infiltration, infiltration rate, and wetting‐front distance (WFD). We also compare the merits and demerits between the new analytical method and other approximate methods. The proposed analytical method provides a new and approximate method to predict the distribution of SWC and estimate the BC model parameters.

An improved capillary pressure model using fractal geometry for coal rock

Based on fractal geometry and the “matchstick” tubes model, an improved capillary pressure model was theoretically derived to assess capillary pressure data for coal. The model was based on fractal geometry and the “matchstick” tubes model. Our improved model can be simplified as Li model and Brooks-Corey (B-C) model when the fractal dimension and tortuosity parameter take specific values in coal porous media. Furthermore, the capillary pressure data of different coals samples collected in the LZ Coal Mine in China were measured employing mercury intrusion method, and the heterogeneity of typical coal samples were evaluated using the pore volumetric percent curves and SEM images. The matching results of the B-C model, Van Genuchten (V-G) model, Li model, and our improved model were assessed in comparison with the test data. The comparison indicated that our improved model had better agreement with the test data relative to the conventional models.

Comparison of relative permeability–saturation–capillary pressure models for simulation of reservoir CO2 injection

Constitutive relations between relative permeability (kr), fluid saturation (S), and capillary pressure (Pc) determine to a large extent the distribution of brine and supercritical CO2 (scCO2) during subsurface injection operations. Published numerical multiphase simulations for brine–scCO2 systems so far have primarily used four kr−S−Pc models. For the S−Pc relations, either the Brooks–Corey (BC) or Van Genuchten (VG) equations are used. The kr−S relations are based on Mualem, Burdine, or Corey equations without the consideration of experimental data. Recently, two additional models have been proposed where the kr−S relations are obtained by fitting to experimental data using either an endpoint power law or a modified Corey approach. The six models were tested using data from four well-characterized sandstones (Berea, Paaratte, Tuscaloosa, Mt. Simon) for two radial injection test cases. The results show a large variation in plume extent and saturation distribution for each of the sandstones, depending on the used model. The VG–Mualem model predicts plumes that are considerably larger than for the other models due to the overestimation of the gas relative permeability. The predicted plume sizes are the smallest for the VG–Corey model due to the underestimation of the aqueous phase relative permeability. Of the four models that do not use fits to experimental relative permeability data, the hybrid model with Mualem aqueous phase and Corey gas phase relative permeabilities provide the best fits to the experimental data and produce results close to the model with fits to the capillary pressure and relative permeability data. The model with the endpoint power law resulted in very low, uniform gas saturations outside the dry-out zone for the Tuscaloosa sandstone, as the result of a rapidly declining aqueous phase relative permeability. This observed behavior illustrates the need to obtain reliable relative permeability relations for a potential reservoir, beyond permeability and porosity data.

An improved method for determining Brooks–Corey model parameters from horizontal absorption

Low-cost, simple, rapid and accurate approaches for measuring soil hydraulic properties are of great importance in the application of hydrologic models of the vadose zone. A recently proposed method of constant-saturation absorption (MCSA) for determining Brooks–Corey (BC) model parameters is promising. However, this method has not been tested using experimental data. In this paper, measured soil–water diffusivity or soil–water retention curves (SWRCs) of 20 soil samples were used to test the reliability of MCSA. The results indicate that MCSA consistently estimated soil–water diffusivities by the Bruce and Klute method, but it substantially overestimated air-entry suctions (hd) and thereby soil suction. A new method (MCPA) is proposed herein to overcome the problems associated with MCSA. Using the improved method, estimated SWRCs are consistent with observation. With the estimated soil hydraulic parameters, HYDRUS-1D generated very accurate simulations of the cumulative absorption curves. Compared with direct or other indirect methods, MCPA is a more accurate, low-cost, and simple method, and it is especially useful for rapid determination of SWRC for soil–water movement simulations. However, if unsaturated soil–water diffusivity is of greater concern, our results also indicate that MCSA more accurately predicts this quantity and thus should be preferred.

A Comparative Study of Multiple Approaches for Predicting the Soil-Water Retention Curve: Hyperspectral Information vs. Basic Soil Properties

Information about the soil–water retention curve is necessary for modeling water flow and solute transport processes in soils. Soil spectroscopy in the visible, near-infrared, and shortwave infrared (Vis-NIR-SWIR) range has been widely used as a rapid, cost-effective and nondestructive technique to predict soil properties. However, less attention has been paid to predict soil hydraulic properties using soil spectral data. In this paper, spectral reflectances of soil samples from the Zanjanrood watershed, Iran, were measured in the Vis-NIR-SWIR ranges (350–2500 nm). Stepwise multiple linear regression coupled with the bootstrap method was used to construct predictive models and to estimate the soil–water retention curve. We developed point and parametric transfer functions based on the van Genuchten (VG) and Brooks-Corey (BC) soil hydraulic models. Three different types of transfer functions were developed: (i) spectral transfer functions (STFs) that relate VG/BC hydraulic parameters to spectral reflectance values, (ii) pedotransfer function (PTFs) that use basic soil data as input, and (iii) PTFs that consider spectral data and basic soil properties, further referred to as spectral pedotransfer functions (SPTFs). We also derived and evaluated point transfer functions which estimate soil–water contents at specific matric potentials. The point STFs and SPTFs were found to be accurate at low and intermediate water contents (R2 > 0.50 and root mean squared error [RMSE] < 0.018 cm3 cm−3), while the point PTFs performed better close to saturation. The parametric STFs and SPTFs of both the VG and BC models performed similarly to parametric PTFs in estimating the retention curve. The best predictions of soil–water contents were obtained for all the three transfer functions when the VG and BC retention models were fitted to the retention points estimated by the point transfer functions. Overall, our findings indicate that spectral data can provide useful information to predict soil—water contents and the soil–water retention curve. However, there is a need to extend and validate the derived transfer functions to other soils and regions.

Derivation of the Relationships between Green-Ampt Model Parameters and Soil Hydraulic Properties

The Green–Ampt model (GAM) is a widely used water infiltration model. However, it lacks a reliable theoretical basis to independently and simultaneously determine the GAM parameters of effective hydraulic conductivity (Kₑ) and the average matric pressure head at the wetting front (Hf) from those commonly measured soil hydraulic properties. In this paper, we derived an approximate analytical solution similar to GAM for one-dimensional vertical infiltration into soils with initially uniform soil moisture distribution, with Kₑ and Hf being simultaneously related to the Brooks–Corey (BC) model parameters. The new relationships are not restricted to the piston-type moisture profile or delta-type water diffusivity like in the traditional GAM (TGAM). Infiltration experiments on three soils of various textures were conducted to validate the new approximate analytical solution and the corresponding GAM parameters. It was demonstrated that the predicted cumulative infiltrations and soil moisture profiles by the GAM with Kₑ and Hf calculated by the new expressions (new GAM, NGAM) generally agreed well with the numerical solutions, especially for initially dry soils. In contrast, cumulative infiltrations were considerably over-predicted by the TGAM using Kₑ = Kₛ and Hf calculated by Neuman’s equation. Our theoretical analysis further indicated that even without air entrapped during infiltration, the effective hydraulic conductivity can still be less than the saturated hydraulic conductivity Kₛ. The relative effective hydraulic conductivity ζ (Kₑ/Kₛ) and the relative average matric pressure head at the wetting front η (-Hf/hd where hd is absolute value of the air-entry suction) show a dependency only on soil pore structure index (n) and effective initial soil-water saturation (Sᵢ). The values of ζ increased but η decreased with Sᵢ and n. The theoretical ranges of ζ and η were from 0.5 and 2 for dry heavy-texture soils to 1 and 0 for saturated soils, respectively, which are consistent with the experimental values reported in literatures.

Effect of soil water retention model on slope stability analysis

Understanding of the relationship between volumetric water content (q) and soil capillary pressure (ψ), and between unsaturated hydraulic conductivity K and ψ is important in the analysis of rainwater infiltration into soil and its effect to slope stability. These relationships are known as the water retention curve and the hydraulic conductivity function, respectively. Much soil water retention-hydraulic conductivity models have been proposed such as Brooks-Corey (BC), van Genuchten (VG) that were derived based on empirical fitting curve, and Lognormal (LN) distribution model derived based on soil pore radius distribution. In this study, numerical simulations were performed using the three models to estimate the extent of rainwater infiltration into an unsaturated slope; the formation of a saturated zone, and the change in slope stability. Comparisons were made in terms of soil moisture, water movement phenomena in a soil slope, and the slope stability characteristic. The results of the numerical simulation shows that although BC, VG and LN models have different value of initial condition, the outcome of soil moisture content, water movement and slope stability characteristic are very similar during rainstorm event. Key words: Soil hydraulic properties, water retention-hydraulic conductivity mode, slope stability analysis.