Modification of the McNeal Clay Swelling Model ...

Soil & Water Management & Conservation

Modification of the McNeal Clay Swelling Model Improves Prediction of Saturated Hydraulic Conductivity as a Function of Applied Water Quality Y. D. Ezlit

Department of Soil and Water Science Faculty of Agriculture University of Tripoli Tripoli, Libya

J. McL. Bennett* S. R. Raine R. J. Smith

National Centre for Engineering in Agriculture Univ. of Southern Queensland Toowoomba, QLD 4350

A review of the McNeal clay swelling model, including its underpinning assumptions and the method for determining its parameters, was undertaken. Limitations of the model include model parameter identification, the fixed threshold exchangeable sodium percentage level at which hydraulic conductivity begins to decline, and the assumption that the expanding clay will always be 10% of the soil. To overcome these problems, an improved form of the model that accommodates a range of clay content is proposed. The modified model was used to estimate the reduction in saturated hydraulic conductivity in the three McNeal groups of soils containing different percentages of expanding clay. The model produced good agreement between the observed and estimated saturated hydraulic conductivities over the entire range of irrigation salinity (3–200 mmolc/L) and sodicity used for the original swelling model. The modified model was also successfully validated against three new sets of relative hydraulic conductivity data. The generalization of interlayer clay swelling in the modified model is more appropriately described as determining the dispersive potential of a given solution, rather than physical interlayer swelling. Consequently, this modified model more accurately predicts the reduction in saturated hydraulic conductivity as a function of the sodicity and salinity of the applied water. Abbreviations: ESP, exchangeable sodium percentage; Ksat, saturated hydraulic conductivity; RKsat, relative saturated hydraulic conductivity; SAR, sodium adsorption ratio; TEC, threshold electrolyte concentration.

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he scarcity of water in arid and semiarid regions has led to an increase in irrigation using saline–sodic water, increasing the potential for soil structural degradation on clay soils. Water use efficiency in these regions can be improved by increasing the spatial and temporal precision of irrigation applications. However, as irrigation efficiency is increased, the risk of increasing salinity and sodicity in the root zone becomes a major concern because of a reduction in leaching (Raine et al., 2007). Therefore, using saline–sodic water for irrigation in such regions without appropriate management can compound any pre-existing salinity and sodicity problems. Quantification of the impact of saline–sodic waters on the stability of the soil structure becomes essential when evaluating the suitability of these waters for irrigation. Modeling soil degradation is complex due to the combined effect of sodicity and salinity on the physical and hydraulic properties of the soil; the extent of which depends on numerous inherent soil factors. Soil type (Felhendler et al., 1974; Quirk and Schofield, 1955), clay content and mineral composition (Goldberg et al., 1991), pH of the soil solution (Suarez et al., 1984; Sumner, 1993), the manner

Soil Sci. Soc. Am. J. 77:2149–2156 doi:10.2136/sssaj2013.03.0097 Received 11 Mar. 2013. *Corresponding author ([email protected]). © Soil Science Society of America, 5585 Guilford Rd., Madison WI 53711 USA All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher.

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of application of irrigation water, the initial soil water content (Dehayr and Gordon, 2005), and the amount of organic matter are all known to influence the degree to which soils swell and disperse. Consequently, soil structural degradation caused by sodicity and salinity will be unique to each soil and its condition (Evangelou and McDonald, 1999). Furthermore, the interrelatedness of these factors makes it difficult to quantify the degradation of soil structure with just a simple equation. Saturated hydraulic conductivity (Ksat) is commonly used to evaluate the degree of degradation of soil structure stability. However, Ksat reduction may be influenced by slaking, dispersion and swelling (the initial form of Ksat reduction in soils with 2:1 clay minerals). Swelling and dispersion are used as the primary components in quantifying the reduction of Ksat in most models, while slaking has historically been ignored. Simunek and Suarez (1997) divided the published models relating changes in Ksat to soil sodicity and salinity into two groups. The first group was those based on the diffuse double layer theory, such as the models of Lagerwerff et al. (1969), Russo and Bresler (1977) and Russo (1988), which are inherently limited by the assumptions of diffuse double layer theory and ionic transfer functions. These models are usually complicated and cannot always be applied because they are highly sensitive to their physical parameters. The second group is empirical and semi-empirical models, such as those of Yaron and Thomas (1968) and McNeal (1968), which are based on measurements of Ksat. Among these models, the McNeal (1968) clay swelling model has been used widely and is incorporated in the water and solute movement and chemical reaction model of Simunek et al. (1996). The McNeal (1968) model is based on an experimental clayswelling function, for montmorillonite clay treated with sodic solutions, derived from Norrish (1954), whereby the combined salinity and sodicity effect on a soil is characterized by a swelling factor. Furthermore, McNeal (1968) used a semi-empirical equation to fit experimental curves relating the relative saturated hydraulic conductivity (RKsat) and swelling factor, which were calculated for different combinations of exchangeable sodium percentage (ESP) or sodium adsorption ratio (SAR) and electrolyte concentration. The relationship between RKsat and the swelling factor (the calculated interlayer swelling of contained montmorillonite) provides a description of RKsat at various combinations of solute concentration and ESP. However, the complexity involved in parameterizing the clay swelling model has led workers to use general parameter values developed using only a narrow range of soils. Unsurprisingly, Simunek and Suarez (1997) noted that using generalized parameters for different soils was not likely to provide an accurate prediction of hydraulic conductivity, but rather would serve to describe the type of changes that could occur during infiltration under specific saline–sodic conditions. To accurately model solute and water movement for a particular soil, the parameters need to be properly calibrated. This paper reviews the McNeal (1968) clay swelling model and suggests modifications to both broaden the applicability of the

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model and enable calibration of the parameters for specific soils using Ksat data.

REVIEW OF THEORETICAL BACKGROUND McNeal Clay Swelling Model Parameters

The principle aim of the McNeal (1968) clay swelling model is to describe RKsat in terms of ESP and solute concentration using a montmorillonite interlayer swelling factor. The relationship between RKsat and the model swelling factor (x) can be written as:

1- RK sat =

cx n (1+ cx n )

[1]

where c and n are constants for a given soil within a specified range of ESP. In estimating x, McNeal (1968) used a graphical methodology based on an adjusted ESP (ESP*) and the solute concentration. In this case, ESP* is calculated as:

ESP* = ESP – ESPT

[2]

where ESPT represents the threshold ESP level at which Ksat begins to decline, and is dependent on the solute concentration. The ESPT function proposed by McNeal (1968) was:

ESPT = 1.24 + 11.63 log Co

[3]

where Co is the solute concentration of the added water. It should be noted that Eq. [3] provides an average threshold level for the set of soils studied by McNeal et al. (1968). The swelling factor is determined based on the modified domain model (Norrish, 1954):

x = (famount)(3.6 × 10–4)(ESP*)(d*)

[4]

where famount is the weighted fraction of montmorillonite in the soil, and d* is an adjusted interlayer spacing that needs to be calculated. McNeal (1968) assumed famount = 0.1. If famount ¹ 0.1, the c parameter in Eq. [1] should be replaced by c’; calculated as:

 f  c' = c  amountactual   f amountassumed 

n

[5]

where c’ is the adjusted c parameter for different montmorillonite contents and n is as per Eq. [1]. The adjusted interlayer spacing, d*, can be determined by (McNeal, 1968):

d* = 0 Å, for Co > 300 mmolc/L d* = 356.4(Co )–0.5 + 1.2 Å, for Co ≤ 300 mmolc/L [6] The transformation constant (3.6 × 10–4) in Eq. [4] accounts for the relative increase of the interlayer spacing volume (cm3) due to swelling. McNeal (1968) assumed that n in Eq. [1] was fixed for a particular soil and was closely related to the ESP. His recommended n values based on ESP were:

n = 1, c = 35, for ESP 300 mmolc/L were excluded because d* = 0, meaning that swelling/dispersion has not taken place and that colloids are considered flocculated. TableCurve 3D software (version 4.0.01e) was used to fit a nonlinear surface to the measured RKsat data for each soil group using Eq. [14a] and [14b]. Regression analyses were performed for the three soil Groups (I, II, and III) to determine the appropriate empirical parameters (i.e., a, b, g, m, l, s, and f). Table 1 shows the fitted parameters and the regression statistics. The r2 values for the fitted surfaces exceed 0.98 and the F test values are highly significant (p < 0.001). This indicates that the model appropriately describes the experimental RKsat data obtained from McNeal et al. (1968) as used in the calibration of the original McNeal (1968) clay swelling model. The standard error values range between 0.055 and 0.065 for the three soil groups. The resultant RKsat surfaces and residuals up to ESP = 100 are shown in Fig. 4. The residuals between the estimated and measured RKsat are low. It is clear that the modified clay swelling model provides a sat- Fig. 3. Three-dimensional plot of the McNeal function with relative saturated hydraulic conductivity limited to 100%.

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Table 1. Summary of the surface fit output for soils in Fig. 4 and Fig. 5.

the soil. Soil samples were settled by dropping the core from a height of 50 mm, three times. Model parameters‡ Fitted 2 The average bulk density of five settled soil Soil† R F value standard TEC§ parameters a b g m f error samples was determined for each soil and five s l cores per soil were re-packed to that soil speGroup I 0.649 0.003 8.837 4.046 0.008 6.356 30.818 0.98 74.75 0.065 Group II 1.000 0.912 1.438 7.29 0.204 4.105 –5.054 0.987 112.48 0.065 cific bulk density. Soil columns were allowed Group III 0.449 1.005 0.846 10.968 0.53 4.0799 –11.15 0.991 157.63 0.055 to capillary wet (-4 cm) for a minimum of Soil 1 0.442 0.242 2.07 4.801 0.182 7.678 –11.412 0.932 75.07 0.087 12 h by placement in a pre-treatment calcium Soil 2 0.103 8.305e–7 1.707 6.06 0.174 10.207 –6.882 0.919 81.1 0.102 chloride (EC 2 dS/cm) solution bath. After Soil 3 0.993 0.430 1.543 4.276 0.223 0.844 –1.359 0.891 58.29 0.080 removal from the bath, 1000 cm3 of calcium † Groups I, II, and III are from McNeal (1968) and Soils 1, 2, and 3 are soils used for validation in chloride pre-treatment solution was applied the current study (ponded-head ~20 mm) to the top of each ‡ Empirical parameters calculated within the dispersive model in Eq. [15b]. column. The interface at the core base was § TEC, threshold electrolyte concentration. open to the atmosphere. The pre-treatment (OMC) were calculated. Clay content was determined using was allowed to drain for 2 h, after the last of the pre-treatment solution particle size analysis consistent with Kachanoski et al. (1988). had infiltrated, to remove the influence of soil slaking on Ksat measureSaturated hydraulic conductivity was measured in soil columns ment. A second pre-treatment calcium chloride (EC 2 dS/cm) solu(internal diameter 87.5 mm, length 50 mm) within polyvinyl chloride tion was applied with a constant hydraulic head (~20 mm measured (PVC) pipe (75 mm length, 90 mm external diameter). As boundfrom the upper surface of the soil column) to each column. Discharge ary flow conditions are taken into account in the relative difference (i.e., flux) from the base of each column was measured continuously of Ksat due to solution concentration (RKsat), the use of small cores is until a constant flux (steady-state condition) was recorded. Saturated appropriate (McNeal et al., 1968). Soil was fixed in place with a fine hydraulic conductivity was then calculated using the Darcy equation. mesh base and a fast (Whatman no. 4) filter paper was placed beneath

Fig. 4. Three-dimensional surfaces of best fit for relative saturated hydraulic conductivity (RKsat) (i.e., between predicted and measured) for the three soil Groups I, II, and III. These soils were grouped by clay content with average clay content of 5.7, 16.2, and 48.5% for Groups I, II, and III, respectively (McNeal et al., 1968); ESP, exchangeable sodium percentage.

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Table 2. Selected soil properties of three southeast Queensland soils used for model validation. Soil

Soil order

Texture

Clay content OMC†

CEC

–%–

cmolc/kg 1 Gray Vertisol medium clay 43.8 2.3 32 2 Brown Alfisol clay loam 39.0 0.5 39 3 Red Aridisol sandy loam 12.7 0.8 5 † OMC, organic matter content; CEC, cation exchange capacity.

A range of up to 10 sequentially increasing SAR treatments were then applied to each of the five columns where each column was subjected to SAR treatments at a single EC (0.5, 1.0, 2.0, 4.0, and 8.0 dS/cm) (Fig. 5). These treatment solutions comprised sodium and calcium chloride salts to achieve the desired EC and SAR. The first treatment applied to each column was SAR 0, and in the case of all treatments, Ksat was measured with a constant ponded-head (~20 mm) after steady-state conditions were achieved. The RKsat of the column was calculated as the ratio between Ksat of the SAR > 0 water quality treatments (EC the same as the column) and Ksat measured when the SAR 0 water treatment was applied. The RKsat data were then used in Eq. [15a] and [15b]. Fitted surfaces for Soils 1, 2, and 3 (Table 2) are shown in Fig. 6.

Fig. 5. Diagrammatic representation of the water quality treatments applied to soils during validation of the modified McNeal clay swelling model. Sodium adsorption ratio was increased with each successive application of treatment solution at a constant electrolyte concentration (electrical conductivity).

For the three soils of different clay properties (Table 2), the modified clay swelling model returned highly significant surface fits (p < 0.001). This demonstrates that the modifications to the original McNeal clay swelling model are appropriate for a broad range of soils. Furthermore, by use of the modified model, use-

Fig. 6. Three-dimensional surfaces of best fit for relative saturated hydraulic conductivity (RKsat) (i.e., between predicted and measured) for the Soils 1, 2, and 3 (Table 2); ESP, exchangeable sodium percentage.

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ful interpretation of the surface can be made to predict a soil’s response to sodicity and salinity interactions.

DISCUSSION McNeal (1968) noted that the original clay swelling model is likely to be less accurate for soil with a low montmorillonite content. While the model can appropriately be used for soils devoid of montmorillonite, parameters for a low montmorillonite soil would need to be applied and calibration undertaken using a solution for which a reduction in Ksat has occurred (McNeal, 1968). Under these conditions the model is predicting the likelihood of soil dispersion and the montmorillonite interlayer swelling values have no physical meaning (McNeal, 1968). This is also true for the modified clay swelling model presented in this paper. As the f value has been generalized and determined empirically it should not be afforded physical meaning and interlayer swelling cannot be determined. Hence, the modified clay swelling model provides a prediction of a solution’s dispersive tendency for a particular soil. For this reason, it would be more appropriate to refer to this modification as a dispersive model. This dispersive model provides a continuous 3-dimensional surface describing the reduction in hydraulic conductivity as a function of solution salinity and sodicity. For a given percent reduction in Ksat, the point where solution sodicity overcomes stabilizing osmotic forces can be identified as the threshold electrolyte concentration (TEC). The dispersive model provides a means to determine this relevant to a specific soil by selecting the salinity/sodicty contour applicable to the percent reduction in Ksat. Quirk and Schofield (1955) suggested a percent reduction in Ksat of 10% defined the TEC, while others suggested 15% (Quirk, 2001) and 25% (McNeal and Coleman, 1966). This reduction percentage is somewhat arbitrary, as reduction in Ksat occurs gradually with increase in solution sodicity and no single point reduction in Ksat truly defines the TEC (Quirk and Schofield, 1955). Irrespective of the chosen RKsat, the dispersive model presented in this paper will allow a particular soil’s reduction in hydraulic conductivity to be plotted as a 2-dimensional function of irrigation water sodicity and salinity. This will provide irrigation practitioners with a means by which to assess the suitability of marginal quality irrigation for use in regions of interest.

CONCLUSIONS Limitations of McNeal’s (1968) clay swelling model were identified. A modified model was developed by clarifying the boundary between flocculation and disaggregation conditions, using a soil specific form of ESPT, and empirically fitting parameters relating to the effect of generic clay swelling. This modified model, which is more appropriately referred to as a dispersion model, was successfully calibrated to McNeal’s (1968) data set and further validated against new data. The procedure outlined for parameterizing the modified model provides more accurate estimates of the steady state saturated hydraulic conductivity produced when saline–sodic water is applied to a specific soil.

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