Selection of Water Retention Parameters and Hydraulic Properties

IV. THE RELATIVE INFLUENCE OF LAND USE CHANGE AND CLIMATE

4.2. Methods

4.2.3. Model Development

4.2.3.2. Selection of Water Retention Parameters and Hydraulic Properties

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curve is vertically stretched [Winter, 1983]. Variation in the parameter 𝑐, however, has a large effect on the sharpness of water retention curve. The smaller the value of 𝑐 (at the same value of 𝐴), the less sharp is the water retention curve [Winter, 1983]. Smaller values of 𝑐 are

characteristic of curves for increasingly finer-grained and more poorly sorted porous media [Winter, 1983]. For example, if 𝑐 = 2, the curve has an “S” shape characteristic of silty loams and silty clay loams [Brooks and Corey, 1966]. The exponent in the approximation of the relationship between water saturation and relative permeability (𝑑 in Equation (4.4)) is directly related to the pore size distribution of the porous media [Winter, 1983]. Brooks and Corey [1966]

show that based on laboratory analysis of many different types of rock samples, the exponent almost always is between three and four. The smaller the value of 𝑑, the closer to linear is the relationship; the curve for 𝑑 = 1 is a straight line [Winter, 1983].

For simplicity, hysteresis is neglected in Equations (4.3) and (4.5). The origin and assumptions underlying Equations (4.4) and (4.5) are given by Brooks and Corey [1966]. Equation (4.2) also contains several simplifications, as discussed by Cooley [1971]: air movement is assumed to be without resistance; the effects of total stress changes at a point caused by changing saturation are neglected; and the effects of variable formation compressibility caused by deformation and changing saturating are neglected.

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the Locke Island landslide. Holes were drilled between January 14, 1998 and April 11, 1998 on the bluffs and between April 15, 1999 and April 20, 1999 on the landslide [Bennett et al., 2002].

The soil texture information contained in the existing geologic logs was derived from lab tests on samples from varying intervals. Average soil texture parameters (i.e., percent sand, percent silt, and percent clay) for each geologic layer were calculated using a weighted average of soil texture parameters from all drill logs; the interval length of each sample was used as the weighting factor. The computer program ROSETTA5 [Schaap et al., 2001] was used to estimate van Genuchten water retention parameters [van Genuchten, 1980] and saturated hydraulic conductivities, as well as unsaturated hydraulic conductivity parameters based on the pore-size model of Mualem [1976] (Table 4-1). Initial finite element model results, however, indicated that the ROSETTA-estimated saturated hydraulic conductivity values were too small to accommodate the increased flow from a doubling of recharge from precipitation. Therefore, saturated hydraulic conductivity values were multiplied by a factor of 1.4273. This multiplier and the associated upslope, fixed head boundary condition were arrived at through several trial-and-error simulations, such that a doubling of recharge from precipitation resulted in an approximate doubling of the groundwater flux at the toe of the landslide. Accurate measurements of specific storage are obtained from multiple well interference tests in the field; however, no field data were found in the literature on specific storage or porosity for any of the media considered in this study. Under such circumstances, specific storage and porosity values for each geologic unit were estimated from representative values in the literature of these parameters for various

geologic materials. All geologic units were assigned the same value for specific storage based on the representative values of specific storage for various geologic materials [Domenico and

5 The ROSETTA program comes with a graphical user interface, and can be downloaded from the United States Salinity Laboratory website: http://www.ussl.ars.usda.gov/, accessed May 15, 2013.

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Mifflin, 1965] as reported in Batu [1998] (Table 4-1). Soil texture information from the geologic logs was used to obtain ranges of representative porosity values for the various materials found within each geologic unit [Das, 2008; Hough, 1969; VSS, 1999]; the porosity ranges were

averaged for each of the different materials found within each unit, and an average porosity value was calculated for each geologic unit (Table 4-1).

Table 4.1 | ROSETTA estimated van Genuchten water retention parameters and saturated hydraulic conductivity for each geologic unit

Geologic Unit

Qe Qgf Qls Trlb Trlc

𝜶 0.5773 0.6055 0.5359 0.5048 0.5733

𝒏 1.8754 1.5736 1.2595 1.1593 1.6588

𝜽_𝒔 0.4366 0.4713 0.4861 0.4934 0.4396

𝜽_𝒓 0.0422 0.0421 0.1026 0.1051 0.0371

𝑲_𝒙𝒙 0.1786 0.1004 0.0341 0.0248 0.1389

𝑲_𝒛𝒛 0.0179 0.0100 0.0034 0.0025 0.0139

𝑺_𝒔 0.0001 0.0001 0.0001 0.0001 0.0001

𝝓 0.3617 0.3850 0.3908 0.4900 0.3500

Notes: ROSETTA was not used to estimate the values for specific storage (𝑆_𝑠) and porosity (𝜙). In absence of field data in the literature on specific storage for any of the media considered in this study, all geologic units were assigned the same value for specific storage based on the representative values of specific storage for various geologic materials [Domenico and Mifflin, 1965] as reported in Batu [1998]. Average porosity values for each geologic unit were calculated using representative values of porosity [Das, 2008; Hough, 1969; VSS, 1999] for the different geologic materials within each geologic unit as determined from drill logs.

The ROSETTA program implements five hierarchical pedotransfer functions (PTFs) for the estimation of water retention, and the saturated and unsaturated hydraulic conductivity. As a

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result of the hierarchy in PTFs, the program can estimate van Genuchten water retention parameters and the saturated hydraulic conductivity using textural classes only and in

combination with more extended input data (e.g., bulk density and one or two water retention points) [Schaap et al., 2001]. The Brooks and Corey [1966] soil water retention model was used within the groundwater model, as fewer stability problems than with the van Genuchten model have been noted by others (e.g., Gu, 2007). Therefore, soil moisture characteristic curves were created for each of the five geologic units using the van Genuchten water retention parameters for each unit prescribed by ROSETTA. The retention function is given by [van Genuchten, 1980]

𝜃(ℎ) = 𝜃_𝑟+ 𝜃_𝑠− 𝜃_𝑟 [1 + (𝛼ℎ)^𝑛]^1−𝑛1

, (4.10)

where

𝜃(ℎ) measured volumetric water content (cm³ cm^-3) at the suction h (cm, taken positive for increasing suctions) [L³L^-3];

𝜃_𝑟 residual water content (cm³ cm^-3) [L³L^-3];

𝜃_𝑠 saturated water content (cm³ cm^-3) [L³L^-3];

𝛼 parameter related to the inverse of the air entry suction (>0, in cm^-1) [L^-1];

𝑛 parameter that is a measure of the pore-size distribution (> 1) [dimensionless].

Combination of Equation (4.10) with the pore-size model of Mualem [1976] produces the following closed-form equation for unsaturated hydraulic conductivity [van Genuchten, 1980]

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𝐾(𝑆_𝑤𝐷) = 𝐾₀𝑆_𝑤𝐷^𝐿 {1 − [1 − 𝑆_𝑤𝐷

𝑛 𝑛−1]

1−_𝑛¹

}

2

, (4.11)

where

𝐾₀ a fitted matching point at saturation (cm day^-1) [LT^-1];

𝐿 an empirical parameter that is normally assumed to be 0.5 [dimensionless];

and the normalized water content or effective saturation, 𝑆_𝑤𝐷, is computed as

𝑆_𝑤𝐷= 𝜃(ℎ) − 𝜃_𝑟 𝜃_𝑠 − 𝜃_𝑟 .

(4.12)

Through direct substitution of the expression for the normalized water content given in Equation (4.3) in place of 𝑆_𝑤𝐷 in Equation (4.12), the volumetric water content, 𝜃(ℎ), can be computed as

𝜃(ℎ) = ( 𝐴

−𝜓^𝑐 + 𝐴) (𝜃_𝑠− 𝜃_𝑟) + 𝜃_𝑟

(4.13)

using the Brooks and Corey [1966] soil water retention model. For each of the five geologic units, the parameters 𝐴 and 𝑐 were adjusted such that the soil moisture characteristic curve based on the Brooks and Corey [1966] soil water retention model best fit the soil moisture

characteristic curve based on the van Genuchten [1980] soil water retention model (Table 4-2).

Saturated and residual water contents (𝜃_𝑠 and 𝜃_𝑟, respectively) for each unit were set to those values prescribed by ROSETTA (Table 4-2).

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Table 4.2 | Estimated Brooks and Corey [1980] water retention parameters

Geologic Unit 𝑨 𝒄 𝜽_𝒓 𝜽_𝒔

Qe 3.6 1.2 0.0422 0.4366

Qgf 5.0 0.9 0.0421 0.4713

Qls 7.5 0.5 0.1026 0.4861

Trlb 8.0 0.4 0.1051 0.4934

Trlc 3.7 0.9 0.0371 0.4396

Notes: The values for the residual water content (𝜃_𝑟) and the saturated water content (𝜃_𝑠) are those prescribed by ROSETTA.