On the hydraulic properties of coarse-textured sediments at intermediate water contents

Transcription

1 WATER RESOURCES RESEARCH, VOL. 39, NO. 9, 1233, doi: /2003wr002387, 2003 On the hydraulic properties of coarse-textured sediments at intermediate water contents Raziuddin Khaleel Fluor Federal Services, Richland, Washington, USA Paula R. Heller UFA Ventures, Richland, Washington, USA Received 5 June 2003; accepted 3 July 2003; published 4 September [1] A modified steady state head control method was used to obtain, on identical samples, direct measurements of soil moisture retention (volumetric water content q versus matric potential y) and unsaturated hydraulic conductivity (K ) as a function of both q and y. The minimum y values for the undisturbed coarse-textured samples were as low as 400 cm, whereas the q values were as low as Of the 79 samples, 41 contained a high gravel fraction (>2 mm size) that ranged from 20 to 71% by weight. The remaining samples were sandy with very little gravel fraction. We examined similarities and differences between the two soil types in their retention and K(q) slopes for the intermediate moisture regime. The retention data for the gravelly soils fell within a narrower range than for the sandy type. The water capacity (dq/dy) estimates for the two soil types showed similar variability. Although both soils are coarse-textured, important differences were noted in two integral measures for y(q) and K(q) measurements. The mean and variance for the Campbell pore-size distribution parameter (b) and K(q) slope (b) estimates for the gravelly type were larger than those for the sandy type. A unique relation was noted between b and b; the relationship was similar for the two soil types with a very dissimilar particle-size distribution. INDEX TERMS: 1875 Hydrology: Unsaturated zone; 1866 Hydrology: Soil moisture; 1894 Hydrology: Instruments and techniques; KEYWORDS: moisture retention, unsaturated hydraulic conductivity, sandy soils, gravelly soils, unit gradient method Citation: Khaleel, R., and P. R. Heller, On the hydraulic properties of coarse-textured sediments at intermediate water contents, Water Resour. Res., 39(9), 1233, doi: /2003wr002387, Introduction [2] Unsaturated hydraulic conductivities ( K ) are often obtained in the laboratory for either K as a function of matric potential y or volumetric water content q. While the mean and variance of K(y) slopes provide important information about the spatial variability of heterogeneous unsaturated soils [Khaleel and Relyea, 2001], it is sometimes preferable to have direct K(q) measurements. An example is the use of the conductivity slope, based on K(q) measurements, to quantify movement of the wetting front during gravity drainage. Also, in modeling fluid flow, a q-based formulation is often used for the Richards equation, thus requiring K(q) functional relations. In situations where the retention data are available for the identical sample, K(y) measurements can be transformed into K(q) functional relations. However, for arid regions where gravelly (>2 mm size) soils are ubiquitous, such an approach presents additional problems. Retention data are typically obtained in the laboratory for the fine fraction (<2 mm size). The measured data are then corrected for the gravel content [Khaleel and Relyea, 1997; Gardner, 1986; Bouwer and Rice, 1984]. Such a correction can lead to Copyright 2003 by the American Geophysical Union /03/2003WR SBH 2-1 uncertainties in q(y) estimates for the bulk (gravels and fine) soil and subsequent estimates for K(q). It is questionable as to whether a simple correction [Gardner, 1986] can be applied for the entire range of q from wet to relatively dry as well as to account for gravels of varying size and shapes. Besides, moisture retention for the gravel itself cannot always be considered negligible [Paruelo et al., 1988; Flint and Childs, 1984]. In addition, conductivity data for gravelly sediments based on corrections for nongravelly K measurements may not always produce consistent results [Mehuys et al., 1975]. [3] Natural sediments often require two or more distribution functions to adequately describe unsaturated properties for the entire pore-size distribution. In fact, a number of multiregion models have been proposed primarily for nongravelly soils having multimodal pore-size distributions [Poulsen et al., 2002; Jacobsen et al., 1999]. Poulsen et al. [2002], for example, used multiregion power functions to represent both moisture retention and K within the macropore (y > 10 cm), the mesopore ( 10 y > 350 cm), and the micropore ( 350 y > 15,000 cm) regions. Little work, however, has been reported on the unsaturated properties for gravelly soils. [4] In this paper, we focus on the mesopore region (i.e., intermediate moisture regime) for the soil samples described by Khaleel and Relyea [2001], who noted important differ-

2 SBH 2-2 KHALEEL AND HELLER: HYDRAULIC PROPERTIES OF SEDIMENTS ences in parameter statistics between the sandy and gravelly soils, although both are coarse-textured. We specifically evaluate the dependence, if any, of the K(q) slope on the retention slope. To avoid uncertainties in q(y) and K estimates for gravelly soils on the basis of measurements for nongravelly soils, we made direct measurements in the laboratory for both soil types, resulting in a triplet of q-y-k measurements for each sample. 2. Power Function Models for Q(y) and K(Q) [5] We explore the use of power function models to represent the q(y) and K(q) measurements for both gravelly and sandy soils. The q(y) data, for example, can often be represented by the Campbell [1974] empirical model q b y ¼ y b where y b is the air entry potential (bubbling pressure), q s is the saturated water content, and b is an empirical fitting parameter. In applying equation (1) to the mesopore region of intermediate moisture regime, we obtain b by defining the moisture retention slope over the range of n( y) and nq values, i.e., q s ð1þ d n y b ¼ ð Þ : ð2þ d nq A plot of n( y) versus lnq for y < y b typically yields a straight line with a slope equal to b. The hydraulic conductivity can be described by a similar power function [Campbell, 1974] over the same moisture regime by q b K ¼ K s where K s is the saturated hydraulic conductivity. Again, we obtain b by defining the slope over the same mesopore region of y-q range as in equation (2), i.e., q s ð3þ b ¼ d nkðþ q : ð4þ d nq Best fit estimates for b and b for a given sample are obtained by least squares fit to q(y) and K(q) measurements, respectively. Note that q s and K s in equations (1) and (3) are simply curve-fitting parameters and obtained by extrapolating the fitted lines. 3. Materials and Methods [6] The samples were collected in conjunction with (cable tool) drilling activities that were conducted as part of a site characterization program at the U. S. Department of Energy s Hanford Site in southeastern Washington. Nearly all samples were obtained from the Hanford formation, which was deposited by a series of cataclysmic glacial floods, the last one occurring about 13,000 years B.P. The samples (up to a maximum depth of 94 m) were obtained from boreholes that were far apart; samples that were from the same borehole were spaced mostly in excess of 3 4 m. The soils are flood deposits and consist of sands and gravels of various sizes. Gravel clasts are randomly distributed and are composed of a wide variety of rock types (e.g., basalt, quartzite, granite, and gneiss) having variable but significantly less porosities than the soil matrix filling the space between gravel clasts. The infilling soil matrix primarily consists of coarse- to fine-grained sand, with much lesser amounts of silt and clay. [7] All experiments were run on the undisturbed, bulk (gravels and fine) samples, which were drawn from sleeves within a lexan-lined split-tube sampler (10.2 cm in diameter, hammered into soil). The flow cells typically were 10.2 cm in diameter and 15.2 cm in height, with a sample volume of about 1000 cm 3. For all samples, q-y-k measurements were first made for the bulk sample, followed by dry bulk density (BD) and particle-size distribution (PSD). Dry sieving was used to determine the PSD. For most samples, K s was obtained as part of the conductivity experiment. For some samples a constant-head permeameter was used to measure K s. [8] A variation of the unit gradient method [Klute and Dirksen, 1986] was used to obtain q(y), K(y), and K(q) measurements. The experimental setup was identical to that of Figure 2 of Khaleel et al. [1995]. It includes a constanthead (drip) water supply, a flow cell, two tensiometers (10 cm apart), and a constant-head outflow system. The soil column was saturated from the bottom to ensure that air was driven out the top of the column as the sample became saturated. At y 100 cm, a vacuum system was used. When the readings for both tensiometers were equal, steady flow and uniform q and y were assumed to exist (i.e., unit gradient conditions). About six steady state q-y-k triplets were obtained for each sample; y values ranged from about 20 to 400 cm. The measured K corresponded to the y and q of the region of the sample in which unit gradient was achieved. The conductivity function was tabulated by proceeding through the series of steady state flows with progressively decreasing values of y, beginning with y close to zero. Measurements of y, liquid volume, and q were continued until the flow rate became too low to measure (about 0.1 ml per day). The samples were weighed at the end of each successive K(y) steady state measurement to determine q and the moisture retention. Following completion of experimental runs, the sample was oven dried at 105 C to determine dry weight and BD. Experimental run times varied from about 2 to 6 weeks per sample, the average being about 5 weeks per sample. 4. Results and Discussion [9] A total of 79 samples (41 gravelly and 38 sandy) were analyzed in the laboratory. A sample was classified as gravelly if it contained more than 20% gravel by weight. The differences in PSD, BD, and K s between the sandy and gravelly soils are summarized by Khaleel and Relyea [2001]. Ranges in texture for the two soil types are indicated in Table 1. [10] Figure 1a shows the measured retention data. The q values for the gravelly soils are generally lower than the corresponding values for the sandy samples, and fall within a narrower range. However, they are well within the range of measured q values for the sandy samples. For each sample, a best fit retention curve was obtained by fitting

3 KHALEEL AND HELLER: HYDRAULIC PROPERTIES OF SEDIMENTS SBH 2-3 Table 1. Ranges in Texture for the Two Soil Types a Soil Type Gravelly (n = 41) Sandy (n = 38) Gravel (>2 Coarse Sand (0.2 2 Soil Texture Fine Sand ( Silt ( Clay (< a No organic matter was present in the soil samples. q(y) data to van Genuchten (VG) model [van Genuchten, 1980]. The purpose for the curve fitting was primarily to obtain dq/dy estimates. During curve fitting, the VG parameters were allowed to vary. Although not shown here, the q values based on the fitted VG model showed excellent agreement with the actual measurements. Figure 1b shows the water capacity, dq/dy for both soil types, calculated on the basis of the fitted VG curve. Similar to the retention data, dq/dy values are quite variable for both soil types. Nonetheless, at the drier end of the moisture regime (y < 100 cm), dq/dy for the gravelly soils trends slightly lower than for the sandy type. [11] Figure 1c shows the measured K and K s values for individual samples. When expressed as a function of q, the measured K values are similar for samples with and without gravels. A lack of apparent difference in K(q) values for the two soil types is similar to findings for K(y) [Khaleel and Relyea, 2001]. However, unlike K(y) data, the variability in K(q) measurements for both soil types is nearly identical and no narrower range is apparent for the gravelly K(q). Our results on measured K for gravelly samples are different from those of Mehuys et al. [1975], who obtained distinct curves for the gravelly and nongravelly samples. However, they reported that a correction of q for the nongravelly samples, based on the volume of gravels for each sample, adequately accounted for differences observed when q was computed on a total volume basis. Of course, unlike Mehuys et al., no corrections were needed, since our gravelly K(q) values were direct measurements. Note that for some gravelly samples at low y, K measurements were not available, although q was measured at those y values (Figure 1a). [12] While the data in Figure 1b are primarily included to illustrate dependence of dq/dy on y, they cannot be used directly to obtain integral measures for soil properties. The parameters b and b provide such measures. Linear regression analyses of n( y) versus lnq yielded Campbell b for each sample; r 2 for individual samples ranged from about 0.86 to Similarly, linear regression analyses of nk versus nq yielded b for each sample; r 2 ranged from about 0.89 to Overall, for individual gravelly and sandy samples, as long as the data near saturation in the macropore region were excluded, single-slope power function models adequately described the y(q) and K(q) measurements for the mesopore region; the r 2 value was used to judge the adequacy of fit. [13] Figure 2 shows scatterplots of the measured data and fitted values for both soil types. No bias is apparent; an almost equal number of data lie above and below the 1:1 line. For the gravelly samples, on the average, the q values for b and b ranged from about to 0.170, with an overall range of For the sandy samples, on the average, the corresponding q values ranged from about to 0.216, with an overall range of On the average, the corresponding y regime for the gravelly samples ranged from about 35 to 245 cm, whereas for the sandy samples, it ranged from 45 to 220 cm. [14] Table 2 lists the summary statistics for b and b. While both soils are coarse-textured, the average b and b estimates for the gravelly type are much larger than those for the sandy type. Especially for the gravelly soils, the average b is almost twice as large, compared with the sandy Figure 1. (a) Measured q(y), (b) dq/dy, and (c) K s and K(q) for both soil types.

4 SBH 2-4 KHALEEL AND HELLER: HYDRAULIC PROPERTIES OF SEDIMENTS Figure 2. (a) Measured and fitted y (r 2 = 0.92) and (b) measured and fitted K (r 2 = 0.98) for both soil types. type. In contrast, the average b for the gravelly soils is only about 1.2 times larger than that for the sandy type. [15] It is interesting to compare our measured K(q) slopes with those predicted by existing models. For example, using the Campbell [1974] model and the average b estimate for the sandy soils, the K(q) slope is predicted to be 8.64 (i.e., 3+2b), which is close to the observed average K(q) slope of 8.12 for the same soil type. However, using the same conductivity model and the average b for the gravelly soils, the average K(q) slope is estimated to be about 14.1, which is much larger than the observed average b of 9.89 for the gravelly type. This simply demonstrates the inappropriateness of using the average gravelly b to estimate the average gravelly b. [16] The fact that our average b and b for the gravelly soils are larger than those for the sandy type is counterintuitive to data in literature that suggest that the power function exponents for coarse-textured soils generally have smaller b and b values, compared with those for fine-textured soils [e.g., Campbell, 1974]. While this is true for the samples reported in literature, a similar extensive database of q(y) and K(q) measurements for undisturbed samples using a single experimental technique on identical samples for sandy as well as gravelly soils is not available. Our results on larger b values for gravelly soils are, however, consistent with those of Mehuys et al. [1975]. Besides our work, Mehuys et al. is the only known work that contains K(q) measurements for both soil types. As discussed later, our results on the relationship between b and b are also consistent with Poulsen et al. [2002] results for undisturbed samples. Note that numerous data sets in literature are based on repacked, sieved samples. Compared to undisturbed samples, differences are expected in the pore structure of texturally similar but repacked samples. The differences can influence integral measures for a soil sample. [17] On the basis of Kolmogorov-Smirnov test [Conover, 1980] results, both b and b estimates for the two soil types followed the identical (lognormal) distribution. This is not surprising since both b and b are integral measures of the same soil sample and the distribution functions for the two parameters should be identical. Nonetheless, this indicates that although the means and variances of b and b are considerably different, K(q) measurements and b for both soils can be considered in a broader grouping (i.e., of the same family of coarse-textured soils) relative to certain measurable physical property such as PSD. [18] Since the integral parameters b and b are related to pore-size distribution, we can expect a priori on physical grounds that they will be correlated. In fact, Figure 3 shows that a unique relationship does exist between the Campbell pore-size distribution parameter b and the K(q) slope b, which spans the same intermediate moisture regime as that for b. A standard t-test shows that the observed r is significantly different from zero at the 0.05 level. The trend line equations and slopes (Figure 3) for the two soil types are not significantly different from each other. This indicates that even though the retention and K(q) slopes are considerably different, the relation between the two integral measures, b and b, for the two soil types is similar for the intermediate moisture regime. This again simply confirms a broad range of applicability for the Campbell b versus b Table 2. Mean and Variance of b and b for the Gravelly and Sandy Samples Soil Type b m High Low s m High Low s Gravelly Sandy b Figure 3. The b versus Campbell b relationship for both gravelly (r 2 = 0.84) and sandy (r 2 = 0.76) samples; the solid lines are the trend lines for the two soil types (b =1.1b +5.1 for sandy and b =1.1b for gravelly).

5 KHALEEL AND HELLER: HYDRAULIC PROPERTIES OF SEDIMENTS SBH 2-5 relation. Furthermore, it is interesting to note that our b versus b relation (Figure 3) for the two soil types is similar to the Poulsen et al. [2002] relation (b =1.2b + 3.2) for the mesopore region of the undisturbed samples they analyzed. [19] Conductivities across the entire pore-size distribution are often estimated using the q(y) and K s measurements [van Genuchten, 1980; Mualem, 1976]. This implicitly assumes invariance across the entire pore-size distribution from saturation to a relatively low q. These models therefore use the same set of parameters to predict K(q) across the entire pore-size distribution from macropore to mesopore region. Given the apparent correlation between b and b, it is not surprising that a predictive method that uses the retention data and a single K measurement in the intermediate moisture regime provides a much better match to measured K values in the mesopore region, compared with the standard van Genuchten-Mualem method [Khaleel et al., 1995]. 5. Concluding Remarks [20] The work resulted in a unique and extensive database of simultaneous q(y) and K(q) measurements for undisturbed gravelly samples, with the gravel fraction ranging from 20 to 71% by weight. Both q(y) and K(q) measurements were conducted on identical bulk (gravel and fine) samples; no gravel corrections were needed. Although both soil types were coarse-textured, important differences were noted in the integral measures for q(y) and K(q) for the intermediate moisture regime. The mean and variance for both b and b estimates for the gravelly type were larger than those for the sandy type. It is encouraging to find the unique relation between b and b and its similarity for the two soil types. The two parameters therefore are more than empirical fitting parameters and depend essentially on the pore-size distribution. Unsaturated conductivities are often predicted on the basis of q(y) measurements and assuming invariance of properties across the entire pore-size distribution. Our work lends support to the use of multiregion models with variable b and b values as a viable alternative in predicting K(q) from q(y). 87RL Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof or its contractors or subcontractors. The views and opinions of the authors do not necessarily state or reflect those of the United States Government or any agency thereof. 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Aguiar, and R. A. Golluscio, Soil water availability in the Patagonian arid steppe: Gravel content effect, Arid Soil Res. Rehabil., 2, 67 74, Poulsen, T. G., P. Moldrup, B. V. Iverson, and O. H. Jacobsen, Three-region Campbell model for unsaturated hydraulic conductivity in undisturbed soils, Soil Sci. Soc. Am. J., 66, , van Genuchten, M. T., A closed-form solution for predicting the conductivity of unsaturated soils, Soil Sci. Soc. Am. J., 44, , [21] Acknowledgments. The support provided by the Westinghouse Hanford Company Geotechnical Engineering Laboratory staff is gratefully acknowledged. Suggestions provided by the associate editor and anonymous reviewers were most helpful in revising the manuscript. The work reported was performed for the U.S. Department of Energy under contracts DE-AC06-99RL14047, DE-AC06-96RL10930, and DE-AC06- P. R. Heller, UFA Ventures, 2000 Logston Boulevard, Richland, WA 99352, USA. R. Khaleel, Fluor Federal Services, P. O. Box 1050, Richland, WA 99352, USA. (raziuddin_khaleel@rl.gov)