HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Abstract Figures Only Full Text (PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in ISI Web of Science Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via ISI Web of Science (2) Citing Articles via Google Scholar Google Scholar Articles by Winfield, K. A. Articles by Martin, P. M. Search for Related Content PubMed Articles by Winfield, K. A. Articles by Martin, P. M. GeoRef GeoRef Citation Agricola Articles by Winfield, K. A. Articles by Martin, P. M. Related Collections Water Retention/Capillary Pressure Vadose Zone Processes and Chemical Transport

ORIGINAL RESEARCH

Resolving Structural Influences on Water-Retention Properties of Alluvial Deposits

^a U.S. Geological Survey, 345 Middlefield Road, MS 421, Menlo Park, CA 94025
^b U.S. Geological Survey, 5735 Kearny Villa Road, San Diego, CA 92123
^* Corresponding author (jrnimmo{at}usgs.gov)

¹ Brand names are given to identify products used in research, and do not imply endorsement by the U.S. Geological Survey.

	ABSTRACT

TOP EXECUTIVE SUMMARY ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
With the goal of improving property-transfer model (PTM) predictions of unsaturated hydraulic properties, we investigated the influence of sedimentary structure, defined as particle arrangement during deposition, on laboratory-measured water retention (water content vs. potential [()]) of 10 undisturbed core samples from alluvial deposits in the western Mojave Desert, California. The samples were classified as having fluvial or debris-flow structure based on observed stratification and measured spread of particle-size distribution. The () data were fit with the Rossi–Nimmo junction model, representing water retention with three parameters: the maximum water content (_max), the -scaling parameter (_o), and the shape parameter (). We examined trends between these hydraulic parameters and bulk physical properties, both textural—geometric mean, M_g, and geometric standard deviation, _g, of particle diameter—and structural—bulk density, _b, the fraction of unfilled pore space at natural saturation, A_e, and porosity-based randomness index, _s, defined as the excess of total porosity over 0.3. Structural parameters _s and A_e were greater for fluvial samples, indicating greater structural pore space and a possibly broader pore-size distribution associated with a more systematic arrangement of particles. Multiple linear regression analysis and Mallow's C_p statistic identified combinations of textural and structural parameters for the most useful predictive models: for _max, including A_e, _s, and _g, and for both _o and , including only textural parameters, although use of A_e can somewhat improve _o predictions. Textural properties can explain most of the sample-to-sample variation in () independent of deposit type, but inclusion of the simple structural indicators A_e and _s can improve PTM predictions, especially for the wettest part of the () curve.

Abbreviations: OG, Oro Grande • PSD, particle-size distribution • PTM, property-transfer model • SC, Sheep Creek

	INTRODUCTION

TOP EXECUTIVE SUMMARY ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
A MORE COMPLETE ACCOUNTING for structural effects is critical for the development of property-transfer models that estimate unsaturated hydraulic properties, including water retention, the relation of water content () to water potential (), and unsaturated hydraulic conductivity K(), from easy-to-measure bulk physical properties. Such models typically use particle-size distribution (PSD) and bulk density (_b) as their primary inputs (e.g., Gupta and Larson, 1979; Arya and Paris, 1981; Haverkamp and Parlange, 1986). Most PTMs rely on textural effects represented by the PSD. However, in many if not most soils, structural effects are at least equally important. Structure is defined as the arrangement of soil components resulting from aggregate formation, natural depositional sorting, animal burrows, shrink–swell phenomena, root channels, and similar processes.

Bouma (1989) introduced the term pedotransfer function to refer to the transfer of soil textural data into hydraulic data using a regression equation. We use a more general term, property-transfer model (PTM), which applies to soils and deeper sediments and to both classes of such models, empirical and quasiphysical. Empirical models rely on statistical methods to determine patterns among the bulk physical and hydraulic properties. These PTMs typically employ multiple linear regression or neural-network procedures to estimate either () or K() from textural variables (particle-size statistics or textural-class percentages) and _b. Quasiphysical models are based on theoretical physical relationships between pore sizes and particle or aggregate sizes (Arya and Paris, 1981; Haverkamp and Parlange, 1986; Nimmo, 1997; Haverkamp and Reggiani, 2002). Empirical PTMs can be further subdivided based on the specific approach chosen. One approach involves fitting a parametric () function (or set of functions) to the () measurements, and developing separate regression equations for each of the () parameters (Campbell, 1985; Saxton et al., 1986; Wösten and van Genuchten, 1988; Vereecken et al., 1989; Campbell and Shiozawa, 1992; Schaap et al., 1998). Another involves developing unique equations for at the values of determined during measurement of () (Gupta and Larson, 1979; Rawls and Brakensiek, 1982; Puckett et al., 1985; Mecke et al., 2002). A third approach uses at least one measured value of (), in addition to bulk physical properties, as input (Gregson et al., 1987; Schaap et al., 1998).

Measures of structure, besides _b, are seldom included as input to PTMs. Arya and Paris (1981) and Haverkamp and Parlange (1986) used PSD and porosity () or _b as inputs to their models, but did not include additional measures of structure. A modification to the Arya and Paris (1981) model to include aggregate-size distribution as an index of soil structure (Nimmo, 1997) improved agreement between modeled and measured () values by R² = 12.4%, on average, for 17 samples tested. Nimmo (1997) also partitioned into textural and structural parts approximating the fraction of related to random and nonrandom aspects of structure, respectively. Qualitative structural descriptors collected as part of a soil survey—such as plasticity, stickiness, consistency, pedality, and root density—have been used in some studies for PTM development. Lin et al. (1999a) derived a system that allowed inclusion of soil structure in PTMs by assigning points to four structural categories (initial moisture state, pedality, macroporosity, and root density), in addition to texture. The final "morphometric index" varied between 0 and 1, allowing interrelations among the morphologic features to be examined. Tomasella et al. (2003), Rawls and Pachepsky (2002), and Lin et al. (1999b) found that including some measure of soil structure, even if qualitative, as input to PTMs led to better predictions of () than if textural data were used alone.

Trapped air content at = 0 may also serve as a structural indicator. It may be taken as A_e, the fraction of the total pore volume that remains air-filled after has been raised from a negative value to 0 by typical soil-wetting processes. Maximum water contents (_max) are sometimes estimated from using a rule of thumb that A_e = 10% for a typical soil (Mualem, 1974). Several researchers have measured the amount of air trapped during ponded infiltration or sprinkler irrigation tests (Fayer and Hillel, 1986; Constantz et al., 1988; Faybishenko, 1995). Fayer and Hillel (1986), in controlled water-table fluctuation tests to measure the amount and persistence of air trapping near the water table, and have observed volumetric trapped air contents (A_e) ranging from 1.1 to 6.3% of the bulk soil volume. (Some authors report A_e or A_e without giving for converting one to the other, so it is necessary to use both quantities in reviewing past work.) The soil profile studied by Fayer and Hillel (1986) graded from a fine sandy loam at the land surface to loamy sand at 1.95 m; the maximum A_e was 13% at 0.6 m where the median particle size was approximately 0.05 mm and the uniformity coefficient was near 3.5. Constantz et al. (1988) found that A_e ranged from 4 to 19% during lab and field ponded infiltration tests. Packed columns (140 cm long) of well-sorted, commercial-grade medium sand had the largest amount of trapped air (A_e = 19%, A_e = 5%) in the upper 50 cm of the transmission zone. Faybishenko (1995) found that the amount of trapped air, in laboratory saturation experiments on loam-textured cores, depended on both the direction of wetting and the saturation method. Values of A_e were as great as 10% by downward infiltration and <5% for upward wetting. After vacuum saturation, A_e decreased to <0.2% for upward wetting. Although the results of these studies agree approximately with the A_e = 10% guideline, the materials studied typically were fine sands and loams without significant gravel content. Other researchers (Orlob and Radhakrishna, 1958; Bond and Collis-George, 1981) suggested that the amount of trapped air is related to the range of pore sizes and mean particle size, with more air trapped in materials with broad pore-size distributions and coarse texture. These observations suggest that A_e, being directly related to the particle packing, might be useful as a measure of structure.

A few laboratory studies (Croney and Coleman, 1954; Elrick and Tanner, 1955; Nimmo and Akstin, 1988; Jayawardane and Prathapar, 1992; Perkins, 2003) showed structural effects on hydraulic properties by comparing samples packed to different _b values or comparing "undisturbed" samples with repacked ones. Croney and Coleman (1954) reported increases in the saturated water content of minimally expansive soils by repacking less densely. The decreased _b only slightly affected the scaling parameter for water potential, _o, defined such that scaling by _o equilibrates the dependence of a set of () curves, and strongly steepened the rapid-drainage portion of the () curve. Perkins (2003) measured () on two deep, aggregated sediment samples in their undisturbed state and after repacking to the same _b. The () curves for the repacked samples had smaller (more negative) _o values and an increased steepness in the middle range of , reflecting the destruction of macropores associated with aggregation. Other studies of repacked soil columns showed similar effects (Elrick and Tanner, 1955; Nimmo and Akstin, 1988; Jayawardane and Prathapar, 1992), in that packing reduced the heterogeneity of pore sizes, decreased the apparent _o value, and steepened the drainage portion of the () curve.

Most PTMs available in the literature have been developed for surficial soils, often with characteristics particular to a given site and soil type, such as Lower Coastal Plain Ultisols (Puckett et al., 1985) or glacially derived Podzols (Mecke et al., 2002). Soil structural descriptors found in soil surveys (e.g., root density, plasticity, aggregate-size distribution, pedality, and stickiness) are not usually available for sediments deeper than the zone of soil development. Reliable PTMs for deeper sediments are needed, however, especially with the increasing application of unsaturated hydraulic properties to aquifer recharge and contaminant transport problems. In this study, we considered sediments that are subject primarily to a single structure-forming process, namely depositional sorting of particle sizes. This process results in relatively uncomplicated structural differences whose influence on hydraulic properties may be more systematic than other processes (e.g., biological), and may be more likely to influence both large and small pores.

The natural deposition of particles of various sizes can produce a relatively random sedimentary structure, as in a debris-flow deposit, or a more ordered structure, as in a normally graded fluvial deposit. Such a structural difference is especially relevant in applying PTMs, such as that of Arya and Paris (1981), which are applicable to sandy media and which do not account for particle arrangement. Hypothetical () curves are shown in Fig. 1 for an identical particle-size distribution in the two deposit types. In a normally graded fluvial deposit consisting of multiple, well-sorted (i.e., having little variation in particle size) layers with different mean particle sizes, large pores are created adjacent to the largest particles. Therefore graded fluvial samples are expected to have a wide range of pore sizes, reflected in the () curve by a gentler slope in the middle range of . In a debris-flow deposit like that in Fig. 1, whether stratified or not, the spaces next to large particles are occupied by smaller particles and large pores are absent. At the other end of the pore-size range, no mechanism exists to make the smallest pores smaller in the debris-flow material. This deposit would thus have a narrower pore-size distribution than a fluvial deposit of identical texture. The larger pores present in normally graded fluvial deposits should cause _o to have smaller magnitude than in debris flow deposits. The filling of large voids with small particles in debris flow deposits should also cause , and likely _max, to be smaller than in fluvial deposits.

View larger version (48K): [in this window] [in a new window]   Fig. 1. Theoretical structural effects on water retention for a fluvial sample and a debris flow sample, both of which are well stratified. A fluvial sample is expected to have a broader pore-size distribution than a debris flow sample of comparable particle-size distribution because of its greater abundance of both small and large pores.

A secondary goal, to directly quantify the degree of structural difference in the types of particle arrangement, could not be straightforwardly achieved because textural variations prevented a strict isolation of structure as an independently apparent characteristic of the available samples. Therefore additional statistical analyses were applied to texture-related and structure-related variables to achieve a similar purpose.

	MATERIALS AND METHODS

TOP EXECUTIVE SUMMARY ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
Site Description and Sampling
Oro Grande (OG) Wash and Sheep Creek (SC) Wash, both part of the upper Mojave River basin of the western Mojave Desert, are ephemeral streams that drain northward from the eastern San Gabriel Mountains of the greater Transverse Range province (Fig. 2 ). The unsaturated zone in this area ranges in thickness from 400 m near the mountain front to 70 m toward the basin. The San Andreas Fault passes through the headwater regions of these streams along the northern margin of the San Gabriel Mountains.

View larger version (40K): [in this window] [in a new window]   Fig. 2. Sheep Creek Wash and Oro Grande Wash and their associated fan deposits in the western Mojave Desert, San Bernardino County, California (adapted from U.S. Geological Survey, 1:250,000 San Bernardino quadrangle and modified from Weldon, 1985). Core samples were collected from the lower reaches of each wash. Boreholes L and L-1 were drilled directly in the channels, while L-2 and F were drilled into the adjacent fan surfaces.

SC Wash is the current trunk stream of the Holocene (Miller and Bedford, 2000) SC fan (Fig. 2), whose source area is located in the San Gabriel Mountains near the town of Wrightwood. Source rocks include a muscovite-quartz-garnet schist known as the Pelona Schist and, to a lesser degree, granite. The Pelona Schist is highly foliated and landslide-prone, and is associated with debris flows and mudflows that have affected Wrightwood (Sharp and Nobles, 1953; Morton and Sadler, 1989) and have reached as far down fan as El Mirage Lake. Along incised portions of the wash (e.g., near Borehole L, Fig. 2), deposits appear to be debris-flow dominated. The incision may have resulted from uplift of the San Gabriel Mountains during the deposition of the fan sediments.

Samples containing a broad range of particle sizes were selected for detecting structural differences of the type shown in Fig. 1. Four boreholes were drilled and core-sampled in 1994, 1995, and 1997 at the lower reaches of the washes (Fig. 2) to depths of approximately 30 m below land surface (Izbicki et al., 1995, 1998, 2000; Izbicki, 1999). Boreholes L and L-1 were drilled directly in the channels and Boreholes L-2 and F were drilled on the adjacent fan surfaces. Two borehole samples from each wash (OGL-1 11.5, OGL-2 82, SCF 57, and SCL 58) were chosen based on textural descriptions in the lithology logs (Izbicki et al., 2000) and their minimally disturbed state. (Note sample nomenclature is as follows: for borehole samples, wash abbreviation followed by borehole number and sample depth in feet; for surficial samples, wash abbreviation followed by sample number, numbered sequentially in order of collection by wash). In 1998, nine shallow core samples were collected along the incised part of each wash. Sampling criteria included apparent texture and deposit type. The collection method involved (i) creating a horizontal bench in the channel wall, (ii) placing a core liner identical to that used for borehole sampling (10-cm diameter, 15-cm length) on the resultant flat surface, and (iii) pushing the liner vertically downward as sediment was carved away from the sample base (Winfield, 2000). For most shallow samples, water was added to the core liners to aid in collection. A subset of three shallow core samples from each wash (OG-1, OG-2, OG-4, SC-1, SC-2, and SC-4) was selected based on apparent textural similarity, determined by measuring PSDs of bulk samples collected adjacent to the core sampling locations. The samples did not display significant aggregation or ped development, and there was no observable caliche, so these samples were suitable for analysis in terms of the simple structural characteristics described above and systematically illustrated in Fig. 3 .

View larger version (63K): [in this window] [in a new window]   Fig. 3. Sample classification scheme, based on geometric particle-size standard deviation and stratification, used to distinguish between fluvial and debris flow sediments.

View larger version (22K): [in this window] [in a new window]   Fig. 4. Laboratory controlled-liquid volume apparatus for measuring wet- to mid-range water retention values on large, undisturbed core samples (Winfield and Nimmo, 2002).

For the controlled-liquid volume and filter paper methods, core samples were kept in their original liners to minimize sample disturbance and to retain the influence of structural features. For the hygrometer method, disturbed samples were acceptable because in the dry range of () water coats particles as thin films, making structural influences on negligible.

Bulk physical properties, including PSD, _b, and particle density (_s), were determined after the () measurements were completed. Bulk sample volume was calculated from the dimensions of the core liner after adjusting the core length to account for recesses and protrusions at the sample ends. Samples were then carefully pushed from their liners, cut in half longitudinally, and examined for stratification or other features that would allow classification of the dominant depositional mode (Fig. 3). Samples were oven dried at 105°C, and _b was calculated from the oven-dry weight and bulk sample volume. Values of _s were determined by the pycnometer method (Blake and Hartge, 1986), using approximately 5 g of material from the size range <0.85 mm. Values of were calculated as 1 – (_b/_s). The relative abundance of particles with effective diameters (d) between 0.85 and 90 mm (for 14 particle-size intervals, or "bins") was determined by dry sieving, and between 4 x 10^–5 and 0.85 mm (for 107 bins) by optical light scattering (Gee and Or, 2002) with a Coulter LS 230 Series (Beckman Coulter, Fullerton, CA) particle-size analyzer. The bin spacing, d, is defined as log₁₀(d_upper) – log₁₀(d_lower), where d_upper represents the upper and d_lower the lower bin limit. The average d changed at 0.85 mm, from 0.0404 for the optical method to 0.1446 for the dry sieve method.

Two other parameters were computed from measured data and used to evaluate structure: A_e and a porosity-based randomness index (_s). The trapped-air fraction (A_e) was computed from the difference between the measured and _max. A medium that has more pronounced structure in terms of greater deviation from a random arrangement of particles will in general have greater . For quantitative emphasis of this effect as a departure from randomness, instead of using directly, we use _s, defined as – 0.30. The value 0.30 was chosen as a value exceeded by of most granular media, and which approximates for particles arranged with perfect randomness (Nimmo, 1997). Negative values of _s are possible because it is a difference from an artificially fixed datum.

Representation of Water-Retention Curves
Measured () points were fit with the Rossi and Nimmo (1994) junction model, represented by different functions in each of three segments of the complete () curve:

[1a]

[1b]

[1c]

where _d is the matric potential at which = 0 (oven-dryness), and c, , , _o, _i, and _j are empirical parameters. This model realistically represents () in the driest as well as the wetter ranges. The parabolic function near saturation allows the pore-size distribution [the first derivative of the () curve] to be computed without a discontinuity near _o.

The model includes constraints of continuity and smoothness at the junction points _i, and _j, which link the empirical parameters such that only two of the six, usually taken as and _o, are independent. Sometimes _o is called the "air-entry" potential, but air actually begins displacing water in the largest pores between _o and 0 (Fig. 1). The parameter indicates the relative steepness of the middle portion of the () curve.

The value of _d was determined based on the SSSA (1997) definition of zero water content and the Kelvin equation:

[2]

where R/M is the ratio of the universal gas constant to the molecular weight of water (461.53 J kg^–1 K^–1), T_o is the oven temperature (378 K), p_o is the vapor pressure of water in the oven, and p_so is the saturation vapor pressure for water at 378 K. Additional assumptions are required to estimate p_o. We assume p_o equilibrates with water vapor pressure in the lab air under typical lab conditions of 50% relative humidity and temperature at 295 K. Then, using values from standard tables (e.g., Dorsey, 1940), _d equals –788 MPa. For convenience and consistency with other reports (Ross et al., 1991; Andraski, 1996; Rossi and Nimmo, 1996), _d = –1000 MPa was used in the model fits.

Nonlinear regression to the () measurements, based on a modified Gauss-Newton least-squares approach, was achieved using custom-written Matlab programs (Statistics Toolbox version 3 of MATLAB 6, Release 12, The Mathworks, Inc., Natick, MA). The values of _o and were optimized, and _max and _d were fixed.

Descriptive Univariate Statistics
Because sediment PSDs typically follow lognormal distributions (Krumbein, 1938; Pettijohn, 1975), core sample PSDs were characterized using geometric particle-size statistics (geometric mean M_g and _g). We chose the mean rather than the median particle diameter to characterize the PSD because the mean incorporates the influence of all particle sizes, including multiple modes and skewness, on the normal distribution. Values of M_g were computed using the method of moments (Beyer, 1991):

[3]

where n is the number of bins, d_ci is the geometric center of the ith bin (or 10^{[log₁₀ (d_upper) + log₁₀ (d_lower11)]/2}), and f(d_ci) corresponds to the frequency of particles occurring within the ith bin assigned to d_ci. Values of _g were calculated by:

[4]

Because d of the measured PSD changed at 0.85 mm, a slight discrepancy exists between the statistical values calculated using the unequal, measured bin sizes and the values calculated from a distribution with an equal d for the entire range of particle sizes. Values of M_g and _g calculated from the PSDs with the original, irregular bin spacing (average d = 0.052) were compared with those calculated from PSDs where the number of bins was reduced from 121 to 40, so that d was equal to 0.16 on average (approximating the d of the sieved particle-size fraction). The average difference between these two ways of calculating M_g was 0.005 mm, with smaller M_g resulting from the larger d (0.16) for all samples. The average difference in _g was 0.009, with smaller _g for about one-half of the samples. These results indicate that the change in d at 0.85 mm does not significantly affect the final values of M_g and _g. Scheinost et al. (1997) treated this problem in a similar way and also concluded that the effect of bin size was small.

	RESULTS AND DISCUSSION

TOP EXECUTIVE SUMMARY ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
Hydraulic and Bulk Physical Properties
The cumulative PSDs for the 10 core samples, divided into groups by wash, are shown in Fig. 5 . Bulk physical properties, including _b, _s, texture, textural class percentages, and geometric particle-size statistics (M_g and _g), are summarized in Table 1. On average, SC Wash samples had larger _s than OG Wash samples because of the greater presence of heavier minerals such as garnet and muscovite (derived from the schistose source rocks). The samples contained significant gravel and ranged in texture from sandy loams to very gravelly sands according to the USDA soil classification system (Soil Survey Staff, 1975).

View larger version (25K): [in this window] [in a new window]   Fig. 5. Cumulative particle-size distributions for core samples collected from (a) Oro Grande Wash and (b) Sheep Creek Wash.

View this table: [in this window] [in a new window]   Table 1. Summary of core samples collected from Oro Grande (OG) Wash and Sheep Creek (SC) Wash, including depths, measured bulk (b) and particle (s) densities, USDA textural class percentages, and geometric particle-size statistics.

View larger version (22K): [in this window] [in a new window]   Fig. 6. Water desorption measurements and curves fitted using the Rossi–Nimmo (1994) junction model for core samples from (a) Oro Grande Wash and (b) Sheep Creek Wash.

Sample Classification According to Depositional Environment
A significant research difficulty arose from the fact that samples from OG Wash displayed debris-flow as well as the expected fluvial structural features and that the converse was true for SC Wash, preventing separation of samples into structural categories independently of observable features of the samples. Both fluvial and debris-flow facies can exist at an individual wash because of possible shifting of positions and local reworking of fan deposits. Therefore, additional means of categorizing the samples were necessary, using combinations of degree of particle-size sorting and stratification, as shown in Fig. 3.

For most samples, the degree of stratification was described by examining the core samples after () measurement. For Samples OG-4 and SC-1, the degree of stratification was discerned from photographs taken along the channel walls during sample collection. In general, samples with three or more visible layers in their 15-cm length were considered well stratified; fewer than this would mean that the sample did not capture a single complete layer.

The degree of particle-size variation within each sample was computed in terms of sorting using sedimentological units [= –log₂(d), where d = effective diameter in millimeters]. The cutoff between moderately sorted to well sorted and poorly sorted materials occurs at 1 , with <1 indicating better sorting (Folk, 1980). Because equivalent sorting definitions do not exist for the geometric standard deviation (_g), we defined the sorting criterion at _g = 5, which approximates a graphical particle-size standard deviation of 2. Samples with _g <5 are considered here as well sorted.

Depositional environment was inferred for each type based primarily on degree of sorting. Types 1, 2, and 4A are inferred to represent fluvial materials because each type is characterized by a narrow range of particle sizes either for the entire sample or for individual layers. Types 3 and 4B are inferred to represent debris flow deposits because the range of particle sizes for each layer or for the entire sample is broad. Type 4A, with well-sorted layers, and Type 4B, with poorly sorted layers, are of most interest for determining structural effects on (), especially for samples of comparable PSDs.

Sample classification results are presented in Table 3. Three samples were identified as fluvial (OG-1, OG-2, and SC-2) and three as debris flow (OGL-1 11.5, OGL-2 82, and SC-1). The remaining four samples could not be classified because of lack of information about sorting within individual layers (Type 4 samples) or about the degree of stratification. Thus there is not enough information to completely correlate observed structural influences as hypothesized in Fig. 1 with features of measured () curves. However, the degree of textural and structural influence may be inferred by comparing () parameters (_max, _o, and ) with the textural indicators M_g and _g,, and the structural indicators A_e and _s.

View larger version (17K): [in this window] [in a new window]   Fig. 7. Textural variables compared with maximum water content (max) and Rossi–Nimmo (1994) fit parameters (scaling parameter for water potential, o; curve-shape parameter, ). Scatter plots show comparisons with (a, c, e) geometric mean particle diameter (Mg) and (b, d, f) geometric standard deviation (g), for n = 10 samples. Symbols indicate sample categories of Fig. 3, with results for individual samples listed in Table 3. Solid symbols represent fluvial samples and open symbols represent debris flow samples.

View larger version (19K): [in this window] [in a new window]   Fig. 8. Structural variables compared with maximum water content (max) and Rossi–Nimmo (1994) fit parameters (o and ). Scatter plots show comparisons with (a, d, g) bulk density (b); (b, e, h) trapped air fraction of porosity (Ae); and (c, f, i) porosity-based randomness index (s), for n = 10 samples. Symbols indicate sample categories of Fig. 3, with results for individual samples listed in Table 3. Solid symbols represent fluvial samples and open symbols represent debris flow samples.

The _o parameter increases toward zero as M_g increases (Fig. 7c), consistent with known textural effects on (). Samples classified as fluvial tend to have larger _o values than debris flow samples, possibly due to a greater abundance of structure-related large pores. The fluvial samples, all with large M_g, also follow the general _o vs. M_g (textural) trend of the entire data set. Smaller _g values for fluvial samples may create, on average, larger pores that effectively increase the _o values. Figure 7d illustrates this effect: as _g increases, _o usually decreases, suggesting a reduction of pore sizes from small particles occupying voids between large particles.

Greater values correspond to increased steepness of the middle range of the () curve. The correlation between and M_g is weak (r = –0.032, Table 4) overall, consistent with Miller and Miller (1956) similitude theory that a linear scaling of all particle and pore sizes of the medium would not affect . In one of the more strongly established trends, Fig. 7f shows that decreases as _g increases, indicating the spread in pore size correlates with the spread in particle size. This trend is consistent with a predominantly textural influence on (), although scatter in the data may result in part from structural influences as well as measurement uncertainty.

The scatter plots (Fig. 7) and correlation coefficients (Table 4) show that the () parameters (_max, _o, and ) are, as expected, influenced by texture, represented by M_g or _g. Of these parameters, M_g strongly affects _max and _o, while _g strongly affects . Structural influences are suggested, however, in that the fluvial samples have consistently larger (closer to zero) _o values and larger values than nearly all other samples. Both of these structural trends are consistent with the hypotheses in Fig. 1. Textural influences on the fluvial samples are also evident; these samples, in general, have larger M_g values and are better sorted (with smaller _g values) than the debris-flow samples. Structural influence on the fluvial samples is suggested by data in Table 2; on average, A_e values were 28% for fluvial samples and 22% for debris-flow samples. This difference goes in the expected direction if greater variation in pore size correlates with greater air trapping, but a larger data set is needed to establish the significance of this trend.

This study's second objective, quantifying structural differences, would ideally be accomplished by comparing samples with identical PSDs. The PSDs of samples in this study vary too much for this objective to be accomplished through direct comparison, but structure may be evaluated in terms of A_e or _s values.

The relations among the () parameters (_max, _o, and ) and the structural parameters (_b, A_e, and _s) are shown in Fig. 8. As expected, and to a large extent required for self-consistency, _max tends to decrease with increasing _b and A_e and tends to increase with _s. Among these, A_e most strongly correlates with _max (r = –0.716; Table 4). The strong correlation of _s with _b (r = –0.955) is necessary by definition, and thus not of interest. Although trends for _o are less clear, _o most strongly correlates with A_e (r = 0.713), increasing toward zero as A_e increases (Fig. 8e). Values of decrease with smaller _b (r = –0.519), but have no clear trends for A_e or _s.

The fluvial samples SC-2, OG-1, and OG-2 have greater A_e values than all other samples except the coarsest sample, OGL-1 11.5, suggesting structural influences that are not obvious from Fig. 7 and 8, and that accord with the hypothetical relationships in Fig. 1. The fluvial samples had larger _s values than all other samples except SCF 57, also consistent with the expected structural trends.

Regression Analysis
Multiple linear-regression analyses were conducted to determine which of the textural and structural parameters were best able to explain the variation in the hydraulic parameters. The "all possible subsets" approach (Draper and Smith, 1981; Rawlings et al., 1998) was used to determine the best set of explanatory variables (among M_g, _{g, b}, A_e, and _s) for estimating each of the three hydraulic parameters (_max, _o, and ). All possible multiple linear-regression equations involving the potential explanatory variables are computed (for 2^m – 1 equations, where m is the maximum number of potential explanatory variables, i.e., m = 5 in our application), and statistics such as the coefficient of determination (R²), adjusted R² (R²_adj), residual mean square, and Mallow's C_p are evaluated. Results are grouped according to the number of variables in the equation (p) and ordered from highest to lowest R². The candidates for "best" model typically have the highest R² per p variable subset. Mallow's C_p suggests the best subset of explanatory variables for each response variable, by comparing computed C_p values to the criterion of C_p = p + 1. Values of C_p < p + 1 (i.e., C_p = C_p – p – 1 is negative) indicate that the model is overspecified, or that more explanatory variables are included in the regression variate than are necessary to fit the data.

Multiple linear-regression analyses were conducted using custom programs written with Matlab (The MathWorks, Inc., Version 6, Release 12) and the Statistics Toolbox utility. In Table 5, the set of explanatory variables with the highest R² is shown for each p variable subset. The best subset for each of the parameters _max, _o, and (underlined in Table 5) had a calculated C_p value closest to the criterion p + 1 while preserving the smallest number of explanatory variables. For _max, the best model occurred for p = 3, and included A_e, _s, and _g. For _o, the best model was for p = 2, and included M_g and _g. This model was slightly overspecified (calculated C_p = 1.56 < p + 1 = 3). Although C_p for the four-variable model was closest to the C_p criterion (C_p = 0.88), this model was not chosen because the slight improvement in fit it may have offered was insufficient to justify the use of two more explanatory variables. For , the best subset involved _g only.

For _max, examination of the goodness of fit of the models in the regression analysis allows further interpretation of the trends noted above, that correlation is strongest with M_g, _b, A_e, and _s. The trend with M_g is noteworthy because of its fundamental independence of _max. Regression analysis shows that although M_g (R² = 0.604) is the best choice for a one-variable model of _max, fit improved as much as 39% for the two- and three-variable models that included A_e, _s, and _g. The correlations with A_e and _s must be discounted because _max is arithmetically determined by these parameters, although other structural indicators not used in this study may have predictive value.

For _o, which correlated most strongly with A_e followed by M_g (Table 4), the one-variable model included A_e, although the variation was best explained by the combination of textural parameters M_g and _g, with R² = 0.735. The addition of A_e in the equation for p = 3 improved the model fit by 6%. The strong collinearity between M_g and A_e (r = 0.778), however, makes this model less desirable than the one involving only M_g and _g. Overall, these results suggest that structural information implicit in A_e has value in a PTM.

For , which correlated most strongly with _g, a one-variable model involving _g best explained the variation in (R² = 0.602). Adding more variables provided only slight improvements in model fit and overspecified the model by the C_p criterion, even though the R² was only 0.602 for p = 1.

Although the data set is small, regression results suggest that in addition to textural information, structural indicators may be useful as explanatory variables to predict (). Most noteworthy is the potential value of A_e for explaining the variation in _o. Independent determination of A_e (e.g., from field studies) may prove useful for estimating _max.

	SUMMARY AND CONCLUSIONS

TOP EXECUTIVE SUMMARY ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
Property-transfer models are generally based more strongly on textural than on structural indicators, and are often considered to work best in media composed primarily of randomly arranged particles, as frequently is true of sands. We explored the validity of these generalizations and the possible benefits of incorporating structural indicators into PTMs for the case of structural influences deriving from the mode of sediment deposition. Because of systematic differences in particle arrangement arising from distinct depositional processes, investigation of structural effects due to deposition is simpler and in some ways more instructive than those due to aggregation or biotic processes. For this evaluation we measured water retention [()] curves on 10 undisturbed core samples from washes in the western Mojave Desert. Samples were categorized as originating from fluvial or debris flow environments by analyzing the stratigraphy of the cores and by comparing _g for the bulk sample. Textural (M_g and _g) and structural (_b, A_e, and _s) parameters were used as candidate explanatory variables in parameter-correlation and multiple linear-regression analyses to evaluate possible improvements in predictions of () parameters (_max, _o, and ) over texture-based PTMs.

Texture had greater influence than structure on the () properties of our samples. Values of _max and _o correlated strongly with M_g (r = –0.777 and r = 0.663, respectively), whereas correlated best with _g (r = –0.776). Values of _o correlated strongly with the structural indicator A_e (r = 0.713), and correlated weakly with all of the structural indicators (r < |–0.519|). Most A_e values exceeded the general guideline of 10% and correlated significantly with texture, being greater for coarser material.

Other evidence of structural influence is apparent in that debris flow samples generally had smaller _s and A_e; the three fluvial samples ranked in the four highest values of both _s and A_e. Smaller _s indicates a more random structure (Nimmo, 1997), which is expected from the more rapid, disorderly deposition of debris flows. Smaller A_e may correlate with a narrower pore-size distribution (Orlob and Radhakrishna, 1958; Bond and Collis-George, 1981), likewise a probable characteristic of debris flows. For predictions, the best one-variable model for _o was based on A_e (R² = 0.508), although the best _o model overall involved M_g and _g (R² = 0.735). While the evidence in this study indicates only a slight influence of structure on (), it should be noted that structure-affecting mechanisms associated with differences in depositional environment (Fig. 1) are subtle compared with those associated with aggregation and macropores.

The development of more general and improved PTMs that can be applied to multiple sites, and that are based on theoretical relationships between the bulk physical and h