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Journal of Hydrology 400 (2011) 5871

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Journal of Hydrology

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Field evaluation of methods for determining hydraulic conductivityfrom grain size data

Thomas Vienken , Peter DietrichUFZ, Helmholtz Centre for Environmental Research, Department Monitoring and Exploration Technologies, Permoserstrae 15, 04318 Leipzig, Germany

a r t i c l e i n f o

Article history:Received 8 April 2010Received in revised form 8 January 2011Accepted 19 January 2011Available online 2 February 2011

This manuscript was handled by P. Baveye,Editor-in-Chief, with the assistance ofHongbin Zhan, Associate Editor

Keywords:Hydraulic conductivitySieve analysisGrain size distributionDirect push slug testSonic samplingBitterfeld

0022-1694/$ - see front matter 2011 Elsevier B.V. Adoi:10.1016/j.jhydrol.2011.01.022

Corresponding author. Tel.: +49 (0) 341 2351382;E-mail address: [email protected] (T. Vienk

s u m m a r y

Determination of hydraulic conductivity (K) and its variation in space is often a major objective of hydro-geological site investigations. However, measurement of K at a high spatial resolution in sedimentaryaquifers is a challenge. There are a number of field methods that can be used to determine K, althoughthey differ greatly in terms of their spatial resolution.

One commonly used approach is to estimate K from grain size analyses, but the reliability of the result-ing K estimates is unclear. The aims of this study are to compare frequently used formulas for the deter-mination of K from grain size data for a broad range of sediment types and to evaluate how well thesemethods predict K. Sonic sampling was used to obtain minimally disturbed cores in a highly heteroge-neous sedimentary aquifer and K values of grain size analyses from 108 core samples were calculated.Despite the high correlation of calculated K derived from different formulas, mean K values differed byseveral orders of magnitude between the formulas. For the evaluation of the reliability of the K estimates,high resolution direct push slug tests (DPSTs) were also performed in the close vicinity of the cores. Ahigh correlation between ln(KDPST) and ln(Kgrain size) was found for most of the applied formulas. Never-theless, sample heterogeneity, i.e. the presence of small clay layers in a generally highly permeable sam-ple, led to Kgrain size estimates that were significantly smaller than the KDPST estimates. Based on theseresults, the applied formulas appear to be suitable for an initial assessment of aquifer K. However, con-sidering the difference in calculated K mean values, results are not sufficiently reliable for the high res-olution analyses of K variations needed for flow or transport modeling.

2011 Elsevier B.V. All rights reserved.

1. Introduction

Information about hydraulic conductivity K (see Table 1 for acomplete list of symbols) and its variation in space is a prerequisitefor the understanding and modeling of flow and transport pro-cesses. One of the challenging tasks hydrogeologists are facing to-day is the high resolution characterization of K in sedimentaryaquifers.

Many tools for the laboratory and field investigation of K exist.Butler (2005) gives a broad overview of approaches includingpumping tests, slug tests, laboratory analyses of core samples, geo-physical logging, borehole flowmeter tests, direct push methods,and hydraulic tomography. These approaches vary significantly inthe volume over which an average K value is measured (supportvolume) and their resolution (aquifer to particles size scale).Sudicky (1986) and Rehfeldt et al. (1992), among others, demon-strate the difficulty of obtaining reliable K estimates in complexstructured sedimentary deposits.

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fax: +49 (0) 341 235 451382.en).

The simplicity and the semi automated sample processing pro-cedures make grain size analyses a standard tool for site investiga-tions. Since the work of Seelheim (1880) and Hazen (1893)formulas for the estimation of K from grain size data have beendeveloped and refined. This has led to a large number of formulas,some of which have well-established forms, while others havebeen reported in a wide range of variations. Often, adaptations ofthe formulas were necessary, as they were derived under labora-tory conditions (Hazen, 1893; Carman, 1937) or with the objectiveof reflecting an average K value at the aquifer scale (Beyer, 1964;Kaubisch and Fischer, 1985). However, the application of formulasto calculate K based on grain size distribution for the high resolu-tion K characterization of individual layers within an aquifer, andthe stochastic analyses of resulting K data has increasingly movedinto the hydrogeological practice within the last decades. Relevantmedia matrix properties, and therefore governing factors of K aregrain- and pore size distribution, grain and pore shape, tortuosity,specific surface, and porosity (see Bear, 1972). Neither porosity nortortuosity can be reliably determined from grain size analysis, asdisturbance of the natural sediment structure during sampling isinevitable. Nevertheless, most of the semi-empirical formulas relyon porosity measurements.

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Table 1List of symbols.

Symbol Denotation

Dgi Weight of the ith fractionDgm Weight of the finest fraction in parts of total weight

e /1/ Void ratiogT Dynamic viscosity at ground water temperatureg10 Dynamic viscosity at 10 Cm Kinematic viscosityr2 Variances v10vT Ratio of kinematic viscosity at 10 C and ground water

temperature/ Total porosityC Dimensionless factorCB Coefficient after BeyerCH f U log 500U Coefficient after HazenCT Coefficient after Terzaghid Effective diameter of the grains1di 12 1du

1dl

Harmonic mean of the ith fraction

di Diameter of grains in the ith percentiledl Lower grain size limit of a grain size fractiondm Diameter of finest fractiondu Upper grain size limit of a grain size fractiond50 Median grain size diameterde 0:13

2DgmdmPin

i2Dgidi

Effective grain size diameter

dw 6S Effective grain size after Beyer (1964)DP Direct pushf1(s) Shape factorf2(/) Porosity factorf (U) Porosity function after Beyer (1964)g Gravitational constantK Hydraulic conductivityKx Hydraulic conductivity determined with method xk Intrinsic permeabilityMax Maximum valueMin Minimum valuem Hydraulic radiusn Population sizeP Percentage of fine grained material

Fig. 2. Selected grain size diameters at different core locations and slug test intervals.

60 T. Vienken, P. Dietrich / Journal of Hydrology 400 (2011) 5871

gravel and sand fractions were determined by sieving; the silt andclay fraction were automatically processed, using an apparatusthat works based on the pipette method, and manually weighed.Results of the grain size analyses are presented in Appendix A.

2. Grain size analyses

Relevant sediment properties and governing factors for K aregrain- and pore size distribution, grain and pore shape, tortuosity,specific surface, and porosity (see Bear, 1972). A general form forthe relationship between grain size diameter and the intrinsic per-meability (k) is given by Bear (1972):

k f1s f2/ d2: 1

where f1(s) is the shape factor; f2(/) is the porosity factor; and d isthe grain size diameter.

In most cases, f1(s) and f2(/) are combined in a dimensionlessfactor C (Bear, 1972). K and k are related by the following equation(Bear, 1972)

K k gm: 2

where g is the gravitational constant; and m is the kinematic viscos-ity. When combining Eqs. (1) and (2), a unit consistent form can bederived (Bear, 1972)

K gm f1s f2/ d2: 3

In this paper, seven different formulas for the calculation of K fromgrain size data were compared (see Table 3). Formulas were chosenthat cover a wide range of different approaches to represent thegrain size diameter, and the shape and porosity functions. Theempirical formulas were those of Hazen (1893), Beyer (1964), USBR(United States Bureau of Reclamation), Seelheim (1880), and Kau-bisch (1986). These formulas, except for Kaubisch (1986), use apower relationship between K and a certain grain size diameter thatis derived from the cumulative grain size curve. Kaubisch (1986)

based his formula upon a power relationship between K and thepercentage abundance of grain sizes

Table 3Summary of the applied formulas, key parameters and citation.

Name Type Formula K in Relevant parameter Application range Tested on References

Hazen Empirical K CH d210 0:7 0:03T m/d d10 in mm U < 5 Laboratory experiments on sandsamples

Hazen (1893)

T = temperature 0.1 < d10 < 3 mm Chapuis (2004)CH = 1000 (coefficient)

Beyer Empirical K CB d210 m/s d10 in mm U < 20 Correlation of grain size analysis andpumping tests

Beyer (1964)

de = effective grain size diameter dwd10 f U 0.06 < d10 < 0.6 mm Vukovic and Soro (1992)

C f U log 500UKozeny-Khler Semi-

empiricalK sR 405 e

3

1e d2e

cm/s de 0:132DgmdmPin

i2Dgidi

in cm Theoretical derivation, supported bysand and glass bead laboratoryexperiments

Kozeny (1953)

e /1/ Dgm = weight of the last, finestfractionin parts of total weight

Carman (1937)

s v10vT Dgi = weight of the ith fraction

Htte (1956)

R = 3.5 after Khler (1965) as cited inHtte (1956)

dm = diameter of last fraction Khler (1965)

1di 12 1du

1dl

Bear (1972)

dl = lower class limit, du = upperclasser limit

Vukovic and Soro (1992)

USBR Empirical K 0:0036 d2:320 m/s d20 in mm U < 5 Vukovic and Soro (1992)

Seelheim Empirical K 0:00357 d250 m/s d50 in mm Laboratory measurements on sand,clay, and elutriated chalk

Seelheim (1880)

Kaubisch Empirical K 100:0005P20:12P3:59 m/s P < 0.06 mm in % 60% > P > 10% Permeameter tests Kaubisch and Fischer (1985)

Kaubisch (1986)

Terzaghi Semi-empirical K CT

g10gt /0:13ffiffiffiffiffiffiffi

1/3p

2 d210

cm/s d10 in cm 0.26 < / < 0.476 Theoretical derivation laboratorytests

Terzaghi (1925a,b)

CT 460800 Vukovic and Soro (1992),Kasenow (2002)

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Table 4Porosity values after Szymczak et al. (2009).

Material Porosity de in mm

Fine silt 0.450.65 0.0020.0063Silt 0.400.55 0.00630.02Coarse silt 0.350.45 0.020.063Fine sand 0.330.40 0.0630.2Sand 0.300.38 0.20.63Coarse sand 0.280.35 0.632Gravel 0.250.35 >2


Also, various derivations of the formula after Terzaghi (1925a,b)exist. In this study, we applied the derivation cited by Vukovic andSoro (1992) referring to the d10 diameter. The Terzaghi formula ischaracterized by the porosity function in form of Terzaghi(1925a,b).

/ 0:13ffiffiffiffiffiffiffiffiffiffiffiffi1 /3

p 6Based on tests in sands, Terzaghi (1925a,b) developed an empiricalfactor (CT) for his formula, ranging from 460 to 800. Other authorsproposed different values. In this study, a value of 800 provided Kvalues that are in good accordance with KDPST. When searching forreferences, it is important to note that Terzaghi used several formsof his name in his publications; two of these forms are Karl von Ter-zaghi and Charles Terzaghi (De Boer, 2005).

Table 3 lists the applied formulas, relevant parameters, applica-tion range and main citations. The formulas were tested on allsamples, even though sedimentary characteristics did not meetthe dedicated application ranges.

Most of the frequently used formulas are not unit consistent(see Vukovic and Soro, 1992). Unit consistency is beneficial whentemperature effects on the fluid viscosity must be considered. Mostequations are based on an average ground water temperature of10 C. At the Bitterfeld test site, where an average groundwatertemperature of 12 C was measured during testing, the tempera-ture difference results in a 5.6% deviation in the kinematic viscos-ity. A table of the water viscosity as a function of temperature canbe found in Kasenow (2002). However, if a term for temperaturecompensation is not included in the respective formula, a simplecorrection factor similar to s as applied in the Kozeny-Khler for-mula can be added to any formula (see Table 3).

Furthermore, a variety of application limits exist. As some for-mulas were originally developed against the background of otherapplications, i.e. as a proxy to predict water fluxes through sand fil-ters (Hazen, 1893), f1(s) and f2(/) were derived from laboratorymeasurements that are not representative of natural geologicalconditions. Often f1(s) and f2(/) were combined into C becausethe individual effects of f1(s) and f2(/) on K are not separable.Conventional sampling methods do not allow reliable laboratorymeasurements of /. The limited accessibility of extensive data setsfor cross validation is a common problem (see Shepherd, 1989).

Formulas developed using actual field data were often corre-lated with average K values from pumping tests (see Table 2). Asthe pumping test employs a large support volume, the respectivelyderived formulas are primarily valid for a general and not high res-olution aquifer characterization. The effect of support volume onparameter resolution and parameter scattering is shown by Bear(1972). Following Bear (1972), Fig. 3 shows a principal sketch ofreduction in parameter scattering and decreasing resolution withincreasing support volume. Grain size analysis, direct push slug

Fig. 3. Principal sketch of reduction in parameter scattering and resolution withincreasing intrinsic volume after Bear (1972).

testing, and pumping tests are plotted regarding their support vol-ume. This sketch illustrates the complex problem of comparing Kvalues derived by methods using different support volumes in het-erogeneous media, especially in the presence of small scale mediavariability.

Ideally, equations should be applicable to a broad range ofunconsolidated clastic sediments and usable for homogeneousand highly heterogeneous sediment samples. However, as alreadydiscussed, certain limitations confine the application range; amongthese are the grain size ranges, the level of uniformity, and theabundance of clay particles. A common model of flow through aporous medium is to visualize the void spaces as being composedof a spatial network of interconnected tubes (Bear, 1972). Hence,the laminated structure of clay minerals, in contrast to the roundedshape of sand grains, causes an important difference in themechanics of the percolation processes when the connected tubesmodel is applied (see Terzaghi, 1925a).

The heterogeneity of a sample is defined by the coefficient ofuniformity expressed by Hazen (1893):

U d60d10

7

Fig. 4. Resulting deviation on calculated K after Kozeny-Khler (1965) and Terzaghi(1925a,b) caused by uncertainties of porosity estimates. The graph shows themagnitude of difference between calculated K with fixed porosity value (Kref) of 0.55in Fig. 4a and 0.30 Fig. 4b and calculated K for porosity values ranging between 0.25and 0.65 (Kdev).

T. Vienken, P. Dietrich / Journal of Hydrology 400 (2011) 5871 63

2.1. Effects of / on K

The porosity function is an important part of the formulas afterKozeny-Khler (1965), and Terzaghi (1925a,b). However, labora-tory porosity measurements on core samples are often not reliable,as many sampling methods alter the structure, packing and com-paction of the sediment sample. Typically, empirical data or equa-tions are used to estimate the total porosity of a sample. Twoapproaches will be briefly discussed here. The first approach is pre-sented by Vukovic and Soro (1992) who approximated / as a func-tion of U, based on literature data as

/ 0:2551 0:83U: 8

Vukovic and Soro (1992) state that for the given formula, significantdeviations are observed for materials comprising clay. In their pro-posed relationship, no distinction is made between total porosityand effective porosity. Especially when working with samples thatcontain clayey materials, the effective porosity must be considered.In that case, a high total porosity is associated with a low effectiveporosity. The second approach is based on / values related to de (seeTable 4). This table cited by Szymczak et al. (2009) represents aver-age / values from the literature. When both approaches were ap-plied, significant differences for / could be observed for the samesample, ranging from 0.55 after Szymczak et al. (2009) to 0.255for the calculated porosity after Vukovic and Soro (1992). This dif-ference was found in seven of the 108 samples. Effects of deviationof / on the calculation of K are demonstrated in Fig. 4. The plot

Fig. 5. Matrix plot of ln(K) derived from grain size analyses. Histogram:

shows the ratio of a reference K value (Kref) calculated for a porosityof 0.55 (Fig. 4a) and 0.30 (Fig. 4b) versus K values (Kdev) calculatedfor porosity ranging from 0.25 to 0.65. When Kref and Kdev are calcu-lated based upon the same porosity value, the ratio is 1. Kref and Kdevare calculated after Terzaghi (1925a,b) and Kozeny-Khler (1965).In the case that porosity estimates range between 0.55 and 0.25for the same sample, the resulting KKozeny-Khler values differ by a fac-tor of 30 and resulting KTerzaghi differ by a factor of 17 for this sample(see Fig. 4).

To follow the hydrogeological practice and in consideration ofthe clay content, we continued to work with the standard / valuescited by Szymczak et al. (2009). Median values for the classes werechosen, as previous studies at the Bitterfeld field site have indi-cated an increased compaction of the sediments due to increasedoverburden stress during glaciation periods.

3. Results of the grain size analyses

Calculated ln(K) values based on the results of the grain sizeanalyses (Appendix A) are presented in the following section. Val-ues derived from different formulas are plotted against each otherin scatter plots that are arranged in the form of a matrix plot. Thisallows for fast visual recognition of linear correlation between theapplied methods. In addition to the data points, a simple regressionline and the line of equality (x = y) are plotted. Histogram plots(Fig. 5) show the relative distribution of ln(K) for each of the ap-plied formulas. While the histogram plots for Hazen (1893), Beyer

x-axis: classes, y-axis: frequency; scatter plots: x- and y-axis: ln(K).

Table 5Correlation matrix for calculated ln(K) values. Triplets are listed top down in form of r, a, and b, where r is the correlation coefficient; a is the slope and b is the intercept of thelinear regression.

KA/KB ln KHazen ln KBeyer ln KTerzaghi ln KKaubisch ln KUSBR ln KSeelheim

ln KBeyer 0.999 1.0001.0262 x0.1935

ln KTerzaghi 0.999 0.998 1.0000.9014 x 0.8771 x1.2426 1.0863

ln KKaubisch 0.972 0.972 0.971 1.0000.8996 x 0.8764 x 0.9963 x1.9986 1.8316 0.7773

ln KUSBR 0.958 0.952 0.957 0.959 1.0000.8664 x 0.8389 x 0.959 x 0.9373 x1.4161 1.3125 0.2452 0.2138

ln KSeelheim 0.777 0.758 0.776 0.749 0.860 1.0000.4925 x 0.4679 x 0.5447 x 0.5128 x 0.6024 x2.0077 2.0469 1.3471 1.3098 0.8474

ln KKozeny-Khler 0.933 0.927 0.931 0.899 0.916 0.8260.3258 x 0.3152 x 0.3602 x 0.3391 x 0.3538 x 0.4553 x9.5476 9.5105 9.1108 9.086 9.2478 9.6952

Table 6Comparison of relevant parameters for calculated K values.

KHazen KBeyer KTerzaghi KKaubisch KUSBR KSeelheim KKozeny-Khler

n 108 108 108 108 108 108 108x 2.57E04 1.68E04 1.51E04 5.22E05 2.49E04 6.94E03 4.30E06Min 5.67E09 2.94E09 1.18E08 3.48E10 1.15E09 1.86E06 1.54E07Max 3.05E03 2.02E03 1.58E03 1.70E04 7.34E03 1.32E01 3.68E05r2 2.25E07 9.29E08 6.12E08 2.28E09 6.81E07 3.66E04 2.56E11


(1964), Terzaghi (1925a,b), and USBR yield similar ln(K) distribu-tions, differences for the remaining formulas can be observed. Re-sults after Kaubisch (1986) show a trend towards higher ln(K)values. This formula is not coupled to the cumulative grain sizecurve, but to the percentage of fine grain material and yields rela-tively high K values for samples with low fine grain content. Calcu-lated ln(K) values after Seelheim (1880) are concentrated in themid-range while results after ln(KKozeny-Khler) show, when com-pared to the other histogram plots, a relatively even distribution.The matrix plot of the results of the 108 analyzed core samples re-veals a qualitatively high level of correlation between the differentapplied formulas over the entire sedimentological spectrum(Fig. 5); correlation coefficients are listed in Table 5. The correla-tion coefficient is a measure of the strength of the linear correlationbetween variables (Brown, 1998). However, a high coefficient ofcorrelation does not imply a 1 to 1 relationship between two vari-ables. To identify differences in the results between applied meth-ods, the line of equality is plotted in addition to the simpleregression line. Large differences between the slope of the line ofequality and simple regression line are especially prominent for re-sults using the Seelheim (1880) and Kozeny-Khler (1965) formu-las, although a high linear correlation exists between the results ofthese two formulas and all other tested methods. To quantify re-sults, Table 6 shows the relevant statistical parameters for the cal-culated Kgrain size values. Results of the calculated K values reflectthe broad sedimentological spectrum of the deposits; differencesof several orders of magnitudes can be observed between min,max and mean values of the applied formulas.

The observed large differences in calculated K values clearlyhighlight the need to test the reliability of calculated Kgrain size with

in situ measured K values obtained utilizing a method working onthe same scale of support volume as the grain size analysis.

4. Comparison with direct push slug test

We demonstrated in the previous section that in situ measuredK values are needed to evaluate the different formulas used to cal-culate K. As explained, these reference K values must be deter-mined by a method that works with a support volume similar tothat of the grain size analysis. This is important when the hetero-geneity of the sedimentary deposits is considered. Direct pushtechnology is especially suitable for high resolution in situ K char-acterization. Dietrich and Leven (2006) describe the growing fam-ily of DP tools used to obtain subsurface investigations by pushingand/or hammering small diameter hollow steels rods into theground. Information about the subsurface is collected by attachingsensors to the end of the rod string that measure soil specificparameters or by collecting soil, soil gas or ground water samples.Different DP tools for high resolution K characterization exist;among these are the DP Injection Logger (Dietrich et al., 2008),the DP Permeameter (Butler et al., 2007), the DP slug test (Butler,2002, 2005; Hinsby et al., 1992), and the DP Hydraulic ProfilingTool (McCall et al., 2009). In this study, we chose to use the DP slugtest as an established method to obtain absolute K values on a deci-meter scale. Therefore DP multi-level slug tests were performed intemporary DP monitoring wells, with a screened interval of 57 cmlength and 0.8 cm inner diameter at the end of the rod string(1.59 cm inner diameter) in close vicinity of the sample locations.For well installation, the rods are driven into the subsurface whilethe screen is protected inside the rods. Upon reaching the desired


depth, an expandable tip is pushed out and the rod string is pulledback, exposing the screen to the formation. As the screen is con-nected to the rod strings, the desired slug test interval can bereached simply by pulling up the rod string (see Sellwood et al.(2005) and McCall et al. (2005) for a description of installation pro-cedures). A semi automated pneumatic DP slug test assembly wasused; here the change of head is induced by compressed air (seeButler et al., 2002). Multi-level slug tests were performed at eachsampling cluster. To assure the reliability of the slug test, guide-lines after Butler (1997) were followed. After well installation,the well was developed until no further turbidity was observedin the pumped water. At each depth, slug tests with three repeatmeasurements with three different initial head displacementswere performed. Then, well development and the series of slugtests were repeated. Only those slug tests were used where nor-malized head plots coincided. However, in low K layers, fewer re-peat measurements were performed. 22 slug tests (Fig. 3) wereused to compare measured in situ KDPST values and calculated Kgrainsize values. Slug tests were analyzed after Zlotnik and McGuire(1998) as well as Butler (1997). Due to the small-scale heterogene-ity of the sedimentary deposits, most of the individual slug testintervals are intersected by different sedimentary layers and Kgrainsize data needed to be averaged over the slug test intervals. Butleret al. (1994) reported on vertical averaging in slug tests in layeredaquifers. However, averaging results vary, depending on the ap-plied averaging procedure. To minimize any possible effects, athickness weighted arithmetic average of the grain size data wasused to calculate an integral Kgrain size value over each individualslug test interval (Appendix B). Cumulative grain size curves weregenerated and relevant parameters for the calculation of Kgrain sizewere derived. In the hydrogeological practice, especially whenworking in strongly heterogeneous deposits, sample heterogeneityis inevitable. With the application of the averaging procedures, ef-fects of sample heterogeneity can be assessed best. Kgrain size valueswere calculated and a temperature correction was applied to allformulas, to account for viscosity effects due to increased ground-water temperatures at the Bitterfeld test site.

For 10 of the 22 slug tests intervals, generally minor core losseswere observed during sampling (Appendix B). Similar to the com-parison of the different formulas, calculated and measured K valuesare plotted in scatter plots arranged in a matrix. Again, linear cor-relation as well as differences in slopes between the simple regres-sion line and line of equality were considered.

Fig. 6 gives an example of the scatter plot for the slug test dataand grain size data calculated after three formulas. Fig. 6 reveals

Fig. 6. Correlation of measured KDPST and calculated Kgrain size. Histogram plo

that the correlation between Kgrain size and KDPST is strongly affectedby three values. These values of high KDPST and low Kgrain size wereidentified as K values derived from test intervals containing highcontents of clay and gravel, resulting in high U values of 198.64,328.47, and 399.69 respectively (Appendix B). These three valueswere removed from the analysis. In addition, two KDPST values wereidentified, that also strongly decreased correlation coefficients.These KDPST values were derived from slug tests intervals wheregrain size analysis revealed the presence of a thin (810 cm) lowK layer in between high K sediments. The presence of the low K lay-ers had only minor effects on measured KDPST values but did signif-icantly lower calculated K values. For these two slug test intervals,a weighted arithmetic average K value was calculated based uponthe Kgrain size values estimated for the individual layers within theslug test intervals instead of using the weighted average of thegrain size data. By directly averaging K, the effects of small isolatedlow K layers within the slug test interval are strongly reduced. Theanalysis was continued with 19 slug test intervals, results areshown in Fig. 7. The correlation coefficients for ln(KDPST) andln(Kgrain size) are presented in Table 7. The box plots (Fig. 8) of theln(K) data for the slug test intervals also demonstrate the widerange of results for measured and calculated K values. The highestcorrelation coefficient with ln(KDPST) values was observed forln(KBeyer) with 0.82, followed by ln(KHazen) with 0.81, ln(KTerzaghi)with 0.79, ln(KKaubisch) with 0.77, and ln(KUSBR) with 0.72. Correla-tion between KKaubisch and KDPST is high, but a difference betweenthe simple regression line and line of equality exists. Lowest valuesof r < 0.7 can be seen for ln(KKozeny-Khler), and ln(KSeelheim). Forln(KKozeny-Khler) and ln(KSeelheim), a large difference between theregression line and equality line can be observed. Table 7 presentsbasic statistics calculated for Kgrain size values obtained from the dif-ferent formulas over the slug test intervals and measured KDPST.Two effects might decrease the correlation of KKozeny-Khler and KDPSTin this heterogeneous aquifer: uncertainties in the estimation of /and calculation of de as harmonic mean. One systematic differencebetween slug tests and the grain size analysis should be furthermentioned: When laboratory data and field data are compared, dif-ferences in K estimates are often found, especially in low perme-able media (Campbell et al., 1990). In complex fluviatile deposits,such as is encountered at the Bitterfeld test site, horizontal K is of-ten greater than vertical K. The slug test measures primarily hori-zontal K, which is one of the fundamental parameters for flowmodeling. However, calculated K values based on grain size datarepresent neither horizontal nor vertical K values, as the sievingprocess destroys the natural sediment structure (Cheng and Chen,

t: x-axis: classes, y-axis: frequency; scatter plots: x- and y-axis: ln(K).

Table 7Comparison of relevant parameters for calculated Kgrain size and measured KDPST; a is the slope and b is the intercept of the linear regression.

KHazen KBeyer KTerzaghi KKaubisch KUSBR KSeelheim KKozeny-Khler KDPST

n 19 19 19 19 19 19 19 19x 2.98E04 1.91E04 1.76E04 5.76E05 2.78E04 7.63E03 4.49E06 4.61E04Min 8.10E06 4.19E06 1.02E05 6.15E06 1.86E05 2.32E04 9.31E07 3.07E06Max 1.54E03 7.96E04 7.94E04 1.45E04 2.80E03 1.06E01 1.49E05 1.67E03r (ln K) 0.81 0.82 0.79 0.77 0.72 0.63 0.67Lin. regr.

a 1.02 x 1.01 x 1.10 x 1.48 x 0.92 x 0.77 x 1.42 xb 0.38 0.73 1.56 6.26 0.19 3.75 9.22

r2 1.42E07 4.73E08 3.95E08 1.85E09 3.72E07 5.47E04 1.34E11 3.00E07

Fig. 8. Box plot of ln(K) values for the slug test intervals.

Fig. 7. Matrix plot of KDPST and calculated Kgrain size. Histogram plot: x-axis: classes, y-axis: frequency; scatter plots: x- and y-axis: ln(K).


2007; Song et al., 2009). Resulting calculated K values will there-fore likely be smaller than the horizontal K but greater than thevertical K average. With the exception of calculated K after Seel-heim (1880), this effect is visible in the distribution of the median

K distribution in Fig. 8. Other authors (e.g. Rovey and Cherkauer,1995) have reported a scale dependency of measured K (K in-creases with scale). In our comparison of slug test and grain sizedata, this effect is not seen.

Calculated K values are either based on the harmonic mean ofthe grain size distribution (Kozeny-Khler, 1965) or rely on a cer-tain grain size diameter determined from the grain size distribu-tion curve of a sample (e.g. Hazen, 1893). In contrast, K valuesmeasured with slug tests represent in many cases an arithmeticK value of the test interval (Butler et al., 1994). However, sedimen-tary deposition often includes sorting processes with a horizontalaccumulation of fine grained material as encountered at the Bitter-feld test site, where alternating layers and lenses with differenthydraulic properties are found. The impact for hydrogeologicalpractice is that the accumulation of fine grained materials as asmall layer in a generally highly permeable sample will lead to asignificant under prediction of calculated K for the entire sample.

5. Conclusion

The objective of this study was to compare commonly usedformulas for the determination of K from grain size data and


to evaluate how well these methods predict K in a highly heter-ogeneous deposit. A large number of empirical and semi-empir-ical formulas exist to calculate K from grain size distribution. Theformulas chosen cover a wide range of different approaches torepresent the effective grain size and the shape and porosityfunctions. The comparison of 108 grain size analyses revealeda high degree of correlation between the tested formulas, butalso that calculated min, max and mean K values differed overseveral orders of magnitude between the applied formulas. Re-sults demonstrated the need to test the reliability of calculatedKgrain size with directly measured K values that are obtained witha method that employs a support volume similar to that of thegrain size analysis. Therefore, multi-level slug tests for high res-olution in situ K characterization were performed in the closevicinity of the sampling points. A high correlation between Kgrainsize and KDPST could be shown for most of the applied formulas.Respective correlation coefficients ranged from 0.82 to 0.63. Inthis study, Kgrain size estimates were in most cases smaller thanKDPST estimates. This trend is attributed to the anisotropic distri-bution of K in the sediments and reflects the differences betweenin situ measured and calculated K. In addition, the presence ofisolated low K layers with limited thickness within a high Ksample, led to Kgrain size estimates that were significantly belowthe KDPST estimates. Calculated K values are based either on theharmonic mean of the grain size distribution, or rely on a certaingrain size diameter determined from the grain size distributioncurve, while KDPST values generally represent the arithmeticmean of the K distribution within the test interval. Effects ofsample heterogeneity must always be considered.

Large uncertainty in the calculation of KKozeny-Khler and KTer-zaghi is introduced by the estimation of porosity. We illustrated

Appendix A

Compilation of relevant grain size parameter for 108 samples; all d

Core Sample Depth from Depth to d10

S1L2 G 2.88 3.02 0.0152S1L2 H 3.02 3.05 0.0698S1L2 I 3.05 3.40 0.0107S1L2 J 3.40 3.60 0.0152S1L3 A 3.60 3.73 0.0143S1L3 B 3.73 3.97 0.0916S1L3 C 3.97 4.10 0.0017S1L3 D 4.10 4.27 0.0019S1L3 E 4.35 4.45 0.0014S1L3 F 5.00 5.10 0.0014S1L3 G 5.15 5.30 0.0444S1L3 H 5.30 5.31 0.1094S1L3 I 5.31 5.35 0.0823S1L3 J 5.35 5.39 0.0179S1L3 K 5.39 5.46 0.0666S1L3 L 5.46 5.54 0.1851S1L3 M 5.54 5.60 0.0882S1L4 A 6.02 6.55 0.0845S1L4 B 6.55 6.96 0.0367S1L4 C 6.96 7.16 0.0387S1L4 D 7.16 7.18 0.0052S1L4 E 7.18 7.48 0.0666S1L4 F 7.48 7.60 0.0991S1L5 A 7.60 7.72 0.0648S1L5 B 7.72 7.76 0.1437

the strong effects deviating porosity estimates have on the cal-culation of K for the same sample. This leads to the assumptionthat the established correlation between KDPST and KKozeny-Khler,respectively KTerzaghi, strongly depends on the applied methodto estimate porosity. The application of the total porosity im-plies a potential overestimation of calculated K as porosity val-ues of total porosity are greater than those of effective porosity,especially for clayey sediments. However, such an effect wasnot observed.

If general K estimates for an initial assessment are needed, thecalculation of K from grain size data is a suitable method. However,in this study Kgrain size data derived for the high resolution aquifercharacterization proved not to be sufficiently reliable for a highresolution assessment of K variations.

With the publication of the underlying data, we want to provideadditional data to those, interested in developing or further evalu-ating methods for estimating K from grain size data.

Acknowledgements

The presented study was funded as part of the MOST Project bythe German Federal Ministry of Education and Research (Bundes-ministerium fr Bildung und Forschung, Frderkennzeichen02WT0982).

Many colleagues have contributed to this study. We would liketo thank Katrin Matthes for analyzing the core samples, SteffenGraupner for performing the slug tests as well as Andreas Schoss-land and Helko Kotas for their craftsmanship in retrieving nearlyperfect cores. We thank Jim Butler and two anonymous reviewersfor their valuable comments and remarks.

values are given in mm.

d20 d30 d50 d60 de

0.0764 0.126 0.2731 0.4164 0.00170.1074 0.145 0.2766 0.4185 0.00320.0639 0.153 0.3907 0.5259 0.00150.1051 0.2051 0.4619 0.5902 0.00170.0846 0.1373 0.2777 0.3737 0.00140.1933 0.2908 0.4841 0.5807 0.00400.0149 0.0433 0.1333 0.1934 0.00090.0198 0.0515 0.1488 0.208 0.00100.0093 0.0233 0.0659 0.1245 0.00070.0088 0.0218 0.0614 0.1193 0.00070.0889 0.1205 0.1836 0.2478 0.00190.2127 0.2657 0.3716 0.4245 0.00480.1609 0.2956 0.7525 1.8663 0.00380.0608 0.0972 0.1691 0.2244 0.00160.1187 0.1663 0.3832 0.5104 0.00300.4854 1.0522 3.1283 4.3819 0.00660.1443 0.2346 0.4905 0.6185 0.00450.1491 0.2468 0.4597 0.5661 0.00290.0853 0.1154 0.1756 0.2267 0.00190.0909 0.1307 0.2246 0.3193 0.00200.0339 0.0707 0.156 0.1987 0.00100.1068 0.147 0.2659 0.3627 0.00220.2092 0.2863 0.4404 0.5175 0.00450.1477 0.2402 0.415 0.5024 0.00270.3103 0.4678 1.5159 2.9356 0.0062

(continued on next page)

Appendix A (continued)

Core Sample Depth from Depth to d10 d20 d30 d50 d60 de

S1L5 C 7.76 7.89 0.0745 0.1503 0.2372 0.3956 0.4748 0.0024S1L5 D 7.89 7.95 0.0017 0.0213 0.0536 0.211 0.3679 0.0009S1L5 E 7.95 8.04 0.0054 0.0348 0.0792 0.3173 0.495 0.0011S1L5 F 8.04 8.08 0.0275 0.1674 0.4826 4.4304 8.2161 0.0019S1L5 G 8.08 8.30 0.0066 0.0525 0.2279 0.7629 1.7853 0.0014S1L5 H 8.30 8.83 0.0009 0.0018 0.0106 0.0448 0.0822 0.0005S1L5 I 8.83 9.02 0.0007 0.0015 0.0039 0.0228 0.0447 0.0004S1L5 J 9.02 9.45 0.2157 0.3361 0.4566 0.9885 1.6287 0.0072S1L5 K 9.45 9.49 0.266 0.3881 0.4814 1.3694 2.2496 0.0096S1L5 L 9.49 9.60 0.2468 0.332 0.4171 0.5874 0.8965 0.0075S1L6 A 9.95 10.30 0.1013 0.2274 0.3577 0.6183 1.4241 0.0048S1L6 B 10.30 10.40 0.1331 0.2997 0.4632 1.8505 3.1825 0.0057S1L6 C 10.40 10.50 0.243 0.4471 0.9379 4.2622 5.9892 0.0102S1L6 D 10.50 11.00 0.1644 0.2614 0.3354 0.4835 0.5575 0.0054S1L2 G 2.88 3.02 0.0152 0.0764 0.126 0.2731 0.4164 0.0017S1L2 H 3.02 3.05 0.0698 0.1074 0.145 0.2766 0.4185 0.0032S1L2 I 3.05 3.40 0.0107 0.0639 0.153 0.3907 0.5259 0.0015S1L2 J 3.40 3.60 0.0152 0.1051 0.2051 0.4619 0.5902 0.0017S1L3 A 3.60 3.73 0.0143 0.0846 0.1373 0.2777 0.3737 0.0014S1L3 B 3.73 3.97 0.0916 0.1933 0.2908 0.4841 0.5807 0.0040S1L3 C 3.97 4.10 0.0017 0.0149 0.0433 0.1333 0.1934 0.0009S1L3 D 4.10 4.27 0.0019 0.0198 0.0515 0.1488 0.208 0.0010S1L3 E 4.35 4.45 0.0014 0.0093 0.0233 0.0659 0.1245 0.0007S1L3 F 5.00 5.10 0.0014 0.0088 0.0218 0.0614 0.1193 0.0007S1L3 G 5.15 5.30 0.0444 0.0889 0.1205 0.1836 0.2478 0.0019S1L3 H 5.30 5.31 0.1094 0.2127 0.2657 0.3716 0.4245 0.0048S1L3 I 5.31 5.35 0.0823 0.1609 0.2956 0.7525 1.8663 0.0038S1L3 J 5.35 5.39 0.0179 0.0608 0.0972 0.1691 0.2244 0.0016S1L3 K 5.39 5.46 0.0666 0.1187 0.1663 0.3832 0.5104 0.0030S1L3 L 5.46 5.54 0.1851 0.4854 1.0522 3.1283 4.3819 0.0066S1L3 M 5.54 5.60 0.0882 0.1443 0.2346 0.4905 0.6185 0.0045S1L4 A 6.02 6.55 0.0845 0.1491 0.2468 0.4597 0.5661 0.0029S1L4 B 6.55 6.96 0.0367 0.0853 0.1154 0.1756 0.2267 0.0019S1L4 C 6.96 7.16 0.0387 0.0909 0.1307 0.2246 0.3193 0.0020S1L4 D 7.16 7.18 0.0052 0.0339 0.0707 0.156 0.1987 0.0010S1L4 E 7.18 7.48 0.0666 0.1068 0.147 0.2659 0.3627 0.0022S1L4 F 7.48 7.60 0.0991 0.2092 0.2863 0.4404 0.5175 0.0045S1L5 A 7.60 7.72 0.0648 0.1477 0.2402 0.415 0.5024 0.0027S1L5 B 7.72 7.76 0.1437 0.3103 0.4678 1.5159 2.9356 0.0062S1L5 C 7.76 7.89 0.0745 0.1503 0.2372 0.3956 0.4748 0.0024S1L5 D 7.89 7.95 0.0017 0.0213 0.0536 0.211 0.3679 0.0009S1L5 E 7.95 8.04 0.0054 0.0348 0.0792 0.3173 0.495 0.0011S1L5 F 8.04 8.08 0.0275 0.1674 0.4826 4.4304 8.2161 0.0019S1L5 G 8.08 8.30 0.0066 0.0525 0.2279 0.7629 1.7853 0.0014S1L5 H 8.30 8.83 0.0009 0.0018 0.0106 0.0448 0.0822 0.0005S1L5 I 8.83 9.02 0.0007 0.0015 0.0039 0.0228 0.0447 0.0004S1L5 J 9.02 9.45 0.2157 0.3361 0.4566 0.9885 1.6287 0.0072S1L5 K 9.45 9.49 0.266 0.3881 0.4814 1.3694 2.2496 0.0096S1L5 L 9.49 9.60 0.2468 0.332 0.4171 0.5874 0.8965 0.0075S1L6 A 9.95 10.30 0.1013 0.2274 0.3577 0.6183 1.4241 0.0048S1L6 B 10.30 10.40 0.1331 0.2997 0.4632 1.8505 3.1825 0.0057S1L6 C 10.40 10.50 0.243 0.4471 0.9379 4.2622 5.9892 0.0102S1L6 D 10.50 11.00 0.1644 0.2614 0.3354 0.4835 0.5575 0.0054S1L6 E 11.00 11.05 0.5028 1.3632 2.2295 3.5796 4.2546 0.0110S1L6 F 11.05 11.20 0.2145 0.295 0.3755 0.5366 0.6171 0.0060S1L6 G 11.20 11.30 0.2024 0.2619 0.3213 0.4403 0.4998 0.0058S1L6 H 11.35 11.40 0.1126 0.222 0.2908 0.4284 0.4972 0.0047S1L6 I 11.54 11.6 0.2352 0.5897 1.1706 2.9807 4.4895 0.0075S2L2 E 2.68 2.75 0.1066 0.2829 0.5591 2.86 4.4826 0.0043S2L2 F 3.05 3.70 0.1003 0.1771 0.2985 0.5545 1.3691 0.0038S2L3 A 3.80 4.00 0.0876 0.1718 0.2655 0.4473 0.5382 0.0045


Appendix A (continued)

Core Sample Depth from Depth to d10 d20 d30 d50 d60 de

S2L3 B 4.00 4.16 0.1003 0.2186 0.362 0.9173 3.1246 0.0049S2L3 C 4.16 4.76 0.0063 0.0514 0.1281 0.32 0.4388 0.0013S2L3 D 4.76 5.02 0.0947 0.1869 0.2931 0.507 0.614 0.0047S2L3 E 5.02 5.22 0.0969 0.158 0.2415 0.404 0.4853 0.0039S2L3 F 5.22 5.31 0.0577 0.0969 0.1329 0.2167 0.3358 0.0027S2L3 G 5.31 5.32 0.0941 0.1526 0.2566 0.5395 0.9588 0.0055S2L3 H 5.32 5.47 0.0586 0.1035 0.1456 0.287 0.4095 0.0023S2L3 I 5.47 5.70 0.0939 0.1608 0.2767 0.5506 0.9965 0.0039S2L4 A 5.80 6.18 0.0698 0.1297 0.2103 0.4384 0.5524 0.0032S2L4 B 6.18 6.62 0.0674 0.1299 0.1915 0.3738 0.4663 0.0026S2L4 C 6.62 6.70 0.0017 0.0178 0.0492 0.1338 0.1808 0.0009S2L4 D 6.70 6.82 0.063 0.1264 0.1884 0.3635 0.4523 0.0024S2L4 E 6.82 6.85 0.0059 0.0414 0.103 0.3124 0.427 0.0012S2L4 F 6.85 7.30 0.1069 0.1796 0.2477 0.3685 0.4289 0.0040S2L4 G 7.30 7.70 0.1892 0.3135 0.4329 0.9121 1.7179 0.0067S2L5 A 7.75 8.04 0.0794 0.134 0.1859 0.367 0.4602 0.0033S2L5 B 8.04 8.15 0.1681 0.277 0.3635 0.5366 0.6231 0.0033S2L5 C 8.15 8.30 0.0014 0.0113 0.032 0.1444 0.2845 0.0007S2L5 D 8.30 8.47 0.0374 0.2087 0.333 0.5815 1.0064 0.0019S2L5 E 8.47 8.70 0.0011 0.0044 0.0197 0.0915 0.2131 0.0006S2L5 F 8.70 8.82 0.0007 0.0015 0.0047 0.0357 0.0594 0.0004S2L5 G 8.82 9.00 0.164 0.365 0.538 1.6948 3.4162 0.0035S2L5 H 9.00 9.08 0.0009 0.0018 0.0106 0.055 0.2263 0.0005S2L5 I 9.08 9.70 0.2898 0.4096 0.4981 1.246 1.777 0.0088S2L6 A 9.90 10.10 0.0786 0.1387 0.1985 0.4102 0.5164 0.0033S2L6 B 10.10 10.22 0.2054 0.3126 0.4198 0.6536 1.2441 0.0041S2L6 C 10.22 10.32 0.1718 0.3199 0.4577 1.1312 1.7995 0.0055S2L6 D 10.32 10.48 0.1367 0.2683 0.3688 0.5697 0.8223 0.0041S2L6 E 10.48 10.75 0.2461 0.4109 0.5643 2.1392 3.5307 0.0045S2L6 F 10.85 11.20 0.5134 1.054 1.5977 4.2958 6.1178 0.0162S2L6 G 11.20 11.70 0.3442 0.5957 2.2314 6.0879 9.725 0.0082S4L2 B 2.93 3.25 0.1763 0.2951 0.4031 0.6192 1.315 0.0062S4L2 C 3.25 3.66 0.1934 0.2979 0.3988 0.6007 1.134 0.0114S4L2 D 3.66 3.83 0.2636 0.4019 0.5247 1.4341 2.0903 0.0088S4L3 A 4.03 4.18 0.2 0.3468 0.4863 1.7405 2.9714 0.0060S4L3 B 4.18 4.30 0.2438 0.3532 0.4626 0.8972 1.4656 0.0090S4L3 C 4.30 4.87 0.0012 0.0061 0.0183 0.0604 0.1393 0.0006S4L3 D 4.87 5.11 0.104 0.2357 0.4141 1.3663 2.546 0.0054S4L3 E 5.11 5.15 0.035 0.0747 0.096 0.1385 0.1598 0.0021S4L3 F 5.15 5.23 0.1644 0.3152 0.4558 1.1667 1.8729 0.0063S4L3 G 5.23 5.26 0.0446 0.0819 0.1076 0.1588 0.1844 0.0024S4L4 A 6.05 6.15 0.176 0.3005 0.4122 0.6639 1.3421 0.0045S4L4 B 6.15 6.45 0.1165 0.2498 0.3682 0.6051 1.2859 0.0059S4L4 C 6.45 6.58 0.1034 0.1699 0.2558 0.4247 0.5092 0.0047S4L4 E 7.21 7.43 0.0087 0.0522 0.0901 0.1624 0.1986 0.0013S4L4 F 7.43 7.71 0.1009 0.2079 0.2685 0.3898 0.4505 0.0041S4L4 G 7.71 7.73 0.0738 0.0955 0.1172 0.1605 0.1822 0.0028S4L4 H 7.73 7.83 0.1352 0.238 0.307 0.445 0.514 0.0063S4L5 A 7.87 7.99 0.0687 0.1065 0.1444 0.2614 0.3773 0.0031S4L5 B 7.99 8.11 0.0838 0.1755 0.2596 0.4142 0.4916 0.0033S4L5 C 8.11 8.19 0.0923 0.1453 0.2372 0.5129 1.0494 0.0047S4L5 D 8.19 8.23 0.0136 0.0528 0.0836 0.1391 0.1669 0.0015S4L5 E 8.23 8.84 0.0669 0.1233 0.1768 0.3851 0.498 0.0026S4L5 F 8.84 9.41 0.1786 0.296 0.4027 0.6161 1.4141 0.0051S4L5 G 9.41 9.66 0.3407 0.6024 1.3265 4.0407 5.8627 0.0114S4L5 H 9.66 9.83 0.0061 0.0482 0.2058 0.5932 1.774 0.0013S4L6 A 9.88 9.98 0.0822 0.1355 0.1864 0.3497 0.4334 0.0033S4L6 B 9.98 10.23 0.1106 0.2328 0.3387 0.5506 0.9905 0.0050S4L6 C 10.23 10.57 0.1182 0.2591 0.3666 0.5816 0.9838 0.0038S4L6 D 10.57 11.04 0.2754 0.4768 1.0359 3.858 5.6276 0.0086S4L6 E 11.07 11.83 0.24 0.3331 0.4262 0.6123 1.4006 0.0087


Appendix B

Relevant grain size parameters of the slug test intervals and KDPST in m/s; C is the core number, CL is core loss in cm within the 57 cmslug test interval, indicates depth intervals where an weighted averaging of K values was applied; indicates values excluded from thedata analysis, all d values are given in mm.

Depth from Depth to SC CL KDPST d10 d20 d30 d50 d60 de

5.16 5.73 1 0.13 9.24E05 0.0645 0.1149 0.1598 0.3728 0.5047 0.00276.93 7.5 1 1.14E04 0.0512 0.0989 0.1392 0.248 0.3459 0.00217.53 8.10 1 3.07E06 0.0257 0.1183 0.2119 0.4274 0.5352 0.00198.15 8.72 1 5.49E05 0.0011 0.0037 0.0168 0.076 0.2185 0.00068.73 9.30 1 1.12E03 0.0015 0.0128 0.0427 0.3292 0.4927 0.00085.34 5.91 2 0.10 1.19E04 0.0762 0.1363 0.1957 0.4461 0.5729 0.00315.93 6.50 2 5.48E05 0.0688 0.1338 0.1985 0.3994 0.5001 0.00286.49 7.06 2 1.31E04 0.045 0.1152 0.1786 0.3379 0.4891 0.00217.08 7.65 2 1.65E04 0.164 0.2702 0.3559 0.5272 0.6129 0.00517.63 8.20 2 0.05 8.12E06 0.0654 0.1379 0.2298 0.4284 0.5277 0.00268.48 9.05 2 6.55E04 0.0013 0.0099 0.0341 0.2846 0.5196 0.00078.83 9.40 2 9.15E04 0.2628 0.3993 0.5358 1.3809 1.9541 0.00589.41 9.98 2 0.20 9.66E04 0.2186 0.3352 0.4517 0.9064 1.4943 0.006610.22 10.79 2 0.04 1.35E03 0.2027 0.3366 0.4706 1.1713 1.8396 0.004610.96 11.53 2 1.67E03 0.3541 0.875 1.7823 5.3048 8.2512 0.01014.87 5.44 4 0.18 1.95E04 0.0889 0.1478 0.2614 0.6501 1.6575 0.00445.97 6.54 4 0.08 7.70E05 0.1135 0.2415 0.3506 0.5689 0.9867 0.00547.8 8.37 4 0.04 3.07E05 0.0694 0.1229 0.1728 0.3636 0.4685 0.00308.38 8.95 4 1.27E04 0.0735 0.1305 0.2078 0.4312 0.5429 0.00299.73 10.30 4 0.05 1.16E03 0.1019 0.199 0.2988 0.4983 0.5981 0.004210.33 10.90 4 2.31E04 0.2015 0.3546 0.4904 1.6086 2.9982 0.005610.93 11.50 4 0.03 1.35E03 0.2433 0.349 0.4546 0.958 1.9228 0.0087


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Field evaluation of methods for determining hydraulic conductivity from grain size dataIntroductionStudy siteSampling

Grain size analysesEffects of on K

Results of the grain size analysesComparison with direct push slug testConclusionAcknowledgementsAppendix AReferencesIntroduction

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