Appendix 1. Spreadsheet and MATLAB Programs Developed to Facilitate the
Estimation of Hydraulic Conductivity from Grain Size Analyses, for Calculation of
Sediment Grain Size Distribution Statistical Moments, and for Comparative
Statistical Analysis of Estimated and Measured Hydraulic Conductivity Values
Program descriptions and user information
Two different programs were developed for analysis of grain size data using 20
numerical analysis methods and statistical comparisons with actual hydraulic conductivity
measurements. These programs are attached as supplementary online files that can be
downloaded and used by all researchers.
The first program, MULTI H_K, is relatively straightforward spreadsheet program with
data entry being the grain size data and if hydraulic conductivity and porosity data are
measured, they can also be input. A single grain size analysis can be input in the front of the
spreadsheet program (Figure A1) or multiple analyses can be entered at another location
(Figure A2). When porosity data are not collected, an estimated value must be entered to allow
some of the hydraulic conductivity estimation methods to function (e.g., Krumbein and Monk,
1943). Up to 100 samples can be input into the program for simultaneous analysis. It is
assumed that the water passing through the sediments is fresh water. Therefore, the
appropriate normalization has to be made to account for viscosity changes when using saline
water.
The program contains annotations pertaining to operation and which analytical
equations should be used for each depositional environment as well as recommendations
regarding special equation coefficients that produce the best statistical results. The output file
provides all estimated hydraulic conductivity values, the statistical moments, and other useful
data (Figure A3).
A3).
Figure A1. Front page of the MULTI_HK program showing the single grain size analysis data
entry column and the arrangement of some of the estimation methods. Note the ability to
enter the measured hydraulic conductivity and the water temperature used in the
measurement to produce a normalized value.
Figure A2. Multiple grain size analysis data entry location within the MULTI_HK program. Up to
100 grain size analyses can be entered into the program in a single run. This number could be
changed within the program by the user based on need. Note that if the program is used solely
for estimation of hydraulic conductivity and porosity is not measured, an estimated porosity
value must be entered to allow several of the methods to yield a hydraulic conductivity value.
Figure A3. Hydraulic conductivity and other data output file within the MULTI_HK program. The
program can be used to archive data and analyses for 100 samples or greater if modified.
The equations used in the program are based on those in the original published papers
or a recent translation of them. It was discovered that alterations to the some of the original
equations have been made, such as for the Hazen equation (Hazen 1892, 1911), which has two
versions based on the original and later modifications (Carrier, 2003). Also, there are various
interpretations in the literature concerning how to calculate some of the coefficients used in
some of the equations and there are significant differences in estimated hydraulic conductivity
estimates based on these discrepancies. The coefficients in the Kozeny (1927, 1953) and
Kozeny-Carman (1937; 1956), Kozeny-Carman Bear (1972) equations are examples. The
methods used in this paper follow the original publication methods as closely as possible, but
are still subject to interpretation.
The second program, Grain Size Hydraulics, was written in MATLAB® to perform the
same fundamental calculations as the spreadsheet model and to check it. This program runs
faster and more efficiently compared to the spreadsheet program, but requires more computer
skills to enter data and to run the program. Grain Size Hydraulics also performs statistical
comparisons of data sets to compare the various numerical methods used for analysis and to
assess the statistical moments for use in developing better correlation of grain size
characteristics to actual hydraulic conductivity measurements. This program allows rapid
analysis of large data sets and can be used in screening of samples for feasibility analysis when
applied to natural filtration system types (e.g., beach and seabed gallery intakes for
desalination facilities). Also, this program can be used in the design of artificial filters of all
types along with some additional software.
Some adjustments were made to the coefficients contained within some of the
empirical methods based on the characteristics of the sediments, including the total porosity,
the sorting, the fines percentage, the grain shape, packing, and others as required for use
within the various methodologies. The adjustments of the coefficients were different for each
depositional environment based on the generalized characteristics of that group. For example,
in using the Kozeny-Carman-Bear method, the value used for the representative grain size was
verified based on the percentage of fines using the method suggested by Koltermann and
Gorlick (1995), but other methodologies do exist (Chapius and Aubertin, 2003). In the Hazen
formula (new) the constant value (C) is based on the degree of sorting and other factors and
can range from 1 to 1000 based on a literature survey conducted by Carrier (2003). The general
default coefficient was set at 125 for the “new” Hazen formula for beginning analysis. This
constant was varied based on the group characteristics in recognition that dune sands are very
well sorted, whereas wadi sediments are very poorly sorted.
A third program was developed once the proposed beta coefficients were calculated.
This program was written in Excel as the first one. It follows the same approach as the latter,
but has a few new additions such as a selection bar (Figure A4), in which the depositional
environment is selected. Selecting a depositional environment gives the program the
appropriate beta coefficient for the calculations.
Figure A4. Selection of the desired depositional environment. This selection provides the
program with the proposed beta coefficients for calculations of hydraulic conductivity.
The estimated hydraulic conductivity for each depositional environment is shown in the
“Results” sheet. It is important to note that the program only provides the calculation for the
best correlated methods accordingly (Figure A5). The equations that had poor correlation in the
second program are not calculated.
Figure A5. Example of a wadi sediment analysis. Note that the program shows values for the
best correlated methods only, unlike the first program that gives all the calculations.
References
Bear, J., 1972. Dynamics of Fluids in Porous Media. New York: Dover Publications, Inc.
Carman, P. C., 1937. Fluid through granular beds. Transactions 15, 150, London: Institution of
Chemical Engineers.
Carman, P. C., 1956. Flow of gases through porous media. London: Butterworth’Scierntific
Publications.
Carrier, W. D., 2003. Goodbye Hazen; Hello, Kozeny-Carman. Journal of Geotechnical
Engineering, November, 2003: 1054-1056.
Chapuis, R. P., and M. Aubertin, 2003, Predicting the coefficient of permeability of soils using
the Kozeny-Carman equation. Report EPM-RT-2003-03, Department CGM, Ecole Polytechnique
de Montreal, 31 pages.
Hazen, A., 1892. Some physical properties of sands and gravels, with special reference to their
use in filtration. Massachusetts State Board of Health, 24th Annual Report, 539-556.
Hazen, A., 1911. Discussion of dams on sand foundations by A. C. Koenig. Transactions of the
American Society of Civil Engineers 73: 199-203.
Koltermann, C. E., and S. M. Gorelick, 1995. Fractional packing model for hydraulic conductivity
derived from sediment mixtures. Water Resources Research 31: 3283-3297.
Kozeny, J., 1927. Uber kapillare leitung des wassers in boden. Sitzungsber Akad. Wiss.Wien
Mathematica Naturwiss. K1, Abt.2a, 136: 271-306 (in German).
Kozeny, J., 1953. Das wasser in boden, grundwasserbewegung. Hydraulik, 280-445.
Krumbein, W. C., and G. D. Monk. 1943. Permeability as a function of the size parameters of
unconsolidated sands. Transactions of the American Institute of Mining, Metallurgical and
Petroleum Engineers, 151: 153-163.