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GRADISTATVersion 4.0
A Grain Size Distribution and Statistics Package for the Analysis of
Unconsolidated Sediments by Sieving or Laser Granulometer
Developed by Simon Blott
Surface Processes and Modern Environments Research Group
Department of Geology
Royal Holloway
University of London
Egham
Surrey TW20 0EX
Email: [email protected]
Tel/Fax: +44 (0)1784 414168
The development of this program was inspired by Dave Thornley and John Jack atPostgraduate Research Institute for Sedimentology at the University of Reading, UK, andDepartment of Geology at Royal Holloway University of London, UK. It is provided in Microsoft format to allow both spreadsheet and graphical output. The program is best suited to analyseobtained from sieve or laser granulometer analysis. The user is required to input the masspercentage of sediment retained on sieves spaced at any intervals, or the percentage of sedimentdetected in each bin of a Laser Granulometer. The following sample statistics are then calculatedthe Method of Moments in Microsoft Visual Basic programming language: mean, mode(s), sorting(standard deviation), skewness, kurtosis, D10, D50, D90, D90/D10, D90D10, D75/D25 and D75D25. Grainparameters are calculated arithmetically and geometrically (in microns) and logarithmically (using thescale) (Krumbein and Pettijohn, 19381; Table 1). Linear interpolation is also used to calculate statisticalparameters by the Folk and Ward (1957)2 graphical method and derive physical descriptions (such“very coarse sand” and “moderately sorted”). The program also provides a physical description textural group which the sample belongs to and the sediment name (such as “fine gravelly coarse sand”)after Folk (1954)3. Also included is a table giving the percentage of grains falling into each size fraction,modified from Udden (1914)4 and Wentworth (1922)5 (see Table 2). In terms of graphical output,program provides graphs of the grain size distribution and cumulative distribution of the data inmetric and phi units, and displays the sample grain size on triangular diagrams. Samples mayanalysed singularly, or up to 250 samples may be analysed together. The program is ideal for the rapid analysis of sieve data and is freely available from the authorthe above address. Please note that the copyright for the program is held by author, and any distributionor use of the program should be acknowledged to him. S. Blott October 2000 1Krumbein, W.C. and Pettijohn, F.J. (1938) Manual of Sedimentary Petrography. AppletonCenturyCrofts, New York.
2Folk, R.L. and Ward, W.C. (1957) Brazos River bar: a study in the significance of grain size parameters. Journal of Sedimentary
Petrology, 27, 326. 3Folk, R.L. (1954) The distinction between grain size and mineral composition in sedimentaryrock nomenclature. Journal
Geology, 62, 344359. 4Udden, J.A. (1914) Mechanical composition of clastic sediments. Bulletin of the Geological Society of America, 25, 655744
5Wentworth, C.K. (1922) A scale of grade and class terms for clastic sediments. Journal of Geology, 30, 377392.
Instructions on the Use of the GRADISTAT Program
Single Sample Analysis 1. Switch to the "Single Sample Data Input" sheet if it is not already active. Enter the aperture sizesthe sieves or Laser Granulometer bins used in the analysis into the cells in column B. Sizes mayentered either in ascending or descending numerical order. For convenience, you can click on onethe standard sieve or Laser Granulometer size intervals and GRADISTAT will enter the size classesyou. Any nonstandard sieve sizes can be used, although some of the statistics may not be calculatedyou have not used sieves with at least whole phi intervals. See the section below if the sample containsunanalysed sediment, such as material retained in the pan after sieving. At least one size class than the largest particles in the sample should also be entered. A large area to the right of thecolumns is provided for the cut and paste of data from other spreadsheets, such as the import of Granulometer data. 2. Enter the weight or percentage of sample beside each size class in column C. When youfinished, make sure there are no data further down the spreadsheet which could cause an error.program will accept data down to row 230. 3. Enter the sample identity, analyst, date and initial sample weight (optional) at the top of the "SingleSample Data Input" sheet. 4. Click the "Calculate Statistics" button and wait a few moments for the program to finish runningWhen the dialog box appears, click "OK". 5. The results are summarised on the "Single Sample Statistics" sheet, which includes a distributionhistogram of the sample. Select "Print..." from the file menu to print the Summary Statistics pagedata is also shown on triangular diagrams on the "Gravel Sand Mud" and "Sand Silt Clay" sheetsFurther cumulative and distribution plots are given on other sheets. Multiple Sample Analysis 1. Switch to the "Multiple Sample Data Input" sheet. Enter the aperture sizes of the sieves or Granulometer bins used in the analysis into the cells in column B. The aperture sizes must be the for all the samples. Sizes may be entered either in ascending or descending numerical orderconvenience, you can click on one of the standard sieve or Laser Granulometer size intervalsGRADISTAT will enter the size classes for you. Any nonstandard sieve sizes can be used, althoughsome of the statistics may not be calculated if you have not used sieves with at least whole phi intervalsSee the section below if samples contain unanalysed sediment, such as material retained in theafter sieving. At least one size class larger than the largest particles in the sample should alsoentered. 2. Enter the weight or percentage of sample in column C onwards. Make sure there are no data furtherdown the spreadsheet which could cause an error. The program will accept data down to row 230. 3. Enter the sample identity, analyst, date and initial sample weight (optional) in the green cells aboveeach sample listing. 4. If you require a Summary Statistics printout for each sample, select a tick in the option box. 5. Click the "Calculate Statistics" button and wait for the program to finish running (this may take severalminutes). GRADISTAT will give a warning if it detects a sample whose combined weight is greaterthe given sample weight. Click "OK" when prompted on the dialog boxes.
the given sample weight. Click "OK" when prompted on the dialog boxes. 6. The resulting statistics for all samples are summarised on the "Multiple Sample Statistics" sheetdata for each sample included in the analysis are also shown on triangular diagrams on the "GravelSand Mud" and "Sand Silt Clay" sheets. Cumulative and distribution plots will show the results forlast sample in the analysis. If graphical plots for other samples are required, use separate single sampleanalyses (above). Unanalysed Sediment Occasionally, samples may contain sediment in a size fraction of unspecified size, such as materialretained in the pan after sieving. Ideally, the whole size range in a sample should be analysed, andmay require further analysis of sediment remaining in the pan after sieving. The larger the quantitysediment remaining in the pan, the less accurate the calculation of grain size statistics, with statisticscalculated by the Method of Moments being most susceptible. Errors in Folk and Ward parametersbecome significant only when more than 5% of the sample is undetermined. If the sample containssediment in the pan the user should do one of the following: 1. Enter the weight or percentage of sample in the pan with a class size of zero (or leave the class
blank). GRADISTAT calculates the statistics assuming all sediment in the pan is larger than 10 f (1The grain size distribution graphs do not however plot the quantity of sediment in the pan. 2. Enter the weight or percentage of sample in the pan with a class size which the user considersthe lower size limit of sediment in the pan. GRADISTAT calculates the statistics assuming all sedimentin the pan is larger than this value and plots this quantity on the grain size distribution graphs. The above two options are recommended where there is less than 1% of the sample remaining pan. 3. Do not enter the quantity of sediment in the pan at all. GRADISTAT calculates the statistics ignoringthe sediment in the pan as if it were not present in the sample. This is recommended where theremore than 1% of the sample remaining in the pan. Samples containing more than 5% of sediment in the pan should ideally be analysed using a differenttechnique, such as sedimentation or laser granulometry. Great care must however be taken merging data obtained by different methods. Graph Scales The size scale used in graphical plots is dependent upon the range of sizes specified on the sampleinput sheets: the first and last values provide the extreme values on the graphs. While one sizelarger than the largest particles in the sample should be entered, other size classes outside thesize range of the sample have no influence on the statistical calculations. These classes may be deletedto narrow the size scale on graphs. Note that unused size classes within the size range of the sampleshould also be deleted, otherwise GRADISTAT assumes that zero sample weight was present in size classes. © Copyright Simon Blott (2000)
Table 1. Statistical formulae used in the calculation of grain size parameters.
f is the frequency in percent; m is the midpoint of each class interval in metric (mm) or
phi (mf) units; Px and fx are grain diameters, in metric or phi units respectively, at the
cumulative percentile value of x.
(a) Arithmetic Method of Moments
Mean Standard Deviation Skewness Kurtosis
100 = m
a
fmx
S
100
)( =
2
ama
xmf Ss 3
3
100
)( =
a
ama
xmfSk
s
S 4
4
100
)( =
a
ama
xmfK
s
S
(b) Geometric Method of Moments
Mean Standard Deviation Skewness Kurtosis
100
lnexp = m
g
mfx
S
100
)ln(lnexp =
2
gm
g
xmf Ss 3
3
ln100
)ln(ln =
g
gm
g
xmfSk
s
S
4
4
ln100
)ln(ln =
g
gm
g
xmfK
s
S
Sorting (sg) Skewness (Skg) Kurtosis (Kg)
Very well sorted
Well sorted
Moderately well sorted
Moderately sorted
Poorly sorted
Very poorly sorted
Extremely poorly sorted
< 1.27
1.27 – 1.41
1.41 – 1.62
1.62 – 2.00
2.00 – 4.00
4.00 – 16.00
> 16.00
Very fine skewed
Fine skewed
Symmetrical
Coarse skewed
Very coarse skewed
< 1.30 1.30 – 0.43 0.43 – +0.43 +0.43 – +1.30
> +1.30
Very platykurtic
Platykurtic
Mesokurtic
Leptokurtic
Very leptokurtic
< 1.70
1.70 – 2.55
2.55 – 3.70
3.70 – 7.40
> 7.40
(c) Logarithmic Method of Moments
Mean Standard Deviation Skewness Kurtosis
100 =
f
f
fmx
S
100
)( =
2
ff
fsxmf S
3
3
100
)( =
f
ff
fs
xmfSk
S
4
4
100
)( =
f
ff
fs
xmfK
S
Sorting (sf) Skewness (Skf) Kurtosis (Kf)
Very well sorted
Well sorted
Moderately well sorted
Moderately sorted
Poorly sorted Very poorly sorted
Extremely poorly sorted
< 0.35
0.35 – 0.50
0.50 – 0.70
0.70 – 1.00
1.00 – 2.00 2.00 – 4.00
> 4.00
Very fine skewed
Fine skewed
Symmetrical
Coarse skewed
Very coarse skewed
> +1.30 +0.43 – +1.30 0.43 – +0.43 0.43 – 1.30
< 1.30
Very platykurtic
Platykurtic
Mesokurtic
Leptokurtic
Very leptokurtic
< 1.70
1.70 – 2.55
2.55 – 3.70
3.70 – 7.40
> 7.40
Table 1. Statistical formulae used in the calculation of grain size parameters.
f is the frequency in percent; m is the midpoint of each class interval in metric (mm) or
phi (mf) units; Px and fx are grain diameters, in metric or phi units respectively, at the
cumulative percentile value of x.
(a) Arithmetic Method of Moments
Mean Standard Deviation Skewness Kurtosis
100 = m
a
fmx
S
100
)( =
2
ama
xmf Ss 3
3
100
)( =
a
ama
xmfSk
s
S 4
4
100
)( =
a
ama
xmfK
s
S
(b) Geometric Method of Moments
Mean Standard Deviation Skewness Kurtosis
100
lnexp = m
g
mfx
S
100
)ln(lnexp =
2
gm
g
xmf Ss 3
3
ln100
)ln(ln =
g
gm
g
xmfSk
s
S
4
4
ln100
)ln(ln =
g
gm
g
xmfK
s
S
Sorting (sg) Skewness (Skg) Kurtosis (Kg)
Very well sorted
Well sorted
Moderately well sorted
Moderately sorted
Poorly sorted
Very poorly sorted
Extremely poorly sorted
< 1.27
1.27 – 1.41
1.41 – 1.62
1.62 – 2.00
2.00 – 4.00
4.00 – 16.00
> 16.00
Very fine skewed
Fine skewed
Symmetrical
Coarse skewed
Very coarse skewed
< 1.30 1.30 – 0.43 0.43 – +0.43 +0.43 – +1.30
> +1.30
Very platykurtic
Platykurtic
Mesokurtic
Leptokurtic
Very leptokurtic
< 1.70
1.70 – 2.55
2.55 – 3.70
3.70 – 7.40
> 7.40
(c) Logarithmic Method of Moments
Mean Standard Deviation Skewness Kurtosis
100 =
f
f
fmx
S
100
)( =
2
ff
fsxmf S
3
3
100
)( =
f
ff
fs
xmfSk
S
4
4
100
)( =
f
ff
fs
xmfK
S
Sorting (sf) Skewness (Skf) Kurtosis (Kf)
Very well sorted
Well sorted
Moderately well sorted
Moderately sorted
Poorly sorted Very poorly sorted
Extremely poorly sorted
< 0.35
0.35 – 0.50
0.50 – 0.70
0.70 – 1.00
1.00 – 2.00 2.00 – 4.00
> 4.00
Very fine skewed
Fine skewed
Symmetrical
Coarse skewed
Very coarse skewed
> +1.30 +0.43 – +1.30 0.43 – +0.43 0.43 – 1.30
< 1.30
Very platykurtic
Platykurtic
Mesokurtic
Leptokurtic
Very leptokurtic
< 1.70
1.70 – 2.55
2.55 – 3.70
3.70 – 7.40
> 7.40
(d) Logarithmic (Original) Folk and Ward (1957) Graphical Measures
Mean Standard Deviation Skewness Kurtosis
3
845016 fff ++=ZM
6.64
5951684 ffffs
+
=I
( )1684
508416
2
2
ff
fff

+=ISk
( )595
50955
2
2
ff
fff

++
( )2575
595
44.2 ff
ff

=GK
Sorting (sI) Skewness (SkI) Kurtosis (KG)
Very well sorted
Well sorted Moderately well sorted
Moderately sorted
Poorly sorted
Very poorly sorted
Extremely poorly sorted
< 0.35
0.35 – 0.50 0.50 – 0.70
0.70 – 1.00
1.00 – 2.00
2.00 – 4.00
> 4.00
Very fine skewed
Fine skewed Symmetrical
Coarse skewed
Very coarse skewed
+0.3 to +1.0 +0.1 to +0.3 +0.1 to 0.1 0.1 to 0.3 0.3 to 1.0
Very platykurtic
Platykurtic Mesokurtic
Leptokurtic
Very leptokurtic
Extremely
leptokurtic
< 0.67
0.67 – 0.90 0.90 – 1.11
1.11 – 1.50
1.50 – 3.00
> 3.00
(e) Geometric Folk and Ward (1957) Graphical Measures
Mean Standard Deviation
3
lnlnlnexp 845016 PPP
M G
++=
÷ø
öçè
æ +
=
6.6
lnln
4
lnlnexp 9558416 PPPP
Gs
Skewness Kurtosis
( )( )
( )( )525
50955
1684
508416
lnln2
ln2lnln
lnln2
ln2lnln
PP
PPP
PP
PPPSkG

++

+=
( )7525
955
lnln44.2
lnln
PP
PPKG

=
Sorting (sG) Skewness (SkG) Kurtosis (KG)
Very well sorted
Well sorted
Moderately well sorted
Moderately sorted
Poorly sorted
Very poorly sorted Extremely poorly sorted
< 1.27
1.27 – 1.41
1.41 – 1.62
1.62 – 2.00
2.00 – 4.00
4.00 – 16.00 > 16.00
Very fine skewed
Fine skewed
Symmetrical
Coarse skewed
Very coarse skewed
0.3 to 1.0 0.1 to 0.3 0.1 to +0.1 +0.1 to +0.3 +0.3 to +1.0
Very platykurtic
Platykurtic
Mesokurtic
Leptokurtic
Very leptokurtic
Extremely leptokurtic
< 0.67
0.67 – 0.90
0.90 – 1.11
1.11 – 1.50
1.50 – 3.00
> 3.00
Table 2. Size scale adopted in the GRADISTAT program, modified from Udden
(1914) and Wentworth (1922).
Grain Size
phi mm
Descriptive term
Very Large
10 1024
Large
9 512
Medium
8 256
Small
7 128
Very small
Boulder
6 64 Very coarse
5 32
Coarse
4 16
Medium
3 8
Fine
2 4
Very fine
Gravel
1 2
Very coarse 0 1
microns Coarse
1 500
Medium
2 250
Fine
3 125
Very fine
Sand
4 63
Very coarse
5 31
Coarse 6 16
Medium
7 8
Fine
8 4
Very fine
Silt
9 2
Clay
(d) Logarithmic (Original) Folk and Ward (1957) Graphical Measures
Mean Standard Deviation Skewness Kurtosis
3
845016 fff ++=ZM
6.64
5951684 ffffs
+
=I
( )1684
508416
2
2
ff
fff

+=ISk
( )595
50955
2
2
ff
fff

++
( )2575
595
44.2 ff
ff

=GK
Sorting (sI) Skewness (SkI) Kurtosis (KG)
Very well sorted
Well sorted Moderately well sorted
Moderately sorted
Poorly sorted
Very poorly sorted
Extremely poorly sorted
< 0.35
0.35 – 0.50 0.50 – 0.70
0.70 – 1.00
1.00 – 2.00
2.00 – 4.00
> 4.00
Very fine skewed
Fine skewed Symmetrical
Coarse skewed
Very coarse skewed
+0.3 to +1.0 +0.1 to +0.3 +0.1 to 0.1 0.1 to 0.3 0.3 to 1.0
Very platykurtic
Platykurtic Mesokurtic
Leptokurtic
Very leptokurtic
Extremely
leptokurtic
< 0.67
0.67 – 0.90 0.90 – 1.11
1.11 – 1.50
1.50 – 3.00
> 3.00
(e) Geometric Folk and Ward (1957) Graphical Measures
Mean Standard Deviation
3
lnlnlnexp 845016 PPP
M G
++=
÷ø
öçè
æ +
=
6.6
lnln
4
lnlnexp 9558416 PPPP
Gs
Skewness Kurtosis
( )( )
( )( )525
50955
1684
508416
lnln2
ln2lnln
lnln2
ln2lnln
PP
PPP
PP
PPPSkG

++

+=
( )7525
955
lnln44.2
lnln
PP
PPKG

=
Sorting (sG) Skewness (SkG) Kurtosis (KG)
Very well sorted
Well sorted
Moderately well sorted
Moderately sorted
Poorly sorted
Very poorly sorted Extremely poorly sorted
< 1.27
1.27 – 1.41
1.41 – 1.62
1.62 – 2.00
2.00 – 4.00
4.00 – 16.00 > 16.00
Very fine skewed
Fine skewed
Symmetrical
Coarse skewed
Very coarse skewed
0.3 to 1.0 0.1 to 0.3 0.1 to +0.1 +0.1 to +0.3 +0.3 to +1.0
Very platykurtic
Platykurtic
Mesokurtic
Leptokurtic
Very leptokurtic
Extremely leptokurtic
< 0.67
0.67 – 0.90
0.90 – 1.11
1.11 – 1.50
1.50 – 3.00
> 3.00
Table 2. Size scale adopted in the GRADISTAT program, modified from Udden
(1914) and Wentworth (1922).
Grain Size
phi mm
Descriptive term
Very Large
10 1024
Large
9 512
Medium
8 256
Small
7 128
Very small
Boulder
6 64 Very coarse
5 32
Coarse
4 16
Medium
3 8
Fine
2 4
Very fine
Gravel
1 2
Very coarse 0 1
microns Coarse
1 500
Medium
2 250
Fine
3 125
Very fine
Sand
4 63
Very coarse
5 31
Coarse 6 16
Medium
7 8
Fine
8 4
Very fine
Silt
9 2
Clay
Jack at the and the
Microsoft Excel analyse data
mass or sediment
calculated using mode(s), sorting
Grain size (using the phi
statistical (such as
description of the coarse sand”) size fraction,
output, the data in both
Samples may be
author at distribution
Sedimentary
Journal of
655744.
aperture sizes of Sizes may be
on one of classes for
calculated if contains
class larger the data of Laser
you have error. The
the "Single
running.
distribution page. The
Clay" sheets.
or Laser the same
order. For intervals and
although intervals.
in the pan should also be
data further 230.
cells above
take several greater than
sheet. The the "Gravel
results for the single sample
material analysed, and this
quantity of statistics
parameters contains
class size
f (1 mm).
considers to be sediment
remaining in the
statistics ignoring where there is
different taken when
the sample size class the grain
be deleted the sample
present in those
Table 1. Statistical formulae used in the calculation of grain size parameters.
f is the frequency in percent; m is the midpoint of each class interval in metric (mm) or
phi (mf) units; Px and fx are grain diameters, in metric or phi units respectively, at the
cumulative percentile value of x.
(a) Arithmetic Method of Moments
Mean Standard Deviation Skewness Kurtosis
100 = m
a
fmx
S
100
)( =
2
ama
xmf Ss 3
3
100
)( =
a
ama
xmfSk
s
S 4
4
100
)( =
a
ama
xmfK
s
S
(b) Geometric Method of Moments
Mean Standard Deviation Skewness Kurtosis
100
lnexp = m
g
mfx
S
100
)ln(lnexp =
2
gm
g
xmf Ss 3
3
ln100
)ln(ln =
g
gm
g
xmfSk
s
S
4
4
ln100
)ln(ln =
g
gm
g
xmfK
s
S
Sorting (sg) Skewness (Skg) Kurtosis (Kg)
Very well sorted
Well sorted
Moderately well sorted
Moderately sorted
Poorly sorted
Very poorly sorted
Extremely poorly sorted
< 1.27
1.27 – 1.41
1.41 – 1.62
1.62 – 2.00
2.00 – 4.00
4.00 – 16.00
> 16.00
Very fine skewed
Fine skewed
Symmetrical
Coarse skewed
Very coarse skewed
< 1.30 1.30 – 0.43 0.43 – +0.43 +0.43 – +1.30
> +1.30
Very platykurtic
Platykurtic
Mesokurtic
Leptokurtic
Very leptokurtic
< 1.70
1.70 – 2.55
2.55 – 3.70
3.70 – 7.40
> 7.40
(c) Logarithmic Method of Moments
Mean Standard Deviation Skewness Kurtosis
100 =
f
f
fmx
S
100
)( =
2
ff
fsxmf S
3
3
100
)( =
f
ff
fs
xmfSk
S
4
4
100
)( =
f
ff
fs
xmfK
S
Sorting (sf) Skewness (Skf) Kurtosis (Kf)
Very well sorted
Well sorted
Moderately well sorted
Moderately sorted
Poorly sorted Very poorly sorted
Extremely poorly sorted
< 0.35
0.35 – 0.50
0.50 – 0.70
0.70 – 1.00
1.00 – 2.00 2.00 – 4.00
> 4.00
Very fine skewed
Fine skewed
Symmetrical
Coarse skewed
Very coarse skewed
> +1.30 +0.43 – +1.30 0.43 – +0.43 0.43 – 1.30
< 1.30
Very platykurtic
Platykurtic
Mesokurtic
Leptokurtic
Very leptokurtic
< 1.70
1.70 – 2.55
2.55 – 3.70
3.70 – 7.40
> 7.40
Table 1. Statistical formulae used in the calculation of grain size parameters.
f is the frequency in percent; m is the midpoint of each class interval in metric (mm) or
phi (mf) units; Px and fx are grain diameters, in metric or phi units respectively, at the
cumulative percentile value of x.
(a) Arithmetic Method of Moments
Mean Standard Deviation Skewness Kurtosis
100 = m
a
fmx
S
100
)( =
2
ama
xmf Ss 3
3
100
)( =
a
ama
xmfSk
s
S 4
4
100
)( =
a
ama
xmfK
s
S
(b) Geometric Method of Moments
Mean Standard Deviation Skewness Kurtosis
100
lnexp = m
g
mfx
S
100
)ln(lnexp =
2
gm
g
xmf Ss 3
3
ln100
)ln(ln =
g
gm
g
xmfSk
s
S
4
4
ln100
)ln(ln =
g
gm
g
xmfK
s
S
Sorting (sg) Skewness (Skg) Kurtosis (Kg)
Very well sorted
Well sorted
Moderately well sorted
Moderately sorted
Poorly sorted
Very poorly sorted
Extremely poorly sorted
< 1.27
1.27 – 1.41
1.41 – 1.62
1.62 – 2.00
2.00 – 4.00
4.00 – 16.00
> 16.00
Very fine skewed
Fine skewed
Symmetrical
Coarse skewed
Very coarse skewed
< 1.30 1.30 – 0.43 0.43 – +0.43 +0.43 – +1.30
> +1.30
Very platykurtic
Platykurtic
Mesokurtic
Leptokurtic
Very leptokurtic
< 1.70
1.70 – 2.55
2.55 – 3.70
3.70 – 7.40
> 7.40
(c) Logarithmic Method of Moments
Mean Standard Deviation Skewness Kurtosis
100 =
f
f
fmx
S
100
)( =
2
ff
fsxmf S
3
3
100
)( =
f
ff
fs
xmfSk
S
4
4
100
)( =
f
ff
fs
xmfK
S
Sorting (sf) Skewness (Skf) Kurtosis (Kf)
Very well sorted
Well sorted
Moderately well sorted
Moderately sorted
Poorly sorted Very poorly sorted
Extremely poorly sorted
< 0.35
0.35 – 0.50
0.50 – 0.70
0.70 – 1.00
1.00 – 2.00 2.00 – 4.00
> 4.00
Very fine skewed
Fine skewed
Symmetrical
Coarse skewed
Very coarse skewed
> +1.30 +0.43 – +1.30 0.43 – +0.43 0.43 – 1.30
< 1.30
Very platykurtic
Platykurtic
Mesokurtic
Leptokurtic
Very leptokurtic
< 1.70
1.70 – 2.55
2.55 – 3.70
3.70 – 7.40
> 7.40
(d) Logarithmic (Original) Folk and Ward (1957) Graphical Measures
Mean Standard Deviation Skewness Kurtosis
3
845016 fff ++=ZM
6.64
5951684 ffffs
+
=I
( )1684
508416
2
2
ff
fff

+=ISk
( )595
50955
2
2
ff
fff

++
( )2575
595
44.2 ff
ff

=GK
Sorting (sI) Skewness (SkI) Kurtosis (KG)
Very well sorted
Well sorted Moderately well sorted
Moderately sorted
Poorly sorted
Very poorly sorted
Extremely poorly sorted
< 0.35
0.35 – 0.50 0.50 – 0.70
0.70 – 1.00
1.00 – 2.00
2.00 – 4.00
> 4.00
Very fine skewed
Fine skewed Symmetrical
Coarse skewed
Very coarse skewed
+0.3 to +1.0 +0.1 to +0.3 +0.1 to 0.1 0.1 to 0.3 0.3 to 1.0
Very platykurtic
Platykurtic Mesokurtic
Leptokurtic
Very leptokurtic
Extremely
leptokurtic
< 0.67
0.67 – 0.90 0.90 – 1.11
1.11 – 1.50
1.50 – 3.00
> 3.00
(e) Geometric Folk and Ward (1957) Graphical Measures
Mean Standard Deviation
3
lnlnlnexp 845016 PPP
M G
++=
÷ø
öçè
æ +
=
6.6
lnln
4
lnlnexp 9558416 PPPP
Gs
Skewness Kurtosis
( )( )
( )( )525
50955
1684
508416
lnln2
ln2lnln
lnln2
ln2lnln
PP
PPP
PP
PPPSkG

++

+=
( )7525
955
lnln44.2
lnln
PP
PPKG

=
Sorting (sG) Skewness (SkG) Kurtosis (KG)
Very well sorted
Well sorted
Moderately well sorted
Moderately sorted
Poorly sorted
Very poorly sorted Extremely poorly sorted
< 1.27
1.27 – 1.41
1.41 – 1.62
1.62 – 2.00
2.00 – 4.00
4.00 – 16.00 > 16.00
Very fine skewed
Fine skewed
Symmetrical
Coarse skewed
Very coarse skewed
0.3 to 1.0 0.1 to 0.3 0.1 to +0.1 +0.1 to +0.3 +0.3 to +1.0
Very platykurtic
Platykurtic
Mesokurtic
Leptokurtic
Very leptokurtic
Extremely leptokurtic
< 0.67
0.67 – 0.90
0.90 – 1.11
1.11 – 1.50
1.50 – 3.00
> 3.00
Table 2. Size scale adopted in the GRADISTAT program, modified from Udden
(1914) and Wentworth (1922).
Grain Size
phi mm
Descriptive term
Very Large
10 1024
Large
9 512
Medium
8 256
Small
7 128
Very small
Boulder
6 64 Very coarse
5 32
Coarse
4 16
Medium
3 8
Fine
2 4
Very fine
Gravel
1 2
Very coarse 0 1
microns Coarse
1 500
Medium
2 250
Fine
3 125
Very fine
Sand
4 63
Very coarse
5 31
Coarse 6 16
Medium
7 8
Fine
8 4
Very fine
Silt
9 2
Clay
(d) Logarithmic (Original) Folk and Ward (1957) Graphical Measures
Mean Standard Deviation Skewness Kurtosis
3
845016 fff ++=ZM
6.64
5951684 ffffs
+
=I
( )1684
508416
2
2
ff
fff

+=ISk
( )595
50955
2
2
ff
fff

++
( )2575
595
44.2 ff
ff

=GK
Sorting (sI) Skewness (SkI) Kurtosis (KG)
Very well sorted
Well sorted Moderately well sorted
Moderately sorted
Poorly sorted
Very poorly sorted
Extremely poorly sorted
< 0.35
0.35 – 0.50 0.50 – 0.70
0.70 – 1.00
1.00 – 2.00
2.00 – 4.00
> 4.00
Very fine skewed
Fine skewed Symmetrical
Coarse skewed
Very coarse skewed
+0.3 to +1.0 +0.1 to +0.3 +0.1 to 0.1 0.1 to 0.3 0.3 to 1.0
Very platykurtic
Platykurtic Mesokurtic
Leptokurtic
Very leptokurtic
Extremely
leptokurtic
< 0.67
0.67 – 0.90 0.90 – 1.11
1.11 – 1.50
1.50 – 3.00
> 3.00
(e) Geometric Folk and Ward (1957) Graphical Measures
Mean Standard Deviation
3
lnlnlnexp 845016 PPP
M G
++=
÷ø
öçè
æ +
=
6.6
lnln
4
lnlnexp 9558416 PPPP
Gs
Skewness Kurtosis
( )( )
( )( )525
50955
1684
508416
lnln2
ln2lnln
lnln2
ln2lnln
PP
PPP
PP
PPPSkG

++

+=
( )7525
955
lnln44.2
lnln
PP
PPKG

=
Sorting (sG) Skewness (SkG) Kurtosis (KG)
Very well sorted
Well sorted
Moderately well sorted
Moderately sorted
Poorly sorted
Very poorly sorted Extremely poorly sorted
< 1.27
1.27 – 1.41
1.41 – 1.62
1.62 – 2.00
2.00 – 4.00
4.00 – 16.00 > 16.00
Very fine skewed
Fine skewed
Symmetrical
Coarse skewed
Very coarse skewed
0.3 to 1.0 0.1 to 0.3 0.1 to +0.1 +0.1 to +0.3 +0.3 to +1.0
Very platykurtic
Platykurtic
Mesokurtic
Leptokurtic
Very leptokurtic
Extremely leptokurtic
< 0.67
0.67 – 0.90
0.90 – 1.11
1.11 – 1.50
1.50 – 3.00
> 3.00
Table 2. Size scale adopted in the GRADISTAT program, modified from Udden
(1914) and Wentworth (1922).
Grain Size
phi mm
Descriptive term
Very Large
10 1024
Large
9 512
Medium
8 256
Small
7 128
Very small
Boulder
6 64 Very coarse
5 32
Coarse
4 16
Medium
3 8
Fine
2 4
Very fine
Gravel
1 2
Very coarse 0 1
microns Coarse
1 500
Medium
2 250
Fine
3 125
Very fine
Sand
4 63
Very coarse
5 31
Coarse 6 16
Medium
7 8
Fine
8 4
Very fine
Silt
9 2
Clay
Single Sample Data Input Screen Enter your data in the columns below, and then click the "Calculate
Statistics" button. See the "Information" sheet for more information.
Sample Identity: VF74103
Analyst:
Date: Auto. add
Initial Sample Weight: (optional) aperturesat:
Aperture Class Weight
(microns) Retained (g or %)
2000 6.1970
1000 2.6600
500 6.8418
250 1.3150
100 5.0753
50 0.1088
20 0.12123
5 0.07942
2 0.02336
0.5 0.10104
Enter your data in the columns below, and then click the "Calculate
Statistics" button. See the "Information" sheet for more information.
SAMPLE STATISTICS
SAMPLE IDENTITY: VF74103 ANALYST & DATE: ,
SAMPLE TYPE: Bimodal, Poorly Sorted TEXTURAL GROUP: Sand
SEDIMENT NAME: Poorly Sorted Very Coarse Sand
GRAIN SIZE DISTRIBUTION
MODE 1: GRAVEL: COARSE SAND: 30.4%
MODE 2: SAND: MEDIUM SAND: 5.8%
MODE 3: MUD: FINE SAND: 17.0%
D10: V FINE SAND: 5.8%
MEDIAN or D50: V COARSE GRAVEL: V COARSE SILT: 0.4%
D90: COARSE GRAVEL: COARSE SILT: 0.3%
(D90 / D10): MEDIUM GRAVEL: MEDIUM SILT: 0.2%
(D90  D10): FINE GRAVEL: FINE SILT: 0.1%
(D75 / D25): V FINE GRAVEL: V FINE SILT: 0.1%
(D75  D25): V COARSE SAND: CLAY: 0.4%
Logarithmic
f
MEAN : 0.902
SORTING (s): 1.377
SKEWNESS (Sk ): 2.148
KURTOSIS (K ): 11.65
483.5
4130.6
METHOD OF MOMENTS
f
0.500
2.661
30.75
2.094
0.351
0.901
2.780
mm
750.0
175.0
138.9
783.8
4269.4
2.816
1.360
4.942
Geometric
mm
79.99
Arithmetic
mm
466.9
7.043
0.484
17.07
0.761
1.828
2.417
0.536
0.484 Very Platykurtic
Description
Coarse Sand
Poorly Sorted
39.3%
Geometric Logarithmic
Very Fine Skewed
f
0.536
FOLK & WARD METHOD
0.0%
98.4%
1.6%
0.0%
0.0%
1610.7
2.099
2.848
0.0%
0.0%
0.0%
592.4 0.755
1.273
mm
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
2.00.02.04.06.08.010.012.0
Cla
ss
We
igh
t (%
)
Particle Diameter (f)
1 10 100 1000
Particle Diameter (mm)
)(x
Multiple Sample Data Input Screen Enter your data in the columns below, and then click the
"Calculate Statistics" button. Enter Sample Info in the green cells.
Aperture Class Weight Retained (g or %) in Different Samples
(microns)
Sample Identity: GU/SCOI 12/1/96  AverageGU/S AF 13/11/03  AverageGU/S AF 17/12/03  AverageGU/S COI 25/11/94  AverageGU/S COI 150068  Average
Analyst:
Date:
Initial Sample Weight:
2000
1400
1000 0 0 0 0 0
710 0 0 0 0 0
500 0 0 0 0 0
355 0.004014 4.675681 0 0.166187 0
250 0.098238 12.99385 0 2.363564 0
180 0.076329 17.273932 1.20501 5.030106 0
125 0.430358 15.738308 4.639825 7.028166 3.987615
90 3.035325 11.668246 8.123842 7.742225 11.953984
63 6.565712 8.669724 11.566525 7.740544 16.974026
44 10.052864 6.974656 14.529959 7.761027 17.514639
31 12.489373 5.337089 15.974208 7.953405 14.464243
22 13.148105 3.518258 14.819778 8.11849 10.116833
15.6 12.150551 2.175727 11.21269 8.095567 6.474093
11 10.123945 1.638512 6.764591 7.763282 4.220675
7.8 7.809071 1.602272 3.311222 7.045425 3.069594
5.5 5.718063 1.604948 1.53618 5.917719 2.45906
3.9 4.191694 1.466198 1.004309 4.608086 2.035881
2.76 3.313934 1.25158 0.977263 3.45722 1.691093
1.95 2.848277 1.035399 0.993582 2.61212 1.393471
1.38 2.515149 0.845574 0.940187 2.05931 1.147202
0.98 2.06598 0.64693 0.818224 1.618779 0.911418
0.69 1.569905 0.461032 0.685058 1.261867 0.711995
0.49 1.153072 0.313739 0.561466 0.993002 0.557877
0.35 0.612441 0.108344 0.330773 0.577167 0.31154
0.24 0.0276 0 0.005306 0.086743 0.004761
0.17
Print summary sheets for each sample?
Auto. add apertures at:
Enter your data in the columns below, and then click the
"Calculate Statistics" button. Enter Sample Info in the green cells.
GU/S COI 150068 b  AverageGU/S 1116  AverageGU/S AF2 12/1/75 b  AverageGU/S AF1 12/1/75  AverageGU/S 150168  AverageGU/S 150168 b  Average
0 0 0 0 0 0.159655
0 0 0 0 0.02729 0.911598
0 0 0 0.124762 2.092459 3.649185
0 0 0 3.062886 7.077386 7.105325
0 0 0.065557 6.489483 9.012115 8.595659
0 0 1.767711 8.054194 7.541572 7.411983
3.604557 3.160243 4.100812 7.931425 5.285283 5.330171
11.495766 13.149202 6.172086 6.775624 4.468872 4.419444
16.642773 24.071202 7.420751 5.610307 5.21201 5.014277
17.477981 26.930851 7.861467 5.060921 6.274257 6.003723
14.714564 18.736395 7.967071 5.094733 6.777713 6.499957
10.473305 7.467365 8.131159 5.423187 6.690072 6.437459
6.748492 1.27392 8.417578 5.839905 6.346932 6.128438
4.344437 0.043211 8.565385 6.167096 5.933774 5.742582
3.083241 0.602259 8.259365 6.232338 5.433718 5.263824
2.438432 0.921616 7.325703 5.886676 4.762462 4.61913
2.033051 0.743472 6.012912 5.231523 4.019686 3.90446
1.717682 0.534033 4.765061 4.503152 3.382727 3.288541
1.435813 0.506627 3.774262 3.77232 2.856974 2.781564
1.18958 0.55053 3.041448 3.059401 2.377375 2.326399
0.946728 0.511933 2.368833 2.284067 1.817072 1.795226
0.740848 0.400658 1.785294 1.603087 1.282018 1.279635
0.581399 0.289489 1.344274 1.128058 0.882235 0.884398
0.326333 0.106993 0.749643 0.595343 0.439634 0.440971
0.005017 0 0.103629 0.069511 0.006364 0.006397
GU/SCOI 30/11/98  Average
0
0
0
0.529458
0.854595
0.455526
0.747293
2.632942
5.928417
9.435427
11.869631
12.536753
11.572834
9.647779
7.543366
5.736241
4.467094
3.7471
3.327422
2.95619
2.398056
1.764383
1.23028
0.610376
0.008838
SAMPLE STATISTICS
ANALYST AND DATE:
SIEVING ERROR:
SAMPLE TYPE:
TEXTURAL GROUP:
SEDIMENT NAME:
METHOD OF MEAN
MOMENTS SORTING
Arithmetic (mm) SKEWNESS
KURTOSIS
METHOD OF MEAN
MOMENTS SORTING
Geometric (mm) SKEWNESS
KURTOSIS
METHOD OF MEAN
MOMENTS SORTING
Logarithmic (f) SKEWNESS
KURTOSIS
FOLK AND MEAN
WARD METHOD SORTING
(mm) SKEWNESS
KURTOSIS
FOLK AND MEAN
WARD METHOD SORTING
(f) SKEWNESS
KURTOSIS
FOLK AND MEAN:
WARD METHOD SORTING:
(Description) SKEWNESS:
KURTOSIS:
MODE 1 (mm):
MODE 2 (mm):
MODE 3 (mm):
MODE 1 (f):
MODE 2 (f):
MODE 3 (f):
D10 (mm):
D50 (mm):
D90 (mm):
(D90 / D10) (mm):
(D90  D10) (mm):
(D75 / D25) (mm):
(D75  D25) (mm):
D10 (f):
D50 (f):
D90 (f):
(D90 / D10) (f):
(D90  D10) (f):
(D75 / D25) (f):
(D75  D25) (f):
:)( as
:)( ax
:)( aSk
:)( aK
:)( gx
:)( gs
:)( gSk
:)( gK
:)( fx
:)( fs
:)fSk(
:)( fK
:)( ZM
:)( Is
:)( ISk
:)( GK
:)( GK
:)( GM
:)( Gs
:)( GSk
% GRAVEL:
% SAND:
% MUD:
% V COARSE GRAVEL:
% COARSE GRAVEL:
% MEDIUM GRAVEL:
% FINE GRAVEL:
% V FINE GRAVEL:
% V COARSE SAND:
% COARSE SAND:
% MEDIUM SAND:
% FINE SAND:
% V FINE SAND:
% V COARSE SILT:
% COARSE SILT:
% MEDIUM SILT:
% FINE SILT:
% V FINE SILT:
% CLAY:
Triangular Diagram
Sand Mud
Gravel
80%
30%
5%
Trace
1:1 1:9 9:1 Sand:Mud Ratio
Gravel %
Gravel
Muddy Gravel Muddy Sandy Gravel
Gravelly Mud Gravelly Muddy Sand
Slightly Gravelly
Mud
Slightly Gravelly Sandy Mud
Slightly Gravelly Muddy Sand
Mud Sandy Mud Muddy Sand Sand
Slightly Gravelly
Sand
Gravelly Sand
Sandy Gravel
Gravel:
Sand:
Mud:
0.0%
98.4%
1.6%
Coarse Gravel:
Medium Gravel:
Fine Gravel:
Coarse Sand:
Medium Sand:
Fine Sand:
Very Fine Sand:
Very Coarse Silt:
0.0%
0.0%
0.0%
30.4%
17.0%
5.8%
0.4%
5.8%
Very Coarse Gravel: 0.0%
Very Coarse Sand:
Coarse Silt:
Clay:
Fine Silt:
Very Fine Gravel:
39.3%
0.0%
Medium Silt:
Very Fine Silt:
0.4%
0.1%
0.1%
0.2%
0.3%
VF74103
TEXTURAL GROUP:
SEDIMENT NAME:
Sand
Poorly Sorted Very Coarse Sand
SAMPLE IDENTITY:
Triangular Diagram
Silt Clay
Sand
90%
50%
10%
1:2 2:1 Silt:Clay Ratio
Sand %
Sand
Clayey Sand Muddy Sand
Sandy Clay Sandy Silt Sandy Mud
Clay Mud Silt
Silty Sand
NOTE Gravel is also present in this sample
VF74103
TEXTURAL GROUP: IGNORING GRAVEL
FRACTION
SAMPLE IDENTITY: Gravel:
Sand:
Mud:
0.0%
98.4%
1.6%
Coarse Gravel:
Medium Gravel:
Fine Gravel:
Coarse Sand:
Medium Sand:
Fine Sand:
Very Fine Sand:
Very Coarse Silt:
Very Coarse Gravel:
Very Coarse Sand:
Coarse Silt:
Clay:
Fine Silt:
Very Fine Gravel:
Medium Silt:
Very Fine Silt:
0.0%
0.0%
0.0%
30.4%
17.0%
5.8%
0.4%
5.8%
0.0%
39.3%
0.0%
0.4%
0.1%
0.1%
0.2%
0.3%
Frequency Distribution Histogram
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
2.0 0.0 2.0 4.0 6.0 8.0 10.0
Cla
ss w
eig
ht
(%)
Particle diameter (f)
Cumulative Frequency Curve
0
10
20
30
40
50
60
70
80
90
100
1.0 1.0 3.0 5.0 7.0 9.0
Cu
mu
lati
ve m
ass r
eta
ined
(%
)
Particle diameter (f)
Frequency Distribution Curve
0
5
10
15
20
25
30
35
40
45
50
1.0 10.0 100.0 1000.0
Cla
ss w
eig
ht
(%)
Particle diameter (mm)
Cumulative Frequency Curve
0
10
20
30
40
50
60
70
80
90
100
1.0 10.0 100.0 1000.0
Cu
mu
lati
ve m
ass r
eta
ined
(%
)
Particle diameter (mm)