I. Grain Size Analyses
Since particle diameters typically span many orders of magnitude for natural
sediments, we must find a way to conveniently describe wide ranging data sets.
The base two logarithmic f (phi) scale is one useful
and commonly used way to represent grain size information for a sediment
distribution. A tabular classification of grain sizes in terms of f units, millimeters, and other commonly used measurement
scales is included for purposes of comparison (see grain size description table
appended at the end).
Logarithmic phi values (in base two) are calculated from particle diameter
size measures in millimeters as follows:
where:
f = particle size in f units
d = diameter of particle in mm
A grain size separation analysis can be a tedious and time consumming task.
The results of grain size distribution analyses on two samples, A and B, taken
from standard sieve tests, are given below. On the following pages you are asked
to prepare histograms depicting percent frequency of particle size occurance,
plots of grain size distribution called cumulative weight percent curves, and
other statistical and hydraulic property measures for samples A and B (see
requirements for Section I below).
To gain an understanding of how to proceed, look at the results of an example
sieve size analysis performed on the MN 104 sample (see Figure 1). Relate those
results to the histogram, and the cumulative distribution curves created from
the analysis data (Figures 2, and 3) as an example of output to produce. Read
Fetter, Sec. 4.2.2, pg. 82, for a discussion of sediment analysis by sieve
sifting into particle size fractions. In addition, an in depth description of
how grain size separations are performed is given toward the end of this
page(see Sec. III, Grain Size Analyses of Sediments).
Study the grain size distribution curves carefully. The curves are cumulative percent frequency distribution curves, that represent the cumulative weight percent by particle size of the sample. In one of the curves (cumulative weight percent passing), the fraction that is finer than each subsequent grain size is shown. In the other curve (cumulative weight percent retained) the fraction that is coarser than each subsequent grain size is shown. Essentially, for each grain size, the curve will tell you how much of the sample was finer or coarser.














































































Figure 1
Requirements for Section I:
(As always, please include
one representative sample calculation for each procedure).
b. Median (graphic) = f_{50} i.e., the
phi size corresponding to the 50% mark on the cumulative frequency
distribution curve.
c. Inclusive (graphic) standard deviation:
d. Coefficient of uniformity:
Note: d_{60} and d_{10} in the formula above represent the grain diameter in mm, for which, 60% and 10% of the sample respectively, are finer than. It will be most convenient to use the cumulative weight percent passing curve, and remember that you need to do the conversion from f units to millimeters. Be sure to show your work graphically on the cumulative curve, as well as your calculation converting f units to millimeters.
where:
d_{10} = Hazen's effective grain size in mm, relative to which
10% of the sample is finer
C = a coefficient that factors in the sorting characteristics of the sediment. In this case, use C = 40. For this particular form of the equation, C also embodies a dimensional conversion factor to obtain K in units of L/T (cm/sec) when the only explicit unit on the right hand side of the equation is L^{2} (mm^{2}). See Fetter, page 99, for a table relating C value ranges for various sediment types.
The Krumbein and Monk equation is:
where:
Gm_{e} = geometric mean grain diameter (in mm) (convert
from Part 4a above)
s_{f} = standard deviation (phi scale) (which was calculated in Part 4c above)
where:
r = density of water = 0.9982 g/cm^{3}
at 20^{o}C
g = acceleration of gravity = 980 cm/sec^{2}
m = dynamic viscosity of water = 0.01 g/(cm sec)
at 20^{o}C
k = permeability (in units of cm^{2}) (conversion factor: 9.87x109 cm2/darcy)
Present all your results above in the form of a single table. Remember to please include one representative sample calculation for each procedure.
Discussion Questions for Section I:
SAMPLE A  
Grain Size (mm) 
Percent of sample retained (by weight) 
Cumulative % finer 
Cumulative % coarser 
Grain Size (f) 
10  0  
9  2  
8  2  
7  6  
5  5  
1  15  
0.75  10  
0.5  10  
0.3  15  
0.09  25  
0.05  5  
0.01  3  
0.009  2 
SAMPLE B  
Grain Size (mm) 
Percent of sample retained (by weight) 
Cumulative % finer 
Cumulative % coarser 
Grain Size (f) 
15  0  
10  2  
8  1.5  
6  1.5  
3  7  
1  10  
0.8  3  
0.5  10  
0.2  10  
0.1  20  
0.06  10  
0.03  15  
0.01  10 
II. More Grain Size Analyses
The purpose of this next portion of the exercise is to aquaint you with the
variations in grain size distributions for different sedimentary deposits. You
are given the data obtained by grain size analysis of three different sediment
samples: a very well sorted friable sandstone, a well sorted sand from a flowing
spring, and a poorly sorted glacial till.
The St. Peter Sandstone has undergone an extensive multicyclic depositional
history. It's last depositional episode was as a beach sand along a
transgressing sea. During at least one of its previous depositional episodes the
sand grains were eolian (wind transported) deposits. Consequently, the range of
particle sizes is somewhat restricted owing to the narrow range of particle
sizes that can be transported by wind. Due to its extensive depositional history
the St. Peter Sandstone is texturally, and mineralogically very mature.
The Boiling Springs sample comes from a fluvial environment of deposition. As
such, the sediment tends to be fairly well sorted. The energy of deposition in a
fluvial environment can fluctuate widely. Consequently, the range of particle
sizes can also be somewhat wide spread. In this particular case, the energy of
deposition was fairly low as evidenced by the fairly fine size of the particles
in the sample.
The Grantsburg Sublobe Till is a glacially deposited sediment. The till was
laid down by the Grantsburg Sublobe of the Des Moines Lobe during the Late
Wisconsinin glaciation approximately 14,000 years ago. As is typically the case
with ice transported sediments, the till is poorly sorted with a concurrent wide
range of particle sizes.
 






































































 




























































 

by Weight 
% Coarser 

































































































Requirements for Section II:
Present your results in the form of a single table.
Discussion Questions for Section II:
III. Grain Size Analysis Of Sediments
The objective of this section is to give you a sense of the physical
procedures and statistical parameters which are involved in performing a
sediment analysis. This section may come in handy if you ever have to do one of
these procedures.
The purpose of this procedure is to determine the distribution of grain sizes
in an unconsolidated sediment sample. This analysis is broken down into several
steps dealing first with the coarse fraction (sand and gravel) and then with the
fine fraction (silt and clay).
Procedure:
A. Removal of organic material
The purpose of removing organic carbon
particles is that they do not represent clastic grains and are therefore not to
be considered in a grain size analysis. Depending on the percentage of organics
in the sediment this step may be quite lengthy. In brief, the procedure involves
adding water and hydrogen peroxide to help remove the organics and disaggregate
the sample.
B. Shaking and Centrifuging
The purpose of this step is to wash the sample
with distilled water to remove salts and help break down agglomeration in the
mud.
C. Dispersion
The purpose of this step is to disperse the aggregates of
clay size particles so that they will be sized as individuals, not as
aggregates. This procedure consists of mixing the sediment with a peptizer
solution, or dispersing agent.
D. Wet Sieving
The purpose of this step is to separate the sediment sample
into coarse and fine fractions. To do this, select a 4 phi size sieve and place
the sediment sample in it. Under the sieve place a tightly fitting funnel with a
1000 ml beaker attached to it. Wash the sample until the stream leaving the
funnel contains no fines and is clear. The material passing into the beaker is
the fine fraction which should be saved for pipette analysis later. The material
on the sieve is the coarse fraction which will be sieved.
E. Sieving the coarse fraction
Select the screens to be used. For accurate
work use the 1/4 phi set. Nest the sieves in order, the coarsest on the top, the
finest on the bottom. Pour the weighed dry sample into the top sieve, cover, and
set the timer for ten minutes. Upon completion of the sieving, the contents of
each sieve are weighed. Be sure to tap the screens firmly on a sheet of paper to
remove lodged grains from the screen and add them to the appropriate sample. Be
sure to strike the table evenly with the rim of the screen. Make sure that all
loose grains get accounted for by repeating this procedure. Weigh to the 0.0001
gram. Each phi size is weighed in this manner and the weights are recorded on a
data sheet.
F. Pipetting the fine fraction
The pipetting technique of size analysis is
based on the differential settling velocities of the particles. Stoke's Law of
Settling Velocities is the basis for this method. Calculations have been made as
to the time a certain grain size will be at a certain depth. After the initial
shaking to homogenize the sediment, aliquots are drawn from a depth and at a
time so that the last particles of a given size are just settling past the
sampling depth. The resulting aliquot gives a weight of the material finer than
the given size. Successive aliquots give the weights in each phi size.
STATISTICAL PARAMETERS
Mode: Mode is the most frequentlyoccurring particle diameter. It is
the diameter corresponding to the steepest point (point of inflection) on the
cumulative curve (only if the curve has an arithmetic frequency scale). It also
corresponds to the highest point on the distribution curve. Advantages: the mode
is quite valuable in sediment genesis transport studies, especially when two or
more sources are contributing. The mode diameter often stays fairly constant in
an area while the other, more "synthetic" measures tend to vary more
erratically. It deserves more common use. The disadvantages are its lack of
common usage, and in fact that it is difficult to determine. Also it is
independent of the grain size of the rest of the sediment, therefore it is not a
good measure of overall average size.
Median: Half of the particles by weight are coarser than the median,
and half are finer. It is the diameter corresponding to the 50% mark on the
cumulative frequency curve and may be expressed either in phi or in mm. The
advantage is that it is by far the most commonly used measure and the easiest to
determine. The disadvantage is that it is not affected by the extremes of the
curve, therefore does not reflect the overall size of sediments (especially
skewed ones) well. For bimodal sediments it is almost worthless. Its use is not
recommended.
Geometric (Graphic) Mean: The best graphic measure for determining
overall size is the graphic mean. It corresponds very closely to the mean as
computed by the method of moments, yet is much easier to find. It is much
superior to the median because it is based on three points and gives a better
overall picture.
Inclusive Graphic Standard Deviation: This formula includes 90% of the distribution and is the best overall measure of sorting. Measurement of sorting values for a large number of sediments has suggested the following verbal classification for sorting for each value of inclusive graphic standard deviation:


under .35 phi  very well sorted 
0.35  0.50 phi  well sorted 
0.50  0.71 phi  moderately well sorted 
0.71  1.0 phi  moderately sorted 
1.0  2.0 phi  poorly sorted 
2.0  4.0 phi  very poorly sorted 
over 4.0 phi  extremely poorly sorted 
The best sorting attained by natural sediments is about .2025 phi, and Texas
dune and beach sands run about .25.35 phi. Texas river sediments so far
measured range between .402.5 phi, and pipetted flood plain or neritic silts
and clays average about 2.03.5 phi. The poorest sorted sediments, such as
glacial tills, mudflows, etc., have values in the neighborhood of 5 phi to 8 phi
or even 10 phi.
Kurtosis: In the normal probability curve, defined by the gaussian
formula; the phi diameter interval between the 5 phi and 95 phi points should be
exactly 2.44 times the phi diameter interval between the 25 phi and 75 phi
points. If the sample curve plots as a straight line on probability paper (i.e.,
if it follows the normal curve), this ratio will be obeyed and we say it has
normal kurtosis (1.00). Departure from a straight line will alter this ratio,
and kurtosis is the quantitative measure used to describe this departure from
normality. It measures the ratio between the sorting in the "tails" of the curve
and the sorting in the central portion. If the central portion is better sorted
than the tails, the curve is said to be excessively peaked or leptokurtic; if
the tails are better sorted than the central portion, the curve is deficiently
or flatpeaked and platykurtic. Strongly platykurtic curves are often bimodal
with subequal amounts of the two modes; these plot out as a twopeaked frequency
curve, with the sag in the middle of the two peaks accounting for its
platykurtic character. For normal curves, kurtosis equals 1.00. Leptokurtic
curves have a kurtosis over 1.00 (for example a curve with kurtosis=2.00 has
exactly twice as large a spread in the tails as it should have, hence it is less
well sorted in the tails than in the central portion); and platykurtic have
kurtosis under 1.00. Kurtosis involves a ratio of spreads; hence it is a pure
number and should not be written with a phi attached. The following verbal
limits are suggested for values of kurtosis:


under 0.67  very platykurtic 
0.67  0.90  platykurtic 
0.90  1.11  mesokurtic 
1.11  1.50  leptokurtic 
1.50  3.00  very leptokurtic 
over 3.00  extremely leptokurtic 
The distribution of kurtosis values in natural sediments is itself strongly
skewed, since most sediments are around .85 to 1.4, yet some values as high as 3
or 4 are not uncommon.
Skewness: This formula simply averages the skewness obtained using the
16 phi and 84 phi points with the skewness obtained by using the 5 phi and 95
phi points, both determined by exactly the same principle. This is the best
skewness measure to use because it determines the skewness of the "tails" of the
curve, not just the central portion, and the "tails" are just where the most
critical differences between samples lie. Furthermore, it is geometrically
independent of the sorting of the sample.
Symmetrical curves have skewness=0.00; those with excess fine material (a
tail to the right) have positive skewness and those with excess coarse material
(a tail to the left) have negative skewness. The more the skewness value departs
from 0.00, the greater the degree of asymmetry. The following verbal limits on
skewness are suggested: for values of skewness:


from +1.00 to +0.30  strongly fine skewed 
from +0.30 to +0.10  fine skewed 
from +0.10 to 0.10  near symmetrical 
from 0.10 to 0.30  coarse skewed 
from 0.30 to 1.00  strongly coarse skewed 
The absolute mathematical limits of the measure are +1.00 to 1.00, and few
curves have skewness values beyond +0.80 to 0.80.
Coefficient of Uniformity: This is a nonstatistical measure of the
spread of the curve. It is similar to the standard deviation, but is used for
samples that don't follow a normal curve. This parameter is defined in different
ways by different people.
IV. Grain Size Scales and Naming Classifications For
Sediments
The objective of this section is to show you a few of the many grain size and
textural naming classification schemes in widespread use today.
UddenWentworth Classification
The grade scale that has traditionally been used for sediments is the
UddenWentworth (1922) size class scale (see classification table appended to
the end of this lab). This scale is a geometric series in which each grade limit
is twice as large as the next smaller grade limit. The scale starting at 1 mm
and changing by a fixed ratio of 2 was first introduced by J. A. Udden (1898),
who also named the sand grades we use today. However, Udden drew the gravel/sand
boundary at 1 mm and used different terms in the gravel and mud divisions. For
more detailed work, sieves were used at intervals of 2^{0.5} and
2^{0.25}.
The base two logarithmic f (phi) scale, devised by
Krumbein (1934) and based on the UddenWentworth geometric series scale, is a
much more convenient way of presenting data than if the values are expressed in
millimeters, and is used almost exclusively in recent work in sedimentology. By
transforming the millimeter scale into phi units, size class divisions of equal
width are created.
Unified Soil Classification System
A commonly used soil classification system found in engineering disciplines
is the Engineering Unified Soil Classification System or simply the Unified
System. This classification system is mainly intended for soil classification
for foundations and hydraulic structures. It is based on grain size and soil
saturation to liquid limit.

Group Symbol  
Coarse  Gravels  Clean Gravel  Gravel, well graded 

Grained  Gravel, poorly graded 
 
Soils  Gravel with Fines  Gravels, mixed, non plastic, fines 
 
Gravels, clayeyplastic, fines 
 
Sands  Clean Sands  Sands, well graded 
 
Sands, poorly graded 
 
Sand with Fines  Sands, mixedplastic, fines 
 
Sands, clayeyplastic, fines 
 
Fine  Silts  Liquid Limit < 50  Mineral silts, low plasticity 

Grained  and  Clays (mineral), low plasticity 
 
Soils  Clays  Organic silts, low plasticity 
 
Liquid Limit > 50  Mineral silts (high plasticity) 
 
Clays (mineral), low plasticity 
 
Organic clays, high plasticity 
 

Organic soils as Peat 

Soil Triangle Of Basic Soil Textural Classes
Another widely used classification system is the soil triangle of basic soil
textural classes. This naming system is commonly used by the U.S. Department of
Agriculture and the U.S. Soil Conservation Service. In this system the relative
percentages of three particle size catagories are considered. The three
catagories of particles are sand, silt, and clay. The triangular diagram is
subdivided into several soil textural classification types, with each soil type
comprising a range of percentages of the three particle types. The soil
classification type is determined by plotting the percentages of each of the
three soil particle classes found within the soil sample on the triangular
diagram. The point of intersection of each of these three particle class
percentages will fall within one of the soil classification types (see Soil
Classification Triangle).
As can be seen by inspection of the triangle, each of the three particle
types can vary from zero to 100% of the content of a sediment sample. For
example, a 100% clay textural composition would plot at the apex at the top of
the triangle. Lesser percentages of clay content would plot somewhere between
the top apex and the base of the triangle. The same technique holds true for
sand or silt content except that the 100% sand or silt content points are
located at the left and right bottom apexes of the triangle respectively. Lesser
contents of sand or silt would plot somewhere between the 100% apex and the side
of the triangle opposite that apex.
U. S. Standard Sieve Mesh 
Millimeters (fractional) 
Millimeters  Microns  Phi (f)  Wentworth Size Class 
(1 Kilometer)  20  
Use  4096  12  
1024  10  Boulder (8 to 12f)  
wire  256  8  Cobble (5 to 8f)  
64  6  
squares  16  4  Pebble (2 to 5f)  
5  4  2  
6  3.36  1.75  
7  2.83  1.5  Granule (1 to 2f)  
8  2.38  1.25  
10  2  1  
12  1.68  0.75  
14  1.41  0.5  Very coarse sand (0 to 1f)  
16  1.19  0.25  
18  1  0  
20  0.84  0.25  
25  0.71  0. 5  Coarse sand (1 to 0f)  
30  0.59  0.75  
35  1/2  0.5  500  1  
40  0.42  420  1.25  
45  0.35  350  1.5  Medium sand (2 to 1f)  
50  0.3  300  1.75  
60  1/4  0.25  250  2  
70  0.21  210  2.25  
80  0.177  177  2.5  Fine sand (3 to 2f)  
100  0.149  149  2.75  
120  1/8  0.125  125  3  
140  0.105  105  3.25  
170  0.088  88  3.5  Very fine sand (4 to 3f)  
200  0.074  74  3.75  
230  1/16  0.0625  62.5  4  
270  0.053  53  4.25  
325  0.044  44  4.5  Coarse silt (5 to 4f)  
Analyzed  0.037  37  4.75  
1/32  0.031  31  5  
by  1/64  0.0156  15.6  6  Medium silt (6 to 5f) 
1/128  0.0078  7.8  7  Fine silt (7 to 6f)  
Pipette  1/256  0.0039  3.9  8  Very fine silt (8 to 7f) 
0.002  2  9  
or  0.00098  0.98  10  Clay  
0.00049  0.49  11  (Some use 2m or 9f  
Hydrometer  0.00024  0.24  12  as the clay boundary)  
0.00012  0.12  13 