Source: GEOTECHNICAL ENGINEERING

7 Particle Size and Gradation

7.1 GRAIN SIZES AND ORDERS OF MAGNITUDE

7.1.1 Size Ranges or Grades

The individual particles that make up a soil vary in size by orders of magnitude.
For example, the size difference between a 0.002 mm clay particle and a 2 m
diameter boulder is 6 orders of magnitude, or about the same as between a
Volkswagen and the Moon. It therefore is convenient to define particle size grades
by defining discrete ranges in particle sizes that define clay, silt, sand, gravel,
cobbles, and boulders. Each size grade covers a range in particle sizes––that is, all
gravel particles obviously are not the same size. ‘‘Clay’’ thus defined relates to a
range in particle sizes without regard to their mineralogy. However, because of a
relationship between weatherability of different minerals and particle size, most
clay-size particles are composed of the special group of minerals designated as clay
minerals. A particular soil therefore will consist of varying percentages of clay,
silt, and sand sizes with occasional coarser material.

7.2 GRADATION CURVES

7.2.1 Logarithmic Grain-Size Scale

Because of the broad range in particle sizes that can make up a particular soil,
sizes are conveniently plotted on a logarithmic scale. The advantage becomes
apparent by comparing Fig. 7.1, where sizes are plotted on a linear scale, with
Fig. 7.2, where the size distribution for the same glacial till soil is plotted
logarithmically. Figure 7.2 also shows the huge variations in particle sizes between
some common soils deposited by wind, water, and ice.

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144 Geotechnical Engineering

Figure 7.1
Plotting
particle sizes to a
linear scale
emphasizes the
wrong end of the
size scale—the
gravel and not the
clay.

Figure 7.2
Semilogarithmic
graph of the same
particle size data
for the glacial till
soil and for
several other
soils.

7.2.2 Particle Size Accumulation Curves

The graphs in Figs. 7.1 and 7.2 show particle size data as ‘‘percent finer’’ than
each size on a dry-weight basis. This is a particle size accumulation curve.

Figure 7.3 shows the relationship between an accumulation curve and a bar graph
or histogram representation of the same data. The data are obtained by passing
soil through a succession of progressively finer sieves and weighing the amount
retained on each sieve. The bar heights in the upper graph show each of these
amounts. Mathematically the upper graph is the differential or slope of the lower
graph, which is the particle size distribution curve. Conversely, the lower graph
represents the integral of the upper graph.

The median or average grain size can be read directly from a particle size
accumulation curve, as shown by the arrows in Fig. 7.3. The median grain size is
defined on the basis that 50 percent of a soil by weight is finer, and 50 percent is
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Particle Size and Gradation 145

Figure 7.3
Relation between a
particle size
accumulation
curve showing a
median grain size
and a histogram
showing modal
sizes.

coarser. In Fig. 7.3 this percentage occurs at 0.021 mm, which is in the size
range for silt. The median grain size is designated by D50. Another reference size
that has been found to relate to the permeability or hydraulic conductivity of soils
is D10.

Example 7.1
What is D10 for the soil in Fig. 7.3?
Answer: Slightly smaller than 0.001 mm.

7.2.3 Modes
The highest bar on a histogram data plot indicates a dominant particle size, which
is designated the mode. Although a mode is not the same as a median size, in
Fig. 7.3 the two are close because of the symmetrical shape of the major portion
of the histogram. This symmetry reflects a statistical normal distribution, not of
particle sizes, but of logarithms of the particle sizes because particles settle
out of a suspension according to the square of their diameter instead of their
diameter.

In Fig. 7.3 another mode occurs in the clay size range smaller than 0.002 mm,
probably due in part to clay adhering to coarser grains when they settled out. Two
or more modes also can indicate soil mixtures, as when two strata are combined in
one sample or sand has infiltrated into interstices in a gravel deposit. B horizon
soils are bimodal because of infiltration by clay from the A horizon. Engineered
soils often are mixtures in order to improve their engineering properties.
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 Particle Size and Gradation

146 Geotechnical Engineering

While a histogram is instructive, an accumulation curve is easier to plot and is

almost universally used in engineering. Modes occur on an accumulation curve
where slopes are steepest, and component soil percentages are indicated where the
curve flattens out.

Example 7.2
Large samples of glacial till often contain a mix of different component soils. What are
component percentages in the glacial till in Fig. 7.2?
Answer: The first steep section of the curve is at 41%, which therefore represents one
component soil. The second break is at 60% so the difference is 60 – 41 ¼ 19%, which
represents a second component. Similarly, the third break at 90% defines 90 – 60 ¼ 30% for
a third component, and a fourth component makes up the remaining 10%. The three
components percentage are 41 þ 19 þ 30 þ 10 ¼ 100%. The respective soils are (a) mainly
clay plus some silt, (b) all silt, (c) mainly fine sand, and (d) a mixture of coarse sand and
gravel.

7.3 DEFINING SIZE GRADES

7.3.1 Making the Grades

Not all sand particles are exactly the same size, which means that ‘‘sand’’ must
cover a range of particle sizes, the only requirement being that they are smaller
than gravel and larger than silt grains. Natural size boundaries occur between
gravel and sand, between sand and silt, and between silt and clay, but the
boundaries are transitional and somewhat arbitrary, and different organizations
have adopted different definitions.

Gravel particles require a higher water velocity to be moved than sand, and wind
does not move them at all. Sand particles move by bouncing, or saltation, and silt
grains are mainly carried in suspension, as the mud in muddy water or the dust
in air. Clay particles are so fine that they are very slow to settle out of suspension
and consist of separate mineral species, the clay minerals.

7.3.2 Sieve Sizes

Soils are separated into size grades by sieving, or sifting through a series or ‘‘nest’’
of standardized wire mesh sieves arranged from the coarsest down to the finest.
Common sieve sizes used in engineering are listed in Table 7.1.

A sieve is a wire fabric, so the sieve number does not describe the size of the
opening but designates the number of wires per inch or millimeter. As a matter of
convenience some size grades are defined on the basis of standard sieve sizes:
gravel, for example, commonly designates particles that are coarser than 2 mm,
which is the size of the opening in a No. 10 (wires to the inch) sieve.

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Particle Size and Gradation 147

No. (wires per inch) Opening, mm Comment Table 7.1

(Lid) –– Standard sieve sizes

4 4.75 Gravel used in geotechnical
10 . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.0 . . . . . . . . . Size separating gravel and sand engineering
20 0.85

40 0.425
60 0.25 Sand
140 0.106 #
200 . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.075 . . . . . . . . . Size separating
sand from silt
(Pan) –– Silt and clay fall on
through and collect in the pane

One complication is that sieve openings are not round; they are approximately
square. Spherical particles can pass through regardless of their orientation, but
few soil grains are spheres. Sieves therefore are vigorously shaken or vibrated for a
prescribed time in a sieve shaker in order to achieve reproducibility of the data.

7.3.3 Details of the Gravel-Sand Size Boundary

Although the most common size boundary between sand-size and gravel-size
particles is 2 mm, this size separation is not universal, even within geotechnical
engineering.

The Unified Soil Classification System used in earth dam and foundation
engineering makes the separation at the No. 4 (3/16 in.) sieve, and material
from 4.76 to 2 mm in diameter is considered ‘‘very coarse sand.’’ These and other
size boundaries are indicated in Fig. 7.2 Because the boundaries differ, it is
important that they be defined or included on graphs showing the particle size
distribution, as indicated by the vertical lines and grade names across the bottom
in Fig. 7.2.

7.3.4 The Sand-Silt Size Boundary

As silt particles are fine enough to be carried in suspension they show little or no
rounding of corners, whereas sand particles typically are abraded and rounded at
the corners and edges from having been transported and bounced along by wind
or water. However, the boundary is transitional, and for convenience it often is
defined on the basis of a sieve size. In geotechnical engineering practice the
boundary between sand and silt usually is that of a 200-mesh sieve opening,
0.075 mm or 75 mm (micrometers). The earlier designation was ‘‘microns.’’) Sand
therefore presents a range in particle sizes between 0.074 and 2 mm diameter,
a size ratio of 27.

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148 Geotechnical Engineering

Soil scientists prefer to make the separation between sand and silt at 0.020 mm or
20 mm. However, as shown by the loess and sand soils in Fig. 7.2, the natural
boundary may be closer to the No. 200 sieve (0.074 mm) or even slightly larger.
Geologists sometimes use 1/16 mm ¼ 0.067 mm, sometimes rounded off to
0.06 mm. However, the occurrence of a natural break in the general vicinity
tends to diminish the influence on constituent percentages.

7.3.5 The Silt-Clay Size Boundary

The most widely accepted size definition of clay is particles that are finer
0.002 mm or 2 mm. An earlier definition was based on the resolving power
and eyepiece calibration of a light microscope at the U.S. Bureau of Soils,
and set the boundary at 0.005 mm (5 mm). Later mineralogical investiga-
tions showed that this boundary is too high, but meanwhile it became estab-
lished and still is occasionally used in geotechnical engineering. The 0.005 mm
size also requires less interpolation from measurements that routinely are
made after 1 hour and 1 day testing time. This is discussed in more detail in
section 7.4.6.

7.3.6 Silt-Clay Boundary Based on Physical Properties

Another approach is to define clay on the basis of its plasticity or moldability with
water, as silt is crumbly while clay is sticky and can be molded into different
shapes. These relationships are quantified by two simple tests called Atterberg
limits. These tests and the relationship to engineering soil classifications are
discussed in Chapter 12. The limits define a moisture content range over which a
soil can be molded. This range is the plasticity index, which is a fundamental soil
property in geotechnical engineering.

In order to avoid possible confusion between the two approaches, a clay content
based on particle size may be referred to as clay-size material.

7.4 MEASURING PARTICLE SIZES

7.4.1 General Approach to Size Measurement

Some shortcuts are in order because so many particles must be measured in order
to obtain statistical reliability. One shortcut is to use sieves and screen a
representative soil sample. Another approach that is used for particle sizes too
small to be separated on sieves is to disperse the soil in water and make a
determination based on the sedimentation rate, with largest particles settling the
fastest.

One of the most important steps in analysis is obtaining a representative

soil sample. Large samples are spread out on a flat surface and ‘‘quartered,’’
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Particle Size and Gradation 149

that is, cut into four pie-shaped sectors and then combining opposing sectors
and returning the other half of the sample to the bag. This procedure is
repeated until the soil sample is small enough to be managed. A more rapid
method for quartering uses a ‘‘riffle-type’’ sample splitter that has parallel
shuts, with half directing the sample one way and the other half the other. Soils
are air-dried prior to quartering and sieving, but as discussed in Chapter 6,
if a soil contains halloysite clay mineral, it should be saved and sealed against
drying.

7.4.2 Sedimentation Analysis

Sieving is appropriate for measuring the amounts of sand and gravel in a soil, but
silt and clay sizes are too small to be separated by sieving. Also, clay particles
tend to be aggregated together into coarser particles and to occur as coatings
on coarser particles. Gravel is removed by sieving, and the rest of the soil
normally is soaked in water and then agitated and dispersed using a chemical
dispersing agent. The suspension then is tested by measuring sedimentation rates,
and finally the part of the soil that is retained on a fine sieve is dried and analyzed
by sieving.

The general procedure is as follows. After sieving to remove gravel and coarser
particles, the soil is soaked in water containing a small amount of a chemical
dispersing agent, usually sodium hexametaphosphate, a water softener that is
available in the detergent department of a supermarket. The dispersing agent
forces substitution of sodium ions for exchangeable calcium ions on the clay by
creating an insoluble phosphate precipitate.

The suspension then is agitated for a set amount of time with a standardized
mechanical or air-jet stirring device. Ideally this will separate but not break
individual soil grains. The soil suspension is diluted to 1 liter in a vertical flask and
stirred in preparation for starting the test.

The starting time is noted and the suspension is allowed to settle for various time
intervals. After each time interval, the density of the suspension is determined at a
particular depth with a hydrometer. An alternative method is to sample the
suspension with a pipette, then dry and weigh the sample.

The larger the weight of particles remaining in suspension, the denser the liquid,
and the higher the hydrometer will float. An engineering hydrometer is calibrated
to read directly in grams of soil per liter of suspension. Readings normally are
taken after 1 minute and at various time intervals to 1 hour and then after
24 hours.

After the sedimentation analysis is completed, the soil is washed on a fine sieve to
remove the silt and clay particles, then dried and the sand fraction analyzed by
passing through a series of sieves.
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Figure 7.4
Sampling theory
in sedimentation
analysis: at a
particular
sampling depth
the suspension
contains a
representative
sample of all sizes
smaller than the
size that will settle
to that depth.

7.4.3 Sedimentation and the Percent Finer

A sedimentation analysis automatically measures the amounts finer than a specific
grain size. This is illustrated in Fig. 7.4: after a certain time all particles larger than
a certain depth have settled a calculated distance and therefore cannot occur at
depths shallower than that distance. On the other hand, finer particles remain
suspended and therefore are measured.

After each hydrometer reading the hydrometer is removed so that particles will
not settle on the bulb. Removal stirs a small portion of the upper part of the
suspension, but the effect is small so long as particles move horizontally and
not vertically relative to the suspension—as the instrument is removed, the level of
the suspension goes down, and when it is replaced the level goes back up.
The depth to the center of volume of the submerged part of the hydrometer
is the effective sampling depth that is used in the calculations, and depends on
the depth of sinking. This depth is obtained from a calibration chart or table,
Table 7.2.
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Particle Size and Gradation 151

Hydrometer reading, g/l Depth, mm Table 7.2

5 155 Depth to hydrometer

10 147 center of volume
15 138
20 130
25 122
30 114
35 106
40 97
45 89
50 81

Note: Adapted from ASTM Designation D-422.

Temperature also must be controlled and measured to enable correction for

changes in the fluid viscosity.

7.4.4 Stokes’ Law of Sedimentation

In 1851 a British mathematician, G. G. Stokes, solved for the settlement
velocity of spherical particles in a suspension by equating their buoyant weight
to viscous drag on the outer surfaces. Surface area increases in proportion to
the radius while weight increases as the radius cubed, so the larger the particle,
the faster it will settle. The classic derivation for Stokes’ formula in the cgs
system is
R ¼ 6
rv ð7:1Þ
where R is the resisting force in g cm/s2, r is the particle radius in cm,  is the fluid
viscosity in poise or g-cm
1s
1, and v is the settlement rate in cm/s. Equating to
the buoyant weight of a spherical soil grain gives
4
6
rv ¼
r3 ð
w Þg ð7:2Þ
3
where  and  w are respectively the density of the soil grain and that of water, and
g is the acceleration of gravity. Solving for velocity v gives
2ð
w Þgr2
v¼ ð7:3Þ
9
Thus, the settlement rate v depends on the square of the particle radius r.

Experiments have confirmed the validity of the formula for particles between
0.001 and 0.10 mm in size, that is, for silt and most clay particles. Sand sizes are
influenced by mass displacement considerations that slow their rates of sinking,

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152 Geotechnical Engineering

and sizes smaller than about 0.001 mm settle more slowly. In 1827 an English
botanist, Robert Brown, noticed that pollen grains suspended in water jiggled
about when observed in a microscope, a movement that now is called Brownian
motion. This grabbed the attention of an employee of the Swiss patent office, who
wrote a brief paper attributing it to random molecular bombardment. The
employee’s name was Albert Einstein, who later became famous for another
matter. Particles smaller than about 0.001 mm tend to remain in suspension and
are referred to as colloidal size particles.

According to eq. (7.3) the rate of settling depends on the specific gravity  of the
particles, which varies depending on the mineral. Because sedimentation is a bulk
test, an average specific gravity is used in the calculations for particle size.
A method for measuring average specific gravity is described later in this chapter.
However, the assumption that all grain densities are average means that particles
of dense minerals will be reported as larger than their true dimensions because
they settle faster.

Sedimentation rate is influenced by the fluid viscosity, , which in turn depends on

temperature. A standardized temperature of 208C (688F) is used for laboratory
analyses. Other temperatures may be used with appropriate correction factors
based on viscosity tables.

An obvious limitation of Stokes’ Law is that it applies only to spherical particles,

whereas silt grains are angular and clay particles flat. Particle sizes determined
from sedimentation rates often are reported in terms of ‘‘equivalent particle
diameters.’’

7.4.5 Simplifying Stokes’ Law

In eq. (7.3), a particle radius in cm equals the diameter 0.05D in mm. The settling
velocity in cm/s equals 600L/T, where L is the settling distance in mm and T is
time in minutes. Substituting values for the acceleration of gravity and the
viscosity gives
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
D ¼ K L=10T ð7:4Þ
where D and L are in mm and T is in minutes. K depends on the specific gravity of
the soil and temperature of the solution; with a representative soil specific gravity
of 2.70, and a standardized temperature of 208C, K ¼ 0.01344. Other values for
this coefficient for different specific gravities and temperatures are given in ASTM
Designation D-422.

Example 7.3
A soil suspension is prepared containing 50 g/l. After 60 minutes the hydrometer reads
22 g/l. The temperature is controlled at 208C. (a) What particle diameter is being measured,
and (b) what is the percent of particles finer than that diameter?

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Answer: (a) The effective depth of the hydrometer is obtained by interpolation of data in
Table 7.2, which gives L ¼ 127 mm. From eq. (7.4),
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
D ¼ 0:01344 127=10  60 ¼ 0:0062 mm ¼ 6:2 mm:

(b) P ¼ 100  22/50 ¼ 44%.

7.4.6 Interpolating the Percent 2 mm Clay from

Hydrometer Analyses
The sedimentation time for a hydrometer analysis to measure 2 mm clay is
approximately 8 hours, which is inconvenient with an 8-hour working day.
However, as this part of the accumulation curve often is approximately linear
on a semilogarithmic plot, the percent 2 mm clay can be estimated from a
proportionality of the respective logarithms. As an approximation,
P002 ¼ 0:4P001 þ 0:6P005 ð7:5Þ

7.5 USES OF PARTICLE SIZE DATA

7.5.1 Median Grain Size

As previously mentioned, the size that defines 50 percent of the soil as being
finer and 50 percent coarser is the median grain size, designated as D50, and is
read from the intersection of the particle size distribution curve with the 50
percent line, as shown in Fig. 7.3. The median approximates but is not the same
as a mean or average particle size, which would be very difficult to determine
because it would involve measuring many individual particles and calculating an
average.

7.5.2 Effective Size and Uniformity Coefficient

A measurement that often is made for sand is the effective size, D10, or the size
whereby 10 percent of the particles are finer, and was shown by an engineer,
Allen Hazen, to correlate with the permeability of filter sands. Hazen defined the
uniformity coefficient, Cu, as the ratio D60/D10. The uniformity coefficient can
be as low as 1.5 to 2 for washed sands that are nearly all one size. For engineer-
ing uses a soil is said to be ‘‘well graded’’ if it contains a wide range of particle
sizes. A well-graded sand-gravel mixture may have a uniformity coefficient of
200–300.

Example 7.4
The sand in Fig. 7.2 has approximate values of D10 ¼ 0.12 mm and D60 ¼ 0.20 mm, from
which Cu ¼ 1.7. For engineering purposes this soil would be described as ‘‘poorly graded.’’
Because D10 is off the chart for fine-grained soils, another measure for degree of
uniformity suggested by a geologist, Trask, is the ‘‘sorting coefficient,’’ So, which
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Table 7.3 Sieve number Weight percent retained Weight percent finer
Mechanical analysis (particle diameter in mm) on each sieve
data and Sieve analysis:
determinations of No. 4 (4.76) 0 100
weight percents finer No. 10 (2.0) 4 100 – 4 ¼ 96
than sizes indicated No. 20 (0.84) 4 96 – 4 ¼ 92
No. 40 (0.42) 3 92 – 3 ¼ 89
No. 60 (0.25) 7 89 – 7 ¼ 82
No. 100 (0.147) 4 82 – 4 ¼ 78
No. 200 (0.075) 13 78 – 13 ¼ 65
Sedimentation analysis:
(0.025) Hydrometer reading ¼ 52
(0.010) ‘‘ 31
(0.005) ‘‘ 21
(0.001) ‘‘ 8

is defined as (D75/D25)1/2. A more complicated calculation also may be made to

obtain a statistical standard deviation.

7.5.3 Example of Mechanical Analysis

Measurement of soil particle sizes is called a ‘‘mechanical analysis.’’ Data from a
mechanical analysis are shown in Table 7.3.

The percent 0.002 mm clay is estimated from eq. (7.4), which gives
D002 ¼ 0.4  8 þ 0.6  21 ¼ 16 percent finer than 0.002 mm. The various size
grades are as follows:
Size grade Calculated percent by weight

Gravel (retained on No. 10 sieve) 4

Sand (retained on No. 200 minus % gravel) (100 – 65) – 4¼ 31
Silt (coarser than 0.002 mm minus % gravel and sand) (100 – 16) – 4 – 31¼ 49
Clay (finer than 0.002 mm) 16
Colloidal clay (finer than 0.001 mm) (8)
Total
100

7.5.4 Granular vs. Fine-Grained Soils

Concrete mixes are designed based on a concept that largest particles are
touching, and progressively finer particles fill in the voids. The same concept
applies to soils, and a broad range of particle sizes is considered to be ‘‘well

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Particle Size and Gradation 155

graded.’’ If coarse grains are in contact and voids between them are filled with
smaller particles, the soil must increase in the volume, or dilate, in order to shear.
This adds appreciably to the shearing resistance.

In many soils the silt and clay content are high enough to separate larger soil
grains so that shearing can occur through the silt-clay matrix without dilatancy,
which causes a marked reduction in the soil shearing strength. Artificial mixtures
of sand plus clay show that this property change occurs at about 25 to 30 percent
clay. The two distinct modes of behavior distinguish ‘‘granular soils’’ from
‘‘fine-grained soils.’’

7.5.5 Soil Mixtures

In Fig. 7.5 a poorly graded silt soil is combined with a poorly graded sand to
obtain a more uniform grading. In this example the mix is 50–50, and the
construction lines are shown dashed. A better grading could be obtained by
reducing the percentage of A and increasing that of B. The effectiveness of an
improved grading can be determined with strength tests. Geologists refer to a well-
graded soil as being ‘‘poorly sorted,’’ which means the same thing even though the
connotations are different.

Flat portions of a particle size accumulation curve indicate a scarcity of those

sizes, and a soil showing this attribute is said to be ‘‘gap-graded.’’ Gap grading
tends to give lower compacted densities and strength, and higher permeability.

7.5.6 Soil as a Filter

Filters are barriers that can transmit water while retaining soil particles that
otherwise would be carried along in the water. Filter soils usually are sands.
A common use of a filter is in the toe drainage area in an earth dam, where control

Figure 7.5
Combining two
poorly graded soils
A and B to obtain a
more uniform
grading A þ B.

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156 Geotechnical Engineering

of seepage is important to prevent water from emerging on the earth slope where it
might lead to piping and failure. Geotextile filters generally are more expensive
but are easier to install than are layers of sand, and are less likely to be damaged
or compromised during construction.

Design
Protective filters act as a drain while resisting clogging by fine particles. They also
cannot permit a breakthrough, and may be required to provide insulation against
frost action. The finer sizes of particles in a soil filter tend to control its
performance. Generally the filter F15 size is compared with the D85 size for the
base soil. (To avoid confusion the filter size is designated with F instead of D.)
A conservative and acceptable guide for design is F15/D8555.

An additional requirement for the retention of clay, for example in the core of an
earth dam, is that F1550.5 mm.

Example 7.5
Is the sand in Fig. 7.2 an appropriate filter for an earth dam constructed from the glacial till
in the same figure?

Answer: The sand has F15 ¼ 0.12 mm, and the till has D85 ¼ 0.4 mm. Then 0.12/
0.4 ¼ 0.355, so the filter should perform adequately. In addition F1550.5 mm so there
should be little or no clay penetration.
Question: What if the dam is constructed from the loess in the figure?

7.5.7 Geotextile Filters

The apparent opening size (AOS) of geotextile fabrics is defined as O95, which is
the size for 95 percent of glass beads of a particular size grade to pass through
during sieving (ASTM Designation D-4751). One criterion in regard to filtration
of soil is that O95/D8552 or 3, where D85 is for the soil.

7.5.8 Grouting
Grouting is pumping of a fluid under pressure into a soil so that it either (a)
permeates the soil, referred to as injection grouting, or (b) displaces the soil, called
compaction grouting. The determination of whether a grout will inject into the soil
pores or displace the soil is mainly dependent on the relations between the
respective particle sizes.

Injection grouting is a common remedial treatment used to solidify loose

foundation soil and rock underneath buildings, dams, and other structures.
Injection grouting also is used to seal leaks under dams or lagoons, to seal off and
contain buried hazardous wastes, and to seal off the groundwater aquifers in
preparation for tunneling.
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Particle Size and Gradation 157

Compaction grouting is a relatively new procedure that normally is intended to

laterally compact and densify loose soil to reduce settlement under a foundation
load.

Regardless of the grouting procedure the maximum grouting pressure is limited by

the overburden pressure of the soil, or lateral planar injections can lift the soil.
When this occurs, pumping pressure should decrease while the pumping rate
increases, referred to as the grout ‘‘take.’’

If the lateral stress existing in the soil is lower than the vertical pressure from
overburden, the pumping pressure at which the ‘‘take’’ occurs is that which causes
vertical radial cracking and is used as an approximate measure of lateral stress in
the soil. This is called ‘‘hydraulic fracturing.’’ It was first developed in the
petroleum production industry to increase the flow of oil into oil wells.

Grout Materials
The most common grout materials for rocks and soils are aqueous suspensions of
Portland cement and/or fly ash. Sand-cement mortar may be used for grouting
rubble that has large voids. Bentonite sometimes is used as a sealing grout, but has
the disadvantage that it will shrink and crack when it dries out.

The first injection grout was developed by Joosten in Germany and uses chemical
solutions of sodium silicates and calcium chloride, which react to make insoluble
calcium silicate and sodium chloride. Some more recent chemical solution
grouts have been removed from the market because of potentially toxic effects
on groundwater. Emulsions of asphalt in water are sometimes used as grout for
sealing cracks and joints in basements.

Soil Groutability
For injection grouting the particle size ratio is reversed from that used design-
ing filters, D15 for the soil and G85 for the grout. To ensure success, the ratio
should be substantially higher than the corresponding ratio of 5 used for
filters. Tests by the U.S. Army Corps of Engineers suggest that the ratio of soil
D15 to cement G85 should be a minimum of 20. G85 for Portland cement typi-
cally is about 0.040 to 0.050 mm. The smaller figure represents high-early strength
cement, and also is fairly representative of fly ashes. Specially ground cements
may have G85 of only 0.005 mm. Bentonite is composed of montmorillonite
particles that expand on wetting, with an effective hydrated G85 of about
0.030 mm.

Example 7.6
Can any of the soils of Fig. 7.2 be injection grouted with cement grout?
Answer: The soil with the largest D15 is the sand, with D15 ¼ 0.12 mm. For cement, assume
G85 ¼ 0.050 mm. Then D15/G85 ¼ 2.4  20, so this sand cannot be injected with cement

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 Particle Size and Gradation

158 Geotechnical Engineering

grout. The sand still may be a candidate for compaction grouting or injection grouting with
chemical solutions, depending on the properties that are required.

As a general guide:
 Gravel or very coarse sand can be injection grouted with cement and/or fly
ashs.
 Medium to fine sand can be compaction grouted with cement/fly ash or
injection grouted with sodium silicate or specially ground fine cement.
 Silt can be compaction grouted.
 Clay cannot be grouted, but expansive clay can be stabilized by a diffusion
process of hydrated lime, which is much slower than the other processes.

Partly because of the difficulty in controlling injection grouting and knowing

where the grout goes, compaction grouting has become increasingly popular in
recent years.

7.6 DESCRIBING PARTICLE SHAPE

7.6.1 Particle Shape and Engineering Behavior

The shapes of soil grains can influence engineering behavior, as round grains
obviously are more likely to slip and roll than angular fragments that mesh or
interlock together. For this reason crushed rock normally creates a stronger
surface of a ‘‘gravel’’ road than do the more rounded particles of gravel. On the
other hand gravel, having been through many cycles of pounding against a beach
or river bottom, is more likely to be harder and less likely to degrade into dust.

The main effect of angularity is harshness, or the tendency for the soil to dilate or
increase in volume during shearing, a matter that can be quantified with strength
tests.

Grain shapes closely relate to their mineralogy and origin; quartz sand grains
derived from disintegration of granite tend to be round, whereas grains of feldpar
derived from the same rock are more angular, and grains of mica are flat. Alluvial
gravel generally is well rounded, sand less so, and silt not at all. Dune sand not
only shows rounding, but the grain surfaces are etched from repeated impacts.

The measurement of shapes of individual grains can be time-consuming, but

measurement of grain profiles can be digitized and automated. A chart that can be
used to estimate shape, or ‘‘sphericity,’’ is shown in Fig. 7.6. Sphericity
theoretically is the ratio of a grain surface area to that of a sphere, but can be
approximated by dividing the intermediate grain width by its length. As this does

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 Particle Size and Gradation

Particle Size and Gradation 159

Figure 7.6
Chart for
evaluating the
shapes of
individual soil
grains from their
profiles, 1.0
representing the
approach to a
sphere.

not take into account the shortest grain dimension, it tends to overestimate
sphericity of flat particles such as mica.

7.6.2 Special Problems with the Shape of Mica Grains

Especially troublesome, is that mica particles are flat and also are springy, so
compacting a soil with a high content of mica is like trying to compact a bucket of
springs. Although micaceous soils are not common, their behavior is such that
they are given a special category in some engineering classifications, and the glitter
is not gold.

7.7 TEXTURAL CLASSIFICATION OF SOILS

7.7.1 Describing Different Proportions of Sand þ Silt þ Clay

The first step in characterizing grain sizes in a soil is to take the soil apart and
assign the component parts to size grades, namely gravel, sand, silt, and clay. Next
let us describe the products when we put them back together. A naturally
occurring gravel deposit almost inevitably will contain some sand, and a naturally
occurring silt deposit almost inevitably will contain some clay, so when does it
stop having ‘‘silt’’ for a soil name and start being a ‘‘clay’’?

‘‘Clay’’ therefore can mean either (a) clay mineral, (b) clay size, or (c) a deposit or
soil that is mainly clay but also contains other minerals and grain sizes. Engineers
tend to use a term such as ‘‘clay’’ interchangeably for its several meanings, and
should be certain that it is used in a context that ensures that everybody will know
what it means.

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 Particle Size and Gradation

160 Geotechnical Engineering

Figure 7.7
A soil textural
chart based on
the 0.075 mm
definition of silt
size and
the 0.002 mm
definition of clay
size.

7.7.2 Soil Textures and Particle Sizes

Soil scientists who do soil mapping in the field originally proposed the term
‘‘texture’’ to describe the ‘‘feel’’ of moist soil squeezed with the fingers. A soil
might have a gritty or sandy feel, or it might have a smooth feel, more like
modeling clay. ‘‘Loam’’ came to mean a somewhat loose and crumbly feel that is
great for agriculture.

Soil textures are quantified by relating them to the percentages of sand, silt, and
clay. The various ranges are shown on a triangular ‘‘textural chart’’ such as
Fig. 7.7. Boundaries on textural charts have been changed from time to time as
size definitions have changed, but the concept remains valid and useful.

The textural chart is read by entering any two of the three percentages and moving
onto the chart in the directions of the corresponding short lines around the edges.
For example, the boundary between clay and clay loam is at 30 percent clay-size
material. It will be seen that a clay texture can contains as much as 55 percent
sand. However, to qualify as a sand texture the soil must contain over 80 percent
sand.

Textural terms apply to the non-gravel portion of a soil, so the percentages are
adjusted for gravel content. If the gravel content exceeds 10 percent the soil is
‘‘gravelly.’’
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Particle Size and Gradation 161

Example 7.7
What is the textural classification for the soil in Section 7.5.3?

Answer: The soil contains 31% sand and 49% silt. These figures are adjusted for the 4%
gravel content: 31/0.96 ¼ 32.6% sand and 49/0.96 ¼ 51.0% silt. The texturally is ‘‘silty clay
loam.’’

7.8 SPECIFIC GRAVITY OF SOIL PARTICLES

7.8.1 Definition and Use

Specific gravity is defined as the density of a material divided by the density of
water at 48C, which is water at its densest. According to eq. (7.3) the specific
gravity is required in order to interpret settlement analyses. Some representative
specific gravities for different minerals are shown in Table 7.4. Most sands have
a specific gravity of 2.65–2.68; most clays, 2.68–2.72.

7.8.2 Measurement
A common method for measuring the specific gravity of a large object is to weigh
it in air and then submerge it in water. The difference equals the weight of the
water displaced, a discovery made by Archimedes in his search for a way to
determine the purity of gold. The weight divided by the weight lost therefore

Gold 19.3 Terribly expensive Table 7.4

Silver 10.5 Pocket change Specific gravities of
Galena (PbS) 7.5 Cubes that look like silver but aren’t some selected solids
Pyrite (FeS2) 5.0 Cubes that look like gold but aren’t
Hematite (Fe2O3) 4.9–5.3 Red iron oxide in soils
Limonite (Fe2O3  nH2O) 3.4–4.3 Yellow or brown iron oxides in soils
Iron silicate minerals 2.85–3.6 Dark minerals in basalt, granite
Calcite (CaCO3) 2.72 Most abundant mineral in limestone
Micas 2.7–3.1 Flakey
Quartz(SiO2) 2.65 Most abundant mineral in soils
Feldspar (Na and Ca silicates) 2.55–2.65 Most abundant mineral in rocks
Kaolinite 2.61 Clay mineral
Smectites 2.2–2.7 Expansive clay minerals
Glass 2.2–2.5 Lead glass ¼ 3
Halite (NaCl) 2.1–2.3 Rock salt
Liquid water (H2O) 1.00 At its densest, 48C
Ice (H2O) 0.918 Floats on liquid water

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 Particle Size and Gradation

162 Geotechnical Engineering

represents the weight divided by the weight of an equal volume of water, which by
definition is the specific gravity:

W
G¼ ð7:6Þ
W
Wb

where G is the specific gravity and W and Wb are the weight and buoyant weight
respectively.

A slightly different procedure is used for soils and is a bit more tricky. A flask
is filled with water and weighed; call this A. Then W, a weighed amount of soil,
is put into the flask and displaces some of the water, giving a new total
weight, C. As shown in Fig. 7.8, the weight of the water displaced is (A þ W
C).
Hence,

W
G¼ ð7:7Þ
AþW
C

Experimental precision is unhappy with subtracting a weight from the

denominator, so measurements are exacting. Recently boiled or evacuated
distilled water ensures that there is no air that might come out of solution to
make bubbles, and clay soils are not previously air-dried. Less critical is a
temperature-dependent correction for the specific gravity of water, which at 208C
is 0.99823. (Specific gravities are reported to three significant figures.) Details are
in ASTM Designation D-854. It will be noted that weights and not masses are
measured, even though the data are usually recorded in grams.

Example 7.8
A flask filled to a reference mark with water weighs 690.0 g on a laboratory scale. When
90.0 g of soil are added, the filled flask weighs 751.0 g. The water temperature is 208C.
(a) What is G? (b) What effect will the temperature correction have? (c) What if as a result
of measurement error the soil weight is 1 g too high, an error of 1.1%?

Fig. 7.8 Using a

pycnometer to
measure specific
gravity.

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Particle Size and Gradation 163

Answer:

(a) G ¼ 90/(690.0 þ 90.0 – 746.0) ¼ 2.65.

(b) Dividing by 0.998 to correct for water temperature does not affect the
answer.
(c) G0 ¼ 91/(690 þ 91 – 746) ¼ 2.53. A suggested assumed value would be
more accurate.

Problems
7.1. Plot a particle size accumulation curve for soil No. 4, Table 7.5, by enter-
ing the data on a computer spreadsheet and selecting the logarithmic
option for the particle sizes. (Optionally this can be done manually using
5-cycle semilogarithmic paper.) (a) Evaluate the effective size and unifor-
mity coefficient. (b) What is the median grain size? (c) Defining clay
as 50.002 mm, silt as 0.002–0.074 mm, sand as 0.074–2.0 mm, and gravel
as 42.0 mm, what are the percentages of clay, silt, sand, and gravel?
7.2. Classify soil No. 4 according to the chart in Fig. 7.7 after adjusting the
percentages for gravel content.
7.3. Plot a particle size accumulation curve for soil No. 1, Table 7.5. (a) Identify
the median and mode(s). (b) If there are two modes, what is the approxi-
mate percentage of each soil in the mixture? (c) Using the size grades
defined in Problem 7.1, find the percentages of clay, silt, sand, and gravel.
(d) Adjust the grade percentages for gravel and classify the soil by the chart
in Fig. 7.7.
7.4. Calculate the effective size and uniformity coefficient for soil No. l.
Answer: D10 ¼ 0.0039 mm, Cu ¼ 192.
7.5. By inspection indicate which of the soils in Table 7.5 should be designated
as gravelly.
7.6. For the first five soils in Table 7.5 compare measured 0.002 mm clay
contents with those interpolated from the 0.001 mm and 0.005 mm clay
contents by eq. (7.5).
7.7. What is meant by a ‘‘well-graded’’ soil? What is the reason for considering
such a soil to be well graded?
7.8. Which soils in Table 7.5 can be injection-grouted with a mixture of Portland
cement, fly ash, and water?
7.9. Soil No. 12 in Table 7.5 is to be separated from No. 14 by means of a filter.
From the two particle size accumulation curves, define (a) desirable
characteristics of a geotextile filter, (b) the gradation(s) required for soil
filter(s): if a single filter layer is not adequate, use two. (c) Select appropriate
soil(s) from the table to use as filter(s).

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 164

Table 7.5 Sieve number and Sedimentation

Mechanical analysis size of opening (mm) size (mm)
of soils: percentage
Soil 1 in. 34 in. 38 in. No. 4 No. 10 No. 40 No. 60 No. 100 No. 200 0.050 0.005 0.002 0.001 LL PI Soil
passing various
No. 26.7 18.8 9.4 4.75 2.00 0.42 0.25 0.149 0.074 No.
Geotechnical Engineering

sieve sizes
1 100 90 80 72 67 56 44 34 24 21 11 7 4 29 7 1
2 100 99 98 97 96 91 80 71 63 34 25 18 39 14 2
3 100 99 96 92 80 73 41 31 23 76 21 3
4 100 97 84 66 50 32 24 5 4 4 54 16 4
5 100 96 85 61 34 31 13 10 7 69 7 5
6 100 95 88 80 54 25 14 5 35 10 6
7 100 99 98 95 9 7 6 80 9 7
8 100 97 76 60 45 35 21 10 35 17 8
9 100 95 88 81 65 59 18 11 6 27 5 9
10 100 99 97 93 70 58 56 44 42 24 17 11 41 12 10
11 100 98 92 82 50 42 35 28 25 12 8 5 38 16 11
Particle Size and Gradation

12 100 93 77 64 48 24 20 16 12 11 8 7 6 13 4 12
13 100 99 84 48 12 8 –– –– –– –– N.P. 13
14 100 99 95 93 68 49 34 86 49 14
15 100 79 60 48 34 30 14 11 9 24 8 15

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16 100 94 89 87 85 81 73 39 24 12 59 43 16
17 100 98 94 48 42 33 26 22 13 11 10 47 24 17
18 100 98 97 96 94 91 90 89 86 80 42 27 16 45 17 18
19 100 45 38 30 22 20 10 7 4 16 6 19
20 100 98 96 95 93 89 64 44 29 84 53 20

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Particle Size and Gradation 165

7.10. Combine soils 1 and 3 in Table 7.5 in such proportions that the resulting
mixture contains 20 percent 5 mm clay. Draw the particle size accumulation
curve of the mixture.

References and Further Reading

Grim, Ralph E. (1962). Applied Clay Mineralogy. McGraw-Hill, New York.
Koerner, Robert M. (1990). Designing with Geosythetics, 2nd ed. Prentice-Hall, Englewood
Cliffs, N.J.
Mitchell, J. K. (1993). Fundamentals of Soil Behavior, 2nd ed. John Wiley & Sons,
New York.
Sherard, J. L., Dunnigan, L. P., and Talbot, J. R. (1984). (a) ‘‘Basic Properties of Sand and
Gravel Filters,’’ and (b) ‘‘Filters for Silts and Clays.’’ ASCE J. Geotech. Engr. Div.
110(6), 684–718.
Sherard, James L. (1987). ‘‘Lessons from the Teton Dam Failure.’’ Engng. Geol. 24,
239–256. Reprinted in G. A. Leonards, ed., Dam Failures, Elsevier, Amsterdam, 1987.

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