2

Grain Size Distribution: The Sieve Analysis

Introduction
In order to classify a soil for engineering purposes, one needs to know the
distribution of the size of grains in a given soil mass. Sieve analysis is a method used to
determine the grain size distribution of soils and in the classification of sands and gravels.
Sieves are made of woven wires with square openings. Note that as the sieve number
increases, the size of the openings decreases. Table 2.1 gives a list of the U.S. standard
sieve numbers with their corresponding size of openings. For all practical purposes, the
No. 200 sieve is the sieve with the smallest opening that should be used for the test. The
sieves that are most commonly used for soil tests have a diameter of 8 in. (203 mm). A
stack of sieves is shown in Fig. 2.1.
The method of sieve analysis described here is applicable for soils that are mostly
granular with some or no fines. Sieve analysis does not provide information as to shape
of particles.
Table 2.1 U.S. Sieve Sizes
Sieve Opening Sieve Opening
No. (mm) No. (mm)

4 4.75 35 0.500
5 4.00 40 0.425
6 3.35 45 0.355
7 2.80 50 0.300
8 2.36 60 0.250
10 2.00 70 0.212
12 1.70 80 0.180
14 1.40 100 0.150
16 1.18 120 0.125
18 1.00 140 0.106
20 0.85 200 0.075
25 0.71 270 0.053
30 0.60 400 0.038
 Grain Size Distribution: The Sieve Analysis 2

Fig 2.1 A stack of sieves with a pan at the bottom and a cover on the top.

Equipment
1. Sieves, a bottom pan, and a cover
Sieve numbers 4, 10, 20, 40, 60, 140, and 200 are generally used for most
standard sieve analysis work.
2. A scale sensitive up to 0.1 g.
3. Mortar and rubber-tipped pestle.
4. Oven.
5. Mechanical sieve shaker.

Procedure
1. Collect a representative oven dry sample. Samples having largest particles of the
size of No.4 sieve openings (4.75 mm) should be about 500 grams. For soils
having largest particles of size greater than 4.75 mm, larger weights are needed
(Fig. 2.2)
 Grain Size Distribution: The Sieve Analysis 3

Fig. 2.2 Soil Sample.

2. Break the soil sample into individual particles using a mortar and a rubber-tipped
pestle. (The idea is to break up the soil into individual particles, not to break the
particles themselves.)
3. Determine the mass of the sample accurately to 0.1 g (W).
4. Prepare a stack of sieves. A sieve with larger openings is placed above a sieve with
smaller openings. The sieve at the bottom should be No. 200. A bottom pan should
be placed under sieve No. 200. As mentioned before, the sieves that are generally
used in a stack are Nos. 4, 10, 20, 40, 60, 140, and 200; however, more sieves can
be placed in between.
5. Pour the soil prepared in Step 2 into the stack of sieves from the top.
6. Place the cover on the top of the stack of sieves.
7. Run the stack of sieves through a sieve shaker (Fig. 2.3) for about 10 to 15
minutes.

Fig. 2.3 The sieve shaker with a stack of sieves.

 Grain Size Distribution: The Sieve Analysis 4

8. Stop the sieve shaker and remove the stack of sieves. (Fig. 2.4)

Fig. 2.4 Sieves separated and bottom pan.

9. Weigh the amount of soil retained on each sieve and the bottom pan.
10. If a considerable amount of soil with silty and clayey fractions is retained on the
No. 200 sieve, it has to be washed. Washing is done by taking the No.200 sieve
with the soil retained on it and pouring water through the sieve from a tap in the
laboratory (Fig. 2.5).

Fig. 2.5 Washing the soil retained on No. 200 sieve.

When the water passing through the sieve is clean, stop the flow of water. Transfer
the soil retained on the sieve at the end of washing to a porcelain-evaporating dish
by back washing. Put it in the oven to dry to a constant weight. (This step is not
necessary if the amount of soil retained on the No. 200 sieve is small.). Determine
 Grain Size Distribution: The Sieve Analysis 5

the mass of the dry soil retained on the No. 200 sieve. The difference between this
mass and that retained on the No. 200 sieve determined in step 9 is the mass of soil
that has washed through.

Sample Data
Description of Soil: Sand with some fines
Weight of oven dry sample, W = 502 grams
Table 2.1
Wt. of Sieve % mass of soil Cumulative
Sieve Sieve Wt. of Mass of soil % Finer,
Sieve with retained on % retained
Opening Opening Sieve retained on
Number aggregate 100- ΣRn
(in) (mm) (g) each sieve (g) each sieve, Rn ΣRn
(g)
4 0.187 4.750 757.2 782.8 25.6 5.1 5.1 94.9
16 0.047 1.191 602.9 711.3 108.4 21.6 26.7 73.3
30 0.024 0.599 584.0 685.1 101.1 20.1 46.8 53.2
60 0.010 0.249 300.4 376.0 75.6 15.1 61.9 38.1
140 0.004 0.106 318.4 458.0 139.6 27.8 89.7 10.3
200 0.003 0.075 339.4 364.3 24.9 5.0 94.7 5.3
Pan N.A. N.A. 373.5 400.2 26.7 5.3 100.0 0.0
 = 501.9 = W 1  = 100.0

Mass loss during Sieve analysis = 0.02 %

Percent Finer vs. Grain Size

100

90

80

70
Percent Finer (%)

60

50

40

30

20

10

0
10 1 0.1 0.01

Grain Size, D (mm)

Fig. 2.6 Plot of Percent Finer vs. grain size from the table 2.1

D10 = 0.104 Cu = D60/D10 = ( 0.75)/(0.104) = 7.2

D30 = 0.19 Cc = (D30)2/(D60xD10) = (0.19)2/(0.75*0.104) = 0.46
D60 = 0.75
 Grain Size Distribution: The Sieve Analysis 6

Calculations
1. Mass of soil retained on each sieve (g) = Wt. of Sieve w/ aggregate – Wt. of Sieve (g)
2. Percent mass of soil retained on each sieve, Rn (%) =
= [Mass of soil retained/ Wt. of oven dry sample] x 100 (%)
i=n

3. Cumulative percent of soil retained on the nth sieve, Rn (%) = Σ R(nth) (%)
i=1

4. Cumulative percent of soil passing through the nth sieve (% finer), 100 -Rn =
i=n

= percent finer = 100 - Σ R(nth) (%)

i=1

5. Mass loss of soil during sieve analysis (g) =

= [(Wt. of sample - mass of soil retained) / Wt. of sample] x 100
= (W – W1) / (W) x 100 (%) (O.K. if less than 2%)

Note: If soil retained on No. 200 sieve is washed, the dry unit weight determined after
washing (step 10) should be used to calculate percent finer (than No. 200 sieve). The
weight lost due to washing should be added to the weight of the soil retained on the pan.

6. The grain-size distribution obtained from the sieve analysis is plotted in a semi-
logarithmic graph paper with grain size plotted on the log scale and percent finer
plotted on the natural scale. Figure 2.6 is a grain-size distribution plot for the data
and calculations shown in Table 2.1. The grain-size distribution plot helps to
estimate the percent finer than a given sieve size which might not have been used
during the test.

From the grain-size distribution curve, grain sizes such as D10, D85, D60, etc. can b
obtained. The D refers to the grain size, or apparent diameter, of the soil particles and the
subscript (10, 85, 60) denotes the percent that is smaller. For example, D10 = 0.104 mm
from the distribution curve means that 10 percent of the sample grains are smaller than
0.104 mm. The diameter, D10, is also referred to as effective size. The effective size is
used for several empirical correlations, such as coefficient permeability. The coefficient of
gradation, Cc, is a parameter which indicates the range of distribution of grain sizes in a
given soil specimen. If Cc is relatively large, it indicates a well-graded soil. If Cc is nearly
 Grain Size Distribution: The Sieve Analysis 7
equal to one, it means that the soil grains are of approximately equal size, and the soil may
be referred to as a poorly graded soil.

The following formula is used to calculate Cc:

7. Cu = (D60 / D10)

8. Cc = (D30)2 / (D60xD10)

The parameter Cc is also referred to as the coefficient of curvature. For sand, if Cu is

greater than 6 and Cc is between 1 and 3, it is considered well graded. However, for a
gravel to be well-graded, Cu should be greater than 4 and Cc must be between 1 and 3.
The D15 and D85 sizes are used for design of filters. The D50 size is used for correlation of
the liquefaction potential of saturated granular soil during earthquakes.

Conclusions
The conclusion should answer the following questions:
1. Of what significance is the sieve analysis to a geotechnical engineer?
2. How much soil mass was lost in the analysis? What are some possible sources for error?
3. What do D10, D85, D60 signify?
4. What do the coefficient of uniformity, Cu, and the coefficient of concavity, Cc indicate
about the test soil?
 Grain Size Distribution: The Sieve Analysis 8

Data Sheet

Grain Size Distribution: The Sieve Analysis

Group: ___________ Date: ______________ Location: _____________

Soil Description: _______________________________________________________

Mass of soil
Sieve Sieve Wt. of Wt. of Sieve % of mass Cumulative % Finer,
Sieve retained on
Opening Opening Sieve with retained on each % retained 100-
Number each sieve
(in) (mm) (g) aggregate (g) sieve, R(nth) ΣRnth ΣRnth
(g)
4
16
30
60
140
200
Pan
 =  =

Notes: