FHG IKJ − −
3.8 PARTICLE SIZE DISTRIBUTION (MECHANICAL ANALYSIS)
3.8.3 Sedimentation Analysis (Wet Analysis)
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INDEX PROPERTIES AND CLASSIFICATION TESTS 49 Assuming G = 2.67, on an average,
v = 1 180
×(9.792 2.67)( −1)
0.001 . D2 = 90.85D2
∴ v ~− 91D2 ...(Eq. 3.20)
where D is in mm and v is in cm/sec.
Using the approximate version of Stoke’s law, one can determine the time required for a particle of a specified diameter to settle through a particular depth; e.g., a particle of 0.06 mm diameter settles through 10 cm in about 1/2 minute, while one of 0.002 mm diameter settles in about 7 hours 38 minutes.
From Eq. 3.19,
v = 1 180.γ
µ
w w
(G – 1) . D2
∴ D = 180
1 . .
( )
µ γ
w w
v G −
If the particle falls through H cm in t minutes v = H/60t cm/sec.
∴ D = 180
1 60 µ γ
w w
H
G t
. ( − ) .
= γ 3µw 1
w G
H t ( − ) ×
∴ D = K H t/ ...(Eq. 3.21)
where K = 3
1 µ
γw(Gw− ) ...(Eq. 3.22)
Here,
G = grain specific gravity of the soil particles,
γw = unit weight of water in kN/m3 at the particular µw = viscosity of water in N-sec/m2 temperature.
H = fall in cm, and t = time in min.
The factor K can be tabulated or gaphically represented for different values of tempera-ture and grain specific gravity.
Stokes’ Law is considered valid for particle diameters ranging from 0.2 to 0.0002 mm.
For particle sizes greater than 0.2 mm, turbulent motion is set up and for particle sizes smaller than 0.002 mm, Brownian motion is set up. In both these cases Stokes’ law is not valid.
The general procedure for sedimentation analysis, which may be performed either with the aid of a pipette or a hydrometer is as follows:
An appropriate quantity of an oven-dried soil sample, finer than 75–µ size, is mixed with a known volume (V) of distilled water in jar. The sample is pretreated with an oxidising agent and an acid to remove organic matter and calcium compounds. Addition of hydrogen peroxide an heating would remove organic matter. Treatment with 0.2 N hydrochloric acid
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would remove calcium compounds. Later, a deflocculating or a dispersing agent, such as so-dium hexameterphosphate is added to the solution. (Further details regarding the prepara-tion of the sample may be obtained from IS: 2720 (Part IV)–1985 and its revised versions). The mixture is shaken thoroughly by means of a mechanical stirrer and the test is started, keeping the jar vertical. The soil particles are assumed to be uniformly distributed throughout the suspension, at the instant of commencement of the test. After the lapse time t, only those particles which have settled less than depth H would remain in suspension. The size of the particles, finer than those which have settled to depth H or more at this instant, can be found from Eqs. 3.21 and 3.22, Hence, sampling at different time intervals (by pipette), or determining the specific gravity of the suspension (by hydrometer), at this sampling depth, would provide the means of determining the content of particles of different sizes. (The logic would become much clearer if all particles are considered to be of the same size). Since, the soil particles are dispersed uniformly throughout the suspension, and according to Stoke’s law, particles of the same size settle at the same rate, particles of a given size, wherever they exist, have the same degree of concentration as at the commencement of the test. As such, particles smaller than a given size will be present in the same degree of concentration as at the start, and particles larger than this size would have settled already below the sampling depth, and hence are not present at that depth. The percentage of particles finer than a specified size may be got by determining their concentration at that depth at different times either with the aid of a pipette or of a hydrometer.
The limitations of sedimentation analysis, based on Stokes’ law, or the assumptions are as follows:
(i) The finer soil particles are never perfectly spherical. Their shape is flake-like or needle-like. However, the particles are assumed to be spheres, with equivalent diameters, the basis of equivalence being the attainment of the same terminal velocity as that in the case of a perfect sphere.
(ii) Stokes’ law is applicable to a sphere falling freely without any interference, in an infinite liquid medium. The sedimentation analysis is conducted in a one-litre jar, the depth being finite; the walls of the jar could provide a source of interference to the free fall of particles near it. The fall of any particle may be affected by the presence of adjacent particles; thus, the fall may not be really free.
However, it is assumed that the effect of these sources of interference is insignificant if suspension is prepared with about 50 g of soil per litre of water.
(iii) All the soil grains may not have the same specific gravity. However, an average value is considered all right, since the variation may be insignificant in the case of particles constituting the fine fraction.
(iv) Particles constituting to fine soil fraction may carry surface electric charges, which have a tendency to create ‘flocs’. Unless these floces are broken, the sizes calculated may be those of the flocs. Flocs can be a source of erroneous results.
A deflocculating agent, such as sodium silicate, sodium oxalate, or sodium hexa-metaphosphate, is used to get over this difficulty.
Pipette Analysis
The sedimentation analysis may be conducted with the aid of a pipette in the labora-tory. A pipette, sedimentation jar, and a number of sampling bottles are necessary for the test.
INDEX PROPERTIES AND CLASSIFICATION TESTS 51 A boiling tube of 500 ml capacity kept in a constant temperature bath may also be used in place of a sedimenation jar. The capacity of the sampling pipette is usually 10 ml.
The method consists in drawing off 10 ml samples of soil suspension by means of the sampling pipette from a standard depth of 10 cm at various time intervals after the start of sedimentation. The soil-water suspension should have been prepared as has been mentioned earlier. The usual total time intervals at which the samples are drawn are 30 s, 1 min., 2 min., 4 min., 8 min., 5 min., 30 min., 1 h, 2h, and 4 h from the start of sedimentation. The pipette should be inserted about 20 seconds prior to the chosen instant and the process of sucking should not take more than 20 seconds. Each of the samples taken is transferred to a sampling bottle and dried in an oven. The weight of solids, WD in the suspension, finer than a certain size D, related to the time of sampling, may be found by careful weighing, from the concentra-tion of these solids in the pipette sample. Let Ws be the weight of soil (fine fraction) used in the suspension of volume V, and WD be the weight of soil particles finer than size D in the entire suspension. Also, let Wp be the weight of solids in the pipette sample of volume Vp.
Then, by the argument presented in the general procedure for sedimentation analysis, W
V W
V
D p
p
= ...(Eq. 3.23)
or WD = W
V V W V
V
p
p p
p
. =
F
HG I
KJ
...(Eq. 3.24)The calculation will be somewhat as follows:
From Equations (3.21) and (3.22), for the known values of H and t, we obtain the size D.
Let the weight of solids per ml in the pipette sample be multiplied be multiplied by the total volume of the suspension; this would give WD as defined in Eq. 3.24.
Percentage of particles finer than the size D, in the fine-fraction, Nf, is given by:
Nf = W W
D s
× 100 ...(Eq. 3.25)
Substituting for WD from Eq. (3.24), Nf = W
W V V
p
s p