TH E HYDROMETER METHO D OF ANALYSIS

SOIL PHASE RELATIONSHIPS, INDEX PROPERTIES AND CLASSIFICATION

Case 4: When the soil is submerged

3.8 TH E HYDROMETER METHO D OF ANALYSIS

The hydromete r metho d wa s originall y propose d i n 192 6 b y Prof . Bouyouco s o f Michiga n Agricultural College , an d late r modifie d b y Casagrand e (1931) . Thi s metho d depend s upo n variations in the densit y of a soi l suspensio n contained in a 100 0 mL graduate d cylinder . The density o f the suspensio n is measured with a hydrometer at determined tim e intervals; then the coarsest diamete r of particles i n suspension at a given time and the percentage of particles fine r than that coarsest (suspended ) diameter are computed. These computations are based o n Stokes' formula whic h is described below .

Stokes' La w

Stokes (1856), an English physicist, proposed an equation for determining th e terminal velocity of a falling sphere in a liquid. If a single sphere is allowed to fall through a liquid of indefinite extent, the terminal velocity, v can be expressed as ,

v=

r

^s

-r

^{w D2}

18// ^ >ZZ;

in which,

distance L v - termina l velocity of fall o f a sphere through a liquid = =_{J F 5 M tlm e f} — Ys = unit weight of solid spher e

Yw = unit weight of liquid H = absolute viscosity of liquid D = diameter of sphere.

From Eq . (3.22) , after substituting for v , we have _ i -"/ - I ^

lta-i)r

^w

V7

⁽³

-

²³⁾

in which ys = Gsyw

If L is in cm, t is in min, y i n g/cm³, \Ji in (g-sec)/cm² and D in mm, the n Eq. (3.23 ) may be written as

D(mm)

or D=

' ^_i

^)7w

V 7

^{= A}

V7

⁽³

-

²⁴⁾

where, K = I ^{30/ /} (3.25 )

by assuming YW ~ lg/cm³

It may b e noted here that the factor K is a function o f temperature T , specific gravity Gs of particles an d viscosit y o f water . Table 3.4 a give s the value s of K fo r th e variou s value s of Gs at different temperature s T. If it is necessary t o calculate D without the use of Table 3.4a we can us e Eq. (3.24) directly. The variation of n with temperature is required which is given in Table 3.4b . Assumptions o f Stoke s La w an d it s Validity

Stokes' law assume s spherica l particle s fallin g in a liquid of infinit e extent , an d al l the particle s have the same unit weight ys- Th e particles reach constant terminal velocity within a few second s after they are allowed to fall.

Since particles are not spherical, the concept of an equivalent diameter ha s been introduced.

A particle is said to have an equivalent diameter Dg, if a sphere of diameter D having the same unit weight as the particle, has the same velocity of fall as the particle. For bulky grains De ~ D, whereas for flaky particles DID = 4 or more.

Soil Phas e Relationships , Index Propertie s and Soil Classification 37 Table 3.4a Value s of /(for us e in Eq. (3.24) fo r severa l specifi c gravity of solid s

and temperature combinations Gs o f Soi l

Temp ° C 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

2.50 0.0151 0.0149 0.0148 0.0145 0.0143 0.0141 0.0140 0.0138 0.0137 0.0135 0.0133 0.0132 0.0130 0.0129 0.0128

Table 3.4b

Temp 4 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

2.55 0.0148 0.0146 0.0144 0.0143 0.0141 0.0139 0.0137 0.0136 0.0134 0.0133 0.0131 0.0130 0.0128 0.0127 0.0126

2.60

0.0146 0.0144 0.0142 0.0140 0.0139 0.0137 0.0135 0.0134 0.0132 0.0131 0.0129 0.0128 0.0126 0.0125 0.0124

2.65 0.0144 0.0142 0.0140 0.0138 0.0137 0.0135 0.0133 0.0132 0.0130 0.0129 0.0127 0.0126 0.0124 0.0123 0.0122

Solids 2.70 0.0141 0.0140 0.0138 0.0136 0.0134 0.0133 0.0131 0.0130 0.0128 0.0127 0.0125 0.0124 0.0123 0.0121 0.0120

Properties of distille d wate r (/ / =

°C Uni t weigh t o f water , 1.00000 0.99897 0.99880 0.99862 0.99844 0.99823 0.99802 0.99780 0.99757 0.99733 0.99708 0.99682 0.99655 0.99627 0.99598 0.99568

g/cm³

2.75 0.0139 0.0138 0.0136 0.0134 0.0133 0.0131 0.0129 0.0128 0.0126 0.0125 0.0124 0.0122 0.0121 0.0120 0.0118

2.80 0.0139 0.0136 0.0134 0.0132 0.0131 0.0129 0.0128 0.0126 0.0125 0.0123 0.0122 0.0120 0.0119 0.0118 0.0117

2.85 0.0136 0.0134 0.0132 0.0131 0.0129 0.0127 0.0126 0.0124 0.0123 0.0122 0.0120 0.0119 0.0117 0.0116 0.0115

absolute viscosity)

Viscosity o f water , pois e 0.01567

0.01111 0.0108 0.0105 0.01030 0.01005 0.00981 0.00958 0.00936 0.00914 0.00894 0.00874 0.00855 0.00836 0.00818 0.00801

The effect of influence of one particle over the other is minimized by limiting the mass of soil for sedimentatio n analysis to 60 g in a sedimentation jar o f 10³ cm³ capacity.

Hydrometer Analysi s

Figure 3. 5 show s a streamline d hydromete r o f th e typ e AST M 15 2 H use d fo r hydromete r analysis. Th e hydromete r possesse s a lon g ste m an d a bulb . Th e hydromete r i s use d fo r th e determination of unit weight of suspensions at different depth s and particular intervals of time. A unit volum e o f soi l suspensio n a t a dept h L an d a t an y tim e / contain s particle s fine r tha n a particular diameter D. The value of this diameter is determined by applying Stokes' law whereas the percentage fine r than this diameter is determined by the use of the hydrometer. The principle of the method i s that the reading of the hydrometer gives the unit weight of the suspension at the center of volume of the hydrometer. The first step in the presentation of this method is to calibrate the hydrometer.

Let the sedimentation jar contain a suspension of volume V with total mass of solids M^s. Let the jar be kept vertically on a table after the solids are thoroughly mixed. The initial density p^;. of the suspension at any depth z from th e surface at time t = 0 may be expressed a s

M M M M

_ _

Pi=~V+ l ~~G^ P»=~V + l~^ (

where po = density of water at 4°C and pw density of water at test temperature T , and Gs = specific gravity of the solids. For all practical purposes p^o = p^w = 1 g/cm³.

After a lapse of time t, a unit volume of suspension at a depth z contains only particles finer than a particular diameter D, since particles coarser than this diameter have fallen a distance greater than z as per Stokes'law. Th e coarsest diameter of the particle in a unit volume of the suspension at depth z and time t is given by Eq. (3.24) where z = L. Let Md b e the mass of all particles finer than D in the sample taken for analysis. Th e density of the suspension p, after an elapse d time t may be expressed a s

M^D

where - = Mas s o f particles o f diameter smalle r tha n diamete r D in the unit volum e of suspension at depth z at an elapsed time t.

From Eq. (3.26b) we may write

" = - T ) P f - (3.26 0

The ASTM 152 H type hydrometer, normally used for the analysis, is calibrated to read from 0 to 60 g of soil in a 100 0 m L soil- water mixture with the limitation that the soil particles hav e a specific gravit y G^s = 2.65. The reading is directly related t o the specific gravity of the suspension.

In Eq. (3.26c ) the mass of the solids MD i n the suspension varies from 0 to 60 grams. The reading R on the stem of the hydrometer (correcte d fo r meniscus) may be expressed a s

(3.^26d) where,

G^s = 2.65, an d V= 100 0 m L

p,= density of suspension per unit volume = specific gravity of the suspension .

Soil Phas e Relationships , Inde x Propertie s an d Soi l Classificatio n 39 From Eq. (3.26d), it is clear that the ASTM 152 H hydrometer is calibrated in such a way that the reading on the stem will be

R = 0 when pf= 1 , and R = 60 when pf= 1.037 4

The ASTM 15 2 H hydrometer gives the distance of any reading R on the stem to the center of volume and is designated a s L as shown in Fig. 3.5. The distance L varies linearly with the reading R. A n expressio n fo r L ma y b e writte n a s follow s fo r an y readin g R fo r th e AST M 15 2 H hydrometer (Fig. 3.5) .

£ = A +Y ( ³-²⁷)

where L^{ = distance fro m readin g R to the top of the bulb

L² = length of hydrometer bulb = 1 4 cm for ASTM 15 2 H hydrometer

When the hydrometer i s inserted int o the suspension, the surface of the suspension rises as shown i n Fig . 3.6. Th e distanc e L in Fig. 3. 6 i s the actua l distanc e throug h whic h a particle o f diameter D has fallen. The point at level Aj a t depth L occupies th e position A² (which coincide s with the center o f volume of the hydrometer) in the figure afte r th e immersion o f the hydrometer and correspondingly the surface of suspension rises from B^l to B². The depth L' is therefore greater than L through which the particle of diameter D has fallen. The effective valu e of L can be obtained from th e equation

T

_Ra

L Meniscu s

60

X

V

Center of bulb

V^h/Aj

V^h/2Aj

Meniscus

L'

Figure 3.5 AST M 15 2 H type hydrometer

Before th e immersion Afte r the immersio n of hydrometer o f hydromete r Figure 3. 6 Immersio n correctio n

Table 3.5 Value s of L (effective depth) fo r

particles for AST M soi luse in Stokes' formul a fo r diameter s o f hydrometer 152 H

Original Origina l

hydrometer hydromete r

reading Effectiv e readin g (corrected fo r dept h L (correcte d fo r meniscus only ) c m meniscu s only )

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

L- L'

16.3 16.1 16.0 15.8 15.6 15.5 15.3 15.2 15.0 14.8 14.7 14.5 14.3 14.2 14.0 13.8 13.7 13.5 13.3 13.2 13.0

V, 1_{h J \ J}

— Li, \ Li~.

2Aj 2

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

y

A;

Original hydrometer

Effective readin g Effectiv e depth L (correcte d fo r dept h L

cm meniscu s only) c m

12.9 12.7 12.5 12.4 12.2 12.0 11.9 11.7 11.5 11.4 11.2 11.1 10.9 10.7 10.5 10.4 10.2 10.1 9.9 9.7 9.6

42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

9.4 9.2 9.1 8.9 8.8 8.6 8.4 8.3 8.1 7.9 7.8 7.6 7.4 7.3 7.1 7.0 6.8 6.6 6.5

(3.28) where V^h = volume of hydrometer (152 H) = 67 cm3; A. = cross-sectional area of the sedimentation cylinder = 27.8 cm2 for 100 0 mL graduated cylinder .

For an ASTM 15 2 H hydrometer, the value of L for any reading R (corrected fo r meniscus) may be obtained from

L = 16.3 -0.1641 R (3.29)

Table 3. 5 give s th e value s o f L fo r variou s hydromete r reading s o f R fo r th e 15 2 H hydrometer.

Determination o f Percen t Fine r

The ASTM 15 2 H hydrometer is calibrated to read from 0 to 60 g of soil in a 1000 m L suspensio n with the limitation that the soil has a specific gravity G = 2.65. The reading is, of course, directly

Soil Phas e Relationships , Inde x Propertie s and Soil Classificatio n 4 1 related t o the specific gravity of the suspension. The hydrometer gives readings pertainin g to the specific gravity of the soil-water suspension at the center of the bulb. Any soil particles large r than those stil l in suspension in the zone shown as L (Fig 3.5) have fallen below the center of volume, and this constantly decreases th e specific gravity of the suspension at the center of volume of the hydrometer. Lesser the specific gravity of the suspension, the deeper the hydromete r will sink into the suspension. It must also be remembered here, that the specific gravity of water decreases as the temperature rises from 4° C. This will also cause the hydrometer to sink deeper into the suspension.

The readings of the hydrometer ar e affected b y the rise i n temperature durin g the test. Th e temperature correctio n i s a constant. The us e of a dispersing agen t als o affect s th e hydromete r reading. Corrections fo r this can be obtained by using a sedimentation cylinde r of water from th e same sourc e an d wit h th e sam e quantit y o f dispersin g agen t a s tha t use d i n th e soil-wate r suspension to obtain a zero correction. This jar of water should be at the same temperature as that of the soil water suspension.

A reading of less than zero in the standard jar of water is recorded a s a (-) correctio n value ; a reading between 0 and 60 is recorded a s a (+) value. All the readings are laken to the top of the meniscus in both the standard jar (clea r water) and soil suspension.

If the temperature during the test is quite high, the density of water will be equally less and hydrometer wil l sin k to o deep . On e ca n us e a temperatur e correctio n fo r th e soil-wate r suspension. Table 3.6 gives the values of temperature correlation Cr The zero correction Co can be (±) and the temperature correction als o has (±) sign .

The actual hydrometer reading Ra has to be corrected a s follows 1. correctio n fo r meniscus Cm only for us e in Eq. (3.24 )

2. zer o correction Co and temperature correctio n C^rfor obtaining percent finer . Reading for use in Eq. (3.24 )

R = Ra+Cm (3.30a )

Reading for obtaining percent fine r

Rc=Ra-Co+CT (3.30b )

Percent Fine r

The 15 2 H hydrometer i s calibrated fo r a suspension with a specific gravity of solids G^s = 2.65. If the specific gravity of solids used in the suspension is different fro m 2.65, th e percent finer has to be corrected by the factor C expresse d a s

Table 3.6 Temperatur e correctio n factor s C^T Temp ° C

15 16 17 18 19 20 21 22

CT

-1.10 -0.90 -0.70 -0.50 -0.30 0.00 +0.20 +0.40

Temp ° C 23 24 25 26 27 28 29 30

CT +0.70 + 1.00 +1.30 + 1.65 +2.00 +2.50 +3.05 +3.80

1.65G

C = i —

58 2.65(G ? -1) (3.31)

Typical values of C^? ar e given in Table 3.7 .

Now the percent fine r wit h the correction factor C^s ma y be expressed a s Percent finer, P ' =

M xlOO (3.32)

where R c = gram s o f soi l i n suspensio n a t som e elapse d tim e t [correcte d hydromete r reading from Eq. (3.30b) ]

Ms = mas s o f soil use d i n the suspensio n in gms (no t more tha n 60 gm fo r 15 2 H hydrometer)

Eq. (3.32) gives the percentage of particles finer than a particle diameter D in the mass of soil Ms use d in the suspension. If M i s the mass of soil particles passing through 75 micron siev e (greater tha n M) an d M the total mass taken for the combined siev e and hydrometer analysis , the percent fine r fo r th e entire sample may be expressed a s

Percent finer(combined) , P = P'% x

M (3.33)

Now Eq. (3.33) with Eq. (3.24 ) give s point s for plotting a grain siz e distributio n curve.

Test procedure

The suggeste d procedur e fo r conducting the hydrometer test i s as follows:

1. Tak e 6 0 g or less dry sampl e fro m th e soil passing throug h the No. 200 siev e 2. Mi x thi s sample wit h 12 5 mL of a 4% of NaPO³ solution in a small evaporatin g dis h 3. Allo w the soil mixture to stand for about 1 hour. At the end of the soaking period transfe r

the mixtur e to a dispersion cup an d ad d distilled water until th e cu p i s about two-thirds full. Mi x fo r abou t 2 min.

4. Afte r mixing, transfer all the contents of the dispersion cup to the sedimentation cylinder , being carefu l no t t o los e an y materia l No w ad d temperature-stabilize d wate r t o fil l th e cylinder to the 100 0 m L mark .

5. Mi x th e suspensio n wel l by placin g the palm o f the hand ove r th e ope n en d an d turning the cylinder upside down and back for a period of 1 min. Set the cylinder down on a table.

6. Star t th e time r immediatel y afte r settin g th e cylinder . Inser t th e hydromete r int o th e suspension just abou t 2 0 second s befor e th e elapse d tim e o f 2 min . an d tak e th e firs t reading a t 2 min . Tak e th e temperatur e reading . Remov e th e hydromete r an d th e thermometer an d place bot h of them in the control jar.

7. Th e contro l ja r contain s 100 0 m L o f temperature-stabilize d distille d wate r mixe d wit h 125 mL of the same 4% solution of NaPO³.

Table 3. 7 Correctio n factor s C fo r uni t weight o f solid s G^s of soi l solids

2.85 2.80 2.75 2.70

Correction factor C 0.96 0.97 0.98 0.99

G^s of soi l solids 2.65 2.60 2.55 2.50

Correction factor C 1.00 1.01 1.02 1.04

Soil Phas e Relationships , Inde x Propertie s an d Soil Classificatio n 4 3 8. Th e hydromete r reading s ar e take n a t th e to p leve l o f th e meniscu s i n bot h th e

sedimentation and control jars.

9. Step s 6 through 8 are repeated by taking hydrometer and temperature readings at elapsed times of 4, 8, 16, 30, 60 min. and 2, 4, 8, 16, 32, 64 and 96 hr.

10. Necessar y computation s ca n b e mad e wit h th e dat a collecte d t o obtai n th e grain - distribution curve.