RELATIVE DENSITY OF SOIL

1. Objective
Porosity of a soil depends on the shape of grain, uniformity of grain size and condition of sedimentation.
Hence porosity itself does not indicate whether a soil is in loose or dense state. This information can
only be obtained by comparing the porosity or void ratio of the given soil with that of the same soil in
its loosest and densest possible state and hence the term, relative density is introduced.

Relative density is the measure of compactness of cohesionless soil. Relative density or density index is
the ratio of the difference between the void ratios of a cohesionless soil in its loosest state and existing
natural state to the difference between its void ratio in the loosest and densest states.

Determination of relative density is helpful in evaluating compaction state of coarse grained soils and
also assessing the safe bearing capacity in case of sandy soils.

Relative Density = (emax - e)/ (emax - emin)

Where,

emax = void ratio of coarse grained soil (cohesionless) in its loosest state.
emin = void ratio of coarse grained soil (cohesionless) in its densest state.
e = void ratio of coarse grained soil (cohesionless) in its natural existing state in the field.

We have,

e =VV/VS
Yd = G YW/(1+e)

Therefore,

e = {G YW/Yd} - 1

So, "e" is inversely proportional to "Yd"

2. Apparatus Required

Fig. 1: Relative Density Apparatus

The Apparatus consists of (a) Cushioned steel vibrating deck 75X75 cm size,
R.P.M : 3600 ; under a net mass of over 45 kg. (b) Two cylindrical metallic
moulds, 3000 cc and 15000 cc conforming to requirements given in IS : 10837-
1984. (c) 10 mm thick surcharge base plate with handle separately for each
mould. (d) Surcharge weights, one for each size having a weight equal to 140 gms
/ sq.cm. conforming to requirements given in IS : 10837-1984. (e) Guide sleeves
with clamps for each mould separately. (f) Calibration bar 75X300X3 mm.
Fig. 2: Mixing Pan

Suitable size are 60 x 90 cm and 10 cm deep and 40 x 40 cm and 5 cm deep.

Fig. 3: Weighing Scale

Portable platform scale, 100 kg capacity with sensitivity of 20 g in accordance with

IS:1435-l960.
3. Reference
IS 2720(Part 14):1983 Methods of test for soils: Determination of density Index (Relative Density) of
Cohesionless Soil (First revision). Reaffirmed- Dec 2015.

4. Procedure

Calibration of mould

a. Measure inside diameter of mould at different depths using a bore gauge and take the average.
b. Keep the mould on a flat surface or flat plate. Measure the height at different positions and take the
average (accuracy = 0.025 mm). Calculate the volume. Volume of the 3000 cm3 mould should be
calculated to the nearest 3 cm3 and that of 15000 cm3 mould to the nearest 30 cm3.
c. Alternatively, fill the mould with distilled water till over flowing takes place. Slide thick glass plate
over the top surface of mould. Weigh the water filling the mould.
d. Note the temperature of water. Obtain density of water for the above temperature from physical
tables.
e. Calculate the volume of the mould which is weight of water filling the mould /density of water.

Preparation of the Sample

A representative sample of soil should be selected. The mass of soil sample to be taken depends
upon the maximum size of particle in the soil as given in Table 1.

Maximum Mass of Pouring Device to Size of

size of Soil be used in Test for Mould
the soil Sample the determination to be
particle required of minimum used
(mm) (kg) density (cm3)
Shovel or extra large
75 45 15000
Scoop
37.5 12 Scoop 3000
19.0 12 Scoop 3000
Pouring Device (25
9.50 12 3000
mm dia Spout)
Pouring Device (12
4.75 12 3000
mm dia Spout)

Table 1 : Mass of the Soil Sample to be taken for the Test

The soil sample should be dried in an oven at a temperature of 105 to 110°C. The soil sample should be
pulverized without breaking the individual soil particles and sieved through the requited sieve.

Minimum Density

The pouring device and mould should be selected according to the maximum size of particle as
indicated in Table 1. The mould should be weighed and the mass recorded. Oven-dry soils should be
used.

Soil containing particles smaller than 9.50 mm should be placed as loosely as possible in the mould by
pouring the soil through the spout in a steady stream. The spout should be adjusted so that the height
of free fall of the soil is always 25 mm. While pouring the soil, the pouring device should be moved in a
spiral motion from the outside towards the centre to form a soil layer of uniform thickness without
segregation. The mould should be filled approximately 25 mm above the top and levelled with top by
making one continuous pass with the steel straight edge. If all excess matter is not removed, an
additional continuous pass should be made. Great care shall be exercised to avoid jarring the mould
during the entire pouring and trimming operation. The mould and the soil should be weighed and the
mass recorded.

Soil containing particles larger than 9.50 mm should be placed by means of a large scoop (or shovel)
held as close as possible to and just above the soil surface to cause the material to slide rather than fall
into the previously placed soil. If necessary, large particles may be held by hand to prevent them from
rolling off the scoop. The mould should be filled to overflowing but not more than 25 mm above the top.
The surface of the soil should be levelled with the top of the mould using the steel straightedge (and
 the fingers, if necessary) in such a way that any slight projections of the larger particles above the top
of the mould shall approximately balance the larger voids in the surface below the top of the mould.
The mould and the soil should be weighed and the mass recorded.

Volume of mould, V, cc

Mass of dry soil, MS, g

(Yd)min = MS/V (g/cc)

emax = {G YW/(Yd)min}-1

Maximum Density

The guide sleeve should be assembled on top of the mould and the clamp assemblies tightened so that
the inner surfaces of the walls of the mould and the sleeve are in line. The lock nuts on the two set
screws equipped with them should be tightened. The third clamp should be loosened, the guide sleeve
removed, the empty mould weighed and its mass recorded.

The mould should then be filled with the thoroughly mixed ovendry soil by the procedure explained in
Para 2 and Para 3 above. The mould filled for the determination of minimum density may also be used
for this test.

The guide sleeves should be attached to the mould and the surcharge base plate should be placed on
the soil surface. The surcharge weight should then be lowered on the base-plate using the hoist in the
case of the 15000 cm3 mould.

The mould should be fixed to the vibrator deck for assembly. The vibrator control should be set at
maximum amplitude and the loaded soil specimen should be vibrated for 8 minutes.

The surcharge weight and guide sleeves should be removed from the mould. The dial gauge readings
on two opposite sides of the surcharge base plate should be obtained and the average recorded. The
mould with the soil should be weighed and its mass recorded.

Volume of mould, V, cc

Mass of dry soil, MS, g

(Yd)max = MS/V (g/cc)

emin = {G YW/ (Yd)max}-1

Natural Density

Weigh the mould with dry soil. Knowing the volume of the mould and weight of dry soil natural density,
Yd, can be calculated.

e = {GYW/Yd}-1

Relative Density = {(emax - e)/ (emax - emin)} X 100

5. Video
Relative Density of Soil