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Relative density is defined as the ratio of difference of void ratios of cohesionless soil in its loosest state and the natural state (emax – e) to the difference between void ratio in its loosest and densest state (emax – emin). Relative density determines the compactness of the cohesionless soil.

The determination of relative density by the laboratory method is explained in this article.

## Relative Density Formula

The relative density (Id) is given by the formula:

Where,

emax = void ratio of cohesionless soil at its loosest state

emin = void ratio of cohesionless soil at its densest state

e= void ratio of cohesionless soil at its natural state

Mostly, the compaction state of coarse grain soils is evaluated by determining the relative density. This is also used to assess the safe bearing capacity of sandy soils.

If the dry density of the soil at its loosest, densest and natural state is known, the relative density (Id) is given by the relation:

## Test to determine the Relative Density of Soil

The test procedure is based on IS 2720(Part 14): 1983; Determination of relative density or density index of cohesionless soil. Fig.1. Relative Density Test Apparatus; Image Courtesy: www.humboldtmfg.com

### Apparatus

The apparatus consists of:

1. Cushioned steel Vibrating Table
2. Cylindrical Metallic molds
3. Guide Sleeves
4. Dial Indicator Gauge
5. Surcharge Base-plate
6. Surcharge weights
7. Weighing Balance
8. Scoop
9. Straight Edge

### Procedure

#### 1. Sample Preparation

The maximum size of the soil particle present in the soil determines the representative sample of the soil. This can be obtained from the table-1 below. The soil finally taken must be dried in an oven at a temperature between 105 to 110 degree Celsius.

Table.1. Mass of the soil sample to be taken for the test

#### 2. Test Procedure

The test procedure involves the determination of minimum, maximum dry densities and bulk density of the soil.

Determination of Minimum dry density

1. The soil prepared is loosely poured into the mold using a scoop or a pouring device.
2. The excess soil is trimmed off with a straight edge.
3. The masses of mold + soil (W1) and mold (W2) alone are determined.

Volume of the mold = V

Mass of dry soil = Ms = W1-W2

Hence, Min. dry density and Minimum void ratio (emin) are given by:

Determination of Maximum Dry Density

1. The empty mold is weighed (W). After which the collar is placed on its top and clamped.
2. The mold is filled with the oven-dry sample until one-third of the collar.
3. The arrangement is placed over a vibrating deck. It is fixed to the table with nuts and bolts.
4. Over the mold, a surcharge weight is placed and the vibrator is turned on for 8 minutes.
5. After 8 minutes, the mold with soil is again weighed (W2)

Mass of dry soil = (W2-W) = Ms

Then, Maximum dry density and Maximum void ratio are given by:

Determination of Natural Density

The natural dry density is calculated by using the volume of the mold ‘V’ and the weight of dry soil.

Knowing e, emax and emin, relative density is determined by the formula: