Relative density test as per IS-2720 part-14 | Geotechnical Engineering

Relative density test as per IS-2720

Theory:

Relative density, sometimes referred as a density index, is an important concept of soil mechanics relating it particularly to cohesionless soils such as sand. Indeed, it throws an insight into the compactness of the soil by a comparison of the void ratio of soil in its natural state with its loosest and densest states. The void ratio is a measure of the empty space, or voids, in a sample of soil relative to the solid particles. Though porosity can be an indication of the amount of voids present, it does not directly communicate whether that soil is loose or dense. That is where relative density comes into play. 

The formula for relative density (Dr) is as follows:

Where:

• $e_{\text{max}}$ is the void ratio of the soil in its loosest state.
• $e_{\text{min}}$ is the void ratio of the soil in its densest state.
• $e$ is the void ratio of the soil in its natural state.

Void Ratio and Dry Density:

The void ratio (e) can be calculated using the following relationship between dry density ($\gamma_d$) and the specific gravity of the soil solids (Gs):

This shows that the void ratio is inversely proportional to the dry density of the soil. The denser the soil, the lower its void ratio.

Need and Scope

There are many practical engineering scenarios in which one needs to find the relative density. Relative density helps assess how compact or loose sandy soils are, so it is very important for understanding their behavior under loads. It's particularly useful in the context of:

• Compaction of cohesionless soils: Knowledge about relative density is a guide for determining the extent to which a particular soil is to be compacted.
• The bearing capacity is evaluated. Relative density values for sandy soils in foundation engineering will help to find the safe bearing capacity for the stabilization of structures.
• If the relative density is greater than one, which is typically found for very dense gravelly sand, then this only means that it is denser than at its theoretical densest state.

Apparatus Required

1. Cushioned steel vibrating deck (75x75 cm), 3600 RPM under a 115 kg load, electrical supply.
2. Cylindrical metallic mold (3000 cc capacity).
3. 10 mm thick surcharge base plate with a handle.
4. Surcharge weights (140 gm/cm²).
5. Guide sleeves with clamps.
6. Funnel.
7. Vernier caliper.
8. Stopwatch.

Sample Preparation

1. Dry the soil sample in an electric oven.
2. Cool the sample to room temperature.
3. Segregate soil lumps without breaking individual particles and sieve through the required sieve size.

Procedure

Minimum Density:

1. Measure the internal diameter and height of the mold at multiple points using a vernier caliper and take the average.
2. Calculate the volume of the mold (V).
3. Weigh the empty mold (W).
4. Pour the dry soil into the mold through a funnel, ensuring a steady fall height of 25 mm with a spiral motion.
5. Level the soil with the top of the mold using a straightedge.
6. Weigh the mold with the soil (W1).
7. Calculate the dry density:
   

      8. Calculate the void ratio in the loosest state: 

Maximum Density:

1. Place the collar on the mold and clamp it securely.
2. Place the mold on the vibrating deck.
3. Fill the mold with oven-dried soil to about 2/3 of the collar’s height.
4. Place the surcharge base plate and weight on top of the soil.
5. Run the vibrator for 8 minutes at 3600 RPM.
6. Weigh the mold filled with the soil (W2).
7. Calculate the dry density:

          8.  Calculate the void ratio in the densest state:

Final Calculation of Relative Density

After determining the values of $e_{\text{max}}$, $e_{\text{min}}$, and $e$ (the natural void ratio), the relative density can be calculated using:

$$\text{Relative Density (Dr)}=\frac{e_{\text{max}}-e}{e_{\text{max}}-e_{\text{min<span style="font-family: Cambria; font-size: large;"></span>}}}$$

This value provides a numerical understanding of how dense the soil is compared to its loosest and densest states, which is essential for various geotechnical applications.