How To Calculate The Volume Of Voids

A void is the volume of space in a material such as sand or gravel not occupied by particles. The volume of voids is made up of tiny gaps between particles of the material. Calculating the volume of voids can be complex, requiring high-tech tools such as measuring lasers.

In other situations, like the one described here, the void calculation is fairly simple. You have to first determine the specific gravity of the material in question. Specific gravity is the ratio of the density of a substance to the density of water (the latter equal to 1 g/ml).

1. Preparing the Test

Fill a 1,000 ml graduated container about half full of water. Weigh the container using a scale calibrated in grams. Record the weight and the exact volume of water in the container.

2. Filling the Voids

Add enough sand to bring the overall level in the container to about 3/4 full. Weigh the container again and record the weight and the volume of material now in the container.

3. Measuring Mass and Volume

Subtract the original weight (water only) from the weight of sand plus water to find the increase in weight. Subtract the original water volume from the volume of sand plus water to find the increase in volume.

4. Calculate Specific Gravity

Divide the increase in weight by the increase in volume to find the specific gravity of the sand. For example, if the weight of sand plus water was 450 g more than of the water alone and the volume increase was 180 ml, you have a specific gravity of 450/180 = 2.5.

5. Prepping to Find Dry Density

Empty and dry the container thoroughly. Weigh the empty container. Fill the container to the 1,000 ml mark with dry sand. Use a straightedge to smooth the surface of the sand so it is level but do not pack the sand down.

6. Calculate Dry Density

Weigh the container of sand and subtract the weight of the empty container to find the weight of the sand. Use the dry density formula (density equals mass divided by volume)

\(D=\frac{m}{V}\)

Divide the weight by the volume (1,000 ml) to find the density of the sand. For example, if the sand weighs 1,500 grams, the density is 1.5.

7. Void Calculation

Subtract the density of the sand from the specific gravity of the sand, then divide the result by the specific gravity to find the voidage (proportion of empty space in the dry sand). For example, with a density for dry sand of 1.5 and a specific gravity of 2.5, you have a voidage of

\(\frac{2.5 – 1.5}{2.5}= 0.4\)

8. Void Volume Calculation

Multiply the voidage by the volume of the dry sand to find the volume of the void. With 1,000 ml of dry sand and a voidage of 0.4, you have a void volume of 400 ml.

Whether working with soils or rocks, the void ratio and porosity difference is important to understand. The void ratio (e) is the ratio of the volume of voids (V_v) to the volume of solids (V_s). Porosity (n), on the other hand, is the ratio of the volume of voids (V_v) to the total volume (V) or volume of the voids plus the volume of the solids (V_v+V_s). The void content formula or void ratio formula would be written as

\(e=\frac{V_v}{V_s}\)

while the porosity formula would be written as

\(n=\frac{V_v}{V}\)

The relationship of void ratio and porosity, expressed mathematically, becomes

\(e=\frac{n}{a-n}\text{ and }n=\frac{e}{1+e}\)