Build a relationship between dry unit density, percentage of air voids and moisture content. Define any constants involved.

The relationship between dry unit density (γd), percentage of air voids (n), and moisture content (w) can be established through the concept of soil mechanics.

1. Dry Unit Density (γd): It is the mass of solids per unit volume, excluding the volume of water and air voids. It is usually expressed in kN/m³ or lb/ft³.

2. Percentage of Air Voids (n): It is the volume of air voids in a soil sample expressed as a percentage of the total volume. It is dimensionless and expressed as a percentage (%).

3. Moisture Content (w): It is the ratio of the weight of water to the weight of solids in a soil sample. It is also dimensionless and usually expressed as a percentage (%).

The relationship between these three parameters can be expressed through the equation of dry density:

γd = Gs * w * γw / (1 + e)

Where:

• Gs is the specific gravity of soil solids, which is a constant that depends on the type of soil and typically ranges from 2.6 to 2.8 for most soils.
• γw is the unit weight of water, which is a constant equal to 9.81 kN/m³ or 62.4 lb/ft³.
• e is the void ratio, which is the ratio of the volume of voids (air and water) to the volume of solids in a soil sample. It can be related to the percentage of air voids (n) through the equation:

e = Vv / Vs = n / (100 - n)

By substitifying the value of e in the dry density equation, we can establish a relationship between dry unit density, percentage of air voids, and moisture content.

Please note that this relationship assumes that the soil is fully saturated, i.e., all voids are filled with water. If the soil is not fully saturated, the relationship becomes more complex as it also depends on the degree of saturation.