Calculating the saturated unit weight of a material, particularly in soil mechanics, involves determining the weight per unit volume when the material's void spaces are completely filled with water. This is a crucial parameter for various engineering calculations.
The exact answer to calculating saturated weight (more accurately referred to as saturated unit weight) is derived from the formula:
γ sat = γ d ⋅ ( 1 + e ) ⋅ sr
However, for a truly saturated condition, the degree of saturation (sr) is always 1 (or 100%). Therefore, the formula simplifies to:
γ sat = γ d ⋅ ( 1 + e )
Understanding Saturated Unit Weight
Saturated unit weight (γ sat) represents the weight of a soil mass, including the weight of the soil solids and the water filling all the pore spaces, divided by the total volume of the soil. It's a fundamental property used in designing foundations, retaining walls, and analyzing slope stability.
The Core Formula for Saturated Unit Weight
The formula provided for calculating saturated unit weight is:
γ sat = γ d ⋅ ( 1 + e ) ⋅ sr
Where:
- γ sat is the saturated unit weight.
- γ d is the dry unit weight.
- e is the void ratio.
- sr is the degree of saturation.
As explicitly stated, for a state of full saturation, the degree of saturation (sr) is equal to 1. This means the formula essentially becomes:
γ sat = γ d ⋅ ( 1 + e )
Key Components of the Formula
Understanding each variable is essential for accurate calculation:
| Symbol | Description |
|---|---|
| γ sat | Saturated Unit Weight: The weight of the soil when all voids are filled with water, per unit of total volume. This is the value you are calculating. |
| γ d | Dry Unit Weight: The weight of only the solid particles of the soil per unit of total volume when the soil is completely dry (i.e., no water in the voids). This value is usually determined by laboratory tests. |
| e | Void Ratio: The ratio of the volume of voids (empty spaces or spaces filled with water/air) to the volume of solid particles in a soil mass. It's a dimensionless quantity that indicates how much space is available between soil particles. |
| sr | Degree of Saturation: The ratio of the volume of water to the total volume of voids in a soil. It is expressed as a decimal or percentage. For saturated conditions, sr = 1 (or 100%), meaning all voids are completely filled with water. In partially saturated soils, sr would be between 0 and 1. For dry soil, sr = 0. |
Practical Application and Example
To calculate the saturated unit weight, you typically need to know the dry unit weight and the void ratio of the soil. Once these are determined (often through laboratory tests), you can directly apply the simplified formula.
For example, if a soil sample has a dry unit weight (γ d) and a void ratio (e), and we assume it is completely saturated (sr = 1), its saturated unit weight can be directly computed. As per a practical scenario, if a given soil is completely saturated, its saturated unit weight could be, for instance, 26.4 kN/m³. This value is derived by applying the formula with specific dry unit weight and void ratio values.
Importance in Geotechnical Engineering
Calculating saturated unit weight is critical for:
- Foundation Design: Ensuring foundations can withstand the loads from saturated soils.
- Slope Stability Analysis: Understanding how water content affects the stability of slopes, especially during rainfall.
- Retaining Wall Design: Designing walls that can resist the increased lateral pressures from saturated backfill soils.
- Earthwork Volume Calculations: Estimating the weight of soil to be moved or compacted in wet conditions.
