The dry unit weight of soil is a fundamental property used in geotechnical engineering to represent the weight of solid soil particles per unit volume, excluding the weight of water. It indicates the density of the soil's solid phase within a given volume, offering insights into its compaction state and potential behavior.
To calculate the dry unit weight of soil, you typically use a standard formula that relates the soil's properties.
Standard Formula for Dry Unit Weight
The standard formula to calculate the dry unit weight (γd) of soil is:
γ d = G s ⋅ γ w / ( 1 + e )
This formula is widely used in soil mechanics and directly relates the dry unit weight to the specific gravity of soil solids, the unit weight of water, and the void ratio of the soil.
Understanding the Variables
Let's break down the terms in the formula:
- γd: This is the dry unit weight of the soil (the value you are calculating). It is typically expressed in units of force per unit volume, such as kN/m³ or lb/ft³.
- Gs: This represents the specific gravity of soil particles. It is the ratio of the density of the soil solids to the density of water at a standard temperature (usually 4°C). It is a dimensionless value, typically ranging from 2.6 to 2.8 for most mineral soils.
- γw: This is the unit weight of water. This value varies slightly with temperature, but a standard value is often used for calculations. As mentioned in the reference, a typical value is 9.81 kN/m³. Other common values include 62.4 lb/ft³.
- e: This is the void ratio of the soil. The void ratio is defined as the ratio of the volume of voids (empty spaces) in the soil to the volume of soil solids. It is also a dimensionless value.
How to Use the Formula
To calculate the dry unit weight using the formula, you need to know or determine the values for Gs, γw, and e for the specific soil you are analyzing.
- Determine Gs: The specific gravity of soil particles (Gs) is typically determined through laboratory testing.
- Determine γw: Use the appropriate unit weight of water (γw) for your calculations. The standard value of 9.81 kN/m³ is commonly used unless specified otherwise.
- Determine e: The void ratio (e) can be determined from other soil properties, such as water content, degree of saturation, specific gravity, and moist unit weight, or through direct measurement methods.
Once you have these values, simply plug them into the formula γ d = G s ⋅ γ w / ( 1 + e ) to calculate the dry unit weight (γd).
Example Calculation
Let's consider a simple example:
| Variable | Value | Units |
|---|---|---|
| Gs | 2.70 | Dimensionless |
| γw | 9.81 | kN/m³ |
| e | 0.65 | Dimensionless |
Using the formula:
γd = (2.70 ⋅ 9.81 kN/m³) / (1 + 0.65)
γd = (26.487 kN/m³) / (1.65)
γd ≈ 16.05 kN/m³
So, the dry unit weight of this soil sample would be approximately 16.05 kN/m³.
Alternative Calculation Methods
While the formula involving specific gravity and void ratio is fundamental, the dry unit weight can also be calculated using other soil properties, depending on the available data. For example:
- From moist unit weight (γ) and water content (w): γd = γ / (1 + w)
- From void ratio (e), water content (w), and specific gravity (Gs): γd = γw ⋅ Gs / (1 + e) (This is the same as the primary formula)
- From moist unit weight (γ) and degree of saturation (S): γd = γ / (1 + w), where w = (S * e) / Gs
However, the core relationship γ d = G s ⋅ γ w / ( 1 + e ) is a cornerstone for understanding how the composition and structure of the soil solids and voids contribute to its dry unit weight.
Calculating the dry unit weight is essential for many geotechnical analyses, including determining bearing capacity, settlement, and compaction requirements.
