Could you please show me how to solve this problem ! The unit weight of a soil is 122 lb/ft^3 at a water content of 12.6%. The specific gravity of the soil is 2.72. Find dry unit weight,porosity,and degree of saturation.
To solve this problem, we will use the formulas for dry unit weight, porosity, and degree of saturation.
1. Dry Unit Weight (γ_d):
The dry unit weight is the weight of the soil solids per unit volume of soil. It is calculated using the following formula:
γ_d = γ - γ_w
where γ is the unit weight of the soil and γ_w is the unit weight of water.
To find the dry unit weight, we need to know the unit weight of water. The unit weight of water is approximately 62.4 lb/ft^3.
Substituting the given values:
γ = 122 lb/ft^3
γ_w = 62.4 lb/ft^3
Now we can calculate the dry unit weight:
γ_d = 122 lb/ft^3 - 62.4 lb/ft^3 = 59.6 lb/ft^3
Therefore, the dry unit weight is 59.6 lb/ft^3.
2. Porosity (n):
Porosity is a measure of the void spaces or air spaces in a soil sample. It is calculated using the following formula:
n = (γ - γ_d) / γ
where γ is the unit weight of the soil and γ_d is the dry unit weight.
Substituting the given values:
γ = 122 lb/ft^3
γ_d = 59.6 lb/ft^3
Now we can calculate the porosity:
n = (122 lb/ft^3 - 59.6 lb/ft^3) / 122 lb/ft^3 ≈ 0.512
Therefore, the porosity is approximately 0.512.
3. Degree of Saturation (S):
The degree of saturation is a measure of how much of the pore space in a soil is filled with water. It is calculated using the following formula:
S = (V_w / V_v) × 100
where V_w is the volume of water and V_v is the volume of voids.
To find the degree of saturation, we need to know the volume of water and the volume of voids.
To find the volume of water, we need to know the water content and the unit weight of water. The water content is given as 12.6% and the unit weight of water is 62.4 lb/ft^3.
Substituting the given values:
Water content = 12.6% = 0.126 (decimal)
Unit weight of water (γ_w) = 62.4 lb/ft^3
Now we can calculate the volume of water:
V_w = (Water content / γ_w) × 100
V_w = (0.126 / 62.4) × 100 ≈ 0.202 ft^3
To find the volume of voids, we can subtract the volume of solids from the total volume:
Since the specific gravity (G_s) is given as 2.72, we can calculate the volume of solids from the volume of soil using the following formula:
V_s = (1 / G_s) × V
Substituting the given values:
Specific gravity (G_s) = 2.72
Volume (V) = 1 ft^3
Now we can calculate the volume of solids:
V_s = (1 / 2.72) × 1 ≈ 0.368 ft^3
Now we can calculate the volume of voids:
V_v = V - V_s = 1 ft^3 - 0.368 ft^3 ≈ 0.632 ft^3
Finally, we can calculate the degree of saturation:
S = (0.202 ft^3 / 0.632 ft^3) × 100 ≈ 31.96%
Therefore, the degree of saturation is approximately 31.96%.
In summary:
- Dry unit weight: 59.6 lb/ft^3
- Porosity: approximately 0.512
- Degree of saturation: approximately 31.96%