What is the dry density of a soil sample with a total density of 110 pcf and a moisture content of 60%?
The dry density of the soil sample is approximately 68.75 pcf, and the closest answer among the options provided is 70 pcf.
The correct answer is option: (c) 70 pcf.
To find the dry density of the soil sample, we need to consider the relationship between total density (γ_total), dry density (γ_dry), and moisture content (MC):
γ_total = γ_dry x (1 + MC)
Given that the total density (γ_total) is 110 pcf and the moisture content (MC) is 60%, we can rearrange the equation to solve for dry density (γ_dry):
γ_dry = γ_total / (1 + MC)
Substitute the known values:
γ_dry = 110 / (1 + 0.6)
γ_dry = 110 / 1.6
γ_dry ≈ 68.75 pcf
Therefore, the correct answer is closest to option (c) 70 pcf.
Calculation Explanation:
Total Density: The total density of the soil sample is given as 110 pcf. Total density is the combination of the solid particles' density and the void space within the soil mass.
Moisture Content: The soil sample has a moisture content of 60%. Moisture content refers to the amount of water present in the soil sample, expressed as a percentage of the total weight.
Dry Density Calculation:
To calculate the dry density of the soil sample, we utilize the relationship between total density, dry density, and moisture content. The equation states that the total density is equal to the dry density multiplied by (1 + moisture content).
By rearranging the equation and substituting the given values for total density and moisture content, we can solve for the dry density of the soil sample. The result is approximately 68.75 pcf, which is closest to the provided option of 70 pcf.
Therefore, when determining the dry density of a soil sample with known total density and moisture content, it is essential to consider the relationship between these factors to obtain an accurate calculation.