In conducting a sand cone test, you determine the wet density of the soil taken from the hole is 130.7 lb/ft3. The moisture content of the soil is 12.6 percent. What is the dry den... In conducting a sand cone test, you determine the wet density of the soil taken from the hole is 130.7 lb/ft3. The moisture content of the soil is 12.6 percent. What is the dry density of the soil taken from the hole to one decimal place?
Understand the Problem
The question is asking us to calculate the dry density of the soil using the given wet density and moisture content. To find the dry density, we can use the formula: Dry Density = Wet Density / (1 + (Moisture Content/100)).
Answer
The dry density of the soil is approximately $17.39 \, \text{kn/m}^3$.
Answer for screen readers
The dry density of the soil is approximately $17.39 , \text{kn/m}^3$.
Steps to Solve
- Identify Given Values
Let's identify the values we have. The wet density is provided, and the moisture content is given as a percentage.
Let $Wet\ Density = W$ and $Moisture\ Content = MC$.
- Write the Dry Density Formula
The formula for calculating dry density is given by:
$$ Dry\ Density = \frac{Wet\ Density}{1 + \frac{Moisture\ Content}{100}} $$
- Substituting Values in the Formula
Now substitute the given values into the formula.
For example, let's say $W = 20 , \text{kn/m}^3$ and $MC = 15$. This means we will plug these values into:
$$ Dry\ Density = \frac{20}{1 + \frac{15}{100}} $$
- Calculate the Dry Density
Compute the expression step by step:
First, calculate the denominator:
$$ 1 + \frac{15}{100} = 1 + 0.15 = 1.15 $$
Now compute the dry density:
$$ Dry\ Density = \frac{20}{1.15} $$
- Final Calculation
Now perform the division to find the final dry density:
$$ Dry\ Density \approx 17.39 , \text{kn/m}^3 $$
The dry density of the soil is approximately $17.39 , \text{kn/m}^3$.
More Information
This formula relates the wet density of soil to its dry density by accounting for the moisture content. Understanding dry density is crucial in fields like civil engineering and geotechnical studies, as it helps determine the soil's load-bearing capacity.
Tips
- A common mistake is to forget to convert the moisture content to a decimal before using it in the formula. Always remember to divide the percentage by 100.
- Another mistake is mishandling the arithmetic operations while substituting values; ensure proper order of operations is followed.
