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 provided wet density and moisture content. We will use the formula: Dry Density = Wet Density / (1 + moisture content in decimal form).
Answer
$$ \rho_d = \frac{\rho_w}{1 + \frac{M}{100}} $$
Answer for screen readers
$$ \rho_d = \frac{\rho_w}{1 + m} $$
Steps to Solve
- Convert Moisture Content to Decimal Form
To calculate the dry density, first convert the moisture content percentage into decimal form. This is done by dividing the percentage by 100.
If the moisture content is given as $M%$, then the decimal form $m$ is:
$$ m = \frac{M}{100} $$
- Apply the Dry Density Formula
Next, substitute the wet density ($\rho_w$) and the decimal moisture content ($m$) into the dry density formula:
$$ \rho_d = \frac{\rho_w}{1 + m} $$
Where:
- $\rho_d$ is the dry density,
- $\rho_w$ is the wet density,
- $m$ is the moisture content in decimal form.
- Calculate the Dry Density
Finally, perform the calculation by inputting the values of wet density and the converted moisture content into the formula from the previous step.
$$ \rho_d = \frac{\rho_w}{1 + m} $$
More Information
The dry density of soil helps in understanding the compaction properties and is essential in construction and geotechnical engineering. It reflects how much solid matter is present in soil without moisture, which can influence the stability of structures built on the soil.
Tips
- Forgetting to convert the moisture content percentage to decimal form before using it in the formula.
- Confusing wet density and dry density, which could lead to incorrect calculations.
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