An empty container weights W1 container with soil sample weights W2, container and oven dried sand weights W3. The Moisture Content of soil is ___________.
Soil Moisture Content Calculation
The moisture content of a soil sample is a fundamental property in geotechnical engineering. It represents the amount of water present in the soil relative to the weight of the dry soil particles. The formula for moisture content ($w$) is expressed as:
$$ w = \frac{W_w}{W_s} \times 100\% $$
Where:
- $W_w$ is the weight of water
- $W_s$ is the weight of solid particles (dry soil)
Understanding the Weights Given
We are provided with three different weights related to the soil sample and the container:
- $W_1$: Weight of the empty container.
- $W_2$: Weight of the container plus the wet soil sample.
- $W_3$: Weight of the container plus the oven-dried soil sample.
Calculating Weight of Water ($W_w$)
The weight of water in the soil sample is the difference between the weight of the wet soil and the weight of the dry soil. Since the container weight is included in both $W_2$ and $W_3$, subtracting $W_3$ from $W_2$ directly gives us the weight of water:
Weight of wet soil + container = $W_2$
Weight of dry soil + container = $W_3$
Weight of water ($W_w$) = (Weight of wet soil + container) - (Weight of dry soil + container)
$$ W_w = W_2 - W_3 $$
Calculating Weight of Dry Soil ($W_s$)
The weight of the dry soil particles is the difference between the weight of the container with dry soil and the weight of the empty container:
Weight of dry soil + container = $W_3$
Weight of empty container = $W_1$
Weight of dry soil ($W_s$) = (Weight of dry soil + container) - (Weight of empty container)
$$ W_s = W_3 - W_1 $$
Determining Moisture Content
Now we can substitute the expressions for $W_w$ and $W_s$ into the moisture content formula:
$$ w = \frac{W_w}{W_s} \times 100\% $$
$$ w = \frac{W_2 - W_3}{W_3 - W_1} \times 100\% $$
This formula gives the moisture content as a percentage based on the given weights.
Comparing with Options
Let's compare the derived formula with the provided options:
| Option | Formula | Match? |
|---|---|---|
| 1 | $\frac{W_2 - W_3}{W_2 - W_1} \times 100$ | No (Denominator is wet soil weight) |
| 2 | $\frac{W_2 - W_3}{W_3 - W_1} \times 100$ | Yes |
| 3 | $\frac{W_2 - W_3}{W_1 - W_2} \times 100$ | No (Denominator is negative) |
| 4 | $\frac{W_1 - W_2}{W_2 - W_3} \times 100$ | No (Numerator is negative) |
The derived formula matches Option 2.
Important Questions from Index Properties
Casagrande’s apparatus is used to determine _______.
In oven drying method, the soil sample is kept in the oven for about ________ hours.
In consistency of soil, the limits are expressed in terms of ______.
- Known the soil properties: e - void ratio, n - porosity, w - water content, G - specific gravity, S - degree of saturation, γ sat - Saturated unit weight of soil; and γ w - unit weight of water. From among the following relations, identify the relation that is INCORRECT.
What will be the correct relationship among the void ratio (e), degree of saturation (S), water content (w) and specific gravity of soil solids (G) of a soil sample?
