Calculating Water Content of Saturated Sand

This problem asks us to find the water content of a saturated sand sample using its given properties: dry unit weight, specific gravity of solids, and the unit weight of water. Understanding the relationships between these soil parameters is key to solving this problem.

Given Soil Properties

• Dry unit weight, $\gamma_d = 18 \text{ kN/m}^3$
• Specific gravity of soil solids, $G_s = 2.65$
• Unit weight of water, $\gamma_w = 9.81 \text{ kN/m}^3$
• The soil sample is saturated, which means the degree of saturation, $S = 1$.

Required Parameter

We need to determine the water content, $w$, of the saturated sand sample.

Relevant Soil Mechanics Formulae

We will use the following standard relationships from soil mechanics:

• The dry unit weight ($\gamma_d$) is related to the specific gravity of solids ($G_s$), void ratio ($e$), and unit weight of water ($\gamma_w$) by the formula:
  $\gamma_d = \frac{G_s \gamma_w}{1+e}$
• The relationship between void ratio ($e$), water content ($w$), specific gravity of solids ($G_s$), and degree of saturation ($S$) is:
  $eS = wG_s$

Step-by-Step Calculation

Step 1: Find the void ratio ($e$)

We can rearrange the first formula to solve for the void ratio ($e$):

Substitute the given values:

The void ratio of the saturated sand sample is approximately 0.4448.

Step 2: Find the water content ($w$)

Now we use the second formula, $eS = wG_s$. Since the soil is saturated, $S=1$. So, the formula becomes:

We can rearrange this to solve for the water content ($w$):

Substitute the calculated void ratio ($e \approx 0.4448$) and the given specific gravity ($G_s = 2.65$):

Resulting Water Content

The calculated water content is approximately 0.1678. Comparing this value to the given options, 0.166 is the closest value.