Understanding Soil Saturation Calculation This problem requires determining the state of a soil sample based on its given properties: void ratio, water content, and specific gravity.

Given Soil Properties

• Void ratio ($e$) = 1.3
• Water content ($w$) = 50%, which is equal to 0.50 in decimal form
• Specific gravity of soil solids ($G_s$) = 2.60

Calculating Degree of Saturation

The degree of saturation ($S$) represents the ratio of the volume of water to the volume of voids in the soil. It indicates how much of the void space is filled with water. The relationship between water content ($w$), specific gravity ($G_s$), void ratio ($e$), and degree of saturation ($S$) is a fundamental concept in soil mechanics, given by the formula:

$w \cdot G_s = S \cdot e$

To find the degree of saturation ($S$), we rearrange this formula:

$S = \frac{w \cdot G_s}{e}$

Now, let's substitute the given values into the formula:

$S = \frac{0.50 \times 2.60}{1.3}$

First, calculate the product in the numerator:

$0.50 \times 2.60 = 1.30$

Next, divide this result by the void ratio:

$S = \frac{1.30}{1.3}$

$S = 1$

Determining the Soil State

The calculated degree of saturation ($S$) is 1. Let's understand what this value signifies:

• When $S = 1$ (or 100%), the soil is fully saturated. This means all the available void space within the soil mass is completely filled with water.
• When $0 \le S < 1$, the soil is partially saturated. The voids contain both air and water.
• The term "over saturation" usually implies $S > 1$, which is not physically possible for a soil sample under normal conditions.
• "Under saturation" is synonymous with partial saturation ($S < 1$).

Since our calculation yields $S = 1$, the soil sample is in a state of full saturation. This matches the second option provided.