Calculation of Mass of Water Required for Full Saturation of Soil

Given:

• Porosity of soil = 40%


• Specific gravity of soil (G) = 2.65


• Water content of soil = 12%


• Volume of soil = 100 m³

Assumptions:

• The soil is completely dry


• There is no air in the soil

Step 1: Calculation of Void Ratio


The void ratio (e) can be calculated using the following formula:

e = porosity / (1 - porosity)

Substituting the given values, we get:

e = 0.40 / (1 - 0.40)
e = 0.67

Step 2: Calculation of Water Content in Saturated Soil


The water content in saturated soil can be calculated using the following formula:

Ws = (G / (1 + e)) x Wd

Where,
Ws = water content in saturated soil
Wd = water content of soil

Substituting the given values, we get:

Ws = (2.65 / (1 + 0.67)) x 0.12
Ws = 0.083 or 8.3%

Step 3: Calculation of Mass of Water Required for Full Saturation


The mass of water required for full saturation can be calculated using the following formula:

M = V x (Ws - Wd)

Where,
M = mass of water required for full saturation
V = volume of soil

Substituting the given values, we get:

M = 100 x (0.083 - 0.12)
M = -3.7 m³

Since the result is negative, it means that we need to remove 3.7 m³ of water from the soil to achieve full saturation.

Explanation:


Porosity is the volume fraction of voids in the soil. In this case, the porosity is given as 40%. The void ratio is the ratio of the volume of voids to the volume of solids in the soil. The void ratio is calculated using the given porosity. The specific gravity of the soil is given as 2.65. The water content of the soil is given as 12%. Using the specific gravity and the void ratio, the water content in saturated soil is calculated. Finally, using the volume of soil and the difference in water content between saturated soil and the given soil, the mass of water required for full saturation is calculated. In this case, the result is negative, which means that water needs to be removed from the soil to achieve full saturation.

6