In a sieve analysis of soil, the total weight of soil taken was 500 g. The mass of soil retained over 4.75 mm sieve was 100 g, mass retained over 2 mm sieve was 150 g, and the mass retained over 425 -micron sieve was 200 g. The effective size of the soil will be:

Explanation:

Sieve Analysis of Soil

• Sieve analysis is a laboratory procedure used to determine the particle size distribution of soil by passing the soil through a set of sieves with progressively smaller openings.
• The effective size (D₁₀) of soil is the diameter of the particle below which 10% of the soil's particles by weight are finer.

Calculation:

Given Data

• Total weight of soil taken: 500 g
• Mass of soil retained over 4.75 mm sieve: 100 g
• Mass of soil retained over 2 mm sieve: 150 g
• Mass of soil retained over 425-micron sieve: 200 g

First, we need to determine the cumulative percentage of soil passing each sieve. The total mass retained and the mass passing through each sieve are calculated as follows:

• Mass retained over 4.75 mm sieve: 100 g
• Mass passing 4.75 mm sieve = 500 g - 100 g = 400 g
• Cumulative percentage passing 4.75 mm sieve = (400 g / 500 g) ×100% = 80%
• Mass retained over 2 mm sieve: 150 g
• Mass passing 2 mm sieve = 400 g - 150 g = 250 g
• Cumulative percentage passing 2 mm sieve = (250 g / 500 g) ×100% = 50%
• Mass retained over 425-micron sieve: 200 g
• Mass passing 425-micron sieve = 250 g - 200 g = 50 g
• Cumulative percentage passing 425-micron sieve = (50 g / 500 g) ×100% = 10%

The effective size (D₁₀) is the diameter of the particle below which 10% of the soil's particles by weight are finer. From the calculations above, we can see that 10% of the soil's particles by weight are finer than the 425-micron sieve.