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Fineness Modulus (FM) Test for Sand
Objective:
The Fineness Modulus (FM) test aims to determine the average particle size of a given fine aggregate (sand) sample. The FM is a single number representing the average size of the particles in the aggregate sample. It is an index number that provides an indication of the fineness or coarseness of the sand.

Importance:
The Fineness Modulus is an important factor in determining the proportioning of sand in the concrete mix design. It affects the workability, strength, and durability of concrete.

Apparatus:
Set of Sieves: Standard sieves with different mesh sizes, typically ranging from 4.75 mm (No. 4) to 0.075 mm (No. 200).
Balance: Accurate to 0.1% of the sample weight.
Drying Oven: Capable of maintaining a temperature of 110 ± 5°C.
Mechanical Shaker: For consistent sieving.
Procedure:
Sample Preparation:

Obtain a representative sample of the sand.
Dry the sample in the oven at 110 ± 5°C to a constant weight and cool to room temperature.
Weighing:

Weigh the sample accurately.
Sieving:

Arrange the sieves in descending order of size.
Place the sample in the top sieve.
Shake the sieves for a specified period using the mechanical shaker.
Separation:

After sieving, weigh the material retained on each sieve.
Calculations:

Calculate the cumulative weight retained on each sieve.
Express this cumulative weight as a percentage of the total sample weight.
Sum the cumulative percentages retained on the standard sieves (typically 4.75 mm, 2.36 mm, 1.18 mm, 0.6 mm, 0.3 mm, and 0.15 mm).
Divide the sum by 100 to obtain the Fineness Modulus (FM).
Formula:
FM
=
The sum of cumulative percentages retained on standard sieves
100
FM=
100
The sum of cumulative percentages retained on standard sieves
​


Example Calculation:
Assume the cumulative percentages retained on the standard sieves are as follows:

No. 4 (4.75 mm): 5%
No. 8 (2.36 mm): 20%
No. 16 (1.18 mm): 45%
No. 30 (0.6 mm): 70%
No. 50 (0.3 mm): 90%
No. 100 (0.15 mm): 95%
Sum of cumulative percentages = 5 + 20 + 45 + 70 + 90 + 95 = 325

FM = 325 / 100 = 3.25

Interpretation:
A lower FM value (e.g., 2.2 - 2.6) indicates finer sand.
A higher FM value (e.g., 3.0 - 3.5) indicates coarser sand.
Standards and References:
ASTM C136: Standard Test Method for Sieve Analysis of Fine and Coarse Aggregates.
ASTM C33: Standard Specification for Concrete Aggregates.
By performing the FM test, engineers can better understand the sand's grading and particle size distribution, which helps optimize the mix design and achieve the desired properties in the final concrete product.