The **fineness modulus** of a fine aggregate is defined as an index number that indicates the average or mean size of the sand particles. It is determined by carrying out the sieve analysis test using standard IS sieves. The fineness modulus is an estimate of the amount of aggregate required to proportion mix designs; it is not a precise measurement.

The term “fine aggregate” refers to a soil that can pass through a 4.75mm sieve. The following sieve sizes are required to determine the fineness modulus of fine aggregate: 4.75mm, 2.36mm, 1.18mm, 0.6mm, 0.3mm, and 0.15mm. To determine the fineness modulus, the cumulative percentages of aggregates retained on all sets of sieves that range from 4.75 mm to 150 microns (0.15mm) are added, and the resulting sum is divided by 100. A finer aggregate has a lower fineness modulus than a coarse aggregate.

## Classification of Sand

Sand is categorized according to the size of the grain as

a) Fine Sand – size ranges between 75 microns or 0.075mm to 425 microns or 0.425mm. Masonry and plastering mortar are the two main applications of fine sand.

b) Medium Sand – 0.425mm to 2mm. Concrete primarily uses medium sand.

c) Coarse Sand – 2mm to 4.75mm. Filler materials include coarse sand.

In terms of strength, coarse sand is the strongest, accompanied by medium sand, and fine sand is the weakest. Medium-coarse sand can be used for wall masonry projects, fine sand is used for short-term projects, and coarse sand is used mostly for reinforced concrete structures. Additionally, coarse sand is appropriate for high-volume concrete, medium sand is appropriate for touching ash or paving bricks, and fine sand is appropriate for slip joints.

The fineness modulus of various types of sand is given below.

Type of Sand | Fineness Modulus |

Fine Sand | 2.2 – 2.6 |

Medium Sand | 2.6 – 2.9 |

Coarse Sand | 2.9 – 3.2 |

Sand with a fineness modulus greater than 3.2 is generally not used to make good concrete.

## Assessment of Fineness Modulus of Sand

Sieve analysis as per IS 2083 Part 4 is typically used to determine the fineness modulus of both coarse and fine aggregates. The IS code for the determination of the fineness modulus of fine aggregate is IS 383 – 1970.

## Procedure

- Weigh the aggregate sample to get an exact 1kg sample. (Be sure to dry all aggregates in an oven at 110°C before measuring.) Note down the weight as W1.
- If there are lumps in particles, break them up with your hands or a mortar and pestle.
- Weigh each empty sieve, then note its gram weight.
- Dust each sieve in preparation for testing. And arrange them all in a hierarchy (highest at the top and smallest at the bottom) according to size. This is done to collect the sieved samples from the top sieve.
- Place the sample (W1) in the upper-most sieve, then secure the lid and pack the sieve stacker.
- For 10 to 15 minutes, start the mechanical sieve shaker. And after the rotating period, turn it off.
- Unpack all of the sieves and weigh each one separately, to determine the weight of aggregates that will be retained on each sieve.
- Subtract the empty weight of each sieve to determine the weight of the material that was retained on that sieve.
- Analyze all of the readings. Make sure the total amount of material retained is equal to the weight of the sample that was taken.
- And at last, calculate the cumulative percentage of material retained on each sieve.

## Calculation of Fineness Modulus of Sand

Cumulative percentage of weight retained = (cumulative weight of retained sample / weight of sample) x 100

Percentage of weight passing = (100 – Cumulative percentage of weight retained)

Total sum of the cumulative percentage retained divided by 100 is the fineness modulus of aggregates

For instance, let’s assume that 4500g of coarse aggregate is the dry weight. Following sieve analysis, the results are tabulated below.

Size of the sieve | Weight retained (g) | Cumulative weight retained (g) | Cumulative percentage weight retained (%) |

4.75mm | 0 | 0 | 0 |

2.36mm | 250 | 250 | 5.56 |

1.18mm | 600 | 850 | 18.89 |

0.06mm | 1250 | 2100 | 46.67 |

0.03mm | 1690 | 3790 | 84.22 |

0.015mm | 710 | 4500 | 100 |

Total | – | – | 255.34 |

Fineness modulus = cumulative percentage retained / 100 = 255.34 / 100 = 2.55

The value 2.55 means the mean size of particles of given sample is in between 2nd and 3rd sieve. (300 microns to 600 microns). It is fine sand.

## Grading Limits for Fine Aggregates (As per IS 383 – 1970)

## Geotechnical Significance of Fineness Modulus

- The modulus of fineness is typically used to determine the aggregate’s coarseness or fineness. When the fineness modulus value is higher, the aggregate is coarser, and when it is lower, the aggregate is finer.
- Concrete contractors can accurately predict how much water they will require to mix the concrete by using the fineness modulus.
- Lower values typically produces more paste, which makes finishing the concrete easier.
- Additionally, it accurately describes the workability of the concrete, which is determined by the slump value. The compressive strength and density of the finished concrete are both fundamentally governed by the modulus of fineness.
- fineness modulus can be used when describing the gradation and coarseness of sand particles. The sand from zone II is ideal for the preparation of concrete; if zone I sand is chosen, the sand proportion should be improved and the quantity of cement should be adequate to fulfill the workability of concrete; and if zone III sand is is used, the sand ratio should be properly lowered to ensure the strength of concrete.

**What is Fineness Modulus?**

It is an index number that indicates the average or mean size of the sand particles.

**Why is it necessary to calculate sand’s fineness modulus?**

It is typically used to determine the aggregate’s coarseness or fineness. Also, it describes the workability of the concrete.

**How is the fineness modulus of sand determined?**

Total sum of the cumulative percentage retained on sieves (4.75mm, 2.36mm, 1.18mm, 0.6mm, 0.3mm, and 0.15mm) divided by 100 gives the fineness modulus of aggregates

**What is the range of the fineness modulus for the three types of sand: fine, coarse, and medium?**

For Fine Sand, the value ranges in between 2.2 – 2.6

For Medium Sand, the value ranges in between 2.6 – 2.9

For Coarse Sand, the value ranges in between 2.9 – 3.2