## What is Fineness Modulus of Coarse Aggregates?

Fineness modulus of coarse aggregates represents the average size of the particles in the coarse aggregate by an index number. It is calculated by performing sieve analysis with standard sieves.

The cumulative percentage retained on each sieve is added and subtracted by 100 gives the value of fine aggregate. Higher the aggregate size higher the Fineness modulus hence fineness modulus of coarse aggregate is higher than fine aggregate.

Coarse aggregate means the aggregate which is retained on 4.75mm sieve when it is sieved through 4.75mm. To find fineness modulus of coarse aggregate we need sieve sizes of 80mm, 40mm, 20mm, 10mm, 4.75mm, 2.36mm, 1.18mm, 0.6mm, 0.3mm and 0.15mm.

Fineness modulus is the number at which the average size of particle is known when we counted from lower order sieve size to higher order sieve. So, in the calculation of coarse aggregate we need all sizes of sieves.

## Determination of Fineness Modulus of Coarse Aggregates

To find fineness modulus we need to perform sieve analysis and for that above mentioned sieve sizes, mechanical shaker and digital weigh scale are required.

**Sample preparation**

Take a sample of coarse aggregate in pan and placed it in dry oven at a temperature of 100 – 110^{o}C. After drying take the sample weight to nearest gram.

### Test Procedure for Fineness Modulus of Coarse Aggregates Calculation

Arrange the sieves in descending order and put the arrangement on mechanical shaker. It is suggested that, to know the exact value of fineness modulus for coarse aggregate, mechanical shaker will give better value than hand shaking because of more no. of sieves and heavy size particles.

After proper sieving, record the sample weights retained on each sieve and find out the cumulative weight of retained particles as well as cumulative % retained on each sieve. Finally add all cumulative percentage values and divide the result with 100. Then we get the value of fineness modulus.

### Example for Fineness Modulus of Coarse Aggregates Calculation

Let us say dry weight of coarse aggregate = 5000g

Sieve size | Weight retained(g) | Cumulative weight retained (g) | Cumulative % retained (g) |

80mm | 0 | 0 | 0 |

40mm | 250 | 250 | 5 |

20mm | 1750 | 2000 | 40 |

10mm | 1600 | 3600 | 72 |

4.75mm | 1400 | 5000 | 100 |

2.36mm | 0 | 5000 | 100 |

1.18mm | 0 | 5000 | 100 |

0.6mm | 0 | 5000 | 100 |

0.3mm | 0 | 5000 | 100 |

0.15mm | 0 | 5000 | 100 |

Sum | = | 717 |

Therefore, **fineness modulus of coarse aggregates** = sum (cumulative % retained) / 100 = (717/100) = **7.17**

Fineness modulus of 7.17 means, the average size of particle of given coarse aggregate sample is in between 7^{th} and 8^{th} sieves, that is between 10mm to 20mm.

### Limits of Fineness Modulus for Coarse Aggregates

Fineness modulus of coarse aggregate varies from 5.5 to 8.0. And for all in aggregates or combined aggregates fineness modulus varies from 3.5 to 6.5. Range of fineness modulus for aggregate of different maximum sized aggregates is given below.

Maximum size of coarse aggregate | Fineness modulus range |

20mm | 6.0 – 6.9 |

40mm | 6.9 – 7.5 |

75mm | 7.5 – 8.0 |

150mm | 8.0 – 8.5 |

**Read More: Fineness Modulus of Sand and its Calculation**