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**What Is Fineness Modulus of Sand?**

Fineness modulus of sand (fine aggregate) is an index number which represents the mean size of the particles in sand. 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 fineness modulus.

Fine aggregate means the aggregate which passes through 4.75mm sieve. To find the fineness modulus of fine aggregate we need sieve sizes of 4.75mm, 2.36mm, 1.18mm, 0.6mm, 0.3mm and 0.15mm. Fineness modulus of finer aggregate is lower than fineness modulus of coarse aggregate.

**Determination of Fineness Modulus of Sand**

To determine the fineness modulus, we need standard sieves, mechanical sieve shaker (optional), dry oven and digital weight scale.

**Sample preparation**

Take a sample of fine aggregate in pan and placed it in dry oven at a temperature of 100 – 110^{o}C. After drying take the sample and note down its weight.

**Test Procedure – Fineness Modulus of Sand**

Take the sieves and arrange them in descending order with the largest sieve on top. If mechanical shaker is using then put the ordered sieves in position and pour the sample in the top sieve and then close it with sieve plate. Then switch on the machine and shaking of sieves should be done at least 5 minutes.

If shaking is done by the hands then pour the sample in the top sieve and close it then hold the top two sieves and shake it inwards and outwards, vertically and horizontally. After some time shake the 3^{rd} and 4^{th} sieves and finally last sieves.

After sieving, record the sample weights retained on each sieve. Then find the cumulative weight retained. Finally determine the cumulative percentage retained on each sieves. Add the all cumulative percentage values and divide with 100 then we will get the value of fineness modulus.

**Calculation of Fineness Modulus of Sand**

Let us say the dry weight of sample = 1000gm

After sieve analysis the values appeared are tabulated below.

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

4.75mm | 0 | 0 | 0 |

2.36mm | 100 | 100 | 10 |

1.18mm | 250 | 350 | 35 |

0.6mm | 350 | 700 | 70 |

0.3mm | 200 | 900 | 90 |

0.15mm | 100 | 1000 | 100 |

Total |
275 |

Therefore, fineness modulus of aggregate = (cumulative % retained) / 100 = (275/100) = **2.75**

Fineness modulus of fine aggregate is 2.75. It means the average value of aggregate is in between the 2^{nd} sieve and 3^{rd} sieve. It means the average aggregate size is in between 0.3mm to 0.6mm as shown in below figure.

**Values of Fineness Modulus of Sand**

Fineness modulus of fine aggregate varies from 2.0 to 3.5mm. Fine aggregate having fineness modulus more than 3.2 should not considered as fine aggregate. Various values of fineness modulus for different sands are detailed below.

Type of sand |
Fineness modulus range |

Fine sand | 2.2 – 2.6 |

Medium sand | 2.6 – 2.9 |

Coarse sand | 2.9 – 3.2 |

**Fineness modulus limits for various zones of sand according to IS 383-1970 are tabulated below.**

Sieve size |
Zone-1 |
Zone-2 |
Zone-3 |
Zone-4 |

10mm | 100 | 100 | 100 | 100 |

4.75mm | 90-100 | 90-100 | 90-100 | 95-100 |

2.36mm | 60-95 | 75-100 | 85-100 | 95-100 |

1.18mm | 30-70 | 55-90 | 75-100 | 90-100 |

0.6mm | 15-34 | 35-59 | 60-79 | 80-100 |

0.3mm | 5-20 | 8-30 | 12-40 | 15-50 |

0.15mm | 0-10 | 0-10 | 0-10 | 0-15 |

Fineness modulus | 4.0-2.71 | 3.37-2.1 | 2.78-1.71 | 2.25-1.35 |

**Read More: Fineness Modulus of Coarse Aggregates and its Calculation**