Sometimes it may happen that the total available on the site does not correspond to the desired grading. In such a case two or more aggregates from different sources may be combined to obtain the required grading.

The fineness modulus value can be used as a technical method for mixing coarse aggregates with fine aggregates to produce the desired grading. Follow the steps shown below to blend the aggregate using the fineness modulus value.

Table of Contents

**A Step-by-Step Guide to Blending Sets Using Fineness Modulus Values**

**step 1 (precisely calculate the fineness modulus of the aggregate)**

- Filter out fine aggregates using a sieve ranging from 80 mm to 150 µm.
- Calculate the cumulative percentage of aggregate retained on each sieve.
- Add up all values of percentage retained on each sieve.
- Divide the amount calculated as above by 100. It precisely gives the fineness modulus value of the set. Let it be
**F**,_{1}

**step 2 (Calculate the fineness modulus of coarse aggregate)**

- Filter the coarse aggregates using a sieve ranging from 80 mm to 150 µm.
- Calculate the cumulative percentage of aggregate retained on each sieve.
- Add up all values of percentage retained on each sieve.
- Divide the amount calculated as above by 100. It precisely gives the fineness modulus value of the set. Let it be
**F**,_{2}

**step 3 (Calculate the fineness modulus of the combined aggregate)**

- Now from the specified grading requirement, calculate the fineness modulus value of the composite aggregate.
- If the specified grading range is given in the passing percentage, then subtract each percentage of the passing value from 100. This will give you the percentage of retention on each sieve.
- Add up all values of percentage retained on each sieve.
- Divide the amount calculated as above by 100. It precisely gives the fineness modulus value of the set. Let it be
**F**,

**step 4 (Calculating the ratio of fine gross and coarse total)**

- Let it happen “
**x**is the percentage of fine aggregates mixed with coarse aggregates.**x**The calculation can be done using the formula given below.

** x = [(F _{2}-F)/(F-F_{1})]*100**

Where,

**F _{1}** = fineness modulus value of the fine aggregate

**F _{2}** = fineness modulus value of coarse aggregate

**F** = fineness modulus value of the composite aggregate

After finding the percentage of fine aggregates to be mixed with coarse aggregates by the above formula, their ratio can be calculated.

**worked example**

**Calculation of Fineness Modulus Value of Fine Aggregate (F.)**_{1},

_{1},

Sieve Size(mm) |
Weight Maintained (g) |
Cumulative Weight Maintained (g) |
Cumulative Percentage of Weight Retained (%) |

80 | 0 | 0 | 0 |

40 | 0 | 0 | 0 |

20 | 0 | 0 | 0 |

10 | 0 | 0 | 0 |

4.75 | 10 | 10 | 2 |

2.36 | 50 | 60 | 12 |

1.18 | 50 | 110 | 22 |

0.600 | 95 | 205 | 41 |

0.300 | 175 | 380 | 76 |

0.150 | 85 | 465 | 93 |

< 0.150 | 35 | 500 | |

Total | 500 grams | total = 246 |

So the fineness modulus value of the fine aggregate (**F _{1}**) = 246/100 = 2.46

**Calculation of fineness modulus value of coarse aggregate (F**_{2},

_{2},

Sieve Size(mm) |
Weight Retained (kg) |
Cumulative Weight Maintained (kg) |
Cumulative Percentage of Weight Retained (%) |

80 | 0 | 0 | 0 |

40 | 0 | 0 | 0 |

20 | 6 | 6 | 40 |

10 | 5 | 1 1 | 73.3 |

4.75 | 4 | 15 | 100 |

2.36 | , | 100 | |

1.18 | , | 100 | |

0.600 | , | 100 | |

0.300 | , | 100 | |

0.150 | , | 100 | |

< 0.150 | , | 100 | |

Total | 15 kg | total = 713.3 |

Then the fineness modulus value of the coarse aggregate (**F _{2}**) = 713.3/100 = 7.133

**Calculation of Fineness Modulus Value of Combined Aggregate (F)**

Sieve Size(mm) |
Pass percentage (%) |
Percentage of Retained (%) |

80 | 100 | 0 |

40 | 100 | 0 |

20 | 98 | 2 |

10 | 61 | 39 |

4.75 | 42 | 58 |

2.36 | 35 | 65 |

1.18 | 28 | 72 |

0.600 | 22 | 78 |

0.300 | 5 | 95 |

0.150 | 0 | 100 |

< 0.150 | 0 | |

total = 509 |

Then the fineness modulus value of the combined aggregate (**F**) = 509/100 = 5.09

**Calculating the ratio of fine aggregate to coarse aggregate**

Percentage of fine aggregates to be mixed with coarse aggregates, (ie **x**) Is

, [(7.133-5.09)/(5.09-2.46)]*100

= (2.04/2.63)*100

= 77%

This means that for every 100 kg of coarse aggregate, we need to add 77 kg of fine aggregate to obtain the specified grading of the composite aggregate.

Click here to learn more about the fineness modulus of aggregates.

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