Fineness modulus of aggregate

Fineness modulus (FM) is an empirical number obtained by adding the cumulative percentages retained on the standard sieves (80, 40, 20, 10, 4.75, 2.36 and 1.18 mm, and 600, 300 and 150 micron) and dividing by 100. It indicates the mean size of the particles in the aggregate.

$$FM = \frac{\sum \text{cumulative percentage retained}}{100}$$

The 150 micron sieve is the last one included. A larger FM means a coarser aggregate. Typical values: fine aggregate 2.0-3.5 (commonly classed as fine sand 2.2-2.6, medium sand 2.6-2.9 and coarse sand 2.9-3.2), coarse aggregate 5.5-8.0, and all-in aggregate 3.5-6.5.

Impact on concrete

• A higher FM (coarser) means less surface area, so less water and cement paste for a given workability; but too coarse a sand gives harsh, segregation-prone mixes.
• A low FM (fine sand) increases water demand, needs more cement and reduces strength, but gives a cohesive mix.
• In mix design, the FM of the fine aggregate is used to select the coarse aggregate volume (ACI method): sand with a higher FM needs a smaller amount of coarse aggregate.
• FM is used to check the uniformity of supply: a change in FM of more than 0.2 indicates a change in grading and needs an adjustment of the mix.

Example

For a sand, the percentages retained on the 4.75 mm, 2.36 mm, 1.18 mm, 600, 300 and 150 micron sieves are 5, 10, 15, 25, 30 and 12 (cumulative 5, 15, 30, 55, 85, 97). The sum of the cumulative values = 287, so FM = 2.87, which is a medium sand (Zone II). In the ACI table, with 20 mm aggregate this sand (FM 2.87) takes a dry-rodded coarse aggregate volume of about 0.61 per m$^3$ of concrete. A finer sand (FM 2.4) allows more coarse aggregate (0.66), and a coarser sand (FM 3.0) allows less (0.60).