# High Packing Denisty

Packing theory is the basic method used for developing dense concrete using different sized particles.Proper application of packing theory can control the fresh and hardened properties of concrete because the improved particulate packing leads to more usable water as a lubricant. The Andreasen andAndersen (A&A) model is commonly used to design UHPC with various solid constituents and highfluidity. According to A&A theory, optimal packaging can be achieved when the cumulative particle sizedistribution (PSD) obeys the following equation:

where, P(D) is the fraction that can pass a sieve with opening D; D*max*) is the maximum particle size ofthe mix. The distribution modulus q has a value between 0 and 1. The Andreasen and Andersen modeldoesn’t contain the minimum particle size. To account for that, a modified version of A&A modelsuggested by Funk and Dinger is commonly used

where, D*min* accounts for the minimum particle size in the mix. Andreasen and Andersen found thatoptimum packing is obtained when q = 0.37. However, for mixtures with a high amount of powders(<250 μm), a smaller q value is recommended in the range of 0.22∼0.25.

Figure above: Particle gradation in UHPC matches the ‘ideal’ one