Estimation of the Protected Paste Volume by Spatial Tessellation Associated with the Point Pattern of Air Voids

Paste volumes protected by air voids against frost attacks were estimated using Dirichlet tessellation tiles. Each tile was regarded as an area protected by air voids. The characteristic distance was defined by the largest tile size to reach a cumulative area fraction of 0.95. The significance of this distance was verified by a Monte Carlo test for the simulation of random point patterns. Comparing the characteristic distance and conventional spacing factor, the latter corresponds to the actual distance required for protecting the local region with the highest vulnerability to frost attack. The tessellation model provides the protection characteristic distance without overlaps even in the region of clustered air voids.