Relationship between fractal dimensions and concrete permeability with experimental validation

Pore structure in concrete is a major factor in water permeability, durability, and strength. Conventional Euclidean approaches fail to characterize the complexity of the cement pore structure. In this research, fractal analysis is used to demonstrate microscopic pore properties and fluid transport in concrete. Two fractal dimensions are introduced: the pore surface area (D f ) and the fractal dimension of the tortuosity of the flow path (D t ), which represent the evolution of the pore structure during hydration. Type II Portland cement concrete was tested for water permeability at 7, 28, and 90 days of curing using a 150 mm side dimension cube specimen and the cylindrical chamber method. Water permeability volumes measured 18.86, 15.82, and 11.97 mL, reflecting a decrease of 16.1 and 24.3% each time. Mercury Intrusion Porosimetry (MIP) analysis of pore structure improved the fractal permeability model. The results show that both D f and D t increase with curing time, indicating more tortuosity and pore surface area.