Statistical analysis of concrete fracture using normal distribution pertinent to maximum aggregate size

A normal distribution methodology is proposed by considering variations in fictitious crack growth Δa _fic at notch-tip in concrete specimens at peak load P _max due to heterogeneous aggregate structures. The variation in Δa _fic leads to normal distributions in measured tensile strength f _t and fracture toughness K _IC . These normal distributions with a small standard deviation can be obtained. The quasi-brittle fracture of concretes with maximum aggregate size d _max = 10–40 mm are analyzed with the simple relation between characteristic crack of concrete a _ch ^* and d _max . The statistical analyses are performed using a new closed-form solution of the boundary effect model, which considers the scatters in the peak load P _max of notched specimens due to the variations in fictitious crack growth Δa _fic . The peak loads P _max with 95% reliability are reliably predicted for notched concrete specimens.