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 Delta a(fic) at notch-tip in concrete specimens at peak load P-max due to heterogeneous aggregate structures. The variation in Delta a(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 Delta a(fic.) The peak loads P-max with 95% reliability are reliably predicted for notched concrete specimens.