Abstract: An analytical method which merely needs the axial compressive strength f_c of concrete to calculate the unstable toughness K^un_Ic of double-K fracture model is proposed in this paper. Massive experimental data indicate that the ratio of critical crack propagation length Δa_c to ligament length (h-a₀) tends to be a constant. According to this regularity and on the basis of the bilinear constitutive relationship of the fictitious crack model, the maximum load P_max of three-point bending notched beam is calculated under equilibrium condition. Then the calculated result of P_max is substituted to the formula and the unstable toughness K^un_Ic of double-K fracture model is calculated. The calculated results of P_max and K^un_Ic are compared with those of test values to verify the accuracy of the method. Results conclude that the calculated results of P_max and K^un_Ic agree well with test values for relatively big size concrete specimens with maximum aggregate size not greater than 40 mm. The maximum load P _max and the unstable toughness K^un_Ic can be predicted by the proposed analytical method.

Key words: concrete, maximum load, unstable toughness, fracture mechanics, analytical calculation, bilinear constitutive relationship, double-K fracture model