Based on the fictitious crack model an analytical model for predicting the effective fracture toughness of concrete for three-point bending notched beams is proposed.The model is applied to calculate the maximum affordable load,critical equivalent crack length and the equivalent fracture toughness K~s-(ⅠC) of the beam.On this basis,the size effect is investigated by calculating the K~s-(ⅠC) and pre-critical crack propagation length Δa-c using the proposed model.The results show that both K~s-(ⅠC) and Δa-c i...