A new fracture toughness calculation method for cementitious materials in the three-point bending test based on the transverse force

The traditional calculation method for the fracture toughness of cementitious materials by the three-point bending test is based on the empirical formula of concrete specimens. There may be some errors in the fracture toughness calculation of cement paste and mortar when the traditional method is applied. In this research, a new fracture toughness calculation method based on transverse force and effective crack model was proposed to calculate the effective crack length of cement paste and mortar, and the fracture toughness was calculated based on experimental data rather than empirical formula. In the new calculation method, the peak point of the transverse force curve can well determine the crack initiation point of the specimen. Based on the three test parameters of crack opening displacement, vertical load, and vertical displacement, the effective crack length and unstable fracture toughness of different specimens can be calculated. The results show that the lower the water-cement ratio and the higher the sand volume fraction, the higher the unstable fracture toughness of the cement paste and mortar. The destabilization point and the crack initiation point of the cement paste are very close, while the two points of the mortar are more distinguishable from each other. The unstable fracture toughness obtained by the new calculation method are slightly lower than those obtained by the empirical calculation method. However, the deviation between the two calculation methods becomes smaller with the increase of the aggregate volume fraction. It can be predicted that if the aggregate volume fraction is high enough, the results calculated by the two methods tends to be consistent.