The fracture behaviors of quasi-brittle materials are commonly specimen size (size effect) and crack size (boundary effect) dependent. In this study, a new failure model is developed for characterizing the size and boundary effects. The derivative of the energy release rate is firstly introduced to predict the nominal strength dominated by the strength mechanism. Combined with the energy criterion for the energy mechanism, an asymptotic model is developed to capture the effect of any crack size on the nominal strength, and its expression for geometrically similar specimens is also established, which is able to characterize the size effect. Detailed comparisons of the proposed model with the size effect law and the boundary effect model are performed, respectively. The nominal strength predictions based on the proposed model are validated with the experimental results of cracked three-point bending beam specimens made of concrete, of limestone and of hardened cement paste and compared with the model predictions given by the size effect law and the boundary effect model.

Due to the complex structure and stress distribution of dam galleries, cracks often appear during the construction, operation and maintenance periods of dams. This paper proposes a method to determine the real strength and fracture parameters of gallery concrete, considering environmental temperature and humidity. The strength and fracture tests were carried out for gallery concrete at various ages and under different curing temperature and humidity conditions. The influence of curing conditions on the mechanical properties of gallery concrete was quantitatively analyzed. The prediction equations of the strength and fracture parameters of gallery concrete under arbitrary temperature and humidity were established. Based on the measured temperature and humidity data, the real mechanical parameters of gallery concrete were predicted. The research results show that the influence of environmental conditions on mechanical parameters cannot be neglected, as this can result in a strength reduction of up to 33.81%. The proposed equations can be used to predict the mechanical parameters of gallery concrete, subject to real environmental conditions, which can help to correct a maximum deviation of 54.62% on parameters calculated using actual ages. The proposed method can provide a scientific basis for the cracking risk analysis and safety assessment of the gallery structure under actual conditions.