A stochastic model considering heterogeneity and crack propagation in concrete: Fid-Bau Portal

A stochastic model considering heterogeneity and crack propagation in concrete

Zeng, Ming-Hui / Wu, Zhi-Min / Wang, Yan-Jie

Highlights • A stochastic numerical model is proposed for crack propagation in concrete. • The heterogeneity of concrete including the randomness of crack initiation is considered in the numerical model. • The validity of the numerical model is verified with experimental results.

Abstract The heterogeneity of concrete results in the uncertainties of its fracture properties which usually affect the actual load bearing capacity and reliability of concrete structures. However, in existing studies of the heterogeneity of concrete, little research has been reported that considers the randomness of crack initiation. The current study presents a stochastic model for predicting the crack growth process of concrete by introducing a mixed-mode $I - II$ crack propagation criterion with initial fracture toughness. Some routine tests are conducted to determine the statistical parameters of the presented model. The effects of the heterogeneity of the concrete on the load versus crack mouth opening displacement (P-CMOD) curve, the fracture process zone (FPZ) length LFPZ and the crack growth trajectory are studied. It is found that compared with the P-CMOD curve based on the homogeneous model, the predicted results based on the stochastic model show obviously discrete changes that reasonably display the discreteness of concrete, and this is more scientific and accurate for describing the actual performance of concrete. During the crack propagation, the heterogeneity of the concrete has little influence on $L_{FPZ}$ before $L_{FPZ}$ reaches a maximum, and thereafter $L_{FPZ}$ is greatly affected by the heterogeneity of the concrete. In comparison with the crack growth trajectory predicted by the homogeneous model, the tortuous trajectories based on the stochastic model are more realistic and show reasonable agreement with the experimental observations obtained from the literature. Additionally, the envelope of these paths can be obtained. The analysis of the values of the predicted peak load $P_{max}$ of the stochastic model statistically indicates that they follow the normal distribution, which can be used for the reliability analysis of concrete structures.