A Statistical Damage Constitutive Model Based on the Weibull Distribution for Alkali-Resistant Glass Fiber Reinforced Concrete

The addition of alkali-resistant glass fiber to concrete effectively suppresses the damage evolution such as microcrack initiation, expansion, and nucleation and inhibits the development and penetration of microcracks, which is very important for the long-term stability and safety of concrete structures. We conducted indoor flat tensile tests to determine the occurrence and development of cracks in alkali-resistant glass fiber reinforced concrete (AR-GFRC). The composite material theory and Krajcinovic vector damage theory were used to correct the quantitative expressions of the fiber discontinuity and the elastic modulus of the concrete. The Weibull distribution function was used and an equation describing the damage evolution of the AR-GFRC was derived. The constitutive equation was validated using numerical parameter calculations based on the elastic modulus, the fiber content, and a performance test of polypropylene fiber. The results showed that the tensile strength and peak strength of the specimen were highest at a concrete fiber content of 1%. The changes in the macroscopic stress–strain curve of the AR-GFRC were determined and characterized by the model. The results of this study provide theoretical support and reference data to ensure safety and reliability for practical concrete engineering.