Damage Model of Steel Fiber-Reinforced Coal Gangue Concrete under Freeze-Thaw Cycles Based on Weibull Distribution

In order to improve the utilization rate of coal gangue and expand the application range of coal gangue concrete (CGC), a certain proportion of steel fiber was added to the concrete, and the freeze-thaw cycles (FTCs) and flexural tests were used to explore the effects of different mass replacement rates of coal gangue (0%, 25%, 50%, 75%, and 100%) and different proportions of the volumetric blending of the steel fiber (0%, 0.8%, 1.0%, and 1.2%) on the frost resistance of steel fiber-reinforced CGC (SCGC). The governing laws of mass loss rate, relative dynamic elastic modulus and load-midspan deflection curve were obtained on the base of the analysis of testing results. The damage mechanisms of the SCGC under the FTCs were analyzed using the results of scanning electron microscopy (SEM). Based on the Lemaitre's strain equivalence principle and Krajcinovic's vector damage theory, a damage evolution model of the SCGC under the FTCs was established by introducing the damage variable of the SCGC satisfying Weibull distribution. The results show an increasing mass loss rate of the SCGC and a decreasing relative dynamic elastic modulus with an increasing mass replacement rate of coal gangue. The proper content of the steel fiber can reduce the mass loss rate of concrete by 10 similar to 40% and the relative loss rate of dynamic elastic modulus of concrete by 2 similar to 8%, thus significantly improving the ductility and toughness of the concrete. The established damage evolution model is well validated by the experimental results, which further help to improve the modelling accuracy. This study provides key experimental data and a theoretical basis for a wider range of proper utilization of coal gangue in cold regions.