Closed-form solution for predicting tensile strength and fracture toughness of ultra-high-performance concrete

As a popular cementitious material in civil engineering in recent years, ultra-high-performance concrete (UHPC) has been used in harsh working conditions for its superior mechanical properties and durability. However, cracking in UHPC is a significant threat to its durability. Thus, studying the fracture properties of UHPC for rational design of crack resistance is important. The aim of this study was to develop closed-form solutions of the size-independent tensile strength (ft) and fracture toughness (KIC) of UHPC. Three-point-bending tests were performed on 80 UHPC beams with different depths and initial crack lengths; the fracture behaviour was comprehensively analysed and a predictive model was proposed to determine ft and KIC. A characteristic microstructure parameter (Cch) and two discrete coefficients (beta and C) were introduced to indicate material heterogeneity and discontinuity, respectively. Cch was determined as the average fibre spacing in this study. These coefficients also quantified the critical effective crack propagation length at the maximum fracture load (Fmax) and the characteristic crack length defined by the bulk toughness and strength properties. A linear rela-tionship of Fmax with respect to ft and KIC was established; the size-independent ft and KIC were obtained after determining Fmax from three-point-bending tests. The effects of Cch, beta, and C on the predicted ft and KIC values were analysed. Although bothft and KIC exhibited certain differences as Cch, beta and C were simultaneously varied, the results were within the upper and lower limits of the ft and KIC values predicted by statistical analysis.