Closed-form solutions for fracture resistance of ultra-high-performance concrete matrix under different loading rates

Ultra-high-performance concrete (UHPC) matrix has a dense matrix due to its low water-cement ratio, only fine aggregates, and ultrafine supplementary cementitious materials. These features lead to fracture behavior markedly different from ordinary concrete, warranting systematic study. This study explored the fracture behavior of UHPC matrix under varying loading rates (v) of 0.02, 0.2, 2, 20, 200 mm/min by three-point bending tests conducted on beams with diverse depths (h) of 50, 100, 150 mm and initial crack length-to-depth ratios (a₀/h) of 0.2, 0.3, 0.4. Two discrete coefficients (β and C) and a characteristic microstructural parameter (C_ch) were introduced to describe material discontinuities and heterogeneity. The parameter C_ch was defined as the average hole diameter within the matrix, representing a deviation from its conventional definition in ordinary concrete (OC). By using C_ch, β and C, a prediction model was formulated to evaluate the size-independent tensile strength (f_t) and fracture toughness (K_IC) of the UHPC matrix under dynamic loading conditions. The results indicated that as v increased from 0.02 to 200 mm/min, f_t and K_IC increased by 1.5 %, 13.9 %, 17.9 %, and 25.9 %, respectively. Moreover, the predicted f_t and K_IC at different loading rates were independent of h and a₀/h for the specimens tested in this study. The prediction model suggested in this paper produced stable computational results that comprehensively elucidated the fracture behavior of UHPC matrix under different loading rates, and contributed to a better understanding of the dynamic fracture properties of fiber-reinforced UHPC in the future.