Influence of grain size on granite strength and toughness with reliability specified by normal distribution

This study presents a simple fracture model linking average grain size G of granite to tensile strength f_t and fracture toughness K_IC. This model only requires the peak load P_max measurements of small notched samples to determine both f_t and K_IC. The influence of G was considered for: (i) quasi-stable crack growth before P_max, and (ii) fracture transition from f_t to K_IC criterion. In-depth analysis was carried out on three-point-bending (3-p-b) results from granite with G ≈ 2.5 mm. The 3-p-b specimens have two different beam widths W = 30 and 70 mm, and the same span/width ratio S/W of 4. Another granite with G ≈ 10 mm reported in literature was also analysed to show the influence of different grain size on both f_t and K_IC. Comprehensive data on rock fracture are explained and compared with the results of this study to substantiate findings of this study. Experimental scatters in P_max with different initial notch lengths a₀ = 0 – 53 mm were analysed by normal distribution, following a recent study (Zhang et al., 2018). The new model with normal distribution predicted the mean and upper and lower limits with 96% reliability covering the experimental scatters.