Statistical analysis of three-point-bending fracture failure of mortar

The normal distribution methodology in the mathematical model is introduced to statistical analyze the fracture failure of the mortar material, and the fracture parameters (fracture toughness K-IC and tensile strength f(t)) without size effect can be obtained. The fictitious crack growth lengths Delta a(fic) and characteristic crack a(ch)* of the mortar specimens are related to the maximum aggregate size g(max), the corresponding fracture parameters can be directly calculated by the improved boundary effect theory. Furthermore, according to the statistical analysis of the normal distribution, the fracture parameter (fracture toughness K-IC and tensile strength f(t)) corresponding to the minimum discrete coefficient delta can be obtained. Based on the analysis of mortar specimens of different relative sizes (W/g(max)), the relationship between fictitious crack growth lengths vafic and relative size (W/g(max)) have been established. The fracture parameters (fracture toughness K-IC and tensile strength f(t)) obtained from the small-size mortar specimens not only establish a complete failure curve, but also predict the peak load P-max of the real structure (W/g(max) = 1000) with 95% reliability, which is close to the failure test results of large-size mortar specimens under laboratory conditions. (C) 2021 Elsevier Ltd. All rights reserved.