A generalized weakest-link model for size effect on strength of quasi-brittle materials

Non‐proportional size scaling of strength of concrete in uniaxial and biaxial loading conditions

“…Note that β > 0 includes 3 scenarios, namely β = 1, 0 < β < 1, β > 1, as exemplified in Lei. 12 When β = 1, the microcracks are uniformly distributed within a material, Equations 12 and 13 reduce to the following in sequence,…”

“…Equation 15 was successfully applied to the proportional size scaling of strength of concrete. 1,12 However, the non-proportional size scaling of strength remains a big challenge. An earlier work 1 suggested to tackle this problem by understanding the following 2 aspects:…”

“…(6) Recent work 12 proposed a more generic weakestlink formulation based on the assumption of power-law spatial distribution of microcracks, which makes the uniform spatial distribution as its special case; (7) Weibull statistics 6 was developed based on the uniform spatial distribution of microcracks; The conventional practice of using a power-law microcrack size distribution to interpret Weibull statistics is invalid, which can be stretched to mimic the 2-parameter Weibull statistics, but fails to formulate the 3-parameter Weibull statistics.…”

“…12 When β = 1, the microcracks are uniformly distributed within a material, Equations 12 and 13 reduce to the following in sequence, 12 When β = 1, the microcracks are uniformly distributed within a material, Equations 12 and 13 reduce to the following in sequence,…”

“…Specific to concrete, some initial results show that β = 1 for uniform spatial distribution of microcracks applies. 1,12 However, the non-proportional size scaling of strength remains a big challenge. Equation 15 was successfully applied to the proportional size scaling of strength of concrete.…”