A meso-scale size effect study of concrete tensile strength considering parameters of random fields

•Develop a statistical framework to evaluate the size effect of concrete by Weibull random fields and the phase-field cohesive zone model.•Perform extensive Monte Carlo simulations with parametric analyses of correlation length and variance in random fields.•Reveal the statistical trend of size effects in tensile strength.•Propose a modified size-effect law considering correlation length and variance by data regression. This study analyses size effects of concrete under uniaxial tension by Monte Carlo simulations, where heterogeneous strength at meso-scale is modelled by Weibull random fields with statistical parameters including correlation length and variance. For a given sample size and different random field parameters, a sufficient number of random field realisations are simulated to obtain statistical information from macroscopic stress-strain curves, while the complex meso-crack initiation and propagation is captured by the phase-field regularized cohesive zone model (PF-CZM). The effects of sample size and material heterogeneity on macroscopic tensile strength are analysed, and the quasi-brittle transition between plasticity and linear elastic fracture mechanics (LEFM) is well simulated using the nonlocal PF-CZM. It is also found that both the correlation length and the variance affect the trend of size effect in varying degrees: larger correlation length and higher variance with higher heterogeneity lead to more dispersed responses that approach the LEFM descending line. A modified law in three-dimensional parametric space is proposed by data regression for effective assessment of size effect and structural reliability.