A Mesoscopic Stochastic Damage Constitutive Model for Concrete under High Temperatures Incorporating Dual Random Fields

Exposure to high temperatures severely deteriorates concrete mechanical performance and aggravates the intrinsic stochasticity of its deformation response, creating critical obstacles to the reliability evaluation of fire-damaged concrete structures. Distinct from concrete at ambient temperature, specimens heated to elevated temperatures display prominent stress–strain dispersion from the very start of uniaxial compression, and this scatter becomes more significant with rising temperatures. Traditional stochastic damage models that merely treat fracture strain as a random variable cannot reproduce this early-stage random fluctuation accurately. Within the mesoscopic stochastic fracture framework, this paper develops a novel constitutive model by introducing two statistically independent random fields for elastic modulus and fracture strain, and derives closed-form analytical formulas for the mean and variance of full-range stress–strain curves. The model is fully calibrated and verified against systematic uniaxial compression test data covering four concrete strength grades and multiple thermal levels with abundant replicate specimens. Validation outcomes revealed that high temperatures generate additional elastic-stage randomness driven by spatially uneven thermally induced microstructural deterioration. The scattered ascending segment of stress–strain curves is governed by the randomness of elastic modulus, whereas peak bearing capacity and postpeak softening evolution are controlled by the variability of fracture strain. Comparative analyses demonstrated that the dual-random-field model outperforms classic single-random-field formulations in capturing both average mechanical behavior and probabilistic dispersion, particularly for the ascending branch under medium and high temperatures. The established model delivers a solid constitutive foundation for probabilistic analysis and fire safety assessment of concrete structures under thermal exposure.