Probabilistic evaluation of torsional resistance of high-performance and ultra-high-performance concrete beams: Bayesian approach

The torsional behavior of high-performance concrete (HPC) and ultra-high-performance concrete (UHPC) beams involves considerable uncertainty due to factors such as material heterogeneity. To address this challenge, this study develops probabilistic models for the cracking and ultimate torque of rectangular HPC/UHPC beams using Bayesian inference in combination with Markov Chain Monte Carlo (MCMC) simulation. The framework integrates mechanics-based theories—thin-walled tube analogy, modified compression field theory, and softened truss model—with experimental databases to obtain posterior distributions of key parameters that explicitly capture both aleatory and epistemic uncertainties. Comparisons with four existing torsional models show that the proposed approach achieves a mean test-to-prediction ratio close to unity and substantially smaller standard deviations. The probabilistic models further reproduce the full distribution of torsional resistance rather than single-point estimates, enabling confidence interval–based predictions. Analyses of confidence levels and parameters reveal shortcomings in current codes: for example, ACI 318–25 overly underestimates ultimate torsional resistance because of neglecting post-cracking tensile contributions of concrete and underrepresenting reinforcement effects. Overall, the proposed Bayesian–MCMC models offer a rigorous and adaptable means to recalibrate deterministic torsional formulas. By deriving design values directly from posterior predictive distributions, the framework provides not only improved accuracy but also a reliability-consistent basis for engineering design of HPC/UHPC beams, with direct implications for future code calibration and update.