Thermodynamics-informed C–S–H gel densification descriptor for concrete creep prediction: A physics-informed hybrid framework

Long-term concrete creep depends on both macroscopic variables and the hydration-dependent state of calcium silicate hydrate (C-S-H) gel, which is not included in conventional design models. This study tests whether low-density (LD) and high-density (HD) C-S-H descriptors can explain part of the residual bias left by the recalibrated fib Model Code 2010 (MC2010). LD and HD C-S-H mass fractions at loading age were estimated from Parrot-Killoh hydration kinetics coupled with GEMS thermodynamic calculations and used in an MC2010-based physics-informed neural network (PINN) framework. The recalibrated MC2010 model provided the physical baseline, while the PINN learned the remaining residual under a monotonicity constraint with respect to loading duration. Based on 20,967 creep measurements, MC2010 recalibration improved global accuracy but did not remove systematic residual patterns across humidity, loading duration, and strength ranges. These patterns varied with the LD/HD ratio, particularly at high LD/HD levels, suggesting that conventional creep formulations may not fully capture the hydration-dependent contribution of gel densification. The PINN reduced this structured bias without replacing MC2010 and limited non-physical trends in creep evolution. The results support the use of C-S-H gel densification as an interpretable descriptor for locating systematic prediction errors in conventional creep models.