A calibrated reaction-transport model for lime-treated marly clay: Experimental validation, cross-validation limits, and parametric surrogate comparison

Abstract

This paper presents a calibrated reaction-transport model (RTM) for lime-treated F3 marly clay from Meknès, Morocco. The coupled ODE–PDE system combines (i) pozzolanic reaction kinetics described by transition-state theory with Arrhenius temperature dependence, (ii) calcium diffusion–reaction with porosity-dependent diffusivity, and (iii) an empirical strength–hydrate correlation linking unconfined compressive strength (UCS) to the local C-S-H concentration. A continuous water-content modulation function η w ( S r , n ) with two free parameters replaces the per-condition discrete factors used in earlier formulations and reproduces the experimentally observed OPM > Dry > Wet strength hierarchy. The model is calibrated against triplicate UCS measurements at 3% and 6% CaO ( R 2 = 0.982 , RMSE = 75 kPa), independently validated against eight thermogravimetric analysis (TGA) measurements of portlandite consumption and C-S-H formation, and spatially verified by SEM-EDS calcium profiles from a column-scale lime-pellet experiment. Cross-validation across compaction conditions ( R 2 = 0.74 –0.99, leave-one-condition-out) and lime dosages ( R 2 = − 1.88 to 0.89, leave-one-lime-out) restricts the predictive domain to interpolation within the calibrated range. Validation at 9% CaO reveals a structural limitation: single-reaction kinetics cannot capture the optimum-lime-content overshoot, and a dual-pathway conceptual extension is proposed to address it. Damköhler analysis (Da ≫ 1) confirms that treatment extent is transport-limited, establishing the physical necessity of the diffusion PDE in field geometries with discrete lime sources. For parametric exploration, Gaussian process, polynomial degree-3, and DeepONet surrogates are compared on 1920 finite-difference training simulations; all achieve R 2 ≥ 0.999 on scalar UCS prediction, indicating that the smooth 1-D problem is well captured by classical regression. A 2-D axisymmetric extension shows that DeepONet outperforms polynomial surrogates on layered and heterogeneous-permeability domains ( R 2 = 0.95 vs. 0.72), supporting its use as a prototype for field-scale applications.