Microstructural $$\eta$$: chemical–mechanical bridge for anchorage design in alkali–activated concretes

Abstract The anchor design for Low-Carbon Concretes still lacks parameters that link microchemistry to structural performance. This work introduces a microstructural coefficient $$\eta$$ η , defined from gel density and interfacial porosity of the N-A - S-H / C - A - S-H networks, to extend the classical Tepfers. The analytical derivation shows that $$\eta$$ η multiplies the circumferential stress solution without altering its geometric scale, predicting a linear increase in initial stiffness and anchor energy. Three-dimensional bar–matrix contact simulations ( FEniCS ) for $$\eta =1.0-1.6$$ η = 1.0 - 1.6 and two cover ratios $$\lambda = d/c = 0.20,\;0.14$$ λ = d / c = 0.20 , 0.14 confirmed this prediction within 3 % for peak hoop stress and 2 % for secant stiffness. A $$2\times 3$$ 2 × 3 factorial pull-out program on fly-ash concretes (two covers, three Si / Al ratios) experimentally validated the proportionality $$K_{\text {exp}} = \eta K_{0}$$ K exp = η K 0 experimentally; two-way ANOVA ranked gel chemistry as the dominant factor, explaining up to 93 % of stiffness variance at 28 days, while residual errors remained negligible. The metric sweeps of the fracture number $$\kappa$$ κ and the friction number $$\textrm{Re}_{\mu }$$ Re μ confirmed that $$\eta$$ η governs the stiffness, $$\kappa$$ κ controls the post-peak toughness and $$\textrm{Re}_{\mu }$$ Re μ scales the residual plateau, delineating a domain of validity of $$\eta \le 1.6$$ η ≤ 1.6 , $$\kappa \ge 0.004$$ κ ≥ 0.004 , $$0.12\le \lambda \le 0.25$$ 0.12 ≤ λ ≤ 0.25 . These convergent results demonstrate that a single parameter captures the chemomechanical enhancement of alkali-activated concretes, providing a direct calibration rule that can be incorporated into future revisions of the ACI 323 Low-Carbon Concrete code.