Identification of Strength-Development Pathways in One-Part Geopolymers Using ESI-MSI-LGP Indices and GMM Clustering

Geopolymer research has usually focused on predicting compressive strength at specific curing ages, while the underlying strength-development behavior remains insufficiently understood. To address this gap, this study proposes a pathway-oriented framework for characterizing strength-development patterns in one-part geopolymers (OPGs). A compiled experimental database was established from published studies, and three dimensionless indices, namely the Early Strength Index (ESI), Mid-age Strength Index (MSI), and Late-stage Growth Potential (LGP), were introduced to quantify temporal strength-development behavior. Then, Gaussian Mixture Model (GMM) clustering was employed in the ESI-MSI-LGP feature space to identify latent strength-development pathways. Based on the available core dataset, three representative strength-development pathways were identified: Fast-hardening, Delayed-hardening, and Balanced-hardening. The Fast-hardening pathway exhibited the highest average ESI and MSI values, indicating rapid early- and mid-age strength attainment. The Delayed-hardening pathway showed lower ESI and MSI values but the highest LGP value, reflecting stronger later-age strength-growth potential after 7 days. The Balanced-hardening pathway was characterized by relatively low ESI, high MSI, and low LGP, suggesting accelerated strength development between 3 and 7 days. Further analysis of mix-design variables indicated that pathway formation was associated with the coupled effects of aggregate-to-binder proportion, activator chemistry, water availability, precursor composition, and curing conditions, rather than being controlled by a single dominant factor. Finally, a smooth probability-based strength-development map was established in the ESI-MSI feature space, providing a practical visualization tool for approximate pathway identification and preliminary mixture-selection support. The proposed framework shifts the focus from conventional strength prediction toward strength-development behavior characterization and offers new insights into the macroscopic hardening patterns of one-part geopolymers.