Using cemented rockfill to replace coal pillars offers an effective solution for reducing solid waste while ensuring the safety of gob-side entries. However, achieving the balance among low cost, high waste recycling rates, and adequate strength remains a significant challenge for cemented rockfill. This study used a composite alkali activator to activate gangue cemented rockfill. The compressive strength, scanning electron microscopy, energy dispersive spectrometer, mercury intrusion porosimetry, X-ray diffraction, and thermogravimetric tests were carried out to investigate the effect of the composite alkali activator proportion on the compressive strength, microstructure, and composition of the cemented rockfill. The calcium silicate hydrate (C–S–H) molecular model of cemented rockfill was constructed to explore the fracture evolution of the nucleated molecular structure under tension. The results show that compressive strength initially increased and then decreased with the activator proportion, the optimal activator proportion of 1:2 resulted in a 31.25% increase in strength at 3 d. This reasonable activator proportion strengthens the pozzolanic effect of gangue, and consumes more calcium hydroxide to inhibit its agglomeration, ultimately achieving the densification of microstructure. The activator proportion inevitably substitutes calcium ions with sodium ions in the C–S–H molecular model. The 12% substitution of calcium ions increases the adhesion between silicon chain layers, which is beneficial to the interlayer stress transfer. This work proposes a method for preparing low-cost cemented rockfill from alkali-activated gangue, which can be used for solid waste recycling and reducing cement consumption to achieve low-carbon goals.

Building upon the foundations of classical fractional derivatives, the general fractional derivative emerges as a significant advancement in the development of constitutive models, especially for materials with complex properties. This derivative distinguishes itself through a kernel function of variable form, enabling it to encapsulate diverse characteristics of the creep process more effectively than its classical counterpart. This study introduces a general-variable order fractional creep constitutive model, ingeniously linking the order of the fractional derivative to Talbot gradation, which describes the aggregate gradation of cemented backfill materials, alongside dosage and confining pressure parameters. The model's innovative design synergizes the kernel function's diversity from the general fractional derivative with the phase adaptability inherent in the variable-order derivative. This integration permits a comprehensive description of each stage of the creep curve for cementitious filling materials in varying compositions, leveraging the Gamma function's properties within the positive real number domain. The model's rationality and validity are substantiated through a comparative analysis between experimental creep curves and theoretical predictions, affirming its relevance and accuracy in practical applications. This approach represents a notable contribution to the understanding of cemented backfill materials' behavior, offering a robust tool for engineering analysis and design.

Water pollution from industrial and domestic sewage demands the accurate modeling of wastewater treatment processes. While the Lawrence–McCarty model is widely used for activated sludge systems, its integer-order formulation cannot fully capture the fractal characteristics of microbial aggregation. This study proposed a fractal Lawrence–McCarty model (FLMM) by incorporating local fractional derivatives (α = ln2/ln3) to describe microbial growth dynamics on Cantor sets. Theoretical analysis reveals that the FLMM exhibits Mittag-Leffler-type solutions, which naturally generate step-wise growth curves—consistent with the phased behavior (lag, rapid growth, and stabilization) observed in real sludge systems. Compared with classical models, the FLMM’s fractional-order structure provides a more flexible framework to represent memory effects and spatial heterogeneity in microbial communities. These advances establish a mathematical foundation for future experimental validation and suggest potential improvements in predicting nonlinear biomass accumulation patterns.