Mix Proportion Optimization of Loess-Based Controlled Low-Strength Material Considering Field Water-to-Solids Ratio Uncertainty

Loess is highly water-sensitive and collapsible, and its conventional use as backfill in road and railway infrastructure may lead to settlement and deformation after wetting. Converting excavated loess into controlled low-strength material (CLSM) provides an alternative for backfilling; however, its engineering performance is strongly dependent on the water-to-solids ratio (W). In field construction, variations in the natural moisture content of loess cause the actual W to deviate from its design value, whereas conventional CLSM mix designs generally assume a fixed W, which may result in insufficient flowability or strength under actual field conditions. A Box–Behnken design was first employed to investigate the effects of the cement-to-soil ratio (C), water-to-solids ratio (W), and polycarboxylate superplasticizer content (P) on flowability (f), bleeding rate (Bᵥ), wet density (ρ), and 28-day compressive strength (qᵤ), based on which regression-based predictive models were developed. The sequential least squares programming (SLSQP) algorithm was then used to optimize mix proportions for backfilling behind abutments, culverts, and retaining walls and for subgrade backfilling. The optimization minimized the material cost per unit volume while requiring all performance indicators to satisfy the specified criteria under variations in W (ΔW = 0%, ±1%, ±2%, and ±3%). The results show that W is the dominant factor governing f, Bᵥ, and ρ, whereas C has the greatest influence on qᵤ. Increasing P markedly improves f but also increases Bᵥ. For backfilling behind abutments, culverts, and retaining walls, when the mean field soil moisture content is overestimated and the actual W is consequently lower than its design value, the mix optimized for ΔW = −3% satisfies the flowability criterion even when the measured flowability is up to 21.3 mm below the design value because of the lower actual soil moisture content. Conversely, when the mean field soil moisture content is underestimated and the actual W exceeds its design value, the mix optimized for ΔW = +3% satisfies the compressive-strength criterion even when the measured strength is up to 0.09 MPa below the design value because of the higher actual soil moisture content. Accounting for possible variations of up to ±3% in the water-to-solids ratio under field conditions, the optimal mix proportions are C13.14W37.64P0.069 for backfilling behind abutments, culverts, and retaining walls and C15.00W34.28P0.097 for subgrade backfilling. These findings provide a basis for the performance control and mix design of loess-based CLSM subjected to variations in the water-to-solids ratio.