Probabilistic Reliability Framework for Nanomaterial-Stabilized Soft Clays: Model Calibration and Geometry Effects

The stabilization of soft clay soils using nanomaterials offers a promising alternative to conventional additives such as lime and cement, yet most studies remain deterministic, neglecting soil variability and treatment geometry. This study proposes an experimental–probabilistic framework combining triaxial shear and model footing tests with Monte Carlo simulations to evaluate nano-SiO₂, nano-MgO, and nano-clay. Dosages from 1% to 5% were examined, and 3% was selected as optimal based on strength improvement and economic feasibility. Classical bearing capacity models (Terzaghi, Meyerhof, Hansen) were applied and calibrated using regression factors, with input variability modeled under normal and lognormal distributions. Results indicate that nano-MgO achieved the lowest probability of failure ( < 0.1), nano-SiO₂ showed intermediate but geometry-sensitive performance, and nano-clay provided limited reliability. The calibrated Terzaghi model (R² = 0.742) yielded the most consistent predictions. Enlarged treatment zones improved stress redistribution and reduced failure risk. The study also identifies priorities for future work: durability under cyclic loading, hybrid nanomaterial blends (e.g., SiO₂ + MgO), and scalability for large infrastructure projects. Collectively, the findings establish a reliability-based framework that integrates probabilistic modeling, calibration, and material geometry optimization for resilient geotechnical design.