Frequency-dependent dynamic characterisation of cement-treated sand using DEM and its application to shallow machine-foundation vibration analysis

Cement-treated sand is increasingly adopted to improve foundation subgrades for vibration-sensitive rotating machinery; however, its dynamic stiffness and damping are not well quantified across the operating frequency range of turbo-generator systems. This study investigates the frequency-dependent dynamic behaviour of cement-treated sand and translates the resulting properties into a design-oriented vibration-assessment procedure for shallow machine foundations. Cyclic triaxial tests were performed on a natural sand treated with 0–3% Portland cement (by dry sand mass) at a water/cement ratio of 0.6 and cured for 28 days. Specimens were tested at confining stresses of 50, 100, and 200 kPa and cyclic stress ratios of 0.2–1.0 at 1 Hz. Shear modulus and damping ratio were evaluated from medium-strain hysteresis loops. A three-dimensional bonded-contact discrete element model was calibrated against the 1 Hz experimental responses using modulus reduction, damping ratio, loop area, and strain accumulation. The calibrated model was then used to numerically explore frequencies of 1–50 Hz and water/cement ratios of 0.3-1.5 under matched stress states. The combined experimental–numerical database was synthesised into closed-form relations for shear modulus and damping ratio as functions of shear strain, cement content, water/cement ratio, confining pressure, and frequency. The proposed framework is not intended as a new soil–foundation dynamic theory, but as a design-oriented integration of experimentally calibrated and DEM-extended dynamic soil properties into a conventional shallow-foundation vibration assessment procedure. Higher cement content and lower water/cement ratio increased stiffness and reduced damping, while higher frequency produced slightly higher stiffness and lower damping.