Integrated Numerical and Experimental Analysis of Sand–Crumb Rubber Layer Performance in Machine Foundations

This study examines the vibration isolation potential of sand–crumb rubber (SCR) layers for machine foundations, particularly in mitigating the production of detrimental dynamic loads. SCR mixtures offer inherent flexibility and damping. However, a comprehensive understanding of their performance under varying dead loads, angular dynamic loads, SCR layer thickness, and depth-to-width (D/B) ratios is crucial due to the complex interplay between these factors. Employing a dual approach of experimental block vibration tests and three-dimensional finite-element analysis with an optimized 30% crumb rubber mixture, we systematically evaluated the effects on resonant frequency (fres), resonant displacement amplitude (Ares), and transmissibility ratio (Tr). The results consistently show that SCR layers significantly reduce fres across all load combinations. However, increasing layer thickness, while reducing fres, significantly increases Ares, highlighting a critical trade-off. The SCR layer’s effectiveness is conditional, highly dependent on specific dynamic and dead load combinations, with increasing foundation dead weight effectively mitigating both fres and Ares. To facilitate practical design, empirical equations were developed for fres (R2 = 0.87) and Ares (R2 = 0.81), enabling engineers to rapidly estimate resonant response and select optimal SCR configurations. Furthermore, the influence of the SCR layer width was also examined and found to have negligible effects on the resonant response. The present study provides crucial insights and practical tools for optimizing machine foundation designs using SCR layers.