Small strain stiffness of sand-rubber mixtures with particle size disparity effect

Abstract

This study systematically investigates the small-strain stiffness of sand-rubber mixtures, focusing on combined particle disparity—both larger sand with smaller rubber and smaller sand with larger rubber—using the discrete element method. The effectiveness of various state variables in capturing stiffness behavior across different rubber contents and size disparities (SDs) is evaluated. Conventional state variables developed for natural sands, such as void ratio and mechanical void ratio were found to be less effective in describing the small-strain stiffness characteristics of sand-rubber mixtures due to distinct properties of rubber. This study then demonstrates that the stiffness contribution of rubber materials could be negligible, emphasizing that particle property disparity is more significant than SD between sand and rubber materials. Therefore, an adapted state variable, considering only active sand particles, shows improved performance for capturing the correlation between small-strain stiffness with increasing rubber contents, suggesting its potential utility over conventional variables. Additionally, a refined void ratio, including inactive sand particles but excluding rubber, offers a practical alternative for capturing small-strain stiffness in experimental and engineering practices, aligning with previous experimental observations. These findings underscore the need for developing more effective state variables that accurately reflect the interactions within heterogeneous materials like sand-rubber mixtures.