Calculation model for the lifting effect of foamed polyurethane grouting on the subgrade settlement of high-speed railway ballastless track

Polyurethane (PU) grouting is widely used to remediate settlement in ballastless track subgrades. The expansion force generated during this process is a key parameter for lifting the track. Generally, a larger grouting volume produces a greater expansion force and a higher lifting capacity. However, in practice, the grouting volume faces two main constraints. First, the allowable track uplift restricts the maximum lifting height. Second, the physical properties of the grouting medium restrict the injection volume. Therefore, a better understanding of the relationship between PU grouting volume and expansion force is needed. Based on traditional slurry diffusion and uplift theories, this paper develops a mechanical model for expansion force in ballastless track subgrades. Custom-designed tests were then conducted to obtain empirical equations for predicting expansion force and consolidation density. Using these equations, we propose a coupled model that links grouting volume to expansion force for track uplift. To verify this model, we performed physical lifting tests on graded crushed stone layers. The theoretical grouting volumes calculated by the coupled model closely match the experimental results. This agreement validates the proposed theoretical model.