Granular materials exhibit complex behaviour, transitioning between solid-, liquid- and gas-like states depending on factors such as compaction, stress and deformation rate. This study proposes a continuous nonlinear model for wave propagation in granular media, inspired by a modified form of the Euler equations and informed by Hertzian contact theory. The model captures the dependence of wave speed on compaction, and deformation tensor invariants are used to extend it and describe shear-induced dilation. Finite-volume simulations demonstrate that the model stabilises granular piles in the quasi-static regime and recovers realistic angles of repose. These results represent a promising step towards the large-scale modeling of granular assemblies, such as railway ballast.