Inertial scaling of mud flows in centrifuge modelling: a modelling of model approach

Debris flows and rapid gravity-driven mass movements, including mud flows, pose major geotechnical hazards in natural and engineered settings. Physical modelling in geotechnical centrifuges offers a controlled framework for investigating these phenomena, provided that appropriate scaling laws are satisfied. This paper presents drum-centrifuge experiments on mud flows, focusing on the assessment of inertial scaling through the modelling of model approach. The theoretical framework is based on a reduced, depth-integrated form of the Navier–Stokes equations for shallow, non-turbulent, non-Newtonian flows. Velocity–displacement relationships obtained at different centrifugal acceleration levels are compared at prototype scale. The results identify a quasi-linear propagation regime associated with an inertial–gravitational balance, in which velocity–displacement trends become approximately linear and converge after prototype-scale normalisation. This convergence provides experimental support for inertial similitude within the identified regime. Outside this interval, deviations arise as temporal acceleration and dissipative mechanisms become more relevant. The findings emphasise that inertial scaling in centrifuge modelling is regime-specific. They also show that, although local kinematic quantities satisfy inertial scaling during propagation, global outcomes such as runout distance are affected by processes outside the similitude regime and should be interpreted with caution.