Inertial drag and lift forces for coarse grains on rough alluvial beds measured using in-grain accelerometers

Quantifying the force regime that controls the movement of a single grain during fluvial transport has historically proven to be difficult. Inertial micro-electromechanical system (MEMS) sensors (sensor assemblies that mainly comprise micro-accelerometers and gyroscopes) can used to address this problem using a “smart pebble”: a mobile inertial measurement unit (IMU) enclosed in a stone-like assembly that can measure directly the forces on a particle during sediment transport. Previous research has demonstrated that measurements using MEMS sensors can be used to calculate the dynamics of single grains over short time periods, despite limitations in the accuracy of the MEMS sensors that have been used to date. This paper develops a theoretical framework for calculating drag and lift forces on grains based on IMU measurements. IMUs were embedded a spherical and an ellipsoidal grain and used in flume experiments in which flow was increased until the grain moved. Acceleration measurements along three orthogonal directions were then processed to calculate the threshold force for entrainment, resulting in a statistical approximation of inertial impulse thresholds for both the lift and drag components of grain inertial dynamics. The ellipsoid IMU was also deployed in a series of experiments in a steep stream (Erlenbach, Switzerland). The inertial dynamics from both sets of experiments provide direct measurement of the resultant forces on sediment particles during transport, which quantifies (a) the effect of grain shape and (b) the effect of varied-intensity hydraulic forcing on the motion of coarse sediment grains during bedload transport. Lift impulses exert a significant control on the motion of the ellipsoid across hydraulic regimes, despite the occurrence of higher-magnitude and longer-duration drag impulses. The first-order statistical generalisation of the results suggests that the kinetics of the ellipsoid are characterised by low- or no-mobility states and that the majority of mobility states are controlled by lift impulses.