Laboratory measurements of pivoting angles for applications to selective entrainment of gravel in a current

Important to grain entrainment by a flowing fluid is the pivoting angle of the grain about its contact point with an underlying grain. A series of experiments has been undertaken to determine how this angle depends on grain shape (rollability and angularity), on the ratio of the size of the pivoting grain to those beneath, and on factors such as imbrication. The experiments involved gravel‐sized spheres (ball‐bearings and marbles), natural pebbles selected for their approximately triaxial ellipsoid shapes, and angular crushed basalt pebbles. The pivoting angles for these grains were measured on an apparatus consisting of a board which can be progressively inclined, the angle of the board being equal to the pivoting angle at the instant of grain movement. The pivoting angles of spheres showed reasonable agreement with a theoretically derived equation, showing much better agreement than in previous studies which utilized sand‐sized spheres. A series of measurements with spheres ranging from sand to gravel sizes reveals that the pivoting angles decrease with increasing particle size. Our results are therefore consistent with the earlier studies limited to sand‐size spheres. The cause of this size dependence is unknown since moisture and electrostatic binding can be ruled out. Similar size dependencies are also found for the ellipsoidal pebbles and angular gravel. The experiments with ellipsoidal pebbles demonstrated a strong shape dependence for the pivoting angle, being a function of the ratio of the pebble's smallest to intermediate axial diameters. This ratio controls the grain's ability to roll and pivot; with small ratios of these diameters the pebbles tended to slide out of position, whereas with ratios closer to unity (circular cross‐section) true pivoting took place and the angles were smaller. Experiments with flat pebbles placed in an imbricated arrangement yielded much larger angles than when the pebbles lay in a horizontal position, the pivoting angle being increased approximately by the imbrication angle. The angular crushed gravel also required high pivoting angles, apparently due to interlocking of the grains resulting from their angularity. Other factors being equal, the measurements of pivoting angles demonstrate that the order of increasing difficulty of entrainment is spheres, ellipsoidal grains, angular grains, and imbricated grains. The results obtained here make possible the quantitative evaluation of these shape effects on grain threshold, as well as evaluation of the selective entrainment of grains from a bed of mixed sizes.