Critical movement of large rocks in currents and waves

Cobbles, boulders, and rocks often are used in a bed protection layer near a structure to protect the underlying sand bed against erosion by combined current and waves. The design of a bed protection layer consisting of loose rocks(rubble mound) requires knowledge of the stability and movement(as bed load) of very coarse materials. If some movement(or damage) is acceptable, the rock diameter can be designed to be smaller. This paper addresses the stability and movement of very coarse materials(cobbles, boulders, and rocks) based on the concept of the critical Shields mobility number. It is shown that the bed load transport of large cobbles, boulders, and rocks can be described by the equations of Meyer-Peter and Mueller(MPM) and Cheng. Both are valid for relatively small Shields mobility numbers.New and general equations for the design of a bed protection layer(including some permissible damage)in conditions with a current with or without waves are proposed based on the Shields mobility parameter and the bed load transport equation of Cheng. Laboratory and field data of critical velocities for pebbles, cobbles, boulders, and rocks have been analyzed and compared to the computed results of the proposed equations. Practical applications are given to demonstrate the general applicability of the proposed equations.