Theoretical development on the effects of changing flow hydraulics on incipient bed load motion

Several decades of flume and field measurements have indicated that in rough turbulent flows the critical Shields stress increases with increasing slope and associated decreasing relative depth. This result contradicts the usual consideration of a decreased critical Shields value on very steep slopes because of increased gravitational effects. However, recent studies have demonstrated that these experimental results could be reproduced with a force balance model if the classical logarithmic velocity profile was replaced with a velocity profile that was more compatible with available velocity measurements over gravel beds. These measurements indicate the existence of a roughness layer that is a zone of almost constant velocity close to the bed, whose properties (mean velocity and turbulence) depended on the flow's relative depth. Unfortunately, velocity profile measurements for low relative depth associated with steep slopes are scarce, and it is still difficult to include such flow properties in a force balance model. Flow resistance data (on the basis of depth average velocity measurements) are very common and cover a wide range of slopes and relative depths. In this paper these data are used to fit a velocity profile including a roughness layer. When used in a force balance model for incipient motion, it adequately reproduced a data set composed of 270 critical Shields values measured in a flume with near-uniform sediments. The relevance of this research to field problems is discussed using a data set composed of 92 critical Shields stresses obtained from field measurements. Finally, a model is proposed for field applications taking into account the slope effect.