Fluvial Entrainment of Protruding Fractured Rock

Fluvial entrainment of fractured rock assessed in terms of bed shear stress, stream power, and time-averaged bed uplift pressures indicates that rock-block stability reduces with increasing protrusion and decreasing surface length (in the direction of flow), with protrusion of only a nominal portion of the block required to significantly decrease block stability. Variations in block uplift pressure coefficient with normalized block protrusion and block surface length can be used to predict the height of a block (of protrusion P and known surface lengths) at the point of entrainment for an open-channel flow (of average depth h and velocity U). Alternatively, entrainment of prismoidal particles of square section in plan by fully turbulent open-channel flows (of $R_{*}>100)$ can be predicted using $({\theta }_C-0.002)=0.0015 (P_{\mathrm{vb}}/L{)}^{-1}\text{,}$ where ${\theta }_C$ is the critical dimensionless shear stress, $R_{*}$ is the grain Reynolds number, L is the particle upper-surface side length, and $P_{\mathrm{vb}}$ is the particle protrusion relative to the virtual-bed level at which the average flow velocity is zero (approximately the tops of the supporting or surrounding particles for the present prismoidal blocks). Owing to the potential occurrence of cavitation on prototype block surfaces, it is recommended that quantitative scaling of the present results be conservatively limited to prototype average velocities (U) of less than approximately 6 m/s (with scale ratios ${\lambda }_U^2={\lambda }_L=29)\text{.}$ In contrast to existing practice, particle protrusion needs to be accounted for when assessing the erodibility of a channel bed using stream-power-based methods such as the erodibility index method reported by Annandale in 1995.