Predicting the equilibrium bed slope in natural streams using a stochastic model for incipient sediment motion

In this paper, a method to predict the equilibrium bed slope in natural streams based on the incipient motion criterion is proposed. The method is based on the criterion suggested by Gessler to simulate the grain size distribution of the armour coat using the concept of critical shear stress of a sediment mixture. In particular, a different expression of the probability for a single particle size to be part of the armour coat is firstly proposed; then, a simple two‐steps criterion is suggested to estimate the safety factor required by the proposed approach. The method is applied in three different Italian regions (Calabria, Basilicata, and Tuscany) and required several field campaigns involving the survey of 251 stream reaches upstream of grade‐control structures. The area including five Calabrian streams is firstly used to test the suitability of the two‐steps approach. In this area, considering the detailed information about the particle size of bed material, the effect of using a simplified grain size distribution for each torrent is also checked. The method is then applied within the two additional areas (Basilicata and Tuscany) in order to check the geographic influence on the prediction of the stable longitudinal profile. A comparison between measured and estimated values of the equilibrium bed slope showed a good agreement for the Calabrian streams, where the number of the investigated stream reaches is greater, and satisfactory results for the torrents located in Basilicata and Tuscany where the field data set is more limited. The overall results encourage the extension of the proposed method to additional field data and suggest the use of this approach by hydraulic designers in order to stabilize the longitudinal profile of natural streams.