water Review Identification of Hydraulic Parameters Influencing the Hydraulic Erodibility of Spillway Flow Channels Aboubacar Sidiki Koulibaly 1, * , Ali Saeidi 1 , Alain Rouleau 1 and Marco Quirion 2   Citation: Koulibaly, A.S.; Saeidi, A.; Rouleau, A.; Quirion, M. Identification of Hydraulic Parameters Influencing the Hydraulic Erodibility of Spillway Flow Channels. Water 2021, 13, 2950. https://doi.org/10.3390/w13212950 Academic Editor: Chiara Biscarini Received: 16 September 2021 Accepted: 15 October 2021 Published: 20 October 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Département des Sciences Appliquées, Université du Québec à Chicoutimi, 555 Boulevard de l’Université, Saguenay, QC G7H 2B1, Canada; ali_saeidi@uqac.ca (A.S.); Alain_Rouleau@uqac.ca (A.R.) 2 Hydro-Québec, Unité de Production et d’Expertise en Barrages, 75 Boulevard René-Lévesque Ouest, Montréal, QC H2Z 1A4, Canada; quirion.marco@hydro.qc.ca * Correspondence: aboubacar-sidiki.koulibaly1@uqac.ca; Tel.: +1-581-235-1247 Abstract: The rock mass erosion of dam spillways, a phenomenon involving the interaction between the hydraulic load of water and the capability of the rock mass to resist its destruction, remains a critical safety issue. The erosion resistance of a rock mass can be estimated through several erodibility indices, including those of Kirsten, Pells or Bollaert. Several indices have been developed to link rock resistance to the hydraulic parameters of water, i.e., the hydraulic load applied on a rock mass. The developed indices use the average flow velocity, the average shear stress on the bottom of the flow channel, the stress applied to the internal joints of fractured rock mass, the dynamic impulse force, and the power dissipation of water to represent the erosive force of water. From these indices, several methods of assessing hydraulic erosion have been developed, and all use the threshold line concept. Nonetheless, several uncertainties are associated with these methods. This paper presents and discusses the various means of calculating the erosive force of water as a hazard parameter for predicting potential rock erosion. The representativeness of these approaches is also discussed, and we clarify nuances associated with each method. We then provide guidelines for future research aimed at improving estimates of the erosive force of the water within spillway flow channels. Keywords: hydraulic erodibility; hydraulic jump; hydraulic load; plunging flow; power dissipation; rock mass 1. Introduction The notion of the hydraulic erodibility of a rock mass emerged around 1900 after observations of the degradation of rock masses under bridges [1]. Several cases of erosion downstream of dam spillways have since been observed, for example, the Tarbela dam in Pakistan in 1976 [2] and the Kariba dam in Zambia in 1962 [3]. Much research has focused on understanding this phenomenon, and several methods have been developed for evaluating the hydraulic erodibility of a rock mass using semi-empirical and semi- analytical methods. These methods have applied the concept of the “threshold line,” [4,5]a correlation between a hydraulic hazard parameter (e.g., shear stress, hydraulic power, and hydraulic energy) and the capacity of the rock to resist destruction. This concept is based on three erosion mechanisms in particular: dynamic block removal, brittle fracturing, and the continuous fragile fracturing of the rock mass [6–8]. Turbulent flow is the flow mode that can produce these different erosion mechanisms. Erosion by the removal of blocks is a process that depends on the water pressure within the joints of the fractured rock mass. The amplitude of the fluctuating pressure changes with time during a turbulent flow, and the pressure applied inside the rock joints can increase pressure directly below the blocks. Moreover, the rock mass is eroded by the dynamic expulsion of the blocks when the lifting pressure under the block exceeds the resistance force of the block in the rock mass (Figure 1). The parameters affecting the Water 2021, 13, 2950. https://doi.org/10.3390/w13212950 https://www.mdpi.com/journal/water