water Article Mountain Road-Culvert Maintenance Algorithm Vladimir Mandi´ c 1 , Miloš Šešlija 2 , Slobodan Kolakovi´ c 2, *, Sr ¯ dan Kolakovi´ c 2 , Goran Jefteni´ c 2 and Slaviša Trajkovi´ c 3   Citation: Mandi´ c, V.; Šešlija, M.; Kolakovi´ c, S.; Kolakovi´ c, S.; Jefteni´ c, G.; Trajkovi´ c, S. Mountain Road-Culvert Maintenance Algorithm. Water 2021, 13, 471. https://doi.org/10.3390/w13040471 Academic Editor: Terry Lucke Received: 7 December 2020 Accepted: 26 January 2021 Published: 11 February 2021 Publisher’s Note: MDPI stays neu- tral with regard to jurisdictional clai- ms in published maps and institutio- nal affiliations. Copyright: © 2021 by the authors. Li- censee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and con- ditions of the Creative Commons At- tribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Faculty of Mechanical and Civil Engineering in Kraljevo, University of Kragujevac, 36000 Kraljevo, Serbia; mandic.v@mfkv.kg.ac.rs 2 Faculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, Serbia; sele@uns.ac.rs (M.Š.); kolak@uns.ac.rs (S.K.); goran.jeftenic@uns.ac.rs (G.J.) 3 Faculty of Civil Engineering and Architecture, University of Niš, 18000 Niš, Serbia; slavisa@gaf.ni.ac.rs * Correspondence: kolakovic.s@uns.ac.rs; Tel.: +381-66-121-916 Abstract: The objective of this research was to determine the probability of road overtopping oc- currence for a road culvert caused by surface runoff from the upstream catchment. A hydrological– hydraulic model was used for the development of an algorithm for road culvert maintenance based on the overtopping occurrence probability (CMOOP algorithm) for small mountain catchments. The hydrological model defines the regression dependence between the runoff hydrograph peak values and the probability of occurrences, whereas the hydraulic model calculates the culvert flow capacity by including in the calculation the level of sediment that culvert is filled with. The relationship between occurrences of overtopping and peak runoff value was defined using the runoff hydrograph transformation model in the accumulation on the upstream side of the road. In addition to the calcu- lation of overtopping occurrence probability for the existing culvert condition, the CMOOP algorithm was used to analyze the impact of rehabilitation and reconstruction works from the perspective of legally based safety criterion for road overtopping occurrence probability (SCROOP). The CMOOP algorithm was appled to 67 concrete culverts located in a mountain road section in the Republic of Serbia. The results show that the application of rehabilitation works on selected culverts will increase the percentage of culverts that satisfy SCROOP from 49.25% to 89.55%, which confirms that the accumulated stone sediment is the main reason for the SCROOP unfulfillment. Keywords: culverts; overtopping occurrence probability; hydrological–hydraulic modeling; maintenance; algorithm 1. Introduction Road culverts are specific engineering structures that, in addition to their primary role of conveying surface water under the road, have several functions such as providing passage for people and vehicles, or safe passage of wild animals under the road [1]. These secondary functions of culverts can sometimes be of such importance that their size is defined to meet these conditions [2]. The available literature offers recommendations for designing and sizing new road culverts according to the different criteria [3–6]. In contrast to road culvert design, the maintenance of the existing road culverts has been much less researched. Road culverts are typically located in the lower part of the road embedment, so they are not easily accessible for inspection and maintenance [7]. The lack of maintenance inhibits the culvert’s primary function, which can consequently result in road overtopping and failure of the road culvert [8]. Road overtopping by floodwater is dangerous, affecting both traffic safety and the stability of the road structure. According to research data, around 75% of flood-related fatalities occur when people drive into or attempt to walk through floodwaters [9–11]. Consequential repairs of the road structure defects, caused by water overtopping over the road may require significant financial resources [12,13]. Water 2021, 13, 471. https://doi.org/10.3390/w13040471 https://www.mdpi.com/journal/water