Contribution of hydraulic modeling and hydrology to flood prevention and design of engineering structures: case study of a bridge over the Oued Ourika – Morocco

. Located downstream of the Ourika watershed near the commune of Chouiter, the bridge studied is built over the Oued Ourika at the level of the N9 (national road linking Marrakech to Ouarzazat). The flood event of November 2014, reaching a peak flow of 347 m3/s, destabilized the bridge's overall structure. Hence, the need to rebuild a new bridge, taking into account the magnitude of these extreme events. Hydraulic modeling involves creating mathematical and computer-based representations of hydraulic systems. Its purpose is to simulate water flow behavior and map flood-prone areas. Before initiating any hydraulic simulation, it is imperative to conduct a hydrological study to provide the input data for the hydraulic model. Precipitation records, evaporation rates, soil permeability, historical peak flow data, and site topography constitute, on the one hand, the product of the hydrological study and, on the other, the inputs for the hydraulic model. The hydraulic model is based on Saint-Vant equations to solve the conservation of mass and momentum equations. The aim of this work is to determine the critical water level at the bridge for a 100-year flood in order to optimize the height of the new bridge.


Introduction
The bridge under study is vitally important for socioeconomic reasons, as evidenced by the heavy road traffic between the two major cities of Marrakech and Ouarzazate.Oued Ourika is known for its destructive floods [1].The 2014 flood caused extensive structural damage with torrential waters overflowing the bridge deck and forming a dam due to the accumulation of transported sediments.The water pressure against the dam destabilized the entire structure, necessitating the urgent construction of a new bridge that could withstand such extreme events.

Geographical location of the study area
The study area is located on the National Road N°9 linking Marrakech to Ouarzazate at the intersection of the Oued Ourika and the road near the commune of Chouiter.The geographical coordinates of the site are 31°34'51.70''N,7°47'49.10''W,Elevation of the site is 523m msl.The location map is shown in Figure 1.

Methodology
The chart below (Figure 2) illustrates the approach adopted to model the critical height reached by the flood at the bridge.The hydrological study is the basis for all the work that is currently underway.The first is the study of the physical parameters of the catchment area in order to calculate the surface area and perimeter of the catchment, establish the hypsometric curve, the slope and the classification of the hydrographic network.The second is statistical hydrology and flood studies, from which frequency analysis is applied [2].The topographical survey of the area is an essential step in the study, in order to establish profiles across the Oued.The topographical data and the 100-year flood discharge are the input files for the hydraulic modelling.The latter is a simulation of the extent of the flood under given conditions, the site conditions being the morphology of the Oued Ourika (width of the minor bed, sinuosity of the Oued, bed roughness index) and the quantity of water transported during the flood (Qp).Modelling in the natural state is the manifestation of the flood in the normal state, i.e. in the absence of the bridge or any structure that may modify the hydrological cycle of the Oued.It is carried out before the modified regime to determine the impact of the change caused by the structure.In this section, we have studied the Ourika catchment in order to identify the physical parameters that control the hydrological behaviour of the catchment.We have used ArcGIS to process the digital terrain model (DTM).A geographic information system (GIS) is defined as a system capable of storing, sharing, consulting and manipulating the objects represented on maps and plans with their geometric description, as well as any information attached to them [3].Tomlin, on the other hand, defined a GIS as a means of presenting and interpreting facts observed on the earth's surface [4].A DTM is a mesh that can be regular square or irregular triangular and represents land surface data [5].Among the important tasks of GIS are risk assessment and decision-making [6].Once the digital terrain model has been acquired, a series of processing steps are applied to calculate the basic parameters required to identify the catchment area.Once these parameters had been identified, we applied frequency analysis to calculate the flow rate of the 100-year flood.
Frequency analysis is defined as a statistical approach whose aim is to characterise a phenomenon (hydrological, for example) based on the study of past events, in order to determine the probability of occurrence in the future.It is used to construct a frequency model, which is an equation used to model the statistical behaviour of a process.These frequency models describe the probability of occurrence of a phenomenon.This method is used when sufficient hydrological data is available for a given site (gauged basin) [7].
We used the HYFRAN PLUS software to apply the frequency analysis.it consists of a series of successive steps.The first involves identifying the aim of the analysis, which in our case is to calculate the flow forecast for the 100-year flood.The second step is to select the data series to be manipulated, i.e. a series of historical flows recorded at the station closest to the study site, in our case the Aghbalou station.Then, this series of values is tested by Kendall's test to verify the presence of trends in the values of the series [8].Table 2 illustrates the result of the test.To accept the H0 hypothesis, the P-value must be below a value pre-determined by the software this value depends on the number of samples and the accepted error tolerance.In our case, H0 is accepted.

Table 1. Physical parameters of the Ourika watershed
The next step is to extrapolate and adjust the values according to frequency models, using 3 models (log normal, Exponential and Gumbel).The results are shown in the figures 3.4 and 5.   Towards the end, we applied the chi-square test to check the fit.The Exponential and Lognormal models were accepted by the test, while the Gumbel model was rejected by the test.To adopt a single model that best estimates the centennial flood discharge, we used the AIC and BIC criteria; Akaike information criterion and Bayesian information criterion respectively.The best adjustments correspond to the lowest values of these criteria [9].The table illustrates the results of this test.In parallel with the frequency analysis, we used an empirical method to estimate the flood discharge based on the Francou-Rodier and Fuller formulas.To sum up, we have adapted the mean between the frequency analysis and the empirical method.The 100-year flood discharge adopted is 1340 m3/s.

Hydraulic modelling
The first part of this study is to distinguish the difference between the natural state of the flow and the modified state (after the installation of the bridge).The use of specialized hydraulic modeling software (HEC-RAS [10]) helps to carry out the task while creating a database composed of the topographical and hydrological study.The figures below show the flow velocity along a section of the wadi (1000 meters with the bridge in the middle).To determine the critical height at the bridge, we will look at the profiles upstream and downstream of the bridge, which show the levels reached by the flood.The Figures 8 and 9 below show that the critical height is 526.8 m msl.

Conclusion
It should be noted that the maximum critical height simulated relates to the topographic elevation of 526.8 metres.Consequently, it is imperative that the design of the bridge deck or the total height of the bridge itself exceeds this critical value.A crucial step in this calculation process is the quality of the data used.Inaccurate or insufficient data can compromise the validity of the results.

Fig. 3 .
Fig. 3. Graph showing the fit of maximum flow rates to the Exponential law.

Fig. 4 .
Fig. 4. Graph showing the fit of maximum flow rates to the lognormal law.

Fig. 5 .
Fig. 5. Graph showing the fit of maximum flow rates to the Gumbel law.

Fig. 6 .
Fig. 6.Flow velocity as a function of distance from the wadi section.

Fig. 8 .
Fig. 8. Cross-section of the upstream and downstream sections of the bridge under modified conditions.