Comparative Hydrodynamic Analysis by Using Two−Dimensional Models and Application to a New Bridge

water Article Comparative Hydrodynamic Analysis by Using Two−Dimensional Models and Application to a New Bridge Jesús Mateo-Lázaro 1,* , Jorge Castillo-Mateo 2 , Alejandro García-Gil 3, José Ángel Sánchez-Navarro 1,Víctor Fuertes-Rodríguez 4 and Vanesa Edo-Romero 1 1 Dept. of Earth Sciences, University of Zaragoza, Pedro Cerbuna, 12, 50009 Zaragoza, Spain; [email protected] (Á.A.S.-N.); [email protected] (V.E.-R.) 2 Dept. of Statistical Methods, University of Zaragoza, Pedro Cerbuna, 12, 50009 Zaragoza, Spain; [email protected] 3 Geological Survey of Spain (IGME), Ríos Rosas 23, 28003 Madrid, Spain; [email protected] 4 Dept. of Geography and Territorial Planning, University of Zaragoza, Pedro Cerbuna, 12, 50009 Zaragoza, Spain; [email protected] * Correspondence: [email protected]; Tel.: +34-(9)-690-609-948 Received: 20 January 2020; Accepted: 30 March 2020; Published: 1 April 2020 Abstract: This document develops a methodology that evaluates the impact on the environment of the rivers produced by the creation of civil infrastructures. The methodology is based on the two-dimensional hydrodynamic calculation by using shallow water equations both in the conditions prior to the creation of the infrastructure, and in the new conditions after the infrastructure is created. Subsequently, several characteristics, such as water depth and velocity, among others, are compared between the initial and final conditions, and a two-dimensional zoning of the changes observed is obtained. The methodology herein presented is useful to verify the impact that the implantation of different infrastructures around the river currents could produce. In addition, it is also relevant for carrying out a study taking into account different infrastructure options related to river currents, as well as for selecting the most suitable one. By using the methodology presented, changes on the regime of the currents caused by the infrastructures can be deduced, including a qualitative and quantitative zoning of the changes, with a special emphasis on some characteristics, such as depth and velocity. The methodology is applied in a case study for the creation of a road bridge over the Jalon River in Spain. Keywords: shallow water equations; floodway; floodplain; computational Fluid Dynamics (CFD); SHEE software; Iber program 1. Introduction The public institutions of countries and communities are responsible for regulating the actions that are carried out in the hydraulic domain of rivers and water bodies. When new infrastructures are created in rivers, such as bridges or water diversion spillways, there are three main concerns that need to be controlled: (1) the increase or generation of risks for the environment around the created infrastructure, for example, the ones derived from overpopulated centers, (2) the security for the users of the infrastructure to be created, and (3) the conservation of the functions and natural conditions of the river itself. Normally, the state agencies impose the control and evaluation criteria for the modifications derived from the new infrastructures. This work aims to apply a control methodology for the three aforementioned aspects. The methodology is based on the comparative evaluation between the initial state of the river Water 2020, 12, 997; doi:10.3390/w12040997 www.mdpi.com/journal/water Water 2020, 12, 997 2 of 14 and the state once the infrastructure is created. To carry out this study, two specific technologies are used. The first one is a two-dimensional numerical model that is able to simulate the flow of water and its main characteristics, such as flow, water velocity, and water depth. The model is generated using a free software called Iber, which was developed by State Agencies and Spanish Universities. The second technique is based on a software able to interpret and compare the results obtained from the two-dimensional numerical model. This model is called SHEE (Simulation of Hydrological Extreme Events), and was developed by the Authors of this paper in the Department of Earth Sciences at The University of Zaragoza. This model has given rise to numerous professional works, research projects and scientific publications. Other hydrodynamic modeling approaches are implemented by employing 1D, 2D or 1D/2D schematizations. Although one-dimensional hydrodynamic models are still in widespread use for many applications [1–8], the use of two-dimensional models is required in urban areas to reproduce the complex, multidirectional flow paths generated by urban features [9–12]. Most of the hydraulic studies on infrastructures or next to rivers are focused on assessing the flooding risk of the infrastructure itself or on the protection of the facilities attached to rivers [13]. It should be noted that, in addition, this study tries to assess the possible increase in flooding that new infrastructures can generate on areas annexed to rivers, including urbanized areas. In relation to the creation of infrastructures and their influence on river currents, there are studies that have quantified the risk of flooding, both considering or disregarding the engineering protection measures, and using the hydraulic approach [14]. The existence of river defense structures is restricted by several factors, such as the unavailability of space, the geotechnical limitations, and aesthetic reasons [15]. Studies have found that individual protection measures (IPM) have the potential to mitigate flood risk [16]. 2. Materials and Methods 2.1. Hydrodinamic Model The numerical model used in this work is the Spanish computer program called Iber, which is a two-dimensional model for the simulation of free surface flow in rivers and estuaries. It is distributed for free in English and Spanish (http://www.iberaula.es/). The Iber application has been generated to obtain a hydroinformatic Computational Fluid Dynamics (CFD) tool for free surface flows. Various academic disciplines such as hydraulics, hydrology, fluid dynamics, soil dynamics, chemistry, etc. are involved. The multidisciplinary creator team comes from different public institutions and universities, mainly located in Spain, such as the Group of Engineering of the Water and the Environment of the University of La Coruña, the group of Fluvial Dynamics and Hydrological Engineering of the Flumen Institute and the International Center for Numerical Methods in Engineering (both from the Polytechnic University of Catalonia), and the Spanish Center for Hydrographic Studies (CEDEX), as well as researchers from other universities like the University of Santiago de Compostela, the University of Vigo, and the Institute for Environmental Sciences of the University of Genoa. Iber solves the full depth-averaged shallow water equations or two-dimensional equations of St. Venant (Equations (1)–(3) in order to compute the water depth and the two horizontal components of the depth-averaged velocity. These equations assume a hydrostatic pressure distribution and a relatively uniform distribution of the velocity with the depth. The equations are solved with an unstructured finite volume solver explicit in time. @h @hU @hUy + x + = M (1) @t @x @y S e 2 2 e @hτ @hUx @hUx @hUxUy @Zs τs,x τb,x g h @ρ @hτxx xy + + = gh + +2W sin λUy + + + Mx (2) @t @x @y − @x ρ − ρ − ρ 2 @x @x @y Water 2020, 12, 997 3 of 14 2 e e @hU τ τ 2 @hτ @hτ @hUy @hUxUy y @Zs s,y b,y g h @ρ xy yy + + = gh + +2W sin λUx + + + My (3) @t @x @y − @y ρ − ρ − ρ 2 @y @x @y where h is the water depth, Ux,Uy are the horizontal velocities averaged with depth, g is the acceleration of gravity, Zs is the elevation of the free surface, τs is the stress on the free surface due to friction caused by the wind, τb is the stress due to the friction of the bottom, ρ is the density of water, W is e e e the angular velocity of rotation of the earth, λ is the latitude of the point considered, τ xx, τ xy, τ yy are the horizontal effective tangential stresses, and Ms,Mx,My are the source/sink terms of mass and of momentum, respectively. The source terms in the hydrodynamic equations include hydrostatic pressure, bottom slope, viscous and turbulent tangential stresses, bottom friction, surface wind friction, precipitation, and infiltration. By using Iber, a large number of numerical models can be made with applications in hydraulics and river morphology. The calculation of flow in rivers, the definition of flood zones, the evaluation of risk areas, and the delimitation of roads of intense drainage, are all assumptions where the flow is two-dimensional, and are some of its fundamental applications. It includes the sediment transport and the bottom transport, along with the tidal flow in estuaries, among other possibilities. The simulation of water passage under bridges, sluices, and spillways can also be done including the effect of wind, and it is possible to model the breakage of rafts and dams. The Iber program simulates non-permanent flow or permanent flow, while maintaining a constant flow. The simulations need, firstly, a digital terrain model (DTM) that can generate two types of mesh: structured (e.g., a GRID model) and unstructured (e.g., a TIN model). Another necessary feature is the roughness of the terrain, which can be incorporated through a GRID coverage. Finally, it is fundamental to establish the boundary conditions of the model which, in an upstream case, consist of the hydrograph entering the domain of calculation. The downstream boundary condition refers to the regime in that section, which may be a critical, supercritical or sub-critical regime. As a result, the Iber program provides different coverages in GRID format. The most used modules are the water depth coverage and the total velocity ones. The main information and reference sources for Iber main modules are described in [17]. There are also specific references for other modules, such as Numerical Schemes and Hydrological processes [18], Water Quality [19], and IberPLUS module [20].

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