hec-ras tutorial

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Héctor García Rábade Subject: COMPUTATIONAL FLUID DYNAMICS I Written in October 2012 Universidade da Coruña Master in Water Engineering

HEC-RAS tutorial Index 11.-Introduction………………………………………………………………………………….1 12.-Equations and calculation procedure………………………………………………………2 13.-Program features……………………………………………………………………………..3 14.-Practical example so as to simulate a river…………………………………………………..4 15.-Same example with known downstream boundary conditions……………………………15 16.-Same example with more spatial discretization……………………………………………20 17.-Same example with an unsteady simulation of the river…………………………………24 18.-Same example with a bridge……………………………………………………………….27 19.-Same example with different Manning’s values…………………………………………37 1. Introduction HEC-RAS (Hydrologic Engineering Centers River Analysis System) is public domain software which was developed by the Hydrologic Engineering Center of the U.S. Army Corps of Engineers. This program evolved from the known HEC-2 incorporating a few improvements, such as the graphic interface, or the possibility of exchanging data with the Geographic Information System ArcGIS through Hec-GeoRAS. The program has been so accepted that it is used in civil engineering projects nowadays. As usual, there are some versions of the software because it is updated by the authors permanently improving its features. The last one (version 4.1) is the first that incorporate a water quality module. Therefore, values of temperature (T), dissolved oxygen (DO), carbonaceous BOD, organic nitrogen, ammonium nitrogen (N-NH4), nitrite nitrogen (N-NO2), nitrate nitrogen (N-NO3), nutrient parameters (atmospheric reaeration,…), meteorology data and more information is necessary together an initial condition of all the calculation variables. Below, the Water Quality Data window where this information is included can be seen:

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The version 3.1.3 (of May 2005) will be used because no problems have been detected with their use. On the other hand, only the hydrodynamics will be evaluated here. The version can be downloaded from the internet in the HEC-RAS website, which is: http://www.hec.usace.army.mil/software/hec-ras/ 2. Equations and calculation procedure The Navier-Stokes equations that rule the behaviour of the fluids are formed by the mass conservation equation (divergence free condition) and the momentum conservation equations (derived from the Newton’s second law particularized for flows). The software has a computational program that solves (through a finite difference method) the simplification of these equations after they are integrated both in depth and width. These one-dimensional equations are usually known as the Saint-Venant equations. Then, as the Navier-Stokes equations, the equations gives values of velocity and depths and therefore leads to hydrodynamic models that study the movement of the free surface water through the physic features of the bottom and the sources and sinks. According to the hypothesis, the accuracy of the solution will be as better as the longitudinal dimension is greater than the other two dimensions. Then, this is a numerical model usually applied for the simulation of rivers and channels, where this condition is approximately verified. The model uses the Manning’s coefficient to evaluate the energy losses and can be used in stationary or transitory simulations. The software incorporates a lot of improvements that produces more adequate results than the results provided by the simple one-dimensional model. In fact, the software has the possibility of a 2D simulation of the surface flow (for one-dimensional flows) which is not based on the resolution of 2D equations but in empirical formulas. The results have been tested with experimental data for a long time which does the model is very reliable. In this way the model has an option denoted by flow distribution with which the Divided Channel Method is applied. This tool allows for the subdivision of each of the three existing parts (main channel, left floodplain and right floodplain) in a determinate number of subsections (defined by the user) in which the mean velocity will be calculated. The calculation in each subsection is done with the next expression where Qi, ki, Ai, Ri and ni are the volumetric flow rate, the hydraulic conductivity, the area, the hydraulic radius and the Manning coefficient in each subsection, and S0 is the longitudinal slope:

1/20i iQ k S with:

2/3i i

ii

A Rkn

Then, HEC-RAS is a good option for the evaluation of the flood area, this is, the section and the part of the floodplain which will be occupied for a certain volumetric flow rate. It will depend on the geometry of the bed, the slope and other factors. The problem is that the momentum transference between the main channel and the floodplains is not considered. In the case of modeling large areas of free surface flow to obtain the same type of results (with both velocity components) with better accuracy, the RMA2 module integrated in the SMS computational software is a good option. This is another software that belong to the U.S. Army Corps of Engineers too and the RMA2 is an hydrodynamic numerical model that solves (through the Finite Element Method) the simplification of the Navier-Stokes equations after

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they are integrated in depth. These two-dimensional equations are usually known as the 2D depth averaged equations or shallow water equations and they need eddy viscosity coefficient to characterize the turbulence losses. The accuracy of the solution will be as better as the horizontal dimensions are greater than the vertical dimension of the fluid (the movement is mainly horizontal). This condition is usually satisfied in lakes and estuaries besides rivers. Then, this is a model usually applied in the simulation of flow around islands, flow under bridges, flow in places where rivers are joined, flow in central pumping channels, coastal areas, estuaries, reservoirs,… The model uses the Manning’s coefficient to evaluate the energy losses and can be used in stationary or transitory simulations. This model would be more appropriate so as to know the lateral distribution of velocities in examples with a main channel and floodplains in which the flood area is evaluated. However, in the most of applications of hydraulic engineering related to the floods, the longitudinal dimension is still much greater than the transversal dimension. Then, it makes sense to use an one-dimensional model based on the Saint-Venant equation for the longitudinal calculation treating the transversal calculation in a separate way through lateral distribution 1D models. Moreover, the two-dimensional model, which modifies more parameters because of the consideration of the hydrodynamics in a more complete way, needs to increment the value of the eddy viscosity so as to achieve numeric stabilizations in many cases (being more adequate to simulate subcritical flows). Then, the simplicity with the greater simplification of equations and the efficiency with the application of the DCM (and other developments) make that HEC-RAS is a better option in this type of cases. 3. Program features The program allows for: - The hydraulic calculation of structures (bridges, spillways, culverts…) - The graphic visualization of data and results. - The graphic edition of sections. - It is executable in the Microsoft Windows environment. The program needs the next input data: So as to use HEC-RAS for simulating a river, geometry data of transversal sections along the river stretch and volumetric flow rate data (constant or variable in the time) must be available. Moreover, roughness coefficient and water level at the input or the output section is essential to represent the real case. In cases more complex (bridges, water quality evaluation) more data must be provided. Following this, some examples are included so as to see a bit more things in each one.

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4. Practical example so as to simulate a river A river stretch through a rural settlement wants to be studied. The initial geometry of the riverbed is modeled with three sections with a separation of 500 m between them. The stretch is straight and the sections are defined with the next geometry: - Section 1 (downstream)

X (m) 0 20 100 120 140 150 250 280 Y Ground level (m) 101 97 96 92 92 95 97 101

- Section 2 The ground levels of the section 1 are increased in 0.5 m. Section with the same shape as the section 1, but narrower (90% of the width) - Section 3 (upstream)

The ground levels of the section 2 are increased in 0.4 m. Section with the same shape as the section 2, but more wide (30% more wide) The volumetric flow rate will be 100 m3/s for a return period of 10 years, 300 m3/s for a return period of 100 years and 500 m3/s for that of 500 years. The friction coefficient (Manning’s coefficient) will be estimated in 0.1 m-1/3s in the floodplains and 0.03 m-1/3s in the rest (riverbed limited by the banks).

a) Simulate the river stretch considering slow regime and a normal depth with a slope of 0.001.

When the program is opened the main window appears:

Firstly, a project has to be created by clicking on File>New Project, introducing a file name, a project name and a path in the new window that appears (click on Create Folder so as to the files of the program are not scattered in the path). Remember that this is better to use names and folders without accents. Now, a name and a path appear for the project in the main window. The project will be open going to File>Open Project wherever the user wants. Help about options can be found in Help>HEC-RAS Help (it is the same as clicking on Help inside any other window).

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If the System International (depths in m, velocities in m/s, volumetric flow rates in m3/s) is not used by default, it should be changed in Options>Unit System. Following this, the geometry data has to be introduced firstly clicking on the next icon (of the main window): Geometry data Now a background image can be put clicking on and selecting an image (click on add) such as a map (there is no problem with bitmap extension .bmp and with .jpeg extension, but .png is not supported and .tif can have problems). Use the tools View>Full Plot, View>Zoom In or View>Pan to place the image (the image has a determined coordinates and the Geometry Data window too). The image can be helpful to plot the river but it is not necessary. Following this, the plotting of the riverbed is drawn with the mouse over the window after clicking . Firstly, the beginning point is put by clicking and the plotting is done clicking on each vertice the user wants to define. Finally by double clicking the name of the river and the reach has to be put being possible to avoid the edition by selecting cancel (or delete once created in Edit>Delete Reach). The river will appear oriented from the first to the last point. The reach name that appears near from the plotting can be modified (Edit>Change name, Edit>Move Object). File>Copy To Clipboard is valid so as to copy a figure from this window. The plotting is independent of the real distance, which will be indicated when defining the sections. Then, if a map is used it is representative to define the distances according to the representation (in the way that the sum of the lengths that will be defined is the same as the distance of the stretch). The sections are defined by clicking on . Another window will appear and the sections are defined from the first section to the last one. The table is prepared to be filled for each section defined (with x, y coordinates that represent the transversal section) and the window contains in the right side the downstream length, the Manning’s values, the position of the banks (in x coordinates) and the contraction/expansion coefficients. The first section will be added with Options>Add A New Cross Section and putting a name (River Station).

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The section firstly indicated (downstream or outlet section) will be the correspondent to the last point (observing the river orientation already defined) and there will not be downstream lengths to a before section. Taking positive length values, if the name is 1 or the number of the last section, the sections will be set in the way that the river orientation goes towards the section 1 following a decreasing order (HEC-RAS follow the number order in the way that the outlet is always the section 1). If the name section defined is 1 the section will be the correspondent to the outlet section as desirable (and sections are not joined due to the null length). This is the same to define firstly any section with the previous consideration. Thus, the input section will have the downstream length and the last number section so as to it makes sense. Sometimes the plan view of the river can appear in a strange way, with sections that are not perpendicular to the stretch (see below image). In this case, the data seems to be wrong. Nevertheless, it is well and this is only matter of representation (affects future representations) as it was checked. The cells of the window are filled by clicking on them (the table is filled with the data of the section). Once defined the banks (if x point does not exist HEC-RAS interpolate a point), Manning can be differenced in each part (main channel and floodplains). A value of the Manning’s coefficient, which depends on many factors, can be found easily in bibliography for different cases (and a table appears clicking on the question mark). In rivers this is usual 0.02<n<0.04 in the riverbed and values as high as 0.1 m can be reached out of the riverbed. Some particular cases are observed going to Help>Mannings n Reference Online in the main window what leads the user to the next website: http://wwwrcamnl.wr.usgs.gov/sws/fieldmethods/Indirects/nvalues/index.htm A contraction coefficient of 0.1 and an expansion coefficient of 0.3 are advised for a typical river and appear by default (see the question mark too). These coefficients are added so as to evaluate the losses of energy between sections in terms of coefficient times the absolute value of the change in velocity head between adjacent cross sections (when the velocity head increases in the downstream direction the contraction coefficient is used). Changes are considered by clicking on Apply Data button. The picture with the section can be seen on the right (after clicking the icon which is near from the Apply Data button if this is not activated) but can also be seen going to Plot>Plot Cross Section. So as to view the longitudinal profile Plot>Plot Profile is clicked. The following sections are added in the same way or through the option Options>Copy Current Cross Section (all cells are copied). Again, a name is put and cells are filled appropriately. If the downstream section was firstly defined, as here, the length to the previous defined section is indicated in all of them. Sections defined can be deleted in Option>Delete Cross Section (and the lengths are modified so as keep the position of the rest).

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Here, second and third sections are edited by multiplying the factors 0.9 and 1.3 going to Options>Adjust Stations>Multiply By A Factor and adding the values 0.5 and 0.4 to the elevation with Options>Adjust Elevations (considering that the length is 500 m as this is the separation section according to the example). The floodplains are a nearly flat land adjacent a stream or river that stretches from the banks. Here, once the section 1 is observed, the banks of the riverbed are considered in X=100 m and X=150 m (90 and 135 in the second and 117 and 175.5 in the third following the same points). Red points will show these limits. The sections are represented in the plan view of the Geometry Data window with a separation equivalent to the lengths defined (since the second cross section is defined). When a section is selected in the cross section data window, will be remarked in the Geometry Data window. Furthermore, as the width appears represented, this is useful so as to compare with a map (if it exists). The geometry of the stretch is shown below. Following this, the geometry definition must be saved (with a name) going to File>Save Geometry Data (in File>Open Geometry Data each defined data can be used). Now, a name and a path appear for the Geometry in the main window (the name could be invisible, formed by spaces). All this saved items can be opened to be modified and saved again. Following this, the steady flow data icon (of the main window) is clicked to introduce the boundary conditions and the next window will appear. For steady flow simulations (stationary solutions)

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As known, the slow or subcritical regime is produced when the velocity of the fluid is lower than the velocity of the gravity wave ( gh ) that accompanies it. The expression that rules the existence of this regime is:

1vFrgh

In this case the water level boundary condition must be given downstream. When Fr (the Froude number) is greater than 1 a fast or supercritical regime appears (velocity faster than the velocity of the gravity wave) and the water level condition must be given upstream. In river, it is usual to find 0.2<Fr<0.4. Then, this is supposed a slow regime in the example, giving adequate boundary condition. If, once executed, strange solutions appear (Fr numbers generated postprocess are greater than 1, boundary conditions are different from the defined), fast regime takes place and the solution will be wrong because of the boundary conditions. Then, the other case is considered. This is the usual procedure. In the top part of the window (number of profiles) three profiles are introduced as three cases are going to be analyzed. Moreover, the last river station is considered (upstream boundary condition, by default). Then, the three volumetric flow rates (flow rates hereinafter) are introduced (below PF1, PF2 and PF3). Then, the Apply Data button is clicked. If the user wants to add a flow rate in the middle of the river (representing an affluent) the river station would be changed and then the button Add A Flow Change Location would be clicked leading to other cell appear to be filled with the flow rate. In Options, the rows and columns of the table can be deleted allowing for an easier edition. Moreover, Options>Edit Profile Names let the user change the profile reference. Thus, PF1 can be changed by T= 10 years so as to have a more clear information. In this window the level water boundary condition can be put by clicking on the button Reach Boundary Conditions. In the upper part of the window there is option of Set the same boundary conditions type for all flow rates, which is taken as this is more common. The other option let the user deal with different boundary condition type for each defined flow rate. The boundary condition types are four (the Downstream cell is selected before they are given). The known W.S. let the user put a determinate water level condition (H=y+Y where y, also denoted by h, is the water depth and Y is the ground level) for each flow rate (in this case there would be three options). A measurement station is interesting so as to have this data for a certain river. If the critical depth (typical condition in spillways) is selected, the program will calculate the water levels so as to reach Fr=1 (downstream) for each flow rate and the user has not to define anything. Then:

v gh

Q

h

yc v

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In this case, the regime is slow and Fr is increased in the flow direction. A transition from the slow regime to the fast regime is produced (through the critical depth) being possible to model this part of the river (boundary condition downstream is adequate). Then, when the solution is obtained, in the Fr tables it must be checked that the behavior is just that. For example if Fr takes the values in defined sections of 0.2, 0.2, 1 this is wrong, and if 0.8, 0.9, 1 appears this is right. If the transition from fast regime to slow regime (hydraulic jump) is going to be analyzed it has to be taken into account that HEC-RAS cannot model this case. If the normal depth is selected, the program calculates the water levels for a certain friction slope (I) which is introduced and which is the same for each flow rate. The value introduced will be that of the geometric slope (i) at the downstream section as when the geometric slope and the friction slope is the same, the normal depth is reached (obviously the value will be the same for all the flow rates). This boundary condition is often applied as this is the depth that usually appears in this section. In the case of a channel (using the z HEC-RAS axis that follows the length):

2 2

4/3 ;2

n v byI RhRh b y

;

If ;2

nn

n

dy byI i Rh ydz b y

HEC-RAS calculates yn from the equation (b and n are already defined) The value given could be that of the mean slope of the river (or the downstream stretch) instead of that which is calculated through the sections. In rivers the most common slope is 0.001 as in the example. Here, this value is the same as the slope of the last stretch from section 1 to section 2, which is 0.5/500 =0.001. Both values are more near as the discretization is lower. Then, the mean slope, which can seem not to be necessary and usually has a different value, can be a better option when the variation of the bottom levels is large what is usual for a refined discretization. Obviously, this will not give exactly the normal depth at the downstream sections, but the solution will be more representative of the normal depth in nearby sections. The solution will not give a normal depth in all the sections if the some of the features varies leading to the different known profiles (M1 or M2) for slow regime. This is, the calculation of the friction slope in other sections will not be equal to the geometry slope in these sections. If the rating curve option is selected, pairs h, Q must be defined according to known values for a determinate river (at the downstream section). Then, for a flow rate the program will interpolate a value of water level. This is approximately the same as the first option (known W.S.). The difference is that water levels have not to be defined for each flow rate used once the curve is created.

yn y

z

y

x

b yn

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Following this, the flow data defined must be saved (with a name) going to File>Save Flow Data (in File>Open Flow Data each defined data can be used). Now, a name and a path appear for the Steady flow in the main window. The last step is to create a plan which will be created for steady simulation. For compute the steady example The plan is constituted with a Geometry Data and a Steady Flow Data (note that the steady flow cannot be defined until the geometry is defined, and the plan cannot be defined until the geometry and the steady flow is defined). Firstly this is generated going to File>New Plan, using a name (for example Normal_depth_and_FirstGeometry) which can be changed (File>Rename Plan Title) and a short identifier with less than 12 characters (for example yn_FirstGeom) that can be modified directly in one of the cells. Then, the last Geometry Data and Steady Flow Data is put in the adequate cells (the last appear by default), and subcritical regime (Fr<1) is selected. The option Options>Encroachments is very interesting as this is useful in order to analyze in six steps the necessary artificial bed to contain a determinate flow rate in certain conditions. For example, for the flow rate for the returned period of 100 years, the program will use walls looking for the walls that let the water level be (for example) a=0.3 m greater than that without encroachment. Thus, walls are modified reducing the section in an iterative process until optimum emplacement is found for this water level. This option is not used in the simulation of the present river. The option Options>Flow Distribution Locations allows the user to subdivide in subsections (slices) the cross sections. HEC-RAS will do a 2D geometric distribution of energy and velocities in different points of the cross section will be obtained (remember that it would be impossible in a 1D model). The number of subsections to be considered, which has a maximum of 45 by cross section, is specified in a separately way for the left overbank, the main channel and the right overbank. Here, three subsections for each part are considered enough. So as to compute flow distribution for all the cross sections, the numbers (3 for LOB, 3 for Channel and 3 for ROB) are specified at the top of the window (Set Global Subsection Distribution) and values are stored in the cells. In other case (so as to set slices at specific locations) the other part of the window is used and values are kept in a table. The same is done for the subdivision indicated (3 for LOB, 3 for Channel and 3 for ROB) if the last section is put as Upstream RS and the section 1 is put as Downstream RS. After defining the slices in this way, the button Set Selected Range has to be clicked. It can be seen that after pressing OK a tip appear in this menu option.

a

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Following this, the plan must be saved going to File>Save Plan (in File>Open Plan each defined plan can be used). Now, the Compute button is clicked. It can be checked that a name and a path appears for the Plan in the main window. Errors can appear before computation due to that the banks or the Manning’s coefficient were not defined. A typical error can appear due to that the ground levels are defined in such a way that the water is not contained by at least one of the sections. After the computation is done a window appear (next above figure), and more specifications can be found by clicking the next icon (in the main window) which leads to another window (right figure) with the errors and warnings reached. If less than 5 warnings are obtained this is considered a good simulation. Summary of errors and warnings Many geometry data files or steady flow data files can have been created (any other defined in the project can be selected when defining the plan) and then, many plans can be defined for the same project. When a different geometry data or a flow data is opened or saved from the

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respective window, the name and the path of the plan will disappear. Then, the plan has to be defined again (with the new files) or an already defined plan has to be selected. The results can be observed by clicking on the next icon (from the main window). View cross sections In Option>Select Plan, the plan can be selected (if more than one plan is defined, they are all calculated). In Option>Select Variables, the variables that want to be seen are selected (water surface or W.S. which is the water level, the Energy Grade or E.G. which is the total energy of the water as the sum of H+v2/2g = h+P/γ+v2/2g from the Bernoulli’s equation, the critical depth which appears if that exists…). The variable Filled in Water Surface allows for seeing the blue water color in the images. In Option>Select Profiles>Select All, all the profiles are selected in the way that three solutions for each variable appear in this case. The option Options>Velocity Distribution>Plot Velocity Distribution allows for seeing the velocities in different colors. Specified information can be obtained clicking over the point of any window of results like this one. Thus, after defining the sections the flow rate boundary condition (one for each return period) has been given, establishing the calculation cases. Following this, the depth boundary condition (normal depth, yn) has been given. Finally, a plan has been defined and the solution can be calculated. The next solutions in the three transversal sections are obtained (blue filling for T=10 years, the lowest flow rate by default): Velocity solutions in the riverbed Values of the critical depth yc, the water surface (WS) and the energy (EG) can be observed for the defined return periods of 10, 100 and 500 years. For example, it can be seen that only in the section 1 there are calculated values for the critical depth (for all the return periods). So as to see the representation of the blue filling for other return periods, the profile has to be the only one selected in Options>Profiles (click on the clear all button and select only the desirable profile by double clicking on the name or using the arrow). For the representation of the velocities the same occurs. The water level for the case of T=500 years along with the velocities for the case of T=10 (all the profiles selected) and T=500 years will be shown in the next figure.

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As can be seen the water is inside the riverbed only for the lowest flow rate (and maximum velocities are lower in this case). So as to see the longitudinal representation of the solution, the next icon (from the main window) has to be selected. The selection of profiles, variables and plans for representations is the same (velocities cannot be represented). Profile plot of the solution The next longitudinal profile in a section between the banks can be obtained for all the profiles (flow rates). Here, the variations in the water depth can be seen in a better way. As a first approach (through the image), the water depth is not near from the critical depth in all the cases. If it is approaching the critical depth, care has to be taken. The solution could have to be calculated for a fast regime with other boundary conditions. Now, solution in the cross sections and longitudinal section can also be seen with the same interface where sections are edited, in the Geometry Data window (or directly in cross sections). Now, some variables are represented in a graph with the next icon (from the main window): Velocities and other variables The selection of profiles and plans for representations is the same. The variable value is what is represented. In the option Standard Plots the different variables can be selected (Velocities, Flow area,…) leading to a representation by variable. The velocities along the river

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(longitudinal representation) in the different areas (left floodplain, main channel and right floodplain) for the three return periods (flow rates) are represented in the graph below left. Selecting Standard Plots>Froude the graph above right is obtained and this is possible to see if the simulation is right. Froude Chl is the Froude number for the main channel and Froude XS is the Froude number for the entire cross section. The maximum value is produced for T=500 in the channel of the second section and for T=100 in the entire second section. This is obtained a maximum value of Fr=0.5 which is a high value for a typical river. If this number is increased as the downstream section is reached, for example, from 0.4 to 0.9 which is a possibly solution, this is possible that the regime is fast (instead slow reaching the critical depth at the downstream). In this case, the another hypothesis should be calculated. This is not the case. The rating curve can be obtained by clicking on the next icon (from the main window): Rating Curve The rating curve is the curve which relates the water level (W.S.) and the flow rate (according to the three cases of the three return periods). These curves give important information in the application of boundary conditions for the hydrodynamic models. In fact, one of the water level boundary condition possibilities is to define a rating curve. In the graph options, only the selection of the plan can be done (variable is fixed and flow rates are represented graphically). In the below figure, the curve (obtained postprocess) is shown for the downstream section. Obviously, the flow rate that goes through section is the same for each case, but the water surface is not. Now, it can observed the sensitivity of the solution with other similar boundary conditions such as the modification of the slope for the calculation of the normal depth, the critical depth,…

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5. Same example with known downstream boundary conditions

b) Simulate considering slow regime and a known water level boundary conditions of 92.5, 95 and 98 m. Check that with the lowest flow rate critical depth appears.

Now, the Steady Flow Data window is open again, and different water depth boundary conditions are given after clicking on the button Reach Boundary Conditions. Within the new window and observing that the cell downstream is selected, the button known W.S. is clicked and the water levels considered are introduced. This steady flow data is saved (now, File>Save Flow Data As so as to not overwrite the existing file) for example with the name known depth (if the water level is known, then the water depth is known because the ground level is data, water level=y+Y). This is the same to save when the window is opened (Save As in this case) being necessary to save again before closing the window. If now, the user open a steady flow data two files appear (see the right window). Now, the plan has disappeared in the main window. Instead open the defined plan, another plan is defined. The new steady flow appears by default in the window where it is done. Following this, a new plan is saved (this is the same File>Save or File>Save As, as there are not any plan defined) with a name (for example, known_depth_and_FirstGeometry) and a short identifier (y_FirstGeom). The subcritical regime is selected and now 45 slices are chosen with the option commented after clicking the button clear all. According to the distribution, 10 slices are considered in the LOB, 25 in the main channel and 10 in the ROB (as can be seen with the global option the maximum by part is 43 being necessary 1 slice in the other parts are selected). Saving the plan and computing, the results are obtained with 5 warnings.

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The geometry is the same as before, but now a known water level has been given in the downstream section. These values are of 92.5, 95 and 98 m respectively for the defined return periods of 10, 100 and 500 years (associated with the flow rates given). The solution in this case in the three cross sections considered is shown below. Now, the representation of the velocity is better. For T=500 years this is: Now, according to the results, in the downstream section (section 1) there are values of critical depth, in the section 2 there are values for the return period of 10 years and in the upstream section (section 3) there is not critical depth value indicated. Curiously, in the downstream section for 10 years (flow rate of 100 m3/s) the value of the water level is just the water level for the critical depth. Then, something strange is occurring. Again, it is expected that the flow is slow (Fr<1) as this is the condition that usually takes place. HEC-RAS will try to simulate as the flow is slow, but this is possible that the calculation is not done for the defined conditions, avoiding HEC-RAS stopping the calculation. In the longitudinal profile, which is shown below for all the return periods, interesting information is obtained about this.

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As can be seen, for 93.24 m the critical value is reached for the lowest flow rate. HEC-RAS has done a calculation for slow regime and solution is not found so as to reach the imposed boundary condition of 92.5 m (in fact this is the last warning that appeared). This is the reason why a red dashed line indicates the critical depth for the stretch between section 2 and section 1. Then, this is checked that for the lowest flow rate and the considered boundary condition in slow regime the critical depth is produced. This is because the critical depth, which is produced for a water level of 93.24 m, is the minimum water level that allows for a slow regime. As it is known, this situation is usual in spillways where slow flow (increasing the Froude number in the direction of the flow) exist upstream appearing the critical depth yc (Fr=1) in the point where the waterbed ends. In this point a transition between slow regime and fast regime could take place. As it was explained the other transition that leads to a hydraulic jump from fast regime to slow regime could not be simulated with HEC-RAS. In the case of having the 92.5 m boundary condition, the flow will be necessarily fast. Thus, the water level boundary conditions have to be given in the upstream section looking for that one that allows for this water level downstream. Now, solution of the two introduced plans can be represented at the same time so as to compare them. For example for the profile of the greatest flow rate, the next image is obtained. In the following images, the comparison of the longitudinal profile of velocities for this flow rate (only flow in the main channel) and the rating curve for the last plan are represented.

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Information can be obtained with tables too. The next icon is selected from the main window so as to see some relevant variables: Tables with results Here, information of certain variables is indicated. The plan, the profile and the section is selected in the window and a lot of variables related to this case are shown. Some of them are presented for the total section on the left (energy grade in meters, velocity head, water surface, flow rate which will be the same for each section in a determinate plan and profile due to the mass conservation,…) and other variables are presented for the LOB (left overbank), the main channel and the right ROB on the right (Manning’s coefficient considered, flow area as the area occupied by the water, the average velocity, the depth,…). This table always shows the warnings of the simulation. In the case of the last plan with the lowest flow rate and the downstream section the left table appears with the warning message pointed out. The right table is obtained for the upstream section. Between these variables, it is the shear stress, that is the stress in the plane of the cross section and that can have importance as measure in some way the tangential force of the fluid. The increment in Froude number can be observed through another type of table instead of the longitudinal profiles of Froude number. Now, the next icon is clicked from the main window in order to use this table: Tables with results by profile

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All the results generated can be shown at the same time clicking on Options>Profiles>Select All in order to see the profiles and clicking on Options>Plans in order to see all the plans. As can be seen sections are separated which makes easier to view it. In Options>Define Table, the user can select the desirable variables (by clicking on Delete Column button after select one or clicking on Insert Column and double click on one of the variables listed below after it). Below, results are shown for all the results on the left, and for the last plan and the lowest flow rate on the right. As the interest is in the Froude number, in this table fewer variables are put (edited table). Another variable of interest is the E.G. Slope (slope of the energy grade line) which is the friction slope defined before (I). Obviously, it is not equal to the geometric slope of 0.5/500=0.001 between section 1 and 2, and 0.4/500=0.0008 between section 2 and 3. This is seen how the velocity of the water is much greater at the downstream section and how the Froude number is increased as the number of the section is lower (can be considered Fr=1 at the downstream section, this is, the value for critical depth). Another type of table can be obtained going to Std Tables. The table which has been used is the Standard Table 1 (appears by default). Another Standard table exists (other variables, same configuration), besides specific tables for culverts, bridges,… The defined configuration of a table disappears once another table is selected (for example selecting the same type of table after its definition) if this is not saved in Options>Save Table. The current simulation can be shown in a table opened from a before simulation only clicking on the Reload Data button.

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6. Same example with more spatial discretization

c) So as to obtain a greater discretization it is proposed to insert sections between that already defined, in the way that slopes are kept and sections are separated by 100 m. Analyze the differences for the known water level condition and obtain a 3D representation.

As it can be observed, the previous warnings indicate the need for additional cross sections. As the length of the stretch is of 1000 m, the subdivision leads to 11 sections in total: 1000/100+1 (closure) = 11 sections Another file with another geometry will be defined for the same project (the plan will disappear from the main window). So as to do it, click on Geometry Data icon again. The file is generated previously for example (remember that this is the same as modifying the geometry and Save As with other name), going to File>Save Geometry Data As and giving a name (for example SecondGeometry). Here, an interpolation between defined sections can be done, going to Tools>XS Interpolation>Within a Reach in this Geometry Data window. The user will indicate the maximum distance between sections in a stretch (between first and last sections or between any two sections that define a part of the entire stretch) and HEC-RAS will put the sections automatically using a lower than or equal distance between each pair of sections in the way that the originally defined sections are maintained. The option Between 2 XS allows for interpolating in the same way but only between two defined sections and allowing the user to have much greater control over the interpolation. Here, the first option is used, and this is taken into account that with the separation of 100 m, original second section is just in the subdivision (HEC-RAS uses this value) and there will be a section each 100 m along the river stretch. In this example, the distance would always be constant in the entire stretch though the user wanted a maximum distance of 22 m (in which case HEC-RAS would use 21.739). The river, the reach, the sections between which sections are added, and the distance are written. Then, the Interpolate XS button is clicked and the window is closed. Following this, the section is saved in File>Save Geometry. As it can be seen, sections are added interpolating all the defined variables (manning, banks, geometry of the cross section,…). In fact, sections are put with a downstream length (to a before section) of 100 m, modifying lengths in originally defined sections (from 500 to 100 m in the section 2 and the section 3) so as to maintain their position. The names of the original sections are maintained, and new names appear with asterisk in a format in which the number of an original section is followed by a reference number. Previous

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calculations are still in the original sections (the section 3 has water, the 2.8* still has not). Now, a new plan (File>Save As) with this interpolated geometry and the known depth boundary conditions is generated going to the appropriate icon. Subcritical simulation is done after the plan is saved. Therefore, a known downstream value of 92.5, 95 and 98 m is given respectively for the return periods of 10, 100 and 500 years. If the discretization is not good, the user can overwrite the second file opening the first file and saving with the name of the second (instead of modifying and saving the second). If the plan was already created, it only has to be selected after the previous step. Now, the geometry is defined with more discretization (8 new sections) leading to a more accurate solutions. However, according to the data, the geometry is not defined with more precision as the cross sections have interpolated values (for example, the waterbed of the section has interpolated values of the points that define the waterbed of the known sections). Following this, the results in the cross sections 1, 1.2* and 2.2* are shown (four warnings were obtained). Here, it is better observed how the water depth is adjusted to the critical depth for the lowest flow rate. A little bit differences due to the discretization are observed. Below, the upstream section is included, comparing this plan with the previous plan (same boundary conditions) for the lowest flow rate (last plan appears by default). In Options>Zoom In a zoom is done (Option>Full Plot return the complete view) and a little outline appears in the left upper part of the window.

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Now, the water level longitudinal profile has a better appearance as can be seen in the left image. A big refinement (sections each 10 m) has been done so as to obtain the right image (three warnings in this case). Take into account that if a plan is selected for the representation deselecting the plan used when computing, the discretization is kept. Thus, if the plan used when computing has a greater discretization, all the cross sections will still appear though some of them without solution. The geometry shown on the right is that of the last simulation. Again, the Froude number will be increased as the distance to the downstream section is lower for the lowest flow rate case. This can be better observed now. The graphic representation of the Froude number along the stretch (only Froude in the main channel) and the table (Standard table 1) with this variable are shown below on the left for this case. On the right, the graph for the greater refinement is included.

A 3D representation of the water level scalar field is obtained by clicking in the next icon (main window):

For 3D representation of the solution

The selection of profiles and plans for representations is the same. The variable to be represented is only the water surface. Here, a customized perspective view of the solution is obtained with the interface that HEC-RAS offers. The image can be rotated around two axis thanks to buttons prepared for it. In this way, the solution can be observed from different angles. Moreover, only a part of the stretch can be seen by selecting the upstream and downstream sections. After running with the geometry for the 100 m discretization, the representation for the lowest flow rate and all the flow rates is included below.

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After running the program for the discretization of 10 m, the figure below is obtained for the lowest flow rate through the animation option. As it was indicated, the program is executed twice so as to the discretization in each case appear. The animation can be done in each results window and allows for a video with the solutions obtained. Profile plots can be animated through different flow rates for steady flow (this is the case). With Options>Animate the solution for each profile appears one by one (though only a profile is selected). Profile plots can be animated through a time series for unsteady flow too, though this option is not carried out here. Then, when a transitory solution (unsteady) is obtained, HEC-RAS solutions for each time step during a certain time interval are used to make the video, which is more representative. When the animation is selected, a window with the scheme of the animation and a control bar appear besides the original window. In the animation control bar, the right button let the user select the animation speed.

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7. Same example with an unsteady simulation of the river

d) Obtain the solution supposing an initial condition of flow of 100 m3/s, a downstream water level boundary condition that depends on the flow rate and a variable upstream flow condition from 100 m3/s to 500 m3/s with a lineal variation during four hours and a constant value of 500 m3/s in the next four hours. See the evolution and calculate the downstream water level in five and seven hours.

Select the unsteady flow data icon from the main window. If the boundary conditions were defined for unsteady flow this icon has to be used: For unsteady flow simulations (transitory solutions) Go to the Initial Conditions menu and set an initial flow in the upstream (by default) by double clicking on the appropriate cell and clicking on the Apply Data button. Then, go to the Boundary Conditions menu. In the cell for downstream section a water level is defined through a rating curve clicking on the appropriate button (the depth will depends on the flow during the simulation). The curve is defined with the values of each return period modifying the last one so as to not reach the critical depth. Following this, a flow curve is defined upstream in the way that a different flow appears at each different time as boundary condition. Then, the Flow Hydrograph button is clicked and the curve is introduced after selecting the cell for the upstream section. Now, the unsteady flow name and the path appear in the main window. Following this, the unsteady flow data is saved in File>Save Unsteady Flow Data. Now, the plan is defined clicking on the icon (main window): For compute the unsteady example The geometry with the discretization of 10 m will be used along with the unsteady flow data and are chosen (set by default) in the window that appears. Then, all the programs to run are selected. Following this, the time and date that define the start and the end of the simulation have to be entered.

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The time step for calculation which is the computation interval has to be small enough (this is good that at least the time of the hydrograph divided by 24 is considered). The hydrograph output interval should be equal or greater than the selected computational interval. The detailed output interval makes that the program has not to print the solution for each computational step being able to avoid the storage of large amount of information (then, it will be equal or greater than the computational interval). Here, a computational interval of 1 minute (instabilities for a greater time were seen), a hydrograph output interval of 20 minutes and a detailed output interval of 20 minutes are taken. The mixed flow regime is an option that is used if there is a transition from subcritical regime to supercritical (draw downs) or from supercritical to subcritical (hydraulic jumps). This is not the case. The plan is saved and the computation is done. Now, all fields of the main window are filled. Only solutions from the animation of the 3D view for this plan are going to be shown. Now, as indicated, there is a profile per printed solution (detailed output interval). The first profile is that in which the maximum water level is produced.

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The water depth is always growing though the flow rate is constant at the end. However, in the last hour almost is the same (stationary solution will be reached if boundary conditions are constant). The water level is for example observed through the longitudinal profile considering that for five and seven hours the profiles for 24:00 and 2:00 hours have to be selected. A water level of 97.77 m is obtained at 24:00 hours and 97.98 m is obtained at 2:00 hours (see the figure below left). At 19:00 hours the water level will be 93.5 m which is in correspondence with 100m3/s according to the rating curve and this is right because the initial condition is a flow rate of 100 m3/s (see the right figure). For the constant boundary condition of 500 m3/s, the stationary solution will be reached for a water level of 98 m because this water level is in correspondence with 500 m3/s according to the rating curve.

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8. Same example with a bridge

e) Near from the central part between the section1 and the section 2 a bridge with three piles of 1 m of diameter wants to be defined. One of the piles will be placed in the riverbed and two in the floodplains. Propose a design with a flat deck which has a level of 98 m in the lower part and 98.6 m in the upper part. Moreover, define ineffective flow areas in the stations X=80 and X=200 m with a level of 98.6 m. Apply the Energy’s, Momentum’s and Yarnell’s Methods. Simulate with the know water level boundary conditions and the geometry with sections each 100 m.

The geometry with the discretization indicated is opened from the Geometry Data window. Then, in the same window, the icon Bridge and Culvert is selected. Now, in the Bridge Culver Data window the option Options>Add Bridge is chosen and the river station has to be introduced. After observing the sections it is decided that the bridge will be collocated in the section 1.5 which is the number to be introduced. This section does not exist and, as the number is between the 1.4* and 1.6* defined sections, HEC-RAS will place this section between them after interpolating (which is just the middle of the first stretch). Thus, the number has to be defined with a value between the number of the two existent sections which will be the bounding sections (1.55 is between 1.5 and 1.6). This is important to know that this number cannot be one of the existents. Automatically, the new interpolated section appears in the window (only this section can be seen here because as many sections as bridges are defined appear) with two buttons to see the bounding sections. The upstream and downstream parts of the new section are drawn in the window. There are some possibilities in this Bridge Culver Data window. For example, the Culvert icon could be clicked to define a culvert. Here, the Deck/roadway icon will be clicked so as to define the deck. The deck of the bridge has a thickness of 0.6 m (by resting values) and will be designed with a width of 4 m and the bridge symmetry axis (the section 1.5) exactly placed in the middle between the sections 1.4* and 1.6*. In this window, the distance is referred to the distance from the next section (1.6*) to the bridge, and the width is the width of the deck. In this way, as the distance from the bridge axis to the section 1.6* will be 50 m, if the distance is 48 m and the width is 4 m (combination as 40 m and 20 m will lead to the same axis position with other widths). Now, the position of the section 1.5 is defined.

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It is important to take into account that no section can be crossed after defining the distance and the width (width + distance <= length) and the distance cannot be null. If the user wants to put the axis of the bridge in one of the original sections, such as the section 1.4* a solution would be to define a distance of 98 m (from section 1.6*) and a width of 2 m and to create another section 1.3 to define a distance of 0.001 m (from section 1.4*) and a width of 1.999 m. This procedure is useful if a big discretization is done and the bridge has a large width. The weird coefficient appears by default with a value of 1.44 which will be kept. In the table of the same window, the shape of the deck is defined. The information for the three columns for the upstream part and the three columns for the downstream part is covered in the same way. In this particular case, the same values will be taken (no variations along the width, variation if there are different values in the horizontal direction of the table which leads to different figures in the upstream and downstream representation) and only the three first columns are edited at first. X=0 (remember that X is the axis along the cross section) is taken as first station so that the value is written in the first row and X=300 is taken as second station so that this value is written in the second row. The maximum level of the deck (98.6) in the high chord cell and the minimum level of the deck (98) in the low chord cell are defined too. The bridge is designed without longitudinal slope and then, the high chord and the low chord values will be the same (no variations along the length, variation if there are different values in the vertical direction of the table). More X values could have been defined but it makes no sense. The values have to be given in the way that the defined points are on the ground (the bridge is supported if X is chosen in that way) leading to a representation in which the deck is supported on the ground. Now, the button Copy US to DS at the end of the table is pressed and the table is appropriately filled. Observe that the option Broad Crested (by default), that is considered here, let the user indicate the maximum submergence when the fluid flows over a bridge (see below left image) with a trapezoidal shape. The option Ogee let the user define this feature when this submergence occurs and the structure has an ogee spillway shape (see below right image). The bridge has three piles of 1 m of diameter and will be designed in the way that they will be placed at X=80, X=120 and X=160 (equidistant piles). So as to define it, the icon from the

Weir

y Max. sumergence

Weir

y Max. sumergence

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Bridge Culver Data window is selected. The piles will be defined upstream and downstream in the same way and there will not be differences between them. Then, at the top of the window that appear, the X station of the first pile is put for the upstream position. In the table that appears below, the pile will be defined through two sections for the upstream section. The first row will have the width (diameter) and a given level for which the position is in the ground as before. The level of Y=0 will assure that the defined point is in the ground. The second row will have the width and a level in such a way that the position is in the deck. The level Y=98.1 is right. Thus, the shape of the section of the pile is constant and more positions would not make sense. Finally, the pile will be painted from the ground to the lower part of the bridge. Now, the downstream information is added (same as upstream) by clicking on Copy Up To Down button. The second pile can be generated by clicking on the button Add and defining it (in the same way) or clicking on the button Copy. As the pile will have the same geometry, the button Copy is used and automatically a second pile will appears with the same values as the previous. Only the value of the X station has to be modified (changing it in the two places where appear or changing it in one place and copying with Copy Us to Down). The third pile is defined in the same way. Now, for the geometry with the indicated discretization, a bridge has been defined as can be observed in Geometry Data window. Ineffective flow areas are defined so as to quantify the energy losses. According to the HEC-RAS implementation, in the ineffective flow areas water will be contained but the velocity is assumed to be zero (the flow rate will be null through them) while the water level is lower than a value. In other words, water is accounted for volumetrically but it is not considered in the conveyance until an elevation is reached. If the depth is less than the ineffective flow elevation, they will be considered as ineffective. The ineffective flow areas could be used for representing zones in which the flow is stagnant due to narrowings of the riverbed (this is a 1D model). In this case, over a level that will be defined for the ineffective area consideration, the narrowing will disappear. Then, a section (or

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sections) will have already a narrowing and this areas will be defined where the stagnation is produced, in the upstream and downstream sections. In the case of a culvert, the ineffective area is used to restrict the flow area to the area of the culvert until flow overtops the roadway. It makes sense as another stagnant water zone (in which in this case the water is accumulated) appears until the water reach the roadway and all the section works as if the culverts does not exist (according to the flow rate). Now, the narrowing will be represented through ineffective areas in the culvert and they will be defined where the stagnation is produced in the upstream and downstream sections too. Near bridges as the designed zones where the water is stagnated appear. The first case can be considered in the river shores as with little depth and the side piles the water is approximately stagnant. When the water level is enough, the second case can be considered, as the water will be accumulated (contained by the deck) forming vortexes until the water overtops the deck. In this way, as the ineffective flow areas will become effective when a defined value is exceeded, in bridges it makes sense to define this value as that of the elevation of the deck. Over this value, all the water in the section is working. The user could take the ineffective areas since an X station near the side piles as an approach. This is more representative if the bridge has anchorage blocks on the sides (more similar to a culvert). In this case, it is good to keep a 1:1 proportion in the way that if the upstream section is 48 m from the upstream bridge face (as in this case), the ineffective areas should be placed 10 m away from each side of the bridge opening. In the downstream section the position will depends on the bridge being possible that the areas begin at the openings, before or farther. Thus, ineffective flow areas will be defined in the upstream section (1.6*) and the downstream section (1.4*). The areas can be defined directly from Bridge Culver Data window by clicking on the Bounding XS’s buttons (1.6* and 1.4* in this case) or from the Cross Section Data window where the original sections were defined (selecting the section and clicking then in Options>Ineffective Flow Areas). According to the example this areas will be defined from the stations X=80 and X=200 (same ground level, the areas are reached at the same time) in both sections. For the first section, the X values are written in the first row, the values for the ineffective consideration (98.6) are written in the second row and the ticks are put on the boxes (permanent). Then, the procedure is repeated for the other section. The Ineffective Flow Areas HEC-RAS option automatically considers the areas for X<80 and X>200 in each section (see the representation of them when the Apply Data button is clicked). The representation of the ineffective flow areas can be seen in the Geometry Data and the Cross Section Data windows. Moreover, they appear in the Bridge Culvert Data as they are considered over the section (in the upstream and downstream parts) of the bridge too.

Q1

Q2>Q1

X=80 X=200 Ineffective until here

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The contraction and expansion coefficients that HEC-RAS has by default will be used (they are the same as before and could be changed in this case using 0.3 and 0.5). Finally the geometry is saved (File>Save Geometry Data As if it was not still saved). Following this, a new plan is generated (Known_depth_BridgeGeometry in this case) using this geometry (and the steady flow for known water level boundary conditions) and the example is executed. The results in the cross sections 1.0, 1.4*, 1.6* besides in the upstream and downstream parts of the section 1.5 (sections 1.5 BR D and 1.5 BR U in the locations 1.5+2m and 1.5-2m) are shown below. Remember that if the bridge was defined with a distance of 96 m, the section BR D would be the section 1.4*. The ineffective flow areas appear here too.

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Following this, the longitudinal representation of the water level and the 3D representations for the lowest and the greatest flow rate are shown. The same water level value is obtained downstream (93.24 m) for the lowest flow rate. The water level varies near the bridge appearing a bit greater depth value upstream of the bridge. As can be observed the water reaches the bridge (without overtopping it) for the greatest flow rate and is under the bridge in other case. On the other hand, the ineffective areas are working for the two greatest flow rates. Below, the graph with the velocities along the stretch and the velocity distribution in the upstream and downstream bridge cross sections for the greatest flow rate are included. The option of the flow distribution in the cross section with 45 slices (the defined before) was used when defining the plan. Note that solutions are not different when computing with this option, only this representation is available (a postprocess treatment of the solution is done).

As was explained, the cross sections have the different velocities which are produced (this is something that is impossible through the 1D equations derived from the simplification). Moreover, the calculation near the bridge is done in an approximate way because though the velocity variations are not simulated, a lower velocity is represented near the pile (greater zone in the downstream section). Enough slices are necessary to observe it. On the other hand, the null velocities in the ineffective areas are also observed. With the steady flow for normal depth boundary conditions warnings are not obtained in the simulation and this is observed that the water does not reach in any case the bridge.

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As can be seen (in the figure with the first profile) the ineffective areas are not remarked with green lines if they are not used (both in the velocity representation and water level representation) appearing only the green arrows. Again, the Standard Table 1 will show the problems for finding the solution for the lowest flow rate in slow regime, reaching the critical depth. Following this, this table is included for the greatest return period. Note that Froude numbers could be too high compared to the numbers that usually appear in river (Fr<0.4), but this is normal as the flow rate is very high for the riverbed section and then the velocity will be high leading to it. This would also occur in case of a flood, being the regime still slow if the number is decreased as the flow advances. Now, other specific tables for bridges are shown for this flow rate. The table shown firstly is obtained going to Std. Tables>Six XS Bridge in the same window that the previous table was obtained. Here, the six sections where the bridge has influence (from 1.2* to 1.8*, two downstream sections, the sections of it and two upstream sections) are shown with the reached values for other variables. Below, the table obtained going to Std. Tables> Bridge Only is presented. This table shows values for the stretch from the section 1.6* to 1.5 BR U.

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Low flow in bridges occurs when the flow goes under the deck. HEC-RAS has four methods for computing losses through the bridge (from 1.5 BR D to 1.5 BR U) when resolving the equations in this case. They are the Energy (standard step method), Momentum (momentum balance), Yarnell (Yarnell equation) and FHWA WSPRO methods. HEC-RAS first will use the momentum equation to identify one of the next three cases and the possibility of applying each method will depend on the case. The water surface through the bridge is completely subcritical (class A for HEC-RAS). Energy losses through the expansion (sections 1.5 BR D to 1.4*) are calculated as friction losses and expansion losses. The average friction slope (I) is based on one of the available alternatives, with the average-conveyance method being the default (as always, see in the Plan window the option Options>Friction Slope Methods). Energy losses through the contraction (sections 1.5 BR U to 1.6*) are calculated as friction losses and contraction losses. The four methods can be used in this situation. The water surface passes through critical depth in the bridge constriction for either subcritical or supercritical profiles (class B). For a subcritical profile, the momentum equation is used to compute an upstream water surface above critical depth and a downstream water surface below critical depth, using a momentum balance through the bridge. For a supercritical profile, the bridge is acting as a control and is causing the upstream water surface elevation to be above critical depth. Momentum is used again to calculate an upstream water surface above critical depth and a downstream water surface below critical depth. The water surface through the bridge is completely supercritical (class C). HEC-RAS can use either the energy or the momentum equation to compute the water surface through the bridge. For the case that the flow goes over the bridge (high flow) there are two options, to use the Energy Only option, or to use the Pressure and/or Weir option, with which: Pressure flow computations are done when the flow comes into contact with the low chord of the bridge. Once the flow comes into contact with its upstream side, a backwater occurs and orifice flow is established. HEC-RAS will handle the case in which only the upstream side of the bridge is in contact with the water (a sluice gate type of equation is used) and the case in which the bridge constriction is flowing completely full (the standard full flowing orifice equation is used). Weir flow computations are done when the flow goes over the bridge. Flow approaching the bridge will be calculated using the standard weir equation. For high tailwater elevations the program will automatically reduce the amount of weir flow to account for submergence on the weir. When the weir becomes highly submerged, the program will automatically switch to calculating losses based on the energy equation. For the discussion of the methods it is recommended to read the chapter 5 of the HEC-RAS Hydraulic Reference Manual, in the pages from 9 to 17 and from 26 to 28. Here, the flow will be slow and under the bridge section in the case of the two lowest flow rates (see before solutions) and then the four methods can be used. This is done going to the Geometry Data window, clicking on the icon Bridge/Culvert, going to Bridge Modeling Approach icon and going to the low computation part which is in the top. The options Use and Computation has to be ticked (the class reference can be seen in the window that appear, which is called the modeling approach editor) to obtain the solution for a method. The user can select a group of these methods in the computations (by ticking some or all the compute options) choosing either

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a single method as the final solution or tell the program to use the method that computes the greatest energy loss through the bridge at section 1.5 BR U (by ticking use). This allows the user to compare the answers from several techniques all in a single execution of the program. Minimal results are available for all the methods computed, but detailed results are available for the method that is selected as the final answer. Then, the methods are selected one by one. Here, three of the methods have to be used as it is indicated in the exercise. Moreover, the computation of the Energy method was selected (by default) in the previous calculations using the option Highest Energy answer (computes the greatest energy loss upstream) which leads to the same as if the option Energy is computed and used. Below, the table obtained going to Std. Tables> Bridge Comparison is shown for the Energy method. This table shows values of the water level for the different calculation methods. Here, the water level (as W.S.) is seen. Then, the solution is presented for the other two computation methods. For high computation the Energy Only option (by default in the below part of the window) is kept. This method only will be used for the greatest flow rate because (slow) flow over the bridge exists. The modeling approach editor will be shown in each case. When using the two methods indicated which are Momentum and Yarnell methods, a loss coefficient value in the pile has to be introduced. The value can be choosing observing the table that appears when clicking on the question mark taking into account that circular shaped piles are considered in this example. The momentum method (only one option for critical depth in the bridge) is firstly used with a coefficient of 1.2 for circular piles leading to the next results for all the flow rates.

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Finally the Yarnell method is used with a coefficient of 0.9 for semicircular nose and tail piles leading to the next results.

Now, the Six XS Bridge Table is included above for the Energy method, below on the left for the Momentum method and below on the right for the Yarnell method. As can be seen the water level result in the bridge for the greatest flow is the same in all the cases, as it is computed as high flow. This value, which is 98.06 m, is the same upstream and downstream. For the lowest flow rate this is obtained a value from 94.27 to 94.29 (upstream and downstream) for the energy method, from 94.41 to 94.29 for the momentum method and the same value of 94.19 for the Yarnell method. For the medium flow rate this is obtained a value from 95.69 to 95.72 for energy method, from 95.86 to 95.72 for the momentum method and the same value of 95.61 for the Yarnell method. Thus, the momentum method is the method that obtains the greatest water level upstream (94.41 and 95.86) and the energy and the momentum methods give the greatest water level downstream (94.27 and 95.72). On the other hand the Yarnell method is the only one that gives the same result upstream and downstream. The best method should be chosen by comparing the solutions with measurements.

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9. Same example with different Manning’s values

f) After the zone is studied, actuations are going to be done in order to reduce the friction both in the riverbed and in the floodplains, generating a concrete channel and promenades in the floodplains. Study the effect of considering 0.04 m-1/3s in the floodplains and 0.015 m-1/3s in the rest. Compare the solutions in the cases a), c) and e) for the energy method.

The values of n=0.015 m-1/3s in the riverbed and n=0.04 m-1/3s in the floodplains for the Manning’s coefficient are typical values for concrete channels and no wooded floodplains respectively. Following this, some points are repeated with these decreased coefficients. Some coefficients can be changed easily, replacing the information in all the sections at the same time, through the tables that can be seen in the Geometry Data window such as Tables>Contraction and Expansion Coefficients and Tables> Manning’s n or k Values. The values can be replaced by other ones in the part of the table the user wants. So as to reduce the Manning’s values (required in this example), this is necessary go to Tables>Manning’s n or k Values and press the Replace button. Then, the value to be changed and the new value are written and the option Entire Table is selected. The effects of the Manning’s coefficient reduction are studied case by case comparing the results with that already obtained (with the water level longitudinal profile and the Standard Table 1). The previous results are shown on the left, and the new results with the reduction are shown on the right. Below, the results for the case a) are included.

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This is observed that when the Manning’s coefficient is decreased the normal depth will be lower (for the same slope of 0.001). Now, the water depth obtained downstream for the lowest flow rate is 93.55 m instead of 94.27 m. For an intermediate value as n=0.018 in the riverbed (the Manning in the floodplains has not influence for this flow rate), the water level would be 93.72 m. Thus, the floodplains are flooded with lower amount of water and are not always flooded for the medium flow rate. Moreover, greater Froude numbers are observed. This is because, as there is lower friction, the velocities are greater as can be seen too. Values as high as Fr=0.7 are obtained in the section 2 for the lowest flow rate and Fr=0.9 for greatest flow rate. However, the flow is still slow as the number is decreased as the flow goes ahead. Following this, the solutions for case c) are included, representing the critical depth too in the longitudinal profile and showing the table only for the lowest flow rate.

Again, the water depth is lower in all the sections apart from the section 1 in which the water level is imposed (floodplains less flooded) or the water level is that of the critical depth again calculated in the case of the lowest flow rate. The differences are smaller for the greatest flow rate and in the case of the medium flow rate the water depth profile has lower progression reaching a water depth almost constant in the last stretch. In the case of the lowest flow rate it is observed that the water depth yc is not dependent of the Manning’s coefficient as it is the same in both cases. Now, the progression is better near the downstream section (the water depth profile is more smooth and the Froude numbers are increased more progressively). Finally, the same results are shown for the discretized case which has the bridge using the energy method both in low flow computations and high flow computations (previously it was always used) as it is by default.

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Comparing the results, now it is observed that, due to the lower water depth, the water level is practically the same as the level of the low chord of the bridge (a little bit lower) for the greatest flow rate. Moreover, it is observed a disconnection of the water level under the bridge with a significant variation for the lowest flow rate, possibly because the critical depth was reached here (momentum equation would have been applied) and a solution is not reached for the equations. Again, the critical depth is reached in the downstream section for the lowest flow rate. In conclusion, with the Manning’s coefficient decrease, the velocity of the flow is greater and the flow is under the bridge for the maximum flow rate considered in the project, that for the return period of 500 years, and for the known water levels downstream (values can be known thanks the existence of a reservoir, for example).

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References The exercise is based on the exercise proposed by Enrique Peña. This exercise, which is much more simple was used in 2010 for the subject “Programas Comerciales en Ingeniería Hidráulica” that belonged to the “Master En Ingeniería Del Agua”. Alberto Andreotti, Gerardo D. Hillman, Cecilia E. Pozzi P., Andrés Rodríguez, e Indigo SA, 2009. Optimización de un modelo hidrodinámico Bidimensional. This is an article written in Spanish in where RMA2 is presented and used for simulating a particular case. The aim is to present some improvements for the model. F. Javier Sánchez San Román, 2007. Manual introductorio a HEC-RAS. Dpto. Geología, Univ. Salamanca (España). This is a HEC-RAS manual very basic, written in Spanish, in where the first steps of this tutorial are commented with more detail. Juan F. Weber and Ángel N. Menéndez, 2003. Desempeño de modelos de distribución lateral de velocidades en canales de sección compuesta. Primer simposio regional sobre hidráulica de ríos. In this document, written in Spanish, a comparison between HEC-RAS and RMA2 is carried out. HEC-RAS Hydraulic Reference Manual. US Army Corps of Engineers. Nowadays the Manual that can be found in the internet is the Manual for the HEC-RAS versions 4.0 and 4.1. This is not a problem as the information will be more complete.

hec-ras tutorial

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