USBPR Bridge

Note: The functionality of the USBPR Bridge unit has been enhanced within the new Bridge unit. We therefore recommend using the new Bridge unit for new model networks. The USBPR Bridge unit remains operational within the software, e.g. for use in existing networks.

Introduction

The USBPR Bridge unit uses methodology developed by the U.S. Bureau of Public Roads (USBPR) to compute afflux—the rise in water level caused by the presence of a bridge during flood events. This assumes the bridge to consist of a flat deck with one or multiple openings beneath it.

In this article: You will learn how to add a USBPR bridge to a 1D river network, in isolation and in parallel with other 1D units, e.g. a spill, (example data is provided), you will learn the definitions of all parameters used within the USBPR bridge unit and you will learn the underlying theory defining the hydraulics of a USBPR bridge.

Uses

This bridge type is particularly useful in 1D hydraulic modelling where accurate representation of flow constriction and backwater effects due to bridge structures is essential.

Often bridges are modelled as the wrong type, e.g. a flat deck as an arch. Thus, review what your structure looks like. If each opening looks like an arch, then it should be modelled as an arch bridge. Whereas, if openings look flat then a ”flat” (USBPR) bridge will be the better option.

Typical structures that can be modelled using the USBPR bridge unit are shown in Photos 1 and 2.

Example Files

1. Simple USBPR Bridge

2. Bridge with overtopping (Spill)

3. Bridge with overtopping and blockage

Adding a USBPR Bridge to a Network

A USBPR bridge structure can be inserted into a network in isolation or in combination with spills, blockages and flood relief culverts. A USBPR bridge structure marks the end of a reach within the network – thus the distance to next of the upstream river section is set to zero. A new reach will start downstream from the bridge. Therefore, a bridge must be connected to river section units both upstream and downstream. It is therefore useful to obtain river cross section survey data from either side of a bridge. However, if your network does not have cross sections defined close to the bridge then a nearby river section unit can be copied or a Replicate unit can be utilised to create river section units at these locations.

Example data is included later in this section, after the instructions, or at the top of the article, in the Example Files.

Simple bridge (in series)

A simple bridge unit set-up is ideal for low-flow conditions, where the bridge structure alone can adequately convey the flow without the need for additional components. It is also appropriate when there are no alternative flood paths or relief culverts present in the system, meaning all flow must pass through the bridge opening. Additionally, if the bridge is connected to a 2D domain where overtopping is accurately represented within the 2D surface, the standalone bridge unit can effectively simulate the hydraulic behaviour without requiring supplementary spill or culvert units. This setup simplifies the model while maintaining accuracy under the right conditions.

How

For a bridge in series with upstream and downstream river section units – upstream label is the upstream river label, downstream label is the downstream river label. This labelling will tell the network to connect the river sections to the USBPR bridge.

How to add a new USBPR bridge unit:

1. Make sure you have a River Section at both the upstream and downstream sides of where the bridge will be placed.

2. In the upstream River Section, set the Distance to next value to 0 (to signify the end of a reach and the start of the structure).

3. Insert the USBPR Bridge

• Select the upstream River Section (either in the table or on the map).

• Go to the 1D River Build tab.

• Open the Bridges dropdown and choose USBPR.

• Manually place the USBPR Bridge unit between the upstream and downstream River Sections (on the map).

• When prompted, enter the node labels:

  • Use the upstream River Section label for the upstream node.

  • Use the downstream River Section label for the downstream node.

• Click OK.

4. Copy Cross-Section Data

• Copy the following data from either the upstream or downstream River Section (whichever is more appropriate) and paste it into the USBPR Bridge unit.

• Click on the column headers to highlight the entire column and copy the data. In order to Paste the data, select the first cell of the column and Paste the previously copied data.

5. Define Bridge Geometry

• Set the Start and Finish cross-chainages for the bridge opening by selecting the chainage from the drop down which lists the cross-chainage points.

• Enter the Springing Level and Soffit Level for the arch.

If the bridge has multiple openings:

• Right-click in the Openings table and select Insert Below.

• Repeat the data entry for each additional opening.

6. Don’t forget to save your network once the bridge is added and configured.

Example file

Simple  USBPR Bridge

Complex (combined with other units)

Setting up a bridge with overtopping (Road flow)

Flow over the top of the bridge is not considered. If this type of flow is likely, the user should place a structure such as a spill in parallel with the bridge, using junctions as necessary.

When modelling overtopping at a bridge, the approach differs depending on whether a 1D or 2D model is used. In a 1D model, it is important to explicitly represent the bridge decking, ensuring that the length of the spill unit matches the length of the cross section or bridge structure to accurately simulate overtopping flow. In contrast, within a 2D model, a spill unit is typically only necessary if the bridge is narrow and not adequately resolved within the 2D mesh. If the bridge is already well represented in the 2D domain, additional spill units are generally not required, as the model can inherently capture the overtopping behaviour.

How

1. Add your Bridge Unit

• Use unique labels for the upstream and downstream ends (e.g. SEV08800BrU1 for upstream, SEV08800BrD1 for downstream).

2. In the Remote Labels section:

• Enter the label of the upstream river section in the Upstream Remote box (e.g. SEV08800)

• Enter the label of the downstream river section in the Downstream Remote box (e.g. SEV08760).

3. Add your Spill Unit

• Use unique labels for the upstream and downstream ends (e.g. SEV08800SpU1 and SEV08800SpD1).

• For help with configuring the spill unit, see this article on setting up a Spill.

4. Add Two Junction Units

• Configure the Upstream Junction

  • Include the label of the river section upstream of the bridge.

  • Add the upstream labels of both the bridge and spill units (SEV08800BrU1, SEV08800SpU1).

• Configure the Downstream Junction

  • Include the label of the river section downstream of the bridge.

  • Add the downstream labels of both the bridge and spill units (SEV08800BrD1, SEV08800SpD1).

• For help with configuring the junction units, see this article on setting up a Junction.

4. Confirm Connectivity

• When prompted to connect labels with the same name, click Yes. This ensures proper linkage between units.

5. Review the Network

• Use the Map View to visually check that all units are connected correctly.

• You can rearrange nodes for better clarity using the Move Tool.

6. Save Your Network

• Don’t forget to save your work once everything is connected and arranged.

Example File

Bridge with overtopping (Spill)

Setting up a bridge with overtopping and blockage

When modelling a bridge that may experience overtopping or blockage, it’s important to configure the structure to reflect these potential flow paths accurately. For overtopping scenarios, refer to the Spill Over Bridge section, which outlines how to simulate flow passing over the bridge deck. To investigate the impact of blockage, adjust the bridge geometry or apply blockage factors to simulate partial or full obstruction of the opening.

How

1. Start from the Spill Unit Setup

   Begin by either:

• Following the same process used in the Spill Unit section, or

• Opening the model where the spill unit has already been added and continue from there.

2. Add the Blockage Unit

• Insert a Blockage Unit into the network.

• Refer to the Blockage Unit article for guidance on how to populate the fields and choose the correct remote labels based on your modelling approach.

• Use the following label configuration:

  • Upstream label: A unique identifier.

  • Downstream label: The upstream label of the Bridge unit.

  • Upstream Ref.: The label of the upstream River Section.

4. Update Junctions

• Add the upstream and downstream labels of both the Blockage and Orifice units to their respective junctions.

5. Review Connections

• Open the Map View to visually confirm that all units are correctly connected.

6. Adjust Node Positions (Optional)

• You can rearrange nodes for better clarity using the Move Tool.

7. Save Your Network

• Once all units are added and verified, save your network to retain your changes.

Example File

Bridge with overtopping and blockage

Data entry

Access the USBPR bridge unit properties by double clicking on the unit in the map view or in the network table (alternatively right-click and select 1D node properties from the menu). A new window will be displayed containing three tabs for data entry.

A different option of editing the network file would be opening the .DAT file externally from the interface (eg text editor). We would recommend not to take this approach as an unexperienced user as it can break the network file if updated incorrectly.

Defining Arches and Piers

There are options when defining a bridge with more than one arch. The bridge could be defined as:

• several arches with no intermediate piers (see Opening definition in Section Data below)

• a single arch with intermediate piers (see Piers definition in Pier Data below)

• a combination of the two

For example, take a look at the example bridge below.

You could define this bridge in several ways:

• as a single span (AF) with Total Pier Width = w + x

• as two spans (AD and EF) with Total Pier Width = w

• as three spans AB, CD and EF with Total Pier Width = 0

General Data

Default tab when opening the properties window of the USBPR Bridge unit.

Remote labels and when to use them

Remote nodes are not required when connecting a Bridge unit directly to a RIVER section (i.e. when the Bridge Node Labels are equal to the RIVER section Node Labels). The function of a remote node label is to inform the computations from where to obtain velocities in order to calculate the afflux. Since for Bridges (and hydraulic structures in general), velocities are not calculated explicitly in Flood Modeller (velocities are only explicitly calculated in channel sections – RIVERs and CONDUITs), one defaults to using velocity from the “best available” channel section, usually the nearest channel section upstream and downstream, respectively. Since this is not always an obvious or unique section, we need to tell the computations from where to obtain these. The exception to this being, of course, when the Bridge is attached directly to a channel section, upstream and/or downstream. A typical occurrence of this would be when schematising a bypass/overtopping flow via a spill or weir unit in parallel.

Section Data

Second tab when opening the properties window of the USBPR Bridge unit. The channel cross section at the bridge location is specified here. Once this is defined then the openings in the USBPR bridge can be added. These must utilise existing cross chainages from the specified cross section for each opening start and finish location.

Data required in the Channel section table is described below.

The number of ensuing data sets describing the cross-section extending along the toe of any embankment on the left floodplain, across the channel, and along the toe of any embankment on the right flood plain. This can be thought of as the river and floodplain section prior to bridge construction

Data required in the Openings table:

Pier Data

The Pier Data tab is activated and pier information needs to be provided only if the ‘Specify Piers’ option is selected under the ‘General’ tab.

Pier Data required is described below:

Flood Relief Culverts

The USBPR bridge allows to provide Flood Relief Culverts data in the unit itself. Flood relief culverts are assumed to be rectangular.

Flow through flood culverts is calculated using a broad-crested weir equation, or an orifice equation if the culvert is flowing full. An iterative method is used to calculate the afflux for the remaining flow through the main bridge arches/openings. This method is not included in the USBPR report.

Click here to view Broad Crested Weir equations

Click here to view Orifice equations

Flow through separate flood relief openings, up to a maximum of twenty per bridge, can be modelled. Typically these are of a smaller aperture than a bridge opening, and raised at a higher level than the bed. These are defined by the user specifying the following physical quantities:

• Elevation of flood relief opening invert above datum

• Elevation of flood relief opening soffit above datum

• Total area

The opening is assumed rectangular in shape, and therefore the breadth can be calculated as area/total depth (total depth = soffit level – invert level).

An orifice equation is assumed when the relief opening is running full, whereas a weir equation applies when running partially full, which can be free or drowned, according to the downstream water level. A round-nosed broad-crested weir equation is used by default, therefore the “weir discharge coefficient” can be used to take into account or adjust for coefficients of discharge and velocity (otherwise assumed unity) or different weir types. The modular limit also applies to the transition between free and drowned weir flow. An orifice coefficient is provided to enable scaling of the discharge from the standard orifice equation, e.g. to match calibration or account for less-efficient orifice flow.

The flood relief opening can work in two different ways: when the bridge calculations are operating in bridge afflux mode, and when the bridge is operating in orifice mode (either can include simultaneous overtopping). In bridge-orifice transition mode, a hybrid between the two applies.

In bridge afflux calculation mode, the bridge afflux and flood relief flow are calculated separately, and an iterative solution is found whereby the combined discharge of the bridge and flood relief openings and upstream water levels both match the total bridge inflow.

In orifice mode, the Flood Relief Opening area is simply added to the bridge opening area. Note that if partially full, only the wetted portion is added.

The flood relief opening area is assumed to be based on the plane of the bridge face. Thus if the bridge has a skew angle defined, the full area along the face should be entered, which is factored (by cosine of the skew angle) internally by the software.

The data needed is described below:

Orifice Data

The bridge units in Flood Modeller may switch to orifice flow at a given depth if the user selects this option from the unit form. This has the benefits of representing surcharged flow as an orifice, which may be more representative, whilst retaining the bridge afflux calculations when not surcharged.

The user can specify a lower level (specified as distance below highest arch soffit) at which the transition from bridge flow to orifice flow commences, and an upper level (specified as distance above highest arch soffit) at which the transition to orifice flow is complete. This allows a smooth transition from bridge to orifice flow to occur.

The orifice equation used is the standard orifice equation in Flood Modeller, although the user may adjust the coefficient by changing the orifice discharge coefficient within the bridge unit.

The unit mode for a bridge is as follows:

• Mode 1 - bridge flow

• Mode 2 - transition flow (between bridge and orifice)

• Mode 3 - orifice flow

Data required in the Orifice Data tab:

Format of data in network (.DAT) file:

See below an example on how a network (.DAT) file looks like in text view accompanied by the format of the data. The .DAT file uses a fixed format whereby each data entry must occupy 10 characters (add extra spaces if the 10 characters are not filled with the data entry). Please open provided .DAT file within this article to inspect the format more closely.

Associated Theory

The US BPR Bridge computes the afflux at bridges using the methodology developed by the US Bureau of Public Roads (US BPR).

The bridge afflux is calculated using the methods described in Hydraulics of Bridge Waterways (1978). You are advised to read the report in order to gain a full understanding of the methodology and limitations of the approach.

The US BPR Bridge requires that the network has a River section upstream of the bridge (or a Replicated river section), ideally at the point of maximum backwater, and a River section downstream of the bridge, ideally where normal water level has been achieved.

Input data for the US BPR Bridge principally comprises two cross sections:

1. The river bed of the un-obstructed river channel along the toe of the bridge and extending into the floodplain (if appropriate)

2. Arch/opening and pier details

Other data include the upstream and downstream node labels, pier, skew and abutment details.

Equations

A practical expression for backwater has been formulated by applying the principle of conservation of energy between the point of maximum backwater upstream from the bridge, and a point downstream from the bridge at which normal stage has been re-established.

Backwater expression

The expression for computation of backwater upstream from a bridge constricting flow is:

The value of the overall backwater coefficient, K^*, which was determined experimentally, varies with:

1. Stream constriction as measured by the bridge opening ratio M

2. Type of bridge abutments

3. Number, size, shape and orientation of piers in the constriction

4. Eccentricity, or asymmetric position of bridge with the floodplains

5. Skewness of bridge and floodplains

It was demonstrated that K^* consists of a base curve coefficient, K_b, to which is added incremental coefficients to account for the effect of piers (∆K_p), eccentricity (∆K_e) and skew (∆K_s). The value of K^* is nevertheless primarily dependent on the degree of constriction of flow at a bridge.

The backwater expression is reasonably valid if:

• the channel in the vicinity of the bridge is essentially straight

• the cross sectional area of the river is fairly uniform

• the gradient of the bottom is approximately constant

• the flow is free to contract and expand

• there is no appreciable scour of the bed in the constriction

• the flow is in the sub-critical range.

Outside these conditions the USBPR method should be used with care. In addition, as the USBPR method is a design procedure based on American rivers, even with the "correct" coefficients and dimensions, the predicted afflux may not agree with observed values of water level when used in other countries.

Friction losses within the bridge are not modelled by the US BPR Bridge . Flow over the bridge parapet (road flow) is not modelled.

If the bridge is skewed, the bridge section data should be specified along the axis of the bridge - its projection normal to the flow direction is performed internally within the software.

The unit state for this unit is the flow through the flood relief culvert (if present).

Base Curve (K_b)

The backwater coefficient base curve, K_b, is dependent on the bridge opening ratio, M, and to a lesser extent the abutment type.

The bridge opening ratio, M, defines the degree of river channel constriction involved. It is defined as the ratio of the flow which can pass unimpeded through the bridge constriction to the total flow of the un-obstructed river.

The base curve is valid for M in the range 0.2 to 1.0 which yields K_b values within the range 2.8 to 0.0 (as M decreases K_b increases).

Effect of Piers, ∆K_p

Backwater caused by introduction of piers in a bridge constriction has been treated as an incremental backwater coefficient designated ∆K_p, which is added to the base curve coefficient K_b when piers are present in the waterway. The value of ∆K_p is dependent on the ratio of the area of the piers to the gross area of the bridge opening (known as J), and the type of piers and the bridge opening ratio, M. For skewed crossings, J is determined using the areas projected normal to the general direction of flow.

A problem arises here, with the distinction between pier and arch. The pier coefficient curves have been determined for the pier ratio, J, in the range 0.0 to 0.18 and M between 0.4 to 1.0. The upper range of J is probably less reliable, being determined by extrapolation, therefore as a guide, to keep J in the range 0.0 to 0.10, the total width of piers normal to flow should not exceed 10% of the unobstructed channel width. If the sum of pier widths exceed 10% of the unobstructed channel, it is recommended that they be treated as arches.

Effect of Eccentricity, ∆Ke

The eccentricity, e, is defined as 1 minus the ratio of the lesser to the greater discharge outside the main bridge opening.

For channels with an eccentricity of 0.80 or greater, ∆Ke values have been determined for M in the range 0.2 to 1.0. For channels with an eccentricity of less than 0.80, ∆Ke is deemed negligible i.e. ∆Ke = 0.

Effect of Skew, ∆K_s

The method of computation for skewed crossings differs from that of normal crossings in that the bridge opening ratio, M, is computed on the projected length of the bridge rather than on the length along the centerline.

The incremental coefficient, ∆K_s, varies with the opening ratio, M, the angle of skew of the bridge θ, with the general direction of flood flow, and the alignment of the abutment faces. The angle of skew, θ, is defined as the angle between the flow direction and the normal to the main axis of the bridge. Abutments are aligned if the abutment faces are parallel with the flow direction (otherwise they are skew).

Dual Bridges

The backwater produced by dual bridges - two bridges of essentially identical design, placed parallel and only a short distance apart - is greater than that for a single bridge, yet less than the value which would result from considering the two bridges separately.

The dual bridge afflux is determined as a function of the single bridge afflux and the ratio Ld/l where Ld is the distance from the upstream face of the upstream bridge to the downstream face of the downstream bridge, and l is the single bridge width. The formulation is applicable for Ld/l between 3 and 11. Dual bridges for which Ld/l is less than 3 may be treated as a single bridge with an increased pier number.

Tips and Tricks

• When setting up new networks, use the Bridge unit (Bridge). This can be applied to all bridge types (including USBPR bridges) and has built-in options to include overtopping, flood relief culverts and blockages

• If a USBPR bridge unit must be used then there is the option to use the intelligent insert tool. This automatically adds the additional units required to define a complex USBPR bridge with spills and/or blockages. When activated, this tool will insert these complex arrangements of multiple 1D river units with a single click (that usually adds just the USBPR bridge unit). This tool is activated from the 1D river settings window - see Defaults & Options

• If missing survey of US/DS face of bridge use replicate or copy US/DS river section