Arch Bridge

Note: This unit has been deprecated (but remains operational within the software)

Introduction

The arch bridge unit can be used to represent any bridge structure but is primarily aimed at typical British stone bridges that consist of one or multiple openings for flow to pass through. The Arch Bridge computes the afflux at a single arch or multiple arched bridges using the HR Wallingford method. The area under each arch is calculated from the soffit and the springing level, assuming that the arch shape is parabolic. Thus, these parameters are needed as data inputs to utilise this unit (all required parameters are provided later in this article).

Uses

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 arch bridge unit are shown in Photos 1, 2 and 3.

Example Files

1. Simple Arch Bridge

2. Bridge with overtopping (Spill)

3. Bridge with overtopping and blockage

Connectivity

An arch bridge structure can be inserted into a network in isolation or in combination with spills, blockages and flood relief culverts. An arch 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.

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 arch bridge.

How to add a new arch 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.

3. Insert the Arch 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 Arch.

• Manually place the Arch Bridge between the upstream and downstream River Sections.

• 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 Arch 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 Arch Bridge

What you can find in Tips and tricks:

1. What to do when you do not have surveyed river cross sections at both faces of the bridge (this would be a link to the tip located at the end of this article)

Complex (combined with other units)

Setting up a bridge with overtopping

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. SEV08800 for upstream, SEV08760 for downstream).

2. In the Remote Labels section:

• Enter the label of the upstream river section in the Upstream Remote box (e.g. 280)

• Enter the label of the downstream river section in the Downstream Remote box (e.g. 280D).

3. Add your Spill Unit

• Use unique labels for the upstream and downstream ends (e.g. SpillU and SpillD).

• 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 (BridgeU, SpillU).

• 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 (BridgeD, SpillD).

• 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)

Tips and tricks

• Use the Bridge unit (Bridge)

• Use the intelligent tool to add the additional units (Defaults & Options)

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

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

Tips and tricks

• Use the Bridge unit (Bridge)

• Use the intelligent tool to add the additional units (Defaults & Options)

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

Data entry

Access the arch 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.

General Data

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

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:

Orifice Data

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 Arch Bridge computes the afflux at single arch or multiple arched bridges using the methodology developed at HR Wallingford and described in Afflux at Arch Bridges (1988). For a full description of the methodology please refer to the report.

For the Flood Modeller implementation of the methodology the area under each arch is calculated from the soffit and the springing level, assuming that the arch shape is parabolic.

The key relationship in the method is the graph which relates the ratio of afflux to downstream depth (dh/D3) to the downstream Froude Number (F3) plotted for different downstream blockage ratios (J3).

The table below lists the actual values of dh/D3 used within the Flood Modeller simulation engine. Values vary dependent on F3 values (column 1) and J3 values (row 1). These values are also shown on the graph.

Road flow and flood culvert flow are not modelled by the Arch Bridge. A Spill or culvert should be added in parallel if necessary. Friction losses are also not modelled.

The Arch Bridge can simulate the effects of dual bridges using the method described in the US BPR Bridge.

The HR Wallingford method for arched bridges was developed from laboratory tests on model bridges and verified with data from prototype bridges in the UK. Prototype data supports the method in the case of single arch bridges; there is insufficient data to give equally close confirmation for multiple arches. Laboratory tests support the method for multiple arches provided the bridge is essentially a single unit with arches separated by typical pier widths. The influence of eccentricity of the bridge to the river channel was found to be insignificant relative to the overall tolerance of the calculation.

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 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

Tips and Tricks

• Use the Bridge unit (Bridge)

• Use the intelligent tool to add the additional units (Defaults & Options)

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