Note: The functionality of the Pier-Loss Bridge unit has been enhanced within the new Bridge unit. We therefore recommend using the new Bridge unit for new model networks. The Pier-Loss Bridge unit remains operational within the software, e.g. for use in existing networks.
Introduction
The pier loss bridge can be used to compute the afflux at bridges where the dominant cause of energy losses is the friction from piers. It utilizes the empirical equation derived by Yarnell (1934).
In this article: This article covers the integration of a pier loss bridge into a 1D river network model. You will learn how to implement the unit both independently and in conjunction with other 1D components, such as spill units. Example datasets are provided to support practical application. The article also defines all relevant parameters within the pier loss bridge unit and explains the hydraulic principles that govern its behaviour.
Uses
This bridge option provides an alternative to the USBPR and Arch bridge units. The pier loss bridge unit provides an improved calculation of flows through bridges where the dominant cause of energy loss is the friction from bridge piers. This is particularly useful when low flows are more frequent. The method utilizes the empirical equation derived by Yarnell (1934). The bridge is defined by a single opening, but then one or multiple piers of user defined thickness can be added to this opening.
This option can be considered for any bridge that incorporates one or more piers. Typical structures that can be modelled using the pier loss bridge unit are shown in Photos 1, 2 and 3 below, which show multiple piers across the channel:
Photo 1 | Photo 2 | Photo 3 |
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Example Files
Adding a Pier-Loss Bridge to a Network
A pier-loss bridge structure can be inserted into a network in isolation or in combination with spills, blockages and flood relief culverts. A pier-loss 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 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.
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.
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 pier loss bridge.
How to add a new Pier-Loss Bridge unit:
Make sure you have a River Section at both the upstream and downstream sides of where the bridge will be placed.
In the upstream River Section, set the Distance to next value to 0.
Insert the Pier-Loss 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 Pier-Loss Bridge.
Manually place the Pier-Loss 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.
Properties window | Network map view | Network table view |
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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 Pier-Loss Bridge unit.
From River Section | To Pier-Loss Bridge Unit |
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x (m) | Cross-Chainage (m) |
y (m AD) | Elevation (m AD) |
Mannings n | Mannings n |
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.
Note: The downstream face of the bridge will be assumed to have the same cross section unless a separate downstream section is entered - there is a checkbox to access this extra data table.
Define Bridge Geometry
In the Upstream section table:
Set the Start and Finish for the bridge opening by selecting LEFT or RIGHT in the Embankments field on the required rows (only one Left and Right should be selected).
Enter the Top Levels for the right and left points of the opening - these are the elevations of the opening where it meets the embankment.
The edge of the bridge opening at the Left and Right embankments is extrapolated based on the levels entered in the column “Top Level (m AD)”. For example, in the figure below, the opening level is set at 11.2m AD at cross chainage 56.50m, thus the top line of the opening is plotted from the first pier location to here, truncated where it meets the edge of the cross section. Alternatively, if the Top Level is 12.5m AD, i.e. above the embankment cross section, the opening would rise vertically at cross chainage 56.50m to meet the top line at the specified level.
In the Pier locations table, for each required pier:
Specify the left “X (m)” for the left edge of the pier and right “X (m)” for the right edge of the pier within the cross section. This also defines the width of the Pier.
For each pier, define the left and right “Top Level (m AD)” values. These are the elevations of the left and right edges of the pier. For a flat opening these values will be the same as the top level values entered in the section table.
Add further Piers by right-clicking on the table and selecting “insert below” (alternatively use keys Ctrl + B or highlight the right column value and press the Tab key).
Bridge Section Data | Bridge Section Plot |
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Don’t forget to save your network once the bridge is added and configured.
Example file
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
Add your Bridge Unit
Use unique labels for the upstream and downstream ends (e.g. SEV08800BrU1 for upstream, SEV08800BrD1 for downstream).
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).
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.
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.
Confirm Connectivity
When prompted to connect labels with the same name, click Yes. This ensures proper linkage between units.
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.
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.
Blockage Properties window
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.
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.
Update Junctions
Add the upstream and downstream labels of both the Blockage and Orifice units to their respective junctions.
Review Connections
Open the Map View to visually confirm that all units are correctly connected.
Adjust Node Positions (Optional)
You can rearrange nodes for better clarity using the Move Tool.
Save Your Network
Once all units are added and verified, save your network to retain your changes.
Example file
Bridge with overtopping and blockage
How to include the bridge section at the downstream face of the bridge?
Although Flood Modeller is able to model a pier-loss bridge unit with just the upstream face data, it is possible to include the Bridge section at the downstream face. To do so, check the box on the top of the Section data window, which says ‘Specify different downstream cross-section‘. This activates a new sub-tab ‘Downstream‘, adjacent to the sub-tab ‘Upstream’. Follow similar steps to enter Downstream section data, as that in the upstream face.
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Data entry
Access the pier loss 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 (e.g. 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 Pier-Loss Bridge unit.
Data
Parameter name | Description | Label name in data file | ||||||||||||||
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Upstream label | Upstream node name – immediately upstream node in network | Label1 | ||||||||||||||
Downstream label | Downstream node name- immediately downstream node in network | Label2 | ||||||||||||||
Upstream river section | Label of upstream RIVER section. Optional: This label is not required if the upstream RIVER section is Label1 | Label3 | ||||||||||||||
Downstream river section | Label of downstream RIVER section. Optional: This label is not required if the downstream RIVER section is Label2 | Label4 | ||||||||||||||
Loss model method | YARNELL. Keyword referring to the modelling method: currently only option is YARNELL, hence this is not included as a setting in the pier loss bridge interface. The software will set this value automatically in your network file. | Keyword | ||||||||||||||
Calibration coefficient | Global calibration coefficient: Can be any non-negative real number. Used to scale the calculated afflux if this is justified by observations. It should normally be set to 1. Setting cali to 0 removes the effect of the bridge (but not the effect of any flood culverts). | cali | ||||||||||||||
Alternative method | Alternative method. Defines calculations to apply when bridge is surcharged. The default option is ORIFICE, set by the 'Model surcharged bridge as orifice flow' checkbox; if unchecked (not recommended, since the Yarnell equation is not validated for surcharged flow), this field is left blank and the Yarnell equation will apply for surcharged flow also. | altmethod | ||||||||||||||
Orifice Discharge Coefficient | Orifice discharge/calibration coefficient – only used when calculations transition to ORIFICE alternative method (i.e. as bridge becomes surcharged). Must be real, non-negative number. | cdorifice | ||||||||||||||
Lower Transition Distance | Lower transition depth (distance below soffit in m or ft). When the upstream water level is below [max soffit level - rlower], the Yarnell bridge equations only are used. When this level is reached, it enters the transition phase between bridge and orifice flow where flow is calculated using both Yarnell and orifice equations and a weighted average is used. Constraint: rupper + rlower ≥ 0 | rlower | ||||||||||||||
Upper Transition Distance | Upper transition elevation (distance above soffit in m or ft). When the upstream water level exceeds [max soffit level + rupper], the bridge to orifice transition ends and full orifice equations apply. Constraint: rupper + rlower ≥ 0 | rupper | ||||||||||||||
Pier coefficient | Pier (or Yarnell) coefficient, K: can be any real value in the range 0.7 to 2.5. This coefficient accounts for differences in friction caused by pier shape. Suggested values for different standard pier shapes are provided in Table 1 below (note this list may not be exhaustive): Table 1: Suggested values of pier coefficient
Note: Adjustment of this coefficient can help with model calibration. | K | ||||||||||||||
Bridge width | Width of bridge (in m or ft), i.e. distance between upstream and downstream faces of bridge. Not currently used by computation, entry is for reference only (in case you want to change to a different bridge type in future that requires this) Should be non-negative real number (can just be left as default = 0.0) | rdlen |
Data for Channel Section at Upstream Face of Bridge
Parameter name | Description | Label name in data file |
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No. of data points | Number of data entries describing the upstream face of the bridge cross-section. Not a data entry - solver sets this based on number of data rows defined in upstream section table. Minimum of 3 data points should be defined, i.e. a triangular section. OR can be set to zero, in which case the downstream section data will be adopted for both bridge faces (and so must be defined) The upstream bridge cross-section extends 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 | npts_us |
Cross-chainage | Cross-chainage (m or ft). Chainage is expected to be a real number and increasing | usxpi |
Elevation | Elevation of bed or flood plain (m or ft AD). Must be a real number | usypi |
Mannings n | Manning roughness coefficient. Must be a positive, real number | usrni |
Embankment indicator | Mandatory field of 1 character; only options are ‘L’ or ‘R’ to indicate left or right embankments of main channel Interface presents options “Left” and “Right” for you to select to set these indicators. The section can only have one left and one right marker. | uschmaini |
Top level | The top level represents the soffit elevation at your specified left and right embankment points (note that any top-level entries on rows that are not embankment indicators will be ignored by the solver). The top-level values should be measured using the same reference datum as the section elevation data. | ustoplev |
Data for Channel Section at Downstream Face of Bridge
Parameter name | Description | Label name in data file |
|---|---|---|
No. of data points | Number of data entries describing the downstream face of the bridge cross-section. Not a data entry – solver sets this based on number of data rows defined in downstream section table. Minimum of 3 data points should be defined, i.e. a triangular section. OR can be set to zero, in which case the upstream section data will be adopted for both bridge faces (and so must be defined) The downstream bridge cross-section extends 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 | npts_ds |
Cross-chainage | Cross-chainage (m or ft). Chainage is expected to be a real number and increasing | dsxpi |
Elevation | Elevation of bed or flood plain (m or ft AD). Must be a real number | dsypi |
Mannings n | Manning roughness coefficient. Must be a positive, real number | dsrni |
Embankment indicator | Mandatory field of 1 character; only options are ‘L’ or ‘R’ to indicate left or right embankments of main channel Interface presents options “Left” and “Right” for you to select to set these indicators. The section can only have one left and one right marker. | dschmaini |
Top level | The top level represents the soffit elevation at your specified left and right embankment points (note that any top-level entries on rows that are not embankment indicators will be ignored by the solver). The top-level values should be measured using the same reference datum as the section elevation data. | dstoplev |
Bridge Pier Data
Parameter name | Description | Label name in data file |
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No. of piers | Number of piers in bridge: must be integer value >0 Not a data entry – solver sets this based on number of data rows defined in pier data table. Minimum of 1 pier must be defined. Pier data used to define blockage ratio (α). | npiers |
Left x | left x-location of pier - must be a positive real number Coordinates of pier edges assumed to use the same reference datum as cross-section chainage. Values should be defined left and right embankment indicators | xleft |
Right x | right x-location of pier - must be a positive real number Coordinates of pier edges assumed to use the same reference datum as cross-section chainage. Values should be defined left and right embankment indicators | xright |
Left height | Height of pier at left x-location. Must be positive real number | htleft |
Right height | Height of pier at right x-location. Must be positive real number | htright |
Check | (Optional) check for duplicate/overlapping entries |
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Field in Data Entry Form | Description | Name in .DAT file |
Upstream Label | Upstream node name | Label1 |
Downstream Label | Downstream node name | Label2 |
Upstream Remote | Label of upstream RIVER section. This label is not required if the upstream RIVER section is Label1 | Label3 |
Downstream Remote | Label of downstream RIVER section. This label is not required if the downstream RIVER section is Label2 | Label4 |
Comment | Add a description or the name of the bridge (optional) | Comment |
Pier Coefficient | Global calibration coefficient used to scale the calculated afflux if this is justified by observations. It should normally be set to 1. Setting cali to 0 removes the effect of the bridge | cali |
Bridge Width | Width of bridge (i.e. distance between upstream and downstream faces of bridge) (m) - only used for modelling dual bridges | rdlen |
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 Pier-Loss Bridge unit. The channel cross section at the bridge location is specified here. Once this is defined then the opening in the pier loss bridge can be added. This is specified by marking the chainage in the section that marks the left and right edges of the opening together with elevations (top levels) of these opening edges.
Data required in the Upstream and (optional) downstream channel section tables is described below.
Data required in the Pier locations table:
Left (start) cross chainage of a pier - Left “X (m)”
Elevation of left edge of top of pier - Left “Top Level (m AD)”
Right (end) cross chainage of a pier - Right “X (m)”
Elevation of right edge of top of pier - Right “Top Level (m AD)”
Orifice Data
The pier loss bridge can be specified to switch to orifice flow only when the bridge becomes surcharged. Thus, this functionality can be utilised as an option to improve hydraulic performance if your bridge is likely to become surcharged.
To enable a smooth transition from bridge to orifice flow, you can specify a “zone” of depths over which there will be a gradual transition to full orifice flow. By default, the standard orifice equation in Flood Modeller is used here, but the orifice discharge coefficient can be changed to adjust this.
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Data required in the Orifice Data tab:
Field in Data Entry Form | Description | Name in .DAT file |
Model surcharged bridge as orifice | Orifice flow flag - if checked (oflag="ORIFICE") then switch to orifice flow when surcharging; otherwise, bridge equations are used for all flows. | oflag |
Lower Transition Distance | Lower transition depth (m below soffit). When the upstream water level is below (max soffit level - rlower), the full bridge equations are used. When this level is reached, it enters the transition phase between bridge and orifice flow. NB rupper + rlower ≥ 0. | rlower |
Upper Transition Distance | Upper transition elevation (m above soffit). When the upstream water level exceeds (max soffit level + rupper), the bridge to orifice transition mode is left, and full orifice equations apply. NB rupper + rlower ≥ 0. | rupper |
Orifice Discharge Coefficient | Orifice discharge/calibration coefficient. Default value = 1.0, recommended adjustment is between 0.75 and 1 (but any positive value is allowed). | cdorifice |
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.
Format of data | .DAT example |
|---|---|
Line 1: BRIDGE (keyword) Line 2: PIERLOSS (keyword to distinguish from other types) Line 3: Label1, Label2, Label3, Label4 (first two: directly connected, second two: remote units) Line 8+npts_us+1: npts_ds Line 8+npts_us+2 to Line 8+npts_us+2+npts_ds: dsxpi, dsypi, dsrni, dschmaini, dstoplev Line 8+npts_us+2+npts_ds+1: npiers Line 8+npts_us+2+npts_ds+2 to line 8+npts_us+2+npts_ds+2+npiers: xleft, xright, htleft, htright. | Line 1: BRIDGE Upton Bridge Line 4: YARNELL Line 5: 1 1 0.1 0.1 Line 6: 0.9 0 Line 7: 12 Line 8: 21.600 13.190 0.035 0.000 52.700 11.520 0.035 0.000 56.500 12.100 0.035 L 11.200 57.800 11.970 0.035 0.000 84.000 4.040 0.035 0.000 86.000 4.040 0.035 0.000 100.000 4.490 0.035 0.000 102.000 4.490 0.035 0.000 122.000 10.060 0.035 0.000 127.000 12.360 0.035 R 11.200 134.900 12.460 0.035 0.000 143.500 12.770 0.035 0.000
Line 10: 68.000 112.000 11.200 12.000 |
Associated Theory
The formula utilized was derived by analysing results from a large number of experiments and on-site measurements. It is known as the Yarnell equation (1) and relates the water stage (H) at the upstream and downstream areas of the bridge.
The subscripts US and DS denote the upstream and downstream sections respectively. The formula shows that the afflux is dependent on the shape of the pier’s (coefficient K), the ratio (α) of the area blocked by the structure to the total effective area upstream of the bridge, and the flow characteristics (velocity and depth) at the downstream end of the structure. In particular, VDS the velocity downstream and ω is the ratio of the velocity head (V2DS/2g) to the downstream water depth.
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Plan view of a bridge showing the relative position of cross sections (numbered) needed to apply Yarnell equation. The embankments are also shown.
Based on the plan view of a bridge shown in the above figure, without the actual pier’s, the river cross sections (2) and (3) are located at the very end of bridge embankments at the upstream and downstream faces of the structure. Sections (1) and (4) are further up or down of the bridge, i.e. the adjacent river cross sections in your network. Note that if your structure is not attached directly to river sections, e.g. attached to a junction to enable incorporation of spill units with bridge, then sections (1) and (4) in the above diagram will be the closest “remote” sections to your bridge.
Tips and Tricks
When setting up new networks, use the Bridge unit (Bridge). This can be applied to all bridge types (including Pier-Loss bridges) and has built-in options to include overtopping, flood relief culverts and blockages
If a pier loss 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 pier loss 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 pier loss 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
If separate flood relief culverts are part of the design of your pier loss bridge then these should be represented by the addition of an orifice unit in parallel with your bridge and spill units, i.e. following the same labelling convention as detailed here for added spill units. The orifice unit provides a means to transfer a component of the calculated flow to another part of the network, e.g. downstream of the pier loss bridge.