--- title: "Pier-loss Bridge | Technical Reference" slug: "pier-loss-bridge" description: "Find the technical reference section for pier-loss bridges. " tags: ["1D river modelling", "bridge", "error messages and diagnostics"] updated: 2026-10-16T18:25:48Z published: 2026-10-16T18:25:48Z canonical: "help.floodmodeller.com/pier-loss-bridge" stale: true --- > ## Documentation Index > Fetch the complete documentation index at: https://help.floodmodeller.com/llms.txt > Use this file to discover all available pages before exploring further. # Pier-loss Bridge The pier loss bridge computes the afflux at bridges where the dominant cause of losses is the friction from piers. It utilizes the empirical equation derived by [Yarnell (1934)](/v1/docs/references-1#yarnell). ## Data Pier-loss Bridge Data | Parameter name | Description | Label name in data file | | --- | --- | --- | | 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 \| Pier Shape \| Pier Coefficient (K) \| \| --- \| --- \| \| Semi-circular nose and tail \| 0.9 \| \| Twin-cylinder piers with connecting diaphragm \| 0.95 \| \| Twin-cylinder piers without diaphragm \| 1.05 \| \| 90-degree triangular nose and tail \| 1.05 \| \| Square nose and tail \| 1.25 \| \| Pier consisting of multiple columns \| 2.5 \| Note: Adjustment of this coefficient can help with model calibration. | K | | Pier Shape | Pier Coefficient (K) | | Semi-circular nose and tail | 0.9 | | Twin-cylinder piers with connecting diaphragm | 0.95 | | Twin-cylinder piers without diaphragm | 1.05 | | 90-degree triangular nose and tail | 1.05 | | Square nose and tail | 1.25 | | Pier consisting of multiple columns | 2.5 | | 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

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 | | --- | --- | --- | | 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 | |
RiverNodesimagesPLdata.pngRiverNodesimagesPLdata.png
Visual Representation of Parameters for Pier Loss Bridge Unit

 Theory and Guidance

Aim

 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). This option can be considered for any bridge that incorporates one or more piers. ### Theory The formula utilized was derived by analyzing 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. ![RiverNodesimagesyarnell.png](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/RiverNodesimagesyarnell.png?sv=2026-02-06&spr=https&st=2026-11-14T10%3A58%3A09Z&se=2026-11-14T11%3A58%3A09Z&sr=c&sp=r&sig=8clJLffrf4TeISbJgzqpbUt3t%2FlAVwA925G3hIjY0Zc%3D) 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 piers (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. ![RiverNodesimagesPL2.png](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/RiverNodesimagesPL2.png?sv=2026-02-06&spr=https&st=2026-11-14T10%3A58%3A09Z&se=2026-11-14T11%3A58%3A09Z&sr=c&sp=r&sig=8clJLffrf4TeISbJgzqpbUt3t%2FlAVwA925G3hIjY0Zc%3D) *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 piers, 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. ### Limitations This method has been validated through multiple experiments and on-site measurements and only applies to bridges where losses are dominated by the friction on the piers. Furthermore, there are some additional limitations to consider when applying this unit. The most important condition that needs to be satisfied is that the flow through the opening has the following criteria: There are some limitations when it comes to applying this modelling technique. The most important condition that needs to be satisfied is that the flow through the opening is a class A, low flow. Specifically, the flow should be: 1. Not surcharged: the water stage should be below the soffit of the bridge opening 2. Subcritical: the Froude number should be below 1 (0.9 for tolerance) 3. Not choked: i.e. specific energy is above the critical value in the constriction The unit can still accommodate surcharging, but in this case the calculated hydraulics will assume an orifice type flow through the defined bridge openings (see below). The other limitation is your bridge must include one or more piers, since a fundamental part of this unit is to calculate the blockage caused by them. Thus, this method will not be suitable for all bridges. ### Orifice Flow The pier loss bridge unit will switch to orifice flow at a given depth, which is defined in 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. You need to 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 you can adjust the coefficient by changing the orifice discharge coefficient within the bridge unit. ## Datafile Format *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 4:* YARNELL (keyword referring to the modelling method) *Line 5:* cali, altmethod, cdorifice, rlower, rupper *Line 6:* K, rdlen *Line 7:* npts_us *Line 7 +1 to Line 7 +npts_us:* usxpi, usypi, usrni, uschmaini, ustoplev *Line 7 +npts_us +1:* npts_ds *Line 7 +npts_us +1 +1 to Line 7 +npts_us +1 +npts_ds:* dsxpi, dsypi, dsrni, dschmaini, dstoplev *Line 7 +npts_us +1 +npts_ds +1:* npiers *Line 7 +npts_us +1 +npts_ds +1 +1 to Line 7 +npts_us +1 +npts_ds +1 +npiers:* xleft, htleft, xright, htright.