- 21 Sep 2022
- 5 Minutes to read
- Updated on 21 Sep 2022
- 5 Minutes to read
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.
Field in Data Entry Form
Name in Datafile
Upstream node name
Downstream node name
Upstream River Section
label of upstream RIVER section. This label is not required if the upstream RIVER section is Label1
Downstream River Section
label of downstream RIVER section. This label is not required if the downstream RIVER section is Label2
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
skew angle of bridge (angle, in degrees, between the flow direction and the normal to the main axis of the bridge - usually set to zero)
width of bridge (ie distance between upstream and downstream faces of bridge) (m) - only used for modelling dual bridges
distance from the upstream face of the upstream bridge to the downstream face of the downstream bridge (m) - only used for modelling dual bridges
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.
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.
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.
orifice discharge/calibration coefficient
Channel Section at Bridge Data
Field in Data Entry Form
Name in Datafile
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
cross chainage (m)
elevation of bed or flood plain (mAD)
Manning roughness coefficient
LEFT or RIGHT(chmain= 'L' or 'R') to indicate left or right embankments of main channel
Bridge Arch Data
number of arches (openings between piers)
horizontal coordinate of left side of arch (must coincide with a coordinate of cross chainage, xp) (m)
corresponding horizontal coordinate of right side of arch (must coincide with a coordinate of cross chainage, xp) (m)
springing level of arch (mAD)
soffit level of arch (mAD)
Theory and Guidance
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 used within the Flood Modeller simulation engine. These values are also shown on the graph.
J3 = 0.2
J3 = 0.3
J3 = 0.4
J3 = 0.5
J3 = 0.6
J3 = 0.7
Table Relating dh/D3 to F3 for Different Values of J3
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
Line 1: keyword 'BRIDGE'
Line 2: keyword 'ARCH'
Line 3: Label1, Label2, [Label3, Label4]
Line 4: keyword 'MANNING'
Line 5: cali, skewb, [rdlen, dual],<blank>, oflag, rlower, rupper, cdorifice
Line 6: npts
Line 7 to Line 6+npts: xpi, ypi, rni[,chmaini]
(subsequent line numbers depend on npts and narch)
Line 8: narch
Line 9 to Line 8+npts: archxli, archxri, springi, asofiti
BRIDGE Example road bridge ARCH UNIT059 UNIT060 MANNING 0.900 10.000 0.000 0.000 4 0.000 2.000 0.020 L 1.000 0.000 0.020 2.000 0.000 0.020 3.000 2.000 0.020 R 1 1.000 2.000 0.000 2.000