Arch Bridge
  • 21 Sep 2022
  • 5 Minutes to read
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Arch Bridge

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Article summary

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.

Data

General Data

Field in Data Entry Form

Description

Name in Datafile

Upstream Label

Upstream node name

Label1

Downstream Label

Downstream node name

Label2

Upstream River Section

label of upstream RIVER section. This label is not required if the upstream RIVER section is Label1

Label3

Downstream River Section

label of downstream RIVER section. This label is not required if the downstream RIVER section is Label2

Label4

Calibration 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

Skew Angle

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)

skewb

Bridge Width

width of bridge (ie distance between upstream and downstream faces of bridge) (m) - only used for modelling dual bridges

rdlen

Dual Distance

distance from the upstream face of the upstream bridge to the downstream face of the downstream bridge (m) - only used for modelling dual bridges

dual

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

Discharge Coefficient

orifice discharge/calibration coefficient

cdorifice

Channel Section at Bridge Data

Field in Data Entry Form

Description

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

npts

Cross-chainage

cross chainage (m)

xpi

Elevation

elevation of bed or flood plain (mAD)

ypi

Mannings n

Manning roughness coefficient

rni

Embankments

LEFT or RIGHT(chmain= 'L' or 'R') to indicate left or right embankments of main channel

chmaini

Bridge Arch Data

Data Field

Description

Datafile Name

n/a

number of arches (openings between piers)

narch

Start

horizontal coordinate of left side of arch (must coincide with a coordinate of cross chainage, xp) (m)

archxli

Finish

corresponding horizontal coordinate of right side of arch (must coincide with a coordinate of cross chainage, xp) (m)

archxri

Springing Level

springing level of arch (mAD)

springi

Soffit Level

soffit level of arch (mAD)

asofiti

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.

dh/D3

J3 = 0.2

J3 = 0.3

J3 = 0.4

J3 = 0.5

J3 = 0.6

J3 = 0.7

0

0

0

0

0

0

0

0.1

0.005

0.005

0.01

0.025

0.04

0.1

0.2

0.01

0.025

0.04

0.08

0.15

0.36

0.3

0.02

0.055

0.1

0.185

0.33

0.81

0.4

0.05

0.11

0.19

0.345

0.58

1.54

0.5

0.1

0.18

0.315

0.55

0.885

 

0.6

0.165

0.27

0.475

0.79

1.13

 

0.7

0.25

0.39

0.67

1.26

 

 

0.8

0.355

0.535

0.9

 

 

 

0.9

0.475

0.7

1.12

 

 

 

1.0

0.6

0.9

 

 

 

 

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.

RiverNodesimagesArchBridge.gifModelling Duel Bridges with the Arch Bridge Unit

General

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.

Orifice Flow

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

Datafile Format

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

Example

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

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