eLearning
River Hydraulics with ISIS
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Bridges are common structures in rivers. They can constrict the flow in a channel causing an increase in the upstream water level. The increase in the upstream water level is called the Afflux. Two methods are available in ISIS for modelling bridges, the US Bureau of Public Roads bridge method and Hydraulics Research Arch bridge method.
The method was developed for modern US highway bridges where the flows are essentially subcritical. The method requires that the model has a river section upstream and downstream of the of the bridge. Conserving energy through the bridge it can be shown that the afflux at the bridge can be given by:
Where:
h1*is the total afflux (backwater).
K* is the total afflux (backwater) coefficient.
α1 is the kinetic energy coefficient at the upstream section.
α2 is the kinetic energy coefficient in the constriction.
ub is theaverage velocity in the constriction.
Ab is the gross water area in the constriction
A4 is the water area in the downstream section.
A1 is the total water area in the upstream section including that produced by the afflux.
The length of the modelled reach is 350m (50m between sections) with a flat bed and crosssection details that correspond to Tutorial 2.1. The discharge has is 30 m3/s, the downstream boundary conditions remain the same the Manning’s roughness coefficient for the bridge is 0.010. A US BPR bridge unit is to be placed between SECT4u and SECT4d. The dimensions of the bridge are given below. Complete the data file. Run a Steady simulation.
The 3 available types of abutment are summarised in the table overleaf, Select type 1.
The Abutment Alignment select ALIGNED (with the normal direction of flow), you can toggle between options.
Dual Distance is not used since there is only one bridge.
Number Of Piers is 1.
Pier Width is 2m.
Pier Shape 1 select Rectangle. For Pier Shape 2 select Semi circular.
The Channel Section can be thought of as the river and floodplain section prior to bridge construction. It describes 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. The coordinates of the proposed bridge pier should appear in this crosssection data. See the diagram below.
In our case the channel section at the bridge is the top rectangular channel which is shown with the associated coordinates. For bridges it is necessary that the coordinates of where the pier(s) will be located are entered. Thus for our bridge the extra coordinates required (either side of the pier(s))are shown in the second section.
Cross Chainage (m) 
Elevation (m AD) 
Manning's n 

10.000

10.000

0.010

0.000

10.000

0.010

10.000

2.000

0.010

24.000

2.000

0.010

26.000

2.000

0.010

40.000

2.000

0.010

40.000

10.000

0.010

50.000

10.000

0.010

Cross section coordinates
Openings: One line in this section represents one opening or arch. Note the coordinates of the arches given here must appear in the Crosssection data entered earlier.
The Soffit Level and The Springing Level are both 10m AOD.
To see the example, consult the downloaded file: Ch2/USBPR.dat
Consider a smooth channel containing a bridge with a central pier. If the depth of flow between the bridge pier and the bank/ abutment is hB (excluding the afflux), the depth of flow just downstream of the pier is h2 , the width of the channel is B and the width of the pier is b. Derive the expression given below assuming there is no energy loss between the two sections:
where ,
This method computes the afflux at bridges with arched soffits using the methodology developed by Hydraulics Research (HR), Wallingford. The HR method for arched bridges was developed from laboratory tests on model bridges and verified with data from prototype bridges in the UK. The method is described fully in the report Afflux At Arch Bridges, SR 182, Hydraulics Research Wallingford 1988.
The ISIS implementation of the method calculates the area under each arch assuming it is parabolic. The afflux is determined using a graph relating to the downstream depth and Froude number.
The hydraulic unit for this method is called Arch. It does not have the capacity to include a flood relief culvert in the bridge unit, unlike the US BPR unit.
Use ISIS to simulate flow through the multiple arch bridge used in US BPR Bridge exercise. The terminology used for the Arch unit and US BPR unit is very similar. If you have problems use the ISIS online help.
To see the example, consult to the downloaded file: Ch2/ArchBridge.dat