# Bridges

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.

## US Bureau of Public Roads Bridge Method

The method was developed for modern US highway bridges where the flows are essentially sub-critical. 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.

## Example

The length of the modelled reach is 350m (50m between sections) with a flat bed and cross-section 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 co-ordinates of the proposed bridge pier should appear in this cross-section 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 co-ordinates. For bridges it is necessary that the co-ordinates of where the pier(s) will be located are entered. Thus for our bridge the extra co-ordinates required (either side of the pier(s))are shown in the second section.

Cross Chainage (m)

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 co-ordinates of the arches given here must appear in the Cross-section data entered earlier.

The Soffit Level and The Springing Level are both 10m AOD.

### Implementation Using ISIS (Video Tutorial)

• Build the channel
• Insert USBPR Bridge Unit
• Specify Bridge Dimension
• Run Simulation

• 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 ,

• Determine the depth of flow hB , check your answer using ISIS.
• Inspect the steady state file (*.zzs), show that the increase in the upstream water level is 0.047m.
• Show that the force on the pier is 14.2kN.
• Increase the width of the bridge pier to 3,4 and 5m. Show that the upstream water levels increase by 0.066m, 0.083m and 0.101m respectively.
• Increase the discharge to 90m3/s change the channel roughness to 0.035 (a global change will not alter the US BPR unit ’n’ values). Set the pier width to 2m. View the long section describe what is happening giving your reasons.
• For the simulation above determine the upstream and downstream flow regimes. Would you say that the US Bureau of Public Roads Bridge Method was appropriate for the situation, give your reasons?

## Hydraulics Research Method For Arched Bridges

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.

## Example

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.

• Compare the surface water profiles for both methods using a Long Section. Describe what you observe.
• Compare the steady state files for the two methods, what is the maximum water level difference between the US BPR and Arch bridge methods. (0.055m)

Related Topics

USPBR Bridge Parameters

The Skew Angle of the bridge (in degrees) between the direction of flow and the normal to the main axis of the bridge (0 for the orthogonal case).

Dual Distance is used if you have two identical bridges a short distance apart. It is the distance from the upstream face of the upstream bridge to the downstream face of the downstream bridge.

Bridge Width is the distance between upstream and downstream faces of bridge.

Number Of Piers is the number of bridge piers in the line of flow at a typical pier location.

Pier Width is the total width of the piers (summed together if more than one pier e.g. 3 piers each 1.5m wide pier width = 3 x 1.5) normal to the flow direction.

The Pier Shapes fields describe the shape of the bridges Piers. Pier Shape 1 describes the primary shape of the pier either rectangular, cylindrical, square, I (For I beam piles) or coefficient (a factor is used to describe the pier). Pier Shape 2 describes the secondary shape of the pier either streamlined pier faces, semi circular pier faces, triangular pier faces or diaphragm wall between piers.

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.

Soffit Level of the arch is the level of highest point in the arch.

Springing Level of the arch is the level at which the arch starts. For horizontal ’arches’ the soffit and springing levels assume the same value. Enter soffit and springing levels of 10m AOD.