6.10 Modeling Two Closely Placed Bridges

Smith Creek is northwest of Melbourne, Australia. The creek has large floodplains on either side. A railway bridge crosses the creek between embankments that substantially block the floodplain.

A second railway bridge was built immediately upstream of the old structure and uses the same embankments as the old bridge. The two bridges have similar cross sections and are separated by a gap of 4 m (13 ft). The upstream ("new") bridge abutments consist of pillars in line with the downstream retaining wall abutments. The issue to be resolved is the upstream water surface elevation, associated with the dual-bridge structure, for the 1% flood of 340 m³/s (12,000 ft³/s).

An initial approach was to model each of the two bridges separately, each with their own values of contraction and expansion coefficients. The contraction into the upstream bridge was characterized by a coefficient of 0.3 and the expansion from the downstream bridge by a coefficient of 0.5. Between the two bridges, values of 0.1 and 0.3 were used.

An issue is the capability of the hydraulic model to reproduce the energy loss across the two bridges, especially under high flows. Under the design flow of 340m³/sec (12,000 ft³/s), the water surface elevation on the downstream side is computed to be 4.44 m (14.57 ft), which is well above the soffit (underside) of the bridges-3.56 m (11.68 ft) for the upstream bridge and 3.58 m (11.75 ft) for the downstream bridge.

Between the two bridges, the water level will be higher than 4.44 m (14.57 ft). The model requires that the flow expand fully throughout the flow depth between the two bridges (that is, up into the "gap" between the two bridges). Additionally, the modeling approach described above produces overtopping flows of the two bridges of 208 m³/s (7,345 ft³/s) (upstream bridge) and 40 m³/s (1,413 ft³/s) (downstream bridge). This would require 168 m³/s (5933 ft³/s) to flow into the waterway at a location between the two bridges. The geometry of the single embankment, which forms a broad crested weir approximately 800 m (2625 ft) wide, makes it impossible for the 168 m³/s (5933 ft³/s) to re-enter the creek at this location, but HEC-RAS does not have the "intelligence" to know this.

These hydraulic characteristics are unrealistic consequences of the separated model of flow through the two bridges. Because the bridges are so close together and are of almost identical waterway areas, it is much more realistic to consider that they act essentially as a single bridge.

It has to be recognized, however, that there will be significant energy dissipation between the two bridges resulting from interaction between the water flowing through the bridge waterway and the "dead" water between the two bridges, which is outside the effective waterway area. The issue is how to realistically reproduce this additional energy loss.

The HEC-RAS model incorporates two options for modeling high flows: a standard step (energy) approach and an orifice combined with a weir. The first of these offers an appropriate method of incorporating the energy loss between the two bridges in an explicit fashion by adjusting the Manning's n values of the two cross sections located within the bridge site.

The second option also offers a possibility by permitting an operator-nominated value of discharge coefficient in the orifice equation. By reducing this value below the standard value of 0.8, an increased energy loss across the bridge site will be calculated. However, this too is in the nature of a de facto method for the geometry under consideration and is not favored.

In the present situation, the standard step approach is particularly appropriate and was utilized in a second model. The primary issue is to determine a reasonable value of Manning's n to assume within the bridge opening to simulate the energy dissipation effect of the flowing water interacting with essentially dead water in the "gap" between bridges. This is a matter for professional engineering judgment. In the present situation, a value of 0.07 was assumed.

In summary, when two bridge structures are located very close together, and both span the same embankments, it is not appropriate to model them as separate structures. Hydraulically, they behave as a single structure, albeit with a substantial effective internal roughness due to the interaction between the flowing water and the dead water between the two bridges.