6.9 Special Situations
Engineers may occasionally encounter special situations when modeling bridges. Some examples of these are multiple openings, parallel bridges, "perched" bridges, low-water crossings, bridges on skew to the direction of flow, and bridges with small openings and much upstream flood storage that serve as dams. The following sections discuss these situations in detail.
Multiple Openings
For roadways crossing wide floodplains, more than one opening for flood flow is normally needed. The main bridge opening allows the majority of flood flows to pass, with one or more supplemental openings providing additional flood capacity. Relief bridge openings for flood flows, culvert openings for smaller streams and ditches, and road underpasses all convey flow through a roadway embankment during a large flood event. Multiple openings may require complex two-dimensional modeling for a roadway crossing of the floodplain that is not reasonably perpendicular to flow. With HEC-2, multiple bridge openings could not be modeled well. The only way this situation could be modeled in HEC-2 was to perform separate split-flow calculations (a time-consuming task) or to simply assume that the energy grade elevation was the same at each opening, an obvious and erroneous simplification.
HEC-RAS performs split-flow analysis for multiple openings and iterates the operation between the full expansion at section 1 (downstream) and the full contraction at section 4 (upstream) until the correct flow split is determined that gives all the flow paths the same energy grade elevation at section 4, the start of contraction. The only additional data needed to model multiple openings are entered with the Multiple Opening Editor located within the Bridge/Culvert Data Editor (refer to Figure 6.23). The modeler specifies the local area of influence for each opening by identifying stagnation points, which represent a dividing line for flow to the different openings through the embankment. Flow to the left of the stagnation point moves toward the opening to the left of the stagnation point. Similarly, flow to the right of the stagnation point moves toward the next opening to the right. It is usually best to have some overlap (50 ft/15 m or more) in identifying these points between bridges and/or culvert groups, thereby allowing the computer program some leeway in determining the splits for each flow path.
From the previous example, a box culvert is added to the sample bridge shown in Figure 6.29 to serve as a relief opening during major floods. The revised road crossing is shown in Figure 6.32. Culvert modeling is presented in Chapter 7. To model the bridge and culvert as a multiple opening requires the modeler to estimate the location of the stagnation points and encode these data in the Multiple Opening Editor. Figure 6.33 shows the data input for the Multiple Opening Editor for the bridge and culvert shown in Figure 6.32. Figure 6.32 also shows the defined stagnation points, called out on the figure by #1 and #2 for the culvert and bridge, respectively. Flow that overtops the road but moves via a separate flow path may also be modeled in the multiple opening, but only by simple friction loss computations (no weir flow), with the overflow location being the first or last flow path on the section. If weir flow occurs, the same energy grade line elevation is used for all flow paths. For the bridge and culvert shown in Figure 6.32, the multiple opening option would not be used for flows overtopping the roadway elevation, because weir flow would be occurring.
Figure 6.32 Cross section illustrating multiple opening analysis.
Figure 6.33 Multiple Opening Analysis Editor for the example bridge and culvert.
HEC-RAS can model up to seven separate flow paths for a long bridge embankment. There may be a different energy elevation at each bridge opening or flow path. The iterations continue until the right balance of flow is achieved that computes the same energy elevation at section 4 (within a specified tolerance or a default of 0.03 ft or 0.009 m) or until the maximum number of iterations is reached (30 iterations is the default). This powerful feature greatly simplifies complex bridge modeling of multiple openings, although the solution is still considered one dimensional. For complicated bridge crossings, such as an embankment that runs upstream or downstream in the floodplain during the crossing, a two-dimensional, unsteady flow solution would likely be needed. Chapter 12 further addresses split flow modeling, which is similar to the analysis for multiple bridge openings.
Parallel Bridges
High-speed road travel, especially on dual highways, often results in two nearly identical bridges located a short distance apart. Tests by the FHWA have found that dual bridges result in more losses than a single bridge but less than if the two structures were independent. Modeling of these structures requires engineering judgment. If the two bridges are fairly close, they can be modeled as a single bridge, simply showing the length between sections BD and BU as the total length from the downstream face of Bridge 1 to the upstream face of Bridge 2. If the openings of the two bridges are very different, or if they are located far enough apart that flows can partly expand after exiting the upstream bridge and then contract back into the downstream bridge, the structures should be modeled as separate bridges and include the partial expansion and contraction paths. When modeled as two separate bridges, each bridge should have separate sections 2 and 3. An additional cross section would be supplied between the two bridges to indicate to the program when the expansion from the upstream bridge changes to a contraction into the downstream bridge. Additionally, ineffective flow area elevations and locations must be specified for both bridges. This complex situation most likely requires additional trials for determination of the ineffective flow area elevations, since there are now four locations where the ineffective flow elevations must be defined rather than the normal two locations for one bridge.
Perched Bridges
Old bridges on secondary or township roads are often perched. That is, the bridge is significantly higher than the floodplain, but the approach road on one or both sides is much lower. The bridge can become an "island" during a flood if the road on both sides is under water. This situation is appropriately addressed by the energy method. The obstructed area caused by the bridge is removed from the available cross-sectional flow area, along with any pier areas, and the losses between bridge sections are computed based on friction losses and expansion or contraction losses. Recall that weir/pressure flow is only appropriate when the roadway is on a significant fill embankment and there is an appreciable head difference between bridge sections 2 and 3. If such a situation does not occur, as is typical with perched bridges, energy computations normally give the most accurate answers. Figure 6.34 displays a perched bridge. If deemed necessary, an alternate solution for profiles at a perched bridge is to analyze the structure using the multiple-opening method presented in Section 6.7. For a perched bridge, the flow around the bridge structure should be modeled as conveyance, and flow through the bridge opening can be modeled with the energy, momentum, or Yarnell methods.
Figure 6.34 Perched bridge.
Low Water Bridges
On minor roads with limited traffic, low water crossings are sometimes used to avoid the expense of building a formal bridge structure. A low water crossing occurs when the roadway is actually in the channel and the roadway elevations are less than those of the bank stations. Figure 6.35 illustrates such a crossing. One or more culverts in the channel allow low flows to pass under the road. These flows normally represent only the base or average low flow, and seldom include any significant allowance for runoff from storm events.
Figure 6.35 Low water crossing.
During a significant rainfall event, the increased discharge rises over the road and often halts all vehicular traffic until the flow drops back to the base level. Obviously, low water crossings are only practical where the flows are not blocking the road for an excessive time and/or where the traffic volume on the road is very low.
For this type of crossing, flow modeling can be simple or complicated. For low flows, only the culverts could be modeled. When flows increase and overtop the road, a combination of weir and pressure flow may exist. As flows continue to increase, the structure has a progressively smaller obstructive effect on flows, and the energy equation becomes the most appropriate solution technique.
To model only flood flows, energy methods are normally applied, and the culvert capacity is ignored as negligible. A low water crossing must be carefully designed, especially for the control of erosion just downstream of the structure. Erosion may not be significant for major floods, because there is little difference in water surface elevation between the upstream and downstream sides. For low flows, however, there is often a significant head difference. Class B flow, or supercritical flow over and just downstream of the bridge, is common, with a hydraulic jump on or near the downstream face of the structure. Scour protection or more formal energy dissipaters are often needed at low water crossings to protect the channel bed and the bridge structure. Low water crossings have frequently been destroyed by erosion shortly after installation, because of the failure to include adequate erosion protection in the design.
Bridges on Skew
Where the bridge and approach embankments cross the valley, the river, or both at a severe angle, the modeler should consider an adjustment for the skew of the structure. Figure 6.36 shows two situations for which a skew adjustment is warranted. In both cases, the river "sees" less opening than is defined from the field surveys, because the field surveys are normally taken parallel to the bridge alignment. The modeler supplies the skew angle between a line perpendicular to the bridge and the main direction of flow, and then HEC-RAS adjusts the bridge opening width for this angle. Bridge stations are adjusted by the cosine of the skew angle (q). The effective width of the bridge is the actual width (b) multiplied by cos q.
Figure 6.36 Effect of skew at bridges.
An old rule of thumb, confirmed by scientific studies (Bradley, 1978), states that the skew angle should be at least 20 degrees before an adjustment for skew is needed. Because the cosine of this value is 0.94, a decrease in bridge opening width of 6 percent will result. Angles less than 20 degrees are considered to provide acceptable flow conditions and no adjustments for skew are typically made. Conversely, the upper limit for skew adjustments is about 30 to 35 degrees. This angle shortens the bridge-opening stations by approximately 14 to 18 percent. Where bridge piers are also skewed to the flow direction, the effective flow width is much smaller because the flow "sees" a wider pier due to the flow's angle of approach. However, good bridge design should orient the bridge piers parallel to the direction of flow, even if the bridge opening is skewed. For example, Figure 6.6 shows a bridge in the background crossing the man-made channel at a sharp angle. Notice, however, that the piers are still aligned parallel to the flow direction.
An adjustment for skew is only appropriate for flow through the bridge opening. During weir flow, the flow across the roadway moves perpendicular to the roadway and the full length of the embankment should be used.
Calculations with skew angles greater than 30 to 35 degrees should be closely examined because the true effective flow width may be more than is determined by the skew adjustment. For a bridge with several piers, such as shown in Figure 6.32, an adjustment for skew may block too large a percentage of the opening. HEC-RAS can apply separate angles for the bridge and for the piers to compute varying amounts of skew. Two-dimensional flow modeling may be necessary for large skew angles if the best assessment of flow patterns and the maximum profile accuracy is desired. Where a skew adjustment is performed, the bounding sections (2 and 3) may also be adjusted in the Cross-Section Data Editor.
The Bridge as a Dam
In certain instances, the road embankment and bridge opening severely throttle the outflow through the bridge opening during large flood events. This condition is more common for culverts under a high embankment, but it is occasionally found at older bridges, especially railroad crossings. In this case, the small opening causes a large backwater effect extending far upstream of the bridge location. When this occurs, the roadway embankment acts as a dam, with the bridge opening serving as the low flow tunnel or conduit. To properly assess the effect of this situation, a hydrologic routing, performed outside of HEC-RAS, is required.
The routing operation uses the storage reach upstream of the embankment to compute the attenuation of the peak discharge caused by the restricted outflow and upstream storage. Discharges for the cross sections downstream of the road (dam) should reflect the reduced discharge through the bridge opening caused by the upstream storage. In Figure 6.37, the width of the opening is a small percent of the width of the floodplain and the roadway embankment is very high, preventing or limiting overflows. A series of profiles for varying discharges are necessary to develop the reach storage versus bridge opening outflow data to use in a hydrologic model, like HEC-HMS. Chapter 8 addresses the development of these data in more detail.
Figure 6.37 Bridge as a dam and conduit.
