Cross Section Locations for Bridges

The bridge routines utilize four user-defined cross sections in the computations of energy losses due to the structure. During the hydraulic computations, the program automatically formulates two additional cross sections inside of the bridge structure. A plan view of the basic cross section layout is shown in the figure below. The cross sections in the figure below are labeled as river stations 1, 2, 3, and 4 for the purpose of discussion within this chapter. Whenever the user is performing water surface profile computations through a bridge (or any other hydraulic structure), additional cross sections should always be included both downstream and upstream of the bridge. This will prevent any user-entered boundary conditions from affecting the hydraulic results through the bridge.

Cross section 1 is located sufficiently downstream from the structure so that the flow is not affected by the structure (i.e., the flow has fully expanded). This distance (the expansion reach length, Le) should be determined by field investigation during high flows, however, is generally not likely that a large event will occur during the scope of your project. Therefore modelers must estimate this distance from known information. The expansion distance will vary depending upon the degree of constriction, the shape of the constriction, the magnitude of the flow, and the velocity of the flow.

Table 5-1 offers ranges of expansion ratios, which can be used for different degrees of constriction, different slopes, and different ratios of the overbank roughness to main channel roughness. Once an expansion ratio is selected, the distance to the downstream end of the expansion reach (the distance L_e in the figure below) is found by multiplying the expansion ratio by the average obstruction length (the average of the distances A to B and C to D from the figure below). The average obstruction length is half of the total reduction in floodplain width caused by the two bridge approach embankments. In Table 5-1, b/B is the ratio of the bridge opening width to the total floodplain width, nob is the Manning n value for the overbank, nc is the n value for the main channel, and S is the longitudinal slope. The values in the interior of the table are the ranges of the expansion ratio. For each range, the higher value is typically associated with a higher discharge. The values shown in this table should be used as rough guidance for placing cross section 1, and determining the expansion reach length.

Table 5-1 Ranges of Expansion Ratios

A detailed study of flow contraction and expansion zones has been completed by the Hydrologic Engineering Center entitled "Flow Transitions in Bridge Backwater Analysis" (RD-42, HEC, 1995). The purpose of this study was to provide better guidance to hydraulic engineers performing water surface profile computations through bridges. Specifically the study focused on determining the expansion reach length, L_e; the contraction reach length, Lc; the expansion energy loss coefficient, Ce; and the contraction energy loss coefficient, Cc. A summary of this research, and the final recommendations, can be found in Appendix B of this document.

The user should not allow the distance between cross section 1 and 2 to become so great that friction losses will not be adequately modeled. If the modeler thinks that the expansion reach will require a long distance, then intermediate cross sections should be placed within the expansion reach in order to adequately model friction losses. The ineffective flow option can be used to limit the effective flow area of the intermediate cross sections in the expansion reach.

Cross section 2 is located a short distance downstream from the bridge (i.e., commonly placed at the downstream toe of the road embankment). This cross section should represent the natural ground (main channel and floodplain) just downstream of the bridge or culvert. This section is normally located near the toe of the downstream road embankment. This cross section should Not be placed immediately downstream of the face of the bridge deck or the culvert opening (for example some people wrongly place this cross section 1.0 foot downstream of the bridge deck or culvert opening). Even if the bridge has no embankment, this cross section should be placed far enough from the downstream face of the bridge to allow enough distance for some flow expansion due to piers, or pressurized flow coming out of the bridge.

Cross section 3 should be located a short distance upstream from the bridge (commonly placed at the upstream toe of the road embankment). The distance between cross section 3 and the bridge should only reflect the length required for the abrupt acceleration and contraction of the flow that occurs in the immediate area of the opening. Cross section 3 represents the natural ground of the channel and overbank area just upstream of the road embankment. This section is normally located near the toe of the upstream road embankment. This cross section should Not be placed immediately upstream of the bridge deck (for example some people wrongly place this cross section 1.0 foot upstream of the bridge deck). The bridge routines used between cross sections 2 and 3 account for the contraction losses that occur just upstream of the structure (entrance losses). Therefore, this cross section should be place just upstream of the area where the abrupt contraction of flow occurs to get into the bridge opening. This distance will vary with the size of the bridge opening.

Both cross sections 2 and 3 will have ineffective flow areas to either side of the bridge opening during low flow and pressure flow. In order to model only the effective flow areas at these two sections, the modeler should use the ineffective flow area option. This option is selected from the cross section data editor.

Cross section 4 is an upstream cross section where the flow lines are approximately parallel and the cross section is fully effective. In general, flow contractions occur over a shorter distance than flow expansions. The distance between cross section 3 and 4 (the contraction reach length, Lc) should generally be determined by field investigation during high flows. Traditionally, the Corps of Engineers guidance suggests locating the upstream cross section one times the average length of the side constriction caused by the structure abutments (the average of the distance from A to B and C to D in the figure above). The contraction distance will vary depending upon the degree of constriction, the shape of the constriction, the magnitude of the flow, and the velocity of the flow. As mentioned previously, the detailed study "Flow Transitions in Bridge Backwater Analysis" (RD-42, HEC, 1995) was performed to provide better guidance to hydraulic engineers performing water surface profile computations through bridges. A summary of this research, and the final recommendations, can be found in Appendix B of this document.

During the hydraulic computations, the program automatically formulates two additional cross sections inside of the bridge structure. The geometry inside of the bridge is a combination of the bounding cross sections (sections 2 and 3) and the bridge geometry. The bridge geometry consists of the bridge deck and roadway, sloping abutments if necessary, and any piers that may exist. The user can specify different bridge geometry for the upstream and downstream sides of the structure if necessary. Cross section 2 and the structure information on the downstream side of the bridge are used as the geometry just inside the structure at the downstream end. Cross section 3 and the upstream structure information are used as the bridge geometry just inside the structure at the upstream end. The user has the option to edit these internal bridge cross sections, in order to make adjustments to the geometry.