through the smaller width of the bridge opening. (The terms length and width of a bridge in hydraulics are exactly the opposite of the meaning used by highway engi-neers or motorists. In hydraulics, the length refers to the distance parallel to the flow and the width refers to the opening perpendicular to the flow. So, while a motorist may see a 1000 ft long bridge that is 50 ft wide, a hydraulic engineer sees a 50 ft long bridge that is 1000 ft wide.)
The amount of flow contraction varies within the contraction reach. During a flood, for example, flow within the channel may not contract significantly, but flow near the floodplain limits may have to cross the entire floodplain, returning to the channel, to move through the bridge opening and continue downstream. Figure 6.1 displays this movement of flow, in an idealized sense, along with the full contraction and expan-sion reaches through the bridge.
Modified from FHWA
Figure 6.1 Flood flow lines for a typical bridge crossing.
Section 6.1 The Effects of a Bridge on Water Flow 169
Flow accelerates as it approaches the bridge opening, due to the smaller cross-sec-tional area through the bridge, and usually reaches a peak velocity near the down-stream face of the opening. Water can move through the bridge at subcritical, critical, or supercritical depth. The water surface may be rapidly varied, passing through criti-cal depth within the bridge opening.
As illustrated in Figure 6.1, downstream of the bridge fast-moving flow expands into the wider valley cross section, resulting in a decrease in velocity as the flow expands across the floodplain. Energy is lost through the bridge, and so the water surface may be significantly higher upstream of the bridge than downstream. The difference in water surface elevations for a selected discharge just upstream of an obstruction is often called the swellhead.
In a low-flow condition, the water surface is below the low chord (low steel) or under-side of the bridge. If the bridge opening becomes submerged, the bridge functions as a sluice gate, orifice, or weir, or as some combination of these, depending on the depth of flow.
Figures 6.1 and 6.2 show the locations of the four key cross sections required for bridge modeling. Cross section 1 is downstream of the bridge, at the end of the flow expansion. Cross section 4 is upstream of the bridge, at the beginning of the flow con-traction. Properly locating these two sections is discussed in Section 6.4. Two more cross sections are placed at the bridge, with the precise locations based on the bridge analysis technique used. For HEC-RAS, these two sections (Nos. 2 and 3) are placed a short distance outside of the downstream and upstream bridge faces, respectively.
The locations of these two sections are discussed in detail in Section 6.4. HEC-RAS automatically adds two more cross sections immediately inside the upstream (BU for bridge upstream) and downstream (BD for bridge downstream) bridge faces, based on sections 2 and 3 and the bridge geometry supplied by the modeler. Thus, in HEC-RAS, bridge modeling is usually performed with a total of six cross sections, with four sections supplied by the modeler and two more developed by the program.
If only flow through a bridge reach is to be modeled, the modeler might think that the data set should start with section 1 and end with section 4. However, section 1 does
USACE
Figure 6.2 Cross-section placement for a typical bridge crossing.
not represent the first cross section in the HEC-RAS data set, even though it does rep-resent the end of the bridge effects. The modeler has to determine how far down-stream of section 1 the additional cross sections are required so that profile convergence occurs before cross section 1. Similarly, the data set should extend fur-ther upstream than section 4 to properly compute any adverse effects of the obstruc-tion. These distances can be estimated with the procedures presented in Section 5.2.
6.2 Low Flow Through Bridges
Low flow is the most common analysis case for a bridge. Low-flow situations exist whenever the discharge passes through the bridge opening and the water surface or energy grade line elevations do not reach the elevation of the bridge low chord. A variety of potential solution methods is available in HEC-RAS for low flow, with low flow classified as Class A, B, or C, based on momentum computations at the bridge.
Figure 6.3 illustrates the water surface profiles for each of the three classifications.
HEC-RAS must first determine the flow regime to properly classify the flow. It accom-plishes this evaluation by computing the momentum at the bridge cross sections (2, BD, BU, and 3). First, HEC-RAS determines the momentum at critical depth at sec-tions BD and BU for the given discharge. The section with the higher momentum is designated as the controlling section. If the two sections have equal momenta, section BU is selected as controlling.
For subcritical flow analysis, the momentum at section 2 is then computed and com-pared to the controlling section in the bridge. If the momentum at section 2 exceeds the critical momentum at the controlling section, the flow is assumed to be Class A throughout the bridge reach. If the momentum at section 2 is less than the critical momentum at the controlling section, Class B flow is assumed, with critical depth occurring within the bridge opening.
For supercritical flow, the momentum at section 3 is computed and compared to the critical momentum at the control section in the bridge opening. If the momentum at section 3 exceeds the critical value, the flow through the bridge is designated as Class C.