Figure 2.39. Submergence of a superstructure.
In Type I flow, the normal water surface is everywhere above critical depth and the flow is
subcritical. Backwater calculations are obtained by applying the conservation of energy principle
between Sections 1 and 4.
In Type II flow, subcritical flow upstream of the bridge passes through critical depth in the
constriction. The backwater curve for the water surface elevation upstream from the constriction
is independent of the water surface elevation downstream. An undulating hydraulic jump (with Fr
< 2) is formed when the water surface elevation dips below critical depth downstream from the
contracted section (Type IIB).
Referring to Type III flow, the flow is supercritical throughout the reach as the normal water
surface is everywhere below critical depth. Such conditions require steep channels as
experienced in, but not limited to, mountainous regions. Backwater should not occur as long as
the flow remains supercritical since the flow is controlled from upstream conditions. However,
significant rise in the water surface might occur in the vicinity of the constriction due to: (1)
changes in the specific energy or specific discharge diagram as indicated in Figures 2.19 and
2.21; (2) cross waves and transitions; and (3) possible hydraulic jumps near the embankments.
Solved problems are presented in Section 2.14 (SI) and 2.15 (English) to illustrate how to
calculate maximum constrictions without causing backwater and to calculate water surface
elevation upstream of a grade control structure.
2.11 COMPUTER MODELS FOR HIGHWAY BRIDGES
2.11.1 One-Dimensional Computer Models
Many one-dimensional computer models are available for computing water surface profiles,
average depth and velocity for open channel flow. However, three have the most utility for
highway bridge analysis. These are FHWA's WSPRO (Arneson and Sherman 1998). The U.S.
Army Corps of Engineers (2001) HEC-RAS (River Analysis System) and UNET (Barkau 1993).
HEC-RAS is the successor the Corps of Engineers HEC-2 water surface profile program.
WSPRO is for steady, nonuniform flow.
2.65
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