Civil Engineering Reference
In-Depth Information
Base-of-rail
High water level at
Q
Area,
A
, required for
Q
b
FIGURE 3.1
River crossing profile without constriction or obstruction.
(Figure 3.1), the required area of the crossing is simply established as
Q
V
u
.
A
=
(3.4)
3.2.3.2.1.1 Constricted Discharge Hydraulics
Where abutments constrict the
channel
(Figure 3.2)
,
the flow may become rapidly varied and exhibit a drop in water
surface elevation (hydraulic jump) as a result of the increased velocity. Four types of
constriction openings have been defined (Hamill, 1999) as follows:
• Type 1: Vertical abutments with and without wings walls with vertical
embankments
• Type 2: Vertical abutments with sloped embankments
• Type 3: Sloped abutments with sloped embankments
• Type 4: Vertical abutments with wings walls and sloped embankments
(typical of many railroad embankments at bridge crossings)
The hydraulic design should strive for subcritical flow (
F <
1.0 with a stable water
surface profile). Discharge flows that exceed subcritical at, or even immediately
downstream of, the bridge may also be acceptable with adequate scour protection.
Supercritical flow (
F >
1.0) is undesirable and may create an increase in water sur-
face elevation at the bridge crossing. However, supercritical flow may be unavoidable
for river crossings with steep slopes [generally
>
0.5-1% (TransportationAssociation
of Canada (TAC), 2004)], and careful hydraulic design is required. In the case of
constrictions, the required area of the crossing is established as
Q
C
c
V
u
A
=
,
(3.5)
where
A
is the minimum channel area required under the bridge;
Q
is the required
or design return frequency discharge (e.g., 1:100);
V
u
is the average velocity of the
existing (upstream) channel for discharge,
Q
; and
C
c
is the coefficient of contraction
