Design of Bridge Deck Drainage: HEC 21 May 1993
Design of Bridge Deck Drainage: HEC 21 May 1993
Design of Bridge Deck Drainage: HEC 21 May 1993
HEC 21
May 1993
Welcome
to HEC
21-Design
of Bridge
Deck
Drainage
Table of Contents
Tech Doc
List of Figures List of Tables List of Charts & Forms List of Equations
1.2.4 Aesthetics
1.3 Systems
1.3.1 Deck and Gutters
8.2.2 Hydroplaning
Symbols
References
List of Figures for HEC 21-Design of Bridge Deck Drainage
A bridge deck gutter is defined in this manual as the section of pavement next to the curb or
parapet that conveys water during a storm runoff event. It may include a portion or all of a travel
lane. Gutter cross sections usually have a triangular shape with the curb or parapet forming the
near-vertical leg of the triangle. The gutter may have a straight cross slope or a cross slope
composed of two straight lines. Parabolic sections are also used.
(4)
Equation (4) neglects the resistance of the curb face. However, this resistance is negligible from
a practical point of view if the cross slope is 10 percent or less. Gutter velocity is determined by
dividing the gutter flow equation by the cross-sectional area of the gutter. The resulting relation is:
(5)
S equivalent =
Sx + Sw (a1/ (a1 + a2))
Go to Chapter 5
Chapter 5 : HEC 21
Bridge Deck Inlets
Go to Chapter 6
The design of the bridge deck inlet is important because it removes water from a bridge deck
within the limits of allowable spread. An inlet is a common location for debris to collect and
potentially clog a drainage system. From a hydraulic point of view, inlets should be large and
widely separated. From a structural point of view, inlets should be avoided or made as small
and as few as possible. This chapter presents typical inlet designs and discusses the factors
that affect inlet interception capacity. In addition, design features to help prevent clogging and
guidance for determining inlet locations are presented.
Figure 5 illustrates extra slab reinforcement for a grate that projects 3 feet from the curb. The
advantage of the extra projection generates the need for extra reinforcing. The inlet chamber
should have as large a transverse slope as possible to avoid clogging. For this grate, projecting
3 feet toward the centerline, and a spread of 10 feet, the interception efficiency is 61 percent.
This assumes all flow within the 3 feet of width is intercepted. Flow across the grate will reduce
the interception efficiency of the inlet on higher slopes because the grate is only 8 inches long
in the direction of the flow and rapid flow will splash over the gap.
Figure 6 illustrates a vertical scupper with several well-thought-out design details. An eccentric
pipe reducer enlarges the circular opening at deck level to 10 inches. While this enlargement is
hydraulically beneficial, bars are necessary to reduce the potential hazard of the rather large
circular opening. Smaller openings of 4 to 6 inches, without the eccentric pipe reducer, are
more typical, but less effective. Note that the pipe discharges below the girder. Such free
discharge can be directed on slight angles to erosion-resistant splash surfaces like the concrete
surfaces placed on side slopes under overpass bridges. A 6-inch diameter vertical scupper has
a capture efficiency of 12 percent for 10 feet of spread and a 2 percent cross slope; a 4-inch
diameter scupper has an efficiency of 7 percent.
For completeness, Figure 7 shows a common practice of using slotted New Jersey type
barriers, which has low-hydraulic utility. Horizontal or nearly horizontal scuppers are poor
managers of spread. Such designs clog easily, are difficult to maintain, and offer only 5 percent
interception capacity for gutter flow having a 10-foot spread. Perhaps the best comment on
their usage is that they may be better than nothing.
(6)
The intercepted flow consists of frontal flow entering the inlet parallel to the gutter, as well as
flow entering from the side of the inlet. For small, rectangular inlets, side flow is assumed to be
small. The ratio of side flow intercepted to total side flow, Rs, is defined by the following
equation:
(7)
Because the side flow is small compared to the total flow, the inclusion of side flow is left to the
discretion of the designer. Equation (8) describes the ratio of frontal flow to total gutter flow, Eo
(Johnson and Chang, 1984):
(8)
The fraction of frontal flow that actually enters the inlet can be expressed as (Johnson and
Chang, 1984):
(9)
Equation (5) can be used to determine gutter velocity, V. Splashover velocity, Vo, is dependent
on the type of grate used. The more efficient the grate, the higher the gutter velocity can be
before splashover (passing over the inlet instead of falling into the inlet) occurs. The efficiency
of a grate inlet depends on the amount of water flowing over the grate, the size and
configuration of the grate, and the velocity of flow in the gutter. The empirical relationship
between Vo and Rf for various types of grates is presented in HEC-12 (Johnson and Chang,
1984) and is also provided as Chart 10 in Appendix C. In addition, manufacturers' literature will
often contain information concerning capture efficiency for particular grate designs.
The interception capacity of grate inlets on grade is dependent upon the grate geometry and
characteristics of the gutter flow. A considerable portion of water may pass over the top of a
drain covered by an improperly designed grate. Flowing water follows a parabola as it leaves
the square lip of a grate opening. If the velocity is high, inlets must be fairly long for water to
drop into the box; otherwise, much of it may splash over the opening. Generally, the steeper
the slope, the longer the openings needed.
The grate geometries with flow directing vanes have inlet efficiencies that are dependent on
direction of flow; in other words, it is conceivable that such a grate could be placed 180 degrees
out of proper alignment. Such an improperly placed grate would have reduced interception
capacity and may be more prone to clogging. Manufacturers should be encouraged to provide
guide keyways to avoid misplacement, and maintenance workers should be instructed as to
proper placement to avoid this mishap.
Rather long curb openings and slotted inlets are required to achieve reasonable interception
capacity. Depressed gutters increase the capacity of inlets. However, depressed gutters or long
openings are not attractive features for bridge decks. Some commercial inlet devices have
small grates combined with side openings; these devices have performance characteristics
described by manufacturers.
The grates1 having empirical frontal flow interception fractions are parallel bar, modified parallel
bar, and reticuline. For hydraulic efficiency, parallel bars are best. They are also less subject to
clogging. However, parallel bars must have clear openings between bars of less than 1 inch to
be bicycle-safe. Non-bicycle-safe parallel bar grates are quite satisfactory on limited access
highway facilities where bicycle use is prohibited. Parallel bar grates have been modified with
transverse vanes or bars to support bicycles. Tilted vanes or bars are better than non-tilted;
curved vanes are better than tilted. Vanes reduce efficiency in comparison to parallel bars.
Reticuline grates have the least hydraulic efficiency but are quite safe for bicycles.
Inlets in sag vertical curves operate as weirs up to depths dependent on grate size and
configuration and as orifices at greater depths. Generally, inlets in sags operate as weirs up to
a depth of 0.4 feet and operate as orifices when depth exceeds 1.4 feet. Between weirs and
orifice flow depths, a transition from weir to orifice flow occurs. The perimeter and clear opening
area of the grate and the depth of water at the curb affect inlet capacity. From a hydraulic
standpoint, a sag located on a bridge deck is very undesirable. If debris collects on a grate, it
can reduce the effective perimeter or clear opening area and generate a standing pond.
At low velocities, a grate inlet will intercept all of the water flowing in the section of gutter
occupied by the grate. This is called frontal flow. A grate inlet will intercept a small portion of the
flow from the triangular wedge of flow on the bridge deck along the length of the grate. This is
called side flow. Bridge deck grates are normally small in comparison to those used for
pavement drainage. The short lengths minimize side flow, which is taken to be negligible in this
manual. Water splashes over the grates on steeper slopes. At slopes steeper than 2 percent,
splashover occurs on reticuline grates and the interception capacity is reduced. At a slope of 6
percent, velocities are such that splashover occurs on all grates except parallel bar and curved
vane grates. On relatively mild slopes, the various grates perform equally.
Theoretical inlet interception capacity and efficiency neglects the effects of debris and clogging
on the various inlets. All types of inlets are subject to clogging, some being much more
susceptible than others. Attempts to simulate clogging in the laboratory have not been very
successful except to demonstrate the importance of parallel bar spacing in debris handling
efficiency. Grates with wider spacings of longitudinal bars pass debris more efficiently.
Problems with clogging are largely local since the amount of debris varies significantly from one
area to another. Some localities must contend with only a small amount of debris while others
experience extensive clogging of drainage inlets. Partial clogging of inlets on grade rarely
causes major problems. Thus, localities need not make allowances for reduction in inlet
interception capacity unless local experience indicates such an allowance is advisable.
Where significant sag vertical curve ponding can occur, it is sound practice to place
flanking inlets on each side of the inlet at the low point in the sag. The flanking inlets
should be placed so that they will limit spread on low gradient approaches to the
level point and act in relief of the inlet at the low point if it should become clogged or
the design storm is exceeded. Use of clogging factors may be appropriate for sag
inlets. It should be noted that sag vertical curves on bridges are poor engineering
practice from a hydraulic standpoint and should be strongly discouraged.
Go to Chapter 6
Chapter 6 : HEC 21
Underdeck Collection and Discharge System
Go to Chapter 7
Runoff leaves the inlet box, enters the outlet pipe, and is conveyed by pipes. Steel tubing,
cast-iron pipe and plastic pipe are all used for the piping. Bridge drainage pipes are generally
large to facilitate maintenance. The inlet conditions generally control the flow capacity. Thus,
the hydraulic characteristics of the pipe system below the inlet seldom controls the flow. Design
is more often governed by maintenance needs and structural and aesthetic considerations.
It is most desirable to convey water straight down from the inlet box. When it is
necessary to curve the pipe, the cleanout opening leading to the next straight run
should be reachable without special equipment from under the bridge. These
criteria represent ideal conditions that are not always attainable. Bends often must
be placed in difficult locations, and cleanouts are not always easily accessible.
However, attaining the most convenient arrangement is worth considerable study
and effort because cleanouts that are inaccessible or difficult to reach simply will not
be cleaned.
Cleanouts should be located according to probable cleaning methods. Access holes
should be provided at the bottom end of a system for pressure backflushing. A
tee-joint will not be satisfactory for pressure backflushing unless there is also
provision for blocking the outlet leg to the discharge point. An open hole into a catch
basin provides the best backflushing access. Where manual flushing systems are
provided, the valves should be easily accessible without hazard from passing traffic.
It may be possible to run a long plumber's auger through to clean it. Cleanouts
should be located so as not to provide a blind alley for the auger (Figure 9).
6.4.1 Capacity
Since the slope of the downdrain is steep, its capacity will be limited by the inlet of
the pipe, which, in turn, may be limited by the capture efficiency of the grating. The
pipe opening will operate as a weir or as an orifice, depending on the depth of water
in the inlet box. Assuming the inlet box is full of water, then the capacity is:
(10)
For a 6-inch opening with Ax = 0.20 ft2 and x between 0.5 and 1.0 feet, the resulting
capacity, qx, is between 0.67 and 0.95 ft3/s, which exceeds the flow passed by a
grate of typical efficiency. Therefore, it is reasonable to expect that the inlet capture
flow is less than the flow that the collection piping system can handle.
Figure 8. A desirable bent downspout.
Figure 9. Blind alley cleanout.
Go to Chapter 7
Chapter 7 : HEC 21
Bridge End Collectors
Go to Chapter 8
Bridge end drainage inlets intercept gutter flow before it gets onto the bridge and remove gutter
flow that leaves a bridge. They are designed using the principles contained in HEC-12
(Johnson and Chang, 1984). The inlets are sufficient to capture all the gutter flow and can be
grate inlets, curb-opening inlets, slotted inlets, or combination inlets. Curb openings or
slotted-drain inlets are not usually effective unless extra cross slope is available.
(11)
(12)
where:
C = Runoff coefficient representative of drainage areas contributing to the inlet,
which will be less than 0.9 if drainage is from road sides, grassed medians,
areas beyond the right-of-way, etc.
i = Rainfall intensity for selected frequency and time of concentration, which is
calculated for the appropriate drainage areas, in/hr.
A = Contributing drainage area, acres.
3. Curbing transitions from the gutter on the bridge to the pavement gutter on the approach
are required.
2. Exit velocities from pipes and ditches that traverse large differences in elevation are high
and reflect the conversion of high potential to kinetic energy. These velocities need to be
dissipated to avoid erosive damage to the toe of the embankment. Information on the
design of energy dissipaters can be found in HEC-14 (FHWA, 1983).
3. Properly designed outlet works will minimize traffic obstacles within the right-of-way. Load
bearing grates are necessary if traffic can traverse inlets. This depends upon the
presence or absence of guardrails, the side slope of the embankment, and the distance of
the structure from traffic lanes.
4. The inlet structures are supported by the embankment. Even though compaction
specifications for embankments would assure sound footing, lighter structures provide
less chance of settlement. They can be lightened by using lesser thicknesses, minimum
vertical drops or lightweight concrete, and also can be placed so as to avoid traffic loads.
Go to Chapter 8
Chapter 8 : HEC 21
Design Procedures
Go to Chapter 9
This chapter presents procedures for designing the drainage systems for constant-slope and flat bridges. Drainage
design procedures for the more complex vertical-curve bridges are presented in Appendix A. This chapter includes
information needed before initiating design, guidance for selecting the design rainfall intensity, and design nomographs.
Discussion of drainage system details and design of bridge end collectors is also included, as is a design checklist.
Examples illustrating the constant-slope and flat-bridge procedures are presented in Chapter 10.
4b. Compute the gutter flow time of concentration, tg, using Equation (3).
4c. Compute the total trial time of concentration, tc = to + tg; note that for a flat (0% slope) bridge,
tc = 5 minutes is used for all deck drainage.
5. Use the IDF curve and the trial tc to estimate a trial i. Check the initial and final trial tc values. If
equal, stop. If not, return to step 3 and make more trials.
8.2.2 Hydroplaning
The prevention of hydroplaning is based on pavement and geometric design criteria for minimizing
hydroplaning. An empirical equation for the vehicle speed that initiates hydroplaning is (Gallaway, et al.,
1979):
(13)
where:
AT, a Texas Transportation Institute empirical curve fitting relationship, is the greater of:
(14)
where:
V = Vehicle speed, mi/h.
TD = Tire tread depth (1/32 in).
TXD = Pavement texture depth, in.
d = Water film depth, in.
Pt = Tire pressure, psi.
SD = Spindown (percent); hydroplaning is assumed to begin at 10 percent spindown. This occurs
when the tire rolls 1.1 times the circumference to achieve a forward progress distance equal
to one circumference.
Inversion of equation (13) and equation (14) determines a film depth, d, associated with selected values for
V, TD, TXD, Pt, and with SD = 10 percent (Young, et al., 1986). An estimate of design d for:
V = 55 mi/h.
TD = 7 (50 percentile level).
TXD = 0.038 in (mean pavement texture).
Pt = 27 psi (50 percentile level).
SD = 10 percent (by definition),
is d = 0.0735 in. This is suggested as a sound design value since it represents the combination of the mean
or median of all the above parameters. However, a designer could compute other values of d based on other
consid erations. For example, a designer could groove a deck, increase TXD and alter d to reflect changed
pavement design. Or, a designer could select d for higher vehicle speeds or for some other combination of
adjustments.
Once a design d is determined, it is assumed that the thickness of the water film on the pavement should be
less than d. Water flows in a sheet across the surface to the edge of the gutter flow. The width of sheet flow
is the width of the deck area, Wp, less the design spread T, or (Wp - T). At the edge of the gutter flow, the
design sheet flow depth is d.
Consider a 1-foot-long sheet flow path from the high point to the edge of the spread. The characteristics of
this flow path are:
depth: The depth varies from 0 at the high point to the design hydroplaning depth, d, at the edge
of the spread.
slope: The slope is the vector sum of the cross-slope, Sx, and the grade, S, or (Sx2 + S2)0.5.
(15)
width: The width is one foot.
design flow: Using the Rational Method, q = CiA, the sheet flow at the edge of the spread is:
(16)
(17)
By equating qR = qs at the edge of the design spread, a design rainfall can be derived as a function of the
design hydroplaning depth, d. Thus,
(18)
and solving for i, gives the hydroplaning design rainfall intensity, as:
(19)
This hydroplaning design rainfall is independent of the return period. Table 2 and Table 3 present
hydroplaning design rainfall intensities for vehicle speeds of 55 and 65 mi/h, respectively (Woo, 1988).
Table 2. Hydroplaning rainfall intensity, i (in/hr), for V = 55 mi/h (hydroplaning sheet flow depth d = 0.08
in)
n = 0.016
C = 0.9
TXD = 0.038 in
(Wp - T)
S Sx 24 36 48 58
0.01 0.01 3.7 2.5 1.9 1.5
0.02 5.9 4.0 3.0 2.5
0.04 8.7 5.8 4.4 3.6
0.06 10.8 7.2 5.4 4.5
0.08 12.5 8.3 6.2 5.1
0.02 0.01 3.0 2.0 1.5 1.2
0.02 5.3 3.5 2.6 2.2
0.04 8.4 5.6 4.2 3.5
0.06 10.6 7.1 5.3 4.4
0.08 12.3 8.2 6.2 5.1
0.04 0.01 2.2 1.5 1.1 0.9
0.02 4.2 2.8 2.1 1.7
0.04 7.5 5.0 3.7 3.1
0.06 9.9 6.6 5.0 4.1
0.08 11.8 7.9 5.9 4.9
0.06 0.01 1.8 1.2 0.9 0.7
0.02 3.5 2.4 1.8 1.5
0.04 6.6 4.4 3.3 2.7
0.06 9.1 6.1 4.6 3.8
0.08 11.2 7.5 5.6 4.6
0.08 0.01 1.6 1.0 0.8 0.7
0.02 3.1 2.1 1.5 1.3
0.04 5.9 4.0 3.0 2.5
0.06 8.4 5.6 4.2 3.5
0.08 10.5 7.0 5.3 4.4
Table 3. Hydroplaning rainfall intensity, i (in/hr), for V = 65 mi/h (hydroplaning sheet flow depth d =
0.047 in)
n = 0.016
C = 0.9
TXD = 0.038 in
S Sx (Wp - T)
24 36 48 58
0.01 0.01 1.5 1.0 0.8 0.6
0.02 2.4 1.6 1.2 1.0
0.04 3.5 2.4 1.8 1.5
0.06 4.4 2.9 2.2 1.8
0.08 5.0 3.4 2.5 2.1
0.02 0.01 1.2 0.8 0.6 0.5
0.02 2.1 1.4 1.1 0.9
0.04 3.4 2.3 1.7 1.4
0.06 4.3 2.9 2.1 1.8
0.08 5.0 3.3 2.5 2.1
0.04 0.01 0.9 0.6 0.4 0.4
0.02 1.7 1.1 0.8 0.7
0.04 3.0 2.0 1.5 1.2
0.06 4.0 2.7 2.0 1.7
0.08 4.8 3.2 2.4 2.0
0.06 0.01 0.7 0.5 0.4 0.3
0.02 1.4 1.0 0.7 0.6
0.04 2.7 1.8 1.3 1.1
0.06 3.7 2.5 1.8 1.5
0.08 4.5 3.0 2.3 1.9
0.08 0.01 0.6 0.4 0.3 0.3
0.02 1.2 0.8 0.6 0.5
0.04 2.4 1.6 1.2 1.0
0.06 3.4 2.3 1.7 1.4
0.08 4.3 2.8 2.1 1.8
8.2.3 Driver Visibility
The following empirical expression (Ivey, et al., 1975) relates rainfall intensity to driver visibility and vehicle
speed:
(20)
where:
Sv = Driver visibility, ft.
i = Rainfall intensity, in/hr.
V = Vehicle speed, mi/h.
This empirical relationship was developed based on test data with the following ranges: rainfall, less than 2
in/hr; visibility, 1,500 to 6,000 feet. This equation may overestimate driver visibility distance for rainfall
intensity greater than 2 in/hr--range with no available test data, but, a range of extremely low occurrence
probability. Velocities of less than 20 mi/h would have less validity (Ivey, et al., 1975). At 55 mi/h, the
nonpassing minimum stopping sight distance is 450 feet (this is the lower value of a range given by
AASHTO).
Substituting these values,
(21)
gives a rainfall intensity of 5.6 in/hr. The research supporting this estimate depicted a single car in rain on a
test track. Note that cars in a travel corridor generate splash and spray that increase water droplet density
over natural rainfall intensity. To compensate for splash and spray, a design intensity of 4 in/hr may be more
realistic as a threshold value that will cause sight impairment. That is, design intensities, i, above 4 in/hr will
probably obscure driver visibility in traffic and decrease sight distances to less than minimum
AASHTO-recommended stopping sight distances.
The discussion is qualified by:
● The warnings of the researchers (Ivey, et al., 1975). The predictive relationship is empirical.
● Splash and spray are recognized and allowed for, but more research is needed to refine relationships.
● Night driving in the rain is very vision dependent. Data supporting the predictive relationship were
secured in daylight.
Therefore, 4 to 5.6 in/hr is a suggested threshold design rain intensity range for the avoidance of driver vision
impairment. Rainfall intensities below this range should not obscure a driver's view through a windshield with
functioning windshield wipers.
The inlet capacity for the typical bridge deck drainage system is less than the above capacities. Therefore, collector size
is not a critical hydraulic decision so long as it is sloped sufficiently to clean out and avoid clogging. Pipe connections
should be Y-shaped rather than at right angles. Vertical downspout members should be at least 6 inches and should be
provided with Y-fittings to allow clean out with flexible snake cables, water under pressure, or compressed air.
When discharging at the surface under the bridge, splash blocks or energy dissipators are needed to control erosion,
unless discharging more than 25 feet from the ground.
2Trials are necessary because both timing Equation (2) and Equation (3) have the intensity as an independent variable.
Go to Chapter 9
Chapter 9 : HEC 21
Bridge Deck Drainage Method
Go to Chapter 10
Methods for determining inlet spacing for constant-slope and flat bridges are presented in this
chapter. More complex procedures for vertical curve bridges are presented in Appendix A. For
all cases, the Rational Method design approach is used. All charts referenced in this chapter
are contained in Appendix C.
3. Starting at the high end of the bridge, the inlet spacing can be computed using the inlet
spacing nomograph in Chart 5 or Equation (22a) and Equation (22b), the derivations of which
are given in Appendix B:
(22a)
or between inlets as,
(22b)
where:
i = Design rainfall intensity, in/hr, (step 1).
Q = Gutter flow, ft3/s, (step 2).
Lc = Constant distance between inlets, feet.
L0 = Distance to first inlet, feet.
C = Rational runoff coefficient.
Wp = Width of pavement contributing to gutter flow, feet.
E = Constant, which is equal to 1 for first inlets in all cases and is equal to capture
efficiency for subsequent inlets of constant-slope bridges.3
Since the first inlet receives virtually no bypass flow from upslope inlets, the
constant E can be assumed to be equal to 1. The computed distance, L0, is then
compared with the length of the bridge. If L0 is greater than the length of the bridge,
then inlets are not needed and only bridge end treatment design need be
considered.
4. If inlets are required, then the designer should proceed to calculate the constant inlet
spacing, Lc, for the subsequent inlets.
4a. Inlet interception efficiencies for particular inlets or scuppers can often be found in the
manufacturers' literature. If such information is not available, then Chart 6, Chart 7, Chart 8,
Chart 9, and Chart 10 can be used to estimate efficiency.
For circular scuppers, Chart 6 summarizes results from a laboratory study conducted at the
University of South Florida (Anderson, 1973). Efficiency curves are provided for grades of 0.2,
2.0, and 5 percent. To use the figure, calculate the ratio of inlet diameter, D, to gutter spread, T,
and enter the graph at the appropriate value along the x-axis. It should be noted that one cross
bar across the circular scupper did not significantly reduce efficiency for a diameter of 4 inches.
Upon intersection with the applicable curve (or appropriate interpolated curve), read efficiency,
E, from the y-axis.
For rectangular inlets, several steps are necessary to calculate flow interception efficiency, E,
which is the ratio of intercepted to total deck flow. Note that such grates in bridge decks need to
be consistent with reinforcing bar spacing. Additional structural details are needed to transfer
the load from the imbedded grate to the reinforced deck slab.
● Find the ratio of frontal flow bound by width of grate, W, to total deck flow, Eo, using Chart
7.
● Find the flow intercepted by the inlet as a percent of the frontal flow. Identify the grate
type using the information shown in Chart 8. The gutter velocity is needed and is provided
by Chart 9.
● Chart 10 is then used to determine the portion of the frontal flow (Rf, the total flow within a
grate width from the curb) that is intercepted by a grate. This will be less than 100 percent
when the gutter velocity exceeds the splashover velocity.
● The interception efficiency, E, is then computed as:
(23)
In using Equation (23), it is assumed that side flow interception is negligible. If the
designer wishes to consider side flow, HEC-12 (Johnson and Chang, 1984) should
be consulted.
● The flow intercepted by an inlet is:
For small rectangular inlets without grates, use Chart 7, Chart 8, and Chart 9 as above
assuming grate type A in Chart 8 and Chart 9. Should such inlets be depressed, use the
boundaries of the depression to define the inlet width (W) and inlet length (Lg).
For side slot scuppers, as in New Jersey Type Barrier, Figure 7 provides guidance on selection
of E. Curb inlet design charts are found in HEC-12 (Johnson and Chang, 1984).
5. Once efficiency, E, has been determined, Chart 5 is used to calculate the constant inlet
spacing Lc. It should be noted that Qf represents the full flow in the gutter for a corresponding
spread, T. Since bridge deck grade and time of concentration are assumed to be constant, the
spacing between inlets will be constant.
6. Continue to space inlets until the end of the bridge is reached. Once L0 and Lc have been
determined analytically, these values may need to be adapted to accommodate structural and
aesthetic constraints.
7. The final step is to design the bridge end treatments, which are recommended for all bridges,
whether they require bridge deck inlets or not.
8. Compare the design rainfall intensity with hydroplaning intensity and visibility criteria.
9.2 Flat Bridges
Chart 11 presents the logic diagram for computing inlet spacing for horizontal bridges. The
procedure is as follows:
1. The time of concentration (tc) to each inlet is assumed to be 5 minutes.
Frequency, design spread (T), pavement width (Wp), bridge length (LB), Manning's
n (n), rational runoff coefficient (C), and gutter cross-slope (Sx) are assumed to be
known. Using a time of concentration of 5 minutes and the selected frequency,
rainfall intensity is determined from the intensity-duration-frequency (IDF) curves.
2. Constant inlet spacing, Lc , can then be computed using the nomograph
presented in Chart 12 or Equation (24) the derivation of which is given in Appendix
B:
(24)
3. The computed spacing is then compared with the known bridge length. If Lc is
greater than the length of the bridge, then there is no need for inlets and the
designer need only be concerned with the design of bridge end treatments. If Lc is
less than the bridge length, then the total needed inlet perimeter (P) can be
computed using the nomograph in Chart 13 or Equation (25), which is based on
critical depth along the perimeter of the inlet (weir flow) as derived in Appendix B.
(25)
Go to Chapter 10
Chapter 10 : HEC 21
Illustrative Examples
Go to Appendix A
This chapter provides five examples of drainage designs for bridges having a constant grade or no
grade. Example 1 is typical of most bridges--no drainage inlets details are needed on the bridge itself.
Examples 2 and 3 are different bridges that need inlets on the deck. Examples 4 and 5 are flat bridges;
this situation occurs for causeways across marshes, swamps, tidewaters, and for flat land bridges,
typically near the oceans. An example for drainage for a more complicated vertical curve bridge is given
in Appendix A.
The pavement width, Wp, is the width of the bridge from the centerline crown to the gutter
edge.
Inlets, if provided, will be 1 foot wide (W = 1), 1.5 feet long (Lg = 1.5), and will have
bicycle-safe, curved vane grates. The bridge has waterproof expansion joint. All upslope
pavement drainage is intercepted by bridge end collector.
Find: Inlet spacing, Lo, Lc.
Solution: Use Chart 1, Chart 2, Chart 3, Chart 4, and Chart 5 in Appendix C and IDF curve for
Charlotte, North Carolina, shown in Figure 15.
Step 1. Compute intensity, i, for time of concentration, tc, to first inlet. Use IDF curve and Chart 2
and Chart 3 in the iterative procedure.
a) Select a trial value for tc of 5 minutes and verify this assumption.
Figure 15. Intensity-Duration-Frequency curves for Charlotte, North Carolina.
b) From the IDF curve (Figure 15), the intensity, i, for a 10-year storm of 5 minutes in
duration is 7.3 in/hr.
c) Compute the overland flow time of concentration using Chart 2 or Equation (2).
d) Compute gutter flow time of concentration using Chart 3 or Equation (3). Since the
upslope bridge end inlet intercepted all approach flow, E = 1.
e) Compute total tc and compare with selected trial value.
f) Since the trial value of 5 minutes and the computed value of 8.86 minutes are not equal,
select another trial tc value of 11 minutes and repeat steps (c) through (e). The intensity at
this duration, from Figure 15, is 6.0 in/hr.
g) The computed time of concentration for the second trial duration is 10.7 minutes, which is
approximately equal to 11 minutes. Therefore, use i = 6.0 in/hr as the design intensity.
Step 2. Compute full gutter flow based on the design spread of 10 feet. Use Chart 4 or Equation (4).
Step 3. Starting at the upslope end of the bridge, compute the distance to the first inlet, Lo, using
Chart 5 with E = 1 or Equation (22a).
Since Lo is greater than the total bridge length (500 ft), drainage inlets are not
required.
Step 4. Design bridge end treatments. With no bridge deck inlets, all bridge deck runoff passes to an
inlet off the bridge.
a) If the curb line and cross slope are extended beyond the bridge, the inlet would be
located 1,837 feet from the high end of the bridge. The inlet would need to accept the
following flow:
b) If the bridge end transitioned to a situation where the deck drainage needed to be
removed from the roadway (like an embankment with shoulders without curb and gutter),
the time of concentration would be reduced to approximately:
by linear interpolation of the bridge length to the length of required inlet calculated above.
This is less than the lower IDF curve values--therefore, use 5 minutes, which gives an
intensity of 7.3 in/hr (see step 1 above). The bridge end treatment would have to handle:
The pavement width, Wp, is the width of the bridge from the centerline crown to the gutter
edge.
Inlets will be 1 feet wide (W=1), 1.5 feet long (Lg=1.5), and will have bicycle-safe, curved
vane grates. The bridge has waterproof expansion joint. All upslope pavement drainage is
intercepted by bridge end collector.
Find: Inlet spacing, Lo, Lc.
Solution: Use Chart 1, Chart 2, Chart 3, Chart 4, and Chart 5 in Appendix C and IDF curve for
Charlotte, North Carolina, shown in Figure 15.
Step 1. Compute intensity, i, for time of concentration, tc , to first inlet. Use IDF for Charlotte, N.C.,
and Chart 2 and Chart 3 in iterative procedure.
a) Select trial value for tc of 5 minutes and verify this assumption.
b) The i for duration of 5 minutes and 10-year storm is 7.3 in/hr from IDF curve.
c) Compute overland flow time of concentration using Chart 2 or Equation (2).
d) Compute gutter flow time of concentration using Chart 3 or Equation (3). Since the
upslope bridge end inlet intercepted all approach flow, E = 1.
f) Since trial value and computed value are approximately equal, use i = 7.3 in/hr as design
intensity.4
Step 2. Compute full gutter flow based on the design spread of 10 feet. Use Chart 4 or Equation (4).
Step 3. Starting at the upslope end of the bridge, compute the distance to the first inlet, Lo, using
Chart 5 with E = 1 or Equation (22a).
Step 4. Since Lo is less than the total bridge length, inlets are needed. Determine the inlet efficiency,
E.
a) Using Chart 7 or Equation (7), compute the frontal flow ratio, Eo.
Step 5. Compute constant spacing between the remainder of the inlets using Chart 5 or Equation
(22b).
Step 6. Adapt spacing to structural constraints. For example, if the bent spacing is 100 ft, use Lo =
400 feet and Lc = 100 feet, rather than 468 and 115 feet. Thus, as illustrated in Figure 17, the number
of inlets per side is (2000 - 400)/100 = 16.
Figure 17. Inlet spacing for example 1.
Step 7. Design bridge end treatments. Two approaches to design flow, Q, estimation are provided
here for guidance to designers. The approaches present calculations for 0 percent and 50 percent
blockage of the inlets on the bridge.
a. 0 percent blockage--assume all the inlets on the bridge are 100 percent functional; the
flow at the bridge end will be the full gutter flow at 10 feet spread, Q = 2.4 ft3/s.
b. 50 percent blockage--This represents a design approach for settings where debris is a
factor. Accept half the runoff from the bridge deck; note that it is necessary to recalculate
the time of concentration. The overland flow time is 0.98 minutes and is calculated in step
1(c), above.
For a first trial, assume tc = 10 minutes (i = 6.1 in/hr) and the bridge end spread, T = 12.5
feet, then using Equation (3) or Chart 3,
For a second trial, adjust the intensity and check the spread. Figure 15 indicates the
10-year bridge end design intensity for a 9-minute duration to be 6.3 in/hr. This intensity will
generate a design flow of
where the first term represents Equation (1), and the second term represents a deduction
representing 50 percent blockage of an unobstructed capture efficiency, E, of 24.5 percent
for 16 gutters operating at a 10-foot spread. The deduction is slightly conservative because
the inlet spread is not a constant 10 feet but varies as the bypass builds up. As a check, this
flow of 4.15 ft3/s develops a spread of T = 12.35 feet using Equation (4) or Chart 4,
indicating a good first guess of 12.5 feet.
Using this approach, the design flow is estimated to be 4.15 ft3/s, and assumes all inlets are
50 percent clogged. At this flow, the bridge end spread is 12.35 feet.
The spread at the first inlet associated with the bridge end intensity of 6.3 in/hr, gives a full
gutter flow of 2.07 ft3/s having a spread of 9.5 feet. Thus, the spread on the bridge at the
inlets is between about 9.5 feet and 12.35 feet.
Commentary: Select a bridge end design flow using one or a variation of the above
approaches. Approach "a," assuming 0 percent blockage, produces a design flow of 2.4
ft3/s. Approach "b," assuming 50 percent blockage, produces a design flow of 4.15 ft3/s.
Select an inlet scheme for the selected design flow using HEC-12 (Johnson and Chang,
1984) and provide a pipe or paved ditch to convey the design flow to the toe of the
embankment. Provide energy dissipation, if necessary, at the toe to achieve nonerosive
velocities. Use similar considerations to design upslope bridge end collectors.
Solution: Use Chart 1, Chart 2, Chart 3, Chart 4, and Chart 5 in Appendix C and IDF curve for
Charlotte, North Carolina, shown in Figure 15.
Step 4. E = 0.245.
Step 6. Adapt the spacing to structural constraints. For example, if the bent spacing is 100 feet, use
Lo = 800 feet and Lc = 200 feet. (The 196 theoretic value is judged close enough to 200 (2 percent
lower) to accept 200 as the practical spacing.) Thus, the number of inlets per side (1200-800)/200=2.
Step 7. Design bridge end treatments. Example 2 discusses procedures for bridge end collection of
drainage. The high end gutters should be clear of flow prior to the bridge and the flow at the low end of
the bridge should be removed with an inlet off the bridge.
The comparison of constant grade examples 1, 2, and 3 follows.
Number
Lo Lc of
Width Distance to first inlet Distance between inlets inlets
Example 1 18 ft N/A N/A 0
500 ft
3% grade
Example 2 34 ft 400 100 16
2000 ft
1% grade
Example 3 34 ft 800 200 2
1200 ft
3% grade
10.4 Example 4--4,000-Foot Long, 68-Foot-Wide Flat
Bridge
Where: Pavement width, Wp, is the width of the bridge from the centerline crown to the gutter edge.
Solution: Use Chart 11, Chart 12, and Chart 13 in Appendix C and IDF curve for Charlotte, North
Carolina (Figure 15).
Step 1. Compute intensity for time of concentration of 5 minutes. From the 10-year IDF curve for
Charlotte, N.C., the design intensity is 7.3 in/hr.
Since L < 4,000 feet (the length of the bridge), inlets are needed.
Step 6. Compare design intensity with hydroplaning and driver vision criteria. For a design
hydroplaning depth, d, of 0.0067 feet (0.08 inches) and vehicle speed of 55 mi/h, the design rainfall
intensity using Equation (18) is:
The threshold for driver vision impairment is estimated as 4 in/hr. The discussion contained
in step 8, example 1, applies here as well.
Figure 19. Scupper spacing for example 4.
Solution: Use Charts 11 through 13 in Appendix C and IDF curve for Charlotte, North Carolina (Figure
15).
Step 4. Adapt spacing to structural constraints. If one adapts to a spacing of 400 feet, then only one
scupper per side would be necessary. A bridge end collector will be placed at the bridge end to remove
runoff from the remaining 400 feet of deck.
Step 6. Compare design intensity with hydroplaning and driver vision criteria. From Equation (18), i
= 18.66 in/hr. The discussion contained in step 8, example 2, applies here as well.
4Lesser grades would have higher flow times and lesser intensities and additional trials would be
necessary as in example 1
Go to Appendix A
Appendix A : HEC 21
Vertical Curve Bridges
Go to Appendix B
The objective of this appendix is to facilitate inlet spacing design for the more complex case of bridges
within vertical curves. Constant-slope and flat bridges are discussed in Chapter 9 and Chapter 10.
(2)
(3)
(4)
5. Inlet Spacing. Equation (22a) and equation(22b)* are the equations for the spacing of
an initial inlet and subsequent inlets on a vertical curve bridge, respectively. The efficiency,
E, is replaced by the interception coefficient, K, for vertical-curve bridges:
(22a)
(22b)
(26)
7. Inlet Efficiency, E.
a) The frontal flow ratio, Eo, is computed with Equation (8)*,
(8)
(5)
(27)
where:
LB = length of bridge, and
g1,g2 = slopes of the tangents of the vertical curve.
Design intensity is determined for the first inlet from the location's IDF curves by iteratively selecting a
trial time of concentration, computing overland and gutter times of concentration, and comparing trial
and computed values.
Starting at the high point of the bridge, the designer works down the grade of the long end of the
bridge. A trial distance to the first inlet, L0, is selected and the grade (S) at this distance is determined
using Equation (27). Gutter flow, Q, for grade S is computed. The intensity and gutter flow are then
used to compute the distance to the first inlet using Equation (22a).
If the computed distance, L0, does not match the trial value, then the computations are repeated until
agreement is achieved. If the slope at the selected distance is less than 0.003, then the nomograph for
flat bridges (Chart 12) shouldbe used as a check. If the distance to the first inlet is greater than the
distance to the end of the bridge, then bridge deck drainage facilities are unnecessary. Many bridges
will fall into this category and will need no bridge deck drainage.
However, if inlets are needed, the design intensity computed for the first inlet is used throughout the
remainder of the analysis. To compute the distance from the first inlet to its nearest downslope
neighbor, a trial spacing value, of about half the first distance, is selected and grade, S, computed.
Gutter flow is recomputed. The interception coefficient, K, is determined from the nomograph in Chart
15 or from Equation (26). Equation (26), as it is applied, results in variable spacing between inlets.
Inlet spacing Li is computed from Equation (22b) or Chart 5 and compared with the trial value selected.
If necessary, the computations are repeated until agreement is achieved. If the slope is sufficiently
small, the segment is treated as flat.
A.3 Bridge Deck Drainage Vertical Curve Drainage
Design Method
The design procedure for a vertical curve bridge is as follows:
1. Compute the lengths of the short and long ends of the bridge, LE1 and LE2, respectively,
by solving Equation (27) with S = 0 for x; the solution provides the distance from the left
edge to the high point (LE1).
2. Determine the rainfall intensity based on the computed time of concentration to the first
inlet.
a. Select trial time of concentration and determine rainfall intensity from the IDF
curve.
b. Compute overland travel time, to, using Equation (2) or Chart 2.
6. Determine spacing to the next inlet on the long end of the bridge.
a. Select a trial L1.
d. Compute inlet efficiency, E, using Chart 6 or Chart 7, Chart 9, and Chart 10.
e. Compute the interception coefficient, K, (K is less than 1 for the inlets
following the first) using Equation (26) or Chart 15.
f. Compute inlet spacing, L1, using Equation (22b) or Chart 5 (substitute K for E
and L1 for Lc on the nomograph), and compare to the trial L1 in Step 6a. If the
computed L1 does not equal the trial L1 value, repeat step 6.
7. Repeat step 6 for the next inlet. Inlet spacings are determined one at a time until the sum
of the inlet spacings exceeds the length of the long side of the bridge. The short side
spacings (starting from the high point and working down) will be the same as the those
determined for the long side (until, of course, the length of the short side is exceeded). That
is to say, the spacing of the vertical curve deck inlets are symmetrical with respect to the
high point of the bridge.
8. Adapt spacing of inlets to accommodate structural constraints.
9. Design bridge end treatments. See step 7, example 1, Chapter 10.
10. Compare design rainfall intensity with hydroplaning and driver vision criteria.
Since the grades near the high point are low, relatively long spacings may be computed for the crown
of the bridge arch. Subsequent spacings are shorter since downslope inlets must capture overflow
from upslope inlets. Inlet spacings should be adjusted according to structural constraints, as
necessary. Analysis ends after design of bridge end treatments.
Inlets will be 1 foot wide (W = 1), 1.5 feet long (Lg = 1.5), and will have bicycle-safe, curved vane
grates.
Find: Inlet spacing, L0, L1, L2, L3, etc.
Solution: Use Chart 15, as well as Chart 2, Chart 3, Chart 4, and Chart 5. Use 10-year IDF curve for
Charlotte, North Carolina, shown in Figure 16.
Step 2. Compute intensity for time of concentration to first inlet. Use IDF curve (such as Figure 15).
a) Select trial time of concentration of 5 minutes. Using IDF curve for Charlotte, North
Carolina (10-year storm), i = 7.3 in/hr.
b) Compute to.
c) Compute tg.
d) Compute tc.
Since trial value and computed value are approximately equal, use 7.3 in/hr as
the design intensity.
Step 3. Select a trial value for the distance from the bridge high point to the first inlet (working down
the long side of the bridge) and compute the local slope.
a) Select L0 = 300 ft (1st trial).
Step 4. Compute full gutter flow, Qf, at design spread (10 ft).
Step 5. Compute distance to first inlet, L0, (K = 1 for first inlet).
Use L0 = 300 ft. Inlets are needed since L0 is less than the length of the long
side of the bridge.
Repeat Step 6. Since computed value for L1 does not equal trial value, select a new trial value for L1
and repeat Step 6.
a) Select L1 = 150 ft (2nd trial).
The slope at the long end is S = 0.0198 and the full gutter flow is:
The off-bridge end collectors should be sized to handle 2.26 ft3/s on the short end and 3.35
ft3/s on the long end. This procedure uses no blockage on the bridge as a basis. For 50
percent blockage, the previous example 2 (see Section 10.2) indicates the bridge end flows
will be about twice as large.
Step 10. Compare design rainfall intensity with hydroplaning and driver vision criteria. Using
Equation (19), a different design rainfall intensity must be computed for each inlet because of the
varying longitudinal gutter slope, S, of a vertical curve bridge. For a hydroplaning sheet flow depth, d =
0.08 inches, the first inlet would have a design rainfall intensity, i:
Similarly, the design rainfall intensities for all the vertical curve bridge segments
(for vehicle speed, V = 55 mi/h and hydroplaning sheet flow depth, d = 0.08
inches) are as follows:
Inlet No. Slope, S Design rainfall
intensity, i (in/hr)
0 0.0045 6.09
1 0.0068 6.00
2 0.0090 5.89
3 0.0115 5.74
4 0.0141 5.58
5 0.0169 5.39
6 0.0198 5.20
As mentioned previously, the threshold intensity for causing sight impairment is estimated
as 4 in/hr, for a vehicle speed, V = 55 mi/h (See Chapter 8).
Go to Appendix B
Appendix B : HEC 21
Derivation of Equations
Go to Appendix C
This Appendix derives the new technology developed for HEC 21 and provides commentary.
(3)
1) Determine Qx, gutter flow at a given point x as a function of Qp, the flow running off
the pavement between the high point and the inlet.
2) Determine Vx, gutter velocity at point x, using:
a) continuity to relate velocity to Qx, and
(28)
where:
(29)
(30)
(31)
= 0.5 Sx Tx2.
Thus,
(32)
(33)
Rearranging Equation (33), Tx2 can be written:
(34)
or by collecting terms
(35)
(36)
Step 3. Integrate Equation (36) to obtain the total gutter flow time.
a) By substituting Equation (35) into (36), dt can be expressed as:
(37)
Let:
(38)
and:
(39)
(40)
(41)
Note that
(42)
(43)
Step 4. The integral equation to obtain total gutter flow time, tg, is:
(44)
(45)
or collecting terms,
(46)
Substitute for M and m using Equation (38) and Equation (39) and
rearranging Equation (46) gives
(47)
(22a)
(4)
Substitute Equation (4) into Equation (22a) and then substitute into Equation
(47) to yield the following relationship:
(48)
Converting tg to minutes:
(49)
Equation (44) assumes no spillover and represents the time of concentration to the first inlet. The
above derivation assumes that the longitudinal slope is constant. For vertical curve bridges, this
assumption is approximately true for the time of concentration to the first inlet, tg. It is interesting to
note that the gutter flow time does not explicitly consider the length or slope of the gutter.
(50)
where the first term is pavement runoff between the upper and lower inlets,
the second term is the bypass flow from the upper inlet, and E is the
interception efficiency (0 < E < 1).
(b) Rearranging Equation (50):
(51)
(4)
(53)
(54)
(22b)
where: S is the local slope at the ith inlet, and Su is the local slope at the i-1
inlet; if S = Su, then Li = Lc.
Commentary: For Equation (26), when E = 1, (the first inlet or a 100 percent
efficient inlet):
and, when Su = S (constant-sloped bridges),
The nomograph, presented in Chart 5, depicts the solution to Equation (22b), with Li labeled as Lc,
to accommodate the most frequent use of this chart--for constant sloped bridges. Annotations on
Chart 5 are provided to extend its utility to the vertical curve case in conjunction with Chart 15.
(24)
(55)
(56)
(58)
(59)
b) Since the longitudinal slope is zero, the friction slope is taken to be the slope of the
water surface,
(60)
Thus,6
(61)
c) Let:
(62)
(63)
(65)
(66)
where: h = water depth at curb for the design water spread, T (x = 0); and,
hc = water depth at inlet, usually a critical depth, (x = L/2), to yield,
(67)
(69)
(70)
(24)
Commentary: The flat bridge case has no precedent in past design practice.
However, it is present in long causeways and bridges are nearly flat at high or
low point stations within vertical curves. If the tangent slopes are relatively
mild, the nearly flat deck can be significant. This appendix and Chart 11
provides rational inlet spacing methods for what is thought to be a situation
that does exist with some, but not very high, regularity. A one-dimensional
analysis in the direction of flow, used herein, has simplified the
two-dimensional flow net.
At the selected spacing, Lc, the flow that the scuppers or inlets must remove
is equal to
where i is selected for 5 minute duration using the design return period.
Assuming critical depth around the perimeter of inlets flowing as weirs,
generates the perimeter selection method depicted in Chart 13.
(71)
where P = the required perimeter length at every spacing station where inlets
are needed.
Let dc be the critical depth at the inlet lip, which is assumed to function as a
weir. Then
(72)
where, A is the flow area normal to the weir lip. Also, the critical depth at the
edge of curb is 2/3 of the depth of spread, or
(73)
(74)
Noting that,
(75)
(22a)
(76)
(77)
(24)
6In subsequent manipulations, square both sides of Equation (61) to eliminate square root.
Go to Appendix C
Appendix C : HEC 21
Design Charts - Bridge Drainage
Go to Appendix D
The designer will need these charts, specific information about the bridge, and an IDF curve.
The IDF curve can be obtained from HYDRO in the HYDRAIN software using the latitude and
longitude coordinates of the site.
CHART NUMBER
1. Logic for computing inlet spacing for a constant-grade bridge.
8. Typical grates.
Go to Appendix D
Appendix D : HEC 21
Selected Glossary
Go to Table of Contents
Breakdown Lanes Lanes on a bridge that correspond to shoulders and that are
used to temporarily locate disabled vehicles; normally 8- to
10-feet wide. These lanes serve a dual purpose as gutters to
convey drainage.
Bypass Flow Flow that bypasses an inlet on grade and is carried in the
gutter to the next inlet downgrade.
Cleanout Plug A removable plug in the piping system that gives access to a
run of piping for cleaning. It is typically located near bends and
Y-shaped intersections.
Drain A receptacle that receives and conveys water.
Drainage System The entire arrangement of gutters, ditches, grates, inlet boxes,
pipes, outfalls, and energy dissipators necessary to collect
water and get it to a disposal point.
Drop Inlet A drain that is used away from a bridge or at bridge ends. It is
usually larger than an inlet chamber and is set in earth in the
subgrade or shoulder of an approach embankment.
Flanking Inlets Inlets placed upstream and on either side of an inlet at the low
point in a sag vertical curve. The purposes of these inlets are
to intercept debris as the slope decreases and to act in relief
of the inlet at the low point.
Frequency The probability that an annual flood can be expected to occur
on the average over a long period of years. The reciprocal of
this frequency is the return period. For example, a flood of
frequency 0.1 or 10 percent has a return period of 1/0.1 = 10
years.
Frontal Flow The portion of flow that passes over the upstream side of a
grate.
Grate The ribbed or perforated cover of an inlet chamber that admits
water and supports traffic loads; current practice is to make
grates that are safe for cyclists.
Gutter That portion of the edge of the bridge deck that is utilized to
convey storm runoff water next to the curb. It may include a
portion of all of a traveled lane, shoulder or parking lane, and
a limited width adjacent to the curb may be of different
materials and have a different cross slope.
Hydroplaning The separation of the automobile tire from the road surface by
a layer of fluid.
Inlet Chamber A typically cast-iron, welded steel, or formed concrete
compartment that is beneath an inlet. It is usually set into the
bridge deck, but is sometimes only an open hole in the deck.
Inlet Efficiency (E) The ratio of flow intercepted by an inlet to total flow in the
gutter.
Outlet Pipe The pipe that leads the water away from an inlet chamber or
drop inlet.
Rainfall Intensity The average rate of rainfall for a selected time interval
measured in inches per hour.
Runoff (Q) Any liquid that can run off the roadway surface. Although the
liquid is generally water, it includes any other liquids and
dissolved solids that can make their way into the drainage
system.
Scupper A small opening (usually vertical) in the deck, curb, or barrier
through which water can flow. The term is nautical and by
analogy relates bridge deck drains to openings in the sides of
ships at deck level to allow water to run out.
Splash-Over Portion of the frontal flow at a grate that skips or splashes
over the grate and is not intercepted.
Spread (T) The top width of the water flowing in the gutter. This measures
the distance the runoff water encroaches into the breakdown
lane. If the spread is wider than the breakdown lane, it
encroaches into travel lanes.
Storm Drain An underground piping system that may connect to a
municipal storm water management system or may be a
separate disposal system for highway and bridge drainage.
Time of Concentration (tc) The time it takes for water to travel from the most remote point
in the surface drainage to the inlet. Typically, the travel path is
from the high point on the bridge deck to the first inlet and
includes sheet flow path to the gutter and then the gutter flow
path.
Travel Lane Portion of the traveled way for the movement of a single lane
of vehicles, normally 12 feet.
Go to Table of Contents
Chapter 1 : HEC 21
Introduction
Go to Chapter 2
The objective of this manual is to support sound, economic, and low maintenance design for
bridge deck and bridge end drainage facilities. For the designer of bridge drainage systems,
water and its removal is a many-faceted problem. Water may collect in pools or run in sheets;
its presence can slow traffic and cause hydroplaning. Water may freeze or fall as ice or snow,
making roadways slick and plugging drains. In addition to its ability to disrupt the main traffic
function of the bridge, rain may also pick up corrosive contaminants, which, if allowed to come
into contact with structural members, may cause deterioration. Uncontrolled water from bridge
decks can cause serious erosion of embankment slopes and even settlement of pavement
slabs. The rain that falls on a structure may cause stains and discoloration on exposed faces if
it is not collected and disposed of properly.
Poor bridge deck drainage is rarely a direct cause of structural failure and thus, bridge
designers often view drainage as a detail. Nevertheless, proper design provides benefits
related to traffic safety, maintenance, structural integrity, and aesthetics. Furthermore, in light of
the movement to control urban stormwater pollution, the potential to improve water quality
using off-bridge detention facilities to settle out solid particles in the drainage is sometimes
considered.
The detrimental effects of runoff emphasize the importance of getting water off the bridge deck
as soon as possible. This points up the need for an efficient drainage system that is always in
good working order. Proper designs and procedures can ensure that drains are working and
bridge decks are free of standing water. This manual provides guidelines and procedures for
designing bridge deck drainage systems, accompanied with illustrative and practical examples.
1.1 Scope
This manual constitutes a compendium of bridge deck drainage design guidance. It features
design theory, step-by-step design procedures, and illustrative examples. Drainage system
design is approached from the viewpoints of hydraulic capacity, traffic safety, structural
integrity, practical maintenance, and architectural aesthetics. System hardware components,
such as inlets, pipes, and downspouts, are described. Guidance for selecting a design gutter
spread and flood frequency are provided. Theory, system details, and existing computer
models are discussed.
1.2 Design Objectives
In designing a system to remove water from the bridge deck, the engineer must develop
solutions that:
● Control the spread of water into traffic lanes, as well as the depth of water
available to reduce tire traction.
● Do not interfere with the architectural beauty or structural integrity of the
bridge.
● Will function properly if clogging is maintainable.
1.2.4 Aesthetics
A pipe system conveying water from deck inlets to natural ground can be affixed to
exterior surfaces of a bridge or encased within structural members. Exposed piping
can be unsightly. Pipes affixed to exterior surfaces of structures, running at odd
angles, can present an unpleasant silhouette and detract from a bridge's
architectural aesthetics. To avoid this, pipes can be run in slots up the backs of the
columns or can be hidden behind decorative pilasters. However, encased piping
poses serious maintenance considerations and is not typically used in Northern
States due to potential freezing damage.
1.3 Systems
The bridge deck drainage system includes the bridge deck itself, bridge gutters, inlets, pipes,
downspouts, and bridge end collectors. The details of this system are typically handled by the
bridge engineer and coordinated with the hydraulic engineer. Coordination of efforts is essential
in designing the various components of the system to meet the objectives described in the
previous section.
Go to Chapter 2
Chapter 2 : HEC 21
Typical System Components
Go to Chapter 3
The components of bridge deck drainage systems introduced in Chapter 1 are described in
greater detail in this chapter. Terminology to be used throughout this manual is introduced.
Additional help for the reader is found in Appendix D. Requirements of the system components
for meeting the design objectives are described.
2.1 Terminology
For the sake of consistency and clarity, a list of terms is provided below.
Cleanout plug: A removable plug in the piping system that gives access to a run of
piping for cleaning. It is typically located near bends and Y-shaped intersections.
Cross slope: The slope of the pavement cross section from the curb to the bridge
deck crown.
Drop inlet: A drain that is used away from a bridge or at bridge ends. It is usually
larger than an inlet chamber and is set in earth in the subgrade or shoulder of an
approach embankment. It has a horizontal or near-horizontal opening.
Drain: A receptacle that receives and conveys water.
Drainage system: The entire arrangement of grates, drains, inlet chambers, pipes,
gutters, ditches, outfalls, and energy dissipators necessary to collect water and
convey it to a disposal point.
Grate: The ribbed or perforated cover of an inlet chamber that admits water and
supports traffic loads; long-established practice is to make grates that are safe for
cyclists. Typically, grates are removable to allow maintenance.
Inlet chamber: The typically small cast-iron, welded-steel, or formed-concrete
compartment that is beneath a grate. Although usually set into the bridge deck, it is
sometimes only an open hole in the deck.
Outlet pipe: The pipe that leads the water away from an inlet chamber or drop inlet.
Runoff, drainage, water: Any liquid that can run off the roadway surface. Although
the liquid is generally water, it includes any other liquids and dissolved solids that
can make their way into the drainage system.
Scupper: A small opening in the deck, curb, or barrier through which water can flow
from the bridge deck. The term is nautical and by analogy relates bridge deck
drains to openings in the sides of ships at deck level to allow water to run out.
Spread: The top width of water measured laterally from the bridge curb.
Storm drain: A beneath-the-bridge and underground piping system that may
connect to a municipal storm drain system or may be a separate collection system
for highway and bridge drainage.
2.2 Requirements
The main requirement of the drainage system is that it remove rainfall-generated runoff from
the bridge deck before it collects and spreads in the gutter to encroach onto the travel roadway
to the limit of a design spread. In accomplishing this purpose, the drainage system must meet
other design criteria, as presented below.
Go to Chapter 3
Chapter 3 : HEC 21
Estimation of Design Storm Runoff
Go to Chapter 4
The Rational Method is presented as the conventional method for determining peak runoff rate for bridge
decks. Alternatives to the Rational Method for determining a design storm runoff for sizing the bridge deck
drainage system are discussed in this chapter. Considerations for selecting the design rainfall intensity
include the Rational Method, hydroplaning, driver vision impairment, and the Least Total Economic Cost
(LTEC).
Both design frequency and spread influence cost-effectiveness. The implications of the use of a criterion for
spread of one-half of a traffic lane is considerably different for one design frequency than for another
frequency. It also has different implications for a low-traffic, low-speed bridge than for a higher functional
class. These subjects are central to the issue of bridge deck drainage and are important to traffic safety.
The objective in the design of a drainage system for a bridge deck section is to collect runoff in the gutter
and convey it to inlets in a manner that provides reasonable safety for motorists, as well as cyclists and
pedestrians, at a reasonable cost. As spread from the curb increases, the risks of traffic accidents and
delays, and the nuisance and possible hazard to cyclists and pedestrian traffic, increase.
The process of selecting the design frequency and spread for design involves decisions regarding
acceptable costs for the drainage system. Risks associated with water on traffic lanes are greater with
high-traffic volumes, high speeds, and higher classifications than with lower volumes, speeds, and bridge
classifications.
A summary of the major considerations that enter into the selection of design frequency and design spread
follows.
1. The classification of the bridge is a good starting point in the selection process since it defines the
public's expectations regarding water on the pavement surface. Ponding on traffic lanes of
high-speed, high-volume bridges is contrary to the public's expectations and the risks of accidents
and the costs of traffic delays are high.
2. Design speed is important to the selection of design criteria. At speeds greater than 45 mi/h, water on
the pavement can cause hydroplaning.
3. Projected traffic volumes are an indicator of the economic importance of keeping the bridge open to
traffic. The costs of traffic delays and accidents increase with increasing traffic volumes.
4. The likelihood of rainfall events may significantly affect the selection of design frequency and spread.
Risks associated with the spread of water may be less in arid areas subject to rare high-intensity
thunderstorms than in areas accustomed to common but less-intense rainfall.
5. Capital costs are neither the least nor last consideration. Cost considerations make it necessary to
formulate a rational approach to the selection of design criteria. Trade-offs between desirable and
practicable criteria are sometimes necessary because of costs. In particular, the costs and feasibility
of providing for a given design frequency and spread may vary significantly between projects. In
some cases, it may be practicable to significantly upgrade the drainage design and reduce risks at
moderate costs. In other instances, where extensive outfalls or pumping stations are required, costs
may be very sensitive to the criteria selected for use in design.
6. This manual takes the viewpoint that inlets are designed not to clog. Their detailed configuration
should keep objects that may plug the drain on the surface and in the gutter. The inlets themselves
are taken to admit flow freely without clogging. This condition of unplugged drains may need to be
taken into account by users of this manual with design situations that include clogging possibilities.
Other considerations include inconvenience, hazards, and nuisances to cyclists and pedestrian traffic.
These considerations should not be overlooked and, in some locations, such as in urban areas, may
assume major importance. Local design practice may also be a major consideration since it can affect the
feasibility of designing to higher standards and because it influences the public's perception of acceptable
practice.
If the bridge drains are designed for the 10-year frequency, they should be checked for hydraulic
performance for a higher frequency, typically the 25-year level. The use of a check event is considered
advisable if a sizeable area that drains to the bridge could cause unacceptable flooding during events that
exceed the design event. Also, the design of any series of inlets should be checked against a larger runoff
event, particularly when the series ends at a sag vertical curve in which ponding could occur.
The frequency selected for use as the check storm should be based on the same considerations used to
select the design storm, that is, the consequences of spread exceeding that chosen for design and the
potential for ponding. Where no significant ponding can occur, check storms are normally unnecessary.
Criteria for spread during the check event may be that one lane of traffic can still cross the bridge without
having to splash through spread. Thus, for a crowned bridge with four 12-foot lanes, the check event
spread could be: 10-foot breakdown lane plus 12-foot outside flooded lane, plus 4 feet of encroachment
into the center lane, equals 26 feet of spread.
2. The probability of exceeding the peak runoff rate is equal to the probability of the average
rainfall intensity used in the method.
3. A straight-line relationship exists between the maximum rate of runoff and a rainfall
intensity of duration equal to or longer than the time of concentration, for example, a
2-in/hr rainfall will result in a peak discharge exactly twice as large as a 1-in/hr average
intensity rainfall.
4. The coefficient of runoff is the same for storms of all recurrence probabilities.
5. The coefficient of runoff is the same for all storms on a given watershed.
Note: For flat slopes and permeable soils, use the lower values. For steep slopes
and impermeable soils, use the higher values.
Information concerning the intensity, duration, and frequency of rainfall for the locality of the
design is necessary to use the Rational Method. Precipitation intensity-duration-frequency (IDF)
curves can be developed from information found in various National Weather Service (NWS)
publications. Data from the NWS have been incorporated into the HYDRO computer program of
the HYDRAIN (Young and Krolak, 1992) software package supported by the Federal Highway
Administration (FHWA). HYDRO determines time of concentration, intensity, and peak runoff
flow from user-supplied location and other information.
Time of concentration is defined as the time it takes for runoff to travel from the most distant
hydraulic point in the watershed to the point of reference downstream. An assumption implicit to
the Rational Method is that the peak runoff rate occurs when the duration of the rainfall intensity
is as long or longer than the time of concentration. Therefore, the time of concentration for the
drainage area must be estimated in order to select the appropriate value of rainfall intensity for
use in the equation.
The time of concentration for bridge deck inlets is comprised of two components: overland flow
time and gutter flow time. The overland flow is sheet flow from the deck high point to the gutter.
If overland flow is channelized upstream of the location at which the flow enters the bridge deck
gutter, a third component is added. These components are added together to determine the
total time of concentration.
A study at the University of Maryland (Ragan, 1971) found that the most realistic method for
estimating overland sheet flow time of concentration is the kinematic wave equation:
(2)
(3)
The total time of concentration, tc , is the sum of to and tg. (Note that Equation (2) and Equation
(3) are represented in Chart 2 and Chart 3 in Appendix C).
Since the time of concentration and rainfall intensity are both independent variables, the
solution for intensity is one of iteration or trial and error. A trial value for tc is first assumed and
the corresponding i determined from the IDF curve for the frequency of the event chosen for the
particular design problem. This i is then used to compute to and tg from Equation (2) and
Equation (3). The procedure is repeated until the trial value and computed value for tc are in
close agreement. The procedure is presented in Chapter 8 and illustrated by example in
Chapter 9. A similar procedure is performed automatically by the computer model, HYDRO.
Go to Chapter 4
Go to Appendix C Go to Chart 3
Chart 11. Logic for computing inlet spacing for a flat bridge.
Go to Appendix C Go to Chart 13
Equation 1
Equation 2
Equation 3
Equation 4
Equation 5
Equation 6
Equation 7
Equation 8
Equation 9
Equation 10
Equation 11
Equation 12
Equation 13
Equation 14
Equation 15
Equation 16
Equation 17
Equation 18
Equation 19
Equation 20
Equation 21
Equation 22a
Equation 22b
Equation 23
Equation 24
Equation 25
Equation 26
Equation 27
Equation 28
Equation 29
Equation 30
Equation 31
Equation 32
Equation 33
Equation 34
Equation 35
Equation 36
Equation 37
Equation 38
Equation 39
Equation 40
Equation 41
Equation 42
Equation 43
Equation 44
Equation 45
Equation 46
Equation 47
Equation 48
Equation 49
Equation 50
Equation 51
Equation 52
Equation 53
Equation 54
Equation 55
Equation 56
Equation 57
Equation 58
Equation 59
Equation 60
Equation 61
Equation 62
Equation 63
Equation 64
Equation 65
Equation 66
Equation 67
Equation 68
Equation 69
Equation 70
Equation 71
Equation 72
Equation 73
Equation 74
Equation 75
Equation 76
Equation 77
The manual provides guidelines and procedures for designing bridge deck drainage systems,
inclusing illustrative examples. Should the design process indicate a drainage system is needed,
utilization of the most hydraulically efficient and maintenance-free system is emphasized. The
manual also stresses the advantages of designing to minimize the complexity of bridge deck
drainage systems. Integration of practical drainage details into overall structural design is
presented. For user's convenience, all design graphs and nomographs appear in the index.
The manual is a compendium of bridge drainage design guidance. It includes design theory,
step-by-step design procedures, and illustrative examples. Drainage systems design is
approached from the viewpoints of hydraulic capacity, traffic safety, structural integrity, practical
maintenance, and architectural aesthetics. System hardware compinents, such as inlets, pipes,
and downspouts, are described. Guidance for selecting a design gutter spread and flood fluency
are provided. System details and existing computer models are discussed.
17. Key Words 18. Distribution Statement
Bridge deck drainage, drainage inlets, bridge scuppers, This document is available to the public
hydroplaning, bridge end treatments, hydraulic design from the National Technical Information
Service, Springfield, Virginia 22151
19. Security Classif. (of this 20. Security Classif. (of 21. No. of Pages 22. Price
report) this page)
129
Unclassified Unclassified
Go to Table of Contents
References
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