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Springer, J., Zhou, K. "Bridge Hydraulics." Bridge Engineering Handbook. Ed. Wai-Fah Chen and Lian Duan Boca Raton: CRC Press, 2000 61 Bridge Hydraulics Jim Springer 61.1 61.2 Hydrology • Bridge Deck Drainage Design • Stage Hydraulics California Department of Transportation Ke Zhou California Department of Transportation Introduction Bridge Hydrology and Hydraulics 61.3 Bridge Scour Bridge Scour Analysis • Bridge Scour Calculation • Bridge Scour Investigation and Prevention 61.1 Introduction This chapter presents bridge engineers basic concepts, methods, and procedures used in bridge hydraulic analysis and design. It involves hydrology study, hydraulic analysis, on-site drainage design, and bridge scour evaluation. Hydrology study for bridge design mainly deals with the properties, distribution, and circulation of water on and above the land surface. The primary objective is to determine either the peak discharge or the flood hydrograph, in some cases both, at the highway stream crossings. Hydraulic analysis provides essential methods to determine runoff discharges, water profiles, and velocity distribution. The on-site drainage design part of this chapter is presented with the basic procedures and references for bridge engineers to design bridge drainage. Bridge scour is a big part of this chapter. Bridge engineers are systematically introduced to concepts of various scour types, presented with procedures and methodology to calculate and evaluate bridge scour depths, provided with guidelines to conduct bridge scour investigation and to design scour preventive measures. 61.2 Bridge Hydrology and Hydraulics 61.2.1 Hydrology 61.2.1.1 Collection of Data Hydraulic data for the hydrology study may be obtained from the following sources: as-built plans, site investigations and field surveys, bridge maintenance books, hydraulic files from experienced report writers, files of government agencies such as the U.S. Corps of Engineers studies, U.S. Geological Survey (USGS), Soil Conservation Service, and FEMA studies, rainfall data from local water agencies, stream gauge data, USGS and state water agency reservoir regulation, aerial photographs, and floodways, etc. Site investigations should always be conducted except in the simplest cases. Field surveys are very important because they can reveal conditions that are not readily apparent from maps, aerial © 2000 by CRC Press LLC photographs and previous studies. The typical data collected during a field survey include high water marks, scour potential, stream stability, nearby drainage structures, changes in land use not indicated on maps, debris potential, and nearby physical features. See HEC-19, Attachment D [16] for a typical Survey Data Report Form. 61.2.1.2 Drainage Basin The area of the drainage basin above a given point on a stream is a major contributing factor to the amount of flow past that point. For given conditions, the peak flow at the proposed site is approximately proportional to the drainage area. The shape of a basin affects the peak discharge. Long, narrow basins generally give lower peak discharges than pear-shaped basins. The slope of the basin is a major factor in the calculation of the time of concentration of a basin. Steep slopes tend to result in shorter times of concentration and flatter slopes tend to increase the time of concentration. The mean elevation of a drainage basin is an important characteristic affecting runoff. Higher elevation basins can receive a significant amount of precipitation as snow. A basin orientation with respect to the direction of storm movement can affect peak discharge. Storms moving upstream tend to produce lower peaks than those moving downstream. 61.2.1.3 Discharge There are several hydrologic methods to determine discharge. Most of the methods for estimating flood flows are based on statistical analyses of rainfall and runoff records and involve preliminary or trial selections of alternative designs that are judged to meet the site conditions and to accommodate the flood flows selected for analysis. Flood flow frequencies are usually calculated for discharges of 2.33 years through the overtopping flood. The frequency flow of 2.33 years is considered to be the mean annual discharge. The base flood is the 100-year discharge (1% frequency). The design discharge is the 50-year discharge (2% frequency) or the greatest of record, if practical. Many times, the historical flood is so large that a structure to handle the flow becomes uneconomical and is not warranted. It is the engineer’s responsibility to determine the design discharge. The overtopping discharge is calculated at the site, but may overtop the roadway some distance away from the site. Changes in land use can increase the surface water runoff. Future land-use changes that can be reasonably anticipated to occur in the design life should be used in the hydrology study. The type of surface soil is a major factor in the peak discharge calculation. Rock formations underlying the surface and other geophysical characteristics such as volcanic, glacial, and river deposits can have a significant effect on runoff. In the United States, the major source of soil information is the Soil Conservation Service (SCS). Detention storage can have a significant effect on reducing the peak discharge from a basin, depending upon its size and location in the basin. The most commonly used methods to determine discharges are 1. 2. 3. 4. 5. Rational method Statistical Gauge Analysis Methods Discharge comparison of adjacent basins from gauge analysis Regional flood-frequency equations Design hydrograph The results from various methods of determining discharge should be compared, not averaged. 61.2.1.3.1 Rational Method The rational method is one of the oldest flood calculation methods and was first employed in Ireland in urban engineering in 1847. This method is based on the following assumptions: © 2000 by CRC Press LLC TABLE 61.1 Runoff Coefficients for Developed Areas Type of Drainage Area Runoff Coefficient Business Downtown areas Neighborhood areas Residential areas Single-family areas Multiunits, detached Multiunits, attached Suburban Apartment dwelling areas Industrial Light areas Heavy areas Parks, cemeteries Playgrounds Railroad yard areas Unimproved areas Lawns Sandy soil, flat, 2% Sandy soil, average, 2–7% Sandy soil, steep, 7% Heavy soil, flat, 2% Heavy soil, average, 2–7% Heavy soil, steep, 7% Streets Asphaltic Concrete Brick Drives and walks Roofs 0.70–0.95 0.50–0.70 0.30–0.50 0.40–0.60 0.60–0.75 0.25–0.40 0.50–0.70 0.50–0.80 0.60–0.90 0.10–0.25 0.20–0.40 0.20–0.40 0.10–0.30 0.05–0.10 0.10–0.15 0.15–0.20 0.13–0.17 0.18–0.25 0.25–0.35 0.70–0.95 0.80–0.95 0.70–0.85 0.75–0.85 0.75–0.95 1. Drainage area is smaller than 300 acres. 2. Peak flow occurs when all of the watershed is contributing. 3. The rainfall intensity is uniform over a duration equal to or greater than the time of concentration, Tc . 4. The frequency of the peak flow is equal to the frequency of the rainfall intensity. Q = Ci A (61.1) where Q = discharge, in cubic foot per second C = runoff coefficient (in %) can be determined in the field and from Tables 61.1 and 61.2 [5,16] or a weighted C value is used when the basin has varying amounts of different cover. The weighted C value is determined as follows: C= ∑C A ∑A j j (61.2) j i = rainfall intensity (in inches per hour) can be determined from either regional IDF maps or individual IDF curves A = drainage basin area (in acres) is determined from topographic map (Note: 1 sq. mile = 640 acres = 0.386 sq. kilometer) © 2000 by CRC Press LLC TABLE 61.2 Runoff Coefficients for Undeveloped Area Watershed Types Soil 0.12–0.16 No effective soil cover, either rock or thin soil mantle of negligible infiltration capacity 0.08–0.12 Slow to take up water, clay or shallow loam soils of low infiltration capacity, imperfectly or poorly drained 0.06–0.08 Normal, well-drained light or mediumtextured soils, sandy loams, silt and silt loams 0.04–0.06 High, deep sand or other soil that takes up water readily, very light well-drained soils Vegetal Cover 0.12–0.16 No effective plant cover, bare or very sparse cover 0.08–0.12 Poor to fair; clean cultivation crops, or poor natural cover, less than 20% of drainage area over good cover 0.06–0.08 Fair to good; about 50% of area in good grassland or woodland, not more than 50% of area in cultivated crops 0.04–0.06 Good to excellent; about 90% of drainage area in good grassland, woodland or equivalent cover Surface Storage 0.10–0.12 Negligible surface depression few and shallow, drainageways steep and small, no marshes 0.08–0.10 Low, well-defined system of small drainageways; no ponds or marshes 0.06–0.08 Normal; considerable surface depression storage; lakes and pond marshes 0.04–0.06 High; surface storage, high; drainage system not sharply defined; large floodplain storage or large number of ponds or marshes The time of concentration for a pear-shaped drainage basin can be determined using a combined overland and channel flow equation, the Kirpich equation: Tc = 0.0195 ( L / S 0.5 )0.77 (61.3) where Tc = Time of concentration in minutes L = Horizontally projected length of watershed in meters S = H/L (H = difference in elevation between the most remote point in the basin and the outlet in meters) 61.2.1.3.2 Statistical Gauge Analysis Methods The following two methods are the major statistical analysis methods which are used with stream gauge records in the hydrological analysis. 1. Log Pearson Type III method 2. Gumbel extreme value method The use of stream gauge records is a preferred method of estimating discharge/frequencies since they reflect actual climatology and runoff. Discharge records, if available, may be obtained from a state department of water resources in the United States. A good record set should contain at least 25 years of continuous records. It is important, however, to review each individual stream gauge record carefully to ensure that the database is consistent with good statistical analysis practice. For example, a drainage basin with a large storage facility will result in a skewed or inconsistent database since smaller basin discharges will be influenced to a much greater extent than large discharges. The most current published stream gauge description page should be reviewed to obtain a complete idea of the background for that record. A note should be given to changes in basin area over time, diversions, revisions, etc. All reliable historical data outside of the recorded period should © 2000 by CRC Press LLC be included. The adjacent gauge records for supplemental information should be checked and utilized to extend the record if it is possible. Natural runoff data should be separated from later controlled data. It is known that high-altitude basin snowmelt discharges are not compatible with rain flood discharges. The zero years must also be accounted for by adjusting the final plot positions, not by inclusion as minor flows. The generalized skew number can be obtained from the chart in Bulletin No.17 B [8]. Quite often the database requires modification for use in a Log Pearson III analysis. Occasionally, a high outlier, but more often low outliers, will need to be removed from the database to avoid _ skewing results. This need is determined for high outliers by using = low QH Q H + K SH , and _ _ outliers by using = + K , where K is a factor determined by the sample size, and QL QL SL QH _ Q L are the high and low mean logarithm of systematic peaks, QH and QL are the high and low outlier thresholds in log units, SH and SL are the high and low standard deviations of the logarithmic distribution. Refer to FHWA HEC-19, Hydrology [16] or USGS Bulletin 17B [8] for this method and to find the values of K. The data to be plotted are “PEAK DISCHARGE, Q (CFS)” vs. “PROBABILITY, Pr” as shown in the example in Figure 61.1. This plot usually results in a very flat curve with a reasonably straight center portion. An extension of this center portion gives a line for interpolation of the various needed discharges and frequencies. The engineer should use an adjusted skew, which is calculated from the generalized and station skews. Generalized skews should be developed from at least 40 stations with each station having at least 25 years of record. The equation for the adjusted skew is Gw = where Gw GS GL MSEGS MSEGL MSEGS (GL ) + MSEGL (GS ) MSEGS + MSEGL (61.4) = weighted skew coefficient = station skew = generalized skew = mean square error of station skew = mean square error of generalized skew The entire Log Pearson type III procedure is covered by Bulletin No. 17B, “Guidelines for Determining Flood Flow Frequency” [8]. The Gumbel extreme value method, sometimes called the double-exponential distribution of extreme values, has also been used to describe the distribution of hydrological variables, especially the peak discharges. It is based on the assumption that the cumulative frequency distribution of the largest values of samples drawn from a large population can be described by the following equation: f ( Q) = e − e where 1.281 a= S b = Q − 0.450 S S = standard deviation Q = mean annual flow © 2000 by CRC Press LLC a ( Q− b ) (61.5) FIGURE 61.1 Log Pearson type III distribution analysis, Medina River, TX. Values of this distribution function can be computed from Eq. (61.5). Characteristics of the Gumbel extreme value distribution are that the mean flow, Q , occurs at the return period of Tr = 2.33 years and that it is skewed toward the high flows or extreme values as shown in the example of Figure 61.2. Even though it does not account directly for the computed skew of the data, it does predict the high flows reasonably well. For this method and additional techniques, please refer to USGS Water Supply Paper 1543-A, Flood-Frequency Analysis, and Manual of Hydrology Part 3. The Gumbel extreme value distribution is given in “Statistics of Extremes” by E.J. Gumbel and is also found in HEC-19, p.73. Results from this method should be plotted on special Gumbel paper as shown in Figure 61.2. © 2000 by CRC Press LLC FIGURE 61.2 Gumbel extreme value frequency distribution analysis, Medina River, TX. 61.2.1.3.3 Discharge Comparison of Adjacent Basins HEC 19, Appendix D [16] contains a list of reports for various states in the United States that have discharges at gauges that have been determined for frequencies from 2-year through 100-year frequencies. The discharges were determined by the Log Pearson III method. The discharge frequency at the gauges should be updated by the engineer using Log Pearson III and the Gumbel extreme value method. The gauge data can be used directly as equivalent if the drainage areas are about the same (within less than 5%). Otherwise, the discharge determination can be obtained by the formula: Qu = Qg ( Au / Ag )b (61.6) where Qu = discharge at ungauged site Qg = discharge at gauged site Au = area of ungauged site Ag = area of gauged site b = exponent of drainage area 61.2.1.3.4 Regional Flood-Frequency Equations If no gauged site is reasonably nearby, or if the record for the gauge is too short, then the discharge can be computed using the applicable regional flood-frequency equations. Statewide regional regression equations have been established in the United States. These equations permit peak flows to be © 2000 by CRC Press LLC estimated for return periods varying between 2 and 100 years. The discharges were determined by the Log Pearson III method. See HEC-19, Appendix D [16] for references to the studies that were conducted for the various states. 61.2.1.3.5 Design Hydrographs Design hydrographs [9] give a complete time history of the passage of a flood at a particular site. This would include the peak flow. A runoff hydrograph is a plot of the response of a watershed to a particular rainfall event. A unit hydrograph is defined as the direct runoff hydrograph resulting from a rainfall event that lasts for a unit duration of time. The ordinates of the unit hydrograph are such that the volume of direct runoff represented by the area under the hydrograph is equal to 1 in. of runoff from the drainage area. Data on low water discharges and dates should be given as it will control methods and procedures of pier excavation and construction. The low water discharges and dates can be found in the USGS Water Resources Data Reports published each year. One procedure is to review the past 5 or 6 years of records to determine this. 61.2.1.4 Remarks Before arriving at a final discharge, the existing channel capacity should be checked using the velocity as calculated times the channel waterway area. It may be that a portion of the discharge overflows the banks and never reaches the site. The proposed design discharge should also be checked to see that it is reasonable and practicable. As a rule of thumb, the unit runoff should be 300 to 600 s-ft per square mile for small basins (to 20 square miles), 100 to 300 s-ft per square mile for median areas (to 50 square miles) and 25 to 150 s-ft for large basins (above 50 square miles). The best results will depend on rational engineering judgment. 61.2.2 Bridge Deck Drainage Design (On-Site Drainage Design) 61.2.2.1 Runoff and Capacity Analysis The preferred on-site hydrology method is the rational method. The rational method, as discussed in Section 61.2.1.3.1, for on-site hydrology has a minimum time of concentration of 10 min. Many times, the time of concentration for the contributing on-site pavement runoff is less than 10 min. The initial time of concentration can be determined using an overland flow method until the runoff is concentrated in a curbed section. Channel flow using the roadway-curb cross section should be used to determine velocity and subsequently the time of flow to the first inlet. The channel flow velocity and flooded width is calculated using Manning’s formula: V= 1.486 A R2 / 3 S1f / 2 n (61.7) where V = velocity A = cross-sectional area of flow R = hydraulic radius S f = slope of channel n = Manning’s roughness value [11] The intercepted flow is subtracted from the initial flow and the bypass is combined with runoff from the subsequent drainage area to determine the placement of the next inlet. The placement of inlets is determined by the allowable flooded width on the roadway. Oftentimes, bridges are in sump areas, or the lowest spot on the roadway profile. This necessitates the interception of most of the flow before reaching the bridge deck. Two overland flow equations are as follows. © 2000 by CRC Press LLC 1. Kinematic Wave Equation: 0.6 6.92 L n 0.6 i 0.4 S 0.3 (61.8) 3.3 (1.1 − C)( L)1/ 2 (100 S)1/ 3 (61.9) to = 2. Overland Equation: to = where to = overland flow travel time in minutes L = length of overland flow path in meters S = slope of overland flow in meters n = manning’s roughness coefficient [12] i = design storm rainfall intensity in mm/h C = runoff coefficient (Tables 61.1 and 61.2) 61.2.2.2 Select and Size Drainage Facilities The selection of inlets is based upon the allowable flooded width. The allowable flooded width is usually outside the traveled way. The type of inlet leading up to the bridge deck can vary depending upon the flooded width and the velocity. Grate inlets are very common and, in areas with curbs, curb opening inlets are another alternative. There are various monographs associated with the type of grate and curb opening inlet. These monographs are used to determine interception and therefore the bypass [5]. 61.2.3 Stage Hydraulics High water (HW) stage is a very important item in the control of the bridge design. All available information should be obtained from the field and the Bridge Hydrology Report regarding HW marks, HW on upstream and downstream sides of the existing bridges, high drift profiles, and possible backwater due to existing or proposed construction. Remember, observed high drift and HW marks are not always what they seem. Drift in trees and brush that could have been bent down by the flow of the water will be extremely higher than the actual conditions. In addition, drift may be pushed up on objects or slopes above actual HW elevation by the velocity of the water or wave action. Painted HW marks on the bridge should be searched carefully. Some flood insurance rate maps and flood insurance study reports may show stages for various discharges. Backwater stages caused by other structures should be included or streams should be noted. Duration of high stages should be given, along with the base flood stage and HW for the design discharge. It should be calculated for existing and proposed conditions that may restrict the channel producing a higher stage. Elevation and season of low water should be given, as this may control design of tremie seals for foundations and other possible methods of construction. Elevation of overtopping flow and its location should be given. Normally, overtopping occurs at the bridge site, but overtopping may occur at a low sag in the roadway away from the bridge site. 61.2.3.1 Waterway Analysis When determining the required waterway at the proposed bridge, the engineers must consider all adjacent bridges if these bridges are reasonably close. The waterway section of these bridges should be tied into the stream profile of the proposed structure. Structures that are upstream or downstream of the proposed bridge may have an impact on the water surface profile. When calculating the © 2000 by CRC Press LLC