Reference Guide for Applying Risk and Reliability-Based Approaches for Bridge Scour Prediction (2013)

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41 4.1 Introduction This chapter includes a brief summary of the data sets used in developing model bias and COV for each of the three individual scour components. For pier scour, both the HEC-18 and Florida DOT equations are assessed using comprehensive data sets from both laboratory and field studies. Contraction scour uses the HEC-18 equation for clear-water scour using labora- tory data only. Abutment scour uses the NCHRP Project 24-20 total scour approach (Ettema et al. 2010), which is recommended in the most recent edition of HEC-18 (Arneson et al. 2012), using laboratory data only. 4.2 Pier Scour Data 4.2.1 Pier Scour Laboratory Data—Compilation, Screening, and Analysis Pier scour data obtained under controlled laboratory conditions were assembled from 22 sources, yielding 699 independent measurements of pier scour in cohesionless soils. All data sets consisted of studies where the following information was documented: (1) scour depth, ys, (2) approach flow depth, y, (3) approach flow velocity, V, (4) median sediment size, d50, (5) pier width, a, and (6) pier shape (e.g., cylindrical, square, rectangular, etc.). Seventeen of the 22 data sources were obtained from NCHRP Report 682 (Sheppard et al. 2011), which provided 569 data points. Data also were acquired from five additional studies, contributing another 130 data points. To determine whether an individual test run was conducted under clear-water or live-bed conditions, the procedure presented in the 5th edition of HEC-18 (Arneson et al. 2012) uses the critical velocity for particle motion given by the following relationship (in U.S. customary units): ( ) = − V 1.486 y K S 1 d n (4.1)c 1 6 s s 50 where: Vc = Critical velocity for particle motion, ft/s y = Approach flow depth, ft Ks = Dimensionless shields parameter for sediment motion (0.03 for gravel, 0.047 for sand) Ss = Specific gravity of particle (assumed equal to 2.65 unless otherwise indicated) d50 = Median particle diameter, ft n = Manning resistance coefficient, estimated as n = 0.034(d50) 1/6 (d50 in ft) C H A P T E R 4 Bridge Scour Equations and Data Screening

42 Reference Guide for Applying Risk and Reliability-Based Approaches for Bridge Scour Prediction Nearly all of the laboratory tests involved cylindrical piers; only 36 tests (about 5% of the data points) used square, rectangular, or multiple-column piers. The 36 tests with non-cylindrical piers all used an orientation aligned with the flow such that a skew angle was not introduced. 4.2.1.1 HEC-18 Pier Scour Equation—Laboratory Data Using the laboratory data, pier scour for each test was predicted using the HEC-18 equation as presented in HEC-18 5th Ed. (Arneson et al. 2012). The HEC-18 equation, normalized to pier width, is: ( ) ( )=ya 2.0 K K K K ya Fr subject to the following limits: (4.2)s 1 2 3 w 0.35 0.43 y a 2.4 for Fr < 0.8 s = y a 3.0 for Fr > 0.8 s = The coefficients and variables of the HEC-18 equation are: ys = Scour depth, ft or m a = Pier width normal to flow, ft or m K1 = Correction factor for shape of pier nose K2 = Correction factor for skew angle (= 1.0 for piers aligned with the flow) K3 = Correction factor for bed forms Kw = Correction factor for very wide piers y = Depth of approach flow, ft or m Fr = Froude number of the approach flow The correction factor Kw for very wide piers is: ( )= <K 2.58 ya Fr for V V 1.0 (4.3)w 0.34 0.65 c ( )= ≥K 1.0 ya Fr for V V 1.0w 0.13 0.25 c K 1.0w ≤ The correction factor Kw is only applied when all of the following conditions are met: y a 0.8< a d 50, and50 > Fr 1.0< Based on the estimated critical velocity using the HEC-18 procedure described in this sec- tion, 495 data tests were conducted under clear-water scour conditions; the remaining 204 tests were conducted with live-bed conditions. The evolution of scour depth over time was not inves- tigated in many of the studies; therefore, the data collection required introducing assumptions regarding the maturity of the scour hole at the end of each test. Following an initial analysis of all 699 data points from the 22 data sources, a method was developed and used to identify and remove outliers. The data quality assessment method developed for this purpose relied only on variables that were directly measured during each

Bridge Scour Equations and Data Screening 43 test; no predictive techniques were used to discriminate among data points. Of the original 699 data points, 119 were identified as outliers (approximately 17% of the total data points), result- ing in a final data set of 580 points for analysis. A detailed description of the outlier identifica- tion method is provided in the Contractor’s Final Report for NCHRP Project 24-34 (Lagasse et al. 2013), which is available at www.trb.org. With the outliers removed, the final data set was plotted and used to analyze the bias and COV of the HEC-18 pier scour prediction equation. Figure 4.1 presents the final data graphi- cally. Table 4.1 provides the final results of the analysis (see Section 2.5.2 for a discussion of the reliability index, b, as a measure of structural safety). 4.2.1.2 Florida DOT Pier Scour Equation—Laboratory Data The pier scour approach in NCHRP Report 682 (Sheppard et al. 2011) is referenced as the Florida DOT (FDOT) Pier Scour Methodology in the 5th edition of HEC-18. The method is referred to as the Florida DOT pier scour equation in this document. As with the HEC-18 equation, the Florida DOT pier scour equation includes flow velocity, depth and angle of attack, pier geometry and shape, but also includes particle size. The Florida Clear water y = 1.1199x Live bed y = 1.4649x 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 y s /a Pr ed ic te d by H EC 18 Eq ua o n ys/a Observed Clear water, V/Vc< 1 Live bed, V/Vc> 1 Figure 4.1. HEC-18 pier scour prediction vs. observed scour for clear-water and live-bed conditions, final laboratory data set (outliers removed). Data Set No. Data Points Bias COV Percent Under- Reliability ( ) Normal Lognormal All data 580 0.82 0.23 17.2% 0.97 1.00 Clear-water subset 402 0.88 0.21 24.6% 0.66 0.73 Live-bed subset 178 0.68 0.16 0.6% 2.92 2.49 predicted Table 4.1. Bias and coefficient of variation of the HEC-18 pier scour equation with laboratory data (all data with outliers removed).

44 Reference Guide for Applying Risk and Reliability-Based Approaches for Bridge Scour Prediction DOT equation combines pier geometry, shape, and angle of attack to compute an effective pier width, a*. In contrast to the HEC-18 equation, the Florida DOT pier scour equation also distin- guishes between clear-water and live-bed flow conditions. The critical velocity equation as given in NCHRP Report 682 (Sheppard et al. 2011), is: V u 5.75 log 1685 y d (4.4)c *c 50 ( )=   where: Vc = Critical velocity for particle motion, ft/s u*c = Shear velocity for 0.1 mm < d50 < 1 mm given by: 0.0377 + 0.0410(d50) 1.4, ft/s u*c = Shear velocity for 1 mm < d50 < 100 mm given by: 0.1(d50) 0.5 – 0.0213(d50) -1, ft/s y = Approach flow depth, ft d50 = Median grain diameter, mm Although the HEC-18 equation provides good results for most applications, the Florida DOT equation should be considered as an alternative, particularly for wide piers (y/a < 0.2) (Arneson et al. 2012). The Florida DOT methodology includes the following equations: = ≤ < y a* 2.5f f f for 0.4 V V 1.0 (4.5) s 1 2 3 1 c = − −       + − −             ≤ ≤ y a* f 2.2 V V 1 V V 1 2.5f V V V V V V 1 for 1.0 V V V V (4.6) s 1 1 c lp c 3 lp c 1 c lp c 1 c lp c y a * 2.2f for V V V V (4.7) s 1 1 c lp c = > f tanh y a* (4.8)1 1 0.4( )=   f 1 1.2 ln V V (4.9)2 1 c 2 = −       f a* D 10.6 0.4 a* D (4.10)3 50 1.13 50 1.33=   +         where: ys = Pier scour depth, ft or m a* = Effective pier width, ft or m V1 = Mean velocity of flow directly upstream of the pier, ft/s or m/s Vlp = Velocity of the live-bed peak scour, ft/s or m/s Vc = Critical velocity for movement of D50 as defined in Equation (4.4), ft/s or m/s D50 = Median particle size of bed material, ft or m ( )=V 5V or 0.6 gy whichever is greater (4.11)lp c 1 where Vc is computed using Equation (4.4).

Bridge Scour Equations and Data Screening 45 The effective pier width, a*, is the projected width of the pier times the shape factor, Ksf. a* K a (4.12)sf proj= The shape factor for a circular or round-nosed pier is 1.0; the shape factor for a square-end pier depends on the angle of attack. K 1.0 for circular or round-nosed piers (4.13)sf = K 0.86 0.97 180 4 for square-nosed piers (4.14)sf 4( )= + piθ − pi where: q = flow angle of attack in degrees The projected width of the pier is: a a cos L sin (4.15)proj = θ + θ where: aproj = Projected pier width in direction of flow, ft or m a = Pier width, ft or m L = Pier length, ft or m The methodology can be accessed through a spreadsheet available at the Florida DOT web- site. It can also be computed from the equations presented in this chapter or by following the following steps. Step 1. Calculate Vc using Equation (4.4) Step 2. Calculate Vlp using Equation (4.11) Step 3. Calculate a* using Equation (4.12) Step 4. Calculate f1 using Equation (4.8) Step 5. Calculate f3 using Equation (4.10) Step 6. Calculate y a* s c− and ys-c (see Note below Equation [4.16]) Step 7. Calculate y a* s lp− and ys-lp (see Note below Equation [4.16]) Step 8. If V1 < 0.4Vc, then ys = 0.0 Step 9. If 0.4Vc < V1 ≤ Vc, then calculate f2 using Equation (4.9) and ys = f2ys-c Step 10. If V1 ≥ Vlp, then ys = ys-lp Step 11. If Vc < V1 < Vlp, then calculate ys from: ( )( ) ( ) = + − − − − − − y y V V V V y y (4.16)s s c 1 c lp c s lp s c Note: Equation (4.16) is an equivalent but simplified version of Equation (4.6); ys-c is the scour at critical velocity for bed material movement (Vc) and is equal to 2.5f1f3a*;and ys-lp is the scour at live-bed peak velocity (Vlp) and is equal to 2.2f1a*. The Florida DOT spreadsheet uses ys-c as the design scour value when it is greater than ys-lp. The Florida DOT methodology for pier scour includes four regions as shown in Figure 4.2. • Scour Region I (see Step 8) is for clear-water conditions with velocity too low to produce scour, which occurs for velocities less than 0.4Vc. However, field data in NCHRP Report 682 include observed scour for this condition, although it was only observed on one occasion for laboratory data.

46 Reference Guide for Applying Risk and Reliability-Based Approaches for Bridge Scour Prediction • Scour Region II is for clear-water conditions with flow velocity large enough to produce pier scour (Vc > V1 > 0.4Vc) as defined by Step 9. • Scour Region IV is defined by the live-bed peak velocity (Vlp), where the maximum live-bed scour occurs at 5Vc or greater. Any velocity greater than Vlp is assigned the scour, ys-lp, com- puted for Vlp (Step 10). • Live-bed scour that occurs for flow velocities between critical velocity and the live-bed peak velocity (Vc < V1 < Vlp) occurs in Scour Region III as defined by Step 11 and Equation (4.16). Pier scour was predicted using the Florida DOT methodology on the same 580 laboratory data points previously analyzed with the HEC-18 equation. Figure 4.3 presents the final data Clear water y = 1.1849x Live Bed y = 1.2734x 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 y s /a P re di ct ed b y FD O T M et ho do lo gy ys/a Observed Clear water, V/Vc< 1 Live bed, V/Vc> 1 Figure 4.3. Florida DOT pier scour prediction vs. observed scour for clear-water and live-bed conditions, final laboratory data set (outliers removed). 0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 5 6 7 V/Vc y s /a* Velocity at live-bed scour peak, Vlp, depends on sediment properties and water depth Actual Predictive equations Vlp /Vc Scour Regions I II III IV Live-bed Cl ea rw at er Figure 4.2. Scour regions for Florida DOT pier scour methodology (from NCHRP Report 683).

Bridge Scour Equations and Data Screening 47 graphically. Table 4.2 provides the final results of the pier scour prediction for the laboratory data using the Florida DOT methodology. 4.2.2 Pier Scour Field Data—Compilation and Analysis Pier scour data from field studies were obtained from NCHRP Report 682 (Sheppard et al. 2011), which provided 943 data points from four sources. From that study, 183 data points were identified as outliers, leaving 760 data points for analysis. The COVs for both the HEC-18 and Florida DOT pier scour equations were significantly higher compared to the laboratory data sets due to the difficulty in estimating the hydraulic conditions associated with the event caus- ing the scour, as well as the uncertainty in determining the maturity of the scour-hole depths. Both equations resulted in substantial overprediction of the observed scour depths. For these reasons, the laboratory data sets were considered much more reliable for purposes of assessing the model uncertainty of the two pier scour equations. The reader is referred to the NCHRP Project 24-34 Contractor’s Final Report (Lagasse et al. 2013), available at www.trb.org, for a detailed discussion of the analyses associated with the pier scour field data. 4.3 Contraction Scour 4.3.1 Clear-Water Contraction Scour Laboratory Data—Compilation and Screening The HEC-18 clear-water contraction scour equation was not developed from laboratory or field data, but instead was derived from sediment transport concepts and theory (Richardson et al. 2001). The HEC-18 clear-water contraction scour equation is: y K Q D W (4.17)2 u 2 m 2 3 2 3 7 =     y y y (4.18)s 2 0= − where: y2 = Depth of flow in contracted section after scour has occurred, ft or m Ku = Conversion factor equal to 0.0077 for U.S. customary units (0.025 for SI units) Q = Discharge in contracted section, ft3/s or m3/s Dm = Representative particle size equal to 1.25 times d50, ft or m W = Width of contracted section, ft or m ys = Depth of scour in contracted section, ft or m y0 = Depth of flow in contracted section before scour occurs, ft or m A definition sketch showing these variables is provided as Figure 4.4. Data Set No. Data Points Bias COV Percent Under- predicted Reliability ( ) Normal Lognormal All data 580 0.78 0.20 6.7% 1.42 1.29 Clear-water subset 359 0.80 0.20 9.5% 1.26 1.55 Live-bed subset 221 0.75 0.18 2.3% 1.78 1.58 Table 4.2. Bias and coefficient of variation of the Florida DOT pier scour methodology with laboratory data (all data with outliers removed).

48 Reference Guide for Applying Risk and Reliability-Based Approaches for Bridge Scour Prediction Contraction scour data obtained under controlled laboratory conditions were assembled from eight sources, yielding 182 independent measurements of contraction scour in cohesion- less soils. Only long contractions were considered, because short contractions include an abut- ment scour effect in addition to the contraction scour. A contraction is considered to be long if the length, L, of the contracted section is greater than the width, W1, of the approach section as shown in Figure 4.4 (Raikar 2004). However, comprehensive studies by Webby (1984) sug- gest that a long contraction is defined when the length, L, is twice the width of the approach section, W1. All data sets considered in this study consisted of laboratory experiments in which the following information was documented: • Scour depth, ys; • Approach flow depth, y1; • Approach flow velocity, V1; • Median sediment size, d50; • Approach width, W1; • Width of contracted section, W2; and • Length of contracted section, L. Data from 182 test runs are summarized in Dey and Raikar (2005) and were obtained from that reference. In that publication, data from other researchers (Komura 1966, Gill 1981, Webby 1984, and Lim 1993) were included along with data from the tests performed by Dey and Raikar. All 182 tests involved clear-water conditions in the approach flow (V1/Vc < 1.0), where Vc is the critical velocity for each test as determined using Equation (4.1). 4.3.1.1 Assessment of Data Quality Because of questions regarding the accuracy of some of the data provided in the Dey and Raikar (2005) table, the original work from all the previous studies was obtained and reviewed during the screening and assessment of the contraction scour data. A detailed review of previous studies found that Dey and Raikar (2005) incorrectly inter- preted the results of the tests conducted by Komura (1966), Gill (1981), and Lim (1993). Specifically, those studies did not actually measure the depth of scour in the contracted W1, q1 W2 , q2 y1, V1 y0 , V0 y2 , V2 Bed after scour Bed before scour A. PLAN B. PROFILE L Figure 4.4. Definition sketch for HEC-18 clear-water contraction scour equation.

Bridge Scour Equations and Data Screening 49 section, but instead assumed that the depth of scour was equal to the difference in flow depths, y2 – y1. Dey and Raikar reported those results as “observed scour”; however, their assumption is not valid because the drawdown effect on the water surface in the contracted section is not accounted for. Therefore, it was concluded in the review that the scour “measurements” from the studies by Komura (1966), Gill (1981), and Lim (1993) are unreliable, and those data points were discarded from further analysis. The Dey and Raikar tests that utilized well-graded bed materials also were re-examined. Although Dey and Raikar do not provide the grain size curves for the materials, they do provide the d50 grain size and the geometric standard deviation, sg, defined as d d (4.19)g 84 16 σ = For the Dey and Raikar tests using well-graded bed materials, sg ranged from 1.46 to 3.60. Further investigation revealed that when sg is greater than 1.9, a sufficient number of larger particles are present in the bed material to create a self-armoring condition that limits the depth of scour. Therefore, the Dey and Raikar tests that used well-graded bed material for which sg was greater than 1.9 were eliminated. After screening the 182 data points as discussed in this section, 119 data points remained with which to assess the HEC-18 clear-water scour equation. 4.3.2 Clear-Water Contraction Scour Laboratory Data—Analysis In practice, at a bridge the depth of flow, y0, in the contracted section before scour occurs is routinely determined by use of a water surface profile model such as HEC-RAS. However, because the laboratory data did not include a direct measurement of this flow depth (presum- ably because, in the laboratory, scour occurs before the target flow conditions are established), y0 must be estimated from available data. As a first approximation, the velocity, V0, and flow depth, y0, in the contracted section before scour occurs are estimated as: From continuity, = ≈V Q A Q y W (4.20)0 1 2 Assuming no energy losses, the specific energy in the contracted section is equal to that in the approach section, so: = + −y y 2g 2g (4.21)0 1 1 2 0 2V V V0 is then recalculated as: V Q A Q y W (4.22)0 0 2 = = For the laboratory data, this approach yielded estimates of y0 which in many cases were unreasonably small and, for a significant number of data points, negative values of y0 were obtained using this first approximation. Further investigation revealed that the contraction ratios W2/W1 in the laboratory tests were severe enough to create a “choked” condition at the

50 Reference Guide for Applying Risk and Reliability-Based Approaches for Bridge Scour Prediction entrance to the contraction. The threshold of choking occurs when the actual contraction ratio is less than the critical ratio s, defined as follows by Wu and Molinas (2005): 3 2 F F (4.23) 1 2 3 2 1 2 ( )σ = +     It was found that 113 of the 119 tests were conducted with some degree of choking. Figure 4.5 presents the dimensionless choking ratio sW2/W1 plotted versus the unit discharge in the con- tracted section. To resolve this issue, the estimate of y0 was refined by comparing the initial depth ratio, y0/y1, to the contraction ratio, W2/W1. If the depth ratio from the initial approximation was less than the contraction ratio, the depth y0 was re-estimated as y1 times the contraction ratio as a limiting condition. This second iteration yielded more reasonable values for assessing the HEC- 18 clear-water contraction scour prediction. During this process, three additional data points were identified as outliers, leaving a final data set of 116 data points for analysis. Figure 4.6 shows the results of the analysis with the final data set. The bias of the HEC-18 clear-water contraction scour equation was determined to be 0.92 as the mean value of the ratio ys (observed) to ys (predicted). The COV of the data is the standard deviation divided by the mean, determined to be 0.21 for this data set. The clear-water scour equation underpredicted the observed scour for 23.3% of the data points (27 tests out of 116). The reliability index, b, for the clear-water contraction scour equation was determined to be 0.44 and 0.52 for normal and lognormal distributions, respectively. These relatively low values of b are not surprising, considering that the HEC-18 clear-water contraction scour equation was not developed from laboratory or field data, but instead was derived from sediment transport concepts and theory. It is therefore a predictive equation, not a design equation, and as such does not have built-in conservatism. Values of b near zero indicate that, on average, observed 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 D im en si on le ss Ch ok in g Ra  o Unit Discharge q2 in Contracted Section, 3/s/ft Choked Not choked Figure 4.5. Dimensionless choking ratio vs. unit discharge in the contracted section.

Bridge Scour Equations and Data Screening 51 scour is underpredicted by about the same magnitude and frequency as it is overpredicted. Table 4.3 provides a summary of the prediction statistics for the HEC-18 clear-water contrac- tion scour equation. 4.4 Abutment Scour Data 4.4.1 Abutment Scour Laboratory Data—Compilation The analyses in this section reflect information from the final reports of NCHRP Project 24-20 (Ettema et al. 2010) and NCHRP Project 24-27(02) (Sturm et al. 2011). Both NCHRP project reports were reviewed and all laboratory data from the NCHRP Project 24-20 study were acquired. This study combines contraction and abutment scour processes to provide an estimate of the total scour at an abutment. This section presents the results of the screening and analysis of the NCHRP Project 24-20 data and includes a similar abutment scour data set (Ballio et al. 2009). Rather than analyzing abutment scour data using the Froehlich and HIRE equations (local scour only at an abutment) and developing scour factors for equations that now appear to be outdated, the predictive capability of the approach taken by NCHRP Project 24-20 and y = 1.1648x 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 y s Pr ed ic te d by H EC 18 , ys Observed ,  Dey and Raikar 2005 uniform sand Dey and Raikar 2005 uniform gravel Dey and Raikar sand, sigma < 1.9 Dey and Raikar gravel, sigma < 1.9 Webby 1984 Figure 4.6. Predicted vs. observed clear-water contraction scour. Data Set No. Data Points Bias COV Percent Under- predicted Reliability ( ) Normal Lognormal All data (clear-water) 116 0.92 0.21 23.3% 0.44 0.52 Table 4.3. Bias and coefficient of variation of the HEC-18 clear-water contraction scour equation with laboratory data (outliers removed).

52 Reference Guide for Applying Risk and Reliability-Based Approaches for Bridge Scour Prediction subsequently endorsed by NCHRP Project 24-27(02) was investigated. Although the Froehlich and HIRE equations still appear in the 5th edition of HEC-18 (Arneson et al. 2012), FHWA guidance suggests that the NCHRP Project 24-20 methodology will provide a better estimate of the combined effects of contraction scour and local scour at an abutment. NCHRP Project 24-20 developed abutment scour equations considering a range of abut- ment types, abutment locations, flow conditions, and sediment transport conditions. These equations use contraction scour as the starting calculation for abutment scour and apply an amplification factor to account for large-scale turbulence that develops in the vicinity of the abutment tip. One important distinction regarding the contraction scour calculation is that the abutment creates a non-uniform flow distribution in the contracted section. The flow is more concen- trated in the vicinity of the abutment and the contraction scour component is greater than for average conditions in the constricted opening. NCHRP Project 24-20 defines three abutment scour conditions: Scour Condition A: Scour that occurs when the abutment is in, or close to, the main channel. Scour Condition B: Scour that occurs when the abutment is on the floodplain and set well back from the main channel. Scour Condition C: Scour that occurs when the embankment breaches and the abutment foun- dation acts as a pier. NCHRP Project 24-20 concluded that there is a limit- ing depth of abutment scour when the geotechnical stability of the roadway embankment or channel bank is reached. Abutment scour conditions A, B, and C are illustrated in Figure 4.7. For purposes of this research project, Scour Condition C (in which the approach embankment is breached) is a special case and is not considered here. Notice that the abutment scour computed from the NCHRP Project 24-20 approach is total scour at the abutment; it is not added to contraction scour because it already includes contraction scour. 4.4.2 NCHRP Project 24-20 Abutment Scour Approach The NCHRP Project 24-20 approach for calculating the depth of scour at abutments uses contraction scour as the starting calculation for abutment scour and applies an amplification factor to account for large-scale turbulence that develops in the vicinity of the abutment. One important distinction regarding the contraction scour calculation is that the abutment creates a non-uniform flow distribution in the contracted section. The flow is more concentrated in the vicinity of the abutment, and the contraction scour component is greater than for average conditions in the constricted opening. The scour equations for Scour Condition A and Scour Condition B are: y y or y y (4.24)max A c max B c= α = α y y y (4.25)s max 0= − where: ymax = Maximum flow depth resulting from abutment scour, ft or m yc = Flow depth including live-bed or clear-water contraction scour, ft or m aA = Amplification factor for live-bed conditions aB = Amplification factor for clear-water conditions ys = Total scour depth at abutment, ft or m y0 = Flow depth prior to scour, ft or m

Bridge Scour Equations and Data Screening 53 Figure 4.7. Abutment scour conditions A, B, and C from NCHRP Project 24-20 (Ettema et al. 2010). 4.4.2.1 Scour Condition A If the projected length of the embankment, L, is 75% or greater than the width of the floodplain (Bf), Scour Condition A in Figure 4.7 is assumed to occur and the contraction scour calculation is performed using a live-bed scour calculation. The contraction scour equation presented in NCHRP Project 24-20 is a simplified version of the HEC-18 live-bed contraction scour equation. The equation combines the discharge and width ratios due to the similarity of the exponents because other uncertainties are more significant. By combin- ing the discharge and width, the live-bed contraction scour equation simplifies to the ratio of two unit discharges. Unit discharge, q, can be estimated either by discharge divided by

54 Reference Guide for Applying Risk and Reliability-Based Approaches for Bridge Scour Prediction width or by the product of velocity and depth. The contraction scour equation for Scour Condition A is: y y q q (4.26)c 1 2 1 6 7 =     where: yc = Flow depth including live-bed contraction scour, ft or m y1 = Upstream flow depth, ft or m q1 = Upstream unit discharge, ft 2/s or m2/s q2 = Unit discharge in the constricted opening accounting for non-uniform flow distribu- tion, ft2/s or m2/s The value of q2 can be estimated as the total discharge in the bridge opening divided by the width of the bridge opening. The value of yc is then used in Equation (4.24) to compute the total flow depth at the abutment. The value of aA is selected from Figure 4.8 for spill-through abutments and Figure 4.9 for wingwall abutments. The solid curves should be used for design. The dashed curves represent theoretical conditions that have yet to be proven experimentally. For low values of q2/q1, contraction scour is small, but the amplification factor is large because flow separation and turbulence dominate the abutment scour process. For large values of q2/q1, contraction scour dominates the abutment scour process and the amplification factor is small. 4.4.2.2 Scour Condition B If the projected length of the embankment, L, is less than 75% of the width of the floodplain, Bf, Scour Condition B in Figure 4.7 occurs and the contraction scour calculation is performed using a clear-water scour calculation. The clear-water contraction scour equation also uses unit discharge, q, which can be estimated either by discharge divided by width or by the product Figure 4.8. Scour amplification factor for spill-through abutments and live-bed conditions (Ettema et al. 2010).

Bridge Scour Equations and Data Screening 55 of velocity and depth. Two clear-water contraction scour equations may be applied. The first equation is the standard equation based on particle size: =  y q K d (4.27)c 2f u 50 1 3 6 7 where: yc = Flow depth including clear-water contraction scour, ft or m q2f = Unit discharge in the constricted opening accounting for non-uniform flow distribution, ft2/s or m2/s Ku = 11.17 English units Ku = 6.19 SI d50 = Median particle diameter with 50% finer, ft or m A lower limit of particle size of 0.2 mm is a reasonable limitation on the use of Equation (4.27) because cohesive properties increase the critical velocity and shear stress for cohesive soils that have finer grain sizes. If the critical shear stress is known for a floodplain soil, then an alternative clear-water scour equation can be used: y nq K (4.28)c c 3 7 2f u 6 7 = γ τ     where: n = Manning n of the floodplain surface material under the bridge tc = Critical shear stress for the floodplain surface material, lb/ft 2 or Pa g = Unit weight of water, lb/ft3 or N/m3 Ku = 1.486 English units Ku = 1.0 SI Figure 4.9. Scour amplification factor for wingwall abutments and live-bed conditions (Ettema et al. 2010).

56 Reference Guide for Applying Risk and Reliability-Based Approaches for Bridge Scour Prediction The value of q2f should be estimated including local concentration of flow at the bridge abut- ment. The value of qf is the floodplain flow upstream of the bridge. The value of yc is then used in Equation (4.24) to compute the total flow depth at the abutment. The value of aB is selected from Figure 4.10 for spill-through abutments and from Figure 4.11 for wingwall abutments. The solid curves should be used for design. The dashed curves represent theoretical condi- tions that have yet to be proven experimentally. For low values of q2f/qf, contraction scour is small, but the amplification factor is large because flow separation and turbulence dominate the Figure 4.11. Scour amplification factor for wingwall abutments and clear-water conditions (Ettema et al. 2010). Figure 4.10. Scour amplification factor for spill-through abutments and clear-water conditions (Ettema et al. 2010).

Bridge Scour Equations and Data Screening 57 abutment scour process. For large values of q2f/qf, contraction scour dominates the abutment scour process and the amplification factor is small. Unit discharge can be calculated at any point in the 2-D flow field by multiplying velocity and depth. Although 2-D modeling is strongly recommended for bridge hydraulic design, HEC- 18 (Arneson et al. 2012) includes a method for estimating the velocity at an abutment. This method is used to size abutment riprap, but can also be used to determine the unit discharge at an abutment. 4.4.3 Abutment Scour Data Screening and Analysis Fifty tests of abutment scour under live-bed conditions (Scour Condition A) and 12 clear- water tests (Scour Condition B) were conducted under NCHRP Project 24-20. An additional 19 clear-water tests were conducted by Ballio et al. (2009). Of the 50 live-bed tests, 6 were con- sidered outliers for which the ratio q2/q1 was less than 1.05 and the scour amplification factor was ambiguous. Of the 31 clear-water tests, 5 tests from the Ballio 2009 data set (Ballio’s Test Series D) also were considered outliers because they were conducted in a different flume and used very small particle sizes (d50 < 0.2 mm) near the silt size range, causing severe under- prediction. After this screening, 70 data points remained for analysis using the NCHRP Project 24-20 abutment scour method. Figure 4.12 shows the results of the analysis. The bias of the NCHRP Project 24-20 abutment scour equation was determined to be 0.74 as the mean value of the ratio ys (observed) to ys (pre- dicted). The COV of the data is the standard deviation divided by the mean, determined to be 0.23 for this data set. The NCHRP Project 24-20 abutment scour equation underpredicted the observed scour for 2.9% of the data points (2 tests out of 70). y = 1.279x 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Pr ed ic te d Sc ou ry s/ y 1 Observed Scour ys/y1 NCHRP 24 20 EQUATION ABUTMENT SCOUR, LABORATORY DATA Ettema spill through, Cond. A Ettema wing wall, Cond. A Ettema L/Bf < 0.75, Cond. A Ettema spill through, Cond. B Ettema wing wall, Cond. B Ballio et al., 2009 Figure 4.12. Predicted vs. observed abutment scour, 70 laboratory tests (outliers removed).

58 Reference Guide for Applying Risk and Reliability-Based Approaches for Bridge Scour Prediction The reliability index, b, for the NCHRP Project 24-20 abutment scour equation was deter- mined to be 1.53 and 1.44 for normal and lognormal distributions, respectively. These relatively high values of b reflect the fact that the curves for the amplification factors aA and aB for both spill-through and wingwall abutments (Figures 4-8 through 4-11) were developed by Ettema et al. (2010) as envelope curves for design. Although the Ballio data tend to be overpredicted by the NCHRP Project 24-20 method, it was important to include an independent data set and not rely solely on Ettema’s data. Table 4.4 provides a summary of the prediction statistics for the NCHRP Project 24-20 abutment scour procedure. Data Set No. Data Points Bias COV Percent Under- predicted Reliability ( ) Normal Lognormal All data 70 0.74 0.23 2.9% 1.53 1.44 Table 4.4. Bias and coefficient of variation of the NCHRP Project 24-20 abutment scour equations with laboratory data (outliers removed).