LIMITATIONS OF TRADITIONAL CAPACITY EQUATIONS FOR LONG CURB 1 INLETS 2 3 4 Frank E. Schalla 5 Center for Water and the Environment 6 Pickle Research Campus, Bldg 119, University of Texas, Austin, TX 78712 7 current affiliation: 8 Aqua Strategies 9 14101 US-290, Dripping Springs, TX 78620 10 Tel: 512-826-2604 11 Email: fschalla@aquastrategies.com 12 13 Muhammad Ashraf 14 Center for Water and the Environment 15 Pickle Research Campus, Bldg 119, University of Texas, Austin, TX 78712 16 Tel: 512-471-3131; Email: mashsayed@utexas.edu 17 18 Michael E. Barrett 19 Center for Water and the Environment 20 Pickle Research Campus, Bldg 119, University of Texas, Austin, TX 78712 21 Tel: 512-471-3131; Email: mbarrett@mail.utexas.edu 22 23 Ben R. Hodges - corresponding author 24 Center for Water and the Environment 25 Pickle Research Campus, Bldg 119, University of Texas, Austin, TX 78712 26 Tel: 512-471-3131; Email: hodges@utexas.edu 27 28 29 Word count: 4627 words text + 9 tables/figures x 250 words (each) = 6877 words 30 31 32 33 34 35 36 Submission Date: July 29, 2016 37 38

Schalla, Ashraf, Barrett, Hodges 2 ABSTRACT 1 Recent work with full-scale experiments indicates that there are fundamental problems with the 2 standard curb inlet design equations when applied to depressed curb inlets on the order of 10 ft 3 (3 m) or longer. Observations from a full-scale laboratory experiment show that the latter part of 4 a long inlet does not have a simple linear water surface profile at 100% interception, which is 5 assumed for the form of Izzard’s equation that is adopted for many common design approaches 6 (including the HEC-22 design equations recommended by FHWA). For a long inlet, thin flow 7 sheets were observed for a substantial portion of the inlet length, which is consistent with some 8 prior observations that have not been incorporated into standard design equations. Experimental 9 results indicate that the HEC-22 design equations significantly overestimate the interception 10 capacity of long, depressed curb inlets for an on-grade gutter. This issue has potential safety 11 implications as the gutter bypass and spread for a design storm will be larger than expected for 12 such inlets. The present work is preliminary, so an L2 measure previously proposed by Izzard is 13 recommended as a maximum inlet length pending the outcome of further studies. 14 15 Keywords: Curb inlet, storm drain, full-scale, interception capacity 16 17

Schalla, Ashraf, Barrett, Hodges 3 INTRODUCTION 1 Curb inlets are sized and placed along a road to maintain a safe spread of water from the curb to 2 reduce the chances of vehicle hydroplaning. Accuracy of curb inlet interception equations is a 3 critical issue for safe roadway design as overprediction of the interception will lead to roads with 4 greater inlet bypass (more gutter flow downstream of an inlet) and a larger spread from the curb 5 than desired. Localized flooding due to inadequate inlet capacity is not uncommon during high-6 intensity convective thunderstorms, but such flooding is typically attributed either to storms 7 beyond the design conditions or watershed runoff changes caused by post-design development. 8 However, similar problems would result if a fundamental inaccuracy in the design equations 9 caused undersizing of curb inlets. In particular, design for high-intensity storms requires either 10 longer curb inlets or a larger number of shorter inlets than an equivalent design for low-intensity 11 rainfall. Because the cost of curb inlet installation is typically driven by the number of inlets 12 rather than their size, there is an economic bias towards using the fewest number of inlets with 13 the longest possible openings that still maintain acceptable ponding behavior. In this paper, we 14 show that standard design equations for long, depressed curb inlets for an on-grade gutter will 15 significantly overpredict the curb inlet interception at design conditions. That is, the design 16 equations for 100% interception are perfectly adequate for common 5 ft depressed curb inlets 17 (under most conditions), but can be dramatically wrong for the 10 ft and 15 ft inlets that are 18 typically used where increased capacity is desired. It follows that present design methods for 19 long depressed inlets can lead to larger bypass flows and greater spread across the roadway than 20 are either expected or safe. 21 Storm-water runoff on roadways is typically collected and conveyed to subsurface pipes 22 using storm drain inlets, including the common curb-opening inlet. Such inlets are vertical 23 openings in the curb that are covered by a top slab. These are assumed to provide weir-like flow 24 into a vault under design conditions. Curb-opening inlets are commonly used instead of 25 horizontal gratings as the inlets are less susceptible to clogging by debris, pose minor 26 interference to traffic operation, and are safe for pedestrians and cyclists (1). The hydraulic 27 design for curb inlet installation requires prediction of the inlet interception (i.e. maximum gutter 28 flow rate captured with zero or minimal bypass) as a function of the installation configuration 29 (road cross-slope and longitudinal slope). 30 Inlet interception increases by increasing the inlet length, roadway cross slope, and 31 roadway roughness. Conversely, the inlet interception decreases by increasing the roadway 32 longitudinal slope (2). Experiments have also shown that depressing the gutter section at an inlet 33 also increases the inlet’s interception (3, 4). Another method of increasing the design inlet 34 interception is by allowing a small portion of the flow in the gutter to bypass the inlet. Because 35 of nonlinearity in the inlet equations, allowing a small bypass flow (< 5%) typically increases the 36 inlet interception greater than the bypassed amount, thus leading to a more cost-effective overall 37 configuration for a series of inlets (5, 6). 38 Curb inlet equations in the literature fall into two major categories: equations based 39 solely on empirical data fit to experiments (e.g., 7, 8), and equations based on theory with 40 empirical coefficients (e.g., 9, 10). Strictly speaking, equations based solely on fits to empirical 41 data should be applied only to inlets matching the tested configuration for road slope, inlet 42 length, and the range of flow conditions. In contrast, equations based on theory with well-43 behaved empirical coefficients can be applied to a wider range of cases, but care still must be 44 taken when extrapolating beyond the tested conditions. Both types of equations are developed 45 using experiments over a wide range of flow bypass conditions, but show the best data fit at high 46 bypass (low efficiency) conditions rather than at design low bypass conditions (e.g. 11). The 47

Schalla, Ashraf, Barrett, Hodges 4 validity of the design equations for zero bypass is an important consideration for design 1 conditions where the bypass must be strictly limited (e.g. upstream of road intersections). 2 Hydraulic Engineering Circular No. 22 (HEC-22) contains the FHWA's guidelines and 3 recommended design procedures (1), which are widely used in design of roadway drainage (9). 4 The curb inlet length to capture 100% of the approaching gutter flow in an undepressed gutter 5 section in HEC-22 is: 6 7

LT= Ku Qg0.42 SL

0.3 1nSx

0.6

(1) 8 9 where Ku=0.82 (SI) or 0.6 (US customary), Qg is the flow rate in the gutter upstream the inlet 10 (cfs or m3/s), SL is the longitudinal slope of the roadway, n is the Manning’s roughness 11 coefficient of the roadway, and Sx is the cross slope of the roadway. The HEC-22 equation has 12 slightly different coefficients but is similar in form to the theoretical equation with empirical 13 coefficients develop by Izzard (12), which is: 14 15

LT= K Qg0.44 SL

0.28 1nSx

0.56

(2) 16 17 where K=1.51 (SI) or 1.03 (US customary) and other terms as in Eq. (1). 18 Izzard’s classic approach treated flow into the inlet opening as flow over a broad-crested 19 weir with three fundamental assumptions: First, the transverse velocity component in the 20 approach flow is assumed negligible and cannot increase flow over the inlet lip. Second, the 21 energy head at the upstream end of the inlet is equal to the depth of the approach flow (or the 22 head is equal to the flow depth plus the depth of depression in case of inlet with depressed 23 gutter), which is effectively an assumption that the kinetic energy of the gutter flow is negligible. 24 Third, and most importantly, that there is a linear decrease in water profile along the length of 25 the inlet so that the depth at any point along the inlet opening is immediately calculable from the 26 depth at the upstream end of the inlet. From the latter it also follows that the head is equal to zero 27 at the end of the inlet for 100% capture. Izzard’s equation was calibrated using curb inlet 28 experiments that included 1:2 and 1:3 scaled models. 29 A critical missing piece in the design equations for depressed inlets appears to be the lack 30 of consideration of length scale L2 (ft), which was defined in Izzard’s later work (19) as: 31 32 L2=3.67FwTW-1/6Sx (3) 33 34 where W is the width of the depression (ft), Fw is the upstream Froude number in the gutter 35 computed at W, and T is the upstream spread (ft). Izzard (19) observed a breakpoint in inlet 36 behavior that occurred when Li > L2, where Li is the installed inlet length. For the section of the 37 curb inlet beyond L2, the flow interception was observed to drop off sharply. It follows that the 38 fundamental assumption of a single linear water surface profile is invalid for inlets whose 39 operating conditions provide Li > L2, which includes the LT equations (above) of Izzard (12) and 40 HEC-22. Unfortunately, the majority of curb inlet studies since 1977 have not cited or 41 considered Izzard (19). In the few works that cited (19), the breakpoint in water surface profiles 42 is not discussed, e.g. (9, 10, 20, 21). Interestingly, FWHA produced a design document in 1979 43 (22) including the breakpoint analysis, but it was removed in HEC-22. 44

Schalla, Ashraf, Barrett, Hodges 5 Many prior experiments have used reduced-scale physical models based on Froude-1 number scaling, e.g., scales of 1:4, 1:3 and 3:4, respectively (9, 10, 11). However, scaling has 2 recently been discussed as a possible reason for significant discrepancies in equation predictions 3 (13, 14). The present study uses full-scale physical models of 5 ft, 10 ft, and 15 ft (1.5 m, 3 m, 4 4.5 m) on-grade curb inlets to test the validity of HEC-22 equations for 100% capture using a 5 range of flow conditions with both Li > L2 and Li < L2 to examine the importance of L2 in 6 computing inlet capacity. 7 8 METHODS9 Physical model10 A physical model of a roadway that can be adjusted for longitudinal and cross slopes was 11 constructed in the early 1990s for a Texas Department of Transportation (TxDOT) study (15). 12 The model is located at the Center for Water and the Environment (formerly Center for Research 13 in Water Resources) laboratory on the J.J. Pickle Research Campus of The University of Texas 14 at Austin. The physical model has a length of 64 ft (19 m), an operational surface width of 10.5 ft 15 (3.2 m), and an on-grade gutter with a curb along the long edge. The physical model has a steel 16 structure supporting the wood deck, curbs, and headbox. One corner rests on a ball bearing that 17 provides a pivot point that allows hoists at the other corners to be used to adjust the cross slope 18 and longitudinal slope. 19 Figure 1 shows the overall layout of the physical model, which has been somewhat 20 modified from the original study of (15). Water is conveyed from an exterior tank by 2 pumps 21 operating in parallel. The pumps were designed to discharge up to 7 cfs (0.2 m3/s). A nominal 22 12 in. (30 cm) diameter pipe provides the water supply into a manifold with five pipes, each with 23 a ball valve, which allows controlled distribution of the flow across the width of the upstream 24 headbox. Water entering the roadway can be further modulated by adjusting hollow concrete 25 blocks in front of the headbox. The road surface is sealed with layers of fiberglass and resin, and 26 is textured with a mean diameter particle size of 1.3 mm (0.051 in). Recent calculations 27 performed by Qian et al. (16) show an average Manning’s roughness coefficient of 0.0166. Tests 28 were conducted during the present study to confirm this roughness value. The curb inlet test 29 section consists of three modules, each of length 5 ft, (1.524 m) for modeling inlets of 5, 10, and 30 15 ft (1.524, 3.048, 4.572 m). This arrangement mimics typical inlet openings used by TxDOT. 31 Figure 1 shows the configuration for a single inlet module, which directs the flow from the inlet 32 to the center approach channel and a V-notch measurement weir. When a second or third inlet 33 module is used, their flows are directed to two adjacent approach channels and separate 34 measurement weirs so that the flow in each section of the inlet can be measured. A fourth 35 downstream weir is used to measure bypass flow. The modeled curb inlet is a standard depressed 36 inlet that is 3 in. (7.62 cm) below the upstream on-grade gutter. From the on-grade gutter to 37 depressed inlet, transitions of 16 in. (0.406 m) width over 10 ft (3.05 m) length and 3 in (7.62 38 cm) depression were installed upstream and downstream of the inlet. The roadway surfaces for 39 the curb inlet and gutter transitions were textured and sealed by layering epoxy sealant and 40 graded sand to obtain the same roughness as the roadway. Further details on the physical model 41 are reported by Schalla (17). 42 43 Validation procedures 44 The headbox was designed to provide a smooth approach flow with a pipe manifold, concrete 45 blocks to redistribute flow, and an adjustable undershot gate that can be set with either a 46 triangular or rectangular opening. To test the sensitivity of the model results to the headbox 47

Schalla, Ashraf, Barrett, Hodges 6 configuration a set of ten tests were performed. For each test, the headbox configuration was 1 changed by adjusting the concrete blocks and the length of the undershot gate opening, while 2 keeping the other conditions of the test the same (road slopes and inflow). The mean captured 3 flow from all tests was 2.99 cfs (0.847 m3/s) with a standard deviation of 0.06 cfs (0.0017 m3/s) 4 and a maximum difference of 7%. These results were relatively insensitive to the headbox 5 configuration. The selected headbox configuration produced a consistent spread upstream of the 6 curb inlet to achieve an equilibrium spread upstream of the transition into the depressed curb. 7 Further details on validation tests, including roughness evaluation, are reported by Schalla (17). 8 9

10 11 FIGURE 1 General layout of the physical model, shown for a single inlet module. 12

Schalla, Ashraf, Barrett, Hodges 7 Experiments 1 The experiments (Table 1) used five longitudinal slopes, three cross slopes, three inlet 2 configurations, and four bypass flows. However, only 128 of the 180 possible experiments 3 implied by these factors were practical. Some slope combinations required flows in excess of the 4 system pump capacity and thus could not be conducted. Details on the specific experiments are 5 reported by Schalla (17). Some test runs for 10 ft and 15 ft inlets were repeated with and without 6 slab supports between the 5 ft inlet modules, but this proved to have a relatively minor effect on 7 interception as reported in Schalla (17). The flow Froude number (based on the depth and 8 average velocity of the flow at beginning of the upstream transition to the depressed inlet) ranged 9 from 0.66 to 2.49 in the different experiments. 10 11 TABLE 1 Experimental configurations 12 13

Property Tested Conditions Longitudinal slope (%) 0.1, 0.5, 1.0, 2.0, 4.0 Cross slope (%) 2.0, 4.0, 6.0 Inlet configuration (# of 5 ft sections) 1, 2, 3 Flow Rate Conditions 100% interception; bypass (0.1, 0.3, 0.5 cfs)

14 The flow rate at 100% interception was determined by slowly increasing the pumped 15 flow rate until a bypass flow was achieved, and then decreasing the flow until only a small 16 trickle of bypass flow was occurring. Experiments with non-negligible bypass flow rates were 17 obtained by slowly increasing the flow rate until the flow measurement at the bypass weir 18 provided the desired value. Figure 2 shows water flowing into the inlet during a test run. 19 20

21 22

FIGURE 2 Model during a test run with 15 ft inlet and two slab supports. 23 24

Schalla, Ashraf, Barrett, Hodges 8

For each test run we collected data on flow rate, water spread, and water depth. Flow rate 1 measurements were taken from each V-notch weir once a steady flow had been achieved 2 (typically about 10 to 30 minutes). Water spread measurements from the curb and inlet, were 3 collected every 2.0 ft (0.61 m) along the roadway starting 18 ft (5.5 m) upstream of the curb inlet 4 to 5 ft (1.5 m) downstream of the end of the curb inlet. These spread measurements were 5 perpendicular to the curb from the curb edge to the edge of the water surface on the roadway. 6 Water depth was measured at 3 locations upstream of the gutter depression transitions at one of 7 the water spread measurement locations. 8

9 RESULTS 10 The experimental results are compared to the predicted HEC-22 equation for 100% interception 11 as implemented in the Hydraulic Toolbox software program developed by FHWA (18). In the 12 Hydraulic Toolbox, the inlet location option was set to Inlet on grade, the local depression was 13 set to zero, and the gutter depression was set to 3 in. (7.62 cm) by entering the corresponding 14 value of the gutter cross-slope. The results of the Hydraulic Toolbox were further confirmed by 15 developing a computer code based on the original design equations provided by HEC-22. 16 Figure 3 shows that our observations and HEC-22 compare reasonably well for a 5 ft 17 inlet, except for configurations with small longitudinal slopes (0.1%) combined with large cross 18 slopes (4%, 6%) where HEC-22 predicts significantly higher interception flows than we 19 observed. These two high flow predictions, as shown in Figure 4, are clearly outliers in the 20 comparison. If these two experiments are neglected, the the root mean square difference (RMSD) 21 between experiment and HEC-22 equation is 0.33 cfs (0.0093 m3/s), which is reasonable 22 agreement for the tested conditions. If we include the outliers, the RMSD is 0.73 cfs (0.021 23 m3/s), which significantly overstates the variability for the tests at larger longitudinal slopes. 24 Note that if we exclude the outliers, then 50% of the experiments show interception somewhat 25 greater than predicted by HEC-22 and 50% of the experiments show interception somewhat 26 smaller than predicted. Thus, the scatter of the 5 ft inlet experiments about the HEC-22 equation 27 does not have detectable bias. 28 29

30 31

FIGURE 3 Comparison of HEC-22 and experiment for 5 ft inlet at 100% interception. 32 33

Schalla, Ashraf, Barrett, Hodges 9

1 2

FIGURE 4 Comparison of HEC-22 and experiment for 5 ft curb inlet at 100% 3 interception. 4 5 Figure 5 shows that observations with a 10 ft inlet significantly diverge from the HEC-22 6 predictions. Although the comparison is clearly worse for the small longitudinal slopes 7 combined with large cross slopes (i.e. similar to the 5 ft inlet), we can no longer call these 8 conditions outliers as they appear to be part of a trend of increasing disagreement with increasing 9 cross slope. The critical point is that all 10 ft inlet experiments show HEC-22 overpredicts the 10 observed interception. Indeed, even if we exclude the experiments that were outliers for the 5 ft 11 inlet, the RMSD for the 10 ft inlet is 2.04 cfs (0.058 m3/s), which is questionable agreement. 12 13

14 15 FIGURE 5 Comparison of HEC-22 and experiment for 10 ft curb inlet at 100% 16 interception. 17

Schalla, Ashraf, Barrett, Hodges 10 Figure 6 for the 15 ft inlet shows that the trend describe above is continued, with the 1 increased length of the inlet resulting in an increasing difference between the HEC-22 equation 2 and experimental observations. Again, HEC-22 overpredicts the flow rate at 100% interception 3 for all tested conditions. Note that the test conditions that provided the outliers in the 5 ft inlet 4 experiments could not be tested in the 15 ft inlet configuration due to the limitations of the 5 pumping system. For the 15 ft inlet, the RMSD between experiment and equations is 4.2 cfs 6 (0.119 m3/s), which is a significant disagreement. 7 8

9 FIGURE 6 Comparison of HEC-22 and experiment for 15 ft curb inlet at 100% 10 interception. 11 12 DISCUSSION 13 The design equations for HEC-22 align with physical experiments for most of the 5 ft curb inlet 14 experiments but overpredict curb inlet interception for the longer 10 ft and 15 ft curb inlets. The 15 key to understanding this problem appears to lie with the original Izzard (12) approximation of 16 the water surface profile as linear over the length of the inlet, which is also the basis for the 17 HEC-22 equations. The later work of Izzard (19) indicate this approximation is limited. The 18 approximation is arguably reasonable in most high bypass (low efficiency) conditions where 19 there is substantial water depth at the downstream end of the inlet. Hence, the excellent 20 agreement between theory and observations for most models under high bypass conditions and 21 the larger scatter that is typically observed at low bypass or full interception. Figure 7 shows the 22 observed water surface profile and the profile predicted for a linear water surface profile for the 23 15 ft inlet at full interception from one of the experiments in the present work. Clearly, the 24 profile is approximately linear over the initial 3 ft (0.9 m), but then becomes a thin layer across 25 the remaining inlet length. Relatively little interception occurs across the majority of the inlet, 26 which accounts for the discrepancy between the large interception prediction of the HEC-22 27 equations and the small interception of the observations. 28 The results herein are similar to observations of a breakpoint in the water surface profile 29 observed by Izzard (19), which is associated with the L2 length of Eq. (3). We can define a non-30 dimensional length parameter for the water surface profile at 100% interception as γL = L2 / Li, 31 where Li is the inlet length. Based on the prior arguments in (19), for γL ≥ 1 the water surface 32

Schalla, Ashraf, Barrett, Hodges 11

1 2 FIGURE 7 Water surface profile (measured from the depressed inlet’s opening) along the 3 length of the curb inlet opening at full interception for 15 ft inlet with SL=2%, Sx=2%. 4 5 profile is expected to follow the approximations Eqs. (1) or (2) for LT. Where γL < 1, the standard 6 equations are expected to fail. These ideas are tested against the experiments in Figure 8, which 7 shows γL vs. the relative prediction error, defined as ε = (QT - Qo)/QT where QT is the predicted 8 100% interception flow rate using HEC-22 and Qo is the observed 100% interception flow rate. 9 Overprediction error (ε > 0) is a maximum for γL < 0.5, and decreases towards zero as γL → 1. 10 Interestingly, there are under-prediction errors (ε < 0) that increase in the negative direction for 11 1< γL < 1.2. Thus, the fundamental approach of HEC-22 and (12) is indeed incorrect for γL < 1, 12 which was the argument in (19), but is also unexpectedly incorrect when γL > 1. That is, the 13 HEC-22 equations are only an unbiased estimate of inlet capacity when γL ~ 1. The HEC-22 14 equations are biased to underestimate the inlet capacity for γL > 1 and overestimate the inlet 15 16

17 18 FIGURE 8 Relative prediction error (ε) corresponding to the water surface length 19 parameter (γL ) for tests at 100% interception condition. 20

Schalla, Ashraf, Barrett, Hodges 12 capacity for γL < 1. The consistency of these results indicates that the Izzard (19) breakpoint 1 represents missing physics in the standard curb inlet equations. This effect has perhaps been 2 previously masked by the curve-fitting approaches for empirical coefficients in curb inlet 3 equations. These curve fits typically have larger scatter at low bypass conditions than at high 4 bypass conditions. Note that the 5 ft inlet experiments that were considered outliers in Figure 4 5 have γL < 1 due to the very small slope. These results are indistinguishable from other results on 6 the trend line in Figure 8. Hence these “outliers” provide further confirmation of the importance 7 of the missing physics inherent in the relationship between L2 and Li. 8

The most important observations that can be drawn from this study are (i) longer 9 depressed inlets (Li > L2) provide significantly lower design interception flows than predicted by 10 HEC-22, (ii) longer depressed inlets with 100% interception might not be effective for increasing 11 overall drainage capacity of a roadway, and (iii) HEC-22 equations underestimate the inlet 12 capacity for shorter depressed inlets (Li < L2). Note that the work reported herein is from 13 experiments with only a single type of depressed curb inlet operating near design capacity (zero 14 bypass) with an on-grade gutter. We have not addressed the wide variety of non-depressed curb 15 inlets or behaviors when the design capacity is exceeded (i.e. high bypass). The observed 16 behavior herein is similar to the analyses in (19), although our analyses show the error increases 17 on either side of the breakpoint defined in (19), implying that the HEC-22 approach is unbiased 18 only when Li ~ L2. As overprediction can be systemically more troublesome than under-19 prediction, designers should maintain γL ≥ 0.95. Thus, until further work is completed, road 20 drainage designers should compute the L2 using Eq. (3) for the design flow and the installed inlet 21 lengths (Li) should be no more than 5% longer than L2. 22

23 SUMMARY AND CONCLUSIONS 24 Full-scale physical models of 5, 10, and 15 ft curb inlets were constructed and tested for a range 25 of flow and roadway slope configurations. Results were compared against HEC-22 design 26 equations and showed good agreement for the 5 ft inlet (except for extremely small longitudinal 27 slopes), but progressively worse agreement with longer inlets. For the long inlet conditions 28 tested, the HEC-22 equations always overpredict the 100% interception capacity. The 29 overpredictions are significant and cannot be ignored in drainage design. The principal 30 deficiency in the existing equations appears to be the assumption of a linearly decreasing water 31 surface over the entire length inlet, which neglects the breakpoint previously identified by Izzard 32 (19) that affects inlets where the installed inlet is longer than a characteristic length scale (L2). 33 Further work is required to understand the complex fluid dynamics and to provide improved 34 design equations that accurately reflect their observed interception. Until such work is completed 35 and further guidance can be provided, designers are advised to consider the L2 length scale as the 36 longest practical inlet for which HEC-22 equations are valid. 37 38 ACKNOWLEDGEMENTS 39 The work presented in this study was supported by the Texas Department of Transportation, 40 Research and Technology Implementation Office in coordination with the Center for 41 Transportation Research at the University of Texas at Austin. Note that this paper includes both 42 text and figures abstracted and edited from the M.S. thesis of the first author (17), which are used 43 without further attribution or quotation. 44 45

Schalla, Ashraf, Barrett, Hodges 13 REFERENCES 1 1. Brown, S.A., J.D. Schall, J.L. Morris, C.L. Doherty, S.M. Stein, and J.C. Warner. Urban 2

Drainage Design Manual. Hydraulic Engineering Circular 22 (HEC-22), Third Edition. 3 U.S. Department of Transportation, Federal Highway Administration Publication No. 4 FHWA-NHI-10-009, September 2009, Revised August 2013. 5

2. Jens, S. W. (1979). Design of Urban Highway Drainage. FHWA Pub. No. TS-79, 225. 6 Chicago, 1979. www.fhwa.dot.gov/engineering/hydraulics/pubs/ts79_225.pdf. Accessed 7 Jul. 5, 2016. 8

3. Karaki, S. S. and Haynie, R. M., Depressed curb-opening inlets supercritical flow - 9 experimental data. Colorado State University Research Foundation, Civil Engineering 10 Sec., Ft. Collins, Colorado, 1961. 11

4. Storm Drainage Research Committee, The Design of Storm-water Inlets. Johns Hopkins 12 University Baltimore, Maryland, 1956. 13

5. Conner, N.W., Design and capacity of gutter, Proceedings, Highway Research Board, 14 Vol. 25, 1945, pp. 101-104. 15

6. Larson, C. L., Experiments on flow through inlet gratings for street gutters. Highway 16 Research Board Research Report, 6-B, Washington, D. C., 1948, pp. 17-29. 17

7. MacCallan, R.M. and R.H. Hotchkiss. Hydraulic Efficiency of Highway Stormwater 18 Inlets - Final Report. Research Report NE-DOT-R-96-1, Department of Civil 19 Engineering, University of Nebraska-Lincoln, 1996, 140 pgs. 20

8. Fiuzat, A. A., C. E. Soares, and B. L. Sill. Design of Curb Opening Inlet Structure. 21 Iranian Journal of Science & Technology, 2000, 24:11-21. 22

9. Hammonds, M.A. and E. Holley. Hydraulic Characteristics of Flush Depressed Curb 23 Inlets and Bridge Deck Drains. Research Report 0-1409-01, Center for Transportation 24 Research, University of Texas at Austin. December 1995. 171 pgs. 25

10. Uyumaz, A. Urban Drainage with Curb Opening Inlets. Global Solutions for Urban 26 Drainage, Proceedings of the Ninth International Conference on Urban Drainage, 27 Portland, Oregon (USA), September 8-13, 2002, 9 pgs. 28

11. Guo, J.C.Y. and K. MacKenzie. Hydraulic Efficiency of Grate and Curb-Opening Inlets 29 Under Clogging Effect. Report No. CDOT-2012-3. Colorado Department of 30 Transportation, DTD Applied Research and Innovation Branch, April 2012, 92 pgs. 31

12. Izzard, C. F. Tentative results on capacity of curb opening inlets, with discussion. 32 Highway Research Board, Research Report No. 11-B, December 1950, pp. 36-54. 33

13. Comport, B.C. and C.I. Thornton. Hydraulic efficiency of grate and curb inlets for urban 34 storm drainage. ASCE Journal of Hydraulic Engineering, 2012, 138:10:878:884. 35

14. Russo, B. and Gómez, M. Discussion of Hydraulic Efficiency of Grate and Curb Inlets 36 for Urban Storm Drainage by Brendan C. Comport and Christopher I. Thornton. ASCE 37 Journal of Hydraulic Engineering, 2014, 140:1:121-122. 38

15. Holley, E.R., C. Woodward, A. Brigneti, and C. Ott. Hydraulic Characteristics of 39 Recessed Curb Inlets and Bridge Drains. Research Report FHWA/TX-03+1267-1F, 40 Center for Transportation Research, University of Texas at Austin. 1992, 89 pgs. 41

16. Qian, Q., X. Liu, R. Charbeneau, and M. Barrett. Hydraulic Performance of Small Scale 42 Bridge Deck Drains, Report FHWA/TX-12/0-6653-1. Center for Transportation 43 Research, University of Texas at Austin. 2013, 112 pgs. 44

17. Schalla, F. E. Effects of flush slab supports on the hydraulic performance of curb inlets 45 and an analysis of design equations. MSc thesis, University of Texas at Austin, Texas, 46 USA. http://hdl.handle.net/2152/39077. Accessed Jul. 1, 2016. 47

Schalla, Ashraf, Barrett, Hodges 14 18. Hydraulic Toolbox. Computer software. Vers. 4.2. Federal Highway Administration. 1

https://www.fhwa.dot.gov/engineering/hydraulics/software/toolbox404.cfm. Accessed 2 Nov. 10, 2015. 3

19. Izzard, C.F. "Simplified method for design of curb-opening inlets." Transportation 4 Research Record 631, 1977. 5

20. Uyumaz, A., “Discharge capacity for curb-opening inlets,” ASCE Journal of Hydraulic 6 Engineering, 1992, 118:7:1048-1051. 7

21. Thompson, D., X. Fang, and G.-C. Om Bahadur. Synthesis of TxDOT Storm Drain 8 Design. Project Report 45553-1, Center for Multidisciplinary Research in 9 Transportation, Texas Tech University, Lubbock, TX. Oct. 2003. 157 pgs. 10

22. Jens, S. W. "Design of urban highway drainage." FHWA Pub. No. TS-79 225, 1979. 11