Revised Clear-Water and Live-Bed Contraction Scour Analysis Training Manual (2021) / Chapter Skim
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APPENDIX Workshop Lesson Schedule
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9 LESSON SCHEDULE REVISED CONTRACTION SCOUR ANALYSIS Session Time Topic (min) Part I Session 1 (30)
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10 REVISED CONTRACTION SCOUR ANALYSIS PART I LEARNING OUTCOMES 1. Describe contraction hydraulics and scour, and current evaluation techniques.
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11 REVISED CONTRACTION SCOUR ANALYSIS WORKSHOP LESSON PLAN FOR PART I Session Title: Revised Contraction Scour Analysis Workshop (Part I) Performance-Based Learning Outcomes: At the end of Part I, Participants will be able to: • Describe contraction hydraulics and scour, and current evaluation techniques • Identify the quality and shortcomings of existing laboratory and field data Topics: • Contraction hydraulics and scour – current practice • Evaluation of existing laboratory and field data Instructional Method: Classroom discussion/presentation consists of three Sessions based on PPT presentations, discussion of contraction hydraulics, and current practice for evaluating contraction scour.
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12 Time Allotment: 165 Minutes • Introduction and Learning Outcomes (30 minutes) • Contraction scour hydraulics and current practice (60 minutes)
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13 LEARNING OUTCOMES (PART I) • Describe contraction hydraulics and scour, and current evaluation techniques.
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14 NCHRP Project 24-47 Revised Clear-Water and Live-Bed Contraction Scour Analysis Objectives "Develop live-bed and clear-water contraction scour equations suitable for use in risk-based bridge design encompassing a wide range of hydraulic conditions including varying contraction ratios." I-2 Key Message: Objectives of NCHRP Project 24-47. Background Information: Lagasse, P., Ettema, R., DeRosset, W.M., Nowroozpour, A., Clopper, P.E., NCHRP Research Report 971: Revised Clear-Water and Live-Bed Contraction Scour Analysis, Transportation Research Board, Washington, D.C., 2021.
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15 I-3 Key Message: Scour is the erosion of bed and bank material due to flowing water. Background Information: FHWA Hydraulic Engineering Circular HEC-18, "Evaluating Scour at Bridges," Fifth Edition, FHWA-HIF-12-003, Washington, D.C., 2013.
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16 TYPES OF SCOUR • Clear-water – No transport of bed material from upstream • Live-bed – Bed material from upstream is transported into the bridge crossing I-4 Key Message: Scour can be either clear-water or live-bed. Background Information: FHWA Hydraulic Engineering Circular HEC-18, "Evaluating Scour at Bridges," Fifth Edition, FHWA-HIF-12-003, Washington, D.C., 2013.
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17 CONTRACTION SCOUR I-5 Key Message: This slide introduces the topic of contraction scour and the first step in analyzing contraction scour – determining critical velocity for particle motion. Background Information: Contraction scour is caused by a constriction of the flow area as water moves through the bridge opening.
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18 I-6 Key Message: The I-5 bridge site helps convey the concept of a constriction or contraction at a bridge crossing. Background Information: See Lessons 11 and 12 of the NHI 135046 course for discussion of I-5 bridge failure.
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19 CONTRACTION SCOUR CLARIFIED • Approach flow hydraulics • Contraction flow hydraulics I-7 Key Message: Channel contraction conditions can be categorized into two sets of conditions. Background Information: Ettema, R., et al.
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20 Instructional Method: Tell (continued) : Approach Flow Hydraulics • Froude number • Choking (or not)
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21 CONTRACTION HYDRAULICS • Short contraction • Long contraction • Choked flow at the contraction entrance I-8 Key Message: Water surface profiles for contraction hydraulics with fixed-bed conditions. Background Information: Ettema, R., et al.
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25 Facilitate a discussion that should cover some of the following points: • Severe contraction ratio, i.e., the bridge is too narrow for the waterway. • Choked flow can occur at bridges in the field (e.g., when ice or debris clogs a bridge opening)
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27 FURTHER COMPLICATIONS • Flow separation • Bed roughness • Sorting of particle size along the contraction • Live-bed contraction scour • Scour in an intermediate contraction – entrance and exit conditions I-13 Key Message: Factors that lead to further complications in the analysis of contraction scour. Background Information: Ettema, R
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28 • Scour of the bed along a contraction of intermediate length may begin at two locations, and then work toward the middle reach of the contraction. This process (scour working from both ends of a contraction)
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29 I-14 Key Message: The live-bed contraction scour equation is derived by applying the principle of sediment continuity from an upstream section (1) to the bridge section (2)
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30 I-15 Key Message: The clear-water contraction scour equation is derived by considering shear stress in the bridge section. As contraction scour develops, shear stress decreases to the point that the particles are no longer mobile.
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31 LEARNING OUTCOME (PART I SESSION 3) • Identify the quality and shortcomings of existing laboratory and field data.
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32 SELECTED STUDIES ON CLEAR-WATER CONTRACTION SCOUR • Laursen & Toch 1956 • Laursen 1963 • Gill 1981 • Webby 1984 • Dey & Raikar 2005 I-17 Key Message: This slide presents a sample of the major studies on clear-water contraction scour, some of which used laboratory data. Background Information: Lagasse, P., Ettema, R., DeRosset, W.M., Nowroozpour, A., Clopper, P.E., NCHRP Research Report 971: Revised Clear-Water and Live-Bed Contraction Scour Analysis, Transportation Research Board, Washington, D.C., 2021.
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33 • Dey and Raikar conducted 131 laboratory experiments in which a wide variety of parameters were varied. They did not provide direct measurements of Y2, and 123 of the 131 data points were under choked flow conditions.
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34 SELECTED STUDIES ON LIVE-BED CONTRACTION SCOUR • Straub 1934 • Laursen 1960 • Komura 1966 • Gill 1981 • Dey & Raikar 2006 I-18 Key Message: This slide presents a sample of the major studies on live-bed contraction scour, some of which used laboratory data. Background Information: Lagasse, P., Ettema, R., DeRosset, W.M., Nowroozpour, A., Clopper, P.E., NCHRP Research Report 971: Revised Clear-Water and Live-Bed Contraction Scour Analysis, Transportation Research Board, Washington, D.C., 2021.
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35 HEC-18 CLEAR-WATER VARIABLES I-19 Key Message: Definition sketch of variables in the HEC-18 clear-water contraction scour equation. Background Information: Lagasse, P., Ettema, R., DeRosset, W.M., Nowroozpour, A., Clopper, P.E., NCHRP Research Report 971: Revised Clear-Water and Live-Bed Contraction Scour Analysis, Transportation Research Board, Washington, D.C., 2021.
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36 provide an acceptable level of reliability in the context of the Load and Resistance Factor Design (LRFD) bridge design procedures.
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37 EVALUATION OF CONTRACTION SCOUR LABORATORY DATASETS • No measurements of the depth of flow • Assumptions on the depth of flow • Most studies done under clear-water conditions I-20 Key Message: Major issues with existing contraction scour datasets. Background Information: Lagasse, P., Ettema, R., DeRosset, W.M., Nowroozpour, A., Clopper, P.E., NCHRP Research Report 971: Revised Clear-Water and Live-Bed Contraction Scour Analysis, Transportation Research Board, Washington, D.C., 2021.
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38 Previous Studies (Webby 1984) What was y0 before scour?
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39 Instructional Method: Tell: Webby studied clear-water contraction scour in a "long contraction." Regarding Slide I-21, a contraction was considered to be long if the length, L, of the contracted section is greater than the width, W1, of the approach section. However, Webby's comprehensive studies suggest that a long contraction is defined when the length, L, is twice the width of the approach section, W1.
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40 Previous Studies (Webby 1984) I-22 Key Message: Evaluation of the clear-water contraction scour data developed by Webby (1984)
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41 CHOKED FLOW I-23 Key Message: This slide shows the dimensionless choking ratio vs. unit discharge in the contracted section for the clear-water laboratory tests that remained after assessing the reliability of all available data for NCHRP Project 24-34.
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42 CLEAR-WATER DATASETS I-24 Key Message: This slide shows predicted vs. observed clear-water contraction scour for 116 laboratory tests (with outliers removed)
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43 ASSESSMENT OF DAY & RAIKAR TESTS • Data Screening • Scour measurements • Bed materials • Useable data points I-25 Key Message: Results of a detailed assessment of one of many Dey and Raikar (2005) clear-water contraction scour datasets.
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44 I-26 Key Message: HEC-RAS analysis of Dey & Raikar Test 7. Background Information: Lagasse, P., Ettema, R., DeRosset, W.M., Nowroozpour, A., Clopper, P.E., NCHRP Research Report 971: Revised Clear-Water and Live-Bed Contraction Scour Analysis, Transportation Research Board, Washington, D.C., 2021.
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45 and contracted reaches, the HEC-RAS cross sections were established at intervals of 0.1 foot. • The no-scour condition was simulated in HEC-RAS with a constant bed elevation set to an arbitrary datum of 100.00 feet.
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46 I-27 Key Message: Pre- and post- scour water surface profiles from a 1D model applied to Dey & Raikar Test 7. Background Information: Lagasse, P., Ettema, R., DeRosset, W.M., Nowroozpour, A., Clopper, P.E., NCHRP Research Report 971: Revised Clear-Water and Live-Bed Contraction Scour Analysis, Transportation Research Board, Washington, D.C., 2021.
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47 DATA RELIABILITY I-28 Key Message: Are the existing contraction scour equations unreliable or are the existing datasets unreliable? Background Information: Lagasse, P., Ettema, R., DeRosset, W.M., Nowroozpour, A., Clopper, P.E., NCHRP Research Report 971: Revised Clear-Water and Live-Bed Contraction Scour Analysis, Transportation Research Board, Washington, D.C., 2021.
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48 contraction is severe enough to create a choked flow condition, this effect is even more pronounced. • Previous investigations: Previous laboratory investigations do not provide hydraulic conditions before scour occurs.
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49 EVALUATION OF LIVE-BED CONTRACTION SCOUR LABORATORY DATASETS • Replicate clear-water shortcomings • Contracted flow hydraulics • Bedform morphology • Armoring • Contraction or abutment scour? I-29 Key Message: No live-bed contraction scour laboratory datasets were considered reliable enough to be used in NCHRP Project 24-34.
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50 EVALUATION OF CONTRACTION SCOUR FIELD DATA • Group Exercise • 10 minutes I-30 Key Message: What problems might be encountered when trying to acquire and use contraction scour field data? Background Information: Lagasse, P., Ettema, R., DeRosset, W.M., Nowroozpour, A., Clopper, P.E., NCHRP Research Report 971: Revised Clear-Water and Live-Bed Contraction Scour Analysis, Transportation Research Board, Washington, D.C., 2021.
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51 EVALUATION OF CONTRACTION SCOUR FIELD DATA • Field conditions more complex than laboratory • Field measurements may be taken long after the event that caused scour • Hydraulic parameters for the flood event may be unknown • How do you distinguish contraction scour from other types of scour that may have occurred? I-31 Key Message: What problems might be encountered when trying to acquire and use contraction scour field data?
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52 from plots of the concurrent bed profile both upstream and downstream of the bridge (Landers and Mueller 1996)
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53 EXAMPLE OF CLEAR-WATER CONTRACTION SCOUR AT A FIELD SITE I-32 Key Message: Factors that complicate the use of contraction scour field data to improve the contraction scour equations. Background Information: Lagasse, P., Ettema, R., DeRosset, W.M., Nowroozpour, A., Clopper, P.E., NCHRP Research Report 971: Revised Clear-Water and Live-Bed Contraction Scour Analysis, Transportation Research Board, Washington, D.C., 2021.
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54 • This slide shows a typical example of clear-water contraction scour at a bridge in the coastal plain of South Carolina (Source: Benedict and Caldwell, 2009)
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55 I-33 Key Message: Factors that complicate the use of contraction scour field data to improve the contraction scour equations. Background Information: Lagasse, P., Ettema, R., DeRosset, W.M., Nowroozpour, A., Clopper, P.E., NCHRP Research Report 971: Revised Clear-Water and Live-Bed Contraction Scour Analysis, Transportation Research Board, Washington, D.C., 2021.
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56 I-34 Key Message: This slide shows a comparison of normalized measured depths of contraction scour at field sites and the scour depth predicted using HEC18. Background Information: Lagasse, P., Ettema, R., DeRosset, W.M., Nowroozpour, A., Clopper, P.E., NCHRP Research Report 971: Revised Clear-Water and Live-Bed Contraction Scour Analysis, Transportation Research Board, Washington, D.C., 2021.
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57 s REVISED CONTRACTION SCOUR ANALYSIS WORKSHOP LESSON PLAN FOR PART II Session Title: Revised Contraction Scour Analysis Workshop (Part II) Performance-Based Learning Outcomes: At the end of Part II, Participants will be able to • Describe the laboratory and computational techniques used in NCHRP Project 24-47.
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58 REVISED CONTRACTION SCOUR ANALYSIS WORKSHOP LESSON PLAN FOR PART II with the revised NCHRP Project 24-47 HEC-18 live-bed equation, and (3) be prepared to discuss and compare the results.
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59 LEARNING OUTCOMES (PART II) • Describe the laboratory and computational techniques used in NCHRP Project 24-47.
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60 CSU LABORATORY SETUP II-2 Key Message: Description of the laboratory setup at CSU. Background Information: P.F.
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61 II-3 Key Message: Views of the 200-ft long recirculating flume at CSU. Background Information: P.F.
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62 MEASUREMENTS AND INSTRUMENTATION • Water surface profiles • Point velocity measurements • Large-scale particle image velocimetry (LSPIV) • Temporal variation of bed elevations • Equilibrium bathymetry (LiDAR)
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63 II-5 Key Message: LiDAR point cloud image of the CSU flume. Background Information: P.F.
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64 II-6 Key Message: Clear-water contraction scour test setup at Severe contraction ratio. Background Information: P.F.
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65 II-7 Key Message: A typical LiDAR scan during clear-water testing. Background Information: P.F.
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66 II-8 Key Message: Bed and water surface profiles for a clear-water test at final conditions. Background Information: P.F.
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67 II-9 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0 10 20 30 40 50 60 70 80 90 Be d El ev .
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68 Key Message: Evolution of water surface and bed profiles during a clear-water test. Background Information: P.F.
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69 II-10 Key Message: Typical views of a live-bed test at a Moderate contraction ratio. Background Information: P.F.
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70 II-11 Key Message: A typical LiDAR scan during live-bed testing. Background Information: P.F.
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71 II-12 Key Message: Water surface profiles and bed elevations at the flume centerline and right wall. Background Information: P.F.
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72 II-13 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0 10 20 30 40 50 60 70 80 90 El ev at io n (ft ) Station (ft)
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73 Key Message: Evolution of water surface and bed profiles during a live-bed test. Background Information: P.F.
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74 MEASUREMENTS OF THE VENA-CONTRACTA 11-14 Key Message: The main regions of the flow field and consequent scour observed within the entrance to the contracted channel. Background Information: P.F.
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75 SCOUR REGIONS ASSOCIATED WITH THE VENA-CONTRACTA II-15 Key Message: Comparison of corner scour and vena-contracta scour. Background Information: P.F.
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76 LSPIV ANALYSES II-16 Key Message: This slide introduces the Large-Scale Particle Image Velocimetry (LSPIV) method used to view the vena-contracta for each experiment and estimate the narrowest width of the vena-contracta.
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77 LSPIV FLOW STREAMLINES II-17 Key Message: A flow streamline image of the vena-contracta region using LSPIV. Background Information: P.F.
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78 MEASUREMENT OF THE VENA-CONTRACTA II-18 Key Message: Measurements to determine the effective width of the vena-contracta. Background Information: P.F.
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79 COMPUTATIONAL ANALYSES II-19 Key Message: 1D, 2D, and 3D analyses were used to supplement the results of the laboratory studies. This slide shows a typical 2D model as a basis for discussing the information of interest for the contraction scour study.
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80 2D MODEL WITH FINE RESOLUTION II-20 Key Message: The 2D model SRH-2D was used to simulate the hydraulic conditions of clear-water test CW_0.25-0.75. Background Information: P.F.
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81 MODEL CALIBRATION RESULTS II-21 Key Message: The initial and final water surface and bed profiles as determined from a HEC-RAS model with the fine cross section spacing test for test CW_0.250.75. Background Information: P.F.
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82 COMPUTATIONAL ANALYSES RESULTS Table 7.4. Clear-Water Test CW_0.25-0.75: Depth and Velocity at the Upstream Approach Section (Station 10.0)
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83 FLOW VISUALIZATION II-23 Key Message: Among the advantages offered by Computational Fluid Dynamics (CFD) as a supplement to traditional laboratory (physical)
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84 LEARNING OUTCOME (Part II Session 2) • Discuss and evaluate the revised contraction scour methodologies developed under NCHRP Project 24-47.
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85 ANALYSIS OF THE HEC-18 EQUATIONS HEC-18 Clear-Water Post-Scour Flow Depth Estimation y = K QD / W II-25 Key Message: Refresher on the HEC-18 clear-water contraction scour equation. Background Information: FHWA, 2012.
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86 ANALYSIS OF THE HEC-18 EQUATIONS HEC-18 Live-Bed Post-Scour Flow Depth Estimation yy = QQ / WW II-26 Key Message: Refresher on the HEC-18 live-bed contraction scour equation. Background Information: FHWA, 2012.
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87 MAXIMUM OBSERVED VENA-CONTRACTA SCOUR VS. HEC-18 PREDICTED SCOUR II-27 Key Message: This slide presents observed maximum scour depths and predicted scour depths using the HEC-18 prediction methods for upstream approach hydraulics.
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88 EQUILIBRIUM VENA-CONTRACTA SCOUR DEPTH VS. HEC-18 PREDICTED SCOUR II-28 Key Message: This slide presents the resulting equilibrium observed vena-contracta scour vs.
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90 ANALYSIS OF THE NCHRP PROJECT 24-20 EQUATIONS NCHRP Project 24-20 Clear-Water Post-Scour Flow Depth Estimation y = qK d II-30 Key Message: Refresher on the NCHRP Project 24-20 clear-water contraction scour equation. Background Information: Ettema, R., Nakato, T., and Muste, M., 2010.
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91 ANALYSIS OF THE NCHRP PROJECT 24-20 EQUATIONS NCHRP Project 24-20 Live-Bed Post-Scour Flow Depth Estimation y = y qq II-31 Key Message: Refresher on the NCHRP Project 24-20 live-bed contraction scour equation. Background Information: Ettema, R., Nakato, T., and Muste, M., 2010.
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92 OBSERVED EQUILIBRIUM y2 VALUES AND PREDICTED POST-SCOUR y2 VALUES USING NCHRP PROJECT 24-20 CONTRACTION SCOUR PREDICTORS II-32 Key Message: This slide presents observed equilibrium y2 values and predicted post-scour y2 values using NCHRP Project 24-20 contraction scour equations and approach-section hydraulics. Background Information: P.F.
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93 PREDICTED NCHRP PROJECT 24-20 POST-SCOUR EQUILIBRIUM FLOW DEPTHS VS. HEC-18 PREDICTED POST-SCOUR DEPTHS II-33 Key Message: This slide presents predicted NCHRP Project 24-20 post-scour depths compared with HEC-18 predicted post-scour depths.
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94 VENA-CONTRACTA ANALYSIS II-34 Key Message: As covered in Slides II-14 through II-18, this study observed and quantified a significant vena-contracta effect for all tests. Background Information: P.F.
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95 VENA-CONTRACTA AND EFFECTIVE WIDTH ADJUSTMENT FACTOR KV II-35 Key Message: This slide shows the vena-contracta data and a best-fit regression line developed from measured data. Background Information: P.F.
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96 HEC-18 REVISED CONTRACTION SCOUR EQUATIONS y = K QD / (K W) yy = QQ / WK W II-36 Key Message: HEC-18 clear-water and live-bed post-contraction scour flow depth equations with vena-contracta modification.
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97 NCHRP PROJECT 24-20 REVISED CONTRACTION SCOUR EQUATIONS y = qK K d y = y qK q II-37 Key Message: NCHRP Project 24-20 clear-water and live-bed post-contraction scour flow depth equations with vena-contracta modification. Background Information: P.F.
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98 ANALYSIS OF THE REVISED HEC-18 AND NCHRP PROJECT 24-20 EQUATIONS II-38 Key Message: Predicted post-scour equilibrium flow depths for the HEC-18 equations incorporating observed values of Kv. Background Information: P.F.
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99 ANALYSIS OF THE REVISED HEC-18 AND NCHRP PROJECT 24-20 EQUATIONS II-39 Key Message: Predicted post-scour equilibrium flow depths for the NCHRP 24-20 equations incorporating observed values of Kv. Background Information: P.F.
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100 NATIONAL BRIDGE INVENTORY DATA II-40 Key Message: Population of low width–to-depth ratio bridges in the NBI. Background Information: P.F.
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101 LEARNING OUTCOMES (Part II Session 3) • In a group workshop setting, apply and discuss the revised methodologies for clear-water and livebed scour.
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102 TEAM ORGANIZATION FOR SESSION 3 • You will work as teams from a DOT Hydraulics Section to evaluate live-bed contraction scour at a typical singlespan riverine bridge. • Group(s)
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103 THE BRIDGE SITE II-43 Key Message: Description of the bridge site. Background Information: P.F.
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104 THE 2D MODEL II-44 Key Message: Numerical mesh and terrain dataset for the US Highway 287 bridge crossing (Image courtesy of Colorado Department of Transportation)
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105 MODEL MESH AND TERRAIN DATASET II-45 Key Message: Approach, contracted, and exit sections for the US Highway 287 bridge crossing (Image courtesy of Colorado Department of Transportation)
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106 HYDRAULIC VARIABLES FOR THE US HIGHWAY 287 BRIDGE Hydraulic Variables for the US Highway 287 Bridge. Variable Description Variable Name Variable Value Flow in the upstream channel transporting sediment Q1 602 cfs Width of the upstream main channel that is transporting bed material W1 11.9 ft Average depth in the upstream main channel y1 8.7 ft Slope of energy grade line S1 0.0077 Flow in the contracted channel Q2 1819.3 cfs Width of main channel in contracted section W2 20.0 ft Existing depth in the contracted section before scour y0 9.8 ft Existing depth in the exit section before scour y3 5.3 ft Median diameter of bed material d50 0.25 mm II-46 Key Message: Hydraulic variables extracted from the 2D model.
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107 RELIABILITY OF THE CONTRACTION SCOUR EQUATIONS • Both the modified HEC-18 and NCHRP Project 24-20 equations predict substantially more scour than the existing equations. • Both methods have an improved statistical reliability factor.
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108 SUPPLEMENTAL RELIABILITY DISCUSSION Reliability: Post-Scour Flow Depth (y2) Predicted vs.
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109 GROUP A COMPUTATION SHEET Hydraulic Variables for the US Highway 287 Bridge Variable Description Variable Name Variable Value Flow in the upstream channel transporting sediment Q1 602 cfs Width of the upstream main channel that is transporting bed material W1 11.9 ft Average depth in the upstream main channel y1 8.7 ft Slope of energy grade line S1 0.0077 Flow in the contracted channel Q2 1819.3 cfs Width of main channel in contracted section W2 20.0 ft Existing depth in the contracted section before scour y0 9.8 ft Existing depth in the exit section before scour y3 5.3 ft Median diameter of bed material d50 0.25 mm Traditional HEC-18 Method The recommended existing method for calculating contraction scour is described in Chapter 6 of the fifth edition of HEC-18 (Arneson et al.
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110 V∗ω = 1.470.11 = 13.4 Therefore, the ratio of shear velocity to fall velocity is and corresponds to a k1 value of 0.69, as given in Section 6.3 of HEC-18. Knowing this value allows the calculation of live-bed contraction scour using Equation 6.2, as given in HEC-18.
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111 q = QW = 602 fts11.9 ft = 50.59 fts q = QW = 1819.3 fts20.0 ft = 90.97 fts Fr = Vgy = ⎝⎛ 5.81 fts32.2 fts (8.7 ft) ⎠⎞ = 0.35 With this result, the vena-contracta coefficient (Kv)
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112 By using the modified HEC-18 equation to account for the vena-contracta and adjusting the scour datum, the expected contraction scour is predicted to lower the bed elevation by . • Be prepared to present and discuss your findings.
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113 GROUP B COMPUTATION SHEET Hydraulic Variables for the US Highway 287 Bridge Variable Description Variable Name Variable Value Flow in the upstream channel transporting sediment Q1 602 cfs Width of the upstream main channel that is transporting bed material W1 11.9 ft Average depth in the upstream main channel y1 8.7 ft Slope of energy grade line S1 0.0077 Flow in the contracted channel Q2 1819.3 cfs Width of main channel in contracted section W2 20.0 ft Existing depth in the contracted section before scour y0 9.8 ft Existing depth in the exit section before scour y3 5.3 ft Median diameter of bed material d50 0.25 mm NCHRP Project 24-20 Method The recommended existing method for calculating contraction scour is described in Chapter 6 of the fifth edition of HEC-18 (Arneson et al.
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114 q = QW = 602 fts11.9 ft = 50.59 fts q = QW = 1819.3 fts20.0 ft = 90.97 fts y = y qq = 8.7 ft 90.97 fts50.59 fts = 14.38 ft This method produces a post-scour flow depth of feet. Equation 6.3 from HEC-18 allows the conversion from the post-scour flow depth (y2)
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115 This can be applied as follows: Fr = Vgy = ⎝⎛ 5.81 fts32.2 fts (8.7 ft)
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116 WORKSHOP SOLUTION Hydraulic Variables for the US Highway 287 Bridge Variable Description Variable Name Variable Value Flow in the upstream channel transporting sediment Q1 602 cfs Width of the upstream main channel that is transporting bed material W1 11.9 ft Average depth in the upstream main channel y1 8.7 ft Slope of energy grade line S1 0.0077 Flow in the contracted channel Q2 1819.3 cfs Width of main channel in contracted section W2 20.0 ft Existing depth in the contracted section before scour y0 9.8 ft Existing depth in the exit section before scour y3 5.3 ft Median diameter of bed material d50 0.25 mm Traditional HEC-18 Method The recommended existing method for calculating contraction scour is described in Chapter 6 of the fifth edition of HEC-18 (Arneson et al, 2012)
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117 Therefore, the ratio of shear velocity to fall velocity is 13.4 and corresponds to a k1 value of 0.69, as given in Section 6.3 of HEC-18. Knowing this value allows the calculation of live-bed contraction scour using Equation 6.2, as given in HEC-18.
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118 q = QW = 1819.3 fts20.0 ft = 90.97 fts Fr = Vgy = ⎝⎛ 5.81 fts32.2 fts (8.7 ft) ⎠⎞ = 0.35 With this result, the vena-contracta coefficient (Kv)
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119 NCHRP Project 24-20 Method The NCHRP Project 24-20 report (Ettema et al.
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120 This can be applied as follows: Fr = Vgy = ⎝⎛ 5.81 fts32.2 fts (8.7 ft)
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information on Chapter Skim is available.