Revised Clear-Water and Live-Bed Contraction Scour Analysis (2021)

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S-1   Overview Bridge waterways commonly narrow or constrict natural channels, forcing water to flow through a contracted area, thereby increasing the magnitude of velocity and turbulent kinetic energy of flow passing through the waterway. If these increases cause erosion of the waterway boundaries, the contracted section may scour. Existing procedures for estimating contraction scour assume a relatively simplified situation where the contracted channel is straight in alignment, rectangular in cross section, with banks that are resistant to lateral erosion. It is also generally assumed that the bed is formed of uniform non-cohesive sediment. The resulting vertical erosion or scour in a constricted channel is commonly termed “contraction scour.” Live-bed and clear-water scour can occur along channel contractions. The former scour condition commonly occurs in the main channel of an alluvial river, while the latter condi- tion is more typical for a floodplain contraction or at a relief bridge located on the floodplain. For clear-water scour, the governing principle is that the depth of scour in the contracted section corresponds to the occurrence of critical bed shear stress or mean flow velocity when scour approaches its equilibrium state. For live-bed contraction scour, the limiting condition is continuity of sediment transport between the upstream approach flow section and the contracted section. Existing equations are based on sediment transport theory using approaches devel- oped over 50 years ago by Laursen (1960; live-bed contraction scour) and Laursen (1963; clear-water contraction scour). Both equations assume that the scour is due solely to the contraction effect and that local effects are negligible (i.e., that the contraction is hydrauli- cally “long”), and both solve for the depth of flow (y2) in the contracted section after scour has occurred. Early work on contraction scour did not take into account additional factors that can influence scour depth that need to be considered for estimation of the actual depth of contraction scour. Objectives The objectives of this research were to 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. A single non-cohesive sediment size was investigated in a large laboratory flume. One of the major contributions of this study was the development of a contraction scour database for live-bed and clear-water condi- tions using a comprehensive suite of instrumentation techniques not available to previous S U M M A R Y Revised Clear-Water and Live-Bed Contraction Scour Analysis

S-2 Revised Clear-Water and Live-Bed Contraction Scour Analysis researchers in this field. Specifically, the following factors associated with the objectives of this study were addressed: • Definition of contraction ratio • Summary of limitations/applicability of existing datasets and approaches • Multiple modeling techniques, such as physical modeling and computational fluid dynamics (CFD) • Hydraulic force decay on the bed • Applicability of new versus existing bridges • Relationship to other scour components • Applicability to one-dimensional (1D) and two-dimensional (2D) modeling techniques • Development of a new paradigm for estimating contraction scour in a bridge reach • Evaluation of the statistical reliability of existing and proposed analysis approaches Research Approach The research approach for NCHRP Project 24-47 included (1) a fundamental re-analysis of the hydraulics of open-channel flow contractions, (2) evaluation of existing contraction scour equations with reference to available laboratory and field data, (3) extensive labora- tory testing to develop more reliable data on clear-water and live-bed contraction scour, (4) computational modeling to supplement the results of laboratory testing, (5) modifica- tions to the existing contraction scour equations, (6) application of the revised equations to a typical field case of contracted flow in a bridge reach and comparison of the results with estimates obtained from the existing equations, and (7) evaluating the reliability of the existing and recommended analysis approaches using the laboratory database developed under this study. Appraisal of Research Results The open-channel contractions of interest for this study were contractions associated with rivers at bridge crossings. Moreover, the contractions were taken to be superimposed on a channel that was initially uniform in width. This arrangement is representative of bridge crossings on rivers having a single main channel and no floodplain. This study did not include channels with a substantial floodplain (i.e., compound channels). An important consideration was defining the key location where the depth of contraction scour should be measured. The analysis indicated that this location is in the vena-contracta region (i.e., the narrowest part of flow through the contraction entrance). Scour also occurs at the corners of the contraction where scour is strongly influenced by the form of the contraction entrance. An additional complicating factor for all measurements was the deformable roughness of a contracted channel with a mobile (loose) bed or boundary. For the laboratory conditions examined, the bed roughness varied along the contracted channel when the bed developed ripple and dune bedforms. A detailed examination and description of open-channel hydraulics were necessary to explain the flow characteristics of a contracted reach. Such a description was missing in all prior studies (i.e., prior studies did not adequately identify the complexity of the flow hydraulics associated with scour along contracted channels). For subcritical flow along a contracted channel, the control section is located at the downstream end of the contracted reach. Consequently, contraction scour may be referenced to the depth of flow below the contraction, rather than the flow depth at the entrance to the contracted channel.

Summary S-3   The approach flow to a contracted channel is non-uniform and assumes the form of a gradu- ally varied flow (backwater) profile. The water surface profile along the remainder of the contracted channel conformed to a gradually varied flow profile in the experiments. While it is convenient to define the approach flow for a contraction in terms of the flow depth measured at or near the approach to a contracted channel (e.g., at a bridge-waterway crossing), it is important to recognize that a flow depth in this region is within the backwater water surface profile created by the contracted channel. None of the published datasets from contraction scour studies measured the depth of flow in the contracted section before scour occurred. To evaluate the datasets this value had to be calculated or estimated. All but one of the published studies assumed that the depth of flow in the contracted section prior to scour was the same as the depth of flow in the approach section, thereby ignoring the importance of upstream backwater and hydraulic drawdown in the contraction. Also, most previous studies were done under clear-water conditions. The flow entering a contracted channel forms a vena-contracta, whereby the actual width of the contracted flow is less than the geometric width of the contracted channel. The scour depth in the vena-contracta region within the contraction entrance gives the deepest scour along a contracted channel (other than the scour at the corners of the entrance). The corner scour at the contraction entrance may be influenced more by an abutment effect than by the width of the contraction, while the scour in the vena-contracta region of the short- contraction segment relates more directly to the contraction effect. A regression equation was developed from the measured data obtained from the flume experiments to estimate a recommended vena-contracta correction coefficient, Kv. This equation agreed well with the measured flume data. The FHWA’s widely used Hydraulic Engineering Circular No. 18 (HEC-18) equations for estimating the depth of contraction scour were adjusted to include the coefficient for estimating the minimum width of the vena-contracta (Arneson et al. 2012). (Note all references to the HEC-18 equations pertain to the equations in Arneson et al. 2012.) The adjustments were made to the HEC-18 equa- tions used for the clear-water and live-bed conditions of contraction scour, and the adjusted equations yielded results that agree well with the measured depths of contraction scour in the vena-contracta region. In addition, the adjustments were also applied to the form of the clear-water and live-bed contraction scour equations used as a base for estimating abut- ment scour under NCHRP Project 24-20, “Estimation of Bridge Scour Depths at Bridge Abutments.” The equations can be found in the NCHRP Project 24-20 Draft Final Report (Ettema et al. 2010). (Note: these equations are referred to as the NCHRP Project 24-20 equations.) Again, the adjusted equations yielded results that agree well with the measured depths of contraction scour in the vena-contracta region. These revised equations are recommended for use when estimating both live-bed and clear-water contraction scour in channels whose beds are formed of non-cohesive sediment, and the width-to-depth ratio and entrance conditions are comparable with those used for this study. In the interim, for bridges that do not meet these criteria, the application of the existing best-practice modeling methods (see, for example, Robinson et al. 2019) and NCHRP Project 24-20 contraction scour equations are recommended. This study also evaluated the statistical reliability of the existing and proposed contrac- tion scour equations using techniques developed under NCHRP Project 24-34 “Risk-Based Approach for Bridge Scour Prediction.” The results indicate that using upstream pre-scour hydraulic conditions as input and applying the vena-contracta correction coefficient, Kv, developed during this research project, substantially reduce the number of underpredictions compared with the standard HEC-18 and NCHRP Project 24-20 equations. This approach

S-4 Revised Clear-Water and Live-Bed Contraction Scour Analysis produces reasonable if slightly underpredicted estimates of equilibrium post-scour con- traction scour flow depth. In addition, the reliability of the contraction scour prediction is significantly increased. The revised NCHRP Project 24-20 contraction scour equations produce less variability and are more conservative than the equations derived directly from HEC-18. Recap This study quantifies the reliability of the HEC-18 and NCHRP Project 24-20 contraction scour prediction methods using comprehensive physical model study results. The study also proposes modifications to improve the reliability of contraction scour predictions for a specific range of conditions using a new paradigm that had not been considered in previous studies. A general conclusion drawn from this study is that the inherently complex nature of contraction scour (involving non-uniform and unsteady flow on a mobile, non-cohesive bed) leads to approximate estimates of depth of contraction scour. However, reliability considerations provide a guide to the variability of contraction scour estimates and suggest methods for improved evaluation techniques for contraction scour of direct use to the practitioner.