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Publication Number: FHWA-RD-03-083
Date: June 2003

Bridge Scour in Nonuniform Sediment Mixtures and in Cohesive Materials: Synthesis Report

3. EFFECTS OF GRADATION AND COARSE MATERIAL FRACTION ON ABUTMENT SCOUR

3.1 GENERAL

The majority of currently available abutment scour predictors, including some of the methodologies recommended by FHWA, relate abutment scour to a characteristic length (such as flow depth, Y, abutment protrusion length, a, etc.) and the approach flow Froude number. Some of these regression equations include sediment size and gradation as independent variables. However, since these relationships were developed from limited laboratory and field data, they cannot reflect effects due to sediment size properties; therefore they often result in unrealistic scour estimations. As shown in figures 26(a) and 26(b), they provide no guidance when applied to graded sediment mixtures such as those used in the present experimental study.

Figure 26. Graph.  Variation of dimensionless abutment scour with Froude number: (A) abutment protrusion length, lowercase A, as characteristic length; (B) L sub lowercase C equals the square root of lowercase A times Y as characteristic length.  Both figure A and B display dimensionless abutment scour on the Y axis and the mean Froude number on the X axis. Figure 26 (A) shows the variation using abutment protrusion length, lowercase A, as characteristic length; Figure 26 (B) shows the same data using L sub lowercase C as the characteristic length. The figure shows the emerging trend line when L sub lowercase C is used in defining Froude number.

Figure 26. Variation of dimensionless abutment scour with Froude number: (a) abutment protrusion length, a, as characteristic length; (b) L subscript c equals the square root of a Yas characteristic length.

This chapter presents results of the experiments to analyze effects of gradation and coarse material fraction on abutment scour. As a result of this study, 384 new abutment scour data points covering a range of selected sediment mixtures have been contributed to the literature. Parameters controlling abutment scour in mixtures have been identified, and two new relationships for estimating abutment scour have been developed. The close agreement of these new relationships with laboratory experiments is encouraging.

3.2 EXPERIMENTAL SETUP AND MEASUREMENTS

This section presents details of the experimental setup, testing procedure, laboratory facilities, and measuring equipment that were utilized in the abutment scour experiments. First, the three laboratory test flumes used to study the effects of gradation on abutment scour are described. Next, individual measurements along with associated instrumentation and their accuracy are discussed. These measurements include initial and final bed topographies and slopes, hydraulic grade line, flow discharge, flow velocity, scour hole topography and its evolution with time, flow visualization, grain size distribution, and sampling of the armor layer. Finally, the experimental procedure followed for the various runs is discussed along with measures taken to ensure the accuracy and reliability of results.

Laboratory Flumes

Three laboratory flumes, designated as the hydrodynamics flume, sedimentation flume, and the river mechanics flume, were simultaneously utilized for conducting the abutment scour experiments in noncohesive sediment mixtures. The former two flumes are sediment recirculating facilities, while the latter does not recirculate sediment. All flumes are housed at the Hydraulics Laboratory of the Engineering Research Center at CSU. The water supply to these flumes is from the nearby Horsetooth Reservoir. The temperature of the water in the laboratory is controlled through a heating pipe system.

Hydrodynamics Flume

The hydrodynamics flume is a tilting, water and sediment recirculating laboratory facility. The flume is 0.6 m wide, 0.75 m deep, and 18 m long and is made of a steel bottom and Plexiglas side walls to facilitate visual observations. The facility is rigidly supported on U-shaped steel frames located every 1.2 m and is equipped with angled upper and lower flange stiffeners. The bottom flanges are supported on two I-beams spanning the full length of the flume and ground supported at the far upstream, middle, and far downstream. Two carefully leveled guide rails are mounted on the top flanges to provide an escorting track for the measuring carriage. The flume can be tilted around its middle lateral axis through the synchronized operation of two mechanical jacks located at the upstream and downstream ends. Flow is supplied to the flume from a ground sump via a 0.3-m diameter steel pipe line, equipped with a 0.15-m diameter bypass for fine tuning of the flow, and a 20-HP centrifugal pump. The flow is first introduced to an upstream head box equipped with a multilayer screen containing gravel at its outlet to serve as a flow guide to provide uniform velocities and turbulence characteristics at the entrance of the flume. A wave suppressor is then introduced to ensure the accomplishment of the previous concerns. The flow depth is controlled by a downstream rotating gate hinged across the bottom of the flume, spanning the full width, and operated by a system of pulleys. Due to the tail gate control and the nature of the flume, a back water effect is sometimes noticed, causing the water depth to increase as the gate is approached. A 23-cm thick uniform sediment layer prepared from the tested mixture is spread along the full length of the flume, with provisions made for a downstream 1.8-m long sediment trap and an upstream 1.8-m long transition zone. The upstream transition zone is composed of coarser sediments, with a sloping profile carefully designed to provide excess friction to ensure the existence of fully developed turbulent flow and with a boundary layer hitting the free surface far upstream of the study reaches for all flow conditions.

Sedimentation Flume

The sedimentation flume is an elevated sediment transport testing facility that provides for both longitudinal tilting and sediment recirculation. The flume is 60 m long, 2.4 m wide, and 1.2 m deep and allows for slope adjustments up to 3 percent through a system of hydraulic jacks. The flume is constructed from steel plates at the bottom and sides with provisions for Plexiglas windows along specific locations at its side. The structure's skeleton is composed of U-shaped lateral steel frames with cantilevers for sidewalks and supported on box-sectioned longitudinal girders. The upper flanges house guide rails for an electrically motorized measuring carriage that can virtually move to any point in the flume. Three different pumps (125, 150, and 250 HP), with a maximum combined capacity of 3 m3/s, can be simultaneously operated to supply water to the flume from a reservoir sump via three separate steel pipe lines. The flow is first introduced to the upstream head box, which contains several guide vanes and flow straighteners followed by a honeycomb mesh. The flow then passes through a gravel-filled screen succeeded by a wave suppressor. Rapid development of the fully turbulent boundary layer is achieved through an upstream concrete ramp and/or artificial roughening of the entrance zone. The flow depth is regulated through a manually operated downstream adjustable tail gate. The sediment bed is built to a thickness of about 0.4 m, with provisions made for a downstream sediment trap that extends for 6 m. To facilitate drainage of the flume after the experiments, a perforated 10-cm diameter PVC pipe was embedded in the bed material and spanned the full length of the study reach.

River Mechanics Flume

The river mechanics flume is a fixed-slope facility. The flume is 6 m wide, 0.9 m deep, and around 30 m long. The test section, however, was 24 m long, 5.1 m wide, and 0.9 m deep, providing for two Plexiglas viewing sections along one side of the flume and a large upstream reservoir to create uniform entrance conditions. I-beam rails are mounted on the side walls to provide a track for the huge measuring carriage. A 75-HP axial pump of maximum capacity around 0.6 m3/s supplies water to the flume through a 0.6-m diameter pipeline. The upstream main ends in a similar size diffuser located orthogonal to the main flow direction to distribute the flow uniformly across the flume width. The flow then passes through a gravel-filled screen followed by an artificially coarsened concrete ramp that joins the main sediment bed. The setup also provides for a downstream sediment trap and a downstream sill for depth regulation.

Measurements

A series of measurements are needed in order to define the relationship between local scour at abutments and the various hydraulic, geometric, and sediment parameters, both quantitatively and qualitatively. These measurements are described below.

Flow Discharge

The water discharge in all three test flumes was measured through a system of orifice-meter and a differential manometer. For the hydrodynamics flume, two orifice plates were available: one mounted on the 0.3-m diameter main and the other attached to the 0.15-m diameter bypass line. Both orifice-plates are connected to a dual water-mercury manometer for detecting the pressure drop across the ends of the plate. The flow discharge was then computed from the calibration curves for the orifices. The pressure tapping across the orifice plate is connected to the manometer through hard vinyl tubing provided with bleeding valves for drainage and for ensuring an air-free environment. The sedimentation flume is equipped with three similar setups for measuring the discharge, each attached to a different pump. Extreme care was taken to ensure the release of air bubbles entrapped in all manometer lines. The error in measuring the discharge in the hydrodynamics flume is around 3 percent, in the sedimentation flume around 4 percent, and in the river mechanics flume around 5 percent. These error estimates are due to the calibration errors of orifice plates, unsteadiness in the pump discharge, and fluctuations in manometer readings.

Flow Velocity

In the hydrodynamics flume, velocities were measured utilizing two different size pitot tubes and a two-dimensional magnetic flow meter depending on the desired accuracy. A 3-mm diameter minute pitot tube, tapered to a 1.5-mm diameter total head sensor that is connected to a membrane-type transducer, was first used to detect the flow velocity with an accuracy of ±1.5 percent. However, the problems encountered with air entrainment and blockage of the sensing and conveying tubing led to the replacement of this pitot tube with a larger one. The second pitot tube had a 3-mm diameter sensing stem with a pressure take-off diameter of 3 mm and a probe length of 0.3 m. The pressure transducer that was connected to the pitot tubes contained a 0.7 kilo pascal (kPa) steel membrane and is commercially available as P7D±5 PSID SER. 11534. The output signals from the transducer are amplified, filtered, and analyzed by a data acquisition board and a personal computer. The velocities sensed by this device are in the order of ±2.5 percent of accuracy. The second method for velocity measurements in the hydrodynamics flume utilized the 2-D electromagnetic Marsh McBirney, Model 523 flowmeter. The flowmeter consists of a spherical electromagnetic probe with cable and signal processor powered by 6-V DC externally charged with 110-V AC. The probe has a diameter of 12 mm and is mounted on a 6-mm diameter vertical standing rod. The analog signals corresponding to the two orthogonal velocities sensed by the probe are intercepted by a multichannel data acquisition board connected to a personal computer. The sampling frequency was 50 Hz. Overall accuracy of the latter setup is around 3.5 percent.

In the river mechanics and sedimentation flumes, velocities were measured with a one‑dimensional Marsh McBirney, Model 2000 electromagnetic flowmeter with a 2.54-cm elliptic probe and a digital display conversion voltmeter. The accuracy of the flowmeter is reported to be ±2 percent by the manufacturer, and its operating range is from -0.015 m/s to +6.1 m/s within temperature extremes of 0 oC to 71 oC. Overall accuracy of the velocity measuring setup is estimated to be 5 percent.

Flow Visualization

Examination of flow field in the vicinity of the abutment was achieved through flow visualization techniques, including:


Free Stream Bed and Scour Hole Topographies

The bed topographies for the scour holes and the free stream approaches are measured using point gauges. In all flumes, the standard topography measurement procedure started with the leveling of instrumentation carriages at each measurement location along and across the flume to account for the potential unevenness of tracks. Choosing an arbitrary fixed level, every location in the flume, as identified by its Cartesian coordinates, was assigned a correction factor reflecting its elevation relative to the fixed level.

In the hydrodynamics flume, three different point gauges were utilized for measuring purposes depending on the location and accuracy desired. The bed topographies at four different approach sections were measured for each abutment model to define the upstream bed elevation. At each cross section, the bed level was considered to be the average of 10 measurements evenly distributed across the flume's width. To define bed topography in the vicinity of local scour requires more intensive measurements. A measuring grid of an average of 17 cross sections, with a minimum of 21 points per section, was adopted to describe the scour hole region for each abutment.

A similar procedure was followed for the other two flumes, with provisions made for measuring the initial as well as the final levels. The raw measurements are adjusted with the leveling correction factors for each location and then regressed together to yield the value of the bed slope. Approximately 400 topography measurements were performed for each abutment model per experiment. Due to the large sampling size, the error in bed measurements is considered to be equal to 0.25 of the D90 grain size.

Hydraulic Grade Line

The water surface elevations were measured using point gauges with a resolution of ±0.3 mm. Water surface elevation measurements were conducted at a minimum of three approach cross sections per abutment and at a minimum of five locations across the flume width at each cross section. At every location in the cross section, the water level was considered to be the average of two minimum and maximum detected values, to account for any residual fluctuations in the supply discharge and any surface waves induced by the setup. This tedious procedure assumes an accuracy of 2 percent in the computed water depth. Again the hydraulic grade line is identified through regressing the measured water surface values after being adjusted with the level correction factors. The regression results in high correlation coefficients (R2 = 0.95). The velocity head was then added to the hydraulic grade line to define the total energy line.

Sampling of the Armor Layer

Surface samples representing the armor coat formed at the approach to the abutment and inside the scour hole were carefully collected after the experiments were over and the bed was dried. Various techniques, including molten paraffin wax, sticky polymers, modeling clay, scraping the surface, and pebble counting from still photographs, were tried. Among these, the modeling clay method proved to be the most practical and the most accurate.

Soft modeling clay, sometimes treated with castor oil to make it softer, was used to prepare a thin paste around 5 mm thick. The paste was placed at the desired sampling location and gently stamped down under a uniformly distributed applied pressure. The paste was then carefully lifted up, thus collecting a patch of adhered sediments representing the armor coat. After waiting for a short time to allow the paste to become drier, the collected sediments were removed by scraping the surface. If the clay is left on for a long time (one day or more) it becomes very stiff and the removal process has to be done under warm water. The following step was to wash the sediments to make sure that no residual clays are present, then oven dry them and finally prepare them for sieve analysis.

Grain Size Distribution

The relative size distributions for the various sediment mixtures and samples was determined using the sieve analysis method. The sieve sizes used were those defined by the U.S. Bureau of Standards, which represents the sieve number by the number of openings it has per square inch. An average shaking time of 10 minutes was applied for all tested samples.

Experimental Procedure

The experimental procedure for the abutment scour experiments is summarized as follows:

  1. The sediment mixture forming the bed of the flume is naturally compacted in layers. A low flow is then introduced to the flume while raising the downstream gate (for the Hydrodynamics and river mechanics flumes), or lowering the downstream gate (for the sedimentation flume), and is allowed to prevail for long enough to saturate the bed and drive away any entrapped air.
  2. The flow is stopped and the bed is leveled to the desired elevation. Initial bed levels are then recorded at the desired sections. The bed around the abutments where local scour is expected to occur is protected with specially prepared shields.
  3. The flow is introduced to flumes at a very slow rate in order to avoid disturbing the bed topography, especially around the abutments. A depth of flow greater than the desired depth for the experiment is maintained within the flume. The shields around the abutments are then removed.
  4. The required flow depth and discharge are then achieved through simultaneous adjustment of the discharge valve and the downstream gate (or sill) position. Recording of scour development with time is immediately started.
  5. Water surface elevations and flow velocities are recorded following the procedure given above.
  6. Flow visualization and video recording, if any, are then performed.
  7. The shut down process includes raising the depth inside the flume through downstream gate adjustment while decreasing the flow rate in steps. At complete shut down, the flume has to be holding a sizable depth of water that is then allowed to drain very slowly. The current step is crucial for preserving the local scour features produced through the run.
  8. After allowing the bed to be completely drained, the final bed topographies are recorded, still camera photography is performed, and sampling of the armor layer is conducted.
  9. The local scour areas are then replenished with new sediments and the previous procedure is repeated for the next experiment.

3.3 EXPERIMENTAL RESULTS

A comprehensive experimental program was designed to investigate the different aspects of gradation and coarse material fraction effects on local abutment scour. These experiments are categorized into 14 different sets of runs labeled set A through set N. The experimental program was carried out concurrently in three different laboratory facilities. Sets A, B, C, G, H, I, J, K, L, M, and N were performed in the hydrodynamics flume, while sets D and E were conducted in the sedimentation flume. The river mechanics flume was assigned to set F experiments. Sixteen different sediment mixtures and 10 different abutment models were subjected to a range of flow conditions, resulting in a total of 384 different abutment case studies. Tables 8 through 21 present these cases. A summary table of the sediment characteristics associated with the different mixtures utilized in the study is given in table 22.

In the abutment scour experiments presented in this section, the effects of the following parameters on local abutment scour were investigated:


The following sections present details of each set of experiments and references to related summary tables whenever applicable.

Hydrodynamics Flume Experiments

The majority of the experiments (304 different abutment case studies) were carried out in the hydrodynamics flume. The details of each set of experiments are given below.

Set A Experiments

Set A consisted of 18 different runs (A-1 through A-18). Four abutment models were tested in each of the runs A-1, A-2, and A-3. All the four abutment models had the same length of 11.4 cm in the direction of flow; however, their protrusion lengths (length orthogonal to flow) varied. The abutment with a protrusion length of 2.54 cm was identified as M1, that with a protrusion length of 5.08 cm was identified as M2, that with a protrusion length of 7.62 cm was identified as M3, and that with a protrusion length of 10.16 cm was identified as M4. In runs A-4 through A-18, the 2.54-cm model (M1) was dismantled, since its small size could introduce undesirable scale effects with the selected sediment sizes and therefore could influence the validity of the results. The bed material tested (sediment Type IV) was coarse graded sand with a D50 of 1.8 mm and a sigmag of 2.1, with an approximate log-normal size fraction distribution. The flow depth to abutment protrusion length (Y/a) varied between 0.5 and 2.0, the average velocity was between 18 cm/s and 40 cm/s, and the mean Froude number ranged from 0.2 to 0.5. Table 8 shows a summary of the experimental conditions for set A runs. It should be noted that flow depth (Y) and flow velocities were all measured at an approach section located at a distance of (10a) upstream from each abutment, where a is the abutment protrusion length.

Set B Experiments

Set B included 16 different runs (B-1 through B-16). Three abutment models (M2, M3, and M4) were tested in each of the runs except for runs B-12 and B-13 where only M2 and M4 were examined. Sediment of Type III, which is a coarse uniform sand with a D50 of 1.8 mm and a sigmag of 1.17, was used throughout this set. The flow depth to abutment protrusion length (Y/a) varied between 0.3 and 2.3, the average velocity ranged between 0.21 m/s and 0.45 m/s, and the mean Froude number was between 0.25 and 0.6. Table 9 presents a summary of the experimental conditions for set B runs.

Set C Experiments

As shown in table 10, 21 case studies were included in set C (C-2 through C-8). Throughout this series and in the remaining sets that were conducted in the 0.61-m-wide flume, only abutment models M2, M3, and M4 were used. The bed material selected for this set was a coarse graded sand with a D50 of 1.8 mm, a sigmag of 3.9, and an approximate log-normal size fraction distribution (Type V sediment). The flow depth to abutment protrusion length (Y/a) varied between 0.38 and 1.7, the average velocity (Vu) was between 0.21 m/s and 0.44 m/s, and the mean Froude number ranged from 0.3 to 0.5. A summary of the experimental conditions for set C runs is presented in table 10.

Set G Experiments

This set was designed to test a second uniform medium sand mixture with a D50 of 0.78 mm, and a sigmag of 1.3 identified as Type II sediment. The set consisted of seven runs, which provided 21 data points as indicated in table 11. The experiments were conducted using a constant flow depth of 0.075 m for M2, 0.08 m for M3, and 0.09 m for M4. Mean velocity in set G experiments varied between 0.13 m/s and 0.3 m/s, and mean Froude number varied between 0.14 and 0.35.

Sets H, I, and J Experiments

Sets H, I, and J were all conducted with fine silica sand with a D50 of 0.1 mm and sigmag of 1.4 (Type I sediment). Set H consisted of 24 cases, all of which were run for a constant depth of 0.10 m. Set I included 18 study cases, all being tested at a constant depth of 0.075 m, and similarly, set J consisted of 18 tests conducted at a constant depth of 0.05 m. Tables 12 through 14 demonstrate the experimental conditions associated with each set. In each of these sets the most severe flow condition resulted in live bed scour, whereas the rest of the experiments were all conducted under clear-water conditions. For set H, velocities and Froude numbers ranged between 0.01 m/s and 0.33 m/s and between 0.09 and 0.3, respectively; for set I, velocities and Froude numbers ranged between 0.075 m/s and 0.40 m/s and between 0.13 and 0.46, respectively; and for set J velocities and Froude numbers ranged between 0.11 m/s and 0.31 m/s and between 0.15 and 0.44, respectively.

Set K Experiments

Table 15 lists test conditions for the seven runs in the set K experiments using Type VII sediment. The Type VII sediment resembles the Type I sediment in all of its features except that the coarsest 15 percent fraction matches that of sediment Type III. All experiments were conducted at an almost constant flow depth of 0.075 m, while the flow velocity varied from conditions which initiated local scour at the abutments to conditions that resulted in the initiation of live-bed scour (clear-water scour limit).

Set L Experiments

This set of experiments is similar to set B in which Type III sediment with a D50 of 1.8 mm and a sigmag of 1.17 was used. However, in this set the flow depth was maintained at a constant value of about 0.08 m. Flow conditions for the 24 cases considered in set L are given in table 16.

Set M Experiments

As shown in table 17, 10 different experiments were performed in set M using a constant depth of 0.075 m. The bed material tested was Type VI sediment, which basically had the same D50 and sigmag as uniform coarse sand of Type III (1.8 mm and 1.17, respectively), while having the D90 (i.e. the same coarsest fraction) of the graded sediment mixture of Type IV. Flow conditions in this set of experiments varied from conditions that initiated scour to conditions that initiated bed forms.

Set N Experiments

This set of experiments is similar to set A, which used Type IV graded coarse sand. However, in these experiments the flow depth was kept at a constant value of 0.075 m. Flow conditions pertaining to set N experiments (27 cases) are given in table 18.

Sedimentation Flume Experiments

Sixty-eight different abutment case studies were tested in the sedimentation flume; these studies constituted about 17 percent of the total number of abutment scour cases involved in this research. All the tests performed in the 2.44-m wide flume were conducted at a constant depth of 0.3 m. A total of eight different sediment mixtures were tested. Five different sand types, all having the same D50 of 0.78 mm but with varying gradation coefficients and ninety-percentile diameters, were selected to study sensitivity to various sediment size characteristics. The experiments are divided into two major sets: D and E.

Set D Experiments

Set D consisted of eight different runs. As shown in table 19, four abutment models were tested in each of these runs. All the abutment models were 0.46 m long (in direction of flow) and were identified as M1, M2, M3, and M4. Abutments M1, M2, and M3 had a protrusion length of 0.22 m, while the protrusion length of M4 was 0.18 m. Abutment models M1 and M4 were used for testing an approximate log-normally graded medium sand mixture of D50 equal to 0.78 mm and sigmag equal to 2.43 (Type VIII sediment). Abutment M2 was designated for testing a mixture similar to that at M1, but with a coarser upper ten-percentile fraction (Type XI sediment). Similarly, a third mixture (Type X sediment), that was basically Type VIII sediment but with a coarser upper five-percentile fraction, was introduced at abutment M3.

Set E Experiments

Table 20 summarizes the 36 test conditions for the set E experiments. Four abutment models, which were also identified as M1, M2, M3, and M4, with protrusion lengths of 0.22 m and 0.45 m, were used in these experiments. In runs E-1 through E-8, abutment M1 was used for testing a graded medium sand mixture of D50 equal to 0.78 mm and sigmag equal to 3.4 (sediment Type IX). Abutment M2 was for testing a mixture similar to that at M1, but with a coarser upper ten-percentile fraction (sediment Type XII). A uniform medium sand with a D50 of 0.78 mm and sigmag of 1.3 (Type II ) was utilized at M3. For comparison purposes, a mixture of sand and clay (70 percent sand and 30 percent clay) was introduced at M4. Runs E-9 and E-10 were conducted using a gravel mixture to examine potential variations due to median sediment size.

River Mechanics Flume Experiments

In the set F experiments, which were conducted in the 5.2-m wide river mechanics flume, a sediment mixture with mean diameter of 0.55 mm, a gradation coefficient of 2.1, and a D90 of 1.3 mm (sediment Type XV) was used. Table 21 summarizes the experimental conditions for this series. Set F experiments were conducted for the qualitative description of the scour hole and related geometric features.

Table 8. Experimental conditions for set A runs for abutment scour.

RUNID MODEL
SIZE
(cm x cm)
FLOW
DISCHARGE
Q (l/s)
APPROACH
DEPTH
Y (m)
AVERAGE
VELOCITY
Vu (m/s)
ABUTMENT
VELOCITY
Va (m/s)
DIVERTED
VELOCITY
Vj (m/s)
SCOUR
DEPTH
Ds (m)
SEDIMENT
TYPE
A1 - M1 2.5x11.4 12.621 0.061 0.34 0.33 0.31 0.016 IV
A1 - M2 5.1x11.4 12.621 0.211 1.06 0.98 0.93 0.072 IV
A1 - M3 7.6x11.4 12.621 0.220 1.01 0.85 0.83 0.089 IV
A1 - M4 10.2x11.4 12.621 0.238 0.94 0.78 0.72 0.098 IV
A2 - M1 2.5x11.4 16.170 0.068 0.39 0.38 0.36 0.023 IV
A2 - M2 5.1x11.4 16.170 0.211 1.24 1.17 1.13 0.072 IV
A2 - M3 7.6x11.4 16.170 0.220 1.17 0.99 0.96 0.089 IV
A2 - M4 10.2x11.4 16.170 0.238 1.11 0.96 0.89 0.098 IV
A3 - M1 2.5x11.4 18.502 0.087 0.35 0.33 0.32 0.025 IV
A3 - M2 5.1x11.4 18.502 0.211 1.14 1.06 1.02 0.072 IV
A3 - M3 7.6x11.4 18.502 0.220 1.04 0.88 0.85 0.089 IV
A3 - M4 10.2x11.4 18.502 0.238 1.01 0.85 0.79 0.098 IV
A4 - M2 5.1x11.4 19.502 0.075 0.42 0.40 0.40 0.073 IV
A4 - M3 7.6x11.4 19.502 0.082 0.39 0.33 0.32 0.054 IV
A4 - M4 10.2x11.4 19.502 0.084 0.38 0.34 0.32 0.083 IV
A5 - M2 5.1x11.4 19.884 0.080 0.41 0.39 0.38 0.064 IV
A5 - M3 7.6x11.4 19.884 0.087 0.38 0.32 0.31 0.054 IV
A5 - M4 10.2x11.4 19.884 0.091 0.36 0.31 0.29 0.052 IV
A6 - M2 5.1x11.4 15.874 0.066 0.40 0.38 0.36 0.048 IV
A6 - M3 7.6x11.4 15.874 0.071 0.37 0.31 0.30 0.040 IV
A6 - M4 10.2x11.4 15.874 0.075 0.35 0.30 0.28 0.042 IV
A7 - M2 5.1x11.4 20.445 0.083 0.40 0.38 0.37 0.062 IV
A7 - M3 7.6x11.4 20.445 0.088 0.38 0.32 0.32 0.053 IV
A7 - M4 10.2x11.4 20.445 0.094 0.35 0.31 0.29 0.066 IV
A8 - M2 5.1x11.4 17.306 0.071 0.40 0.38 0.37 0.059 IV
A8 - M3 7.6x11.4 17.306 0.076 0.38 0.32 0.31 0.055 IV
A8 - M4 10.2x11.4 17.306 0.080 0.36 0.31 0.29 0.060 IV
A9 - M2 5.1x11.4 14.130 0.065 0.36 0.34 0.32 0.047 IV
A9 - M3 7.6x11.4 14.130 0.069 0.33 0.28 0.27 0.043 IV
A9 - M4 10.2x11.4 14.130 0.074 0.31 0.27 0.25 0.044 IV
A10 - M2 5.1x11.4 10.227 0.049 0.34 0.32 0.31 0.026 IV
A10 - M3 7.6x11.4 10.227 0.055 0.30 0.25 0.25 0.030 IV
A10 - M4 10.2x11.4 10.227 0.062 0.27 0.22 0.20 0.029 IV
A11a - M2 5.1x11.4 4.573 0.029 0.26 0.23 0.22 0.007 IV
A11a - M3 7.6x11.4 4.573 0.030 0.25 0.21 0.20 0.010 IV
A11a - M4 10.2x11.4 4.573 0.039 0.19 0.15 0.13 0.006 IV
A11b - M2 5.1x11.4 7.232 0.039 0.30 0.28 0.26 0.015 IV
A11b - M3 7.6x11.4 7.232 0.044 0.27 0.22 0.22 0.016 IV
A11b - M4 10.2x11.4 7.232 0.050 0.24 0.19 0.17 0.010 IV
A11c - M2 5.1x11.4 20.454 0.082 0.41 0.39 0.38 0.068 IV
A11c - M3 7.6x11.4 20.454 0.086 0.39 0.33 0.32 0.062 IV
A11c - M4 10.2x11.4 20.454 0.093 0.36 0.32 0.30 0.067 IV
A15a - M2 5.1x11.4 13.790 0.102 0.22 0.20 0.18 0.010 IV
A15a - M3 7.6x11.4 13.790 0.113 0.20 0.17 0.16 0.005 IV
A15a - M4 10.2x11.4 13.790 0.121 0.19 0.14 0.13 0.005 IV
A15b - M2 5.1x11.4 13.790 0.077 0.29 0.27 0.25 0.023 IV
A15b - M3 7.6x11.4 13.790 0.087 0.26 0.22 0.21 0.008 IV
A15b - M4 10.2x11.4 13.790 0.096 0.24 0.19 0.17 0.010 IV
A16 - M2 5.1x11.4 13.529 0.057 0.39 0.37 0.36 0.049 IV
A16 - M3 7.6x11.4 13.529 0.059 0.38 0.32 0.31 0.061 IV
A16 - M4 10.2x11.4 13.529 0.062 0.36 0.32 0.30 0.080 IV
A18a - M2 5.1x11.4 15.263 0.065 0.39 0.36 0.35 0.057 IV
A18a - M3 7.6x11.4 15.263 0.067 0.37 0.31 0.31 0.047 IV
A18a - M4 10.2x11.4 15.263 0.073 0.34 0.30 0.28 0.075 IV
A18b - M2 5.1x11.4 15.574 0.068 0.37 0.35 0.34 0.043 IV
A18b - M3 7.6x11.4 15.574 0.073 0.35 0.30 0.29 0.043 IV
A18b - M4 10.2x11.4 15.574 0.080 0.32 0.27 0.26 0.049 IV

Notes:

  1. Average Velocity: Mean velocity prevailing at the approach cross section.
  2. Abutment Velocity: Velocity measured along the longitudinal passing through the abutment nose at the approach section.
  3. Diverted Velocity: Integrated mean velocity prevailing across the deflected flow portion
  4. All experiments are performed in a 0.61‑m wide flume measured at the approach section.
  5. Bed slope is set to a value of 0.0037.

Table 9. Experimental conditions for set B runs for abutment scour.

RUN
ID
MODEL
SIZE
(cm x cm)
FLOW
DISCHARGE
Q (l/s)
APPROACH
DEPTH
Y (m)
AVERAGE
VELOCITY
Vu (m/s)
ABUTMENT
VELOCITY
Va (m/s)
DIVERTED
VELOCITY
Vj (m/s)
SCOUR
DEPTH
Ds (m)
SEDIMENT
TYPE
B1 - M2 5.1x11.4 14.130 0.064 0.365 0.341 0.329 0.1173 III
B1 - M3 7.6x11.4 14.130 0.064 0.362 0.296 0.293 0.1295 III
B1 - M4 10.2x11.4 14.130 0.066 0.349 0.304 0.285 0.1494 III
B2 - M2 5.1x11.4 11.118 0.048 0.384 0.361 0.349 0.0832 III
B2 - M3 7.6x11.4 11.118 0.046 0.395 0.322 0.321 0.1256 III
B2 - M4 10.2x11.4 11.118 0.052 0.348 0.303 0.284 0.1347 III
B3 - M2 5.1x11.4 8.011 0.037 0.352 0.328 0.315 0.0811 III
B3 - M3 7.6x11.4 8.011 0.038 0.348 0.283 0.281 0.1140 III
B3 - M4 10.2x11.4 8.011 0.040 0.329 0.283 0.264 0.1222 III
B4 - M2 5.1x11.4 4.876 0.027 0.298 0.274 0.258 0.0472 III
B4 - M3 7.6x11.4 4.876 0.026 0.303 0.247 0.243 0.0622 III
B4 - M4 10.2x11.4 4.876 0.028 0.282 0.234 0.215 0.0634 III
B5 - M2 5.1x11.4 6.895 0.035 0.326 0.301 0.287 0.0680 III
B5 - M3 7.6x11.4 6.895 0.039 0.292 0.238 0.234 0.0716 III
B5 - M4 10.2x11.4 6.895 0.045 0.252 0.204 0.187 0.0457 III
B6 - M2 5.1x11.4 8.011 0.036 0.369 0.345 0.333 0.0872 III
B6 - M3 7.6x11.4 8.011 0.042 0.312 0.254 0.251 0.0719 III
B6 - M4 10.2x11.4 8.011 0.048 0.272 0.223 0.205 0.0515 III
B7 - M2 5.1x11.4 11.117 0.046 0.395 0.373 0.362 0.1000 III
B7 - M3 7.6x11.4 11.117 0.048 0.382 0.311 0.310 0.1207 III
B7 - M4 10.2x11.4 11.117 0.052 0.350 0.305 0.286 0.1122 III
B8 - M2 5.1x11.4 9.121 0.040 0.372 0.349 0.336 0.0899 III
B8 - M3 7.6x11.4 9.121 0.044 0.343 0.280 0.277 0.0838 III
B8 - M4 10.2x11.4 9.121 0.052 0.290 0.242 0.224 0.0796 III
B9 - M2 5.1x11.4 9.121 0.048 0.311 0.286 0.271 0.0393 VI
B9 - M3 7.6x11.4 9.121 0.051 0.294 0.240 0.236 0.0402 VI
B9 - M4 10.2x11.4 9.121 0.055 0.274 0.226 0.208 0.0244 VI
B10 - M2 5.1x11.4 11.118 0.048 0.378 0.355 0.342 0.0241 VI
B10 - M3 7.6x11.4 11.118 0.050 0.366 0.298 0.296 0.0323 VI
B10 - M4 10.2x11.4 11.118 0.052 0.352 0.308 0.288 0.0372 VI
B12 - M2 5.1x11.4 8.011 0.036 0.362 0.338 0.325 0.0896 III
B12 - M4 10.2x11.4 8.011 0.050 0.264 0.215 0.197 0.0664 III
B13 - M2 5.1x11.4 33.980 0.120 0.463 0.445 0.440 0.1167 III
B13 - M4 10.2x11.4 33.980 0.152 0.366 0.323 0.304 0.1149 III
B14 - M2 5.1x11.4 9.504 0.042 0.368 0.345 0.332 0.078 III
B14 - M3 7.6x11.4 9.504 0.052 0.297 0.242 0.238 0.068 III
B14 - M4 10.2x11.4 9.504 0.058 0.269 0.221 0.203 0.076 III
B15 - M2 5.1x11.4 7.862 0.048 0.271 0.247 0.231 0.027 III
B15 - M3 7.6x11.4 7.862 0.055 0.235 0.192 0.187 0.023 III
B15 - M4 10.2x11.4 7.862 0.062 0.206 0.160 0.145 0.020 III
B16 - M2 5.1x11.4 11.742 0.054 0.359 0.335 0.322 0.091 III
B16 - M3 7.6x11.4 11.742 0.056 0.345 0.282 0.279 0.117 III
B16 - M4 10.2x11.4 11.742 0.063 0.304 0.256 0.237 0.126 III

Notes:

  1. Average Velocity: Mean velocity prevailing at the approach cross section.
  2. Abutment Velocity: Velocity measured along the longitudinal passing through the abutment nose at the approach section.
  3. Diverted Velocity: Integrated mean velocity prevailing across the deflected flow portion.
  4. All experiments are performed in a 0.61‑m wide flume measured at the approach section.
  5. Bed slope is set to a value of 0.0037.

Table 10. Experimental conditions for set C runs for abutment scour.

RUN ID MODEL
SIZE
(cm x cm)
FLOW
DISCHARGE
Q (l/s)
APPROACH
DEPTH
Y (m)
AVERAGE
VELOCITY
Vu (m/s)
ABUTMENT
VELOCITY
Va (m/s)
DIVERTED
VELOCITY
Vj (m/s)
SCOUR
DEPTH
Ds (m)
SEDIMENT
TYPE
C2 - M2 5.1x11.4 7.553 0.039 0.318 0.293 0.278 0.003 V
C2 - M3 7.6x11.4 7.553 0.042 0.297 0.242 0.238 0.004 V
C2 - M4 10.2x11.4 7.553 0.046 0.270 0.221 0.204 0.005 V
C3 - M2 5.1x11.4 17.306 0.071 0.402 0.380 0.370 0.024 V
C3 - M3 7.6x11.4 17.306 0.075 0.381 0.311 0.309 0.038 V
C3 - M4 10.2x11.4 17.306 0.078 0.362 0.319 0.299 0.038 V
C4 - M2 5.1x11.4 4.876 0.033 0.243 0.220 0.204 0.003 V
C4 - M3 7.6x11.4 4.876 0.035 0.228 0.186 0.181 0.003 V
C4 - M4 10.2x11.4 4.876 0.038 0.210 0.164 0.148 0.005 V
C5 - M2 5.1x11.4 20.454 0.084 0.401 0.379 0.369 0.026 V
C5 - M3 7.6x11.4 20.454 0.086 0.392 0.321 0.319 0.033 V
C5 - M4 10.2x11.4 20.454 0.090 0.374 0.332 0.313 0.045 V
C6 - M2 5.1x11.4 14.298 0.062 0.375 0.352 0.340 0.010 V
C6 - M3 7.6x11.4 14.298 0.070 0.335 0.273 0.270 0.011 V
C6 - M4 10.2x11.4 14.298 0.076 0.310 0.263 0.244 0.022 V
C7 - M2 5.1x11.4 21.912 0.081 0.443 0.424 0.417 0.039 V
C7 - M3 7.6x11.4 21.912 0.087 0.414 0.339 0.338 0.032 V
C7 - M4 10.2x11.4 21.912 0.093 0.388 0.348 0.329 0.039 V
C8 - M2 5.1x11.4 19.502 0.075 0.428 0.408 0.400 0.032 V
C8 - M3 7.6x11.4 19.502 0.079 0.405 0.331 0.330 0.035 V
C8 - M4 10.2x11.4 19.502 0.082 0.390 0.351 0.332 0.036 V

Notes:

  1. Average Velocity: Mean velocity prevailing at the approach cross section.
  2. Abutment Velocity: Approach velocity measured along the longitudinal passing through the abutment nose.
  3. Diverted Velocity: Integrated mean velocity prevailing across the deflected flow portion measured at the approach section.
  4. All experiments are performed in a 0.61‑m wide flume.

Table 11. Experimental conditions for set G runs for abutment scour.

RUN ID MODEL
SIZE
(cm x cm)
FLOW
DISCHARGE
Q (l/s)
APPROACH
DEPTH
Y (m)
AVERAGE
VELOCITY
Vu (m/s)
ABUTMENT
VELOCITY
Va (m/s)
DIVERTED
VELOCITY
Vj (m/s)
SCOUR
DEPTH
Ds (m)
SEDIMENT
TYPE
G1 - M2 5.1x11.4 7.552 0.076 0.163 0.144 0.130 0.006 II
G1 - M3 7.6x11.4 7.553 0.086 0.144 0.118 0.113 0.005 II
G1 - M4 10.2x11.4 7.553 0.092 0.135 0.099 0.087 0.001 II
G2 - M2 5.1x11.4 8.990 0.083 0.178 0.158 0.143 0.020 II
G2 - M3 7.6x11.4 8.990 0.094 0.158 0.129 0.124 0.022 II
G2 - M4 10.2x11.4 8.990 0.098 0.151 0.112 0.099 0.012 II
G3 - M2 5.1x11.4 9.751 0.075 0.214 0.192 0.176 0.047 II
G3 - M3 7.6x11.4 9.751 0.082 0.195 0.160 0.154 0.042 II
G3 - M4 10.2x11.4 9.751 0.092 0.173 0.131 0.117 0.030 II
G4 - M2 5.1x11.4 11.010 0.073 0.246 0.222 0.207 0.079 II
G4 - M3 7.6x11.4 11.010 0.086 0.210 0.172 0.167 0.068 II
G4 - M4 10.2x11.4 11.010 0.092 0.197 0.152 0.137 0.046 II
G5 - M2 5.1x11.4 11.941 0.076 0.258 0.234 0.218 0.084 II
G5 - M3 7.6x11.4 11.943 0.089 0.220 0.180 0.175 0.077 II
G5 - M4 10.2x11.4 11.943 0.095 0.207 0.161 0.145 0.049 II
G6 - M2 5.1x11.4 12.884 0.080 0.265 0.241 0.225 0.098 II
G6 - M3 7.6x11.4 12.884 0.093 0.227 0.186 0.181 0.093 II
G6 - M4 10.2x11.4 12.884 0.096 0.221 0.174 0.158 0.066 II
G7 - M2 5.1x11.4 14.130 0.076 0.304 0.280 0.265 0.113 II
G7 - M3 7.6x11.4 14.130 0.089 0.260 0.213 0.207 0.117 II
G7 - M4 10.2x11.4 14.130 0.091 0.253 0.205 0.188 0.119 II

Notes:

  1. Average Velocity: Mean velocity prevailing at the approach cross section.
  2. Abutment Velocity: Approach velocity measured along the longitudinal passing through the abutment nose.
  3. Diverted Velocity: Integrated mean velocity prevailing across the deflected flow portion measured at the approach section.
  4. All experiments are performed in a 0.61-m wide flume.

Table 12. Experimental conditions for set H runs for abutment scour.

  RUN #   MODEL
SIZE
(cm x cm)
FLOW
DISCHARGE
Q (l/s)
APPROACH
DEPTH
Y (m)
AVERAGE
VELOCITY
Vu (m/s)
ABUTMENT
VELOCITY
Va (m/s)
DIVERTED
VELOCITY
Vj (m/s)
SCOUR
DEPTH
Ds (m)
SEDIMENT
TYPE  
H1 - M2 5.1x11.4 8.155 0.119 0.112 0.098 0.087 0.008 I
H1 - M3 7.6x11.4 8.155 0.123 0.108 0.089 0.085 0.002 I
H1 - M4 10.2x11.4 8.155 0.129 0.104 0.074 0.064 0.003 I
H2 - M2 5.1x11.4 10.228 0.116 0.144 0.127 0.114 0.026 I
H2 - M3 7.6x11.4 10.228 0.121 0.139 0.114 0.109 0.035 I
H2 - M4 10.2x11.4 10.228 0.125 0.134 0.098 0.086 0.036 I
H3 - M2 5.1x11.4 11.941 0.119 0.164 0.145 0.131 0.040 I
H3 - M3 7.6x11.4 11.941 0.123 0.159 0.130 0.125 0.047 I
H3 - M4 10.2x11.4 11.941 0.128 0.153 0.114 0.101 0.048 I
H4 - M2 5.1x11.4 14.464 0.122 0.195 0.173 0.158 0.060 I
H4 - M3 7.6x11.4 14.464 0.126 0.188 0.155 0.149 0.064 I
H4 - M4 10.2x11.4 14.464 0.129 0.184 0.140 0.125 0.084 I
H5 - M2 5.1x11.4 16.605 0.122 0.224 0.201 0.186 0.087 I
H5 - M3 7.6x11.4 16.605 0.124 0.220 0.181 0.175 0.105 I
H5 - M4 10.2x11.4 16.605 0.128 0.213 0.167 0.151 0.125 I
H6 - M2 5.1x11.4 17.913 0.122 0.241 0.218 0.202 0.105 I
H6 - M3 7.6x11.4 17.913 0.124 0.237 0.195 0.189 0.125 I
H6 - M4 10.2x11.4 17.913 0.127 0.232 0.184 0.167 0.132 I
H7 - M2 5.1x11.4 19.502 0.122 0.262 0.238 0.222 0.119 I
H7 - M3 7.6x11.4 19.502 0.123 0.259 0.213 0.208 0.129 I
H7 - M4 10.2x11.4 19.502 0.126 0.254 0.205 0.188 0.139 I
H8 - M2 5.1x11.4 25.683 0.125 0.336 0.312 0.298 0.115 I
H8 - M3 7.6x11.4 25.683 0.126 0.333 0.274 0.270 0.129 I
H8 - M4 10.2x11.4 25.683 0.129 0.326 0.279 0.260 0.140 I

Notes:

  1. Average Velocity: Mean velocity prevailing at the approach cross section.
  2. Abutment Velocity: Approach velocity measured along the longitudinal passing through the abutment nose.
  3. Diverted Velocity: Integrated mean velocity prevailing across the deflected flow portion measured at the approach section.
  4. All experiments are performed in a 0.61-m wide flume.

Table 13. Experimental conditions for set I runs for abutment scour.

RUN ID MODEL
SIZE
(cm x cm)
FLOW
DISCHARGE
Q (l/s)
APPROACH
DEPTH
Y (m)
AVERAGE
VELOCITY
Vu (m/s)
ABUTMENT
VELOCITY
Va (m/s)
DIVERTED
VELOCITY
Vj (m/s)
SCOUR
DEPTH
Ds (m)
SEDIMENT
TYPE
I1 - M2 5.1 x 11.4 6.881 0.071 0.158 0.140 0.126 0.0393 I
I1 - M3 7.6 x 11.4 6.881 0.076 0.148 0.121 0.116 0.0299 I
I1 - M4 10.2 x 11.4 6.881 0.080 0.140 0.103 0.091 0.0335 I
I2 - M2 5.1 x 11.4 8.438 0.073 0.190 0.169 0.154 0.0594 I
I2 - M3 7.6 x 11.4 8.438 0.076 0.182 0.149 0.143 0.0524 I
I2 - M4 10.2 x 11.4 8.438 0.080 0.173 0.130 0.116 0.0640 I
I3 - M2 5.1 x 11.4 9.990 0.077 0.213 0.190 0.175 0.0914 I
I3 - M3 7.6 x 11.4 9.990 0.079 0.208 0.170 0.165 0.1052 I
I3 - M4 10.2 x 11.4 9.990 0.080 0.204 0.158 0.143 0.1219 I
I4 - M2 5.1 x 11.4 11.330 0.075 0.249 0.225 0.209 0.1082 I
I4 - M3 7.6 x 11.4 11.330 0.075 0.249 0.203 0.198 0.1210 I
I4 - M4 10.2 x 11.4 11.330 0.075 0.247 0.199 0.181 0.1362 I
I5 - M2 5.1 x 11.4 18.501 0.076 0.398 0.376 0.365 0.1167 I
I5 - M3 7.6 x 11.4 18.501 0.077 0.395 0.323 0.322 0.1356 I
I5 - M4 10.2 x 11.4 18.501 0.077 0.392 0.353 0.334 0.1402 I
I6 - M2 5.1 x 11.4 5.768 0.075 0.127 0.111 0.099 0.0046 I
I6 - M3 7.6 x 11.4 5.768 0.079 0.119 0.098 0.093 0.0027 I
I6 - M4 10.2 x 11.4 5.768 0.081 0.117 0.084 0.074 0.0009 I

Notes:

  1. Average Velocity: Mean velocity prevailing at the approach cross section.
  2. Abutment Velocity: Approach velocity measured along the longitudinal passing through the abutment nose.
  3. Diverted Velocity: Integrated mean velocity across the deflected flow portion measured at the approach section.
  4. All experiments are performed in a 0.61‑m wide flume.
  5. Bed slope is set to a value of 0.0017.

Table 14. Experimental conditions for set J runs for abutment scour.

  RUN ID   MODEL
SIZE
(cm x cm)
FLOW
DISCHARGE
Q (l/s)
APPROACH
DEPTH
Y (m)
AVERAGE
VELOCITY
Vu (m/s)
ABUTMENT
VELOCITY
Va (m/s)
DIVERTED
VELOCITY
Vj (m/s)
SCOUR
DEPTH
Ds (m)
SEDIMENT
TYPE  
J1 - M2 5.1 x 11.4 3.786 0.045 0.137 0.120 0.107 0.0162 I
J1 - M3 7.6 x 11.4 3.786 0.048 0.128 0.104 0.100 0.0216 I
J1 - M4 10.2 x 11.4 3.786 0.053 0.118 0.085 0.074 0.0104 I
J2 - M2 5.1 x 11.4 5.295 0.054 0.160 0.141 0.128 0.0460 I
J2 - M3 7.6 x 11.4 5.295 0.054 0.162 0.132 0.127 0.0747 I
J2 - M4 10.2 x 11.4 5.295 0.055 0.158 0.118 0.105 0.0829 I
J3 - M2 5.1 x 11.4 6.711 0.052 0.210 0.188 0.173 0.0823 I
J3 - M3 7.6 x 11.4 6.711 0.050 0.222 0.181 0.176 0.0948 I
J3 - M4 10.2 x 11.4 6.711 0.049 0.226 0.178 0.162 0.1076 I
J4 - M2 5.1 x 11.4 7.561 0.051 0.245 0.222 0.206 0.0969 I
J4 - M3 7.6 x 11.4 7.561 0.047 0.266 0.217 0.212 0.1024 I
J4 - M4 10.2 x 11.4 7.561 0.045 0.275 0.226 0.208 0.1158 I
J5 - M2 5.1 x 11.4 10.449 0.059 0.290 0.266 0.250 0.1052 I
J5 - M3 7.6 x 11.4 10.449 0.055 0.311 0.253 0.250 0.1036 I
J5 - M4 10.2 x 11.4 10.449 0.054 0.320 0.272 0.254 0.1234 I
J6 - M2 5.1 x 11.4 3.455 0.045 0.126 0.110 0.098 0.0021 I
J6 - M3 7.6 x 11.4 3.455 0.049 0.116 0.095 0.091 0.0009 I
J6 - M4 10.2 x 11.4 3.455 0.049 0.116 0.083 0.073 0.0003 I

Notes:

  1. Average Velocity: Mean velocity prevailing at the approach cross section.
  2. Abutment Velocity: Velocity measured along the longitudinal passing through the abutment nose at the approach section.
  3. Diverted Velocity: Integrated mean velocity prevailing across the deflected flow portion.
  4. All experiments are performed in a 0.61‑m wide flume measured at the approach section.
  5. Bed slope is set to a value of 0.0017.

Table 15. Experimental conditions for set K runs for abutment scour.

RUN ID MODEL
SIZE
(cm x cm)
FLOW
DISCHARGE
Q (l/s)
APPROACH
DEPTH
Y (m)
AVERAGE
VELOCITY
Vu (m/s)
ABUTMENT
VELOCITY
Va (m/s)
DIVERTED
VELOCITY
Vj (m/s)
SCOUR
DEPTH
Ds (m)
SEDIMENT
TYPE
K1 - M2 5.1 x 11.4 6.895 0.073 0.155 0.136 0.123 0.0021 VII
K1 - M3 7.6 x 11.4 6.895 0.076 0.148 0.121 0.117 0.0009 VII
K1 - M4 10.2 x 11.4 6.895 0.081 0.140 0.102 0.090 0.0006 VII
K2 - M2 5.1 x 11.4 8.444 0.072 0.193 0.172 0.157 0.0128 VII
K2 - M3 7.6 x 11.4 8.444 0.075 0.185 0.151 0.146 0.0043 VII
K2 - M4 10.2 x 11.4 8.444 0.080 0.174 0.132 0.118 0.0034 VII
K3 - M2 5.1 x 11.4 9.992 0.079 0.208 0.186 0.170 0.0287 VII
K3 - M3 7.6 x 11.4 9.992 0.078 0.209 0.171 0.166 0.0250 VII
K3 - M4 10.2 x 11.4 9.992 0.080 0.204 0.158 0.143 0.0277 VII
K4 - M2 5.1 x 11.4 11.640 0.074 0.257 0.233 0.217 0.0491 VII
K4 - M3 7.6 x 11.4 11.640 0.073 0.261 0.213 0.208 0.0631 VII
K4 - M4 10.2 x 11.4 11.640 0.073 0.262 0.214 0.196 0.0728 VII
K5 - M2 5.1 x 11.4 12.898 0.073 0.290 0.266 0.251 0.0762 VII
K5 - M3 7.6 x 11.4 12.898 0.072 0.293 0.239 0.235 0.0741 VII
K5 - M4 10.2 x 11.4 12.898 0.073 0.292 0.243 0.225 0.0860 VII
K6 - M2 5.1 x 11.4 14.626 0.076 0.316 0.292 0.277 0.0835 VII
K6 - M3 7.6 x 11.4 14.626 0.074 0.323 0.264 0.260 0.0933 VII
K6 - M4 10.2 x 11.4 14.626 0.074 0.325 0.279 0.260 0.1149 VII
K7 - M2 5.1 x 11.4 16.889 0.078 0.356 0.333 0.319 0.0884 VII
K7 - M3 7.6 x 11.4 16.889 0.075 0.370 0.302 0.300 0.1012 VII
K7 - M4 10.2 x 11.4 16.889 0.075 0.368 0.326 0.306 0.1244 VII

Notes:

  1. Average Velocity: Mean velocity prevailing at the approach cross section.
  2. Abutment Velocity: Velocity measured along the longitudinal passing through the abutment nose at the approach section.
  3. Diverted Velocity: Integrated mean velocity prevailing across the deflected flow portion.
  4. All experiments are performed in a 0.61‑m wide flume measured at the approach section.
  5. Bed slope is set to a value of 0.0017.

Table 16. Experimental conditions for set L runs for abutment scour.

RUN ID MODEL
SIZE
(cm x cm)
FLOW
DISCHARGE
Q (l/s)
APPROACH
DEPTH
Y (m)
AVERAGE
VELOCITY
Vu (m/s)
ABUTMENT
VELOCITY
Va (m/s)
DIVERTED
VELOCITY
Vj (m/s)
SCOUR
DEPTH
Ds (m)
SEDIMENT
TYPE
L1 - M2 5.1 x 11.4 11.327 0.075 0.249 0.225 0.209 0.0290 III
L1 - M3 7.6 x 11.4 11.327 0.077 0.241 0.197 0.192 0.0283 III
L1 - M4 10.2 x 11.4 11.327 0.080 0.234 0.186 0.169 0.0302 III
L2 - M2 5.1 x 11.4 15.106 0.077 0.323 0.298 0.284 0.0991 III
L2 - M3 7.6 x 11.4 15.106 0.076 0.325 0.266 0.262 0.1015 III
L2 - M4 10.2 x 11.4 15.106 0.077 0.324 0.277 0.258 0.1082 III
L3 - M2 5.1 x 11.4 16.888 0.079 0.350 0.326 0.312 0.1082 III
L3 - M3 7.6 x 11.4 16.888 0.079 0.352 0.288 0.285 0.1109 III
L3 - M4 10.2 x 11.4 16.888 0.077 0.359 0.316 0.297 0.1222 III
L4 - M2 5.1 x 11.4 18.882 0.081 0.381 0.358 0.346 0.1155 III
L4 - M3 7.6 x 11.4 18.883 0.077 0.400 0.327 0.326 0.1183 III
L4 - M4 10.2 x 11.4 18.882 0.078 0.399 0.361 0.342 0.1433 III
L5 - M2 5.1 x 11.4 20.453 0.084 0.402 0.380 0.369 0.1201 III
L5 - M3 7.6 x 11.4 20.453 0.080 0.422 0.345 0.345 0.1253 III
L5 - M4 10.2 x 11.4 20.453 0.078 0.432 0.400 0.382 0.1420 III
L6 - M2 5.1 x 11.4 9.992 0.073 0.226 0.203 0.188 0.0027 III
L6 - M3 7.6 x 11.4 9.992 0.075 0.219 0.179 0.174 0.0018 III
L6 - M4 10.2 x 11.4 9.992 0.078 0.211 0.165 0.149 0.0015 III
L7 - M2 5.1 x 11.4 9.251 0.073 0.207 0.186 0.170 0.0003 III
L7 - M3 7.6 x 11.4 9.251 0.076 0.201 0.164 0.159 0.0003 III
L7 - M4 10.2 x 11.4 9.251 0.078 0.194 0.149 0.134 0.0003 III
L8 - M2 5.1 x 11.4 13.790 0.078 0.291 0.267 0.251 0.0692 III
L8 - M3 7.6 x 11.4 13.790 0.078 0.289 0.236 0.232 0.0732 III
L8 - M4 10.2 x 11.4 13.790 0.079 0.285 0.237 0.219 0.0741 III

Notes:

  1. Average Velocity: Mean velocity prevailing at the approach cross section.
  2. Abutment Velocity: Velocity measured along the longitudinal passing through the abutment nose at the approach section.
  3. Diverted Velocity: Integrated mean velocity prevailing across the deflected flow portion.
  4. All experiments are performed in a 0.61‑m wide flume measured at the approach section.
  5. Bed slope is set to a value of 0.0017.

Table 17. Experimental conditions for set M runs for abutment scour.

RUN ID MODEL
SIZE

(cm x cm)
FLOW
DISCHARGE
Q (l/s)
APPROACH
DEPTH
Y (m)
AVERAGE
VELOCITY
Vu (m/s)
ABUTMENT
VELOCITY
Va (m/s)
DIVERTED
VELOCITY
Vj (m/s)
SCOUR
DEPTH
Ds (m)
SEDIMENT
TYPE
M1 - M2 5.1 x 11.4 13.441 0.075 0.293 0.269 0.253 0.0232 VI
M1 - M3 7.6 x 11.4 13.441 0.077 0.287 0.235 0.230 0.0238 VI
M1 - M4 10.2 x 11.4 13.441 0.079 0.279 0.231 0.213 0.0344 VI
M2 - M2 5.1 x 11.4 14.627 0.075 0.320 0.296 0.281 0.0283 VI
M2 - M3 7.6 x 11.4 14.627 0.075 0.320 0.262 0.258 0.0280 VI
M2 - M4 10.2 x 11.4 14.627 0.076 0.317 0.270 0.251 0.0421 VI
M3 - M2 5.1 x 11.4 15.571 0.075 0.341 0.317 0.303 0.0293 VI
M3 - M3 7.6 x 11.4 15.571 0.076 0.338 0.276 0.273 0.0344 VI
M3 - M4 10.2 x 11.4 15.571 0.077 0.333 0.286 0.267 0.0546 VI
M4 - M2 5.1 x 11.4 17.169 0.076 0.373 0.349 0.337 0.0479 VI
M4 - M3 7.6 x 11.4 17.169 0.075 0.377 0.308 0.306 0.0515 VI
M4 - M4 10.2 x 11.4 17.169 0.076 0.371 0.329 0.310 0.0762 VI
M5 - M2 5.1 x 11.4 17.714 0.077 0.378 0.355 0.343 0.0527 VI
M5 - M3 7.6 x 11.4 17.714 0.076 0.384 0.314 0.312 0.0594 VI
M5 - M4 10.2 x 11.4 17.714 0.076 0.384 0.344 0.325 0.0866 VI
M6 - M2 5.1 x 11.4 18.372 0.077 0.389 0.367 0.355 0.0588 VI
M6 - M3 7.6 x 11.4 18.372 0.076 0.396 0.323 0.322 0.0671 VI
M6 - M4 10.2 x 11.4 18.372 0.076 0.399 0.361 0.342 0.0887 VI
M7 - M2 5.1 x 11.4 19.502 0.079 0.407 0.385 0.375 0.0728 VI
M7 - M3 7.6 x 11.4 19.502 0.077 0.413 0.338 0.337 0.0744 VI
M7 - M4 10.2 x 11.4 19.502 0.077 0.415 0.380 0.361 0.1113 VI
M8 - M2 5.1 x 11.4 20.685 0.079 0.430 0.410 0.401 0.0789 VI
M8 - M3 7.6 x 11.4 20.685 0.077 0.438 0.358 0.359 0.0796 VI
M8 - M4 10.2 x 11.4 20.685 0.074 0.456 0.431 0.412 0.1177 VI
M9 - M2 5.1 x 11.4 22.128 0.084 0.433 0.413 0.405 0.0853 VI
M9 - M3 7.6 x 11.4 22.128 0.082 0.444 0.364 0.364 0.0856 VI
M9 - M4 10.2 x 11.4 22.128 0.081 0.449 0.422 0.404 0.1228 VI
M10 - M2 5.1 x 11.4 11.327 0.076 0.245 0.221 0.206 0.0037 VI
M10 - M3 7.6 x 11.4 11.327 0.077 0.242 0.198 0.193 0.0030 VI
M10 - M4 10.2 x 11.4 11.327 0.079 0.235 0.188 0.171 0.0055 VI

Notes:

  1. Average Velocity: Mean velocity prevailing at the approach cross section.
  2. Abutment Velocity: Velocity measured along the longitudinal passing through the abutment nose at the approach section.
  3. Diverted Velocity: Integrated mean velocity prevailing across the deflected flow portion.
  4. All experiments are performed in a 0.61‑m wide flume measured at the approach section.
  5. Bed slope is set to a value of 0.0017.

Table 18. Experimental conditions for set N runs for abutment scour.

RUN ID MODEL
SIZE
(cm x cm)
FLOW
DISCHARGE
Q (l/s)
APPROACH
DEPTH
Y (m)
AVERAGE
VELOCITY
Vu (m/s)
ABUTMENT
VELOCITY
Va (m/s)
DIVERTED
VELOCITY
Vj (m/s)
SCOUR
DEPTH
Ds (m)
SEDIMENT
TYPE
N1 - M2 5.1 x 11.4 13.441 0.075 0.294 0.270 0.254 0.0098 IV
N1 - M3 7.6 x 11.4 13.441 0.076 0.289 0.237 0.232 0.0079 IV
N1 - M4 10.2 x 11.4 13.441 0.080 0.277 0.229 0.210 0.0158 IV
N2 - M2 5.1 x 11.4 14.463 0.075 0.315 0.291 0.276 0.0207 IV
N2 - M3 7.6 x 11.4 14.463 0.076 0.311 0.255 0.250 0.0174 IV
N2 - M4 10.2 x 11.4 14.463 0.078 0.303 0.255 0.236 0.0213 IV
N3 - M2 5.1 x 11.4 15.416 0.077 0.331 0.306 0.292 0.0235 IV
N3 - M3 7.6 x 11.4 15.416 0.076 0.332 0.271 0.268 0.0283 IV
N3 - M4 10.2 x 11.4 15.416 0.077 0.327 0.280 0.261 0.0360 IV
N4 - M2 5.1 x 11.4 17.029 0.078 0.358 0.334 0.321 0.0338 IV
N4 - M3 7.6 x 11.4 17.029 0.077 0.362 0.296 0.294 0.0347 IV
N4 - M4 10.2 x 11.4 17.029 0.077 0.364 0.321 0.302 0.0610 IV
N5 - M2 5.1 x 11.4 18.372 0.078 0.386 0.364 0.352 0.0488 IV
N5 - M3 7.6 x 11.4 18.372 0.076 0.397 0.325 0.323 0.0619 IV
N5 - M4 10.2 x 11.4 18.372 0.074 0.407 0.371 0.352 0.0914 IV
N6 - M2 5.1 x 11.4 19.502 0.079 0.407 0.385 0.375 0.0527 IV
N6 - M3 7.6 x 11.4 19.502 0.077 0.418 0.342 0.342 0.0689 IV
N6 - M4 10.2 x 11.4 19.502 0.077 0.416 0.382 0.363 0.0963 IV
N7 - M2 5.1 x 11.4 20.685 0.080 0.423 0.403 0.394 0.0619 IV
N7 - M3 7.6 x 11.4 20.685 0.078 0.435 0.356 0.356 0.0728 IV
N7 - M4 10.2 x 11.4 20.685 0.078 0.437 0.406 0.388 0.1045 IV
N8 - M2 5.1 x 11.4 22.128 0.085 0.427 0.406 0.398 0.0689 IV
N8 - M3 7.6 x 11.4 22.128 0.082 0.443 0.362 0.363 0.0789 IV
N8 - M4 10.2 x 11.4 22.128 0.080 0.456 0.431 0.413 0.1128 IV
N9 - M2 5.1 x 11.4 11.740 0.075 0.257 0.233 0.217 0.0040 IV
N9 - M3 7.6 x 11.4 11.740 0.076 0.253 0.207 0.202 0.0027 IV
N9 - M4 10.2 x 11.4 11.740 0.079 0.243 0.195 0.178 0.0021 IV

Notes:

  1. Average Velocity: Mean velocity prevailing at the approach cross section.
  2. Abutment Velocity: Approach velocity measured along the longitudinal passing through the abutment nose.
  3. Diverted Velocity: Integrated mean velocity prevailing across the deflected flow portion.
  4. All experiments are performed in a 0.61‑m wide flume measured at the approach section.
  5. Bed slope is set to a value of 0.0017.

Table 19. Experimental conditions for set D runs for abutment scour.

RUN ID MODEL
SIZE
(cm x cm)
FLOW
DISCHARGE
Q (l/s)
APPROACH
DEPTH
Y (m)
AVERAGE
VELOCITY
Vu (m/s)
ABUTMENT
VELOCITY
Va (m/s)
DIVERTED
VELOCITY
Vj (m/s)
SCOUR
DEPTH
Ds (m)
SEDIMENT
TYPE
D1 - M1 21.6 x 45.7 184.060 0.323 0.233 0.236 0.235 0.0579 VIII
D1 - M2 21.6 x 45.7 184.060 0.326 0.231 0.206 0.195 0.0320 XI
D1 - M3 21.6 x 45.7 184.060 0.326 0.231 0.195 0.192 0.0323 X
D1 - M4 17.8 x 45.7 184.060 0.326 0.231 0.175 0.161 0.0253 VIII
D2 - M1 21.6 x 45.7 176.980 0.324 0.224 0.222 0.216 0.0472 VIII
D2 - M2 21.6 x 45.7 176.980 0.326 0.223 0.191 0.189 0.0122 XI
D2 - M3 21.6 x 45.7 176.980 0.326 0.223 0.186 0.180 0.0137 X
D2 - M4 17.8 x 45.7 176.980 0.317 0.229 0.172 0.155 0.0198 VIII
D3 - M1 21.6 x 45.7 198.218 0.308 0.264 0.247 0.244 0.0625 VIII
D3 - M2 21.6 x 45.7 198.218 0.309 0.263 0.219 0.204 0.0140 XI
D3 - M3 21.6 x 45.7 198.218 0.314 0.259 0.201 0.189 0.1234 X
D3 - M4 17.8 x 45.7 198.218 0.316 0.257 0.183 0.172 0.0256 VIII
D4 - M1 21.6 x 45.7 229.366 0.317 0.296 0.267 0.265 0.0686 VIII
D4 - M2 21.6 x 45.7 229.366 0.321 0.293 0.234 0.219 0.0204 XI
D4 - M3 21.6 x 45.7 229.366 0.323 0.291 0.219 0.213 0.0344 X
D4 - M4 17.8 x 45.7 229.366 0.326 0.288 0.202 0.192 0.0445 VIII
D5 - M1 21.6 x 45.7 257.117 0.324 0.325 0.300 0.299 0.1103 VIII
D5 - M2 21.6 x 45.7 257.117 0.331 0.319 0.265 0.250 0.0299 XI
D5 - M3 21.6 x 45.7 257.117 0.334 0.316 0.255 0.244 0.0485 X
D5 - M4 17.8 x 45.7 257.117 0.325 0.325 0.249 0.216 0.0564 VIII
D6 - M1 21.6 x 45.7 295.628 0.327 0.371 0.331 0.329 0.1692 VIII
D6 - M2 21.6 x 45.7 295.628 0.331 0.367 0.299 0.277 0.0451 XI
D6 - M3 21.6 x 45.7 295.628 0.329 0.369 0.289 0.274 0.0671 X
D6 - M4 17.8 x 45.7 295.628 0.327 0.371 0.265 0.245 0.0817 VIII
D7 - M1 21.6 x 45.7 242.392 0.327 0.304 0.272 0.271 0.0866 VIII
D7 - M2 21.6 x 45.7 242.392 0.333 0.299 0.241 0.229 0.0320 XI
D7 - M3 21.6 x 45.7 242.392 0.336 0.296 0.231 0.223 0.0421 X
D7 - M4 17.8 x 45.7 242.392 0.336 0.296 0.219 0.202 0.0415 VIII
D8 - M1 21.6 x 45.7 144.416 0.311 0.191 0.189 0.183 0.0204 VIII
D8 - M2 21.6 x 45.7 144.416 0.311 0.190 0.165 0.152 0.0024 XI
D8 - M3 21.6 x 45.7 144.416 0.312 0.190 0.158 0.149 0.0076 X
D8 - M4 17.8 x 45.7 144.416 0.312 0.190 0.146 0.131 0.0058 VIII

Notes:

  1. Average Velocity: Mean velocity prevailing at the approach cross section.
  2. Abutment Velocity: Velocity measured along the longitudinal passing through the abutment nose at the approach section.
  3. Diverted Velocity: Integrated mean velocity prevailing across the deflected flow portion.
  4. All experiments are performed in a 2.44‑m wide flume measured at the approach section.
  5. Bed slope is set to a value of 0.0007.

Table 20. Experimental conditions for set E runs for abutment scour.

RUN ID MODEL
SIZE
(cm x cm)
FLOW
DISCHARGE
Q (l/s)
APPROACH
DEPTH
Y (m)
AVERAGE
VELOCITY
Vu (m)
ABUTMENT
VELOCITY
Va (m)
DIVERTED
VELOCITY
Vj (m/s)
SCOUR
DEPTH
Ds (m)
SEDIMENT
TYPE
E1 - M1 21.6 x 45.7 147.25 0.279 0.216 0.206 0.204 0.0189 IX
E1 - M2 21.6 x 45.7 147.25 0.284 0.213 0.182 0.173 0.0168 XII
E1 - M3 21.6 x 45.7 147.25 0.292 0.207 0.166 0.155 0.0320 II
E1 - M4 21.6 x 45.7 147.25 0.283 0.213 0.152 0.136 0.0213 XIII
E2 - M1 21.6 x 45.7 172.73 0.305 0.232 0.236 0.234 0.0317 IX
E2 - M2 21.6 x 45.7 172.73 0.297 0.238 0.202 0.188 0.0213 XII
E2 - M3 21.6 x 45.7 172.73 0.293 0.242 0.183 0.178 0.0774 II
E2 - M4 21.6 x 45.7 172.73 0.299 0.237 0.155 0.155 0.0579 XIII
E3 - M1 21.6 x 45.7 202.47 0.293 0.283 0.268 0.265 0.0152 IX
E3 - M2 21.6 x 45.7 202.47 0.299 0.278 0.230 0.223 0.0229 XII
E3 - M3 21.6 x 45.7 202.47 0.305 0.272 0.212 0.204 0.0844 II
E3 - M4 21.6 x 45.7 202.47 0.301 0.276 0.193 0.168 0.0457 XIII
E4 - M1 21.6 x 45.7 232.20 0.294 0.324 0.300 0.297 0.0360 IX
E4 - M2 21.6 x 45.7 232.20 0.300 0.317 0.260 0.248 0.0256 XII
E4 - M3 21.6 x 45.7 232.20 0.305 0.312 0.243 0.233 0.0957 II
E4 - M4 21.6 x 45.7 232.20 0.299 0.319 0.213 0.173 0.0579 XIII
E5 - M1 21.6 x 45.7 263.35 0.299 0.362 0.332 0.329 0.0500 IX
E5 - M2 21.6 x 45.7 263.35 0.303 0.357 0.298 0.286 0.0399 XII
E5 - M3 21.6 x 45.7 263.35 0.313 0.345 0.272 0.267 0.1481 II
E5 - M4 21.6 x 45.7 263.35 0.301 0.359 0.251 0.223 0.0671 XIII
E6 - M1 21.6 x 45.7 311.49 0.293 0.437 0.416 0.417 0.1094 IX
E6 - M2 21.6 x 45.7 311.49 0.298 0.429 0.356 0.337 0.0884 XII
E6 - M3 21.6 x 45.7 311.49 0.307 0.417 0.320 0.292 0.2060 II
E6 - M4 21.6 x 45.7 311.49 0.287 0.446 0.337 0.320 0.1301 XIII
E7 - M1 21.6 x 45.7 368.12 0.306 0.493 0.477 0.475 0.1576 IX
E7 - M2 21.6 x 45.7 368.12 0.310 0.488 0.412 0.395 0.1027 XII
E7 - M3 21.6 x 45.7 368.12 0.315 0.479 0.383 0.360 0.2652 II
E7 - M4 21.6 x 45.7 368.12 0.288 0.524 0.405 0.386 0.2103 XIII
E8 - M1 21.6 x 45.7 450.24 0.307 0.601 0.593 0.583 0.3216 IX
E8 - M2 21.6 x 45.7 450.24 0.308 0.600 0.511 0.501 0.2188 XII
E8 - M3 21.6 x 45.7 450.24 0.297 0.621 0.506 0.486 0.0884 XIV
E8 - M4 21.6 x 45.7 450.24 0.296 0.625 0.390 0.309 0.2149 XIII
E9 - M3 21.6 x 45.7 478.55 0.299 0.657 0.649 0.612 0.1890 XIV
E9 - M4 21.6 x 45.7 478.55 0.274 0.715 0.519 0.496 0.1728 XVI
E10 - M3 21.6 x 45.7 518.20 0.283 0.750 0.713 0.685 0.3158 XIV
E10 - M4 21.6 x 45.7 518.20 0.274 0.775 0.669 0.601 0.3136 XVI

Notes:

1. Average Velocity: Mean velocity prevailing at the approach cross section.

2. Abutment Velocity: Velocity measured along the longitudinal passing through the abutment nose at the approach section.

3. Diverted Velocity: Integrated mean velocity prevailing across the deflected flow portion.

4. All experiments are performed in a 2.44‑m wide flume measured at the approach section.

5. Bed slope is set to a value of 0.0007.

Table 21. Experimental conditions for set F runs for abutment scour.

RUNID MODEL
SIZE
(cm x cm)
FLOW
DISCHARGE
Q (l/s)
APPROACH
DEPTH
Y (m)
AVERAGE
VELOCITY
Vu (m/s)
DIVERTED
VELOCITY
Vj (m/s)
SEDIMENT
TYPE
F1 - MA 20.3 x 96.5 277.505 0.226 0.226 0.241 XV
F1 - MB 21.6 x 96.5 277.505 0.216 0.216 0.253 XV
F1 - MC 64.8 x 96.5 277.505 0.223 0.223 0.241 XV
F1 - MD 43.2 x 96.5 277.505 0.213 0.213 0.253 XV
F2 - MA 20.3 x 96.5 351.129 0.226 0.226 0.308 XV
F2 - MB 21.6 x 96.5 351.129 0.213 0.213 0.323 XV
F2 - MC 64.8 x 96.5 351.129 0.219 0.219 0.308 XV
F2 - MD 43.2 x 96.5 351.129 0.210 0.210 0.323 XV
F3 - MA 20.3 x 96.5 390.772 0.198 0.198 0.393 XV
F3 - MB 21.6 x 96.5 390.772 0.185 0.185 0.411 XV
F3 - MC 64.8 x 96.5 390.772 0.192 0.192 0.393 XV
F4 - MD 43.2 x 96.5 390.772 0.183 0.183 0.411 XV

Notes:

  1. Average Velocity: Mean velocity prevailing at the approach cross section.
  2. Abutment Velocity: Velocity measured along the longitudinal passing through the abutment nose at the approach section.
  3. Diverted Velocity: Integrated mean velocity prevailing across the deflected flow portion.
  4. All experiments are performed in a 5.2‑m wide flume measured at the approach section.
  5. Bed slope is set to a value of 0.0007.

Table 22. Properties of sediment mixture types used in abutment scour experiments.

SEDIMENT TYPE D16
(mm)
D50
(mm)
D84
(mm)
D90
(mm)
D95
(mm)
D100
(mm)
sigmag
I 0.07 0.10 0.14 0.15 0.17 0.25 1.40
II 0.59 0.78 1.00 1.10 1.15 1.19 1.30
II 1.60 1.80 2.20 2.30 2.35 2.38 1.17
IV 0.86 1.80 3.70 4.10 5.00 5.60 2.07
V 0.36 1.80 5.50 6.70 8.00 10.00 3.91
VI 1.60 1.80 2.20 3.90 4.80 5.60 1.17
VII 0.07 0.10 0.14 2.20 2.35 2.83 1.40
VIII 0.31 0.78 1.83 2.10 2.35 4.00 2.43
IX 0.23 0.78 2.65 3.20 4.20 9.00 3.40
X 0.31 0.78 1.83 2.10 2.35 10.00 2.43
XI 0.31 0.78 1.83 2.80 5.00 10.00 2.43
XII 0.23 0.78 2.65 4.76 6.40 9.00 3.40
XIII 0.02 0.65 0.95 1.05 1.10 1.20 6.60
XIV 2.00 3.10 4.20 4.50 5.00 7.00 1.45
XV 0.25 0.55 1.10 1.30 1.50 2.38 2.10
XVI 1.30 2.70 3.70 3.90 4.20 7.00 1.68

Notes:

D16, D50, D84, D90, D95, D100 = Sediment size for which 26, 50, 84, 90, 95, and 100 percent of sediment is finer by weight, respectively.

sigmag = Gradation Coefficient, (D84 /D16)0.5.

3.4 ANALYSIS

In the following analysis, the governing parameters that were found to be affecting abutment scour are presented first. Second, the results of scour experiments utilizing fine uniform sand with 0.1-mm median diameter are given. Third, adjustments to nonuniform mixtures are discussed as a function of gradation coefficients. Finally, the newly developed equation for nonuniform sediment mixtures is presented, including adjustments for coarse fractions.

Governing Parameters

In designing the experimental program given in section 3.3, series of geometry, flow, and sediment properties were considered for relating the local scour to physical parameters. Among the geometric properties, abutment protrusion length is the most commonly used scaling parameter. In a physical sense, the larger the vertically projected length of the protrusion into the flow, the larger the expected local scour. However, as commonly observed in the field, beyond a certain protrusion length, the stagnation zone that forms in front of the abutment alters the behavior. Along with the protrusion length, the second commonly used parameter in relating scour to a physical length dimension is the flow depth. For this purpose, various depth values at various locations along and across the channel have been proposed in the past. Since the present experiments were conducted in a rectangular channel with no overbank regions, and since the main focus of the study was quantifying effects of sediment properties, the effects of return flows could not be accounted. However, to account for the governing geometric length parameter, after examining various scaling parameters, the square root of the blocked flow area was adopted for the length scaling.

 

  Equation 17. L sub lowercase C equals the square root of the product of lowercase A times Y sub lowercase J. (17)

Figure 27. Graph. Variation of dimensionless abutment scour with deflected flow excess velocity. In this figure, dimensionless abutment scour is defined as depth of scour divided by characteristic length.  The numerous experimental data points follow a trend-line where increasing excess velocity increases dimensionless scour almost linearly at the beginning and more gradually beyond a threshold.

Figure 27. Variation of dimensionless abutment scour with deflected flow excess velocity.

where Yj is the average depth in the approach to the abutment. Flow parameters considered in the analysis included: average free stream velocity, Vu, abutment in-line velocity, Va, depth- and width-averaged deflected flow zone velocity, Vj, and the Froude number, momentum, and energy of the deflected flow . Among these flow variables, Va and Vj were found to be the most significant parameters. Since Vj reflects the approach region upstream from the abutment, and since it is related to the abutment nose velocities, it was chosen as the dominant velocity parameter. Using an approach similar to the approach for pier scour, a dimensionless velocity termed as deflected flow excess velocity was derived. This velocity is given by:

 
Equation 18. Greek phi sub lowercase J equals the sum of V sub lowercase J minus V sub lowercase I divided by V sub lowercase C.
(18)

where Vc and Vi are the critical velocity at the approach mobilizing the bed, and scour initiating velocity at the abutment nose, respectively. These two quantities were measured in the experiments. However, they can be obtained through Neill's equation(19):

 
Equation 19. V sub lowercase C equals 1.58 times open bracket open parenthesis S sub lowercase S minus 1 closed parenthesis times lowercase G times D sub 50 closed bracket to the one-half power times open parenthesis Y divided by D sub 50 closed parenthesis to the 0.167 power.
(19)

and Vi . 0.4 Vc for abutment scour initiation. According to Abdou(7), in computing Vc for nonuniform mixtures using equation 19, the term D50 should be replaced by D90. Utilizing Ds / Lc and Greek phi sub lowercase J equals the sum of V sub lowercase J as the dependent and independent parameters, the data in figure 26 are replotted in figure 27. As can be seen, the improvement is remarkable.

Scour in Uniform Mixtures

To eliminate the effects of coarse size fraction on the resulting abutment scour, a series of experiments was conducted using a uniform fine sand mixture with median diameter of 0.1 mm. The scour corresponding to these conditions represents an envelop condition where adjustments for size gradation and coarse fraction can be applied. Using Ds /Lc and Nj, and accommodating a residual correction factor due to (Y/a), the following relationship was derived (20):

 
Equation 20. D sub lowercase S divided by L sub lowercase C equal to K sub Greek phi times Greek phi sub lowercase J.
(20)

where

 
Equation 21. K sub Greek phi equals 3.75 minus 0.41 times the quotient of lowercase A divided by Y.
(21)

Figure 28(a) presents the measured and computed abutment scour for the uniform fine sand. The uniform scour relationship given above can be adjusted for gradation and coarse fraction effects by introducing additional parameters. For this purpose two different approaches are followed. The first approach makes gradation corrections to the predicted scour values, whereas the second approach introduces a coarse fraction correction. These approaches are given below.

Scour in Graded Mixtures

The scour in mixtures with different gradations can be adjusted by introducing a gradation adjustment factor, Ks. This adjustment factor was determined from experimental data by obtaining ratios of scour in graded material and uniform mixtures. A series of curves was developed for 0.78-mm and 1.8-mm sand. These curves, which exhibited very similar features, were then combined into a single set of curves given in figure 28(a). As shown in this figure, Ks is not a constant but varies with flow intensity. Similar to the pier scour corrections, the scour reductions are negligible for low flows and for flows with high intensities. However, the adjustments are significant for a wide range of intermediate flows. The values obtained from figure 28(a) can be directly applied to uniform scour estimates from equation 20 to obtain gradation adjusted estimates for given deflected flow excess velocities.

Coarse Material Adjustments

Experimental results from the study have shown that abutment scour in nonuniform mixtures is greatly affected by the presence of coarse sizes. It was found that the sediment size corresponding to the coarsest 15 percent have a significant effect on the resulting scour. Using results of experiments, the following coarse fraction correction was developed.

 
Equation 22. D sub lowercase S divided by L sub lowercase C equals K sub lowercase N times K sub Greek theta times K sub 15 times K sub Greek phi times Greek phi sub lowercase J.
(22)

where the adjustments and K2 (flow inclination factor in HEC-18(13)) are given by:

 
Equation 23. K sub Greek phi equals 3.75 minus 0.41 times the quotient of lowercase A divided by Y.
(23)
 
Equation 24. K sub Greek theta equals the quotient of Greek theta divided by 90 to the 0.13 power.
(24)

and Kn is abutment shape factor (given in HEC-18 as 1.0 for vertical wall abutments; 0.82 for wing-wall abutments; and 0.55 for spillthrough abutments). The factor K15 is to account for the composition of the coarsest 15th percentile and is obtained from figure 28(b) graphically. It is expressed by Abdeldayem(20) in terms of a sediment weighing factor Wg:

 
Equation 25. K sub 15 equals lowercase F open parenthesis W sub lowercase G closed parenthesis.
(25)

where

 
Equation 26. W sub lowercase G equals summation from lowercase J equals 85 to lowercase J equals 100 of lowercase P sub lowercase J times the square of lowercase D sub lowercase J.
(26)

pj is the fraction falling into a size group j (percent finer by weight), and dj is the sediment size for which j percent of sediment in the mixture are finer. The term Wg is a term similar to the coarse fraction size Dcfm used earlier in chapter 2. It represents the size of the coarse fraction by the ratio of areas occupied by them rather than the mean size represented by Dcfm. Figure 29 shows the agreement of this equation with the experimental data.

Figure 28. Graph.  Adjustment factors for gradation and coarse material fraction: (A) gradation reduction factor; (B) coarse fraction adjustment, K sub 15.  This figure consists of two graphs.  Graph A shows the variation of gradation reduction factor with deflected flow excess velocity.  The gradation reduction factor is reduced sharply from 1.0 (no effect) to 0.2 for the range of excess velocities from 0 to 0.3 and increases back to 1.0 for excess velocities ranging from 0.3 to 0.9. The behavior is similar for different sediment gradation factors but the location of minimum and its value show variation.  In this figure, only two cases are presented corresponding to Greek sigma sub lowercase G equal to 2.3 and 3.4.  Graph B shows the variation of the adjustment factor for coarse material fraction K sub 15 with sediment parameter W sub lowercase G in millimeters squared as a curve.  This is a gradual decay curve that declines from 1.0 to 0.8 for sediment parameter values ranging from 0 to 10.  For W sub lowercase G values between 0 and 2, the function shows an abrupt increase to 1.45 and back to 0.9.

Figure 28. Graph.  Adjustment factors for gradation and coarse material fraction: (A) gradation reduction factor; (B) coarse fraction adjustment, K sub 15.  This figure consists of two graphs.  Graph A shows the variation of gradation reduction factor with deflected flow excess velocity.  The gradation reduction factor is reduced sharply from 1.0 (no effect) to 0.2 for the range of excess velocities from 0 to 0.3 and increases back to 1.0 for excess velocities ranging from 0.3 to 0.9. The behavior is similar for different sediment gradation factors but the location of minimum and its value show variation.  In this figure, only two cases are presented corresponding to Greek sigma sub lowercase G equal to 2.3 and 3.4.  Graph B shows the variation of the adjustment factor for coarse material fraction K sub 15 with sediment parameter W sub lowercase G in millimeters squared as a curve.  This is a gradual decay curve that declines from 1.0 to 0.8 for sediment parameter values ranging from 0 to 10.  For W sub lowercase G values between 0 and 2, the function shows an abrupt increase to 1.45 and back to 0.9.

Figure 28. Adjustment factors for gradation and coarse material fraction: (a) gradation reduction factor; (b) coarse fraction adjustment, K15.

(a)

Figure 29. Graph. Measured and computed abutment scour for the hydrodynamics flume experiments: (A) for uniform mixtures; (B) all mixtures. This is a two-part figure that shows measured and computed abutment scour.  In graph A, the comparison is for uniform mixtures.  The data from different uniform sand experiments lie along a straight line at 45 degrees.  In graph B, the comparison is shown for data from all mixtures.  The data from different experiments lie along a straight line at 45 degrees that defines perfect agreement.

(b)

Figure 29. Graph. Measured and computed abutment scour for the hydrodynamics flume experiments: (A) for uniform mixtures; (B) all mixtures. This is a two-part figure that shows measured and computed abutment scour.  In graph A, the comparison is for uniform mixtures.  The data from different uniform sand experiments lie along a straight line at 45 degrees.  In graph B, the comparison is shown for data from all mixtures.  The data from different experiments lie along a straight line at 45 degrees that defines perfect agreement.

Figure 29. Measured and computed abutment scour for the hydrodynamics flume experiments: (a) for uniform mixtures; (b) all mixtures.

3.5 CONCLUSIONS

The following summarizes conclusions from this study:

  1. It is experimentally proven that clear-water scour at abutments is controlled primarily by the coarse fractions available in the sediment mixture. Sediment mixtures with the same coarse fraction distributions produce the same scour regardless of their mean diameter and gradation coefficients if they are subjected to the same flow intensities.
  2. A new clear-water scour predictor that relates the normalized scour depth (Ds / Lc) to the deflected flow excess velocity () was developed. This equation, which provides adjustments for the presence of coarse material in nonuniform mixtures, is given as:

 
Equation 22. D sub lowercase S divided by L sub lowercase C equals K sub lowercase N times K sub Greek theta times K sub 15 times K sub Greek phi times Greek phi sub lowercase J.
(22)
  1. Gradation reduction factors for different flow conditions can be obtained from the Ks versus chart given in figure 28(a). These factors can be used in conjunction with the clear-water scour predictor given by:

 
Equation 20. D sub lowercase S divided by L sub lowercase C equal to K sub Greek phi times Greek phi sub lowercase J.
(20)
  1. Local scour at abutments is related to flow parameters that represent the deflected mass of fluid that is diverted from its natural path due to the presence of the abutment.
  2. For graded sediment mixtures, clear-water scour at abutments is primarily dependent on the diverted velocity (~V 2.5), then on the abutment protrusion length (~ a 1.1), and then to a lesser extent on the flow depth (~Y 0.27).
  3. The characteristic length, Lc , is a favorable length factor for normalizing the scour depth.
  4. The deflected flow excess velocity (phi subscript j) can successfully describe the local scour phenomenon.
  5. For clear-water conditions, uniform sediments preserve the value of the gradient (Partial differential D subscript 5 /  partial differential V subscript j), and regardless of their mean size, result in the same ultimate scour.
  6. The available clear-water scour data are enriched with 384 case studies covering a wide range of hydraulic, geometric, and sediment conditions.
  7. Available data provide definite trends that support the dependence of local scour on the momentum and energy of the deflected flow to be explored in future studies.

The relationships derived in this study were aimed at quantifying the effects of sediment properties on abutment scour. Therefore, the experimental program was limited in its use of protrusion length-to-flow depth ratios (0.3 less than or equal to Y / a less than or equal to 3.0). For conditions involving ratios beyond the study, these effects must be adequately represented.

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The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT).
The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT). The hydraulics and hydrology research program at the TFHRC Federal Highway Administration's (FHWA) R&T Web site portal, which provides access to or information about the Agency’s R&T program, projects, partnerships, publications, and results.
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