LOCAL STRUCTURE INDUCED SEDIMENT SCOUR
D. Max Sheppard Department of Coastal and Oceanographic Engineering and
Alan Wm. Niedoroda Hunter Services
LOCAL STRUCTURE INDUCED SEDIMENT SCOUR
D. Max Sheppard'
Alan Wm. Niedoroda 2
When a structure is placed in the vicinity of the water bottom it will alter the local flow field. This in turn will modify the bottom shear stress near the structure and can affect the local sediment transport (erosion/accretion). In general, the shear stress is increased resulting in local erosion or scour. The scour that results from the flow modification due to the structure is called local structure induced scour and is the topic of this chapter.
The extent and volume of scour depends on the shape and size of the structure, it's location relative to the bottom, the nature of the primary flow, and the sediment parameters. The flow field in the vicinity of even the most simple of structures is complex and impossible to analyze analytically for situations of practical significance. Researchers in this field have attempted to obtain a general understanding of the physics of these processes through flow visualization in laboratory experiments and by analyzing laboratory and field data. The study that resulted in this publication collected and analyzed published laboratory and field data uncovered in an extensive computer and manual literature search. New empirical equations for dimensionless maximum scour depth as functions of independent dimensionless groups involving structure, sediment and flow variables were developed. A comparison of these equations with others in the literature is presented in appendix B. These equations form the basis of the computer program that accompanies this chapter.
1 Department of Coastal & oceanographic Engineering,
University of Florida, Gain6sville, Florida, 32611.
2 Hunter Services, Gainesville, Florida, 32602.
In spite of the vast number of technical publications on this subject (see the bibliography in Appendix A) there are still many practical situations that have not been investigated or at least not to the point of producing a useable solution. Some of the more important aspects of the structure induced scour problem that need further work are described in appendix C.
This chapter deals with the specific structural shapes where sufficient data exists to predict scour depths and volumes. The structural elements treated here are vertical cylinders, horizontal cylinders, vertical elongated cylinders/piers, and vertical rectangular cross-section piers. In addition, an attempt has been made to compute scour depths and volumes for vertical cylinder groups even though little quantitative information exists for this situation. It should also be pointed out that since most of the available data on structure induced scour was collected in the laboratory, the range of the important dimensionless groups is less than desirable for use in predicting scour in the field. For example, it is not possible to achieve the same flow Reynolds numbers in the laboratory as those experienced in the field. The computer program checks the values of these parameters to see if they fall within the general range of the data. If the input data is such that one or more of the parameters is out of bounds the program changes one of the variables until the parameters are all within range and then computes the scour depth and volume. The output file gives the modified input conditions with the corresponding values of scour depth and volume. The program then determines if the input variables are such that they fall within the extended or extrapolated range (see figures in appendix G). If the data is within this extrapolated range of validity then the scour depth and volume are computed. If the data is out of this range then the velocity is reduced until it comes within range and the scour information computed and written to the output file along with the modified velocity. Thus, even if the input data is out of the extrapolated range the results of the above two computations will be helpful in estimating the actual scour.
DESCRIPTION OF PROCESSES
The process of structure induced scour is somewhat different for waves than for steady currents. The general conclusion by several investigators (e.g. Eadie (1986)) is that the largest scour depths occur with steady currents. Waves alone generate scour but with lesser depths than "equivalent" currents. The addition of waves to currents will accelerate the rate of scour but will have little effect on the maximum scour depth. Since most circumstances of practical significance will involve both waves and currents this simplifies the problem of computing scour depth and volume. That is, one need not be too concerned with the duration of the storm since the presence of waves will, in
most cases, assure that the maximum scour for the given conditions will be reached.
When a steady current flows over a bottom as shown in Figure 1, the boundary layer (water layer affected by the boundary) encompasses the entire depth of the flow. This results in a significant decrease in velocity with depth. When this flow impacts a vertical cylinder the flow is brought to rest (stagnates) along the leading edge of the cylinder producing a "stagnation pressure". The stagnation pressure at any level is proportional to the square of the free stream velocity at that level. Since the velocity decreases with depth the stagnation pressure along the leading edge of the cylinder decreases even more dramatically (due to the velocity squared dependency) resulting in a strong vertical pressure gradient. The pressure gradient in turn generates a vortex with a horizontal axis as shown in Figure 1. when viewed from above this vortex has the appearance of a horseshoe and thus is called a horseshoe vortex. The bottom shear stress and the near bottom turbulence g-en-e-r-aTed by this secondary flow is the main scour mechanism for steady flow around blunt vertical structures.
A second, somewhat independent, scour producing flow process exists due to flow acceleration around the structure and due to flow separation on the structure. The flow moving around a cylinder accelerates until it reaches the maximum breath of the cylinder. This accelerated flow results in an increased bottom shear stress which in turn can produce a scour depression. once the flow passes the maximum width of the cylinder it experiences an increasing pressure with distance (adverse pressure gradient). The fluid adjacent to the cylinder is slowed by the increasing pressure and comes to rest at a point (line) called the point of separation. Beyond the separation point the time mean flow is in the opposite direction and is more turbulent and disorganized than the upstream flow. The nature of the flow in the wake region (region between the separation streamlines; see Figure 1) depends on the Reynolds number based on the cylinder diameter for the flow. For a range of Reynolds numbers an "organized" heading of vortices known as the Karman Vortex Street occurs in the wake. These vortices increase the bottom shear stress in their vicinity and assist in maintaining sediment in suspension thus promoting scour. Most researchers agree, however, that for most steady flow situations around blunt vertical structures the primary scour mechanism is the horseshoe vortex.
Shallow water wave induced flow is almost uniform in depth with a very thin boundary layer near the bottom (see Figure 2). The flow is unsteady and complex but since the flow is (near) uniform the pressure gradient resulting from the variation in stagnation pressure does not exist. The horseshoe vortex is minimal and confined to the very thin boundary layer. The mechanism of flow separation and wake formation discussed above applies here as
well. As the wave progresses and the flow direction reverses, vortices and turbulence in the wake are swept back and forth across the structure thus creating a complex, turbulent flow field near the structure. Acceleration of the flow around the cylinder along with the vorticies and turbulence generated by flow separation are the primary sources of increased bottom shear stress and scour for structures subjected to shallow water waves only.
The discussion thus far has concentrated on the flow field and the bottom shear stress (i.e. the shear stress exerted on the bottom by the moving fluid). The processes by which sediment is placed and maintained in motion are complex but at present it is assumed that if the bottom shear stress exceeds a certain value the sediment entrainment in the flow will occur. If the sediment is made up of a range of particle sizes and densities the critical shear stress (shear stress needed to initiate particle motion) will vary from particle to particle. Thus for a given bottom shear stress the smaller less dense particles may be in motion in suspension (suspended transport), the medium size and density particles may be moving along the bottom (bed load transport) with the even larger and more dense particles remaining stationary on the bottom. For a given water density, viscosity, grain size, and density the critical shear stress can be obtained from the modified Shields curve shown in Figure 3. If the flow is fully developed and steady the bottom shear stress can be related to the depth average velocity by the expressions:
U = 2.5u, ln [3.31--,;
when u. k8 < 5.0
Uc 2.55u ln h
when 5.0 <~ k8 70.0
Uc 2. 5u, ln[ 11.0h
when u > 70.0
where = critical depth average velocity
U= = critical time mean friction velocity
ks = roughness height of bed (bottom)
h = mean water depth
u=1E4= water dynamic viscosity!/ mass density
= kinematic viscosity
z= the turbulent roughness parameter (obtained from
the plot in Figure 4.
For more information on these expressions, see Sleath (1984). The modified Shields curve, Figure 3, the above equations, and the zo curve, Figure 4, are all incorporated into the scour program and used to compute the critical depth average velocity.
Evolution of the scour hole near a vertical cylinder due to a steady current can be described as follows. First consider the "clear water scour" case. Clear water scour means that the current is not sufficient to generate the critical bottom shear stress away from the structure. The flow intensification and enhanced turbulence adjacent to the structure does locally produce bottom shear stresses above the critical entrainment values. Thus, sediment is scoured near the structure and not replaced from upstream. Assume that the sediment consists of a cohesionless quartz sand with a relatively narrow range of diameters and densities. Scour will continue until the scour hole is sufficiently large to alter the flow and reduce the bottom shear stress near the structure to below the critical value. Scour will not proceed beyond this maximum depth unless the flow, sediment or structure conditions change.
Next consider the case where the depth average velocity is sufficient to exceed the critical bottom shear stress away from the structure. This situation will be referred to as "live bed scour". once sediment motion occurs along the bottom, the bottom boundary condition for the flow changes from a no slip condition to one with the velocity of the sediment. This alters the velocity distribution and the bottom shear stress. In addition, there is a constant stream of sediment flowing into and out of
the scour hole. when the sediment flow into the scour hole is equivalent to the flow out the equilibrium or maximum scour depth has been reached. Experimental data indicates that there is at least, a local maximum in the nondimensional maximum scour depth (scour depth divided by structure diameter) just prior to reaching the live bed scour condition. This is illustrated in the sketch in Figure 5.
The flow around horizontal structures on or near the bottom is similar to that for vertical structures but with some significant differences. The case of a steady current over a horizontal cylinder is shown in Figure 6. Flow separation occurs as in the case of a vertical cylinder but the wake is unsymmetrical due to the vertical velocity gradient. once a gap between the cylinder and the bottom exists the flow in this constriction will be accelerated and the bottom shear stress increased. As for other orientations, the scour hole will increase until the bottom shear stress falls below the critical value. Mao (1986) solved for the potential (inviscid, irrotational) flow around a horizontal cylinder (pipeline). The scour depth was increased until flow at the bottom in the scour hole reached the "free stream" value. The free stream value was assumed to be that necessary to produce the critical value of bottom shear stress. The approach is promising but insufficient results were presented to provide useful information. This potential flow problem was solved as part of this study using a finite element analysis. The problem was set up so as to allow a parameter study to be made. That is, set up to allow different initial gaps between the cylinder and the bottom. This would, in general, require the generation of a new grid and starting over for each case considered. A description of this analysis along with figures of the grid and flow are included in appendix C.
When there are multiple vertical structures in close proximity to each other there can be flow interaction which results in additional scour. The existence and/or extent of this interaction depends on the shape, size, spacing and orientation of the structures. As the spacing between the structures is reduced the group begins to "act" like a single porous structure with the associated increased and somewhat homogeneous turbulence within the structure along with a drop in pressure due to blockage of the flow. The level of turbulence and the magnitude of the bottom shear stress reaches a maximum at some spacing of the individual structures. As the spacing is reduced beyond this critical value the flow and turbulence is reduced and in the limit, of course, goes to zero.
There is a range of spacings where the group is in effect a large porous structure. The structure induced scour for this large "group" structure is called dishpan scour after its dish shape (see Figure 7). Shallow water offshore oil platforms have experienced dishpan scour and reported this in the literature but
in a very qualitive way, Posey (1971), Chow (1977) and Chow (1978).
METHOD OF ANALYSIS
The flow and sediment transport processes described above defy a purely analytical treatment at this time. Flow visualization studies and some carefully executed experiments have, however, resulted in a reasonable understanding of the processes involved and the important variables and dimensionless parameters. Armed with this descriptive understanding of the important mechanisms a dimensional analysis can be performed to obtain the pertinent independent dimensionless groups for the problem. Such analyses have been performed by several investigators (e.g. Baker (1978), Eadie (1986)) each with similar results. A dimensional analysis was performed in this study (see Appendix D) with results similar to those obtained earlier. Data from a number of investigators were reanalyzed in this study using the parameters developed in this analysis in an attempt to obtain the best surface fit possible. This analysis (as well as most of the others) resulted in a large number of pertinent independent groups. Many of these could not be considered since values for the variables in these groups were not measured or at least not reported. Different investigators used different parameters, however, and for the most part only fit their own data. In this study three parameters (dimensionless groups) were settled on after numerous attempts with two, three and four groups and combinations of groups. The details of the physics of the problem were strongly considered in selecting the final parameters. The parameters chosen are:
Y= de = Dimensionless Maximum Scour Depth
X1 -1 = Sediment Transport Regime Number
D Structure Aspect Ratio
X 3 = Froude Number based on water depth
where de = maximum scour depth
D = diameter of structure
5 = depth average velocity
Uc = critical depth average velocity
h = water depth
g = acceleration of gravity.
Plots in the literature and plots made in this study suggested that a cubic surface in four dimensions with all cross terms had the right properties to fit the data. Least squares cubic surface fit routines in four and five dimensions were developed to analyze the data. The nineteen term cubic expressions produced by the four dimension analysis are contained in the accompanying scour program for analyzing those structural shapes with sufficient data in the literature to produce reliable coefficients. These equations have the following form:
Y K1 + 2X1 +K3X1 + 4X1
+ KX + KX 2+K X3
5 2 6 2 7 2
"+KX + 2+ K X3
8 3 9 3 103
+ K X X 2+K XX +K XX
14 1 2 12 1 32 3
+ K X X 2+K X 2X
+ K XX2 + K X2X
16 1 3 17 1 3
where K 1-*K19 = coefficients determined by the least square
surface fit routine.
The data used for steady flow around vertical cylinders consisted of laboratory results by Baker (1978), Shen (1966), Jamn (1979) and Chabert (1956) and field data by Arkhipov (1984). These data as well as data used for the other vertical structural shapes are given in Appendix E. Data for scour near vertical and horizontal cylinders subjected to waves only was obtained from a recent paper by Sumer etal (1989). This data is also included in Appendix E.
When analyzing a complex structure or group of structures the following philosophy must be adopted. First the structure must be separated into its components. Some thought must be given as
to the proximity of these components and to how the flow field associated with the individual components will interact. At this point an equivalent model structure or group of structures (constructed of shapes and orientations contained in the computer program) must be created. Experience using the scour program will improve the user's ability to model complex structures with structure producing equivalent scour. Example problems are presented in the scour program documentation that lead the user from beginning to end in a calculation of maximum scour depths and volume of sediment removed for actual DNR problems.
Initial Flow Field for a Steady Current Around a Vertical Cylinder
Instantaneous Velocity Profile Due to Shallow
Vortex Formed During Previous Half Cycle of Wave
Instantaneous View of Streamlines
Initial Flow Field for a Vertical Cylinder in a Wave only Environment
S.= Z (s-1)g zo
Figure 3 Modified Shields Parameter
0.01 I I I !1 I I 1
1 10 100 1000
Turbulent Roughness Parameter Zo as a Function Reynolds Number
IMaximum Scour at Threshold Velocity
SWater I Live-Bed Scour
__. V Sco ur
MEAN VELOCITY, U
Figure 5 Sketch of Equilibrium Scour Depth as a Function of Mean
Approach Flow Velocity
Small KC Number
Large KC Number
_ 1- 1
Figure 6 Structure Induced Scour Near a Horizontal Cylinder for
Two Different Values of Keulegan-Carpenter Number
Figure 7 Dishpan Scour For a Group of Vertical Cylinders
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_ 6~=h =10 ft.
8.0 5 h=5ft
4.0 6= h= 1 ft
0.0 5.0 10.0 15.0 20.0
CYLINDER DIAMETER, D (ft)
Figure G-5 Extrapolated Ranges of validity of structure-Induced Scour Equation. sediment Diameter = 0.25 mm,
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Appendix B -- Recommendations for Future Work
Recommendations For Future Work
Two areas of critical need were identified during the course of this investigation. One deals with local scour depth and volume, the other with global or dishpan scour depth and volume. The majority of scour data reported in the literature is for steady flow around vertical pile-like structures but even here the data are sparse. This study synthesized laboratory and field data for a variety of structural shapes and produced a predictive equation for local scour depths that far exceeds previous equations in range of applicability and accuracy. In addition, for the first time, bounds on the use of a predictive scour equation were established. These bounds provide a way of determining where additional data is needed. For example, the physics of local scour suggest that for a given structure, sediment, and sediment distribution there should be an upper limit to scour depth and volume as the depth mean velocity is increased. The upper limits on velocities used in laboratory experiments thus far have, for the most part, been controlled by scaled practical limits of river flow velocities since much of this work was done for scour near bridge piers. Thus the existence of upper bounds on scour has not been established. For most permitting situations encountered by DNR the geometries and environmental conditions are so complex that accurate prediction of flow velocities is very difficult. If the velocities where maximum scour depths occur are within the range anticipated for severe storm events then using the maximum depths and volumes for the given structure and sediment conditions would be appropriate. If on the other hand, the limiting scour depth is larger than that anticipated under severe storm events better ways of predicting flow velocities are needed. These scour depth bounds need to be determined.
The second problem area is also one of importance to DNR due to its potential impact on the stability of the beach/dune system. If a beach structure is supported by a number of vertical pile-like components, as is usually the case, there is, in addition to local scour near each member, a global or dishpan scour. Dishpan scour gets its name from its dish like shape and extends beyond the structure in all directions a distance of about half the structure diameter and with measured depths up to 15 feet. The collection of piles can be thought of as a single "porous" structure with the dishpan-shaped scour hole being the scour associated with this large composite. The total scour is then the sum of the dishpan scour and the local scour for the individual piles. Dishpan scour is important both from the standpoint of structural integrity and for the loss of sand from the beach/dune system due to the large quantities of sediment involved. Unfortunately, this phenomena is not well understood
and at present no technique exists for its quantification. Not only is there a void in data for dishpan scour (only some few papers giving rough estimates of scour hole size and depth with no information on the environmental conditions causing the scour) to date no one has even suggested a methodology for approaching the problem. A pilot or exploratory study is needed to answer such fundamental questions as; can the processes causing dishpan scour be produced in laboratory scale experiments? if so can the results be extrapolated to prototype scale conditions?, are prototype field studies technically and economically feasible? can an idealized analytical approach provide some insight into the mechanisms causing the scour and help in designing laboratory and/or field experiments?
ADDendix C -- Finite Element Analysis of Horizontal Members
Appendix D -- Dimensional Analysis
The quantities that are important in structure induced scour around vertical cylindrical piles are listed below along with their symbols and dimensions.
Quantity Symbol Dimensions
1. Equilibrium scour depth de L
2. Cylinder diameter D L
3. Sediment diameter ds L
4. Mass density of sediment PS ML-3
5. Mass dinsity of water Pw ML-3
6. Water depth h L
7. Absolute viscosity of water p ML-1T-1
8. Depth mean average velocity U LT-I
9. Depth mean aveage critical
velocity corresponds to the
threshold Shield's parameter Uc LT10. Wave length % L
11. Acceleration due to gravity g LT-2
M = mass
L = length
T = time.
It is assumed that the waves will be depth limited. Thus, specification of the water depth and wave length uniquely determines the wave height and eliminates the need to include it in the analysis.
Using the Buchingham n theorem we obtained the following independent dimensionless groups:
1 = D
2 = Dpi
I3 p '
T5 = 2
By manipulating and combining the above groups, we can obtain the following independent groups that are physically more meaningful.
-1 D T' =T 1
2 2 v
T' = h
Tq = [T 6 ]1
Sediment Transport Regime number, Pile Reynolds number, Structure Aspect Ratio, Froude Number based on water depth, wave length to structure diameter ratio.
Appendix E -- Data Analyzed and Curve Fit Procedures
Data Analyzed And Curve Fit Procedures
A least squares curve f it program for a cubic equation in four dimensional space was used to analyze the data. The cubic
equation includes all of the cross product terms and thus has nineteen terms. It has the following form:
K X 3 1
K X 6 2
K X 9 3
+ K X
+ K X
Y = K + K X +
1 2 1
+ K X +
+ K X +
+ K X
+ K X X
11 1 2
+ K X X
14 1 2
+ K X X
16 1 3
+ K X X
18 2 3
+ K X X +
12 1 3
+ K X X
15 1 2
+ K X X
17 1 3
+ K X X
19 2 3
K X X 13 2 3
where K ... K coefficients determined by the least square
surface fit routine. The data from five different investigators were reanalyzed to obtain the values of the dimensionless groups used in this study. The reanalyzed data is given in Table E-1.
Table E-1. Scour Data for Vertical Cylinders Subjected to Steady Currents
de/DIA U/Uc 1
1.402 -0.255 1.615 -0.170 1.615 -0.064 1.615 -0.017 1.459 0.217 1.459 0.294 1.270 0.387 1.361 0.562 0.738 -0.802 1.008 -0.730 1.320 -0.646 1.197 -0.679
1.344 -0.640 1.164 -0.688 0.992 -0.230 1.016 -0.089 1.246 0.183 1.205 0.264 1.131 0.345
Re DEPTH/DIA FROUDE D/SED.DIA W.DEPTH(CM)
2828 8.681 0.214 3036 8.661 0.230 3383 8.661 0.257 3817 8.661 0.289 4007 8.661 0.304 4962 8.661 0.376 5274 8.661 0.400 5655 8.661 0.429 6367 8.661 0.483 1613 4.331 0.061 2204 4.331 0.084 2885 4.331 0.109 2616 4.331 0.099 2938 4.331 0.111 2544 4.331 0.096 12560 2.165 0.238 14850 2.165 0.282 19291 2.165 0.366 20609 2.165 0.391 21928 2.165 0.416
27.7 27.7 27.7 27.7 27.7 27.7 27.7 27.7 27.7 55.5
55.5 55.5 55.5 110.9 110.9 110.9 110.9 110.9
11.00 11.00 11.00 11.00 11.00 11.00 11.00 11.00 11.00 11.00 11.00 11.00 11.00 11.00 11.00 11.00 11.00 11.00 11.00 11.00
de/DIA U/Uc Re DEPTH/DIA FROUDE D/SED.DIA W.DEPTH(CM)
1.020 0.585 56022 0.746 0.416 635.0 11.37
1.180 0.344 49634 1.438 0.272 635.0 21.92
0.820 -0.175 28840 0.770 0.213 635.0 11.73
0.880 0.155 40376 0.760 0.300 635.0 11.58
1.100 0.952 68447 0.782 0.502 635.0 11.92
1.148 2.235 114378 0.754 0.844 635.0 11.49
1.080 2.649 137299 0.770 0.949 635.0 11.73
1.300 1.632 93585 1.014 0.612 635.0 15.45
1.180 1.036 77486 1.040 0.472 635.0 15.85
0.980 0.692 69247 0.994 0.403 635.0 15.15
1.040 0.240 50753 1.026 0.291 635.0 15.64
0.924 0.002 40300 0.986 0.239 635.0 15.03
0.880 -0.038 40860 1.422 0.199 635.0 21.67
1.120 0.277 48363 1.350 0.266 635.0 20.57
1.380 0.478 55373 1.380 0.306 635.0 21.03
1.200 0.764 72397 1.360 0.370 635.0 20.73
1.180 0.858 70594 1.398 0.382 635.0 21.31
1.220 0.350 56914 1.728 0.258 635.0 26.33
0.750 0.128 48360 1.760 0.214 635.0 26.82
1.088 0.121 58181 1.156 0.290 331.3 17.62
CHABERT & ENGELDINGER'S DATA
de/DIA U/Uo 1 Re DEPTH/DIA FROUDE D/SED.DIA W.DEPTH(CM)
1.250 0.044 85000 2.000 0.607 33.3 20.00
1.233 0.044 127500 1.333 0.607 50.0 20.00
1.740 0.044 38000 2.000 0.768 16.7 10.00
1.310 0.044 76000 1.000 0.768 33.3 10.00
1.960 0.121 33000 4.000 0.471 33.3 20.00
1.700 0.121 66000 2.000 0.471 66.7 20.00
1.353 0.121 99000 1.333 0.471 100.0 20.00
1.900 -0.278 20000 3.940 0.288 96.2 19.70
1.220 -0.278 40000 1.970 0.288 192.3 19.70
0.993 -0.278 60000 1.313 0.288 288.5 19.70
1.800 0.085 21000 7.000 0.227 96.2 35.00
1.200 0.085 42000 3.500 0.227 192.3 35.00
0.913 0.085 63000 2.333 0.227 288.5 35.00
1.150 0.101 37000 1.000 0.374 192.3 10.00
0.887 0.101 55500 0.667 0.374 288.5 10.00
0.869 -0.007 39000 0.385 0.429 260.0 5.00
de/DIA U/c -1 Re DEPTH/DIA FROUDE D/SED.DIA W.DEPTH(CM)
0.417 -0.283 1806000 1.167 0.062 26250.0 490.00
0.451 -0.062 2933600 1.630 0.097 9650.0 629.00
0.830 0.135 4796000 2.589 0.103 10000.0 1139.00 0.942 0.446 4633100 2.584 0.102 27062.5 1119.00 1.020 0.809 7889000 3.147 0.131 19600.0 1542.00 0.820 1.452 3141500 0.295 0.347 15250.0 90.00
0.852 1.783 3904000 0.426 0.359 15250.0 130.00
1.246 2.018 5246000 1.049 0.307 15250.0 320.00
1.311 2.273 5490000 0.918 0.344 15250.0 280.00
1.410 2.541 6588000 1.377 0.337 15250.0 420.00
1.705 3.533 8296000 1.311 0.434 15250.0 400.00
de/DIA U/Uc 1 Re DEPTH/DIA FROUDE D/SED.DIA W.DEPTH(CM)
1.654 0.760 25400 2.008 0.500 203.2 10.20
1.949 1.640 38100 2.008 0.750 203.2 10.20
2.244 2.520 50800 2.008 1.000 203.2 10.20
1.693 -0.028 25400 2.008 0.500 33.9 10.20
1.713 0.263 33020 2.008 0.650 33.9 10.20
1.693 0.458 38100 2.008 0.750 33.9 10.20
1.929 0.652 43180 2.008 0.850 33.9 10.20
2.264 0.944 50800 2.008 1.000 33.9 10.20
2.539 1.332 60960 2.008 1.200 33.9 10.20
1.909 -0.253 25400 2.008 0.500 20.3 10.20
1.437 -0.073 31496 2.008 0.620 20.3 10.20
1.476 -0.989 38100 2.008 0.750 20.3 10.20
2.028 -0.975 50800 2.008 1.000 20.3 10.20
2.106 -0.962 60960 2.008 1.200 20.3 10.20
1.713 -1.000 41656 4.862 0.527 20.3 24.70
2.224 -0.996 71628 4.252 0.969 20.3 21.60
1.850 -0.994 40132 4.744 0.514 20.3 24.10
1.181 -0.977 50800 1.004 0.500 406.4 10.20
1.476 -0.967 76200 1.004 0.750 406.4 10.20
1.565 -0.953 101600 1.004 1.000 406.4 10.20
1.299 -1.005 50800 1.004 0.500 67.7 10.20
1.211 -1.001 66040 1.004 0.650 67.7 10.20
1.220 -1.019 76200 1.004 0.750 67.7 10.20
1.368 -1.019 86360 1.004 0.850 67.7 10.20
1.516 -1.019 101600 1.004 1.000 67.7 10.20
1.713 -1.019 121920 1.004 1.200 67.7 10.20
1.575 -1.015 50800 1.004 0.500 40.6 10.20
1.388 -1.015 62992 1.004 0.620 40.6 10.20
1.368 -1.015 76200 1.004 0.750 40.6 10.20
1.467 -1.014 101600 1.004 1.000 40.6 10.20
1.565 -1.014 121920 1.004 1.200 40.6 10.20
Appendix F -- Comparison of Emperical Scour Prediction Formulas
1. Equation used in this study
Y~~~~ 0.90490f- 15 1)' g ..
= 0.29-0.49 + 0.15 1)
-o.oo00 (51 1) 0.14 (A) + 0.091 ()
-0.0068 A) + 3.2( ) 5.0
+ 0.21 h)()
+0.55 ( ) ( ) + 0.72 (h)
-0.018 1) (h)2 0.044 ( 1)2 (h)
-0.24 ( ) )' +0.12 (2) ( )' 0.
- 0.093 ( 1) 2 (") 11 (
2. CSU's Equation
de 2.0 (D)0.65 ()0.43
3. Jain and Fischer's Equations
for u-u > 0.2
e -= 2.0 0.25 .5
D- 2.0 k_ ~.
for "clear water scour" < 0
de/ 0.25 h 0.
= 1.84 0gh (ho~.
4. University of Auckland's Equations
for L > 18
where K is a function of gradation of sediments
for D < 18
de = 0.45K ( D ) 0.53
Table 1. Scour Depth Prediction Equations and
Average Percent Difference
30.7 92.6 37.1
Maximum Percent Difference
133.0 735.8 277.7
Minimum Percent Difference
0.40 0.93 0.00
Results of Comparison Test.
Average Maximum Minimum Percent Percent Percent Difference Difference Difference
5. Froelich's Equation 32.9 246.4 0.27
for live-bed scour (i.e. U > ~c)
d= 0.32 ) 0.46 0.20D 0.08+
6. Arkhipov's Equation 24.1 147.3 0.25
deC 0' ( h
C, a and ( are functions of ) presented in a graph.
7. Laursen's Equation 49.9 285.1 0.93
de = 1.5 (h)0.3
8. Baker's (1980) Equation 180.0 718.0 2.56
d = 2.0 tanh [2.0- 1.o0] where
( 1 gd,
A r U c
9. Baker's (1981) Equation 104 360 1.08
d 2 tanh ) f f2f3
0 .0 <0.5
f-= 2E 1 0.5 < <1.0
1.0 1.0 < U U.7
f2 and f3 depend on structure shape and flow orientation, and
f2 = f3 = 1.0 for vertical cylinders.
Table 1. Scour Depth Prediction Equations and Results of Comparison Test.
APPENDIX G -- RANGES OF VALIDITY OF SCOUR DEPTH EQUATION
Ranges of Validity Of Scour Depth Equation
Figures G1-G5 are provided to illustrate the effect of the variation of physical quantities like depth mean velocity, cylinder diameter and water depth on the dimensionless scour depth for typical values of sediment diameter and density. The lightly
shaded area of the surface in Figure G2 shows the input conditions under which the dimensionless groups will be within the range of the data used to generate the scour depth equation. Input
conditions that fall within this range are said to be "within the range of validity" of the equation. The scour depths computed in this range of conditions will be the most reliable.
When the environmental conditions (velocity, grain size,
density etc.) and/or structure dimensions yields values of the independent dimensionless groups (Sediment Regime Number, Reynold's Number, Structure Aspect Ratio and Froude Number) that are beyond the domain established by the 98 data points, the "surface" must
be extrapolated. Examination of the data and the surfaces in figures G1-G3 (and other similar figures) led to the conclusion that the surfaces (and thus the equation) follow the trend of the data for some distance beyond the bounds set by the data. This region is indicated as the darker shaded area in Figure G2. These
three dimensional plots are good for visualizing trends but are difficult to use when actual values must be taken from the curves,
thus two dimensional plots of the projections of these surfaces in the horizontal plane are given in Figures G4 and G5. A quick look at the appropriate plot will let the user know if the input data is within the "range of validity", or if not, if it is within the "extrapolated range of validity".
The computer programthat accompanies this report will test to see if the input data is such that the dimensionless groups 1) fall within the range of validity, and 2) fall within the extended range of validity of the equation. If the conditions are outside the range of validity the input conditions are adjusted until the conditions are within bounds and the scour information (depth and
volume) computed. If the conditions are outside the extrapolated range of validity again the conditions are adjusted until they are within these bounds and the scour information computed.
Figure G-1 Surface Plot Using Structure-Induced Scour Equation
For Vertical Cylinders. Sediment Diameter =0.25 mm,
Sediment Mass Density = 165 lb M/ft'.
Water Depth = 5 ft.
Within Rance of
Figure G-2 Surface Plot Using Structure-Induced Scour Equation
For Vertical Cylinders. Sediment Diameter = 0.25 mm,
Sediment Mass Density = 165 lb /ft.
Water Depth = 10 ft.
Figure G-3 Surface Plot Using Structure-Induced Scour Equation
For Vertical Cylinders. Sediment Diameter = 0.25 mm,
Sediment Mass Density = 165 lb M /ft
Water Depth = 20 ft.
5.0 10.0 15.0
CYLINDER DIAMETER, D (ft)
Figure G-4 Ranges Of Validity Of Structure-Induced scour Equation
Sediment Diameter = 0.25 mm, Sediment Mass Density=
165 lb M/ft3 Water Depths = 1, 5, 10, 20 ft.