UFL/COEL-90/019
LOCAL STRUCTURE INDUCED SEDIMENT SCOUR
By
D. Max Sheppard Department of Coastal and Oceanographic Engineering and
Alan Wm. Niedoroda Hunter Services
March 1990
LOCAL STRUCTURE INDUCED SEDIMENT SCOUR
D. Max Sheppard'
and
Alan Wm. Niedoroda 2
March 1990
INTRODUCTION
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.
I
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. h
U = 2.5u, ln [3.31--,;
when u. k8 < 5.0
Uc 2.55u ln h
c2.72z 0
when 5.0 <~ k8 70.0
Uc 2. 5u, ln[ 11.0h
when u > 70.0
U
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
p
= 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
where
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
D
X1 -1 = Sediment Transport Regime Number
1 Uc
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:
2 3
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.
FIGURES
Side View
Figure 1
Surface
- ~.'
Vortex
VHorsesh
Top View
Initial Flow Field for a Steady Current Around a Vertical Cylinder
Instantaneous Velocity Profile Due to Shallow
(Water Wave
Vortex Formed During Previous Half Cycle of Wave
Instantaneous View of Streamlines
TOP VIEW
SIDE VIEW
Figure 2
Initial Flow Field for a Vertical Cylinder in a Wave only Environment
0 'N
0) Ii
II
S.= Z (s-1)g zo
4v
Figure 3 Modified Shields Parameter
Figure 4
0.04 1
0.03
zo
~Hydraulically
0.02 R
Hydrauically~
Smoo
0.01,
0.01 I I I !1 I I 1
1 10 100 1000
V
Turbulent Roughness Parameter Zo as a Function Reynolds Number
C)
IMaximum Scour at Threshold Velocity
0
C.,
CI
2 Clear-I
SWater I Live-Bed Scour
__. V Sco ur
-j Scour
MEAN VELOCITY, U
Figure 5 Sketch of Equilibrium Scour Depth as a Function of Mean
Approach Flow Velocity
Small KC Number
L
Large KC Number
v
L F
_ 1- 1
Figure 6 Structure Induced Scour Near a Horizontal Cylinder for
Two Different Values of Keulegan-Carpenter Number
Original Bottom
Scour
Figure 7 Dishpan Scour For a Group of Vertical Cylinders
Dishpan Scour
APPENDICES
Appendix A -- Bibliography
Abad, G. and J.L. Machemehl, (1974) "An Experimental Study of Scour
Around Marine Foundations Due to Oscillatory Waves &
Unidirectional Currents." The Center for Marine and Coastal
Studies, North Carolina State University, Report No.74-5.
Abel, W. and N.D. Wilson, (1973) "Seafloor Scour Protection for a
Semi-Submersible Drilling Rig on the Nova Scotian Shelf." 5th Annual Offshore Technol. Conf. Preprint No. OTC 1891, II, 631646.
Abou-Seida, M.M., (1963) "Sediment Scour at Structures." University
of California, Hydr. Eng. Lab., Tech. Report, 29 p.
Acrivos, A., L.G. Leal, D.D. Snowden, and F. Pan, (1968) "Further
Experiments on Steady Separated Flows Past Bluff Objects." J. of
Fluid Mechanics, Great Britain, V.34(1), 1-18.
Altinbilek, H.D., (1969) "Localized Scour Around a Vertical Circular
Pile in Oscillatory Flow." Ph.D. Thesis, Georgia Inst. of Tech.,
123 p.
Altinbilek, H.D., (1971) "Similarity Laws for Local Scour with
Special Emphasis on Vertical Circular Pile in Oscillatory Flow."
Proc. Intern. Assoc. for Hydraulic Research, 14th Congress, 29
August-Sept., V.3, "Hydraulic Research and its Impact on the
Environment", paper C41.
Anderson, A.G., (1974) "Scour at Bridge Waterways A Review."
Federal Highway Administration, Offices of Res. & Dev., Report
No. FHWA-RD-75-89, 29 p.
Angus, N.M. and R.L. Moore, (1982) "Scour Repair Methods in the
Southern North Sea." Proc. 14th Annual Offshore Technology Conf.,
Houston, TX, USA, May 3-6, V.4, 385-399.
Arkhipov, G.A., (1984) "Consideration of Sediment Transport when
Calculating Local Scour." Hydrotechnical Construction (English
trans. of Gidrotekhnicheskoe Stroitel'Stvo), April, V.18(4), 149153.
Armbrust, S.F., (1982) "Scour About a Cylindrical Pile Due to Steady
and Oscillatory Motion." Thesis, 136 p.
Bagnold, R.A., (1946) "Motion of Waves in Shallow Water Interaction
Between Waves and Sand Bottoms." Royal Society of London, Proc., Series A. Mathematical and Physical Sciences, V.187(1008), 1-18.
Baker, C.J., (1978) "Vortex Flow Around the Bases of Obstacles."
Ph.D. Dissertation, Univ. of Cambridge, 216 p.
Baker, C.J., (1980) "Turbulent Horseshoe Vortex." J. of Wind
Engineering and Industrial Aerodynamics, V. 6, No. 1-2, 9-23.
Baker, C.J., (1980) "Theoretical Approach to Prediction of Local
Scour Around Bridge Piers." J. of Hydraulic Research, V.18(1), 112.
Baker, C.J., (1981) "New Design Equations for Scour Around Bridge
Piers." J. Hydraulics Division, ASCE, Technical note, (HY4), 507511.
Bea, R.G., (1965) "Drilling Platforms B.I.P.M. Part II. Scour Around
Columns." Hydraulics Laboratory, Report EP 35689, 13 p.
Bea, R.G., (1965) "Drilling Platforms B.I.P.M. Part I. Scour Around
Columns." Hydraulics Laboratory, Report EP 35689, 8 p.
Best, A. de, E.W. Bijker and J.E.W. Wichers, (1971) "Scouring of a
Sand Bed in Front of a Vertical Breakwater." 1st Int. Norw. Tech.
Univ. Port and Ocean Eng. Under Artic Cond. Conf. Proc., V.2,
1077-1086.
Beyl, W. de., (1965) "De brug voor gewoon verkeer over de
Oosterschelde." De Ingenieur, 14 mei pag. B75-B84.
Bijker, E.W., (1966) "The Increase of Bed Shear in a Current Due to
Wave Motion." Proc. 10th Coastal Engineering Conf., V.1(2),
Chap.43, 746-765.
Bijker, E.W., (1967) "Some Considerations About Scales for Coastal
Models with Moveable Bed." Delft Hydraul. Lab, Pub. 50.
Bijker, E.W., (1971) "Longshore Transport Computations." J. Waterways
and Harbours ASCE, V.97, (WW4), 687-701.
Bijker, E.W., (1974) "Coastal Engineering and Offshore Loading
Facilities." Proc. 14th Coastal Engineering Conf., Copenhagen,
Den., V.1, 45-65.
Bijker, E.W., E. van Hijum and P. Vellinga, (1976) "Sand Transport by
Waves." Proc. 15th Coastal Engineering Conf., Hawaii, V.2,
Chap.68, 1149-1167.
Bijker, E.W., (1976) "Wave-Seabed-Structure Interaction." Presented
at Behavior of Offshore Structures Conf., Norwegian Institute of
Technology, 830-845.
Bijker, E.W., (1978) "Science and Design of Navigation Channels and
Off-Shore Trenches." Proc. of 8th World Dredging Conf., Publ by
Cent. Dredging Assoc., Delft, Neth., 69-76.
Bijker, E.W., (1980) "Sedimentation in Channels and Trenches." Proc.
17th Coastal Engineering Conf., Sydney, Australia, V.2, 17081718.
Bijker, E.W. and W. Leeuwestein, (1983) "Interaction Between
Pipelines and the Seabed Under the Influence of Waves and
Currents." Proc. of Symposium, Seabed Mechanics, Sept. 5-9, 1983,
Sect.7, No.22, 235-242.
Bijker, E.W., (1987) "Scour Around Structures." Proc. 20th Coastal
Engineering Conf. Publ. by ASCE N.Y. NY, USA, V.2, 1754-1768.
Blaisdell, F.W., C.L. Anderson and G.G. Hebaus, (1981) "Ultimate
Dimensions of Local Scour." J. of the Hydraulics Division, ASCE,
V.107, HY3, 327-337.
Bornhold B.D. and C.P. Summerhayes, (1977) "Scour and Deposition at
the Foot of the Walvis Ridge in the Northernmost Basin, South
Atlantic." Deep-Sea Research, V.24, 743-752.
Bowers, R., (1963) "A High-power, Low-frequency Sonar for Sub-Bottom
Profiling." J. of the British Institution of Radio Engineers,
V.25(5), 457-460.
Bratteland, E. and P. Bruun, (1974) "Tracer Tests in the Middle North
Sea." Proc. 14th Coastal Engineering Conf., Denmark,. V.3,
Chap.56, 978-990.
Bratteland, E. and P. Bruun, (1975) "Tracer Project-Ekofisk, the
North Sea." Proc. of the 2nd Intern. Iceland University Port &
Ocean Engineering under Arctic Cond. Conf., 205-209.
Breese, G.B.H., P.G.S. Dove and S.G. Hanna, (1988) "Deepwater
Moorings for the Green Canyon Block 29 Development." Proc. 12th
Offshore Tech. Conf., Vol.4, No.5844, 331-342.
Breusers, H.N.C., (1971) "Local Scour Near Offshore Structures."
Offshore Hydrodynamics Symposium, Proc., Oosterveld, M.W.C.
Wageningen, Netherlands, August 25-26, x,1-x, 16 p.
Breusers, H.N.C., (1972) "Local Scour Near Offshore Structures."
Delft Hydraulics Laboratory, Delft, the Netherlands, Publication
No. 105, Series 1, Group 18, Section 18.84, 16 p.
Breusers, H.N.C., (1975) "Computation of Velocity Profiles in Scour
Holes." Int. Assoc. for Hydraul. Res., 16th Congr., Proc., V.2,
Subj B, 300-306.
Breusers, H.N. C., G. Nicollet and H.W. Shen, (1977) "Local Scour
Around Cylindrical Piers." J. of Hydraulic Research, V.15(3),
211-252.
Bruce, P., (1972) "Scour Control System for Submerged Structures."
U.S. Patent Office, Patent No. 3,686,887.
Carstens, M.R. and C.S. Martin, (1963) "Four Topics Pertinent to
Sediment Transport and Scour." Georgia Inst. of Technology, Tech.
Report No. 3, Project No. A-628, 28 p.
Carstens, M.R., (1966) "Similarity Laws for Localized Scour." J. of
the Hydraulics Division, ASCE., Paper 4818, May, V.92(HY2), 1336.
Carstens, T. and H.R. Sharma, (1975) "Local Scour Around Large
Obstructions." Int. Assoc. for Hydraul. Res., 16th Congr., Proc.,
V.2, Subj. B, 251-262.
Carstens, T., (1975) "Seabed Scour by Currents Near Platforms." Proc.
Third Int. Conf. on Port and Ocean Engineering Under Arctic
Conditions., V.2, 991-1006.
Carstens, T., A. Brebner and J.W. Kamphuis, (1976) "Seabed Mobility
Under Vertical Pressure Gradients." BOSS 76', V.1, 423-438.
Carstens, T., (1976) "'Wave-Seabed-Structure Interaction,' by
Bijker." Discussion of paper presented at Behavior of Offshore
Structures Conf. Norwegian Institute of Technology, V.2, 558-562.
Cartwright, D.E. and M.S. Longuet-Higgens, (1956) "The Statistical
Distribution of the Maxima of a Random Function." Royal Society of London, Proc., Series A. Mathematical and Physical Sciences,
V.237 No.1209, 212-232.
Chabert, J. and P. Engeldinger, (1956) "Etude des affouillements
autour des piles de ponts." Lab., Nat. de Hydr. Chatou.
Chang, H.H., (1984) "Modeling General Scour at Bridge Crossings."
Second Bridge Engineering Conf., Minneapolis, MN, Sep. 24-26,
Transportation Research Board, Federal Highway Admin. Washington,
DC, Transportation Research Record 950, V.2, 238-243.
Chari, T.R. and S.N. Guha, (1978) "Model Study of Iceberg Scouring in
North Atlantic." Offshore Technol. Conf. 10th Annu. Proc.,
Houston, TX, May 8-10, Paper OTC 3316, V.4, 2319-2326.
Chari, T.R. and K. Muthukrishnaiah, (1978) "Model Studies of Ocean
Floor Scouring by Icebergs." Proc. of the (ASCE) Conf. on Appl.
Tech. for Cold Environ. Cold Reg. Spec. Conf., Anchorage, Alaska,
May 17-19, Pub. by ASCE, N.Y. NY, V.2, 828-839.
Chesnutt, C.B. and R.C. Schiller, Jr., (1971) "Scour on Gulf Coast
Beaches Due to Wave Action." Offshore Technology Conf., No. OTC
1352, 10 p.
Chesnutt, C.B. and R.C. Schiller, Jr., (1971) "Scour of Simulated
Gulf Coast Sand Beaches Due to Wave Action in Front of Sea Walls and Dune Barriers." Coastal and Ocean Engineering Division, Texas
A & M Univ., C.O.E. Report No. 139, 54 p.
Chiew, Y.M. and B.W. Melville, (1987) "Local Scour Around Bridge
Piers." J. of Hydraulic Research, V.25(1), 15-26.
Chow, W.Y., (1977) "Scour Around a Group of Piles Due to Oscillatory
Wave Motion." Texas A&M Univ., M.S. Thesis, 115 p.
Chow, W.Y. and J.B. Herbich, (1978) "Scour Around A Group of Piles."
10th Annual Offshore Tech. Conf., May 8-11, OTC No. 3308, 22432254.
Christoffersen, J.B., (1980) "A Simple Turbulence Model for a ThreeDimensional Wave Motion on a Rough Bed." Inst. Hydrodynamics and
Hydraulics, Tech. Univ. Denmark., Internal. Rep., No.l.
Clark, A., P. Novak and K. Russell, (1982) "Modelling of Local Scour
with Particular Reference to Offshore Structures." Proc. Int.
Conf. on Hydraulic Modelling of Civil Engineering Structures,
BHRA, Coventry, 411-423.
Clark, A., P. Novak and K. Russell, (1982) "Local Scour at Slender
Cylindrical Piers: A Review and Experimental Analysis." Proc.
Int. Symp. Engineering in Marine Environment, Koninklijke Vlaamse
Ingenieursveringing, Brugge, 2, 43-55.
Clark, A. and P. Novak, (1983) "Local Erosion at Vertical Piles by
Waves and Currents." Proc. of Symposium, Seabed Mechanics, Sept.
5-9, 1983, Sect.7, No.23, 243-249.
Coleman, N.L., (1971) "Analyzing Laboratory Measurements of Scour at
Cylindrical Piers in Sand Beds." Intern. Assoc. for Hydraulic
Research, 14th Congress, 29 August-3 September, Proc., V.3
"Hydraulic Research and its Impact on the Environment", paper
C37.
Costello, C.R., H.L. Kloth, S.W. Liesesmer and K.K. Song, (1979)
"Anti-Scour Method Uses Air Lift Idea." Offshore, V.39(2), 49-50,
(ISSN 0300608).
Crickmore, M.J. and G.H. Lean, (1962) "The Measurement of Sand
Transport by Means of Radioactive Tracers." Royal Society of London. Proc., Series A. Mathematical and Physical Sciences,
V.266(1326), 402-421.
Cry, G.W., (1965) "Tropical Cyclones of the North Atlantic Ocean:
Tracks and Frequencies of Hurricanes and Tropical Stormes 18711963." U.S. Dept. Commerce Weather Bureau Tech., Paper No.55, 148
p.
Delft Hydraulics Laboratory, (1970) "Model Studies on Local Scour."
Hydro Delft, Delft Hydraulics Lab., V.21(7), 5-12.
Delft Hydraulics Laboratory, (1972) "Drilling Platform 'Sedco J'
Scour Around Footings." Report on model investigations, M1180,
Waterloopkundig Laboratorium, Delft, the Netherlands, 46 p.
Delft Hydraulics Laboratory, (1982) "Behaviour of the L1OA/F
Pipelines." Delft., Pub. No. M1818.
Demissie, M., T.W. Soong, N.G. Bhowmik, W.P. Fitzpatrick, W. Hall and
C. Maxwell, (1986) "Secondary Circulation in Natural Streams."
Res. Rep. Univ. Ill. Urbana Champaign Water Resour. Cent.,
No.200, 93 p.
Demissie, M., V.A. Tsihrintzis, W.C. Bogner and N.G. Bhowmik, (1988)
"Scour Channel Development after Spillway Failure." J. of
Hydraulic Engineering, August, V.114(8), 844-860.
Dickson, R.R., D.N. Langhorne, R.S. Millner and E.G. Shreeve, (1978)
"An Examination of a Dredged Channel Using Sector Scanning Sonar in Side-Scan Mode." International Council for the Exploration of
the Sea, J., V.38(1), 41-47.
Dobson, M., (1969) "The Oblique Asdic and its Use in an Investigation
of a Marine High-Energy Environment." Sedimentology, V.13, 105122.
Donnelly, P. and R. Boivin, (1970) "Pattern of Wave Induced Erosion
under Caisson-Type Breakwater." Proc. of the l1th Amer. Soc. of
Civil Eng. Coastal Eng. Conf., V.1, Pts. 1-2, 599-605.
Draper, L., (1967) "Wave Activity at the Sea Bed Around Northwestern
Europe." Marine Geology, V.5, 133-140.
Dungan S.J. and S.R. McLean, (1984) "Model for Flow in Meandering
Streams." Univ. of Washington, Geophysics Program, Seattle, Wash.
USA, Water Resources Research, Sept., V.20(4), 1301-1315.
Eadie, R.W. and J.B. Herbich, (1987) "Scour About a Single,
Cylindrical Pile Due to Combined Random Waves and a Current."
Proc. 20th Coastal Engineering Conf., V.3, 1858-1870.
Edwards, K.W., (1970) "Method of Anchoring Artificial Seaweed formed
of Synthetic Elongated Flexible, in Water Buoyant Elements
Secured to Anchoring Bodies, to a Floor." Shell Intern. Res. Mij
NV, Gr. Brit. 1, 191, 614, C 5/13/70, F 1/22/69.
Einstein, H.A. and R.L. Wiegel, (1970) "A Literature Review on
Erosion and Deposition of Sediment Near Structures in the Ocean."
Contract N62399-69-C-0007 to the U.S. Naval Civil Eng. Lab., Port
Hueneme, Calif., Report HEL 21-6, Hydraulic Eng. Lab., College
of Eng. Univ. of Calif. Berkeley, Calif., 195 p.
Emery, K.O., (1980) "Relative Sea Levels from Tide-Gage Records."
Proc. Natl. Acad. Sci., V.77, 6968-6972.
Espy, W.H. Jr., (1963) "A New Test to Measure the Scour of Cohesive
Sediments." Tech. Report No. Hyd 01-6301, Hydraulic Engineering Lab., Dept. of Civil Engineering, Univ. of Texas, Austin, Texas,
April, 42 p.
Etkins, R., and E.F. Epstein, (1983) "Global Mean Sea Level:
Indicator of Climatic Change?" Science, V.219, 997-998.
10.0
_ 6~=h =10 ft.
8.0 5 h=5ft
o 6.0
z
6 .0
4.0 6= h= 1 ft
I
I:L
LU
2.0
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,
Sediment mass Density = 165 lb Mift3.
Water Depths = 1, 5, 10, 20 ft.
Filson, A.D., A.D. Henderson, L.S. Edelblum and R.D. Pickard, (1988)
"Modification of the Penrod 72 for Green Canyon Block 29
Development." Proc. 20th Offshore Tech. Conf., Vol.4, No.5845,
343-351.
Fisher, A.C. and P.C. Klingeman, (1984) "Local Scour at Fish Rocks."
Water for Resource Development, Proc. of the Conf. Coeur d'Alene,
ID, Aug. 14-17, Pub. by ASCE, N.Y. NY, Inland Empire Section,
286-290.
Fisher, E.A. and P.C. Berner, (1988) "Non-Integral Production Riser
for Green Canyon Block 29 Development." Proc. 20th Offshore Tech.
Conf., V.4, No.5846, 353-360.
Froehlich, D.C., () "Analysis of Onsite Measurements of Scour at
Piers." J. of Hydraulic Engineering,
Gallagher, K.A., (1976) "Performance of the Foundation of the
Christchurch Bay Tower." Proc. of Conf. of Int. Delft, Univ.
Technol. et al Behaviour of Off-Shore Structures, V.2, 549-552.
Gallez, B. and J.N. Butte, (1971) "Regime Non-Stationnaire AutoExcite et Affouillement des Piles." Intern. Assoc. for Hydraulic
Research. 14th Congress, 29 August-3 September, Proc., V.3,
"Hydraulic Research and its Impact on the Environment." paper
C35.
Gautreaux, A.N., (1988) "An Overview of Green Canyon Block 29
Development." Proc. 20th Offshore Tech. Conf., Vol.4, No.5843,
323-330.
Gawne, C.E., (1966) "Shore Changes on Fenwick and Assateague Islands,
Maryland and Virginia" Univ. of Illinois, B.S. Thesis.,
Gaythwaite, J.W., (1978) "Structural Design Considerations in the
Marine Environment." Crandall Dry Dock Engineering, Inc., Dedham, MA. J. of Boston Society of Civil Engineers Sect. ASCE, V.65(3),
67-92.
George, C.B. and J.F.A. Sleath, (1979) "Measurements of Combined
Oscillatory and Steady Flow Over a Rough Bed." J. Hydraulics
Research, V.17, 303-313.
Glazik, G., (1975) "Hydraulic Scale Model Tests on Local Scour Near
Offshore-Structures Under Wave Action." Intern. Assoc. for
Hydraulic Research, V.1, Subj. A, 1-7.
Grass, A.J., (1971) "Structural Features of Turbulent Flow Over
Smooth and Rough Boundaries." J. Fluid Mechanics, V.50, 233-255.
Green, H.P. and T.R. Chari, (1981) "Sediment Compaction Below Iceberg
Furrows." Oceans '81, Conf. Record: The Ocean...An International
Workplace. Boston, Mass. USA, Sept. 16-18, Pub. by IEEE, Oceans
81, V.1, 223-227.
Gundlach, E.R. and S.J. Siah, (1987) "Cause and Elimination of the
Deflation Zones along the Atlantic City (New Jersey) Shoreline."
Coastal Zone '87, Proc. of the Fifth Symposium on Coastal and Ocean Management. Publ. by ASCE, N.Y. NY, USA, V.2, 1357-1369.
Hancu, D.I.S., (1971) "Sur le Calcul des Affouillements Lacaux dans
la Zone des Piles du Pont." Intern. Assoc. for Hydraulic
Research, 14th Congress, 29 August-3 September, Proc., "Hydraulic Research and its Impact on the Environment.", V.3 paper C36, 7 p.
Hansen, E.A., J. Fredsoe, J. and M. Ye, (1986) "Two-Dimensional Scour
Below Pipelines." Proc. of the Intern. Offshore Mechanics and
Arctic Engineering Symposium 5th. Apr. 13-18, Pub. by ASME, N.Y.
NY, V.3, 670-678.
Hattori, M. and R. Kawamata, (1979) "Restoration of Sandy Beaches
Fronting Seawalls." Coastal Structures '79, 388-404.
Herbert, F.G., (1972) "Scour Detection at Bridge Piers and the Like."
Data Design Labs, U.S. 3, 617, 996, C 11/2/71, F 11/24/69.
Herbich, J.B., H.D. Murphy and B. van Weele, (1965) "Scour of Flat
Sand Beaches Due to Wave Action in Front of Sea Walls." Proc. of
the Santa Barbara Specialty Conf. on Coastal Engineering, 705728.
Herbich, J.B. and S.C. Ko, (1968) "Scour of Sand Beaches in Front of
Seawalls." Proc. 11th Coastal Engineering Conf., 622-643.
Herbich, J.B., (1969) "Beach Scour at Seawalls and Natural Barriers."
Texas Engineering Experiment Station, Texas A & M Univ., C.O.E.
Report No. 107.
Herbich, J.B., (1970) "Comparison on Model and Beach Scour Patterns."
Proc. 12th Coastal Engineering Conf., V.2, Chap.80, 1281-1300.
Herbich, J.B., (1977) "Wave-Induced Scour Around Offshore Pipelines."
Ninth Offshore Technology Conf., Texas A & M Univ. Houston, TX.
Offshore Technology Conf., Prepr. 9, V.4, 79-90.
Herbich, J.B., (1981) "Scour Around Pipelines and Other Objects."
Offshore Pipeline Design Elements, Chap. 3, 43-73.
Herbich, J.B., R.E. Schiller, W.A. Dunlap and R.K. Watanabe, (1984)
Seafloor Scour: Design Guidelines for Ocean-Founded Structures.
Pub. by Marcel Dekker Inc, N.Y., NY, and Basel, Switz., 331 p.
Herbich, J.B., (1985) "Hydromechanics of Submarine Pipelines: Design
Problems." Canadian J. of Civil Engineering, Dec., V.12(4), 863874.
Herbich, J.B., (1990) [Preprint of chapter in: Herbich, J.B. [ed],
Handbook of Coastal and Ocean Engineering, Gulf Publ., Houston.],
14 p.
Hesketh-Prichard, R.M. and K. Walsh, (1988) "Production and Workover
Control Systems for the Green Canyon Block 29 Development." Proc.
20th Offshore Tech. Conf., Vol.4, No.5848, 371-379.
Hjorth, P., (1975) "Studies on the Nature of Local Scour." Dept. of
Water Resources Engineering, Lund Institute of Technology, Lund,
Sweden, Bulletin Ser. A, No. 46.
Hughes, W.C., (1980) "Scour Velocities in Ephemeral Channels." J. of
the Hydraulics Division, ASCE, V.106(HY9), 1435-1441.
Hunt, J.C.R., (1973) "A Theory of Turbulent Flow Around Two
Dimensional Bluff Bodies." J. of Fluid Mechanics, Great Britian,
V.61, Part 4, 625-706.
Hutchinson, P.S. and A.J. Raudkivi, (1984) "Case History of a Spaced
Pile Breakwater at Half Moon Bay Marina, Auckland, New Zealand."
Proc. 19th Coastal Engineering Conf., V.3, 2530-2535.
Hydraulics Research Station, (1967) "Drilling Rig Scour Tests an
Investigation of Scour Around the Legs of a Drilling Rig in TwoWay Flow." Wallingford, Berkshire, England, Report No. Ex 377, 31
P.
Ibrahim, A. and C. Nalluri, () "Scour Prediction Around Marine
Pipelines." 697-684.
Ibrahim, A.A., (1987) "Prediction of Scour Velocity Profile at Bridge
Pier." J. Institusi Jurutera Malaysia, No.40, 52-59.
Imberger, J., D. Alach and J. Schepis, (1983) "Scour Behind Circular
Cylinders in Deep Water." Proc. 18th Coastal Engineering Conf.,
V.2, 1522-1554.
Inman, D.L., (1987) "Accretion and Erosion Waves on Beaches." Shore
and Beach, V.55(3-4), 61-66.
Irie, I., S. Sato and N. Tanaka, (1971) "Study on Scouring at the
Foot of Coastal Structures." Coastal Eng. Jap., V.12, 83-98.
Jacobs, E.L., (1984) "Gabions: Flexible Solutions for Urban Erosion."
Proc. 1984 Inter. Symp. on Urban Hydrology, Hydraulics and
Sediment Control. Univ. of Kentucky, Office of Engineering
Services, (Bulletin) UKY BU 135. Pub. by Univ. of Kentucky, Coll.
of Engineering, Lexington, KY, 121-128.
Jain, S.C. and E.E. Fischer, (1979) "Scour Around Circular Bridge
Piers at High Froude Numbers." U.S. Dept. of Commerce, National Technical Information Service, Document No. PB 80-139322., 68 p.
Jain, S.C. and E.E. Fischer, (1980) "Scour Around Bridge Piers at
High Flow Velocities." J. of the Hydraulics Division, ASCE, Nov.,
V.106(HY11), 1827-1842.
Jain, S.C., (1981) "Maximum Clear-Water Scour Around Circular Piers."
American Society of Civil Engineers, J. of the Hydraulics
Division, May, V.107(5), 611-626.
Jansen, E.F.P., (1981) "Scour Underneath a Pipe." [In Dutch]. Delft
University of Technology, Coastal Engineering Group.
Johnson, G.M., (1977) "Use of a Weakly Cohesive Material for Scale
Model Scour Studies in Flood Spillway Design." Hydraulic
Engineering for Improved Water Management: Intern. Assoc. for
Hydraulic Research Congress. 17th., V.4, 509-512.
Jonsson, I.G., (1965) "Friction Factor Diagram for Oscillatory
Boundary Layers." Coastal Engng. Lab., Tech. Univ. Denmark.,
Prog. Rep. 10.
Jonsson, I.G., (1966) "Wave Boundary Layers and Friction Factors."
Proc. 10th Coastal Engineering Conf., Tokyo., V.1(1), 127-148.
Jonsson, I.G. and N.A. Carlsen, (1976) "Experimental and Theoretical
Investigation in an Oscillatory Turbulent Boundary Layer." J.
Hydraulics Research, V.14, 45-60.
Jonsson, I.G., (1978) "A New Approach to Oscillatory Rough Turbulent
Boundary Layers." Inst. Hydrodyn. Hydraul. Engng., Tech. Univ.
Denmark, Paper 17.
Kadib, A., (1963) "Beach Profiles as Affected by Vertical Walls."
Beach Erosion Board Tech., Memo. No. 134.
Kamphuis, J.W., (1978) "Attenuation of Gravity Waves by Bottom
Friction." Coastal Engineering, V.2, 111-118.
Kana, T.W. and L.G. Ward, (1980) "Nearshore Suspended Sediment Load
During Storm and Post-Storm Conditions." Proc. 17th Coastal
Engineering Conf., Australia, V.2, Chap.71, 1158-1173.
Kawata, Y. and Y. Tsuchiya, (1988) "Local Scour Around Cylindrical
Piles Due to Waves and Currents Combined." Proc. 21st Coastal
Engineering Conf., Spain, V.2, Chap.97, 1310-1322.
Katsui, H. and E.W. Bijker, (1986) "Expected Transport Rate of
Material on Seabed." J. Hydraulic Engineering, V.112(9), 861-867.
Kelly, W.E., R.C. Gularte and V.A. Nacci, (1979) "Erosion of Cohesive
Sediments as Rate Process." J. of the Geotechnical Engineering
Division, ASCE, Technical Notes, V.105(GT5), 673-676.
Kemp, P.H. and R.R. Simons, (1982) "The Interaction Between Waves and
a Turbulent Current: Waves Propagating With the Current." J.
Fluid Mechanics, V.116, 227-250.
Kemp, P.H. and R.R. Simons, (1983) "The Interaction of Waves and a
Turbulent Current: Waves Propagating Against the Current." J.
Fluid Mechanics, V.130, 73-89.
Keulegan, G.H. and L.H. Carpenter, (1958) "Forces on Cylinders and
Plates in an Oscillating Fluid." J. of Research., U.S. National
Bureau of Standards, V.60(5), 423-440.
Khanbilvardi, R.M., M.W. Akhtar and A.S. Rogowski, (1988) "Local
Scour Around Cylindrical Objects." Water Res. Bull., American
Water Res. Assoc., Vol.24, No.4, 839-845.
Kjeldsen, S.P., (1974) "Experiments with Local Scour Around Submarine
Pipelines in a Uniform Current." ,
Klein Breteler, M., (1982) "Scour Underneath a Pipeline Due to
Waves." Delft University of Technology, Coastal Engineering Group
Klingman, P.C., (1973) "Hydrologic Evaluations in Bridge Pier Scour
Design." J. of the Hydraulics Division, ASCE, Dec., V.99(HY12),
2175-2184, Proc. Paper 10224.
Knight, D.W., (1975) "A Laboratory Study of Local Scour at Bridge
Piers." Intern. Assoc. for Hydraulic Research, V.2, Subj. B, 243250.
Ko, S.C., (1967) "Scour of Flat Sand Beaches in Front of Seawalls."
Lehigh Univ., Fritz Engineering Lab., Report No. 293.5.
Kobayashi, N. and K.S. Han, (1988) "Erosion at Bend of Gravel
Causeway Due to Waves." J. of Waterway, Port, Coastal and Ocean
Engineering, V.114(2), 297-314.
Komura, S. and H.W. Shen, (1970) "Alternate Scours in Straight
Alluvial Channels." Proc. Japan Soc. Civ. Eng., No. 184, 129-141.
Koutitas, C., N. Kitou and I. Katopodi, (1985) "Model for Circulation
& Sediment Transport by Winds & Waves Around Groyne Systems."
Inter. Conf. on Numerical and Hydraulic Modelling of Ports and
Harbours. Birmingham, Engl., Apr. 23-25, Pub. by BHRA, Cranfield,
Engl., 175-180.
Kubo, K., (1985) "Experimental Study on the Scour Protection Methods
for Sit-On-Bottom Type Offshore Structures." Ocean Space
Utilization '85, Proc. of the Inter. Symp. Tokyo, Japan. June,
Pub. by Springer-Verlag, V.1, 451-458.
Laursen, E.M. and A. Toch, (1953) "A Generalized Model Study of Scour
Around Bridge Piers and Abutments." ,
Laursen, E.M., (1969) "Bridge Design Considering Scour and Risk."
Transportation Engineering J., ASCE, V.96(TE2), 149-164, Proc.
Paper 7262.
Lbrahim, A. and C. Nalluri, (1986) "Scour Prediction Around Marine
Pipelines." Proc. of the Fifth Intern. Offshore Mechanics and
Arctic Engineering (OMAE) Symp. Tokyo, Japan, Apr. 13-18., V.3,
679-684.
LeClerc, J.P., (1971) "Recherche des Lois Regissant les Phenomenes
d'Affouillement au Pied des Piles de Pont Premiers Resultats."
Inter. Assoc. for Hydraulic Research, 14th Congress 29 August-3
September, Proc., Hydraulic Research and its Impact on the
Environment, V.3, paper C39, 8 p.
Leeuwenstein, W. and H.G. Wind, (1984) "Computation of Bed Shear in a
Numerical Model." Proc. 19th Coastal Engineering Conf., V.2,
1685-1702.
Leeuwestein, W., (1983) "MATS-Pipelines, Scour." Delft University of
Technology, Coastal Engineering Group [in Dutch], Vol.I
Lepetit, J.P. and A. Hauguel, (1978) "Numerical Model for Sediment
Transport." Proc. Coastal Eng. Conf. 16th., Hamburg, Ger., Aug.
27-Sep. 3, Pub. by ASCE, N.Y. NY, V.2, 1715-1724.
Luque, R.F., R. Eijpe and C. Niestadt, (1967) "Improvement of
Platform-Leg Stability by Scour Prevention." Koninklijke/Shell,
Exploration en Produktie Laboratorium, Rijswijk, the Netherlands,
Research Report 1255, 21 p.
Luque, R.F. and C. Niestadt, (1968) "Instability of the Drilling
Platform 'Sedneth II' Due to Scour." Exploratie en Produktie
Laboratouium RIJSWIJK, The Netherlands, Investigation 7.27.122,
37 p.
Luque, R. and C. Niestadt, (1969) "Prevention of Scour Around the
Spuds of Existing Drilling Platforms." Exploratie en Produktie Laboratouium RIJSWIJK, The Netherlands, Investigation 7.27.122,
17 p.
Machemehl, J.L. and G. Abad, (1975) "Scour Around Marine
Foundations." Offshore Technology Conf. 7th, Preprints, paper
2313, 691-702.
Machemehl, J.L., (1979) "Pipelines in the Coastal Ocean." Pipeline in
Adverse Environments. American Society of Civil Engineers
Pipeline Division Specialty Conf. New Orleans, V.1, 204-221.
Maidl, B. and W. Schiller, (1979) "Testing and Experiences of
Different Scour Protection Technologies in the North Sea." Ruhr
University, Bochum, Germany, Offshore Technology Conf. 11th
Annual Proc., Houston, TX. April 30 May 3, V.2, 981-987.
Manohar, M., (1955) "Mechanics of Bottom Sediment Movement Due to
Wave Action." U.S. Army, Corps of Engineers, Beach Erosion Board,
Tech. Memo. No. 75., 101 p.
Mao, Y., (1986) "Interaction Between a Pipeline and an Erodible Bed."
Series Paper, Technical University of Denmark, Institute of
Hydrodynamics and Hydraulic Engineering, No.39, 178 p.
Mao, Y. and B.M. Sumer, (1986) "Experiments on Scour Below Pipelines
Exposed to Waves." Inst. Hydrodyn. and Hydraulic Engrg. Tech.
Univ. Denmark, Prog. Rep. 64, 3-12.
Mazurkiewicz, B. and M. Topoinicki, (1978) "Local Scour Around
Offshore Structures, Part 1." [Erozja lokaina dna wokol
hydrotechnicznych buydowli pelnomorskich, czesc 1], (Polish)
Archiwum Hydrotechniki, V.25(3), 403-423.
Melville, B.W. and A.J. Raudkivi, (1977) "Flow Characteristics in
Local Scour at Bridge Piers." J. of Hydraulic Research, V.15(4),
373-380.
Melville, B.W., (1984) "Live-Bed Scour at Bridge Piers." J. of
Hydraulic Engineering, Sept., V.110(9), 1234-1247.
Melville, B.W. and A.J. Sutherland, (1988) "Design Method for Local
Scour at Bridge Piers." J. of Hydraulic Engineering, V.114(10),
1210-1226.
Mendoza, C. and H.W. Shen, (1987) "Refined Modeling to Estimate
Sediment Discharge." Conf. Hydraulic Engineering, Proc. Publ by
ASCE, New York, NY., 1034-1039.
Meng, C.Y., (1986) "Scour at Bridge Piers." Nanyang Technical Inst.
Singapore, JIMAEH.
Miller, J.P. and L.B. Leopold, () "Simple Measurements of
Morphological Changes in River Channels and Hill Slopes." Changes
of Climate, Proc. of the Rome Symposium organized by United
Nations Educational, Scientific, and Cultural Organization and
the World Meteorological Organization, 421-427.
Mitchell, A.C. Jr., (1969) "Method and Apparatus for Alleviating
Scouring About Legs of a Marine Structure." Mobil Oil Corp., US
3,453, m830, C 7/8/69, F 3/13/68.
Mitchell Energy Corporation, (1979) "Scour Formulation." WoodwardClyde Consultant, Houstan, Texas, Draft Report, 67 p.
Moore, W.L., and F.D. Masch Jr., (1962) "Experiments on the Scour
Resistance of Cohesive Sediments." J. of Geophysical Research,
V.67(4), 1437-1449.
Murase, Y., K. Ninomiya and K. Tagaya, (1971) "A Study on Suction and
Breaker and Scouring of a Submersible Offshore Structure." 3rd Annual Offshore Technol. Conf., Preprint No. OTC-1445, II, 297308.
Murase, Y., K. Ninomiya and K. Tagaya, (1972) "A Study on Suction and
Scouring of Sit-On-Bottom Type Offshore Structure." 4th Annual
Spe. of Aime. Offshore Technol. Conf., Preprint OTC-1605, I, 869886.
N.N., (1964) "Ontgronding pijlers Oosterscheldebrug." Waterloopkundig
Laboratorium, Report R 262.
N.N., (1965) "Booreilanden B.I.P.M." II. Ontgronding rond
drijflichamen op de bodem. Waterloopkundig Laboratorium, Report
M II-848 p.
Nakagawa, H. and K. Suzuki, (1975) "An Application of Stochastic
Model of Sediment Motion to Local Scour Around a Bridge Pier."
Int. Assoc for Hydraul. Res. 16th Congr. Proc., Prepr. Fundam.
Tools to be Used in Environ. Probl., Fluvial Hydraul, Univ. of
Sao Paulo, Braz, Jul. 27-Aug. 1, V.2(subj B), 228-235.
Nakagawa, H. and K. Suzuki, (1976) "Local Scour Around Bridge Pier in
Tidal Current." Kyoto Univ., Dec., Coastal Engineering in Japan,
V.19, 89-100.
Nakagawa, H., K. Otsubo and M. Nakagawa, (1982) "Characteristics of
Local Scour Around Bridge Piers for Nonuniform Sediment." Kyoto Univ, Dept. of Civil Engineering, Kyoto, Japan, Transactions of
the Japan Society of Civil Engineers, V.13, 189-181.
Neill, C.R., (1964) "Local Scour Around Bridge Piers A Comparative
Analysis of Model Experiments and Field Data." Research Council
of Canada, Highway and River Engineering Division.
Neill, C.R., (1970) "Local Scour Around Bridge Piers." [Discussion],
J. of the Hydraulics Division, ASCE, V.96(HY5), 1224-1227.
Nicollet, G. and M. Ramette, (1971) "Affouillements au Voisinage de
Piles de Pont Cylindriques Circulaires." Inter. Assoc. for
Hydraulic Research, 14th Congress, 29 August-3 September Proc.,
"Hydraulic Research and its Impact on the Environment", V.3,
paper C38, 8 p.
Niedoroda, A.W., C. Dalton and R.G. Bea, (1981) "The Descriptive
Physics of Scour in the Ocean Environment." Offshore Technology
Conf. 13th, Preprints, paper 4145, 297-304.
Niedoroda, A.W. and C. Dalton, (1982) "A Review of the Fluid
Mechanics of Ocean Scour." Ocean Engng., V.9(2), 159-190.
Nielsen, P., (1979) "Some Basic Concepts of Wave Sediment Transport."
Inst. Hydrodyn. Hydraul., Tech. Univ. Denmark., Ser. Pap. No.20,
160 p.
Ninomiya, K., K. Tagaya and Y. Murase, (1971) "A Study on Suction
Breaker and Scouring of a Submersible Offshore Sturcture."
Offshore Technology Conf., Houston Texas., paper OTC 1445, 12 p.
Ninomiya, K., K. Tagaya and Y. Murase, (1972) "A Study on Suction and
Scouring of Sit-on-bottom Type Offshore Structures." Offshore
Technology Conf. 4th, Preprints, paper 1605, 869-886.
Ninomiya, K., K. Tagaya and Y. Murase, (1973) "Study of Suction and
Scouring of Bottom-Sitting Offshore Structures." Mitsubishi Heavy
Industries, Ltd., Hiroshima, Japan. J. of Petroleum Technology,
V.25, 279-287.
Nouh, M, (1984) "Scour at Bridge Piers in Meandering Channels I."
Channels and Channel Control Structures, Proc. of the ist Intern.
Conf. on Hydraulic Design in Water Resources Engineering, Pub. by
Computational Mechanics Cent. Southampton, Engl., P.1, 75-83.
Nouh, M, (1984) "Scour at Bridge Piers in Meandering Channels II."
Channels and Channel Control Structures, Proc. of the ist Intern.
Conf. on Hydraulic Design in Water Resources Engineering, Pub. by
Computational Mechanics Cent. Southampton, Engl., P.1, 85-90.
Nummedal, D. and J.W. Snedden, (1987) "Sediment Exchange Between the
Shoreface and Continental Shelf Evidence from the Modern Texas
Coast and the Rock Record." Coastal Sediments '87, Proc. of a
Specialty Conf. on Advances in Understanding of Coastal Sediment
Processes, Publ. by ASCE, N.Y. NY, USA, V.2, 2110-2125.
Nuytten, P., (1973) "Mobil Oil Canada's Sable Island Strike Uses
Antiscour Blanket." Offshore, V.32(13), 98-100.
Owen, M.W. and M.F.C. Thorn, (1978) "Sand Transport in Waves and
Currents." Hydraul. Res. Stn, Annual Rep., HMSO, London.
Owen, M.W. and M.F.C. Thorn, (1978) "Effect of Waves on Sand
Transport by Currents." Proc. 16th Coastal Engineering Conf.,
Chap. 100, 1675-1687.
Palmer, H.D., (1968) "Scuba Techniques for Shallow Water Foundation
and Scour Investigations." Offshore Exploration Conf. (OECON),
3rd., 587-602.
Palmer, H.D., (1969) "Wave-Induced Scour on the Sea Floor." Presented
at Civil Engineering in the Oceans-II, Miami Beach, Florida, 703716.
Palmer, H.D., (1970) "Wave-Induced Scour Around Natural and
Artificial Objects." Univ. of Southern California. (Ann Arbor,
Mich.: University Microfilms), Ph.D. thesis.
Pedersen, K.I. and W.F. Cavanaugh, () "Anti-Scour Means for Submarine
Structures." U.S. Patent Office, patent no. 3,859,803.
Berlin, M. and R.G. Dean, (1985) "3-D Model of Bathymetric Response
to Structures." J. of Waterway, Port, Coastal and Ocean
Engineering, March, V.111(2), 153-170.
Porter, W.J. and D.L. Bell, (1975) "Development of Quantitative
Remote Acoustic Indices for Location and Mapping of Sea Floor
Spoil Deposits." Offshore Technology Conf., 7th., Preprints,
paper 2288, 411-418.
Posey, C.J., (1963) "Erosion Protection of Production Structures."
9th Congress I.A.H.R. Dubrovnik, 1157-1162.
Posey, C.J., (1970) "Protection Against Underscour." 2nd annual
Offshore Technol. Conf., Preprint No. OTC-1304, II, 747-752.
Posey, C.J., (1971) "Protection of Offshore Structures Against
Underscour." J. of the Hydraulics Division, ASCE., proc. paper
8230, V.97(HY7), 1011-1016.
Posey, C.J., (1974) "Tests of Scour Protection for Bridge Piers." J.
of the Hydraulics Division, ASCE. December, Proc. paper 11017,
V.100(HY12), 1773-1783.
Powell, K.A., (1987) "Toe Scour at Sea Walls Subject to Wave Action."
Hydraulics Research, Wallingford, Report SR 119, 40 p.
Powers, J.T., (1983) "Hazards to Marine Pipelines in the Breaking
Wave Zone." Proc. of the Conf. on Pipelines in Adverse
Environments 2. San Diego, Calif, USA. Nov. 14-16, 144-158.
Price, W.A. and D.H. Willis, (1976) Trends in the Application of
Research to Solve Coastal Enginering Problems. John Wiley & Sons,
New York, 111-121.
Proot, M.A., (1983) "Scour Underneath a Pipeline Due to Uniform
Current." Delft University of Technology, Coastal Engineering
Group [in Dutch].
Qadar, A., (1981) "Vortex Scour Mechanism at Bridge Piers." Proc. of
the Institution of Civil Engineers (London), Sept., V.71(2), 739757.
Qadar, A, (1981) "Scour by Vortices." J. of the Institution of
Engineers (India), Part CI: Civil Engineering Division, Jan.,
V.61(CI4), 226-231.
Qadar, A., (1983) "Ultimate Bridge Pier Scour." Aligarh Muslim Univ.,
Dept. of Civil Engineering, Aligarh, India, Irrigation and Power,
V.40(1), 77-80.
Raudkivi, A.J. and R. Ettema, (1982) "Scour at Bridge Piers." Papers,
3rd Congress of the Asian and Pacific Regional Division of the Intern. Assoc. for Hydraulic Research., Aug. 24-26, Available
from Int. Assoc for Hydraulic Res. V.B, 277-285.
Raudkivi, A.J. and R. Ettema, (1982) "Stability of Armour Layers in
Rivers." J. of the Hydraulics Division, ASCE, V.108(HY9), 10471057.
Raudkivi, A. and R. Ettema, (1983) "Clear-Water Scour at Cylindrical
Piers." Univ. of Auckland, Acukland, NZ, J. of Hydraulilc
Engineering, V.109(3), 338-350.
Raudkivi, A.J., (1983) "Thoughts on Ripples and Dunes." J. of
Hydraulic Research, V.21(4), 315-321.
Raudkivi, A.J. and S.K. Tan, (1984) "Erosion of Cohesive Soils." J.
of Hydraulic Research, V.22(4), 217-233.
Raudkivi, A.J. and R. Ettema, (1985) "Scour at Cylindrical Bridge
Piers in Armored Beds." J. of Hydraulic Engineering, Apr.,
V.111(4), 713-731.
Raudkivi, A.J., (1986) "Functional Trends of Scour at Bridge Piers."
J. of Hydraulic Engineering, Jan., V.112(1), 1-13.
Richardson, P.D., (1968) "The Generation of Scour Marks Near
Obstacles." J. of Sedimentary Petrology, V.38(4), 965-970.
Roper, A.T., V.R. Schneider and H.W. Shen, (1967) "Analytical
Approach to Local Scour." Proc. 12th Congr. Int. Assoc. Hydraulic
Res. Fort Collins, Colo., V. 3, paper C18, 151-161.
Russell, J.V. and P.H. Kemp, (1977) "A Suggestion of Interaction of
Suspended Sediment with Turbulence in the Thames Estuary." Proc.
6th Australasian Hydraulics and Fluid Mechanics Conf., Adelaide.
Sato, S., N. Tanaka and I. Irie, (1968) "Study on Scouring at the
Foot of Coastal Structures." Proc. 11th Coastal Engineering
Conf., V.1, Chap.37, 579-598.
Savenko, V.Y., (1978) "Calculation of Channel Scouring Under Bridges
with Consideration of the Two-Dimensional Problem."
Hydrotechnical Construction (English trans. of Gidrotekhnicheskoe
Stroitel'Stvo), Feb., No.2, 168-172.
Sawaragi, T., (1966) "Scouring Due to Wave Action at the Toe of
Permeable Coastal Structure." Proc. 10th Coastal Engineering
Conf., 1036-1047.
Scand. Oil Gas Mag., (1975) "New Method Against Sapping of
Platforms." Scand. Oil Gas Mag., V.3(9), 14-15.
Shen, H.W., V.R. Schneider and S.S. Karaki, (1966) "Mechanics of
Local Scour, Data Supplement." Colorado State University. Civil
Engineering Dept., Pub. No. CER66HWS22. U.S. NTIS Pub. No. PB174314, 40 p.
Shen, H.W., V.R. Schneider and S.S. Karaki, (1969) "Local Scour
Around Bridge Piers." J. of the Hydraulics Division, ASCE., Paper
6891, V.95(HY6), 1919-1940.
Shen, H.W. and V.R. Schneider, (1970) "Effect of Bridge Pier Shape on
Local Scour." Presented at the ASCE National Meeting on
Transportation Engineering, July 13-17, Boston Mass., Preprint
1238, 14 p.
Shen, H.W. and B.C. Yen, (1984) "Advances in Open-Channel Hydraulics
after V.T. Chow's Book." J. of Hydrology, V.68, No.1-4, 333-348.
Shiau, J.C. and W.W. Durgin, (1974) "Local Scour at Intake Structures
Due to Waves and Currents, A Model Study for the Donald C. Cook Nuclear Plant." Alden Research Laboratories, Worcester Polytech.
Inst., Holden, Mass. 01520, 45 p.
Silvester, R. and G.R. Mogridge, (1970) "Reach of Waves to the Bed of
the Continental Shelf." Proc. 12th Coastal Engineering Conf.,
V.2, Chap.40, 651-667.
Silvester, R., (1975) "Scour Under a Vertically Oscillating Leg."
Proc. 14th Coastal Engineering Conf., Copenhagen, Denmark, V.2,
1627-1640.
Silvester, R., (1976) "Interaction of Soils-Structures-Waves." Proc.
of BOSS '76, Intern. Conf. on the Behavior of Off-Shore
Structures, Norwegian Institute of Technology, Trondheim, Norway,
V.2, 543-548.
Silvester, R. and L.R. Curtis, (1977) "Scour Due to Flow-Induced
Motions of Offshore Structures." Hydraulic Engineering for
Improved Water Management: Intern. Assoc. for Hydraulic Research
Congress, 17th., V.4, 387-394.
Simons, D.B., R.M. Li and G.K. Cotton, (1984) "Mathematical Model for
Estimating Scour Through Bridge Crossings." Second Bridge
Engineering Conf., Minneapolis, MN, Sep. 24-26, Transportation
Research Board, Federal Highway Admin. Washington, DC,
Transportation Research Record 950, V.2, 244-251.
Sleath, J.F.A., (1978) "Measurements of Bed Load in Oscillatory
Flow." Proc. ASCE, Waterways Port Coastal Ocean Div., V.104(WW4),
291-307.
Smith, R.A., () "Underwater Erosion Control Structure." U.S. Patent
Office, Patent No. 4,337,007.
Soulsby, R.L. and K.R. Dyer, (1981) "The Form of the Near-Bed
Velocity Profile in a Tidally Accelerating Flow." J. Geophysical
Research, V.86 No.C9, 8067-8074.
Stammers, A.J., (1971) "Minimizing Scouring Action in Water Flow
Channels." U.S. 3,563,037, C 2/16/71, F 12/17/68, PR GR BRIT
7/18/68.
Stephens, H.S.(Ed.)and C.A. Stapleton (Ed.), (1982) Papers Presented
at the Intern. Conf. on the Hydraulic Modelling of Civil
Engineering Structures. Coventry, Engl., Sept. 22-24, Pub. by
BHRA Fluid Eng. Cranfield, Bedfordhire, Engl., 552 p.
Stride, A.H. and D.E. Cartwright, (1958) "Sand Transport at Southern
End of the North Sea." Dock and Harbor Authority, V.38, 323-324.
Stuip, J., T. van Heuvel, D. Kranenburg and E.W. Bijker, (1986)
"Shoaling of Channels in Muddy Regions." Conf. World Org. of
Dredging Assoc. 11th Congress, Publ. by Central Dredging Assoc.
Delft, Neth., 34-48.
Suzuki, K., (1982) "Study on the Clear Water Scour Around a
Cylindrical Bridge Pier." Trans. Japan. Soc. Civil Engrs., V.13,
187-188.
Swain, A., (1985) "Equilibrium Beach Profiles: Prediction of Coastal
Erosion Due to Severe Storms." Coastal Zone '85, Proc. of the
Fourth Symposium on Coastal and Ocean Management., Baltimore MD,
July 30 Aug. 2, Pub. by ASCE, N.Y. NY, V.2, 1963-1970.
Teers, M.L., T.M. Stroud and A.J. Masciopinto, (1988) "Subsea
Template and Trees for Green Canyon Block 29 Development." Proc.
20th Offshore Tech. Conf., Vol.4, No.5847, 361-369.
Teramoto, S., K. Tagaya, K. Yatagai, Y. Murase and K. Ninomiya,
(1974) "Study on Scouring of Sit-on-Bottom Type Offshore
Structure." Mitsubishi Nippon Heavy Ind. Tech. Rev., V.10(1), 2324.
Terwindt, J.H.J., H.N. Breusers and J.N. Svasek, (1968) "Experimental
Investigation on Erosion-Sensitivity of Sand-Clay Lamination."
Sedimentology, V.11(1-2), 105-114.
Tesaker, E., (1976) "Erosion Threat at Offshore Structures." Northern
Offshore, V.5(7), 6, 8-9.
Thomas, I.Z., (1971) "Settlement of a Cylindrical Body Placed on the
Surface of an Alluvial River Bottom." Intern. Assoc. for
Hydraulic Research, 14th Congress Proc. V.3, "Hydraulic Research
and its Impact on the Environment.", paper C40.
Titman, R.T.G., (1968) "A Device for Preventing or Reducing Scours at
the Lower Ends of Members Supporting Marine Structures." Gr.
Brit. 1,134,154, C 11/20/68, F 4/24/67, Delta Diving Lt.
Townsend, D.R. and D.W. Farley, (1973) "Design Criteria for Submarine
Pipeline Crossings." American Society of Civil Engineers, J. of
the Hydraulics Division, V.99(HY10), 1659-1678, Paper 10070.
Tsujimoto, T. and T. Mizukami, (1985) "Analytical Approach to Local
Scour Around a Bridge Pier with Continuous Sediment Motion."
Memoirs of the Faculty of Technology, Kanazawa University., Dept.
of Constuction & Environmental Engineering, Oct., V.18(2), 23-31.
Tsujimoto, T. and T. Mizukami, (1986) "Effect of Dune Migration to
Local Scour Around a Bridge Pier." Memoirs of the Faculty of
Technology, Kanazawa University. March, V.19(1), 25-34.
Tsujimoto, T., S. Murakami, T. Fukushima and R. Shibata, (1987)
"Local Scour Around Bridge Piers in Rivers and Its Protection
Works." Memoirs of the Faculty of Technology, Kanazawa
University, V.20(1), 11-21.
Turzillo, L.A., (1972) "Method and Means for Protecting an Earth
Situs Against Scour." CAN 892,885, C2/15/72, F 12/13/68, PR US
3/28/68.
Uda, T. and H. Saito, (1987) "Beach Erosion on the Ogawarako Coast
and Prediction of Shoreline Evolution" Coastal Sediments '87,
Proc. of a Specialty Conf. on Advances in Understanding of
Coastal Sediment Processes. New Orleans, LA, USA, May 12-14, Pub.
by ASCE, N.Y. NY, V.1, 484-489.
van Ast, W. and P.L. de Boer, (1973) "Scour Underneath a Pipeline Due
to Current and/or Waves." Delft University of Technology, Coastal
Engineering Group [in Dutch].
van Meerendonk, E. and A.J.G.M van Roermund, (1981) "Scour Underneath
Pipelines Due to Current." Delft University of Technology,
Coastal Engineering Group [in Dutch].
van Dijk, R.N., (1981) "Experience of Scour in the Southern North
Sea." Society for Underwater Technology J., V.7(1), 18-22.
Vemulakonda, S.R., (1984) "Erosion Control of Scour During
Construction: Report 7, Current -A Wave-Induced Current Model."
Tech. Rep. US Army Eng. Waterw. Exp. Stn. Hl-80-3, Sept., 104 p.
Vickery, B.J., (1966) "Fluctuating Lift and Drag on a Long Cylinder
of Square Cross-Section in a Smooth and in a Turbulent Stream."
J. of Fluid Mechanics, Great Britian, V.25(3), 481-494.
Wang, W.C. and H.W. Shen, (1980) "Statistical Properties of Alluvial
Bed Forms." Proc. of the 3rd Int. Symp. on Stochastic Hydraulics,
Japan Soc. of Civ. Eng., 371-389.
Watanabe, A., K. Maruyama, T. Shimizu and T. Sakakiyama, (1986)
"Numerical Prediction Model of Three-Dimensional Beach
Deformation Around a Structure." Coastal Engineering in Japan,
V.29, 179-194.
Watanabe, A., (1987) "3-Dimensional Numerical Model of Beach
Evolution" Coastal Sediments '87, Proc. of a Specialty Conf. on
Advances in Understanding of Coastal Sediment Processes. New
Orleans, LA, USA, May 12-14, Pub. by ASCE, N.Y. NY, V.1, 802-817.
Watson, T., (1973) "Scour in the North Sea." Annual European Meeting,
2nd Preprints, Society of Petroleum Engineers of AIME, London,
England, April 2-3, paper 4324.
Wells, D.R. and R.M. Sorensen, (1970) "Scour Around a Circular Pile
Due to Oscillatory Wave Motion." Texas A&M University. Sea Grant
Program. Sea Grant publication No. 208., U.S. NTIS publication
No. PB-190681, 136 p.
White, W.R., (1975) "Scour Around Bridge Piers in Steep Streams."
Int. Assoc for Hydraul. Res. 16th Congr. Proc., Prepr. Fundam.
Tools to be Used in Environ. Probl., Fluvial Hydraul, Univ. of
Sao Paulo, Braz, Jul. 27-Aug. 1, V.2, subj B, 279-284.
Wilson, N.D. and W. Abel, (1973) "Seafloor Scour Protection for a
Semi-Submersible Drilling Rig on the Nova Scotian Shelf."
Offshore Tech. Conf., 5th, Preprints, paper 1891, 631-646.
Yalin, S. and R.C.H. Russell, (1962) "Similarity in Sediment
Transport Due to Waves." Proc. 8th Coastal Engineering Conf.,
Ch.12, 151-167.
Zaleski, L.C., (1976) "Anti-Scour Protection by Means of Perforated
Wall." Proc. of Conf. Int. Delft. Univ. Technol. et al Behaviour
of Off-Shore Structures, V.2, 553-555.
Appendix B -- Recommendations for Future Work
Appendix B
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
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
where
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:
de
1 = D
2 = Dpi
Ps
I3 p '
4 2
d
T5 = 2
h
T6 D
x
TI =
Tr7 D'
8
Uc
By manipulating and combining the above groups, we can obtain the following independent groups that are physically more meaningful.
0
1 8
UC
Oc
-1 D T' =T 1
2 2 v
h
T' = h
3 6D
-1i
Tq = [T 6 ]1
TI' =TI
5 7D
U
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
Appendix E
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:
2
K X 3 1
2
K X 6 2
2
K X 9 3
3
+ K X
4 1
3
+ K X
7 2
Y = K + K X +
1 2 1
+ K X +
5 2
+ K X +
8 3
+ K X
10 3
+ K X X
11 1 2
2
+ K X X
14 1 2
2
+ K X X
16 1 3
2
+ K X X
18 2 3
+ K X X +
12 1 3
2
+ K X X
15 1 2
2
+ K X X
17 1 3
2
+ K X X
19 2 3
K X X 13 2 3
where K ... K coefficients determined by the least square
1 19
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
BAKER'S DATA
de/DIA U/Uc 1
1.254 -0.308
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 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
SHEN'S DATA
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
ARKHIPOV'S DATA
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
JAIN'S DATA
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)()
UcD
+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
Do
where K is a function of gradation of sediments
for D < 18
Dso
de = 0.45K ( D ) 0.53
D \Dso
Table 1. Scour Depth Prediction Equations and
Average Percent Difference
9.6
30.7 92.6 37.1
Maximum Percent Difference
40.9
133.0 735.8 277.7
Minimum Percent Difference
0.05
0.40 0.93 0.00
(2. )3
+2.3( '0
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+
DDg= \D50
6. Arkhipov's Equation 24.1 147.3 0.25
deC 0' ( h
where
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
U
( 1 gd,
and
A r U c
-1) gd,]I
9. Baker's (1981) Equation 104 360 1.08
d 2 tanh ) f f2f3
where
0 .0 <0.5
f-= 2E 1 0.5 < <1.0
U- Uc1.0.
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.
(cont.)
APPENDIX G -- RANGES OF VALIDITY OF SCOUR DEPTH EQUATION
Appendix G
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.
N
Nz N
CD
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.
Extrapolated
Range
Within Rance of
Parameters
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.
0
C
0
Co
2:
LU
z
o
1.5
1.0.
0.5
0.0.
<
Figure G-3 Surface Plot Using Structure-Induced Scour Equation
For Vertical Cylinders. Sediment Diameter = 0.25 mm,
3
Sediment Mass Density = 165 lb M /ft
Water Depth = 20 ft.
10.0
8.0 6.0
4.0 2.0
0.0
0.0
5.0 10.0 15.0
20.0
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.
|