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## Material Information- Title:
- Local structure-induced sediment scour at pile groups
- Series Title:
- Local structure-induced sediment scour at pile groups
- Creator:
- Smith, Wendy L.
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- Gainesville, Fla.
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- Coastal & Oceanographic Engineering Dept. of Civil & Coastal Engineering, University of Florida
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- English
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- University of Florida
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UFL/COEL-99/003
LOCAL STRUCTURE-INDUCED SEDIMENT SCOUR AT PILE GROUPS By Wendy L. Smith February, 1999 LOCAL STRUCTURE-INDUCED SEDIMENT SCOUR AT PILE GROUPS By WENDY L. SMITH &THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 1999 ACKNOWLEDGMENTS My sincere gratitude is extended to Dr. D. Max Sheppard as my advisor and chairman of my supervisory committee and Dr. Daniel Hanes and Dr. Ashish Mehta for serving on my committee. I would also like to thank Justin Rostant for his assistance, dedication, and endless enthusiasm which made this research easier and more enjoyable. My thanks also go to the staff at the Coastal and Oceanographic Laboratory, Danny Brown, and Bill Studstill for their spirited assistance with all of the models and equipment for this research. I am also grateful to Mr. Sterling Jones of the Federal Highway Administration for his financial support and professional interest. I would also like to express my heartfelt appreciation to all of the people who supported me through this challenge, including my family, Tom, Lisa, Eric, Tom, Matt, Pete, Ed, Joel, Tiffany, Carrie, and Becky. TABLE OF CONTENTS ACKNOWLEDGMENTS ........................... ii KEY TO SYMBOLS ................................................... v ABSTRACT ........................................................ Viii CHAPTERS 1 INTRODUCTION ...................................................1I 2 SCOUR PROCESSES ................................................ 3 Flow Around a Single Cylindrical Pile ..................................... 4 Parameters ......................................................... 6 Flow Around Pile Groups .............................................. 9 Parameters ........................................................ 11 3 SCOUR PREDICTION............................................... 14 Equations for Predicting Maximum Equilibrium Scour Depth At Single Piles ...........19 University of Florida equation ....................................... 19 HEC- 18 scour prediction equation .....*................................ 21 Equations for Predicting Maximum Equ.ilibrium Scour Depth Around Pile Groups .......24 4 TIME DEPENDENCE OF SCOUR...................................... 29 5 DESIGN LOCAL SCOUR DEPTHS AT PILE GROUPS....................... 33 Illustration of Model Use.............................................. 38 Example 1 ..................................................... 38 Example 2 ..................................................... 40 6 EXPERIMENTAL PROCEDURES...................................... 43 iii Flum e ................................................................ 44 Test Preparation ........................................................ 50 Test Conditions ......................................................... 55 Test Results ........................................................... 56 7 RESULTS AND CONCLUSIONS .......................................... 68 APPENDIX ............................................................... 74 REFERENCES ............................................................ 80 BIOGRAPHICAL SKETCH .................................................. 84 KEY TO SYMBOLS A cross-sectional area of the flow a skew angle b diameter/width of a single pile c1.6 coefficients for the University of Florida scour prediction equation c empirical coefficient for equation 3-9 D* effective diameter/width of pile group D16 sediment size D50 median sediment diameter D84 sediment size D90 sediment size dse maximum equilibrium scour depth d.(a) maximum equilibrium scour depth for a pile group at skew angle a ds(a = 0) maximum equilibrium scour depth for a pile group at zero skew angle dses maximum equilibrium scour depth around an equivalent solid pier ds submerged pile group maximum equilibrium scour depth of a submerged pile group dsps maximum equilbrium scour depth around a skewed pile group Fr Froude number g acceleration due to gravity H dune height H flow head (equation 6-1) h* manometer reading I-P height of pile above the bed k. Nikuradse roughness K. skew angle correction factor/ parameter Kh degree of submergence parameter K. spacing correction factor (equation 3-13) K3 shape parameter (equation 5-3) K spacing parameter K, shape correction factor K2 skew angle correction factor K3 bed condition correction factor K4 bed armoring conection factor K5, K6 empirical coefficients (equation 3-10) L length of pier m number of piles in line with the flow n number of piles normal to the flow Q flow rate s distance between the pile centerlines S.F. safety factor normalizing parameter based on effective width of pile group o sediment size distribution te the time required for the scour hole to develop to a depth at which the increase in depth does not exceed 5 percent of the pier diameter in the succeeding 24 hours U depth averaged approach flow velocity U. critical velocity associated with incipient sediment motion w width of pier WP projected width of a pile group onto a plane normal to the flow Y. depth of approach flow Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science LOCAL STRUCTURE-INDUCED SEDIMENT SCOUR AT PILE GROUPS By Wendy L. Smith May 1999 Chairperson: D. M. Sheppard Major Department: Coastal and Oceanographic Engineering The objective of this thesis is to investigate local scour at pile groups in order to accurately predict the maximum clearwater equilibrium scour depth. The differences between the scour mechanisms and the fluid, flow, sediment, and structure parameters influencing scour depth for single piles and pile groups are discussed. The assumption is made that the relationships between these parameters that have been established for single cylindrical piles are also valid for pile groups. An attempt is made to relate scour depths at pile groups to those at a single cylindrical piles by determining an "effective width" of the pile group that may be applied to the predictive equation for a single cylindrical pile. The additional structure characteristics influencing scour at pile groups include: spacing, group configuration, shape, skew angle, and degree of submergence. To investigate these effects, flume tests were conducted on pile groups with varying spacing, configuration, skewness to the flow, and degree of submergence. It was determined that spacing, configuration, shape, and skew angle all influence the "effective width" of the structure. The influence of each was determined based on laboratory tests conducted for this thesis and the relationships developed by previous researchers. As a component of a complex bridge pier, the degree of submergence of the pilings was also investigated to determine the influence on scour depth. A relationship was determined based on test results where the height of the pile group was varied relative to a constant water depth. These results may be used in conjunction with the results of the tests currently being conducted by the Federal Highway Administration on the other components (pile cap and pier) to determine the total local scour depth of a complex bridge pier. CHAPTER INTRODUCTION Frequently, bridge failure is due to excessive scour, the removal of sediment around the bridge piers. Excessive scour can cause the piles to be undermined and no longer support the bridge. Design against this type of failure is based on the prediction of the maximum depth of scour. Thus, the accuracy of this prediction is important because under-predicting can result in structural damage and possible loss of life, while over-predicting can waste millions of dollars in over design. The phenomenon of scour around bridge piles has been investigated by numerous researchers over several decades. Most of the research was conducted on single cylindrical piles in coliesionless sediment under steady flow conditions. As a result of these laboratory experiments, it is now possible to predict maximum scour depths for a wide range of laboratory scale structures with the use of empirical equations. Because of the volume of work and the level of understanding of the scour processes around simple cylindrical piles, these data sets are valuable for quantifying the effects of many of the relevant factors influencing the scour depth. However, bridge designs are often more complex, using multiple pile bridge piers. The scour mechanisms for multiple pile bridge piers are much more complex than for a simple, cylindrical pile and thus design scour depths are more difficult to predict. This is especially true when the piles are not aligned with the flow. In order to investigate scour around complex bridge piers, it is important to understand the scouring processes and the hydrodynamic effects of the flow around the structure. 2 The objective of this research was to build and improve upon the existing methods and procedures for estimating design scour depths for complex pier geometries by investigating scour at groups of square piles. This work investigates subaerial and submerged rectangular pile group arrays both in-line and skewed to the flow. CHAPTER 2 SCOUR PROCESSES Scour is the removal of sediment caused by flow over an erodible bed. When the flow velocity exceeds the value needed to produce the critical shear stress of the bed material, bedload transport is initiated. The mechanisms of scour at bridge-Eke structures are usually separated into three categories: bed degradation, constriction scour, and local scour. Bed degradation is the general erosion of bed material throughout the waterway. This degradation could change the slope, elevation, and/or contours of the bed, altering the flow. Constriction or contraction scour is that caused by a reduction in the cross-sectional area of the flow, i.e., the presence of a large obstruction in a narrow waterway, constricting the flow. The reduction of flow area causes an increase in velocity and bed shear stress at that location. In practice, the scour caused by constriction is considered negligible when the area of the obstruction is less than approximately 10 percent of the waterway cross-sectional area. Local scour is that due to the alteration of the flow field by the obstruction (e.g., a bridge pier). Local scour is initiated when these effects produce bed shear stresses that exceed the critical value for the bed sediment. 4 For a bed of cohesionless sediment, there are two types of local scour: clearwater and live-bed. Clearwater scour refers to local scour that occurs when the upstream bed shear stress is below the value needed to initiate sediment motion on a flat bed. Equilibrium scour depth is reached when the bed shear stress in the scour hole is reduced to the critical value. Live-bed scour occurs when the upstream bed shear stress exceeds that required for sediment transport. In this case, equilibrium scour depth is reached when the quantity of sediment leaving the scour hole is equivalent to that which is entering the hole. Flow Around a Single Cylindrical Pile The placement of a bridge pile in cohesionless sediment under a uniform, steady flow creates numerous hydrodynamic effects (figure 2-1): o horseshoe vortices at the base and in front of the pile, * downflow on the front edge of the pile, bow wave at the surface on the upstream side of the pile, upflow in the wake region, & wake vortices behind the pile, and * higher flow velocities (spatially accelerated flows around the pile). The introduction of a pile in a uniform, steady flow causes the flow to increase in velocity as it flows around the pile. The increased velocity (and corresponding increased shear stress) initiates scour at the sides of the pile which develops into a scour hole at the pile. The size of the scour hole increases as the surrounding sediment avalanches into the hole and is carried away by the Bow Wave SenWv Horseshoe Vortex A Upflow IWake ~'Vortices Figure 2-1. Flow patterns associated with local scour accelerated flow. A horseshoe vortex is formed by the vertical gradient in stagnation pressure on the leading edge of the pile. As the hole deepens, flow separation occurs at the edge of the scour hole causing a downflow at the front of the pile which enhances the horseshoe vortex at the base of the pile. This vortex is swept around the sides where it narrows in cross section and trails downstream creating a "horseshoe" shape when viewed from above. Numerous researchers (Hannah 1978, Nakagawa and Suzuki 1975, Gosselin 1997, Shen et al. 1966, Melville 1975) have concluded that this horseshoe vortex is the primary mechanism of local scour. Once a sediment particle is put into suspension by the horseshoe vortex, it is swept around the side of the pile. As more sediment is removed, the scour hole is expanded in both width and depth. The horseshoe vortex grows in diameter as the hole deepens, descending into the hole. Melville (1975) observed that as the size and circulation of the horseshoe vortex increases, the Stern Wave 10 1 I 6 strength of the vortex decreases, reducing the velocity near the bottom of the hole, thus the scour process slows as the hole deepens. Other hydrodynamic effects that aid in the removal of sediment are the bow wave, upflow in the wake region, and wake vortices. A bow wave is the rise in flow surface as the kinetic energy of the flow is converted into potential energy at the pile. This creates a surface vortex that rotates opposite to the horseshoe vortex. A pressure difference on the bed from the front to the back of the pile can cause groundwater flow from upstream to downstream. Some researchers think that this has an impact on the rate and depth of local scour. Vertical (wake) vortices are formed at the structure just downstream of the points of flow separation on the pile. Just as in tornadoes, these vortices have a vertical flow component in their interior. The general principles of local scour due to these effects are: * the rate of scour will equal the difference between the capacity for transport out of the scour hole and the rate of supply to the hole, * the rate of scour will decrease as the flow section is enlarged due to the scour, and there will be a limiting extent to the scour depth that depends on the structure shape and size, the sediment properties, and the flow conditions. Parameters Because of the complexity of the flow and sediment transport processes, analytical treatment of scour has not produced meaningful results. Numerous researchers have investigated the simplest case of scour around a single cylindrical bridge pile (Jones, Sheppard, Ettema, Melville, Chiew, Hannah, Gosselin, Shen, Bruesers, and others). Most of them agree that the scour depth produced 7 by flow around a single cylindrical pile in cohesionless sediment depends. the parameters which characterize the critical shear stress of the bed, energy of the flow, and the size and strength of the vortices: 0 fluid: density and viscosity, 0 flow: depth of approach flow, approach flow velocity, 0 sediment: size, density, shape, grain size distribution, and 0 structure: size, shape. The critical shear stress governing sediment transport is a function of the fluid properties (density and viscosity), flow depth (vertical velocity distribution), sediment properties (grain size, shape, and density), and bed roughness (ripples, dunes, etc.). The bed roughness affects the kinetic energy of the flow near the bed and the roughness is a function of the sediment size and bed forms. It is this roughness along with the depth averaged flow velocity that defines the shape of theupstream velocity profile and boundary layer and thus, the bed shear stress. The size of the surface vortex depends directly on the magnitude of the stagnation pressure generated by the approach flow along the pile's centerline. The size of the pile governs the size of the vortices. The larger the pile, the larger the horseshoe vortex. It has been found (Melville and Sutherland 1988, Mostafa et al. 1995b) that if the pile is not cylindrical, the shape has an impact on the equilibrium scour depth. Streamlining the upstream edge of a pile reduces the strength of the horseshoe vortex, thereby reducing scour depth. Streamlining at the downstream end reduces the strength of wake vortices also reducing scour depth. A square-nose pile will have scour depths about 20 percent greater than a sharp-nose pile and 10 percent greater than either a cylindrical or round-nose pile (Richardson and Richardson 1989). 8 Often, piles are subjected to flows that approach from an angle (to the sides of the pile). This may be due to the bridge being skewed to the waterway or the result of a shift in flow direction under storm conditions. The angle between the pile (at design conditions) and the flow direction is called the flow skew angle. As the skew angle changes, the shape of a non-cylindrical pile changes relative to the flow and alters the local flow field, thus influencing the scour depth. Laursen and Toch (1956) is probably the best- known research on the influence of skew angle on scour depth for single, solid structures. They investigated rectangular piers, varying the skew angle (a) and aspect ratio (11w) where L is the length of the pier and w is the width. Figure 2-2 shows the influence of a and J.Jw. k~ is defined as the ratio of the projected width of the pile (at skew angle) to the width at zero skew angle. These curves are based on both laboratory and field data; however, no data was presented in their plot. Mostafa, et al (1 995b) conducted numerous experiments (120) at the University of Iowa and the University of Alexandria in an attempt to better predict the scour depth at piers skewed to the flow. Single rectangular and oblong piers with the same pier width were tested, varying 11w for skew angles between 00 and 900. They found that the Laursen and Toch curves underpredict the maximum equilibrium scour depth for rectangular piers at large skew angles (a > 50'). 0 15 30 45 60 Angle of Attack in Degrees 75 90 Figure 2-2. Flow skew angle correction factor by Laursen and Toch (1956) Flow Around Pile Groups The scour processes for flows around single cylindrical piles in a cohesionless sediment have long been recognized (Laursen and Toch 1956, Shen et al. 1966, Melville 1975, Nakagawa and Suzuki 1975, Breusers et al. 1977, and others) for steady flow conditions. However, the flow field is much more complex when there is more than one pile and they are in close proximity to each other (figure 2-3). aJ Y l I/ 1 -0 I 10 Hannah (1978) studied local scour at cylindrical pile groups under uniform, steady flow conditions, concluding that local scour at these groups is affected by four basic mechanisms: 9 reinforcing, 9 sheltering, 0 shed vortices, and * compressed horseshoe vortices. Shed and Wake Vortices Bow Wave Stern Wave C ( Upflow Vortex Reinocn Downflow Shetein Figure 2-3. Flow around multiple piles in close proximity For a pile group where the piles are spaced such that the scour holes overlap, the vortices around the piles interact with each other, and thus the downstream piles reinforce scour at the 11 upstream piles. The downstream piles also aid the scouring at the upstream piles by decreasing the exit slope of the scour hole and lowering the bed level behind the hole. This reduces the energy required (in the scour hole) to transport material out of the hole. As pile separation distance increases, reinforcing of the vortices diminishes. A sheltering effect is observed when an upstream pile blocks the flow to the downstream pile, reducing the approach flow velocity (and thus the shear stress), causing less scour to occur at the downstream pile. This sheltering effect limits the scour behind the front piles, but with development of the hole, material from the rear of the pile is eroded both by the shed vortices and by sliding into the scour hole and being removed by the vortex system. Shed vortices are the eddies that usually form just downstream of the point of flow separation on the pile. These vortices provide low-pressure pockets that assist in Ming sediment from the scour hole, aiding in the scour process at piles in the path of the vortices. When piles are in close proximity, the trailing arms of the horseshoe vortices are compressed. This results in an increase in the velocity of the vortex and a corresponding increase in bed shear stress and scour. Parameters The scour depths produced at pile groups are also influenced by the size and shape of the structure through the skew angle, pile spacing, and group configuration (number and arrangement of piles). However, all of these structure parameters are interrelated, complicating scour depth analysis. 12 Skew angle. Zhao (1996) studied the effects of skew angle on scour depth at Rx8 arrays of cylindrical and square in-line piles. Both groups were composed of uniform-diameter piles with constant pile spacing. The skew angle, a, was varied between 00 and 900. Thao observed the changing influence of the scour mechanisms as the skew angle varied. When the skew angle was small (a < 15' for cylindrical and < 200 for square piles), the compressed horseshoe vortex dominated the scour process and the maximum scour depth occurred near the front of the pile group. When the skew angle was large (a > 200 for cylindrical and > 25* for square piles), the interaction of the wake vortices from the upstream piles on downstream piles dominated and the maximum scour depth occurred along the upstream side of the pile group. Zhao also found differences in the maximum equilibrium scour depth of the skewed pile groups based on the shape of the pile. The maximum depth occurred at a skew angle of 250 for cylindrical piles and approximately 700 for the square piles. The scour depth at skewed pile groups not only varies for different pile shapes and skew angles, but for different pile spacings as well. Pile spacing. Pile spacing influences the vortices created around the piles which interact with each other and the acceleration of the flow due to constriction created by the adjacent piles. These effects are greatly influenced by the distance between the piles. Salim and Jones (1996) and Sheppard et al. (1995a) studied these effects by looking at the ratio s/b where s is the distance between the pile centerlines and b is the diameter/width of a single pile. Salim and Jones investigated groups of square piles in in-line arrays of 3x3, Rx5, and 4x5, varying s/b between 1.5 and 10. Sheppard et al. examined square pile groups in arrays of 3x2, 303, 13 and 3x8, varying s/b between 1 and 9. Both researchers observed an increase and then a decrease in scour depth as s1b increased from 1 to about 3. For values of s/b greater than 3, the scour depths continued to decrease out to approximately 10 where the scour depth was that of a single pile. Group configuration. The arrangement of the piles and number of piles normal to the flow influence the hydrodynamics around the pile group due to the changes in the size of the structure and the interaction of the vortices due to the number of piles. Salim and Jones (1996) investigated the effects of pile arrangements by looking at square piles in a staggered array, 5 piles long and alternating between 3 and 4 piles wide. They found that the group behaved similarly to an equivalent solid structure, even as the structure was rotated with respect to the flow direction. However, at certain angles, the piles lined up with one another, making the structure appear much smaller. Copps (1994) and Hannah (1978) investigated the influence 'of the number of piles normal to the flow, n. Copps analyzed R8, 5x8, and 7x8 arrays of square in-line piles. Hannah examined W, 2xl, 2x2, and 2x3 arrays of in-line cylindrical piles. They both concluded that an increase in the number of piles normal to the flow (increasing the effective width of the structure) increases scour depth. It was observed that this effect decreases as spacing between the piles increases. Hannah's (1978) research also included an investigation of the influence of the number of piles in line with the flow, m, on scour depth. He concluded that for in-line pile groups, m has only a minor effect on the maximum depth of scour. CHAPTER 3 SCOUR PREDICTION There has been an increased interest in the prediction of structure-induced scour in the last decade. As a result of numerous laboratory experiments, it is now possible to predict equilibrium scour depths for a limited range of laboratory scale structures through the use of empirical equations. The variables that must be included in a scour predicting equation are those that characterize the primary local scour mechanisms. Several researchers (Melville and Sutherland 1988, Sheppard 1998, Raudkivi 1986, and Ettema 1980) have examined the influence of the numerous parameters influencing scour around a single cylindrical pile. Most agree that the primary fluid, flow, sediment, and structure parameters that influence scour depth near single piles in cohesionless sediments are: * depth of approach flow, y., * sediment size, D50, * sediment size distribution, a, * depth averaged approach flow velocity, U, * critical velocity associated with incipient sediment motion, U~, and * structure width, b. However, these researchers have come to different conclusions regarding the dimensionless groups formed from these parameters that should be used to predict the equilibrium scour depth, d, 15 Melville and Sutherland used the parameters, b/D50, yjb and U/U to characterize non-dimensional equilibrium scour depth, d./b. They concluded that as b/D50 exceeded a value of 25, the scour depth becomes independent of this parameter (even though some of their own data showed dependence beyond that value). Sheppard et al. (1995b), using the data from several researchers including their own, found the non-dimensional equilibrium scour depth dependence on the reciprocal of this parameter, D5Job, to go beyond the range reported by Melville and Sutherland. Others have concluded that scour depth is dependent on other dimensionless groups such as Froude Number. Because the number of parameters associated with the scour process is quite large, there have been numerous empirical equations for predicting scour depths. Jones (1984) compared the equations available at that time and found the results to be quite different. Even the best correlations have a reasonable amount of scatter in the data plots. A number of factors have contributed to scatter in laboratory data. These include: conducting tests for too short a duration to obtain equilibrium depths, not measuring (or at least not reporting) some of the important variables; not measuring and/or not maintaining uniform compaction of sediments from one experiment to the next, etc. Therefore, even though a large number of experiments appear in the literature, only a portion of the data are usable for creating or evaluating predictive equations. Using only data from laboratory experiments of sufficient duration that equilibrium scour depths were achieved, Sheppard has found that the data for single cylindrical piles correlates well with the dimensionless parameters yob, U/U, and D5db. dA/ = f(y/b, U/UC, D5db) (3-1) 16 yj-b. The flow depth to structure diameter ratio (yo/b) describes the relationship between the surface and bottom horizontal vortices at the upstream side of the pile, i.e., the interaction of the counter-rotating surface vortex near the water surface and the horseshoe vortex at the base of the pile. When yjb is small, the flow associated with the surface vortex interacts with and weakens the horseshoe vortex at the base of the pile. It is generally accepted by researchers (Laursen and Toch 1956, Sheppard 1998) that the relative scour depth (djb) increases as the relative flow depth (y/b) increases until a certain limiting value of yjb is reached, after which the relative scour depth is independent of y.b. The limit expressed by most researchers is in the range of 2< y0Ib< 3. Laboratory data (Ettema 1980, Sheppard 1998) indicates that if the other two parameters (U/Uc, D5o/b) are held constant, the relative scour depth increases rapidly with yo/b from zero. It then approaches a constant value when y,/b reaches between 2.5 and 3.0, indicating that when the flow depth to structure diameter ratio exceeds this value it no longer has an influence on the scour depth (figure 3-1). ULU. The depth averaged approach flow velocity to critical velocity ratio (U/U,) is a measure of the flow intensity. The critical velocity is that associated with critical shear stress at the point of incipient sediment transport. Critical velocity is a function of the fluid properties (density and viscosity), flow depth (vertical velocity distribution), sediment properties (grain size, shape, and density), and bed roughness (ripples, dunes, vegetation, etc.). Laboratory data (Sheppard 1998, Hannah 1978, Ettema 1980, Melville 1984) shows that for single cylindrical piles, local equilibrium scour is initiated at approximately U/U. = 0.45 and increases rapidly with increasing U/U, up to transition from clearwater to live-bed conditions (U/Uc =1). Early researchers of local scour (Jain and Fischer 1980) concluded that the maximum 17 equilibrium scour depth occurs at the transition from clearwater to live-bed conditions. But Melville (1984) and Raudkivi (1986) found that the peak scour depth in the live-bed range could be larger than that at transition if the sediment is in the ripple-forming range (D50 < 0.6 mm). Figure 3-2 is a schematic drawing of the general variation of relative scour depth with U/Ut for the clearwater and live-bed regimes. DA. The median sediment diameter to structure diameter ratio (D5o/b) is actually the ratio of two Reynolds Numbers, one based on the sediment grain diameter and one on the structure diameter. Both Reynolds numbers are important in characterizing the flow and sediment transport in the vicinity of the structure. Baker (1986) and Ettema (1980), using the data of Raudkivi and Ettema (1977), concluded from their clearwater scour data that the equilibrium non-dimensional scour depth, dsjb, increased with decreasing Dsob until D50/b reached a value of 0.04-0.05. For values less than this, the scour depth was thought to be independent of D5o/b. Sheppard et al. (1995b), using data from several researchers (including Ettema, 1980) and their own (collected at the University of Florida), found the scour depth dependence to extend to lower values of D5o/b as shown in figure 3-3. Note that both yjb and U/Uc are held constant in this plot. The reduction in scour depth with decreasing values of D.Ib is very important since 1) most prototype situations have very small values of Do/b and 2) this relationship is needed to properly interpret laboratory data from model scour tests. Sheppard et al. are presently conducting experiments with larger piles in order to extend the data to even smaller values of DAob. U/Uo= constant Dso5b = constant 0 I 0 1 2 3 4 yo/b Figure 3-1. Variation of relative local scour depth with yo/b Clearwater Live-bed D5/b =0.016 dse/b Dso/b = 0.0003 yo/b= const. U/ULC Figure 3-2. Variation of relative scour depth with U/Uc 19 U/UC = constant D5o/b = constant Figure 3-3. -6 -4 -2 0 log (D5o/b) Variation of relative scour depth with D5ojb Equations for Predicting Maximum Equilibrium Scour Depth Around a Single Pile University of Florida equation Sheppard et al. (1995b) developed the following empirical predictive clearwater scour depth equation for a single cylindrical pile in a cohesionless sediment, penetrating the water surface, and subjected to a steady flow. The assumption is made that the relative scour depth can be expressed as a product of three functions (equation 3-2) of the relevant dimensionless parameters discussed above, y/b, U/U,, and D5/b. The coefficients in this equation were determined by a regression analysis and have been confirmed with more recent and reliable data. The equation allows for a safety factor (S.F.) to be 20 added so as to be an envelope or design equation rather that one that best fits the data. It is shown in equations 3-2, 3-3, 3-4, and 3-5 in its most recent form. Table 3-1 shows the most recently determined coefficients. djb = S.F.* f1(yjb) f2 (U/Ue)" f3(D5o/b) (3-2) f1(yj/b) = ci tanh (c2* y/b) (3-3) f2(U/Uc) = 1 + c3 (U/Uc) + c4" (U/Uc)2 (3-4) f3(Dso5b) = logo(Dsob) expi{c5 [-logo (Dso/b)] '61 (3-5) Table 3-1. Coefficients for equations 3-2, 3-3, 3-4, and 3-5 c, c2 c3 c4 C5 C6 S.F. 4.81 1.0 -2.87 1.43 -0.18 2.09 1.35 The safety factor ensures conservative over-prediction of scour depths. Figure 3- 4 shows the accuracy of this equation. It should be noted that data from controlled laboratory tests do not exist for large structures, so it is uncertain how well laboratory results predict scour at prototype scale structures. For prototype situations, U/U, and yj/b will be approximately the same as those for laboratory studies, however, the value of Dso/b can be significantly smaller for the prototype. For this reason, Sheppard et al. are presently conducting experiments with a 3-foot diameter pile in a 20-foot wide by 21-foot deep flume. Sheppard recommends that, at present, if Dso/5b is less than 3. 1x103 that Ds/b be set to 3.1x103 when using the equation. 3 . r CD 2 0 ." * 0 = . C2= 1-.8 .a C3 = -2.87 " ."c4 = 1.43 C5 = -0. 18 c6 = 2.09 S.F. = 1.35 0 0 0 12 3 ds./b measured Figure 3-4. djb measured vs. djb predicted The effect of pile shape has been accounted for by the use of a multiplicative coefficient such as, that shown in equation 3-6 for a square pile. d,jb (square pile) 1.1 djb (cylindrical pile) (3-6) HEC- 18 scour prediction equation The current method recommended by the Federal Highway Administration (FHWA) for predicting design scour depths at bridge piles uses an equation based on the one developed at Colorado State University by Richardson et al. (1988). This equation is presented in the FHWA Hydraulic Engineering Circular No. 18 (HEC-18) "Evaluating Scour at Bridges" (1996). d.Jb=2.0 KI. K2- K3 K4 (y/b)0.35- (Fr)043 (3-7) where K = shape correction factor for pile nose shape; K2 = skew angle correction factor; K3 = bed condition correction factor; K4 = correction factor for armoring by bed material size; and Fr = Froude number = U/(gyo). This equation is for both live-bed and clearwater conditions. The shape correction factor, K1, estimates the influence of the shape of the upstream edge of the pile. However, for skew angles greater than five degrees, K, = 1.0. Table 3-2. Shape correction factor, K square nose round nose circular cylinder group of sharp nose cylinders 1.1 1.0 1.0 1.0 0.9 The skew angle correction factor, K2, adjusts the predicted scour depth based on aspect ratio and skewness to the flow. The following table estimates the influence of skew angle based on the aspect ratio (L/b) where L is the pile length and b is the pile width. Table 3-3. Skew angle correction factor, K.2 K(2__ Skew Angle L1b =4 b = 8 Ub = 12 0 1.0 1.0 1.0 15 1.5 2.0 2.5 30 2.0 2.75 3.5 45 2.3 3.3 4.3 90 2.5 3.9 5.0 The bed condition correction factor, K(3, results from the fact that for plane-bed conditions, the maximum scour may be 10 percent greater than predicted (30 percent if large dunes exist). Table 3-4. Bed condition correction factor, K(3 Bed condition Dune Height (in) K(3 Clearwater scour NA 1.1 Plane-bed and Antidune NA 1.1 flow Smallidunes 3 >H ;,.0.6 1.1 Medium d-anes 9 >H 2t 3 1.2 to 1.1 Large dunes H 2t 9 1.3 24 The bed armoring correction factor, K4, decreases the predicted scour depth due to armoring of the scour hole by bed materials in which D50 2 0.06 meters. This factor is necessary because it has been observed that finer grains are transported away from the structure at a lesser velocity than is required to remove D50-size sediment, thus leaving larger grains to "armor" the scour hole. Jones developed an equation for determining K4 based on velocity ratio and grain size, D90 from research conducted for FHWA by Molinas at Colorado State University. The Froude number characterizes the local energy or hydraulic gradients driving the flow into or around the scour hole. It expresses the relative sizes of the stagnation pressure at the leading edge of the pile (U2I2g) and the flow depth, y,. The acceleration due to gravity is g. Fr = U/(gy) 0.5 (3-8) Equations for Predicting Maximum Equilibrium Scour Depth Around Pile Groups One approach to predicting scour depths at pile groups associates an "effective width" or diameter of the group and computes the scour depth for a single structure using this diameter. A circular pile was chosen as the single structure in this work because it is the best understood and most researched structural shape. The assumption is made that the local scour at a pile group is related to the local scour that would occur for a single cylindrical pile subjected to the same fluid, flow, and sediment conditions. It is also assumed that the group has a similar functional dependence on the independent parameters with the exception that an "effective diameter/width", D*, must be used in place of b. The functional dependence of the "effective diameter" on the group properties (number of piles, spacing. etc.) must then be determined. 25 Copps (1994) examined the effective width of pile groups as a function of pile diameter (width) to centerline spacing (s/b), and the number of piles normal to the flow (n), and developed the relationship: D* = (n-1).b/(s/b)c +b (3-9) where the value of c (0.55) was determined from a regression analysis of University of Florida (UF) laboratory data. This equation was modified by Sheppard et al. (1995a) to the following form: D*/b = 1 + (n-I) (s/b)r' exp{K6 (s/b 1)2) (3-10) where K5 and K were evaluated using regression analysis of experimental data (collected at UF) to be 0.27 and -0.05, respectively. However, these equations are only applicable to in-line pile groups (i.e. pile arrays that are in rows and columns) which are aligned with the flow (no skew angle). It has been well documented (Laursen and Toch 1956, Chabert and Engeldinger 1956, Hannah 1978, Mostafa et al. 1993, 1995b, 1996, Zhao and Sheppard 1996, Salim and Jones 1996) that skewness of a pile group to the flow direction has a significant influence on the maximum depth of local scour due to the increased effective size of the structure and the added complexity of the flow field. For pile groups skewed to the flow, Jones (1989) concluded that pile groups that project above the stream bed can be analyzed conservatively by representing them as a single width structure equal to the projected width of the piles, ignoring the clear spaces between the piles. This is currently the methodology used in 26 predicting the maximum equilibrium scour depth in HEC-18. It should be noted that the duration of his tests was only 4 hours. The most comprehensive research on the influence of skew angle on scour depth at pile groups was done by Zhao (1996). Zhao studied the effects of skew angle for a 3x8 array of in-line cylindrical piles and a 3x8 array of in-line square piles both with s/b = 3. Six tests were conducted on each of the circular and square pile groups with the skew angle varying between 0' and 900. The duration for each test was 26 hours, the time at which Zhao had estimated the scour depth had achieved 90 percent of the maximum equilibrium scour depth. Zhao defined a skew angle correction factor, K. to account for the skewness of a pile group: K. = d.,e(a)/d,,e(--O) (3-11) where ds(a) = the maximum equilibrium scour depth for the pile group at skew angle a and ds (a--0) = the maximum equilibrium scour depth for the same pile group at zero skew angle. Figure 3-5 shows the variation of K with the skew angle for both the square and cylindrical pile groups. All of his tests were conducted at U/Uc values between 0.60 and 0.66. It should also be noted that as the skew angle (and effective width of the structure) increased, y. was held constant for these tests. Thus, yD* fell far below the value at which scour depth is independent of this parameter (see figure 3-1). In addition, as the effective width of the group increased, a longer time was needed to reach maximum equilibrium scour depth. Thus, 26 hours was not a sufficient duration to accurately determine the maximum equilibrium scour depth at large skew angles. + 3X8 =Am pil 70 A US e ple 7mu - Lansarmfveftrlb-3.14 220 HEC1 s K2 for b 3.14 / 1.80- ./ 1.40 A / /," + +, + 1.40- ,, A T 1 0 15 30 45 Figure 3-5. Fow skew angle (degrees) Skew angle correction factor Salim and Jones (1996) investigated two groups of square piles at various skew angles in order to determine a skew angle correction factor for pile groups. One group was a 3x5 array of in-line piles and the other was a staggered design, 5 piles long and alternating between 3 and 4 piles wide. Spacing between the piles was varied for different tests with the staggered array. The experimental results showed that the skew angle correction factor for a group of square piles is reasonably close to that for a solid pier with the same overall width to length ratio. They defined K, as: K = (d ,VK)/d = (3-12) where d., = the scour depth around the skewed pile group; + 60 75 9 28 K. = a spacing correction factor (equation 3-13); and dse = the scour depth around an equivalent solid pier, set at the same skew angle. The spacing correction factor was determined empirically to be: Ks = 0.47 (1- e1 ) + e 5(1 sb) (3-13) where s is the center to center spacing of piles and b is the width of a single pile. It now appears that much of the earlier work on the influence of flow skew angle on scour depths at pile groups is of limited value due to 1) the duration of the tests being insufficient to allow the accurate prediction of equilibrium depths, 2) water depths being less than 3D* for some of the skew angles, and 3) the flume width being too narrow for the effective width of the structure. That is, if there is a scour depth dependence on y/D*, as most researchers believe, then as the skew angle, a, is increased, the effective structure width, D*, increases and thus the value of yJD* decreases. If yo/D* decreases below a value of approximately 3, then the equilibrium scour depth is reduced below the value it would have been were this not the case. This must be taken into consideration in analyzing much of the earlier data by most of the researchers. CHAPTER 4 TIME DEPENDENCE OF SCOUR Due to the complexity of local scour processes, the majority of research has concentrated on determining the maximum equilibrium scour depth for given flow and sediment conditions while relatively few researchers have delved into the dependence of these processes on time. It has been determined that the time to reach an equilibrium depth is dependent on the scour regime. For clearwater scour, the rate of scour slowly approaches an asymptotic value (equilibrium). For live-bed scour, the depth of scour oscillates around the equilibrium value with an amplitude equal to the amplitude of the sand waves migrating into and out of the scour hole (figure 4-1). Chiew and Melville (1996) investigated the time required to reach equilibrium scour depth for clearwater conditions in an attempt to standardize the criteria for determining the equilibrium value. Data was collected from 35 experiments using single cylindrical piles covering a wide range of cylinder diameters, flow depths, and approach flow velocities. The experiments were run for a sufficient duration to ensure that the maximum equilibrium scour depth had been reached. The time when the scour hole develops to a depth at which the increase in depth does not exceed 5% of the pier diameter in the succeeding 24-hour period was defined as te. They found that the time to reach equilibrium is dependent on flow and structure characteristics. The flow energy available for scouring can be characterized by the mean approach flow velocity, U, and pile size, b. The pile size affects the strength of the horseshoe vortex and the associated vertical flow components of scour. 30 The data showed that te increased with increasing U/U, holding other variables constant. This is because greater velocity ratios are associated with greater depths of scour, therefore, it would take longer to reach equilibrium. The duration of the tests (and pile sizes) used thus far for analysis have varied widely. Hannah's tests were run for 7 hours, Jones' for 4 hours, Copps' for 26, Mostafa et al. for several hours, and Zhao's for 26 hours. According to the results of the time-dependent investigations, the time effects can be significant and the use of shorter duration tests for larger structures can lead to confusing results. Scour tests with too short a duration are one of the major causes of scatter in published data. dse, live 1 ,. 0 U Live Bed Scour Clear Water Scour Figure 4-1. Scour depth as a function of time in the live-bed and clearwater regimes To exemplify the variation in scour depth as a function of time, figure 4-2 shows the time history data of an experiment conducted for 6 days in the clearwater regime in the flume at the University of Florida. The structure was a single cylindrical pile with a diameter of 6 inches, yf/b of 3.2, UIIJ of 0.93, and D5o/b of 1.18x103. In 4 hours, the scour depth had reached approximately 66% d.. In 7 hours, the scour depth had reached approximately 73% d,,. And in 26 hours, the scour depth had reached approximately 90% dse. However, these ratios change with fluid, flow, sediment, and structure parameters. Figures 4-3 and 4-4 show how the size of the structure changes these percentages. after 26 hours - 90% d,. after 7 hours -= 73% d.1 after 4 hours = 66% d.. University of Florida 6-day test single cylindrical pile b = 6 inches 1 2 3 4 5 6 time (days) Figure 4-2. Time history of scour around a single cylindrical pile 10.0 8.0 after 7 hours - 68% d,, = 58% d,, 10.0 8.0 2.0 0.01 1 2 3 4 5 6 time (days) Figure 4-3. Time history of scour around an array of square piles normal to the flow 15.0 12.0 vr ,,_.,-- f' =73% d,. 9.0 after 7 hours =55% d,. "a after 4 hours -=48% USGS Flume 0 6.0 U 6-day test 3x8 square pile array 70o skew angle 3.0 projected width = 28.8 inches 1 2 3 4 5 6 time (days) Figure 4-4. Time history of scour around an array of square piles skewed 700 to the flow after 26 hours 81% d,, USGS Flume 5-day test 8x3 square pile array b = 10 inches CHAPTER 5 DESIGN LOCAL SCOUR DEPTHS AT PILE GROUPS A more generalized method for predicting local scour depths at pile groups is proposed in this chapter that accounts for pile size, spacing, flow skew angle, and, where applicable, the degree of submergence of the piles. As discussed earlier in this thesis, local scour processes are very complex, even for seemingly simple structures such as single cylindrical piles. For pile groups, the flow is more complex and there is much less scour data for these structures reported in the literature. In addition, most of the data that exists for pile groups is only for clearwater flow conditions while there is substantial data for single cylindrical piles in both the live-bed and clearwater regimes. For this reason, it was decided that, at least until more data is available, the best way to estimate scour depths at pile groups is to continue to relate it to the scour that would be produced by a circular pile with the equivalent or "effective" diameter of the group, D*. The problem then becomes one of determining the effective diameter, D*, for the group. From the work of Salim and Jones (1996) and Copps (1994) it is known that D* is a function of pile size, shape, centerline spacing, and the number and arrangement of piles. It is assumed that these effects can be treated separately as indicated in the following equation: where Wp = the projected width of the piles onto a plane normal to the flow and upstream of the structure, accounting for size, and the number and arrangement of piles; 34 Kv = the parameter that accounts for the centerline spacing between the piles; and K, = the parameter that accounts for the shape of the piles. V_,. Jones (1989) suggested that the effective width of a pile group could be conservatively approximated by the projected width of the group, ignoring the clear spaces in between. This works well for certain centerline spacings, but is increasingly over-conservative for centerline distances-todiameter ratios greater than about 3. In this analysis, WP is the sum of the (non-overlapping) projected widths of each pile onto a plane normal to the flow and upstream of the forward most pile. Note that only the portion of the projected width that is not "blocked" by upstream piles is counted. This method accounts for the number of piles, the arrangement of the piles, and the change in the width of a pile as it is skewed to the flow. Because this method accounts for the skew angle, a skew angle correction factor is not needed in the predictive equations. This approach seems to work well for the limited (but reliable) data that is available at this time. 4. K, corrects the effective width of a pile group based on pile centerline spacing. Similar to the findings of Salim and Jones (1996) and Sheppard et al. (1995a), the value of K, decreases with increased spacing, thus decreasing the effective width of the pile group. At an s/b value of 1, the piles are touching, and the group acts as a single pile. As the centerline spacing is increased, the influence will gradually decline until a value of approximately 10 at which point the piles act independently and the effective diameter, D*, is the width of a single pile, b. The following relationship was found to work well for computing K, as a function of s/b and b/WP. Kp = I 0.003078(1-b/Wp)(s/b 1)33/exp(O.015(s/b)2) (5-2) 1.00 0.80 0.60 - b/VWp = 0.5 0.40 bIWp = 0.334 0.20 b/Wp = 0.125 0.00 1 3 5 7 9 11 s/b Figure 5-1. K, pile spacing parameter Figure 5-1 shows this equation plotted for three different values of b/WP. Note that both Saim and Jones and Sheppard et al. found a modest increase in D* for s/b values between 1 and 3. More data is needed in this range of s/b in order to verify this finding and to quantify it. K. K, is the parameter that accounts for the pile shape. The influence of pile shape on scour depth (discussed in chapter 3) has been investigated by several researchers such as Richardson and Richardson (1989). Values for a variety of shapes are given in HEC-18. K. for cylindrical piles is equal to 1. However, for non-cylindrical piles, the shape of the pile relative to the flow changes as the flow skew angle changes. For example, a square pile at a 450 skew angle has a sharp nose shape. Using the shape factors for square and sharp-nose shaped piles from HEC-18 and data from 0.9 0.8 0 0.4 0.8 1.2 1.6 o (radians) Figure 5-2. Shape correction factor, K, for square piles a 700 flow skew angle test, the following expression was developed for square piles where the skew angle, a, is in radians: K, = 0.85 + 0.811 a-7t/414 (5-3) Figure 5-2 depicts this relationship. The D* computed from WpPKwI (equation 5-1) can be substituted for b into the predictive equations for a single cylindrical pile to determine the maximum equilibrium scour depth at the pile group. Note that if the HEC-18 equation is used, the shape correction factor, KI, and the skew angle correction factor, K2, should both be set equal to 1 because they are accounted for in the K, and Wp parameters, respectively. If the piles are submerged, the degree of submergence is also important. Submerged pile groups are encountered less frequently than subaerial groups, but they are none-the-less important. As a component of a composite structure such as a complex bridge pier (figure 5-4), consisting of 37 a pier, pile cap, and pile foundation, they may be the greatest contributor to the scour hole. Sheppard et aL (1995a) and Salim and Jones (1996) have independently approached the problem of predicting local scour at complex piers by decomposing these structures into their components and attempting to determine the scour contribution due to each component. Recently, Sheppard and Jones (1998) have joined forces in order to produce a more unified approach to this problem. Part of the motivation for the work on submerged pile groups in this thesis was to support this effort. The equilibrium scour depth's dependence on the height of the pile group above the bed is similar to its dependence on the ratio y]D*. It was determined that if the water depth is greater than 3.5 times the effective width of the pile group (D*), submerging the piles will have little affect on the scour depth until the height of the piles falls below this value. For those situations where the piles are submerged, a parameter K can be used to account for the effect of the submergence on the scour depth. dse submerged pile goup = Kb dse (D.) (5-4) The scour depth's dependence on pile height is found in equation 5-5 (and figure 5-3) in the relationship between K. and HPV/J where Hpg is the height of the piles above the bed and i is the normalizing factor based on the effective width of the pile group. If the water depth, y., is greater than 3.5D*, iV equals 3.5D* and if the water depth is less than or equal to 3.5D*, *r is equal to the water depth. The value of 3.5D* was arrived at empirically. (5-5) Kb = -0.0011 + 2.68 (Hpg/) 3.55 (Hpg/Ij)2 + 1.87 (Hpg/14y)3 1 0.8 0.6 0.4 0.2 0 1 0 0.2 0.4 0.6 0.8 1 Hdw Figure 5-3. Kbvs Hp = 3.5D* for yo > 3.5 D* s = yo for 0 y 3.5D* (5-6) Illustration of Model Use Example 1 The following example illustrates how to use this model to predict the design scour depth at a multiple pile bridge pier (figure 5-4). The prototype conditions are: b = 0.5 meters; stb = 3; yo = 5.0 meters; U/U = 1; D50 = 0.22mm; n = 3, m = 3, a = 180, and the piles are square. The pile cap is above the water line under design conditions, thus the pile group is subaerial. n=3 Figure 5-4. Prototype multiple pile bridge pier The projected width of the structure at a flow skew angle, a = 1.80, is 4.4 meters, thus, WP = 4.4 meters. To determine K,, the value of b/WP is calculated: b/Wp = 0.5/4.4 = 0.144. Using equation 5-2 with b/WP = 0.144 and s/b = 3, Kv = 0.98. K. is determined from equation 5-3 where a = 180 = 0.314 radians. K. = 0.89. The effective diameter is calculated by equation 5-1 to be: D* = WPKY,I = 4.4 (m) 0.98 0.89 = 3.84 meters Substituting this D* for b into the University of Florida scour prediction equation (equation 3-2) with the given flow and sediment conditions; d8D* = 1.35" f" -f2 -f3 f, = 4.81 tanh(1' (5/3.84) = 4.147 (equation 3-3) 40 f2 1 + (-2.87 1) + 1.43 (1)2 = -0.44 (equation 3-4) f3= logo (0.22mm/3.84 m) exp{-0.18 [-logjo (0.22mm/3.84m)]2"9} =-0.106 (equation 3-5) dD*= (1.35 4.147 -0.44 -0.106) = 0.261 dse.*) = 0.261 3.84 (m) = 1.0 meters The piles extend above the water surface so IK = 1. d,, = 1.0 meters 17 F-, S I n- b UU U n'= 3 Figure 5-5. Prototype multiple pile bridge pier with submerged piles and no pile cap Example 2 The following example illustrates how to use the submerged pile parameter, K (equations 5-4 and 5-5). The prototype conditions (figure 5-5) are: 41 b = 1.0 meter; s/b = 6; yo = 7.0 meters; U/U = 1; Dso = 0.22 mm; n = 3,m= 3, a = 50, and the piles are square. The piles are submerged below the water line and the pile group has no pile cap. The height of the piles above the bed, H,, is 5.0 m. The projected width of the structure at a flow skew angle, a = 50, is 4.82 meters, thus, WP = 4.82 meters. To determine K~, the value of b/W is calculated: b/Wp, = 1/4.82 = 0.207. Using equation 5-2 with b/WP = 0.207 and s/b = 6, KV = 0.71. K, is determined from equation 5-3 where a = 5' = 0.0873 radians. K, = 1.04. The effective diameter is calculated by equation 5-1 to be: D* = WPKKI, = 4.82 (m) 0.71 1.04 = 3.56 meters Substituting this D* for b into the University of Florida scour prediction equation (equation 3-2) with the given flow and sediment conditions; dJD*= 1.35-f f, f2 f3 f, = 4.81. tanh(1l (7/3.56) = 4.625 (equation 3-3) f2= 1 + (-2.87 1) + 1.43 (1)2 = -0.44 (equation 3-4) f3= logo0 (0.22mm/3.56 m) exp{-0.18[-logIo (0.22mm/3.56m)]2'9} =-0.112 (equation 3-5) dsJe/D*= (1.35 4.625 -0.44 -0.112) = 0.308 ds,.) = 0.308 3.56 m = 1.1 meters Because the piles are submerged, the K, parameter must be considered. 3.5 D* = 3.5 3.56 m = 12.46 m. 3.5 D* > yo so by equation 5-6, 4r = yo = 7.0 m 42 -IpVh = 5.0/7.0 = 0.71 From equation 5-5, Kh = 0.78 By equation 5-4, dse submerged pile group = 0.78 1.1 meters .dse submerged pHe group = 0.86 meters. CHAPTER 6 EXPERIMENTAL PROCEDURES Ten pile group scour experiments were performed as part of the work for this thesis. Attempts were made to avoid problems with previous experiments such as test duration, effects of water depth, and constriction scour. Nine experiments were conducted using a 3x8 array of square in-line piles with a centerline spacing to pile diameter ratio, s/b = 3. One experiment was performed with a 2x4 array with s/b = 6. The height of the piles above the bed was varied so as to obtain the effect of this height on the scour depth. Four of these experiments were conducted with 3 piles normal to the flow, 4 were conducted with 8 piles normal to the flow, I test with 2 piles normal to the flow and 1 at a flow skew angle of 700. Tests at ratios of pile height above the bed (Hpd)to the flow depth (y0) of 1, 0.75, 0.5, and 0.25 were conducted. Eight of the 10 experiments were conducted in the flume at the University of Florida and 2 in the USGS-BRD flume in Turners Falls, Massachusetts. The USGS flume was needed for some of the tests because of UF flume width and depth limitations. The pile group used for 9 of the tests was a 3x8 rectangular array of 1.25 inch wide square aluminum tubes with s/b = 3. The 2x4 array was rectangular with 1.25 inch wide square piles as well, but with s/b = 6. For the tests where the piles were submerged, the piles were bolted to an aluminum base that was placed on the bottom of the test section. For the tests where the piles extended above the water surface, the piles were secured at the top by an aluminum pile cap placed 44 above the water line. Scales were glued to the front of each pile in order to measure the scour depth as a function of time. Flume The University of Florida flume (figures 6-1 through 6-5) is approximately 100 feet long, 2.5 feet deep, and the main section is 8 feet wide. The main section of the flume has zero bed slope. The maximum water depth is approximately 22 inches. A 20-foot long test section (which is located midway between the entrance and exit) is 1.13 feet deeper than the rest of the channel The test section is filled with quartz sand with a 135 of 0. 172 num and a standard deviation, a, of 1.38 (figure 6-6). Flow in this recirculating flume is driven by a 100 horsepower pump (figure 6-4) with a 38.8 ft/second discharge capacity. The pump produces a constant discharge. Flow in the flume is controlled with a bypass system that diverts a portion of the pump discharge back to a reservoir. The flume is equipped with a series of flow straighteners and energy dampening devices designed to produce a uniform flow upstream of the test section. A screen is located upstream of the test section to ensure that no debris interferes with the test. The water depth is controlled by a sluice gate at the downstream end of the flume (figure 6-3). A manometer measures the water elevation upstream of a sharp-crested rectangular weir. The manometer reading, h*, is in centimeters. The following equation is used to calculate the flow head, H, in centimeters: H =h* 15.95(6) (6-1) 45 The flow rate in ft3Is is calculated using the equation for a sharp-crested weir, calibrated for this flume: Q = 24.96 H'5 (6-2) where H is in feet. The upstream depth averaged velocity is calculated by: U =Q/A (6-3) where A is the cross-sectional area of the flow in ft' calculated at the test section. A movable carriage sits atop the flume on rails, able to traverse the length of the flume. The carriage provides a stable platform from which observations are made. A video camera system collects the time history scour data from the carriage. The camera is mounted inside of a long PVC tube with a plexiglass plate on one end. The plexiglass end extends just below the water surface. From this vantage point, the camera can view the scour at the front piles. A control system was designed to turn on the lights, video camera, and VCR at specified times and durations to record scour depths as a function of time. Both the time interval between recordings and the duration of the recording can be changed. A VCR records the scour depths at the piles in the camera's view (using the scales attached to the piles) and the time of the measurement. The camera is directed at the region of anticipated maximum scour depth, thus the camera does not have to be moved during the test. At the start of the test, the scour activity is recorded for 15 continuous minutes, then for one minute periods at varying intervals that are increased as the test progresses and the scour rate decreases. Figure 6-1. UF flume: flow straighteners, screen, weir, and energy dampening devices Figure 6-2. UF flume: main section exit. sluice gate Figure 6-3. UF flume: sluice gate, turning vanes Figure 6-4. UF flume: pump We ir Screen Energy Dampening Devices and Flow Straighteners Figure 6-5. Schematic drawing of the University of Florida Civil Engineering flume 49 100 7 -r- 7 - _I lI I I I1 I II I I I I 1 1 11i~ 6 0.134 fn I 80 4 I 60 ------- --- -o-- -S 40 L I 20 oI!!I 111111I I I 1.00 0.10 0.01 Grain Size (mm) Figure 6-6. UF flume grain size distribution The USGS flume (figures 6-7 through 6-10) has three channels. All channels are 126 feet long and 21 feet deep. The main channel is 20 feet wide and is located between the other two 10 feet wide channels. The main channel was used for all of these experiments. The channel has zero bed slope. A 30-foot long test section is located about 2/3 of the channel length from the entrance. The test section of the flume is 6 feet deep, filled with quartz sand with a D50 of 0.22 mm and a standard deviation, o, of 1.57 (figure 6-11). The remainder of the flume is filled with a coarse base material covered by a filter material and a 1-foot layer of the test section sediment. The flow is generated by a head difference between the entrance and exit section of the flume. Control structures in the Connecticut River create the head difference between the flume entrance and exit. Screen filters upstream of the flume prevent debris from interfering with the test. The flow 50 depth is controlled by the height of a sharp-crested weir at the downstream end of the flume. The average velocity was calculated from the water elevation above the weir (head) and measured with two electromagnetic current meters located 2/3 of the depth from the water surface upstream and on either side of the structure. After the water flows through the flume, it is discharged back into the river downstream of the control structures. Observations are made from a fixed platform located above the test section. Scour depths are measured using two cameras mounted to the platform. One is located upstream, viewing down in front of the test structure. The other camera is located to the side of the structure, viewing the scour from the side. The cameras are mounted inside of streamlined PVC and plexiglass housings designed and constructed in the Coastal Engineering Laboratory at the University of Florida for this application. A video system, identical to the one used for the UF tests, is used to record the scour depths (read from scales located on the front of the piles) as a function of time. Test Preparation To prepare for the tests, the models are set in the center of each test section and the sand is compacted with an electric compactor in the UF flume and a diesel powered compactor in the USGS flume. Attempts were made to obtain a uniform and repeatable compactness of the sediment similar to that found in a natural setting. The sand is then leveled throughout the USGS flume and to the surrounding fixed bed in the UF flume. The flumes were then filled slowly so as not to disturb the sand. Photographs and slides were taken upon completion of leveling to document the condition of the bed before testing. PTf 11 Figure 6-7. USGS flume with base material (prior to placement of test sediment) Figure 6-8. USGS flume with test sediment and 3x8 structure Flow Intake from Reservoir Testhannl -)- A10 oflow flo H 20 B B L* A 10 A Model Area 1 Plan View NOT TO SCALE Flow Discharge All dimensions in feet To Connecticut River 20 Water Test Sediment Section A- H 21 6 T NOT TO SCALE All dimensions in feet H = 9' for 3' pile H = 4' for 4.5" and 12" piles Section B- IU 7 80 60 40 20 7- 7 17 17 FI-7 ib o ='o. 2d mn I I I I I Il'i I I1 I I I I I I I I I II I I i I I I I K : ', I i 1.00 0.10 0 Grain Size (mum) re 6-11. USGS flume sediment grain size distribution .01 Test Conditions All of the tests aimed to maintain a U/U, velocity ratio at slightly less than transition from the clearwater to live-bed regime (-0.9). The critical depth averaged velocity was determined from Shield's parameter based on the water density, viscosity, and depth: median sediment diameter and density; and bed roughness. For all tests, the sediment density for quartz sand is assumed to be 2650 kg/m3. To maintain this condition, the temperature was closely monitored and used to determine the fluid density and viscosity properties. Minor adjustments to the flow velocity were made during the tests in an attempt to maintain constant upstream bed shear stress and U/U,. That is, as ripples formed on the upstream bed, the bed roughness changed causing minor changes in bed shear stress and thus Figu 56 in the critical velocity. The tests were run until such time that no increase in scour depth was observed for a period of 24 hours to ensure that the maximum equilibrium scour depth had been reached. This duration varied from test to test. While the automated video recorded the time history of scour depth, the water depth, temperature, manometer reading, and scour depths were manually collected and recorded periodically. After each test, a vernier point gage was used to survey the test section to obtain a complete picture of the scoured bed. Test Results The test conditions and measured results are presented in table 6-1. Photographs of the tests, before and after each experiment, are depicted in figures 6-12 through 6-31. Time-history plots of the scour depths are included in Appendix A. Relative bed n) Yo (in) D50 (mm) Temp "C roughness U, (ft/s) U (fls) U/UC (ae) (k/D50 (aye) I 3.50 14.00 0.172 31.6 10 0.82 0.75 0.92 2 'A 3.50 14.00 0.172 32.9 7.5 0.81 0.74 0.91 3 '2 7.25 14.50 0.172 32.1 7.5 0.85 0.76 0.90 4 '/2 7.38 14.75 0.172 32.5 7.5 0.84 0.77 0.92 5 '/4 11.56 15.40 0.189 33.0 7.5 0.84 0.74 0.88 6 3/4 11.00 14.70 0.189 32.1 7.5 0.89 0.81 0.91 7 1 15.00 15.00 0.172 29.8 10 0.83 0.79 0.95 8 1 47.28 47.30 0.220 24.8 10 1.13 1.08 0.96 9 1 47.16 47.20 0.220 24.8 10 1.13 1.00 0.89 10 1 15.00 15.00 0.172 30.8 10 0.82 0.74 0.90 Test # Skew angle n m b s/b Test duration ds, measured (minutes) (inches) 1 90 8 3 1.25 3 3506 3.0 2 0 3 8 1.25 3 4467 2.7 3 90 8 3 1.25 3 6918 4.5 4 0 3 8 1.25 3 5406 3.8 5 90 8 3 1.25 3 6499 5.75 6 0 3 8 1.25 3 2327 4.0 7 0 3 8 1.25 3 5759 5.2 8 90 8 3 1.25 3 6710 9.5 9 70 3 8 1.25 3 8190 14.96 I0 0 2 4 1.25 6 3899 3.35 Figure 6-12. Test 1, Hpg/Yo = 1/4, 900 skew angle, before test Figure 6-13. Test 1, Hpg/yo = 1/4, 900 skew angle, after test Figure 6-14. Test 2, Hpg/yo = 1/4, 0o skew angle, before test Figure 6-15. Test 2, Hpg/yo = 1/4, 00 skew angle, after test Figure 6-16. Test 3, Hpg/yo = 1/2, 900 skew angle, before test Figure 6-17. Test 3, Hpg/yo = 1/2, 900 skew angle, after test Figure 6-18. Test 4, Hpg/yo = 1/2, 0' skew angle, before test Figure 6-19. Test 4, Hpg/yo = 1/2, 00 skew angle, after test Figure 6-20. Test 5, Hpg/yo = 3/4, 900 skew angle, before test Figure 6-21. Test 5, Hpg/yo = 3/4, 900 skew angle, after test Figure 6-22. Test 6, Hpg/yo = 3/4, 0' skew angle, before test Figure 6-23. Test 6, Hpg/yo = 3/4, 00 skew angle, after test Figure 6-24. Test 7, Hpg/yo = 1, 0o skew angle, before test Figure 6-25. Test 7, Hpg/Yo = 1, 00 skew angle, after test Figure 6-26. Test 8, Hpg/yo = 1, 900 skew angle, before test Figure 6-27. Test 8, Hpg/yo = 1, 900 skew angle, after test Figure 6-28. Test 9, Hpg/yo = 1, 700 skew angle, after test Figure 6-29. Test 9, Hpg/yo = 1, 70' skew angle, after test Figure 6-30. Test 10, s/b = 6, 0' skew angle, before test Figure 6-31. Test 10, s/b = 6, 0' skew angle, after test CHAPTER 7 RESULTS AND CONCLUSIONS The results of the pile group experiments are presented in table 7-1. The effective width of the pile group was computed based on the model developed in chapter 5 (equation 5-1). Figures 7-1, 7-2, and 7-3 show the data on the WP, Y., and Y., plots. This D* and the flow and sediment parameters from each experiment were then applied to the University of Florida scour prediction equation (equation 3-2 without the safety factor) to determine d,, for an equivalent diameter single cylindrical pile. Equation 5-4 was then applied to account for the degree of submergence of the pile groups. Figure 7-4 shows the submerged pile data on the Y., curve. Figure 7-5 shows good agreement between the measured and predicted (without the safety factor) non-dimensional scour depths. Figure 7-6 shows the data with the safety factor in equation 3-2 applied. The model conservatively over-predicts the scour depths. This model works exceptionally well for the available (reliable) scour data on pile groups. However, due to the limited amount of such data (i.e. long duration, deep water, limited constriction scour), additional tests are needed to investigate the effects of skew angles and pile spacing on submerged and subaerial pile groups. Submerged piles are one component of complex bridge piers. The results of this study can be used in conjunction with models being developed by Sheppard and Jones (1998) to estimate each component's contribution to local scour depth. d.,/D* d /D* dsJeD* Test D* (in) Yo (inches) D50 (mm) UUc s Hpg On) (n) Hpg Kh predictedw/o measured predicted w/o SF SF e with SF 1 11.37 14.00 0.172 0.92 0.70 3.50 14.00 0.25 0.43 0.30 0.26 0.41 2 4.26 14.00 0.172 0.91 1.22 3.50 14.00 0.25 0.52 0.63 0.63 0.86 3 11.37 14.50 0.172 0.90 0.71 7.25 14.50 0.50 0.65 0.46 0.40 0.62 4 4.26 14.75 0.172 0.92 1.23 7.38 14.75 0.50 0.73 0.90 0.89 1.21 5 11.37 15.42 0.189 0.88 0.74 11.57 15.42 0.75 0.83 0.61 0.51 0.83 6 4.26 14.67 0.189 0.93 1.28 11.00 14.67 0.75 0.77 0.99 0.94 1.33 7 4.26 15.00 0.172 0.95 1.25 15.00 14.91 1.01 1.00 1.25 1.22 1.69 8 11.37 47.28 0.220 0.96 0.94 47.28 39.80 1.19 1.00 0.94 0.84 1.27 9 24.61 47.16 0.220 0.89 0.61 47.16 47.16 1.00 1.00 0.61 0.61 0.82 10 2.38 15.00 0.172 0.90 1.46 15.00 8.33 1.80 1.00 1.46 1.41 1.97 Test skew Wp(in) angle Wp s/b K, I D* (in) 1 90 10.00 3 0.98 1.16 11.37 2 0 3.75 3 0.98 1.16 4.26 3 90 10.00 3 0.98 1.16 11.37 4 0 3.75 3 0.98 1.16 4.26 5 90 10.00 3 0.98 1.16 11.37 6 0 3.75 3 0.98 1.16 4.26 7 0 3.75 3 0.98 1.16 4.26 8 90 10.00 3 0.98 1.16 11.37 9 70 28.83 3 0.97 0.88 24.61 10 0 2.50 6 0.82 1.16 2.38 0 10 20 Projected Width (in) Figure 7-1. WP, plotted for test results b/Wp = 0.5 b/Wp = 0.334 b/Wp= 0.125 1 3 5 7 9 11 s/b Figure 7-2. Test data on K curve 1.00 0.80 0.60 0 0.40 0.20 0.00 1.2 1.1 0.9 0.8 0 0.4 0.8 1.2 ax (radians) Figure 7-3. Test data on K, curve 1 0.8 0.6 0.4 0.2 0 0 0.2 0.4 Hpj/ 0.6 0.8 1 Figure 7.4. Test data on K, curve . 1.2 no safety factor 0 0. N 0.8 skew angle 0 0 90 skew angle 0.4 X 0 skew, s/b = 6 * 70 skew angle 0 -7 -T -T7I I ' 0 0.4 0.8 1.2 1.6 2 ds/D* measured Figure 7-5. Predicted vs. measured non-dimensional scour depth, without safety factor with a safety factor: S.F. = 1.35 * 0 skew angle o 90 skew angle X 0 skew, s/b = 6 * 70 skew angle 0 0.4 0.8 1.2 1.6 dsID* measured Figure 7-6. Predicted vs. measured non-dimensional scour depth, with safety factor The results showed the anticipated correlation between effective size of the pile group and the duration to reach ds. The larger the size, the deeper the scour depth, and the longer the time needed to reach dse* For the 4 arrays which had 8 piles normal to the flow, the degree of submergence influenced the time required to reach de. As the pile height was reduced, the scour depth decreased, and less time was needed to reach dse. The 4 arrays having 3 piles normal to the flow also displayed this trend of decreasing scour depth with reduced pile height, however, the time required toreach d, varied with pile height (i.e. the shortest pile group required a longer time to reach d,, than some of the taller pile groups under the same fluid, flow, and sediment conditions). This may have been due to equipment problems causing the scour depths to be recorded at inconsistent intervals of time, thus the d. may have been reached before the time it was documented. Portions of this model were developed based on previous researchers findings which may have been subject to the problems discussed throughout this thesis: insufficient test duration, small values of U/IC, small values of yA/, etc. which produce inaccurate values of d,,,. Other portions were developed based on limited data. Thus, further research is needed to fully investigate the effects of the skewness of a pile group, spacing of the piles, and the number of piles normal to and in-line with the flow, in which these problems have been corrected. APPENDIX TIME HISTORY SCOUR PLOTS 6.0 5.0 a) S4.0 0m .3.0 - 2.0 1.0 0.0 6.0 5.0 -. 4.0c .c 3.0 . 3.0 0) 0 C.) 1.0 0.0 Subnerged Piles H = 1/4 yo SkewAngle = 0 I I I I 1 2 3 4 5 6 Time (days) Figure A- 1. Test 1 Submerged Piles H = 1/4 yo SkewAngle = 90 II I I I 1 2 3 4 5 6 Time (days) Figure A-2. Test 2 * 6.0 5.0 U) 0) c .4.0 S3.0 a) 8 2.0 0 CO, 1.0 0.0 Submerged Piles Hp = 1/2 yo SkewAngle = (0 I I I I 1 2 3 4 5 6 Time (days) Figure A-3. Test 3 6.0 5.0 CD) - 4.0 c -) C S3.0 0 8 2.0 CO 1.0 0.0 Submerged Piles H = 1/2 yo SkewAngle = 90' 1 2 3 Time (days) 4 5 6 Figure A-4. Test 4 Submerged Piles H = 3/4 yo SkewAngle= ( 1 2 3 4 5 6 Time (days) Figure A-5. Test 5 Submerged Piles Hpg = 3/4 yo SkewAngle = 90 1 2 3 Time (days) 4 5 6 Figure A-6. Test 6 6.0 5.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 1 2 3 4 5 6 Time (days) Figure A-7. Test 7 Subrerged les H = yo SkewAngle= 90' 1 2 3 4 5 6 Time (days) Figure A-8. Test 8 Su~ed Ailes H = Yo SkewAngle = 0 10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 15.0 12.5 10.0 7.5 5.0 1 2 3 4 5 6 Time (days) Figure A-9. Test 9 Submerged Piles H = yo SkewAngle= 0 s/b=6 1 2 3 Time (days) 4 5 6 FigureA-10. Test 10 Subnmerged Rles Hg = Yo SkewAngle = 70' REFERENCES Baker, R.E. 1986. "Local Scour at Bridge Piers in Non-Uniform Sediment." University of Auckland, Department of Civil Engineering, Report No. 402, Auckland, New Zealand. Batuca, D., and B. Dargahi 1986. "Some Experimental Results on Local Scour Around Cylindrical Piers for Open and Covered Flows." Proceedings of the Third International Symposium on River Sedimentation. Breusers, H.N., G. Nicollet, and H.W. Shen 1977. "Local Scour Around Cylindrical Piers." Journal of Hydraulic Research 15, no.3: 211-52. Chabert, J., and P. Engeldinger 1956. "Etude des affouillements autour des piles de ponts." Rep., Laboratoire National d'Hydraulique, Chatou, France. Chiew, Y.M. 1984. "Local Scour at Bridge Piers." Department of Civil Engineering, University of Auckland Report to National Roads Board, New Zealand. Chiew, Y.M., and B.W. Melville 1996. "Temporal Development of Local Scour at Bridge Piers." Proceedings of the ASCE North American Water and Environment Conference, Anaheim, CA (August). Copps, T.H. 1994. "Prediction of Local Scour Depth Near Multiple Pile Structures." Master's thesis, UFL/COEL-94/001, Coastal and Oceanographic Engineering Department, University of Florida, Gainesville, FL. Ettema, R. 1980. "Scour at Bridge Piers." Ph.D. Dissertation, Department of Civil Engineering, University of Auckland, Auckland, New Zealand, Report No.216. Ettema, R., B.W. Melville, and B. Barkdoll 1996. "Pier Width and Local-Scour Depth." Proceedings of the 1996 ASCE North American Water and Environment Congress. Gosselin, M.S., and D.M. Sheppard 1995. "Time Rate of Local Scour." Proceedings of the ASCE 1" International Coniference onWaterResources Engineering, San Antonio; TX 1: 775-79. Gosselin, M.S. 1997. "The Temporal Variation of Clear Water Local Scour Around a Single Circular Cylinder." Ph.D. Dissertation, Department of Coastal and Oceanographic Engineering, University of Florida, Publication No. TR- 114. Hannah, C.R. 1978. "Scour at Pile Groups." Department of Civil Engineering, University of Canterbury. Master of Engineering Report, No.78/3. HEC-18. 1996. "Evaluating Scour at Bridges." Hydraulic Engineering Circular No. 18, Third Edition, U.S. DOT, FHWA, Pub. No. FHWA-IP-90-017, revised February 1996. Jain, S.C., and E.E. Fischer 1980. "Scour Around Bridge Piers at High Flow Velocities." Journal of Hydraulic Engineering, 106, no. HY 11 (November). Johnson, P.A., and E.F. Torrico 1994. "Scour Around Wide Piers in Shallow Water." 73rd Annual Meeting of the Transportation Research Board (January). Johnson, P.A. 1996. "Pier Scour at Wide Piers." Proceedings of the 1996 ASCE North American Water and Environment Congress. Jones, J. S. 1984. "Comparison of Prediction Equations for Bridge Pier and Abutment Scour." Transportation Research Record 950, Second Bridge Engineering Conference, Volume 2, Transportation Research Board, Washington, D.C. Jones, J. S. 1989. "Laboratory Studies of the Effects of Footings and Pile Groups on Bridge Pier Scour." Proceedings of the Bridge Scour Symposium (October). Report Number FHWA-RD-90035: 3401-60. Laursen E.M., and A. Toch 1956. "Scour at Bridge Crossings." Iowa Highway Research Board Bulletin No.4, Iowa Institute of Hydraulic Research, Iowa State Highway Commission, and the Bureau of Public Roads (May). Melville, B.W. 1975. "Local Scour at Bridge Sites." University of Auckland, School of Engineering, Auckland, New Zealand, Report no. 117. Melville, B.W. 1984. "Live-Bed Scour at Bridge Piers." Journal of Hydraulic Engineering, 110, no.9 (September). Melville, B.W., and A. J. Sutherland 1988. "Design Method for Local Scour at Bridge Piers." Journal of Hydraulic Engineering, ASCE 114(10): 1210-1226. Mostafa, E.A., A.A. Yassin, R. Ettema, and B.W. Melville 1993. "Local Scour at Skewed Bridge Piers." Hydraulic Engineering '93. Proceedings of the 1993 Conference. 1:1037-42. Mostafa, E.A., A.A. Yassin, R. Ettema, and B.W. Melville 1995a. "Parametric Approach for the Estimation of Bridge Pier Non-Alignment Effect on Maximum Equilibrium Scour Depth." Alexandria Engineering Journal 34, no. 4 (October). Mostafa, E.A., A.A. Yassin, R. Ettema, and B.W. Melville 1995b. "Systematic Investigation of Skewness Effect on Maximum Equilibrium Scour Depth at Skewed Bridge Piers." Alexandria Engineering Journal 34, no. 3 (July). Mostafa, E.A., A.A. Yassin, R. Ettema, and B.W. Melville 1996. "Simplified Approach for the Prediction of Maximum Equilibrium Scour Depth at Skewed Bridge Piers." Alexandria Engineering Journal 35, no. 2 (March). Nakagawa, H., and K. Suzuki 1975. "An Application of Stochastic Model of Sediment Motion to Local Scour Around a Bridge Pier." Proceedings of the 16' IAHR Congress, Sao Paulo, Brazil, 2:228-35. Ontowirjo, B. 1994. "Prediction of Scour Near Single Piles in Steady Currents." Master's thesis, UFL/COEL-94/001, Coastal and Oceanographic Engineering Department, University of Florida, Gainesville, FL. Raudkivi, A.J., and R. Ettema 1977. "Effects of Sediment Gradation on Clear Water Scour." Journal of the Hydraulics Division, 103, no. HY 10 (October). Raudkivi, A.J. 1986. "Functional Trends of Scour at Bridge Piers." Journal of Hydraulic Engineering, 112, no.1 (January). Richardson, E.V., D.B. Simons, and P.Y. Julien 1988. "Highways in the River Environment." 2nd ed. U.S. Dept. of Transportation, FHWA, Ft. Collins, CO. Richardson, E.V., and J.R. Richardson 1989. "Bridge Scour." Proceedings of the Bridge Scour Symposium, October 17-19, 1989, Report No. FHWA-RD-90-035. Salim, M., and J.S. Jones 1996. "Scour Around Exposed Pile Foundations." Proceedings of the ASCE North American Water and Environment Conference, Anaheim, CA (August). Shen, H.W., V.R. Schneider, and S.S. Karaki 1966. "Mechanics of Local Scour." Civil Engineering Department, Colorado State University, Fort Collins, CO Pub. No.CER66HWS22. Sheppard, D.M., G. Zhao, and T.H. Copps 1995a. "Local Scour Near Multiple Pile Piers in Steady Currents." Proceedings of the 1' International Conference on Water Resources Engineering, San Antonio, TX. 1804-08. Sheppard, D.M, G. Zhao, and B. Ontowirjol995b. "Local Scour Near Single Piles in Steady Currents." Proceedings of the ASCE Water Resources Engineering Conference, San Antonio, TX. Sheppard, D.M. 1998. "Conditions of Maximum Local Scour." Compendium of Scour Papers from ASCE Water Resources Conferences, Eds. E.V. Richardson and P.F. Lagasse (September 1998). Sheppard, D.M., and J.S. Jones 1998. "Scour at Complex Pier Geometries." Compendium of Scour Papers from ASCE Water Resources Conferences. Eds. E.V. Richardson and P.F. Lagasse (September 1998). Sumer, B.M., N. Christiansen, and J. Fredsoe 1992. "Time Scale of Scour Around a Vertical Pile." Proceedings of the 2nd International Offshore and Polar Engineering Conference, San Francisco, CA. 308-15. Yanmaz, M., and D. Altinbilek 1991. "Study of Time-Dependent Local Scour Around Bridge Piers." Journal of Hydraulic Engineering 117, no. 10: 1247-68. Zhao, G. 1996. "The Effect of Flow Skew Angle on Local Sediment Scour Near Pile Groups." Master's thesis, UFIJCOEL-96/001, Coastal and Oceanographic Engineering Department, University of Florida, Gainesville, FL. Zhao, G., and D.M. Sheppard 1996. "The Effect of Flow Skew Angle on Sediment Scour Near Pile Groups." Proceedings of the 1996 ASCE North American Water and Environment Congress. |