BRIDGE SCOUR Abstract Introduction

BRIDGE SCOUR BY E. V. RICHARDSON Ph.D., P.E. and J. R. RICHARDSON Ph.D. CIVIL ENGINEERING DEPARTMENT COLORADO STATE UNIVERSilY Ff. COLLINS, COLORADO Abstract Total scour at highway crossings is composed of long term aggradation and degradation, contraction and local scour. In general these components are additive. Additionally lateral shifting of the stream or river can also cause bridge stability problems. Analysis of scour, especially contraction and local scour, is complicated by conditions of flow and geometry. In September, 1988, the Federal Highway Administration issued a Technical Advisory (fA) on bridge scour. This advisory recommended procedures for estimating total scour at bridges for both design of new bridges and evaluation of existing bridges for vulnerability to scour. In the development of theTA, many equations for computation of total scour were evaluated and the best were selected for inclusion in theTA It should be noted however, that all of the equations which were evaluated, were developed based upon laboratory data with limited field data. Actual field measurements were only obtained for pier scour. Presently there is a determined effort to by the Federal and State governments to collect field data on total scour at highway stream crossings. These data are to be used to increase the accuracy of scour prediction equations. In the analysis of these field data, equations other than the ones provided in theTA should be investigated also. In this paper, the more promising equations that were considered in the preparation of the TA for prediction of contraction scour, and pier scour at abutments and piers, are presented. Furthermore, the topic of armoring and equations for predicting local scour for coarse bed streams are presented. It should be noted that the use of any of the equations in this paper will require a degree of sound engineering judgment because of the limited data for which all of these equations are based. Introduction All material in a stream bed will erode. It is just a matter of time. However, some material such as granite may take hundred's of years to erode. Whereas, sand bed streams will erode to the maximum depth of scour in hours. Sandstone, shales, and other sedimentary bedrock materials, do not erode in hours or days but will, over time, if subjected to the erosive forces of water, erode to the extent that a bridge will be in danger unless the substructures are founded deep enough. Cohesive bed and bank material such as clays, silty clays, silts and silty sands or coarser bed material such as glacial tills, which are cemented by chemical action or compression, will erode if subjected to the forces of flowing water. The erosion of cohesive and other cemented material is slower than sand bed material but their ultimate scour will be as deep if not deeper than the scour depth in a noncohesive sand bed stream. It might take the erosive action of several major floods but ultimately the scour hole will be equal to or greater in depth than with a sand bed material. Major floods tend to scour the material around the piers of a bridge during the rising limb of the flood and refill these scour holes during the recession limb. In many cases, the redeposited material in the scour hole is more easily eroded by subsequent floods. Because of this, even bridges which span so called bed rock streams may ultimately fail due to erosion of the material around the pier. In most of these cases, this failure is the result of several major floods. During post-flood inspection of pier foundations, it may at first indicate that the material around the foundations are adequate, when in fact, the bridge is in jeopardy of failing during the next flood. This does not mean that every bridge foundation must be buried below the calculated scour depth determined for non bed rock streams. But it does mean that so called "bed rock streams" must be carefully evaluated.

1 Total Scour Total Scour at a highway crossing is composed of three components. In general the components are additive. These components are long term aggradation and degradation, contraction scour and local scour. Each of these types of scour are introduced separately below. 2.1 Long Term Aggradation and Degradation The change in river bed elevation (aggradation or degradation) over long lengths and time due to changes in controls, such as dams, changes in sediment discharge and changes in river geomorphology, such as changing from a meandering to a braided stream is defined as long term scour. Long term aggradation and degradation may be natural or man induced. 2.2 Contraction Scour Scour that results from the acceleration of the flow due to either a natural or bridge contraction is termed contraction scour. Contraction scour may also result from the orientation of the bridge on the stream. For example, it's location with respect to a stream bend or it's location upstream from the confluence with another stream. In this latter case, the elevation of the downstream water surface will affect the backwater on the bridge, hence, the velocity and scour. Contraction scour may occur during the passage of a flood, scouring during the rising stage, and refilling on the falling limb of the runoff. 2.3 Local Scour The scour that occurs at a pier or abutment as the result of the pier or abutment obstructing the flow is called local scour. These obstructions accelerate the flow and create vortexes that remove bed material around them. Generally, scour depths from local scour is much larger than the other two, often by a factor often. But if there are major changes in stream conditions, such as a large dam built upstream or downstream of the bridge or severe straightening of the stream, long term bed elevation changes can be the largest contributor to total scour. 2.4 Lateral Shifting or the Stream In addition to the above, lateral shifting of the stream may also erode the approach roadway to the bridge and, by changing the angle of the flow in the waterway at the bridge crossing, increase total scour. Long Term Bed Elevation Changes Long term bed elevation changes (aggradation or de.gradation) may be the natural trend of the stream or may be the result of some modification to the stream or watershed condition. The stream bed may be aggrading, degrading or not changing in the bridge crossing reach. When the bed of the stream is neither aggrading or degrading it is considered to be in equilibrium with the sediment discharge supplied to the bridge reach and the long term bed elevation does not change. In this section we will only consider long term trends, not the cutting and filling of the bed of the stream that might occur during a runoff event. A stream may cut and fill during a runoff event and also have a long term trend of an increase or decrease in bed elevation. The problem for the engineer is to determine what the long term bed elevation changes will be during the life time of the structure. This requires assessing what the current rate of change in the stream bed elevation is. Is the stream bed elevation in equilibrium? Is the stream bed degrading? Is it aggrading? What is the future trend of the stream bed elevation? During the life of a bridge, present trends may change. These long term changes are the result of modifications of the state of the stream or watershed. Such changes may be the result of natural processes or the result of man's activities. The engineer must also assess the present state of the stream and watershed and determine future changes in the river system, and from this, determine the long term stream bed elevation changes. Factors that affect long term bed elevation changes are: dams and reservoirs upstream or downstream of the bridge; changes in watershed land use (urbanization, deforestation, etc.); channelization; cutoff of meander bends (natural or man made); changes in the downstream base level (control) of the bridge reach; gravel mining from the stream bed; diversion of water into or out of the stream; natural lowering of the total system; movement of a bend; bridge location in reference to stream plan-form and stream movement in relation to the crossing. Examples of long term bed elevation changes are given in Chapter VII of "Highways in the River Environment" (HIRE) (Richardson et. al1975, 1988).

2 Analysis of long term stream bed elevation changes must be made using the principals of river mechanics in the context of a fluvial system analysis. Such analysis of a fluvial system require the consideration of all influences upon the bridge crossing ie: runoff from the watershed to the channel (hydrology); the sediment delivery to the channel (erosion); the sediment transport capacity of the channel (hydraulics); and the response of the channel to these factors (geomorphology and river mechanics). Many of the largest impacts are from man's activities, either in the past, the present or the future. Analysis requires a study of the past history of the river and man's activities on it; a study of present water and land use and stream control activities; and finally contacting all agencies involved with the river to determine future changes to the river system. A method to organize such an analysis is to use a three level fluvial system approach. This method provides three levels of detail in an analysis, they are; (1) a qualitative determination based on general geomorphic and river mechanics relationships; (2) engineering geomorphic analysis using established qualitative and quantitative relationships to establish the probable behavior of the stream system to various scenarios of future conditions; and, (3) quantifying the changes in bed elevation using available physical process mathematical models such as (HEC-6), straight line extrapolation of present trends, and, engineering judgement to assess the result of the changes in the stream and watershed. Recent FHWA reports such as "Stream Channel Degradation and Aggradation: Analysis of Impacts to Highway Crossings" (Brown et al, 1981) and "Highways in the River Environment" (Richardson et. al. 1975 and 1988) discuss methodologies for analysis for stage 1 and 2 of the three level approach. Contraction Scour Contraction scour at a bridge can be caused by a decrease in channel width, either naturally or by the bridge. This decreases flow area and increases velocity and results in contraction scour. Contraction scour can also be caused by short term (daily, weekly, yearly or seasonally) changes in the downstream water surface elevations that control backwater, and hence, the velocity through the bridge opening. Because this scour is reversible it is included in contraction scour rather than in long term scour. Contraction scour can result from the location of the bridge with regard to a bend. If the bridge is located on or close to a bend the concentration of the flow on the outer part of the channel can erode the bed. Contraction scour can also be cyclic. That is, during a runoff event the bed scours during the rise in stage (increasing discharge) and refills on the falling stage (deposition). Contraction scour occurs when the flow area of a stream is decreased either by a natural constriction or by a bridge. With the decrease in flow area there is an increase in average velocity and bed shear stress. Hence, there is an increase in stream power at the contraction apd more bed material is transported through the contracted reach than is transported into the reach. The increase in transport of bed material lowers the bed elevation. It is important to note that as the bed elevation is lowered due to scour, the flow area increases and the velocity and shear stress decreases until equilibrium between the bed material transported into the reach is equal to that which is transported out of the reach. The contraction of the flow by the bridge can be caused by a decrease in flow area of the stream channel as a consequence of abutments projecting into the channel and by the piers. Contraction can also be caused by the approaches to the bridge cutting off the overland flow that normally flows the flood plain during high flow. This latter case causes clear-water scour at the bridge section because the overland flow normally does not transport any bed material sediments. This clear water picks up additional sediment from the bed when it returns to the bridge crossing. In addition, if overbank flow returns to the stream channel at an abutment local scour increases at the abutment. A guide bank can be used to decrease the risk of abutment scour caused by returning overbank flow. Relief bridges in the approaches can be used to decrease the scour problem at the bridge cross section by decreasing the amount of overbank flow returning to the natural channel. Factors that can cause contraction scour are: 1) a natural stream constriction; 2) long approaches over the flood plain to the bridge; 3) ice formation or jams; 4) berm forming along the banks by sediment deposits; 5) island or bar formations upstream or down stream of the bridge opening; 6) debris; and 7) the growth of vegetation in the channel or flood plain.

3 To determine the magnitude of contraction scour from a variable backwater requires a study of the stream system to; (1) determine if there will be variable backwater; and (2) determine the magnitude of contraction scour for this condition. The WSPRO computer model is of particular value in determining whether variable backwater affects exist, and to access magnitude of these influences on the velocity and depth. Contraction scour of the bridge opening may be concentrated in one area. If the bridge is located on or close to a bend the scour will be concentrated on the outer part of the bend. In fact, there may be deposition on the inner portion of the bend, further concentrating the flow, which increases the scour at the outer part of the bend. Also at bends, the thalweg (the part of the stream where the flow or velocity is largest) will shift toward the center of the stream as the flow increases. This can increase scour and the non-uniform distribution of the scour in the bridge opening. Often the magnitude of contraction scour can not be predicted and inspection is the solution for contraction scour problems. Physical model studies can also be used to estimate contraction scour. 4.1 Predicting Contraction Scour There are several methods and equations for estimating the magnitude of contraction scour. Unfortunately the equations are based on laboratory studies with limited field data. In general, however contraction scour can be caused by different bridge site conditions. The four main conditions (cases) which contribute to contraction scour are diagramed in Fig. 1 and are as follows: Case 1. Overbank flow on a flood plain forced back to the main channel by the approaches to the bridge. The bridge and/or the channel width is narrower than the normal stream width. Case 2. The normal river channel width narrowed because of the bridge itself, or by the bridge site being on a narrower reach of the river. Case 3. A relief bridge in the overbank area with little or no bed material transport in the overbank area. Case 4. A relief bridge over a secondary stream in the overbank area.

4 r, •r1 ·r, CONTRACTION SCOUR \-----·f]::q- ---ROAD-·------} CASEI. OVERBANK STREAM.

STREAM NARROWS, BRIDGE 14T UPPER END OF' NAftROWS, NO OVERBANK FLOW

STREAM NARROWS, IRIOGE LOCATED DOWNSTREAM OF NARROW SECTION

BRIDGE CONTRACTS A STREAM

CASE 2.

RELIEF BRIDGE ON Fl.OOD PLANE

o, • o,• 0'",.. ,.,..., CASE 3 CASE 4 CASE 3 AND 4.

Fig. 1. The four main cases of contraction scour.

5 4.1.1 Case 1 When overbank flow on a flood plain is forced back to the main channel by the approaches to the bridge, the bridge and/or the channel width is narrower than the normal stream width. For this case, Laursen's (1960) equation, (Eq. 1) can be used to predict the depth of scour, y,, in the contracted section.

Eq.1 Where;

y, - y 2 - y 1 Average scour depth

y 1 = average depth in the main channel

y 2 = average depth in the contracted section

W 1 = Width of the main channel

w 2 =Width of the contracted section Q, = flow in the contracted section Q c = flow in main channel

n 2 = Manning n for contracted section

n 1 = Manning n for main channel 0 5 V •c =is the shear velocity ( (gy 1 s 1 ) · ) w =fall velocity ofD5o of bed material. Can be determined using Fig. 2. g = gravity constant, 32.2 ft/sec2

S 1 = slope of friction (energy grade line) for the main channel. 6 <2 •e> See T bl A- 7(3+•> ( a e 1),

B = 7 <::.> (See Table 1) and,

(! is a transport factor.

Table 1. Transport Coefficients For Laursen's Contraction Scour Equation

V •c - w e A B ModeofBed Material Transport <0.5 0.25 0.59 0.066 Primarily Contact Load 0.5> 1.0>2.0 1.00 0.64 0.21 Mixed Contact and Suspended Load >2.0 2.25 0.69 0.37 Primarily Suspended Bed Material

For most applications, the fall velocity can be determined using Fig. 2. In this figure the fall velocity for various sand sizes, shape factors, and water temperatures is given. For most cases naturally occurring sands have a shape factor of about 0.7. Therefore the center group of curves are recommended for the determination of the fall velocity. It should be noted that the ratio of Manning's n can be significant if a channel has dunes in the main channel and plane bed, washed out dunes or antidunes in the contracted channel (see Chapter III of HIRE).

Furthermore, the average width of the bridge opening W 2 is normally taken as the top width of the channel less the width of the piers.

6 10 1 SF. 0.7 100 0.1 I S.F. O.t 10 50 Foil V•locity, In em /see

Fig. 2. Fall velocity for sand grains at various temperatures. (From U.S. Inter-Agency Committee on Water Resources, Sub-Committee on Sedimentation, 1957) Currently, Laursen's equation is the best equation to use. However, a long contraction will overestimate the depth of scour at the bridge, if the bridge is located at the upstream end of the contraction or if the contraction is the result of the bridge abutments and piers.

4.1.2 Case2 The stream channel narrows naturally or by the bridge abutments encroaching on the channel, but there is no overbank flow. Flows are confined to the channel. If the contraction of the channel is less than 10 percent, the contraction scour should be negligible. For this case, contraction scour is estimated using Laursen's equation, Eq. 1, by setting Q, equal to Q c·

4.1.3 Case3 This is the case of a relief bridge where there is no bed material transport on the upstream flood plane. To estimate the contraction scour for this case the use of Laursen's equation (Laursen, 1980) Eq. 2, given below is recommended.

Eq.2 Where;

W 1 is the width upstream of the relief bridge. This width can be estimated by assuming the location of stagnation between the main bridge openings and the relief bridge opening in feet.

V 1 is the average velocity one bridge length (relief bridge) upstream of the opening (ft/sec).

D 50 is the median diameter of the bed material at the relief bridge in feet. As in previous cases the subscripts 1 and 2 refer to the value of these variables upstream and in of the bridge opening respectively.

7 4.1.4 Case 4 This is the case of a relief bridge with bed material transport upstream of the relief bridge opening. For this case use the equation given for Case 1 with appropriate adjustments of the variables. This is also applicable for bridges over secondary channels on the flood plain.

Local Scour Formation of vortexes is the basic mechanism causing local scour at piers or abutments. The formation of these vortexes results from the pileup of water on the upstream face and subsequent acceleration of the flow around the nose of the pier or abutment. The action of the vortex removes bed materials away from the base region. If the transport rate of sediment away from the local region is greater the transport rate into the region, a scour hole develops. As the depth of scour is increased, the strength of the vortexes are reduced, thus reducing the transport rate. As, equilibrium is reestablished scouring ceases and the scour hole will not enlarge further. A typical vortex around a pier is illustrated in Fig. 3. For piers there is also an additional vertical vortex downstream of the pier, which is denoted as the wake vortex. Both vortexes remove material from around the pier. In many cases the material which is removed by these vortexes is redeposited immediately downstream of the pier. This is common for long piers.

Fig. 3. Schematic representation of scour at a cylindrical pier.

5.1 Factors Effecting Local Scour The factors that effect local scour at a pier or abutment are as follows: 1) width of the pier, a; 2) projection length , a of the abutment into the flow; 3) length of the pier, L;

4) depth of approach flow, y 1; 5) velocity of the approach flow;

6) size of the bed material D 50 ; 7) angle of the approach flow to the pier or abutment (angle of attack); 8) shape of the pier or abutment; 9) bed configuration; 10) ice formation or jams; and 11) debris.

8 1. The width of pier has a direct affect on the depth of scour. With an increase in pier width, the velocity of flow in the bridge opening is increased to maintain continuity and consequently, there is an increase in scour depth. 2. Projected length of an abutment into the stream affects the depth of scour. With an increase in the projected length of an abutment into the flow there is an increase in scour. However, there is a limit on the increase in scour depth with an increase in length. This limit is reached when the ratio of projected length into

the stream (a ) to the depth of the approaching flow ( y 1) exceeds 25. Also, the length of an abutment may not be as important as the ratio of the flow in the main channel to the flow in the overbank. 3. Generally, the length of a pier has no appreciable affect on scour depth as long as the pier is parallel with the flow. However, if the pier is at an angle to the flow, the length has a very large affect. At the same angle of attack doubling the length of the pier can increase scour depth by 33 percent. Some equations take the length factor into account by using the ratio of pier length to depth of flow or pier width and the angle of attack of the flow to the pier. Others uses the projected area of the pier to the flow in their equations. 4. Flow depth has a direct affect on scour depth. For Pier scour an increase in flow depth can increase scour depth by a factor of 2 or more. For abutments the increase ranges from 1.1 to 2.15 depending on the shape of the abutment. 5. The velocity of the approach flow increases scour depth. The larger the velocity the deeper the scour depth will be. There is also a high probability that the scour depth will depend on whether the flow is subcritical of supercritical. In fact, Jain and Fisher (1979) showed that scour depths increases with an increase in Froude number. Unfortunately however, most research and data are for flows with Froude Numbers much less than one and therefore, the quantitative influence of supercritical flow on local scour is limited. 6. Depth of local scour in sands does not depend on the grain size. For larger size bed material the ultimate or maximum scour is unaffected by the grain size. These materials will be moved by the approaching flow or by the vortexes and turbulence created by the pier or abutment. However the time that it may take for these materials to be removed does depend on the size of the material. The time that it may take to reach ultimate scour may be very large. Very large particles in the bed material, (ie. cobbles or boulders) may armor the scour hole. But in the case of the Schoharie Creek bridge collapse, large riprap was ultimately removed from around the piers by a series of large flows (Richardson, et al, 1987). The size of the bed material also determines whether the scour at a pier or abutment is clear-water of live-bed scour. This topic is discussed later in this section. Fine bed material (silts and clays) will have scour depths as deep or deeper than sand bed streams. This is true even if bonded together by cohesion. The affect of oohesion is to determine the time it takes to reach the maximum scour. With sand bed material the maximum depth of scour is measured in hours. With cohesive bed materials it may take days, months or even years to reach the maximum scour depth. 7. Angle of attack of the flow to the pier or abutment has a large affect on local scour as was pointed out in the discussion of the affect of pier length above. The affect on piers will not be repeated here. With abutments the depth of scour is reduced for embankments angled downstream and is increased if the embankments are angled upstream. According to the work of Ahmad, (Richardson et. al., 1975 and 1987) the maximum depth of scour at an embankment inclined 45 degrees downstream is reduced by 20 percent. Whereas, the scour at an embankment inclined 45 degrees upstream is increased about 10 percent. 8. The shape of piers and abutments have a significant affect on scour. With a pier, streamlining the front end reduces the strength of the horseshoe vortex and reduces scour depth. Streamlining the downstream end of piers reduces the strength of the wake vortices. However increasing the angle of attack will decrease or negate the decrease of scour depth which would be realized by streamlining the piers. A square-nose pier will have maximum scour depths about 20 percent larger than a sharp-nose pier, and 10 percent larger than a cylinder or round-nose pier. Abutments with vertical walls on the stream side and upstream side, will have scour depths about double that of spill slope abutments. 9. Bed configuration also affects the magnitude of local scour. In streams with sand bed material the shape of the bed, (bed configuration), may be ripples, dunes, plane bed and antidunes (Simons and Richardson, 1963 and Chapter III of HIRE). The bed configuration depends on the size distribution of the sand bed material, flow conditions and fluid viscosity. The bed configuration may change from dunes to plane bed or antidunes during an increase in flow or velocity. It may change back with a decrease in flow. The bed configuration may also change with a change in water temperature or change in concentration of silts and clays suspended in the flow.

9 10. Ice and debris; by increasing the width of the piers, changing the shape of piers and abutments, increasing the projected length of an abutment or causing the flow to plunge downward against the bed, can increase both the local and contraction scour. The magnitude of the increase is still largely undetermined. Debris however, can be accounted for in the scour equations by estimating the extent that the debris will increase the width of the pier or length of the abutment. Debris and ice effects on contraction scour can also be accounted for by estimating the amount of flow blockage (decrease in width of the bridge opening) in the equations for contraction scour. Field measurements of scour at ice jams indicate the scour can be in the tens of feet. 5.2 Clear-water and Uve-Bed Scour aear-water scour occurs when there is no movement of the bed material of the stream upstream of the crossing, but the acceleration of the flow and vortices created by the piers or abutments causes the material at their base to move. Live-bed scour occurs when the bed material upstream of the crossing is also moving. Bridges over coarse bed material streams often have clear-water scour at lower flows, live-bed scour at the higher discharges and then clear-water scour for the falling stages. aear-water scour reaches its maximum over a longer period of time than live-bed scour, Fig. 4. This is because clear-water scour occurs mainly on coarse bed material streams. In fact clear-water scour may not reach its maximum until after several floods have been experienced. Also, maximum clear-water scour is about 10 percent greater than the maximum live·bed scour. Live-bed scour in sand bed streams with a dune bed configuration fluctuates about an equilibrium scour depth, Fig. 4. This is caused by the fluctuating nature of the sediment transport of the bed material in the approaching flow when the bed configuration of the stream is dunes. In this case (dune bed configuration in the channel upstream of the bridge) maximum depth of scour is about 30 percent larger than equilibrium depth of scour. The maximum depth of scour is the same as the equilibrium depth of scour for live-bed scour with a plain bed configuration. With antidunes occurring upstream and in the bridge crossing the maximum depth of scour, based on the limited research of Jain and Fisher (1979), is about 20 percent greater than the equilibrium depth of scour.

MAXIMUM SCOUR DEPTH _{__ -[-EQUILIBRIUM SCO-UR-::..D...:.E:::=~P-T-H .. X 1- wQ. 0 LIVE BED SCOUR 0: ::l 0 0 (/) CLEAR-WATER SCOUR

TIME

Fig. 4. Scour Depth as a Function of Time.

10 5.3 Annoring Armoring occurs on a stream bed or in a scour hole when the forces of the water during a particular flood are unable to move the larger sizes of the bed material. This larger material protects the underlying material from movement. Scour around an abutment or pier may initially occur but as the scour hole deepens the coarser bed material moves down in the hole and protects the bed so that the full scour potential is not reached. When armoring occurs, the coarser bed material will tend to remain in place or quickly redeposit so as to form a layer of riprap-like armor in the scour holes, thus limiting further scour for a particular discharge. This armoring effect can decrease scour hole depths which were predicted to occur based on formulae developed for sand or other fine material channels. When larger flow conditions occur the armor layer can be broken and the scour hole deepened until either a new armor layer is developed or the maximum scour as given by the sand bed equations is reached. UNFORTUNATELY KNOWLEDGE OF HOW TO PREDICT THE DECREASE IN SCOUR HOLE DEPTH WHEN THERE ARE lARGE PARTICLES IN THE BED MATERIAL IS lACKING. Research in New Zealand by Raudkivi (1986) and in Washington State (Copp and Johnson, 1987) gives a bases for calculating the decrease in scour depth by armoring but their equations need field verification. The results of this research for pier scour will be given later.

5.4 Estimating Local Scour Depths Equations for estimating local scour are based on three methods of analysis. These methods are; 1) Dimensional analysis of the basic variables causing local scour. 2) The use of transport relations in the approaching flow and in the scour hole. 3) Regression analysis of the available data. Equations for estimating local scour at abutments or piers developed by the three methods are given in the next sections. In HEC 18 (FHWA, 1989) and in "Interim Procedures for Evaluating Scour at Bridges" (FHWA, June 1988), only one method or equation is recommended. The additional equations are given in this report for basis of comparison, to be used in additional study of a particular bridge site and for use in research. It should be noted that these equations were developed from laboratory experiments with limited field data. To analyze scour, the engineer should evaluate his problem and select the equation or method that in his judgement best suits the case at hand. IT MAY BE NECESSARY TO USE MORE THAN ONE EQUATION OR METHOD AND THEN USE ENGINEERING JUDGEMENT IN SELECTING THE LOCAL SCOUR DEPTH. For example, if the stream contains large quantities of coarse bed material, then both the sand bed equation and the armoring equation should be used. Then, based on knowledge of the stream, the bed material, the flows and type of bridge crossing, select the value of the scour.

S.S Maximum Depth or Scour For live-bed scour with a dune bed configuration, the maximum depth of scour is about 30 percent greater than equilibrium scour depth given by the equations such as Liu, et. al.'s (1961) equation for abutments and CSU's equation for piers. Therefore, the values of scour that are calculated using these equations should be increased by 30 percent when the bed form upstream of the bridge is dunes. The reason for this is that the research used for determining scour depth for the live-bed scour case was conducted with a dune bed and equilibrium scour was measured. When the bed configuration is plane bed or antidunes with live bed scour the depth of scour should be increased by ten (10) percent. For clear-water scour, the maximum depth of scour is about 10 percent greater than live-bed scour. However, there is no need to increase the scour depths because the equations predict the maximum scour.

11 Local Scour at Abutments 6.1 General Equations for predicting scour depths at abutments are based almost entirely on either laboratory data or inductive reasoning from sediment continuity equations. There are little field data to compare abutment scour equations. For example, Froehlich's (1988), Laursen's (1980) and Liu et.al's (1961) equations are based entirely on laboratory data. 6.1.1 Types of Equations Equations for estimating abutment scour are derived by three methods. 1) The first type of abutment scour equations are derived from dimensional analysis of the variables. These methods determine the scour depth by developing relationships among the major dimensionless

parameters. Common dimensionless parameters are; the ratio of scour depth, y, to flow depth y 1; ratio of

abutment length a to flow depth y 1 ; the Froude Number Fr; and others. An example of this form of scour depth equation is Liu, et. al.'s (1961) equation given in this text. 2) A second type of scour depth equation are derived from transport relations and the change in transport due to acceleration of the flow caused by the abutment. Laursen's (1980) equation which is presented in this paper is an example of this type local abutment scour equation. 3) A third type of abutment scour equations are developed from regression analysis of available data. Froehlich's (1988) equation, which is presented in this paper is an example. All of the equations for abutment scour do not account for the existence of slow flow, or cohesive, tree lined and vegetated banks. For example, Liu, et. al.'s (1961) experiments were conducted in laboratory flumes using sand. For these studies, the abutments projected out into the flow various distances. With these studies, the velocity and depth upstream of the abutment were about the same as in the channel. Other abutment scour experiments by other researchers were similar and no attempt was made to simulate shallowed depths, the existence of trees on the banks, cohesive vegetated banks or low velocities which often occur in the field. Because of the nature of the experiments which were used to develop equations for abutment scour, these equations represent WORST CASE CONDITION. Actual field conditions will mitigate, to some degree, abutment scour. Abutment scour equations give maximum scour depths Cor the conditions they represent Cor reasons discussed in the previous paragraph. Therefore, engineering judgment is required in the design or foundations Cor abutments. IC the design Dow conditions are different than those used to define the abutment scour equations, then the abutment can be designed using a shallower depth or scour. However, If shallower design scour depths are used, then rip-rap should be installed extending 2-5 feet below the bed or the channel. Additionally, the installation or a guide bank, or spur dike should be considered.

6.1.2 Position of Abutments Abutments can be set back from the natural stream bank, set at the bank or can project out into the flow. Abutments can have various shapes and can be set at an angle to the flow. The most common shape of abutments are either vertical walls and spill through slopes. These two shapes are diagramed in Fig. 5. Scour at abutments can be live-bed or clear-water scour. Finally, there can be varying amounts of overbank flow that is intercepted by the approaches to the bridge and returned to the stream at the abutment. All of these conditions influence scour at abutments. These influences can occur singly, or as is more common, in combination with other conditions mentioned above. Various conditions (cases) are presented and illustrated in Table 2 and Fig. 6, Fig. 7, and Fig. 8. In Table 2, equations for computation of abutment scour are recommended for each case. No single equation is recommended for a given situation when more than one equation is applicable, because, with the lack of field data for verification, it is not know which equation is best. It is recommended that the designer determine what case fits the design situation and then use all equations that apply to the case. IT IMPORTANT THAT THE COMMENTARY ON EACH OF THE EQUATIONS BE READ AND UNDERSTOOD PRIOR TO AITEMPTING TO USE TilE EQUATIONS FOR DESIGN PURPOSES. Engineering judgment, based upon the computed abutment scour depths and other characteristics of the crossing, must be used to select the depth of foundations. The designer should take into consideration the potential cost of repairs to an abutment and danger to the travelling public in selecting scour depths. Finally, design measures such as spur dikes and riprap should be used to increase the safety of the bridge.

12 Elevation Elevation \ I l I i I. i i Plan

~rrr.,..,.,.,....,,_,_, ,-r- "'''''.lfiT\\ ,., , ,,A -rr?~;,..,.,,..., ,_,_7"7-_ Section A- A' Sec lion A-A'

(a) Spill Through (b) Vertical Wall

Fig. 5. Common Shapes of Abutments

13 Table 2. SUMMARY OF ABUTMENT SCOUR EQUATIONS

Case Abutment Overbank Value of BedLoad Abutment Equation

Location Flow? a/y 1 Condition Type Number

1 Projects No <25 Uve Vertical 4, 5, into Bed Wall 6,9 Channel Spill 3, 5, Through 6, 9 Clear Vertical 7, 8 Water Wall Spill 7,8 Through 2 Projects Yes <25 Uve Vertical s, 11 into Bed Wall 1 Channel Clear Verticttl 7,11 Water Wall 3 SetBack Yes <25 Clear Verticttl 7 From Main Water Wall Channel 4 Relief Bridge Yes <25 Clear Vertic!I 7 on Water Wall Floodplain 5 At Edge of Yes <25 Uve Vertical 11 Main Channel Bed Wall 1 6 Not Yes >25 Not Spill 12 Designated Designated Through 7 Skewed to ------• Stream

1 Correction factor giver for other abutment types • Adjust scour estimate for equations 4-12 using Fig. 15. Notes: • Except for Case 6, the equations for all cases are based on laboratory studies with little or no field data.

• The factor a I y 1 = 25 as a limit for Cases 1-5 is arbitrary, but it is not practical to assume that scour depth would continue to increase with an increase in abutment length. • Depth of scour is about double for vertical wall abutments as compared with spill through abutments.

14 r a

______l ______

CONTRACTION SCOUR

CASE I. ABUTMENTS PROJECT INTO CHANNEL, NO OVERBANK FLOW.

CASE 2. ABUTMENTS PROJECT INTO CHANNEL AND THERE IS OVERBANK FLOW.

Fig. 6. Abutment Scour - Cases 1 and 2

15 '

MAIN BRIDGE

y =AVG. APPROACH 1 DEPTH I I \\ I I \\ CASE 3. ABUTMENT SETBACK FROM THE CHANNEL MORE THAN 2.7~ Ya. CASE 4. RELIEF BRIDGE. ~\_"'I JIll/_/~

--~~-----~--~----._------~~--~~------

CASE 5 ABUTMENT SET AT EDGE OF CHANNEL, OVERBANK FLOW

Fig. 7. Abutment Scour- Cases 3, 4 and 5

16 CASE 6 ABUTMENT LENGTH, a, TO FLOW DEPI'H 1 • Yl 1 RATIO > 2 5

CASE 7 ABUTMENT SET AT AN ANGLE, e, TO TilE FLOW

Fig. 8. Abutment Scour - Cases 6 and 7

17 6.2 Calculating Abutment Scour for the Different Cases Case l Abutments Project Into Channel, No Overbank Flow, Fig. 9.

Scour

Fig. 9. DEFINffiON SKETCH FOR CASE 1 ABUTMENT SCOUR. Seven equations are applicable for this case. They are Eqs. 3, through 9. These equations are based on dimensional analysis, transport relations and regression analysis and are limited to cases where a ly 1 < 25.

Case 6, which is presented later, discusses the computation of abutment scour if a I y 1 > 25. • Liu, eL al.'s Equations Live-bed Scour With a Spill Through Abutment According to the studies of Liu, et al., (1961) the equilibrium scour depth for local live-bed scour in sand at a stable spill slope abutment for subcritical flow is determined by Eq. 3. y ---.! = 1.1 (a- )o.4 Fr 1 o.33 y 1 y 1 Eq.3 y, = equilibrium depth of scour (measured from the mean bed level to the bottom of the scour hole).

y 1 = average upstream flow depth in the main channel a = abutment and embankment length (measured along the design flood water surface, normal to the bankline of the channel, from where the water surface intersects the bank to the outer edge of the abutment).

0 5 Fr 1 = upstream Froude number= V 1 /(gy .) · Live bed scour at a vertical wall abutmenL If the abutment terminates at a vertical wall and the wall on the upstream side is also vertical, then the scour hole in sand as calculated using Eq. 4 is nearly doubles the abutment scour for a spill through abutment. This was shown by Liu, et al, (1961) and Grill (1972).

y (a )o.4 33 ---.! = 2.15 - Fr 1 °' y 1 y 1 Eq.4

18 • Laursen's Equations. Live-bed Scour at Vertical Wall Abutment. Laursen (1980) suggested two relationships for scour at vertical wall abutments. One for live-bed scour and another for clear-water scour depending on the relative magnitude of the bed shear stresses to the critical shear stress for the bed material of the stream. For live-bed scour ( -r 1 > -r c:), Eq. 5 and Eq. 6 are recommended.

~= 2.75Ys[[ Ys + 1]1.7 -1] Yt Yt 11.5Yt Eq.S Simplified form: Y s ( a )o.4a -=- 1.5 - y l y l Eq.6

Clear-water scour ( "t 1 < -r c) at vertical wall abutment. Eq. 7 is used for the clear water case of Laursen (1980). 7 y 1 )6 ( ~= ll.Sy 1 + l _ l 2.75Ys I Yt Yt C:Y Eq.7

-r 1 = shear stress on the bed upstream -r c: = critical shear stress of the Dso of the bed material and can be obtained from Fig. 10.

2 I I I I I • I I I I I I - ~ ~ 1.0 - u - 0.8 - - 0.6 - 0.4 - 0.3 .. Very Hioh Fine ~ - 0.2 - Sediment Concentr~ tion ,~ :a-' ~ - . ~~ u 0.1 - I I ---~~ ~ ~ Shield's Curve -- -:: ...... "" i/ // .. 0.08 - H~-- V ~ Noncohesive Soil - 0.06 v - ~.~.... ,- i' - 0.04 v~ 0.03 - ,,// 0.02 \..0~'· ,~ - ~ - ...,.,..,. v 0.01 :.l I I I I I I I I I l 0.1 Q2 0.4 0.6 2 4 6 810 20 406080100 D,mm

Fig. 10. Critical shear stress as a function of bed material size and suspended fine sediment.

19 • Scour at other abutment shapes usine Laursen's Equations. Scour values given by Laursen's equations are for vertical wall abutments. He suggests the following multiplying factors for other abutment types for small encroachment lengths:

Abutment JYpe Multipl!lng Factor 45 degree Wing Wall 0.90 Spill-Through 0.80

Laursen's equations are based on sediment transport relations. TilEY GIVE MAXIMUM SCOUR AND INCLUDE CONTRACTION SCOUR. FOR THESE EQUATIONS, DO NOT ADD CONTRACTION SCOUR TO OBTAIN TOTAL SCOUR AT THE ABUTMENT. Laursen's equations require trial and error solution. Curves developed by Chang (1987) to solve these equations are given in Fig. 11. Note that the equations have been truncated at a value of :· equal to 4. It is

Y • recommended that the maximum value of y be taken as 4 because laursen's equations are open ended and field data for Case 6 did not exceed 4 times y 1 •

cq ., 't. Cll 9 0 0 a 0 0 a Qo• !a. . .. " . 1a W ...... -1 ... .:-t ..• ..-, ... - Ye 0.1 yl -, · Ye Yo 0.1 Ow*Yo 0.5 0.2 0,02 0.2 O.OJ 1.0 0.1 1.! 0.5 0.1 0.5 2.0 0.5 0.2 z.s 3.0 0.5 3.5 1.0 1.0 4.0 1.0 0.! 4.!1 1.0 5.0

8.0 1.& 1.5 1.0 1.~ 1.5 r.o 2.0 8.0 2.1 1.5 9.0 3.0 2.0 2.0 2.0 5.5 2.0 10.0 4.0 2.5 2.5 2.5 2.5 &.0"·' !.0 8.0 !.5 15.0 1.0 3.0 -4.0 3.0 3.0 1.0

"·'5.0 1.0 10.0 3.5 5.5 3.5 20.0 3.5 8.0 11.0 1.5 12.0 7.0 4.0 4.0 4.0 15.0

ForEq.S ForEq. 7 For Eq.11 Fig. 11. Nomograph for Abutment Scour.

20 • Froehlich's Equations. Clear-water scour at an abutment. Froehlich (1987), using dimensional analysis and multiple regression analysis of 164 clear-water scour measurements in laboratory flumes developed the following equation (Eq. 8):

, )0.63 ( )0.43 7 y s = 0. 7 8 K K F r 1. 19 .!.!._ G - 1.a + 1 1 2 ~ Y 1 ( Y 1 Dso Eq.8 Live-bed scour at an abutment. Froehlich (1989) also analyzed 170 live-bed scour measurements in laboratory flumes to obtain the following equation (Eq. 9):

a')o.43 0 61 s = - ' + y 2. 27 K 1 K 2 F r 1 Y1 (Yt Eq.9 Where:

K 1 coefficient for abutment shape

K 2 coefficient for angle of embankment to flow K2 = (0/90)o.tJ

9 is the angle of the embankment to the flow in degrees a length of abutment projected normal to flow

a'-A,Iy 1 A. is the flow area of the approach cross-section obstructed by the embankment. Fr Froude number of approach flow upstream of abutment. G geometric standard deviation of bed material G = (Da41 D t6)o.s

D 84 , D 50 • D 16 Are the grain sizes of the bed material. The subscript indicates the percent finer at which the grain size is determined.

y 1 depth of flow at abutment

y s scour depth

Description K• Vertical Abutment 1.00 Vertical Abutment 0.82 With Wingwalls Spill Through 0.55 Abutment The constant term of unity ( + 1) in Froehlich's equation is a safety factor that makes the equation predict a scour depth larger than any of the measured scour depths in the experiments. This safety factor should be used for design purposes.

21 Case 2 Abutment Projeds Into The Channel, With Overbank Flow.

No bed material is transported in the overbank area and a I y 1 < 25. This case is illustrated in Fig. 12.

Fig. 12. Bridge Abutment in Main Channel and Overbank Flow. For this case, with vertical wall abutments, Laursen's equations (Eq 5 or 7) should be used to calculate the scour depth using an abutment length determined by Eq. 10. Eq. 11 can also be used for this case with the appropriate selection of variables. For live bed scour (,; 1 > ,; c) use equations 5 and 11. For clear water scour

( ,; 1 < -c c) use equations 7 or 11. If the abutment shapes are different than vertical, used Laursen's correction factors which were discussed for case 1. It should be noted that equations given by Liu and Froehlich in Case 1 would normally give the maximum (worst case) scour for case 2 and could be used as a check. Only when the overbank flow was very large and concentrated at the abutment would the scour be larger than that computed by either Liu's or Froehlich's equation. As was mentioned earlier, sound engineering judgment must be used in deciding the appropriate scour depth and foundation design for the abutment. Qo a=-- VtYt Eq.10

-c 1 = shear stress in the main channel.

-c c = Critical shear stress of the Dso of the bed material in the main channel obtained from Fig. 10.

Q o = Flow obstructed by abutment and bridge approach.

y 1 = Average upstream flow depth in the main channel.

V 1 = Average velocity in the main channel. It should be noted that for this equation, it is assumed that there is little or no bed material transport by the overbank flow. If there were bed material transported in the overbank, the abutment scour would be less. However, this is assumed to not be the case for case 2

22 Case 3 Abutment Is Set Back From Main Channel More Than 2.75 y,

For this case, there is overbank flow with no bed material transport (clear-water scour) as illustrated by Fig.13.

Main Bridoe

y1 =Avo. Approach Depth

Fig. 13. Bridge Abutment Set back from Main Channel Bank and Relief Bridge.

With no bed material transport in overbank flow and ,; o < ,; c, the scour at a vertical wall bridge abutment set back more than 2. 75 times the scour depth from the main channel bank line, can be calculated using Eq. 7 from Laursen (1980) using:

,; o = Shear stress on the overbank area upstream of the abutment.

-.: c = Critical shear stress of material in overbank area. a = With relief bridges, this variable is taken as am in Fig. 13. For other abutment shapes, use the correction factors defined by Laursen and described for Case 1. Eq. 7 can also be used when -.: o > -.: c with no bed material transport in the overbank. This situation can occur when the overbank flow occurs over grass. For this particular situation, set ,; 1 I,; c equal to unity. If there is substantial bed material transport in the overbank flow, then equation 5 can be used. Again engineering judgment must be used to determine whether 'the sediment transported in the overbank will be sufficiently large enough to significantly decrease the scour at the bridge abutment. The lateral extent of the scour hole is nearly always determinable from the depth of scour and the natural angle of repose of the bed material. Laursen suggested that the width of the scour hole is 2.75 times y,.

Case 4 Abutment Scour At Relief Bridge Scour depth· at a vertical wall abutment for a relief bridge on the overbank flow area having no bed material transport is calculated using Equation 7. This case is similar to Case 3. For this case, y 1 is the average flow depth on the flood plain. Use a r for a in the equation. If ,; 1 > ,; c on the flood plane, but there is no sediment transport, use Eq. 7 with ,; 1 I,; c equal to unity To determine the stagnation point, it is recommended that stream lines be drawn, or to observe field conditions. (See Fig. 13). The stagnation point delineates the location where the water splits and moves either to the main bridge opening or to the relief bridge. For other abutment shapes, use the correction factors described for Case 1 which were developed by Laursen.

23 Case 5 Abutment Set At Edge Of Channel The case of vertical wall scour around an abutment set at the edge of the main channel as sketched in Fig. 14 can be calculated using Eq. 11 (Laursen, 1980) when -co< -c con the flood plain. This equation can also

be used if -c 1 > ,; c on the flood plane provided there is still no bed material transport on the flood plane. For other shapes of abutments Laursen's correction factor from Case 1 can be used.

"~"• > Tc I ' Main I I I I I ' Channel hTf ~rrl To< Tc II I \ I I I \ Overbank I J I \ I I I \ 1 I I \ I I I I I \ I I I 'I \

Fig. 14. Abutment set at Edge of Main Channel.

Qo Ys[[ y Ji J q me Yo = 2 •7 5 Yo 4 • 1~ o + 1 - 1 Eq.11

qrnc = QIW The unit discharge in the main channel. Discharge in the main Channel Width of the Main Channel Discharge in the overbank Depth of flow in the overbank

Case 6 Scour At Abutments When a I y 1 > 25 Field data for scour at abutments for various size streams are scarce, but data collected at rock dikes on the Mississippi indicate the equilibrium scour depth for large a I y 1 values can be estimated by Eq. 12 (Richardson, et. al., 1975, 1988). The shape of these dikes is similar to that of a spill through abutment.

--y s- 4 F r O.JJ y 1 1 Eq.12 The data are scattered, primarily because equilibrium depths were not measured. Dunes as large as 20 to 30 feet high move down the Mississippi at a frequency which is very large in comparison to time required to create live-bed local scour. Nevertheless, it is believed that these data represent the limit in scale of scour depths as compared to laboratory data and enables useful extrapolation of laboratory studies to field installations.

Accordingly, it is recommended that Eqs. 3 through 11 be applied for abutments when 0 < a I y 1 < 25, and, Eq. 12 be used when a I y 1 > 25.

24 Case 7 Abutments Skewed To The Stream With skewed crossings, the approach embankment that is angled downstream has the depth of scour reduced due to streamlining. Conversely, the approach embankment which is angled upstream will have a deeper scour hole. For skewed crossings, the calculated scour depth should be adjusted in accordance with the curve of Fig. 15 which is patterned after Ahmad (1953).

1.4 1.2 1.0

.8 .6 .4 t / .2 I I ~·~ 0 0 45 90 lJS 180

Angle of inclination,~. dao.

Fig. 15. Scour estimate adjustment for skewed abutments.

2S 6.3 Comparison of Abutment Scour Equations Values of calculated scour depths using Laursen's equations for Case 1 through 5 are given in Fig. 16.

4.0 , 1/ j ..,j ;'/ I / flif ~~ 3.0 J I I I I j J v !/ I 7 I 2.0 II J ~ J I Y, v I ~ Yo / /VJ I; J or I "' , I i 0~ 4'%_•'/ I A~; ~-~ ~ / y• I .., J I / I 1.0 I I I ~ o/ 1/ ll I ll; Jv v ~ ~ / 0.5 v I J J 0.1 1.0 10.0 Q or0 Yt

Fig. 16. Calculated Scour Depth for Laursen's Abutment Equations (A is Eq. 7, B is Eq. 5 and Cis Eq. 11)

26 Local Scour at Piers 7.1 Introduction Local scour at piers is a function of bed material size, flow characteristics, fluid properties and the geometry of the pier. Pier scour has been studied extensively in the laboratory and there is also some field data. As a result of the many studies there are many equations. In general, the equations are for live-bed scour in cohesionless sand bed streams. All of these many equations produce similar results. Several equations for the computation of pier scour are presented in this section. These equations will be as follows: 1. Colorado State University's (CSU) equation (Richardson et. al. 1975, 1988), 2. Jain and Fisher's (1979) equation, 3. Graded and/or armored streambed equations, and, 4. Froehlich's (1987, and 1988) equations. As will be explained in the following paragraphs the CSU equation is recommended. The other equations are given for comparison, research, and for special cases such as streams with a large quantity of large size particles. It is believed that the CSU equation will, for most applications, give the ultimate scour. Engineering judgment will be needed in the case of the other equations. Sterling Jones (1983) compared many of the more common pier scour equations. His comparison of these equations is given in Fig. 17 using a Froude number of 0.3 for purposes of comparing these commonly used scour equations. It should be noted that some of these equations use velocity as a variable (normally in the form of a Froude number). However, others, such as Laursen, do not include velocity. It should be noted however that Laursen's (1960) equation was actually a special case of CSU's equation with the Froude number set at 0.5 (Chang 1987). In Fig. 18, these equations are compared with field data measurements. As can be seen from these two figures, the CSU equation encloses all the observed data and estimates lower, more reasonable, values of scour than Jain, Laursen and Niell's equations. It is important to note that the CSU equation includes the velocity of the flow just upstream of the pier by including the Froude Number.

5 .. CD -c. 3 '~ -.,Q. 0 .. 2 :I 0 CJ -t/) Bruesera

2 3 4 5 6 7 8 y/a (Flow Depth/Pier Width)

Fig. 17. Comparison Of Scour Formulas For Variable Depth Ratios y I a (Jones 1983).

27 Fig. 18. Comparison Of Scour Formulas With Field Scour Measurements (Jones, 1983). The comparisons of different equations by Jones (1983) did not take into account the possibility that larger bed material sizes could armor the scour hole. That is, that large bed material particles will, at some depth of scour limit the scour depth. Raudkivi (Raudkivi and Sutherland, 1981, and Raudkivi and Ettema, 1983, Raudkivi, 1986) studied pier scour in streams with large particles in the bed. Using this research, the Washington State Department of Transportation (Copp and Johnson, 1987, and Copp, Johnson, and Mcintosh, 1988) developed an equation for streams with a large range of particle sizes which would tend to armor the scour hole. However, the significance of armoring of the scour hole over a long time period and over many floods is not known. Therefore, their equation is not recommended for use at this time. For completeness, this equation is presented in this paper. For the determination of pier scour, Colorado State University's equation is recommended for both live-bed and clear water scour. With a dune bed configuration the equation predicts equilibrium scour depth. Maximum scour will be approximately 30 percent greater in the presence of dunes. For flow with plane bed configuration or antidunes, CSU's equation will give the maximum scour. The extent to which a pier footing or pile caps influence local scour at piers is not clearly understood. Under some circumstances a footing may serve as a scour arrester, impeding the horseshoe vortex and reducing the depth of scour hole. In other cases where the footing extends above the stream bed into the flow, it may serve to increase the effective width of the pier, thereby increasing the local pier scour. Field and model measurements of the scour at Pier 3 of the bridge over Schoharie Creek resulted in a value of 14 and 15 feet of scour respectively (Richardson, et. al. 1987 and 1988b). For this pier, the top of the footing was set at the top of the stream bed and was 19ft. wide. The pier itself was 16ft. wide. Using CSU's pier equation, the computed scour at this pier was 16 ft. if the pier width was used and 29ft. if the footing width was used in the equation. Additional flume studies (Santoro 1989) of this pier, using a 1:15 scale model, with the top of the footing at the top of the bed, and using an angle of attack of 0 and 10 degrees, and using these pier scour equations, indicated that the usage of the pier width produced the best estimates of the pier scour. It should be noted that the CSU equation consistently produced the best estimates of the pier scour for this particular case.

28 As an interim guide, based upon the above laboratory and field results, if the top of the pier footing is slightly above or below the stream bed elevation (taking into account the effect of contraction scour), use of the width of the pier shaft for the value of a in the pier scour equation is recommended. If the pier footing projects well above the stream bed to the extent that it significantly obstructs the flow, use the width of the pier footing for the value of a . Interpolation between these two values, depending upon the extent to which the footing may be expected to influence the local scour patterns is also recommended. 7.2 Pier Scour Equations 7.2.1 CSU's Equation The Colorado State University's equation (Richardson et al, 1975 and 1988) is presented in Eq. 13.

y s = 2.0 K K ( ~ )o.6s Fro.43 1 2 1 Yt Yt Eq.13 Where; y,= Scour depth Flow depth just upstream of the pier Correction for pier shape (See Table 3) Correction for angle of attack of flow (See Table 4)

a= Pier width

0 5 Fr 1= Froude number= V 1/(gy 1 ) · VI= Average velocity just upstream of the pier

Table 3. Correction Factor, K 1 for Pier Type

TypeofPier Kl a Square Nose 1.1 b Round Nose 1.0 c Cylinder 1.0 d Sharp Nose 0.9 e Group of Cylinders 1.0

The shapes of piers described in the table for K 1 are illustrated in Fig. 19.

29 L ~a ill (a) SQUARE NOSE (b) ROUND NOSE (c) CYLINDER md (d) SHARP NOSE (e) GROUP OF CYLINDERS

Fig. 19. Common Shapes of Piers

Table 4. Correction Factor, K 2 for Angle of Attack of the Flow

Angle Lla -4 Lla -8 Lla -12 0 1.0 1.0 1.0 15 1.5 2.0 2.5 30 2.0 2.5 3.5 45 2.3 3.3 4.3 90 2.5 3.9 5.0 Note: Angle = Skew angle offlow to pier L = Length of the pier Cylindrical piers have been widely investigated in the laboratory. The exponents in Eq. 13 were determined from laboratory data shown in Fig. 20 . In this figure, the Froude number on the abscissa is 3 multiplied by (a I y 1) spread the data.

30 10 .. ~ Symbol Source Sediment size dao""" A ChOllbtrl a O 52 - Ent;~ekhnger{9) • Choubert 8 0.26 I !- • Engtldiflf.Jer\9) - - -- - ;:::;::::: 0 csu 0.24 ~ 1 c· ~lt. ~ • ! .•. ...--tr!!. . t • -7--~ -·_ .. _ I l ---+-o~ :.d ~ ~~ .. - I It· -r-r-;- : I ~_.! e 2.0 (..!. F 0.4! r-- •+- ~· -- '\ ·...!!. ru I ! I ,, r, rl t ~~a:: ! : .... :"1f~ r-:-- ll .1 i I II I r--tlTr·l

Fig. 20. Results of laboratory experiments for scour at circular piers.

7.2.1.1 Jain and Fisher's Equation Jain and Fisher (1979) studied, in the laboratory, local pier scour at large Fronde numbers. They found that scour at a circular pier in sediment transport regime ( F r > F r c) initially decreases slightly, then increases as the Froude number increases. Furthermore, they found that the scour depth at high Froude numbers is larger than the maximum clear-water scour. The contribution of bed-form scour to the total scour depth in the upper flow regime becomes significant with higher flow velocities. Based on this research, they developed Eq. 14 and Eq.15: For live-bed scour ( F r - F r c) > 0.2;

Eq.14 For maximum clear-water scour;

Eq.15

These equations are functions of the critical Froude number F r c• The procedure for computing F r c is as follows: 1. Estimate the median diameter, D5o, for the bed material;

2. Determine ,; r: from Fig. 10; 3. Compute the shear velocity as; 0 5 U • r (-cciP ) · ;

4. Compute 6 = 11.6v/U •u where; v is the kinematic viscosity and can be assumed to be equal to 1.08 X to-5 rt2/s); 5. Compute k,/6 using D5o for k,; 6. Select Einstien's X from Fig. 21, using the computed value of k, I 6;

31 ?.Compute Ve=U.e(2.5ln(llylX/Dso)) and;

0 5 8. Compute Fr e = V el(gy 1 ) · It is recommended that the scour depth for 0< ( F r- F r e)< 0.2 can be assumed equal to the larger of the two values of scour obtained from Eqs. 14 and 15. For shapes different than circular piers, and pier alignment other than parallel with the flow direction, correct the results from Jain and Fishers equation by multiplying by the correction coefficients given in Tables 3 and 4.

1.8

1.6

1.4

1.2 X 1.0 .a

.4 .1

Fig. 21. Einstein's Factor X in the Logarithmic Velocity Equations (Einstein, 1950)

7.2.1.2 Graded and/or Armored Stream Bed Equations There are only limited field data for determining the decrease in scour depth as the result of coarse particles in the bed material of a stream. However there are good indications from laboratory and a few field studies, that larger size particles in the bed material can armor the scour hole and decrease scour depths. Although field data is limited, equations are given here for this case. Until additional field data is available they should be used with care and use of sound engineering judgement. The equations (adapted from equations developed by Washington State Department of Transportation (Copp and Johnson, 1987, and Copp, Johnson, and Mcintosh, 1988) for streams with a large range of particle sizes which would tend to armor the scour hole, are as follows: University of Aukland (UAK) Equations

For (a/ D 50 > 18);

Eq.16

For (a/ D 50 < 18);

Eq.17 Where;

32 a = Pier width y, = Scour depth

K 1 = Correction for pier shape (See Table 3)

K 2 = Correction for angle of attack of flow (See Table 4))

K 3 = Correction for gradation of sediments, determined from Fig. 22

0 5 K f1 is used to determine K 3 and is; K fl = (Ds4/ D 16) ' Copp and Johnson (1987) recommend that values obtained from the above equations be multiplied by a factor of safety k 1, due to the limited amount of actual field data. They state the following:

A purely heuristic approach is to select k 1, equal to 1 I K 3 whenever K f1 is less than about 2.0. If K 3 is greater than 20, select k 1, = 1.5. This nullifies scour depth reductions for material

gradations when K 3 < 2. 0 but allows for the full depth ofscour when K 3 > 2 0.

d50 (mm) d <0.7mm 50 0 0.55 • 0.85 l:l 1.90

d50 > 0.7 mm

o~------~------_.------~------~------1 2 3 4 5 6

Fig. 22. Particle Size Coefficient, K 3 , Vs. Geometric Deviation, K fl (Ettema, 1980).

7.2.1.3 Froehlich's Equation Live-bed Scour Using linear regression analysis of 83 field measurements of pier scour Froehlich (1988) developed the following equation:

y s ( a , ) o.62 ( Y 1 ) o.46 0 _20 ( a ) o.oa -=0.32K - - Fr - +1 a 1 a a Dso Eq.18

33 K 1 = Coefficient for pier type. Froehlich obtained K 1 = 1.3 for a square-nosed pier, 1.0 for round and round-nose piers, and 0.7 for sharp-nosed piers. This is in close agreement with values given for CSU's equation. a , = Pier width projected normal to the approach flow. a' - a cos a+ L sin a =Pier width projected normal to the approach flow. a is the angle of attack and; L is the length of the pier. The addition of 1.0 to Eq. 18 provides a factor of safety for design purposes. The regression analysis without this factor of safety computes the expected value of the scour depths. However, fifty percent of the scour holes could be deeper and fifty percent shallower. When the factor of safety is included in the computations, the computed value of pier scour is greater than all the measured values of scour. Clear-water scour Froehlich (1988) classified his data as to being either clear-water or live-bed scour data on the basis of Neill's (1968) equation given below: y )0.167 V c = l . 58 ( ( S s - 1 ) g D 50 ) o.s ( D : 0 Eq.19 S. = 2.65 and was assumed for all measurements.

V r: = Critical mean velocity

If v r: is larger than the mean velocity of the flow, then the scour would be clear water scour. In actuality, all the clear water scour depths in the data that Froehlich used were less than the magnitude computed using Eq. 19. Therefore, the live bed pier scour equation developed by Froehlich, can be used for clear-water scour also.

Literature Cited Ahmad, M., 1953, Experiments on Design and Behavior ofSpur Dikes, Proc. IAHR, ASCE Joint Meeting, Univ. of Minn., Aug. Brown, S. A, McQuivey, R. S., Keefer, T. N., 1981, Stream Channel Degradation and Aggradation Analysis of Impacts to Highway Crossings, Final Report FHWA/RD/-80/159, Federal Highway Admin., Washington, D.C. 20590, 202p. Chang, F. M., 1987, Personnel Communication Copp, H.D., Johnson, I.P., 1987, Riverbed Scour at Bridge Piers, Washington State Dept. of Trans. Rept. No. WA-RD 118.1,June. Copp, H. D., Johnson, I. P. and Mcintosh, 1988, Prediction Methods Local Scour at Intennediate Bridge Piers, Paper presented at the 68 Annual. TRB meeting, Washington D. C. Ettema, R., 1980, Scour at Bridge Piers, Report No. 216. Univ. of Auckland School of Engineering, Feb. FHWA, 1988, Interim Procedures for Evaluating Scour at Bridges, Office of Engineering , Bridge Div., U. S. Dept. of Trans., Washington, D. C., June. Einstein, H.A 1950, The Bed-Load Function for Sediment Transport in Open Channel Flows, Tech. Bull. No. 1026, Sept 1950, U.S. Dep. of Ag., Soil Cons. Service, Wash. D.C. FHWA, 1988, Interim Procedures for Evaluating Scour at Bridges, U.S. Dep. of Trans., Fed. Highway Admin., Technical Advisory, "Scour at Bridges", Washington, D.C.. FHWA, 1989, Scour at Bridges, Hydraulic Engineering Circular No. 18, Washington D.C.. Froehlich, D.C., 1989, Abutment Scour Prediction, Paper presented at the 68 TRB Annual meeting, Washington D. C.

34 Froehlich, D. C. 1988, Analysis of On-Site Measurements of Scour at Piers, Proc. ASCE National Hyd. Eng. Conf. Colorado Springs, Colo. Froehlich, D. C., 1987, Local Scour at Bridge Piers Based on Field Measurements, Personal Communication. Gill, M. A, 1972, Erosion of Sandbeds Around Spur Dikes, Jour. Hyd. Div., ASCE, Vol. 98, No. Hyd. 9, Sept., pp 1587-1602 Jain, S. C. and Fisher, R. E., 1979, Scour Around Bridge Piers at High Froude Numbers, Report no. FHWA-RD-79-104, Federal Highway Administration, Washington, DC, April. Jones, J. S., 1983, Comparison of Prediction Equations for Bridge Pier and Abutment Scour, TRB 950, Second Bridge Engineering Conf., Vol. 2 TRB, NRC, Washington, D.C. Laursen, E. M., 1960, Scour at Bridge Crossings, ASCE Hyd. Div. Jour., V 89, No. Hyd 3, May. Laursen, E. M., 1980, Predicting Scour at Bridge Piers and Abutments, Gen. Report No.3, Eng. Exp. Sta., College of Eng. Univ. of Arizona, Tu~on, AZ. Liu, H. K., Chang, F. M. and Skinner, M. M. 1961, Effect ofBridge Constriction on Scour and Backwater, Dept. of Civil Eng., Colo. State Univ., Report No. CER60-HKL22, Feb. Neill, C. R., 1968, Note on Abutment and Pier Scour in Coarse Bed Material, Jour. of Hyd. Res. Raudkivi, AJ., 1986, Functional Trends ofScour at Bridge Piers, ASCE Hyd. Div. Jour. v. 112 n. 1, Jan. Raudkivi, A J. and Ettema, R., 1977, Effect of Sediment Gradation on Clear-Water Scour, ASCE, V. 103, No. Hyd 10. Raudkivi, A J., and Sutherland, A J. 1981, Scour at Bridge Crossings, Bulletin 54, National Roads Board, Road Research Unit, New Zealand. Raudkivi, A J. and Ettema, R., 1983, Clear-water Scour at Cylindrical Piers, ASCE, V. 109 No. 6. Richardson, E. V., Ruff, J.F., and Brisbane, T.E. 1988a, Schoharie Creek Bridge Model Study, Proc. ASCE, Hyd. Div. Conf., Colorado Springs, CO, August. Richardson, E. V., Simons, D. B., Karaki, S., Mahmood, K., and Stevens, M.A, 1975, Highways in the River Environment, first ed, U. S. Dept. of Transportation, FHWA, Ft. Collins, Co. Richardson, E. V., Simons, D. B. and Julien, P. Y., 1988, Highways in the River Environment, second ed., U. S. Dept. of Transportation, FHWA, Ft. Collins, Co. Richardson, E. V., Lagasse, P. E., Schall, J.D., Ruff, J. F., Brisbane, T. E. and Frick, D. M., 1987, Hydraulic, Erosion and Channel Stability Analysis of the Schoharie Cr. Bridge Failure, New York. Resources Consultants, Inc. and Colorado State Univ., Ft. Collins, Co. Simons, D. B., and Richardson, E. V., 1963, Forms of Bed Roughness in Alluvial Channels, Trans. ASCE, Vol. 128. Santoro, V.C., 1989, Experimental Study on Scour and Velocity Field Around Bridge Piers, Masters Thesis, Department of Civil Engineering, Colorado State University, Ft. Collins CO. U.S. Inter-Agency Committee on Water Resources, Sub-Committee on Sedimentation, 1957, The development ofthe VISUal-Accumulation Tube, Report 11, of" A Study of Methods used in Measurement and Analysis of Sediment Loads in Streams, 28 p.