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PIER AND CONTRACTION SCOUR IN COHESIVE SOILS SUMMARY SCOUR TYPES Bridge scour is the loss of soil by erosion due to water flowing around bridge supports. Bridge scour includes general scour and local scour. General scour is the aggradation or degradation of the riverbed not related to the presence of local obstacles. Aggradation is the gradual and general accumulation of sediments on the river bottom. Degradation is the gradual and general removal of sediments from the riverbed. Local scour is the scour around obstacles to the water flow. Local scour includes pier scour, abutment scour, and contraction scour. Pier scour is the removal of the soil around the foundation of a pier; abutment scour is the removal of soil around an abutment at the junction between a bridge and embankment; and contraction scour is the removal of soil from the bottom of the river due to a narrowing of the river channel created by the approach embankments for a bridge. SOILS: A DEFINITION Soils can be defined as loosely bound to unbound, naturally occurring materials that cover the top few hundred meters of the Earth. By opposition, rock is a strongly bound, naturally occurring material found within similar depths or deeper. Intermediate geo- materials occur at the boundary between soils and rocks. For soils, the classification tests consist of grain size analysis and Atterberg Limits. The D50 grain size is the grain size corresponding to 50% of the soil weight passing a sieve with an opening equal to D50. The first major division in soils classification is between large-grained soils and fine-grained soils. Large-grained soils have D50 larger than 0.075 mm; fine-grained soils have D50 smaller than 0.075 mm. Large-grained soils include gravels and sands that are identified on the basis of their grain size. Fine-grained soils include silts and clays that are identified on the basis of Atterberg Limits. Gravels and sands are typically referred to as cohesionless soils; silts and clays are typically referred to as cohesive soils. THE PROBLEM ADDRESSED This project deals with pier scour and contraction scour in cohesive soils. A previous project performed by the same team of researchers began in 1990 and was sponsored by

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2 the Texas Department of Transportation (TxDOT). This previous project dealt with pier scour in cohesive soils. In the TxDOT project, the piers were cylindrical and the water depth was more than two times the pier diameter (deepwater case). In the TxDOT project, a new tool called the Erosion Function Apparatus (EFA) was conceived, built, patented, and commercialized to measure the erodibility of soils. The EFA test, which gives the erosion function for a soil, became an integral part of the Scour Rate In COhe- sive Soils (SRICOS) Method. The SRICOS-EFA Method developed at the end of the TxDOT project predicted the scour depth as a function of time when a cylindrical pier founded in a layered soil was subjected to a long-term deepwater flow-velocity hydro- graph. In this NCHRP project, the SRICOS-EFA Method was extended to the case of complex piers and contraction scour. Complex piers are piers with various shapes, flow attack angles, spacing between piers, and existing in any water depth. Contraction refers to a narrowing of the flow channel by an embankment with a given encroachment length, embankment width, and transition angle. WHY WAS THIS PROBLEM ADDRESSED? The reason for solving this problem was that, in the absence of a solution, calcula- tions have been based on the solution developed for cohesionless soils. Within the bridge engineering community, there were concerns that such an approach was sometimes very conservative and, therefore, costly. Indeed, overly conservative scour depths lead to foundations that are considered deeper than necessary. The major difference between cohesionless soils and cohesive soils is the following. Floods create peak velocities that last a few days. A few days is a length of time that is usually sufficient to generate the maximum scour depth in cohesionless soils. This means that only the peak velocity needs to be used in the calculations of scour depth for cohesionless soils and that such a scour depth is the maximum scour depth for that velocity. The velocities used are typ- ically the 100-year flood velocity and the 500-year flood velocity. In cohesive soils, scour and erosion rates can be 1,000 times slower than in cohesionless soils and a few days may generate only a small fraction of the maximum scour depth. Therefore, for cohesive soils, it becomes necessary to consider the rate of erosion and to accumulate the effect of multiple floods. This complicates the problem significantly, but is neces- sary in order to get an accurate prediction. APPROACH SELECTED TO SOLVE THE PROBLEM The approach selected to solve the problem of predicting the scour depth versus time for complex piers in a contracted channel and for a given velocity hydrograph was based on a combination of a review of existing knowledge, flume tests, numeri- cal simulations, fundamental principles in method development, and verification of the method against available data. The review of existing knowledge avoided dupli- cation of effort and helped to establish a solid foundation. The flume tests gave the equations for the maximum scour depth and the influence of various factors. The flume tests also gave a calibration basis for the numerical simulations. These numerical sim- ulations were used to generate the equations for the maximum initial shear stress at the initiation of scour. The method was assembled by linking the calculated initial ero- sion rate (given by the numerical simulation results and the results of the EFA test) to the calculated maximum scour depth (given by the flume test results) through the use of a hyperbolic model. The multiflood hydrograph and multilayer soil were included through simple accumulation algorithms. Verification was based on comparison with

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3 existing databases as well as performing calculations for example cases and evaluat- ing the reasonableness of the results based on experience. ERODIBILITY OF COHESIVE SOILS Erodibility is not an index but a relationship or function between water velocity (or, better, the shear stress at the water-soil interface) and the erosion rate of the soil. Erodi- bility is represented by this erosion function. Two important parameters help describe the erosion function: the critical shear stress and the initial slope of the erosion function. Although the critical shear stress of a cohesive soil is not related to its mean grain size, the common range of critical shear stress values for cohesive soils (0.5 N/m2 to 5 N/m2) is comparable to the range obtained in sands. This explains why the maximum scour depth in cohesive soils is comparable to the one obtained in sands. The initial slope of the erosion function can be many times less than the one in sand (e.g., 1,000 times less) and, therefore, the scour depth can develop very slowly in some cohesive soils. Thus, it would be advantageous to develop a method that can predict scour depth as a function of time for a given hydrograph (cohesive soil) rather than a maximum depth of scour for a design flood (sands). This was the goal of this project. It also was found that the critical shear stress and the initial slope were not related to soil properties because the R2 of the regres- sions were all very low. Therefore, it is recommended that Erosion Function Apparatus (EFA) be used to determine the erosion function. EROSION FUNCTION APPARATUS (EFA) The EFA was developed in the early 1990s to obtain the erosion function. A soil sample is retrieved from the bridge site using an ASTM-standard thin-walled steel tube (Shelby tube), placing it through a tight-fitting opening in the bottom of a rectangular cross-section conduit, pushing a small protrusion of soil into the conduit, sending flow- ing water over the top of the sample at a chosen velocity, and recording the corre- sponding erosion rate. This is repeated for several velocities and the erosion function is obtained in this fashion. SRICOS-EFA METHOD FOR CYLINDRICAL PIERS IN DEEP WATER SRICOS stands for Scour Rate In COhesive Soils. Since the method makes use of the erosion function measured in the EFA, the method is referred to as the SRICOS- EFA Method. For a given velocity hydrograph at a bridge, a given soil exhibiting a multilayered stratigraphy with an erosion function defined for each layer, and a given cylindrical pier in deep water (water depth larger than 1.6 times the pier diameter), the SRICOS-EFA Method (program) gives the scour depth as a function of time for the period covered by the hydrograph. The method is based on the calculation of two basic parameters: the maximum depth of pier scour and the initial rate of scour. The maximum depth of scour is based on an equation obtained from flume tests and the initial rate is based on an equation giving the initial shear stress obtained from numerical simulations. The initial rate of scour is read on the EFA erosion function at the corresponding value of the calculated initial shear stress. A hyperbola is used to connect the initial scour rate to the maximum or asymptotic scour depth and describes the complete scour-depthversustime curve. Robust algorithms are used to incorporate the effect of varying velocities and multi- layered soil systems. This earlier method was developed by the authors under TxDOT

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4 sponsorship and was verified by satisfactory comparison between predicted scour and measured scour at eight bridges in Texas. SRICOS-EFA METHOD FOR MAXIMUM SCOUR DEPTH AT COMPLEX PIERS A set of flume experiments was conducted to study the maximum depth of scour for a pier, including the effects of shallow water depth, rectangular shapes, angle of attack on rectangular shapes, and spacing between piers positioned in a row perpendicular to the flow. The proposed equation for the maximum depth of scour is in the form of the equation for the cylindrical pier in deep water with correction factors based on the results of the flume tests: Zmax ( Pier ) in mm = K w K sp K sh (0.18 Re0.635 ) where Zmax(Pier) is the maximum depth of pier scour in millimeters; Re is the Reynolds number equal to VB/v; V is the mean depth velocity at the location of the pier if the bridge were not there; v is the water viscosity; the K factors take the shallow water depth, spacing, and shape into account; and the angle of attack being considered through the use of the projected width B in the calculation of the Reynolds Number. SRICOS-EFA METHOD FOR INITIAL SCOUR RATE AT COMPLEX PIERS A set of numerical simulations was performed to study the maximum shear stress around a pier, including the effects of shallow water depth, rectangular shapes, angle of attack on rectangular shapes, and spacing between piers positioned in a row per- pendicular to the flow. The proposed equation for the maximum shear stress is in the form of the equation for the cylindrical pier in deep water with correction factors based on the results of the numerical simulations. max ( Pier ) = kw ksh ksp ka 0.094V 2 - 1 1 log Re 10 where max(Pier) is the maximum shear stress around the pier; Re is the Reynolds Num- ber equal to VB/v; V is the mean depth velocity at the location of the pier if the bridge were not there; v is the water viscosity; B is the pier diameter or pier width; and the k fac- tors take shallow water depth, pier shape, pier spacing, and attack angle into account. SRICOS-EFA METHOD FOR MAXIMUM CONTRACTION SCOUR DEPTH A set of flume experiments was conducted to study the depth of scour associated with the contraction of a channel, including the effects of the ratio of the contracted chan- nel width over the approach channel width, contracted channel length, and transition angle. The proposed equation for the maximum depth of contraction scour is c 0.5 1.49Vhec Zmax (Cont ) = K K L 1.90 H1 - 13 0 gH1 gnH1 where Zmax(Cont) is the maximum depth of contraction scour; H1 is the water depth along the center line of the uncontracted channel after scour has occurred; Vhec is the mean depth water velocity at the location of the pier in the contracted channel; c is the

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5 critical shear stress of the soil; is the mass density of water; g is the acceleration due to gravity; n is the Manning's Coefficient; and the K factors take the transition and contracted channel length into account. Note that the parentheses in the equation is a factored difference between the Froude Number and the critical Froude Number. Equations are also proposed for the uniform contraction scour depth as well as the location of the scour depths. SRICOS-EFA METHOD FOR INITIAL CONTRACTION SCOUR RATE A set of numerical simulations were performed to study the maximum shear stress around the contraction of a channel, including the effects of the ratio of the contracted channel width over the approach channel width, transition angle, water depth, and con- tracted channel length. The proposed equation for the maximum shear stress is in the form of the equation for the shear stress at the bottom of an open and uncontracted channel with correction factors based on the results of the numerical simulations. ( - max (Cont ) = kc - R kc - kc - H kc - L n 2 V 2 Rh 3 1 ) where max(Cont) is the maximum shear stress along the centerline of the contracted channel; is the unit weight of water; n is the Manning's Coefficient; V is the upstream mean depth velocity; Rh is the hydraulic radius defined as the cross section area of the flow divided by the wetted perimeter; and the k factors take the contraction ratio, tran- sition angle, water depth effect, and contracted length into account. Equations are also proposed for the location of the maximum shear stress. SRICOS-EFA METHOD FOR COMPLEX PIER SCOUR AND CONTRACTION SCOUR IN COHESIVE SOILS Once the equations were established, the SRICOS-EFA Method was assembled. Care was taken not to simply add complex pier scour and contraction scour to get total pier scour. Instead, advantage was taken of the fact that at the end of the maximum con- traction scour, the velocity is at the critical velocity and the maximum pier scour should be calculated using the critical velocity of the soil and not the initial velocity in the con- tracted channel. In addition, the rules of accumulation due to the hydrograph and the multilayer system developed for the simple pier scour method were adapted for the complex pier and contraction scour method. The superposition and accumulation rea- soning led to the following steps that enabled the SRICOS-EFA Method to predict the scour depth at a complex pier in a contracted channel. This step-by-step procedure has been automated in a computer program. 1. Collect the input data: velocity and water depth hydrograph, geometry of the pier and of the contracted channel, erosion functions of the soil layers; 2. Calculate the maximum contraction scour depth for the ith velocity in the hydro- graph; 3. Calculate the maximum complex pier scour depth using the ith velocity in the hydrograph at the pier location if there is no contraction scour in Step 2, or the critical velocity for the soil if there is contraction scour in Step 2; 4. Calculate the total pier scour depth as the total of Steps 2 and 3; 5. Calculate the initial maximum shear stress for pier scour using the ith velocity in the hydrograph;

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6 6. Read the initial scour rate corresponding to the initial maximum shear stress of Step 5 on the erosion function of the soil layer corresponding to the current scour depth; 7. Use the results of Steps 4 and 6 to construct the hyperbola describing the scour depth versus time curve for the pier; 8. Calculate the equivalent time for the given curve of Step 7. The equivalent time is the time required for the ith velocity on the hydrograph to scour the soil to a depth equal to the depth scoured by all of the velocities occurring prior to the ith velocity; 9. Read the additional scour generated by the ith velocity starting at the equivalent time and ending at the equivalent time plus the time increment; and 10. Repeat Steps 2 to 9 for the (i+1)th velocity and so on until the entire hydrograph is consumed. VERIFICATION OF THE SRICOS-EFA METHOD Several full case histories were identified for verification, but none could satisfy the requirements necessary to verify the method developed. Some did not have enough details on the observed scour depth, some turned out not to be made of cohesive soil after drilling, some did not have a gage station nearby. The study team decided to com- pare the maximum scour depth for pier and contraction to existing databases. These databases were mostly in sand, however, and included those collected by Mueller (pier scour), Froehlich (pier scour), and Gill (contraction scour). The comparisons between the predicted and measured scour depths are very satisfactory, although it is not clear whether they should be given that the soils were not primarily cohesive. Nevertheless, these comparisons give an indication that the SRICOS-EFA Method may not be limited to cohesive soils. Indeed, the fact that the method is based on site-specific testing of the erosion function permits incorporating the soil behavior directly into the predictions. FUTURE HYDROGRAPHS AND SCOUR RISK ANALYSIS A novel technique is presented on generating future hydrographs. Indeed, since the SRICOS-EFA Method predicts the scour depth as a function of time, it is necessary to input the hydrograph over the design life of the bridge into the program. The proposed technique consists of using a past hydrograph (from a gage station, for example), preparing the frequency distribution plot for the floods within that hydrograph, sam- pling the distribution randomly, and preparing a future hydrograph. This future hydro- graph is for the required period and has the same mean and standard deviation as the measured hydrograph. This process is repeated 10,000 times and, for each hydrograph, a final scour depth (the depth reached at the end of the design life of the bridge) is gen- erated. These 10,000 final depths of scour are organized in a frequency distribution plot with a mean and standard deviation. That plot can be used to quote a scour depth with a corresponding probability of occurrence, or better, to choose a risk level and quote the corresponding final depth of scour. EXAMPLE PROBLEMS A set of example problems is presented to help the reader become more familiar with the SRICOS-EFA Method. Some examples are performed using hand calculations; some use the computer program.

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7 RECOMMENDATIONS It is recommended that 1. The proposed method be incorporated in the next version of HEC-18; 2. The SRICOS-EFA Method program be transferred to a WindowsTM environment; 3. The project be continued to solve abutment scour, the last major unsolved scour problem in cohesive soils; and 4. A set of short courses be offered across the country to teach the new SRICOS- EFA Method.