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Estimation of bridge pier scour for clear water & live bed scour condition

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  • 1. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME92ESTIMATION OF BRIDGE PIER SCOUR FOR CLEAR WATER &LIVE BED SCOUR CONDITION1Prof. P.T. NimbalkarProffesor, Deptt. Of Civil Engineering; Bharati Vidyapeeth Deemed University, College OfEngineering, Pune-(411043)2Mr.Vipin ChandraPost Graduate (M.Tech. Hydraulic Engineering) Student at Bharati Vidyapeeth DeemedUniversity, College Of Engineering, Pune-(411043)ABSTRACTScour is the Local Lowering of Stream Bed Elevation which takes place in theVicinity or around a Structure Constructed in Flowing water.Scour around Bridge Piers takesplace due to Modification of Flow Pattern in such a way as to cause Increase in Local ShearStress. For Bridges Estimation of Correct Depth of Scour Below Stream Bed is veryImportant since that determines the Depth of Foundation.Hydraulic Engineers haveDeveloped Equations to estimate scour depth with the help of Prototype and LaboratoryInvestigations. For this Study Commonly used Bridge Pier Scour Predictors are Testifiedagainst Published Laboratory data Obtained from Literature to ascertain which of thePredictors produce a reasonable estimate of Scour Depth. The Relative Accuracy of Variousmethods is determined by carrying out Statistical Tests, comparing measured & computedScour Depth graphically &by Computing Percentage Difference in Computed & measuredScour Depth .Keywords: Local Scour, Laboratory Data, Scour Predictors.1) INTRODUCTIONAlluvial Streams are Sometimes Partially obstructed by Hydraulic Structures such asSpurs, Bridge Piers, Abutments, Guide Banks etc. In some other cases High Velocity Sheetsof Water from Spillways & Sluice Gates Flow over loose Alluvial Material. In all these casesINTERNATIONAL JOURNAL OF CIVIL ENGINEERING ANDTECHNOLOGY (IJCIET)ISSN 0976 – 6308 (Print)ISSN 0976 – 6316(Online)Volume 4, Issue 3, May - June (2013), pp. 92-97© IAEME: www.iaeme.com/ijciet.aspJournal Impact Factor (2013): 5.3277 (Calculated by GISI)www.jifactor.comIJCIET© IAEME
  • 2. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME93the Bed Level in the Vicinity of the structures is Lowered as a result of Interaction betweenthe high Velocity Flow and the Loose Bed & Consequent Modification in the Flow Pattern,such Local Drop in the Bed Level is known as Local Scour.The Knowledge of the Maximum Depth of Scour around such Structures is essentialfrom the Point of View of Safety of these Structures; Excessive Scour can undermine theFoundations and lead to the Failure of the Structure. Proper design requires that theFoundation be taken down to a Level Lower than the Anticipated level of the Scour hole. Ithas been Reported that Since 1950 over 500 Bridges have Failed in U.S.A. & Majority ofFailures were Due to Scour of Foundation Material.Laursen(1963) has defined Scour as Enlargement of a Flow Section by Removal of MaterialComprising the Boundary through the Action of the Fluid in Motion. Such Scour takes placewhenever the rate at which the Sediment is Transported at a point is greater than the rate ofSediment Supply. Since, in General, the Rate of Sediment Transport Increases with Increasein Shear Stress for a given Sediment, Scour Results when the Changed Flow Conditionscause an increase in the Shear Stress on the Bed. Therefore, Analytical Prediction of LocalScour can be done by First Predicting the Distribution of Shear Stress on a Channel Bed dueto the Introduction of a Structure. As Scour Progress the Shear Stress will Reduce & Scourwill reach its Limit when, at any point, the Shear Stress is Critical or the amount of Sedimentcoming in equals the amount of Sediment going out.AIMS & OBJECTIVES1) To Study various Equations given by various Researchers used for Estimation ofBridge Pier Scour under Clear Water & Live Bed Scour conditions.2) To Check the Validity of these Equations using the Data available from Literature.3) To Test the Predictive ability of Selected equations by comparing Computed ScourDepth with Observed Scour Depth by using Three- Statistical Tests.DATA & METHODOLOGYThe Experimental Tables & data are Collected from Research Papers &Literaturespublished by Various Authors from their Studies (see references) which are as follows -:-- SCOUR DEPTH EQUATIONS CONSIDERED IN THE PRESENT STUDY--EQUATIONS FOR CLEAR WATER SCOUR & LIVE BED SCOUR BOTHa) Richardson’s(1977)ௗ௦௘஽ൌ 2.0 ‫ܭ‬ଷ ቀ௬బ஽ቁ଴.ଷହ‫ܨ‬଴.ସଷWhere K3accounts for Bed Forms ( It is 1.1 for plane Bed & Small Dunes, 1.1 to 1.2 forMedium Dunes. 1.3 for Large Dunes.)
  • 3. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME94b) Melville’s equation (1997)ௗ௦௘஽ൌ ‫ܭ‬ூ ‫ܭ‬ௗ ‫ܭ‬௬ௗWhere KI = V/Vc if V/Vc ≤ 1 and KI =1 Otherwise,Kd =0.57 log (2.24D/ D50) if D/ D50≤ 25 ,Kd= 1 Otherwise,KyD=2.4 if D/y0 ≤ 0.7 ,, KyD =2 ൈ ට௬బ஽Otherwise.c) Jain’s݀௦௘‫ܦ‬ൌ 1.84 ൬‫ܦ‬‫ݕ‬଴൰଴.ଷ଴ሺ‫ܨ‬௥௖ሻ଴.ଶହd) Hancu’s݀௦௘‫ܦ‬ൌ 3.3 ൬݀ହ଴‫ݕ‬଴൰଴.ଶ൬‫ܦ‬‫ݕ‬௢൰଴.ଵଷe) Coleman݀௦௘‫ܦ‬ൌ 1.49ሺሺܷሻଶ/݃‫ܦ‬ሻ଴.ଵ଴EQUATIONS FOR CLEAR WATER SCOUR ONLYa) Breusers et al. (1997)Presented an Equation that was a Function of V/Vc and y0/D Only.݀‫݁ݏ‬‫ܦ‬ൌ ‫ܭ‬௏ ‫݄݊ܽݐ‬ሺ‫ݕ‬‫ܦ‬ሻWhere Kv= 0 for V/Vc ≤ 0.5 ,Kv=2 (V/Vc)- 1 for V/Vc ≤ 1, Kv= 1 for V/Vc ≥ 1b) Ettema et al (2011)݀௦௘‫ܦ‬ൌ 2.5 ‫݄݊ܽݐ‬ ቆ൬‫ܦ‬‫ݕ‬଴൰଴.ସቇc) Laursen and Toch(1956)݀௦௘‫ܦ‬ൌ 1.5 ൬‫ܦ‬‫ݕ‬଴൰଴.ଷ଴
  • 4. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME95ANALYSIS OF RESULTS & DISCUSSIONS1. Statistical parameters for validation of different equationsThree Statistical Tests were carried out to find the Equation which gives theminimum error in the computation of Scour Depth. These parameters include Theil’sCoefficient (U), Mean Absolute Error (MAE) and Root Mean Sqaure Error (RMSE)which are mathematicallydescribed by following equations;U=ቂభ೙∑ ሼሺௗೞሻ೎ିሺௗೞሻ೚ሽమ೙೔సభ ቃభమቂభ೙∑ ሺௗೞሻ೎మ೙೔సభ ቃభమାቂభ೙∑ ሺௗೞሻ೚మ೙೔సభ ቃMAE =∑ |௘೔|೙೔సభ௡RMSE =ට∑ ௘೔మ೙೔సబ௡If U=0; for model of Perfect Prediction and U=1 for Unsuccessful ModelsThe values of Theil’s Coefficient (U),MeanAboslute Error (MAE) & Root Mean SqaureError (RMSE) Calculated by different equations for different author’s data are Summarizedin Table No. (a) & (b).a) FOR CLEAR WATER CONDITIONFollowing Table is made by Collecting data from the Research Papers of variousAuthors mentioned as following -:Table 1-:Data obtained from D.Max Sheppard et al., 2004,Table 2-:Data obtained from Jihn- Sung Lai1et al., 2009,Table 3,4& 5-:Data Obtained from D.S. Jeng et al., 2006.ScourDepthPredictorsTheil’s Coefficient;(U) Mean Absolute Error (M.A.E.) Root Mean Square Error (R.M.S.E.)ForTable(1)ForTable(2)ForTable(3)ForTable(4)ForTable(5)ForTable(1)ForTable(2)ForTable(3)ForTable(4)ForTable( 5)ForTable(1)ForTable(2)ForTable(3)ForTable(4)ForTable(5)Richardson 0.099 0.247 0.129 0.126 0.169 0.205 0.395 0.392 0.350 0.475 0.256 0.336 0.455 0.486 0.537Melville 0.281 0.316 0.365 0.086 0.237 0.779 0.866 1.03 0.267 0.535 0.910 0.918 1.566 0.337 0.644Breusers etal.0.276 0.504 0.374 0.292 0.685 0.495 0.500 0.755 0.765 1.119 0.573 0.254 0.955 0.855 1.27Ettema etal.0.300 0.350 0.207 0.190 0.251 0.960 1.040 0.791 0.668 0.790 1.023 1.25 0.839 0.683 0.931Laursen&Touch0.259 0.342 0.146 0.303 0.290 0.509 0.794 0.516 0.891 0.726 0.699 0.798 0.553 1.30 0.955Jain 0.296 0.348 0.317 0.315 0.299 0.573 0.784 0.794 0.921 0.740 0.749 0.783 1.09 1.178 1.01Hancu 0.284 0.466 0.280 0.260 0.242 0.543 1.533 0.699 0.736 0.578 0.630 2.915 0.914 0.923 0.792Coleman 0.136 0.332 0.179 0.193 0.198 0.246 0.423 0.444 0.518 0.477 0.316 0.347 0.575 0.658 0.568
  • 5. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME96b) FOR LIVE BED SCOUR CONDITIONFollowing Table is made by Collecting Data from the Research Papers of variousAuthors mentioned as FollowingTable 6-Data Obtained from D.S. Jeng et al., 2006.Scour DepthEquationTheil’sCoefficient(U)MeanAboluteError (MAE)Root MeanSquare Error(RMSE)For Table (6) For Table (6) For Table (6)Richardson 0.204 0.6470.755Melville 0.223 1.394 1.420Jain 0.406 1.570 3.674Hancu 0.4791.238 2.048Coleman 0.2720.779 0.756For Both the Tables i.e. a & b; The Minimum Values (Best Prediction) of StatisticalParameters; U, MAE and RMSE are mentioned in BOLD UNDERLINED for differentequations,indicate more appropriate results for Scour Depth calculations. As per thecalculations of the Statistical Parameters, in case of Live Bed scour & Clear Water Scourconditions reveals that in general, Richardson Method produce more reasonable estimate ofScour Depth as compared to other methods given by various Authors.CONCLUSIONFollowing Conclusions are derived from Three Statistical Parameters i.e. Theil’sCoefficient (U), Mean Absolute Error (M.A.E.) & Root Mean Square Error (RMSE).Eight Commonly used equations namely by Richardson, Melville, Breusers et al.,Ettema et al., Laursen& Touch, Jain, Hancu, & Coleman for estimation of Scour Depth inClear Water conditions were selected & validated using Experimental Data of variousAuthors. The study shows that The Richardson Formula gives a reasonable estimate ofLocal Scour depth.In case of Live Bed Scour conditions; Five Commonly used equations namely byRichardson, Melville, , Jain, Hancu, & Coleman for estimation of Scour Depth were selected& validated using Experimental Data of various authors. The study shows that TheRichardson Formula only gives the reasonable estimate of Local Scour Depth.
  • 6. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME97NotationsD= Pier diameterdse= Equilibrium Scour depthdse/D = Dimensionless Equilibrium Scour depth.ሺ݀௦ሻ௢ = Scour Depth Obtained from Field Observations.ሺ݀௦ሻ௖ = Scour Depth Predicted from the Application of the Selected Scour Equation.d50= Sediment Size for Which 50% of the Sediment is Finer.Kd = Sediment Size Factor.Kyd= Flow Depth Adjustment FactorKI= V/VcK3= Bed form Adjustment Factor.F = Froude Number of Incoming Flow Velocity.Frc = Froude Number of Critical Velocity.g= Gravitational force.V= Approaching Flow Velocity.Vc = Critical approaching flow velocity.U= Theil’s Coefficient.MAE = Mean Absolute Error.RMSE = Root Mean Square Error.REFERENCES1)B.W.Melville & A.J Sutherland (J. Of Hydraulic Engg. 1988.114:1210-1226) “ DesignMethod For Local Scour At Bridge Piers”.2)D.Max Sheppard,M.ASCE1,MufeedOdeh M.ASCE2& Tom Glasser(J. Of HydraulicEngg.October,2004.130:957-963; ASCE/OCTOBER 2004/959) “ Large Scale Clear–Water LocalPier Scour Experiments”.3)D.S. Jeng; S.M. Bateni; E. Lockett (2006; The University Of Sydney,Deptt. Of CivilEngineering,Enviornmental Fluids/Winds Group) “Neural Network Assessment For Scour DepthAround Bridge Piers- Research Report No. R855”.4)Jau-Yau Lu, M.ASCE1; Zhong-Zhi Shi2;Jian-Hao Hong3;Jun-Ji Lee; Ph.D.4; &Rajkumar V.Raikar (Journal Of Hydraulic Engineering 2011.137:45-56; ASCE/JANUARY 2011 ) “TemporalVariation Of Scour Depth at Non-Uniform Cylindrical Piers.5)Jihn- Sung Lai1; Wen-Yi Chang2; & Chin Lien Yen, , F.ASCE3(Journal Of HydraulicEngg.2009.135:609-614; ASCE/JULY 2009) “ Maximum Local Scour Depth at Bridge PiersUnder Unsteady Flow”.6) R.J. Garde; K.G. RangaRaju (2000, New Age Publications); Mechanics Of SedimentTransportation & Alluvial Stream Problems”.7)Seung Oh Lee1& Terry W. Sturm, M.ASCE2(Journal Of Hydraulic Engg.2009.135:793-802) “Effect Of Sediment Size Scaling On Physical Modelling Of Bridge Pier Scour ”.8)Subhasish Dey1,Sujit K. Bose2,&Ghandikota L.N. Sastry3.(J. Of Hydraulic Engg.1995.121.869-876) “Clear Water Scour at Circular Piers: A Model”.9)Thamer Ahmed Mohamed; MegatJohari M.M. Noor; Abdul HalimGhazali&Bujang B.K. Huat(Am. J. Environ. Sci 1 (2):119-125,2005) “Validation Of Some Bridge Pier Scour FormulaeUsing Field & Laboratory Data”.10)Wen- Yi Chang1; Jihn – Sung Lai2;& Chin Lien Yen, F.ASCE3(Journal Of Hydraulic Engg.2004.130:905-913; ASCE/SEPTEMBER 2004) “ Evolution Of Scour Depth at Circular BridgePiers ”.