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

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

  1. 1. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME 92 ESTIMATION OF BRIDGE PIER SCOUR FOR CLEAR WATER & LIVE BED SCOUR CONDITION 1 Prof. P.T. Nimbalkar Proffesor, Deptt. Of Civil Engineering; Bharati Vidyapeeth Deemed University, College Of Engineering, Pune-(411043) 2 Mr.Vipin Chandra Post Graduate (M.Tech. Hydraulic Engineering) Student at Bharati Vidyapeeth Deemed University, College Of Engineering, Pune-(411043) ABSTRACT Scour is the Local Lowering of Stream Bed Elevation which takes place in the Vicinity or around a Structure Constructed in Flowing water.Scour around Bridge Piers takes place due to Modification of Flow Pattern in such a way as to cause Increase in Local Shear Stress. For Bridges Estimation of Correct Depth of Scour Below Stream Bed is very Important since that determines the Depth of Foundation.Hydraulic Engineers have Developed Equations to estimate scour depth with the help of Prototype and Laboratory Investigations. For this Study Commonly used Bridge Pier Scour Predictors are Testified against Published Laboratory data Obtained from Literature to ascertain which of the Predictors produce a reasonable estimate of Scour Depth. The Relative Accuracy of Various methods is determined by carrying out Statistical Tests, comparing measured & computed Scour Depth graphically &by Computing Percentage Difference in Computed & measured Scour Depth . Keywords: Local Scour, Laboratory Data, Scour Predictors. 1) INTRODUCTION Alluvial Streams are Sometimes Partially obstructed by Hydraulic Structures such as Spurs, Bridge Piers, Abutments, Guide Banks etc. In some other cases High Velocity Sheets of Water from Spillways & Sluice Gates Flow over loose Alluvial Material. In all these cases INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND TECHNOLOGY (IJCIET) ISSN 0976 – 6308 (Print) ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), pp. 92-97 © IAEME: www.iaeme.com/ijciet.asp Journal Impact Factor (2013): 5.3277 (Calculated by GISI) www.jifactor.com IJCIET © IAEME
  2. 2. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME 93 the Bed Level in the Vicinity of the structures is Lowered as a result of Interaction between the 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 essential from the Point of View of Safety of these Structures; Excessive Scour can undermine the Foundations and lead to the Failure of the Structure. Proper design requires that the Foundation be taken down to a Level Lower than the Anticipated level of the Scour hole. It has been Reported that Since 1950 over 500 Bridges have Failed in U.S.A. & Majority of Failures were Due to Scour of Foundation Material. Laursen(1963) has defined Scour as Enlargement of a Flow Section by Removal of Material Comprising the Boundary through the Action of the Fluid in Motion. Such Scour takes place whenever the rate at which the Sediment is Transported at a point is greater than the rate of Sediment Supply. Since, in General, the Rate of Sediment Transport Increases with Increase in Shear Stress for a given Sediment, Scour Results when the Changed Flow Conditions cause an increase in the Shear Stress on the Bed. Therefore, Analytical Prediction of Local Scour can be done by First Predicting the Distribution of Shear Stress on a Channel Bed due to the Introduction of a Structure. As Scour Progress the Shear Stress will Reduce & Scour will reach its Limit when, at any point, the Shear Stress is Critical or the amount of Sediment coming in equals the amount of Sediment going out. AIMS & OBJECTIVES 1) To Study various Equations given by various Researchers used for Estimation of Bridge 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 Scour Depth with Observed Scour Depth by using Three- Statistical Tests. DATA & METHODOLOGY The Experimental Tables & data are Collected from Research Papers &Literatures published 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 BOTH a) Richardson’s(1977) ௗ௦௘ ஽ ൌ 2.0 ‫ܭ‬ଷ ቀ ௬బ ஽ ቁ ଴.ଷହ ‫ܨ‬଴.ସଷ Where K3accounts for Bed Forms ( It is 1.1 for plane Bed & Small Dunes, 1.1 to 1.2 for Medium Dunes. 1.3 for Large Dunes.)
  3. 3. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME 94 b) Melville’s equation (1997) ௗ௦௘ ஽ ൌ ‫ܭ‬ூ ‫ܭ‬ௗ ‫ܭ‬௬ௗ Where 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 ൈ ට ௬బ ஽ Otherwise. c) Jain’s ݀௦௘ ‫ܦ‬ ൌ 1.84 ൬ ‫ܦ‬ ‫ݕ‬଴ ൰ ଴.ଷ଴ ሺ‫ܨ‬௥௖ሻ଴.ଶହ d) Hancu’s ݀௦௘ ‫ܦ‬ ൌ 3.3 ൬ ݀ହ଴ ‫ݕ‬଴ ൰ ଴.ଶ ൬ ‫ܦ‬ ‫ݕ‬௢ ൰ ଴.ଵଷ e) Coleman ݀௦௘ ‫ܦ‬ ൌ 1.49ሺሺܷሻଶ /݃‫ܦ‬ሻ଴.ଵ଴ EQUATIONS FOR CLEAR WATER SCOUR ONLY a) Breusers et al. (1997) Presented an Equation that was a Function of V/Vc and y0/D Only. ݀‫݁ݏ‬ ‫ܦ‬ ൌ ‫ܭ‬௏ ‫݄݊ܽݐ‬ሺ ‫ݕ‬ ‫ܦ‬ ሻ Where Kv= 0 for V/Vc ≤ 0.5 ,Kv=2 (V/Vc)- 1 for V/Vc ≤ 1, Kv= 1 for V/Vc ≥ 1 b) Ettema et al (2011) ݀௦௘ ‫ܦ‬ ൌ 2.5 ‫݄݊ܽݐ‬ ቆ൬ ‫ܦ‬ ‫ݕ‬଴ ൰ ଴.ସ ቇ c) Laursen and Toch(1956) ݀௦௘ ‫ܦ‬ ൌ 1.5 ൬ ‫ܦ‬ ‫ݕ‬଴ ൰ ଴.ଷ଴
  4. 4. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME 95 ANALYSIS OF RESULTS & DISCUSSIONS 1. Statistical parameters for validation of different equations Three Statistical Tests were carried out to find the Equation which gives the minimum error in the computation of Scour Depth. These parameters include Theil’s Coefficient (U), Mean Absolute Error (MAE) and Root Mean Sqaure Error (RMSE) which are mathematicallydescribed by following equations; U= ቂ భ ೙ ∑ ሼሺௗೞሻ೎ିሺௗೞሻ೚ሽమ೙ ೔సభ ቃ భ మ ቂ భ ೙ ∑ ሺௗೞሻ೎ మ೙ ೔సభ ቃ భ మ ାቂ భ ೙ ∑ ሺௗೞሻ೚ మ೙ ೔సభ ቃ MAE = ∑ |௘೔|೙ ೔సభ ௡ RMSE =ට ∑ ௘೔ మ೙ ೔సబ ௡ If U=0; for model of Perfect Prediction and U=1 for Unsuccessful Models The values of Theil’s Coefficient (U),MeanAboslute Error (MAE) & Root Mean Sqaure Error (RMSE) Calculated by different equations for different author’s data are Summarized in Table No. (a) & (b). a) FOR CLEAR WATER CONDITION Following Table is made by Collecting data from the Research Papers of various Authors mentioned as following -: Table 1-:Data obtained from D.Max Sheppard et al., 2004, Table 2-:Data obtained from Jihn- Sung Lai1 et al., 2009, Table 3,4& 5-:Data Obtained from D.S. Jeng et al., 2006. Scour Depth Predictors Theil’s Coefficient;(U) Mean Absolute Error (M.A.E.) Root Mean Square Error (R.M.S.E.) For Table (1) For Table (2) For Table (3) For Table (4) For Table (5) For Table (1) For Table (2) For Table (3) For Table (4) For Table ( 5) For Table (1) For Table (2) For Table (3) For Table (4) For Table (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 0.537 Melville 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 0.644 Breusers et al. 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 1.27 Ettema et al. 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 0.931 Laursen& Touch 0.259 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 0.955 Jain 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 1.01 Hancu 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 0.792 Coleman 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. 5. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME 96 b) FOR LIVE BED SCOUR CONDITION Following Table is made by Collecting Data from the Research Papers of various Authors mentioned as Following Table 6-Data Obtained from D.S. Jeng et al., 2006. Scour Depth Equation Theil’s Coefficient (U) Mean Abolute Error (MAE) Root Mean Square Error (RMSE) For Table (6) For Table (6) For Table (6) Richardson 0.204 0.647 0.755 Melville 0.223 1.394 1.420 Jain 0.406 1.570 3.674 Hancu 0.479 1.238 2.048 Coleman 0.272 0.779 0.756 For Both the Tables i.e. a & b; The Minimum Values (Best Prediction) of Statistical Parameters; U, MAE and RMSE are mentioned in BOLD UNDERLINED for different equations,indicate more appropriate results for Scour Depth calculations. As per the calculations of the Statistical Parameters, in case of Live Bed scour & Clear Water Scour conditions reveals that in general, Richardson Method produce more reasonable estimate of Scour Depth as compared to other methods given by various Authors. CONCLUSION Following Conclusions are derived from Three Statistical Parameters i.e. Theil’s Coefficient (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 in Clear Water conditions were selected & validated using Experimental Data of various Authors. The study shows that The Richardson Formula gives a reasonable estimate of Local Scour depth. In case of Live Bed Scour conditions; Five Commonly used equations namely by Richardson, Melville, , Jain, Hancu, & Coleman for estimation of Scour Depth were selected & validated using Experimental Data of various authors. The study shows that The Richardson Formula only gives the reasonable estimate of Local Scour Depth.
  6. 6. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME 97 Notations D= Pier diameter dse= Equilibrium Scour depth dse/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 Factor KI= V/Vc K3= 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. REFERENCES 1)B.W.Melville & A.J Sutherland (J. Of Hydraulic Engg. 1988.114:1210-1226) “ Design Method For Local Scour At Bridge Piers”. 2)D.Max Sheppard,M.ASCE1 ,MufeedOdeh M.ASCE2 & Tom Glasser(J. Of Hydraulic Engg.October,2004.130:957-963; ASCE/OCTOBER 2004/959) “ Large Scale Clear–Water Local Pier Scour Experiments”. 3)D.S. Jeng; S.M. Bateni; E. Lockett (2006; The University Of Sydney,Deptt. Of Civil Engineering,Enviornmental Fluids/Winds Group) “Neural Network Assessment For Scour Depth Around 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 ) “Temporal Variation Of Scour Depth at Non-Uniform Cylindrical Piers. 5)Jihn- Sung Lai1 ; Wen-Yi Chang2 ; & Chin Lien Yen, , F.ASCE3 (Journal Of Hydraulic Engg.2009.135:609-614; ASCE/JULY 2009) “ Maximum Local Scour Depth at Bridge Piers Under Unsteady Flow”. 6) R.J. Garde; K.G. RangaRaju (2000, New Age Publications); Mechanics Of Sediment Transportation & 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 Formulae Using 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 Bridge Piers ”.

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