SCOUR HOLE CHARACTERISTICS AROUND A VERTICAL PIER UNDER CLEARWATER SCOUR CONDITIONS

Transcription

1 ARPN Journal of Engineering and Applied Siene Aian Reearh Publihing Network (ARPN). All right reerved. SCOUR HOLE CHARACTERISTICS AROUND A VERTICAL PIER UNDER CLEARWATER SCOUR CONDITIONS Padmini Khwairakpam, Soumendu Sinha Ray, Subhaih Da, Rajib Da and Ai Mazumdar Shool of Water Reoure Engineering, Jadavpur Univerity, Kolkata, India hanukp@rediffmail.om ABSTRACT A erie of lear water our experiment have been onduted in a tilting flume with a irular pier under different ondition of denimetri Froude number and inflow depth. Tet ued a ingle pier of 50 mm diameter embedded in a and bed of mean partile ize d 50 = mm. It wa oberved that the entire our geometry (our depth, length, width, area and volume) depended on the denimetri Froude number (F D50 ) and inflow depth (h). On the bai of the obtained reult, empirial equation are propoed for our depth, our length, our width, our area and our volume. Sour hole parameter alulated from the propoed equation have been ompared with thoe obtained from experimental reult and are found to be very loe to eah other. Keyword: our, tilting flume, vertial pier, threhold ondition, denimetri froude number. INTRODUCTION Loal our i reognized a one of the prime reaon for failure of hydrauli truture. Though there have been extenive tudie by everal reearher on the effet of loal our around bridge pier, it i very rare to find any ingle analytially derived equation for predition of our. Due to the omplex nature of the problem, uh a ombined effet of omplex turbulent boundary layer, time-dependent flow pattern, and ediment tranport mehanim in the our hole, omplete predition of loal our depth around bridge pier beome diffiult. Raudkivi and Ettema (1983) tudied relationhip of loal our depth with partile ize ditribution of bed ediment, mean partile ize of the bed ediment relative to pier diameter in lear-water ondition. The author alo preented a formula for etimating the maximum depth of loal our. Numerou tudie have been onduted with the purpoe of prediting our, and variou equation have been developed (Lauren and Toh, 1956; Liu et al., 1961; Shen et al., 1969; Breuer et al., 1977; Jain and Fiher, 1979; Raudkivi and Ettema, 1983; Melville and Sutherland, 1988; Froehlih, 1989; Melville, 1992; Abed and Gaer, 1993; Rihardon and Rihardon, 1994; Lim, 1997 and Heza et al., 2007). Mot of thee empirial equation were baed on laboratory reult and field data and they differ from eah other with repet to the fator onidered in ontruting the our model, parameter ued in the equation, laboratory or ite ondition, et. Among thee equation, one of the mot ommonly ued pier our equation in the United State i the Colorado State Univerity equation reommended in the Hydrauli Engineering Cirular No. 18 of U.S. Department of Tranportation (HEC-18 Federal Highway Adminitration, 1993). While thee propoed equation have been demontrated to be appliable with good auray for a ertain et of data, there ha been oniderable unertainty when uing thee equation to predit our in field pratie. To tet the auray of the developed bridge our equation, omparative tudie have been onduted by many reearher (Jone, 1984; Johnon, 1995; Mueller, 1996 and Lander and Mueller, 1996). Oliveto and Hager (2002) preented a our equation and the author found that denimetri Froude number i the dominant parameter governing the our proe. The propoed equation for temporal our evolution wa further jutified with a large et of experimental reult (Oliveto and Hager, 2005). Yanmaz (1989) indiated that the relative our depth (d/b) i a funtion of relative approah flow depth (h/b), where d i the equilibrium our depth and b i the pier diameter. The author preented a relationhip between relative our depth and relative approah depth through urve. Earlier, uh urve were developed by Melville (1975), Chiew and Melville (1987), Melville and Sutherland (1988), Gűnyakti (1989) and Breuer et al. (1977). The purpoe of the experimental program wa to invetigate the our hole harateriti around a ingle vertial pier in Clearwater ondition and to develop empirial relationhip on the bai of obtained reult. EXPERIMENTAL SETUP The experiment were onduted in a flume 10 m long, 0.81 m wide and 0.60 m deep, loated in the Fluvial Hydrauli Laboratory of Shool of Water Reoure Engineering, Jadavpur Univerity, Kolkata, India. Water wa upplied to the flume from a reirulating tank with the help of a entrifugal pump. The flow rate in the flume wa adjuted uing a valve provided in the inlet pipe. The eleted water depth for eah run wa maintained with the help of a adjutable vertial lit type tailgate provided at the downtream end of the flume. A mobile bed (tilling bain) zone 3 m long, 0.81 m wide and 0.25 m depth wa prepared at a ditane 1.7 m downtream of the flume beginning, and wa filled with ediment of median partile ize d 50 =0.365 mm and tandard deviation of partile ize ditribution, σ g =( d 84 /d 16 ) 0.5 =1.7. A vertial irular pier of diameter 50 mm wa plaed in the enter of the tilling bain. A hemati diagram of the experimental etup i 649

2 ARPN Journal of Engineering and Applied Siene Aian Reearh Publihing Network (ARPN). All right reerved. hown in (Figure-1). The mobile bed wa ompated and leveled before the tarting of eah tet run. During the tet run the flow diharge and the flow depth were kept ontant, o a to attain a fixed inflow Froude number. Three different flow depth (0.06m, 0.07m and 0.08m) were teted and for eah inflow depth three different diharge were teted. It wa oberved that after about 28 hour, there wa no ignifiant hange in the our depth and profile. Hene it wa onidered that equilibrium our depth wa obtained after about 28 hour. A point gauge wa then ued to meaure the our depth at variou point aro tranvere and longitudinal ro etion. Tranvere meaurement were taken at every 10 mm interval while in the longitudinal diretion; interval of 20 mm to 40 mm were ued and were ontinued till about 1 m downtream of the pier. Table-1 give the ummary of ondition for the tet performed. where, f = Funtion ymbol d = Equilibrium our depth U = Inflow veloity h = Inflow depth ρ = Water denity ρ = Sand denity g = Aeleration due to gravity ν = Kinemati vioity b = Pier diameter d = Partile mean diameter 50 σ g = Partile ize ditribution [= (d 84 /d 16 ) 0.5 ] t = Time Figure-1. Shemati diagram of the experimental etup. DIMENSIONAL ANALYSIS FOR SCOUR HOLE CHARACTERISTICS Sour at pier i influened by variou parameter (Breuer et al., 1977), uh a ize of pier, ediment harateriti, approahing flow ondition, fluid propertie, and time et. The relationhip howing the influene of variou parameter on the equilibrium our depth d at pier an be given in funtional form a follow: (,, ρ, ρ,, ν,, 50, σ, ) d = f U h g b d t (1) g The influene of kinemati vioity (ν) i inignifiant for a turbulent flow over rough bed (Yalin, 1977). In ediment- water interation, the parameter g, ρ and ρ are ombined into one parameter where = (ρ /ρ)-1 (Dey and Debnath, 2001 and Dey and Raikar, 2005). Sine in the preent tudy only one bed material i ued and equilibrium our depth i being onidered, the term σ g, and t an be ignored. Therefore equation (1) an be written a: (,,,, ) d = f U h g b d (2) 50 Uing Bukingham π-theorem, the relative our depth D =(d/b) an be expreed in non-dimenional form a a funtion of denimetri Froude number (=U/( gd 50 ) 1/2 ) and relative flow depth. Denimetri Froude number F D50 an be onidered a a very important parameter ine it take into aount the both the mean partile ize of the ediment and inertia fore. D = f F h b 2(a) D50, Similarly for our length (l ) 650

3 ARPN Journal of Engineering and Applied Siene Aian Reearh Publihing Network (ARPN). All right reerved. L = f F h b 2(b) D50, and our width ( w ) W = f F h b 2() D50, Multiplying equation 2(b) and 2(), the reulting equation an be regarded a non-dimenional area of our hole, A = (a /a p ) where a and a p are the area of our hole and pier, repetively. A = f F h b 2(d) D50, Further, multiplying 2(a), 2(b) and 2(), a new non-dimenional term known a relative volume of our hole, V = v /v p an be introdued where v and v p are the volume of our hole and pier, repetively. V = f F h b 2(e) D50, INCIPIENT MOTION CONDITION Figure-2 how the Shield experimental reult whih relate ritial Shield parameter ( Θ ) and ritial hear Reynold number ( R ) and i known a Shield diagram. The threhold of ediment motion our when Θ > Θ or τ 0 > τ 0 oru > u. From the above figure it i lear that the diharge meaured during eah experimental run wa lower than the minimum diharge required for the inipient motion or threhold ondition where u = hear veloity, that i u τ 0 ρ RESULTS AND DISCUSSIONS A deign method for the etimation of equilibrium depth of loal our at bridge pier wa preented by Melville and Sutherland (1988). A funtional relationhip wa propoed uing laboratory data in the form: d b = K K K K K K 3(a) I y d σ α Where K I = flow intenity fator, K y = flow depth fator, K d = ediment ize fator, K σ = ediment gradation fator, K = pier hape fator and K α = pier alignment fator. To validate the preent work data, the our depth d alulated with equation 3 i plotted with meaured our depth of the preent work a hown in Figure-3. It an be een from Figure-3 that the data of the preent work mathe well with the equation reommended by Melville and Sutherland (1988). = 1 Experimental obervation Shield Diagram Critial Shield parameter Laminar Flow at bed Sediment Motion No Sediment Motion Partile Critial Reynold Number Turbulent Flow at bed Figure-2. Experimental data plotted on hield diagram. of the bed partile. Therefore, it an be aid that all the experiment were arried out under lear water our ondition. In all the experiment, the flow wa hydraulially rough [Shear Reynold number R 70 by Nikurade (1933)] in nature. Therefore viou ub-layer doe not exit here. Yalin (1977) alo mentioned that the influene of kinemati vioity (ν) i inignifiant for a turbulent flow over rough bed. Here, R = hear Reynold number, that i u d 50 /ν; Figure-3. Comparion between alulated Eq. 3(a) our depth and meaured our depth (author data). For Deign purpoe, an envelope urve wa alo reommended by Melville and Sutherland, 1988: K I U ( Ua U) = 2.4, if U ( U a U ) U U < 1 3(b) Where, U= Approah flow veloity, U = Approah flow veloity at threhold ondition and U a = Approah flow veloity at armor peak (= 0.8 approah flow veloity beyond whih armoring of hannel bed i impoible). The data of the preent work wa plotted with thi envelope urve a hown in Figure-4 and it i evident that the our depth obtained in the preent work i le than the our depth obtained from the deign urve (Figure-4). 651

4 ARPN Journal of Engineering and Applied Siene Aian Reearh Publihing Network (ARPN). All right reerved. Figure-4. Comparion of our depth (author data) with deign urve of Melville and Sutherland (1988) Eq. 3(b). Sour Depth From dimenional analyi, it ha been oberved that the our depth i a funtion of denimetri Froude number and inflow depth. In order to etablih a relationhip among them, relative (non-dimenional) our depth (D ) i plotted againt denimetri Froude number (F D50 ) with inflow depth (h) a parameter a hown in Figure-5. Figure-5. Sour depth D veru denimetri froude number F D50. Sour depth inreae with denimetri Froude number for all the teted inflow depth. Linear trend line for the urve indiate their dependene on inflow depth whih take the following form: D = C F + D (4) 1 D50 1 Where, C 1 and D 1 are ontant depending on inflow depth. Generalized equation for C 1 and D 1 are further obtained by plotting the different value with their orreponding inflow depth. The propoed equation for our depth take the final form a reprodued below whih i a funtion of denimetri Froude number and inflow depth. D = { 0.744( h b) 0.367} FD50 + { 2.438( h b) } (5) Length and Width of Sour Hole Dimenional analyi ha indiated our length a a funtion of denimetri Froude number and inflow depth. However, it ha been hown in the preeding etion that our depth i dependent on denimetri Froude number a well a inflow depth. Hene, meaured relative (non-dimenional) our length (L ) are plotted againt the alulated relative our depth with inflow depth a variable parameter. Linear trend line for the relative our length for different inflow depth aume the following form: L = C D + D (6) 2 2 Where, C 2 and D 2 are ontant whih depend on inflow depth. Further, value of C 2 and D 2 for different inflow depth are plotted againt non-dimenional flow depth (h/b) and equation for C 2 and D 2 are obtained. Finally, relative our length i propoed a follow: { } { } L = h b D + h b + 6(a) Similarly empirial equation for width of our hole an alo be analyzed uing plot between relative (non-dimenional) our width (W ) and non-dimenional our depth (D ). Relationhip to evaluate nondimenional our width i propoed a W = { 6.204( h b) 5.412} D + { 4.435( h b) } 6(b) Area of Sour Hole For developing propoed equation for our hole area, the meaured our area i plotted a a funtion of alulated our depth with inflow depth a parameter and it i notied that our area inreae with inreaing our depth. However, it alo varie with inflow depth. Hene the our area i expreed a a funtion of nondimenional our depth. 3 A C e DD = 3 (7) After finding C 3 and D 3 in imilar manner a explained earlier, the our area an be expreed a a funtion of alulated our depth D and inflow depth h/b, a hown in equation 7(a). { } { 1.229( h b) } D A = h b e 7(a) Volume of Sour Hole The oberved our hole volume i plotted a a funtion of alulated our depth for different inflow depth and in thi ae alo it i oberved that the our volume inreae with inreaing non-dimenional our depth. Moreover, for the ame non-dimenional our depth, the our volume inreae with dereaing inflow depth. Hene the our volume i expreed a a funtion of non-dimenional our depth. 4 V C e DD = (8) 4 652

5 ARPN Journal of Engineering and Applied Siene Aian Reearh Publihing Network (ARPN). All right reerved. After determining and ubtituting for C 4 and D 4, our volume i expreed a a funtion of alulated our depth D and inflow depth h/b, a hown in equation 8(a). { 1.568( hb) 0.716} D V = h b e 8(a) { } Comparion of Calulated and Meaured Value Froude number. All the fourteen experimental run atify the Shield Diagram where in eah ae the diharge meaured during eah experimental run wa leer than the minimum diharge required for the inipient motion or threhold ondition of the bed partile whih atifie the lear water our ondition. Primary our hole harateriti uh a depth, length and width have been meaured phyially while our hole area and volume have been determined uing Surfer appliation. Reult from the tet indiate influene of denimetri Froude number and inflow depth on our hole geometry. Dimenional analyi indiate our hole harateriti a a funtion of inflow depth and denimetri Froude number. Propoed equation for our hole parameter exhibit a good agreement with meaured value. Lit of ymbol Figure-6(a). Comparion between meaured and alulated value of our depth, length and width. Sour hole harateriti viz. depth, length, width, area and volume have been alulated uing the orreponding propoed equation preented in previou etion. Thee value have been ompared with thoe obtained by meaurement from the onduted experiment a hown in Figure 6(a) and 6(b). A good agreement i oberved for all the harateriti a indiated in Figure 6(a) and 6(b). Figure-6(b). Comparion between meaured and alulated value of our area and volume. CONCLUSIONS Clear water our tet have been performed on a ingle pier under varying inflow depth and denimetri The following notation are ued in the preent tudy. h Approah flow depth b Pier diameter d xx Partile ize diameter, where xx% material finer d Loal equilibrium our depth l Sour length w Sour width a Planar our area a p Pier plan area v Sour hole volume v p Pier volume inide the our hole U Approah flow veloity σ g Standard deviation of ediment partile ize ditribution [(d 84 / d 16 ) 0.5 ] ρ Water denity ρ Sand denity t Time g Aeleration due to gravity g Redued gravitational aeleration [{(ρ /ρ)-1} g] F Froude number [U/ (gh) 1/2 ] F D50 Denimetri Froude number [U/ ( gd 50 ) 1/2 ] D Relative our depth (d /b) L Relative our length (l /b) W Relative our width (w /b) A Relative our area (a /a p ) V Relative our volume (v /v p ) U Approah flow veloity at threhold ondition U a Approah flow veloity at armor peak (= 0.8 approah flow veloity beyond whih armoring of hannel bed i impoible) u Shear veloity u Critial hear veloity τ 0 τ 0 Θ Θ Average hear tre at the boundary Threhold hear tre at the boundary Shield parameter Critial Shield parameter 653

6 ARPN Journal of Engineering and Applied Siene Aian Reearh Publihing Network (ARPN). All right reerved. R R K I K y K d K σ K K α C x,d x Shear Reynold number Critial hear Reynold number Flow intenity fator Flow depth fator Sediment ize fator Sediment gradation fator Pier hape fator Pier alignment fator Coeffiient Lander M. N. and Mueller D. S Evaluation of eleted pier-our equation uing field data. Tranp. Re. Re. 1523: Lauren E. M. and Toh A Sour around bridge pier and abutment. Vol. 4, Iowa Highway Reearh Board, Ame, Iowa, USA. Lim S.Y Equilibrium lear-water our around an abutment. J. Hydraul. Eng. 123(3): REFERENCES Abed L. and Gaer M. M Model tudy of loal our downtream bridge pier. Pro., National Conf. on Hydrauli Engineering, San Franio. pp Breuer H. N. C., Niollet G. and Shen H. W Loal our around ylindrial pier. J. Hydraul. Re. 15(3): Chiew Y. M. and Melville B. W Loal our around bridge pier. Hydr. Re. 25(1): Dey S. and Debnath K Sediment pikup on tream wie loping bed. J. Irrig. Drain. Eng. 127(1): Dey S. and Raikar R.V Sour in long ontration. J. Hydraul. Eng. 131(12): Froehlih D. C Loal our at bridge abutment. Pro National Conf. on Hydrauli Engineering, New York, USA. pp Gűnyakti A Charateriti of alluvial tream and river training. Pro. Sediment Tranport Tehnology. Vol. 2 UNESCO, General Diretorate of State Hydrauli Work, Ankara, Turkey. Heza Y. B. M., Soliman A. M., and Saleh S. A Predition of the our hole geometry around expoed bridge irular-pile foundation. J. Eng. Appl. Si. 54(4): Jain S. C. and Fiher E. E Sour around bridge pier at high Froude number. Rep. No. FHWA-RD , Federal Highway Adminitration, Wahington D.C. USA. Johnon P. A Comparion of pier-our equation uing field data. J. Hydraul. Eng. 121(8): Jone J. S Comparion of predition equation for bridge pier and abutment our. Pro., Tranportation Reearh Reord, Seond Bridge Engineering Conf. Vol. 2, Tranportation Reearh Board, Wahington, D.C. USA. pp Liu H. K., Chang F. M. and Skinner M. M Effet of bridge ontrition on our and bakwater. Rep. No. CER60HKL22, Department of Civil Engineering, Colorado State Univerity, Fort Collin, Colo, USA. Melville B. W Loal our at bridge abutment. J. Hydraul. Eng. 118(4): Melville B.W Loal our at bridge ite. Report No. 117, Univerity of Aukland, New Zealand. Melville B. W. and Sutherland A. J Deign method for loal our at bridge pier. J. Hydraul. Eng. 114(10): Mueller D. S Loal our at bridge pier in nonuniform ediment under dynami ondition. Ph.D. thei, Colorado State Univerity Fort Collin, Colo, USA. Nikurade J Stromunggeetze in rauhen rohren. Verein Deuther Ingenieure, Forhungheft Oliveto G. and Hager W.H Temporal evolution of lear-water pier and abutment our. J. Hydrauli Engineering. 128(9): Oliveto G. and Hager W.H Further reult of timedependent loal our at bridge element. J. Hydrauli Engineering. 131(2): Raudkivi A.J. and Ettema R Clear-water our at ylindrial pier. Journal of Hydrauli Engineering. 109(3): Rihardon J. R. and Rihardon E. V Pratial method for our predition at bridge pier. Pro. ASCE National Conf. on Hydrauli Engineering, Buffalo, N.Y. USA. pp Shen H. W., Shneider V. R. and Karaki S Loal our around bridge pier. Pro. ASCE. 95(6): Yanmaz A.M Time dependent analyi of lear water our around bridge pier. Ph.D. Thei, Middle Eat Tehnial Univerity, Ankara, Turkey. Yalin M. S Mehani of ediment tranport, Pergamon Pre, New York, NY, USA. 654