BED FORM DEFORMATION DUE TO UPSTREAM GROUP PILES

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1 BED FORM DEFORMATION DUE TO UPSTREAM GROUP PILES TAE HOON YOON Prfessr Emeritus Deartment f Civil Engineering Hanyang University, Seul, Krea taehyn@htmail.cm Abstract Defrmatin f be frms by assing thrugh a gru f vertical iles installe ustream in an en channel was examine exerimentally. With Frue number the heights an lengths f unes are increase an the steeness f unes ecreases. The heights f iles were fun t have negligible imact n the variatin f be frms. The ile iameter is a significant factr that causes the reuctin in the imensins f unes. Increase in number f iles er unit area efine as a ile ensity brings abut the ecrease in the size f une as much as 60%. Hwever, there exists an uer limit f the ile ensity beyn which the efrmatin f une becmes ineenent f the ensity. The steeness f unes becmes steeer with increase f the ensity. The efrme be frms resume their riginal states at a istance wnstream X/L 6 frm the en f ile zne.. Intructin Deening n the flw arameters an seiment rerties, an alluvial stream may unerg ifferent be frms. Fr the lwer regime f a subcritical flw, the stream be can exhibit riles an unes with the water surface being arximately flat. Kenney(1969) argue that the ccurrence f be frms is ue t (1) the result f an rerly attern f scur an esitin, (2) the instability henmenn an (3) the flw arameters an seiment rerties. Yalin(1977) inte ut that the unes are cause by a iscntinuity(rige) f a lane initial be, which inuces an alternatin in velcity rfile thrugh isturbance f turbulence structure an in cnsequence the velcity alternatin is resulte in the ecrease f seiment transrt, the grwth f accretin must take lace, an the variatin f be level by the Exner equatin must be accmanie. Base n the afrementine reasnings, any hysical aitin t a flw, which causes an alternatin in the flw structure an in the alluvial stream be features, will bring abut change in seiment transrt. Such change will lea t either increase r ecrease the magnitues f be frm gemetries such as the imensins f unes. Placing iles n the stream be may be ne f the aitins resulting in the alteratin, ssibly reuctin, f the imensins f unes. In alluvial streams, when the trughs f unes ass hyraulic structures, substantial art f their funatin may be exse t flw an it may enanger the safety f structures. Therefre, fr rer management, maintenance an safe esign f hyraulic structures, it is very 1

2 imrtant t evel measures t reuce the magnitues f unes r antiunes assing hyraulic structures r eliminate them entirely if ssible. The bjective f this aer is t examine hw the imensins f unes are affecte by assing thrugh a gru f iles with ifferent cmbinatin f ile installatin n the be in an en channel. Exeriments Exeriments were cnucte in a recirculating tilting flume that is 20m lng, 0.9m wie an 0.4m ee. Unifrm be seiments with a meian article iameter f 0.45mm were lace with the eth f 10cm in the flume be. The iles were sitine at the central regin f the flume with ifferent cmbinatin f ile iameter, istance amng iles an ile ensity. Fig.1 shws the efinitin sketch f exerimental setu. The evelment uratin f san waves varies frm 20min t 20hr eening n the value f τ / τ c (Yalin 1979). Hwever, each exeriment was run fr a uratin f 4 hur since the exeriments were aime t fin hw the alternatin f unes take laces. Fig. 1 Definitin sketch f exerimental setu Fig. 2 Layut f ile installatin The heights an lengths f unes were measure by a int gage an a ruler. At each run mre than ten measurements were mae an their imensins were average. Mst f exeriments were erfrme uner cnitins f flw eth f y = 13cm an flw velcity f u = 0.6m/s. The sitining f iles was rather arbitrary, i.e. the lngituinal istance an transverse sacing between iles were set as 52cm an 20cm, resectively as shwn in Fig. 2. The lngituinal istance f 52cm is the average length f unes at y = 13cm an u = 0.6m/s. Thrughut the exeriments the ile zne was a rectangular f 156cm in the irectin f flw an 60cm in the transverse irectin. 2

3 Table 1. Flw cnitins an average imensins f unes Flw eth (cm) Velcity (m/s) Fr Av height (cm) Av length (cm) Table 2. Prerties f iles Diameter (mm) Height ( h /y 0 ) Density (cm 2 /cm 2 ) x10 3 Dunes A une is ne f tyical be frms with shae that has an ustream face with a gentle, graually varying sl an an abrut wnstream face with a cnstant sle, which is arximately equal t the tangent f the rese angle f be material. Dunes fun in a subcritical flw regin f F r = (Mercer 1971) are nt statinary but they mve in the irectin f flw. The imensins f the be frms are eenent n the rerties f the flw, flui an be material. Yalin(1964) shwe a linear relatin f L = 5 y an Hin(1969) rerte a similar relatin f L = 7 y. Allen(1963) resente the fllwing relatinshi frm the bserve ata. lg y = lg H (1) lg H = lg L (2) in which L is the length f a san wave r une an H is the height f a une. Frue numbers f the flw that inuce the unes in this stuy fall in the range f 0.18 an 0.62(Table 1), which agrees with the finings by Gswami(1967). As can be seen in Fig. 3 the heights an lengths f unes are nte t be eenent n Frue number fr a given flw eth Fr 4.174Fr H/ y =0.0407e, L/ y = e (3a,b) where Fr is the Frue number ( u / gy ). The ltte ata f the heights versus lengths shwn in Fig.4 might be sai t agree t Allen s relatinshi f Eq.2 if it stans fr large riles, an the steeness f unes 3

4 Fig. 3 Increase f une imensins with Frue number Fig.4 Plt f heights versus lengths f unes fr ifferent velcities has the value f 1/14, whereas Yalin(1964, 1977) shwe H/L=1/30 1/5. The steeness was fun t be a functin f Frue number fr a given flw eth. In this articular case it can be efine in terms f Frue number Fr as 0.289Fr H/L = e (4) Effects f Piles n Dimensins f Dunes Effect f ile height : As shwn in Fig. 5, the effect f ile height at the ensity f iles f 1.47/1000 is negligible n bth heights an lengths f unes regarless f the iameter f ile. Meanwhile, the flw in an en channel are influence significantly by the height f vegetatin zne lace ustream(yn et al. 2004). The effect f vegetatin height n the velcity rfile leas t the reuctin in the scuring eth arun a ier with ifferent vegetatin height. The abve facts call fr further research fr the effect f ile height n the be frms with higher ensity f iles. Frm Fig. 5 it is nte that the variatin f heights an lengths f unes with ifferent ile height is negligible. Effect f ile iameter: Fig. 6 shws the variatin f the heights an lengths f unes in the wnstream regin f the ile zne f X 0-1.0m r X/L 0-2.0, where X starts at the wnstream en f the ile zne. It is nte that the heights an lengths f unes ecrease with increase f ile iameter an the reuctins amunt t 24% an 40% f the riginal sizes at D / y =1.0. Base n the limite ata in Fig.6, the imensins f unes wnstream regin f the ile zne can be reicte as 4

5 H H = ( D 2 ), y u L L u D = ( ) y 2 (5a,b) u=0.6m/s y 0 =13cm H av =4.26cm L av =52.73cm 0.2 wnstream 0-1m H/H av wnstream 0-1m L/L av D / y 0 Fig. 5 Effect f ile height n height Fig. 6 Effect f ile iameter n an length f unes imensins f unes Effect f ile ensity: The ensity f iles is efine as the rati f areas f ile gru an ile zne. Fr the sitins f iles within the ile zne, three rw f iles are lace in the transverse irectin an in the lngituinal irectin the number iles were varie in the range f tw t ten iles resulting in ensities ranging frm δ = 0.97/1000 t 4.93/1000. Fig. 7 Effect f ile ensity n Fig. 8 Effect f ile ensity n height f unes length f unes 5

6 The facts nte in Figs. 7 an 8 are that the effect f ile ensity is significant in the reuctin f the imensins f unes an there exists a limiting ensity f iles f ρ =3.45/1000 beyn which the imensins f unes are cease t ecrease. The steeness f une was fun t increase with the increase f ile ensity an the imensins f unes are reuce with the ensity f iles. Alternatin f unes in wnstream regin f ile zne: Figs.9 an 10 shw the variatins f the heights an lengths f unes in the wnstream regin f the ile zne an they inicate that the reuce heights an lengths f unes ue t assing thrugh Fig. 9 Heights f unes with istance wnstream Fig. 10 Lengths f unes with istance wnstream frm ile zne fr ifferent ile iameters frm ile zne fr ifferent iameters the ile zne increase with istance in wnstream irectin frm the ile zne, i.e. the reuce heights an lengths f unes are recvering graually t their riginal imensins befre entering the ile zne. At the istance f X=3m r X/L 6 wnstream frm the ile zne the reuce heights an lengths f unes resume arximately 90% f their riginal imensins Estimatin f alternatin f unes ue t assing thrugh ile zne: Uner the limite cnitins f be seiment 50 = 0.45mm, D/ y 108, an 0.97/1000 ρ 4.93/1000, the altere heights an lengths f unes after assing thrugh the gru f ile lace ustream may be estimate in terms f flw eth y, ile iameter D, ile ensity ρ an Frue number Fr as D H = { ( ) 6.19 ρ } e 3.89Fr y (6) y ρ 0 0 6

7 D = { ( ) ρ } (7) 4.17 Fr L e y ρ 0 y0 where H an L are the height an length f unes in the wnstream regin after assing the ile zne. Cnclusins The efrmatin f unes by assing a gru f iles in an en channel was investigate exerimentally an the finings are summarize. The imensins f unes are an increasing functin f Frue number in a subcritical flw regin, an ver a wie range f the length f unes a cnstant steeness revails an the steeness can be estimate in terms f Frue number. At a lwer ensity f iles such as ρ =1.47/1000, the effect f ile height is negligible an it nees further stuy at higher ensity f iles if the significant effect f vegetatin is cnsiere. With increase f ile iameter, reuctin in the heights an lengths f unes amunts t 24% an 40%, resectively at D / y = The imensins f unes are reuce significantly with the ensity f iles but there exists an uer limit f ρ =3.45/1000 abve which the unes cease t ecrease further. The reuce unes in their size in the wnstream regin f the ile zne resume their riginal magnitue graually as they mve wnstream an at X/L 0.6 they reach 90% f the riginal size. Equatins were erive t be able t reict the heights an lengths f unes in terms f arameters f flw an iles at a given rerties f be material. References Allen, J. R. L.(1963). Asymmetrical rile marks an the rigin f water-lai csets f crss-strata, Liverl an Manchester Gelgical Jurnal, 3, Gswami, A. C.(1967). Gemetric stuy f riles an unes, M.S. Thesis, Det. f Civil Engineering, Clra State University, Frt Cllins, Clra. Hin, M.(1969). Equilibrium range sectre f san waves frme by running water, J. Flui Mechanics, 34(3), Kenney, J. F.(1969). The frmatin f seiment riles, unes, an antiunes, Annual Review f Flui Mechanics, W. R. Sears, E., vl. 1, Annual Reviews, Inc., Pal Alt, Calif., Mercer, A. G.(1971). Analytically etermine be-frm shae, J. f Engineering Mech., ASCE, 97(1), Yalin, M. S.(1964). Gemetrical rerties f san waves, J. f Hyraul. Div., ASCE, 90(5), Yalin, M. S.(1977). Mechanics f Seiment Transrt, 2 n Eitin, Pergamn Press, New Yrk. 7

8 Yalin, M. S. an Karahan, E. (1979). Steeness f seimentary unes, J. f Hyraul. Div., ASCE, 105(4), Yn, T. H., Kim, Y. D., an Kim, S. T.(2004). Effects f a vegetatin zne n flw an scur arun a wnstream brige ier, J. f Krean Sc. f Civil Engineers, Water Engineering, 23(6B),