Effect of river bed slope and particle size distribution on washing out condition of trees in rivers

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1 Effect of river bed lope and particle ize ditribution on wahing out condition of tree in river J. Yagiawa, and N. Tanaka, Intitute for Environmental Science & Technology Saitama Univerity 55 Shimo-Okubo, Sakura-ku, Saitama JAPAN Graduate School of Science and Engineering Saitama Univerity 55 Shimo-Okubo, Sakura-ku, Saitama JAPAN Abtract: In previou tudie, wahing out of tree can be evaluated uing Breaking or Overturning Index(BOI) and Wahing-Out Index(WOI). However, the applicability of thoe indice were only validated ome middle-tream river where the bed lope i not o teep. For validating the indice at different river condition from pat tudie, thi urvey carried out at 7 river with different bed lope. Accordingly, a relationhip between WOI and particle ize ditribution became clear. Bed lope i found to have no influence on the critical condition of BOI, but particle ize ditribution can affect the critical wah-out condition for WOI. Keyword: tree trunk breakage, tree wah out, breakage or overturning index(boi), wah-out index (WOI), particle ize ditribution of river bed material. INTRODUCTION Foretation inide a river (Johnon, 994) ometime caue a problem, not only becaue it reduce river flow capacity downtream, but becaue debri by flood, i.e., broken tree trunk and branche, increae the drag force on bridge pier in river. The debri attached to and accumulate around a pier caue a large cour hole around it and ometime break the pier (Melville and Dongol, 99). In addition, exceive foretation by a ingle tree pecie or an invaive exotic tree pecie ometime affect the biodiverity of a river ecoytem (Stoke, 008). For rejuvenation of a gravel bed river, it i neceary to get the information on how flood affect the formation of a plant community in a river. In particular, the characteritic of and depoited by the flood event (i.e., particle ize, nutrient content) (Owalt and King, 005), flood diturbance frequency (Gilvear and Willby, 006) and intenity (Vervuren et al., 003), and bed degradation due to flooding (Kamrath et al., 006) are reported to be important factor that affect the plant community. Conidering the above ituation, it i neceary to know the wah-out and breaking condition of river vegetation due to flood. Condition of plant uprooted by trong wind or flooding have been analyzed mainly in term of drag moment acting on the plant (TRCRD, 994; Gardiner et al., 000) or bed hear tre (dimenionle hear tre) (Temple, 980; Egger et al., 007). Recently, Tanaka and Yagiawa (009) conducted field invetigation in Tamagawa river for a flood in 007 and reported breaking and wahing out of tree can be evaluated uing Breaking or Overturning Index(BOI) and Wahing-Out Index(WOI), repectively. However, the applicability of thoe indice wa only validated for ome middle-tream river where the bed lope i not very teep. Therefore, the objective of thi tudy wa to clarify the effect of river bed lope and particle ize ditribution of river bed material on critical value of BOI and WOI. To fulfill the objective, field invetigation were conducted in the Arakawa River, Miyagawa River (in Mie Pref), Miyagawa River (in Gifu Pref.), Fujigawa River, Kamanahigawa River, Ooigawa River and Abegawa River for finding out the breaking and wah-out condition of tree by flood. 9

2 . MATERIALS AND METHODS.. River flow analyi The baic equation included in the hydrodynamic model are the conervation of fluid ma equation and momentum equation (Reynold equation). The baic governing equation in Carteian coordinate are hown a follow: Continuity equation: h M N + + = 0 () t x y Momentum equation in x and y direction: M Mu Mv Z 0 x fx + + = gh + ( u h) + ( u ' v ' h) () t x y x ρ ρ x y N Nu Nv Z 0 y f y + + = gh + ( u ' v ' h) + ( v h) (3) t x y y ρ ρ x y where t i the time; h i the water depth; u and v are the depth-averaged velocitie in x and y direction, repectively; M=uh and N=vh are the flux in x and y direction, repectively; 0x and 0y are the bed hear tre in x and y direction, repectively; f x and f y are the drag force per unit area in x and y direction, repectively; u u v and v are depth-averaged Reynold tree; g i the gravitational acceleration, h i the water depth, ρ i the fluid denity; and Z i the water level. Depth averaged Reynold tree are calculated by the ame method with Hooda (00) a follow: ' u u = Dh k (4) x 3 ' u v uv = Dh + (5) y x ' v v = Dh k (6) y 3 D h = αhu * (7) where, D h i the kinetic eddy vicoity, k i the depth averaged turbulent energy, α i contant (α i et a 0.3 in thi tudy), u * i the friction velocity. k i given a hown below equation (Nezu and Nakagawa(993)). k =.07u* (8) For grid tranformation from the Carteian coordinate to generalized coordinate ytem, the method by Hooda et al. (996) wa applied. Finite volume method wa ued to olve the partial differential equation. The applicability of the model wa validated for river flow (Tanaka and Yagiawa 009).To analyze the moment acting on a tree, M, we conidered the drag force, F, including the tree tand tructure (Tanaka et al., 006) wa conidered a hown in Eq. (9) and (0), and bed hear tre,, wa evaluated by Eq. (). h h d( z) Cd ( z) ( f x, f y ) = ( u, v) mρ Cd ref dbh u + v dz = ( u, v) mρcd ref dbh u + v α ( z) β ( z) dz (9) 0 d C 0 M = Cd ref BH ( u + v ) d ref h ρ d BH zα( z) β ( z) dz (0) 0 b ρgn u + v ( 0 x, 0 y) = ( u, v), = 0x + 0 y () 3 h where z (m) i the vertical axi from the ground where tree are vegetated, m (number of tree/m ) i the tree denity per unit area, C d-ref i the reference drag coefficient (= conidering a circular cylinder in thi tudy), C d (z), d(z) i the drag coefficient, cumulative width of tree trunk, and branche (m) at height z, repectively, d BH i the tree trunk diameter at breat height (m), n b (m -/3 ) i the Manning roughne coefficient without vegetation, α(z) i an additional coefficient expreing the vertical tree tructure, and β(z) i an additional coefficient repreenting the effect of leave and the inclination of 0

3 branche (for detail, ee Tanaka et al. (006))... Study area and field invetigation Before and after typhoon No.9 on 007, field invetigation wa conducted on gravel bar (AR and KU) in Arakawa River, Japan. For other river repreented in Figure, field invetigation were conducted before and after typhoon No. and 5 on 0. In each ite, () particle ize ditribution of river bed material (d 50 and d 90 ), () tree characteritic (a like trunk diameter at breat height (d BH ) and tree Figure Location of tudied river/tudy area River Table Characteritic of invetigated river Ditance from river mouth (km) River bed lope Particle ize of river bed material d 50 (cm) d 90 (cm) Tree characteritic Trunk diameter at breat height d BH (cm) Tree height H t (m) Miyagawa River (Mie Pref.) 7-78 /6 - / Miyagawa River (Gifu Pref.) /76 - / Kamanahigawa River 8 / Ooigawa River / Fujigawa River / Abegawa River 4 / Arakawa River /

4 height(h t )), (3) tree breaking or wahed out ituation due to flood and (4) maximum trace water depth at each flood event (H max ) were meaured. Particle ize ditribution of river bed material at each ite were determined. d 50 and d 90 were etimated by two method in thi tudy. One wa to take a photo of the river bed and conduct image analyi to determine the particle ize ditribution when the particle ize i large and the creening tet cannot be ued. The econd wa to ample bed material from the river bed urface to 5 cm depth and creen them by uing five ieve with 3.7 mm, 9. mm, 9.5 mm, 5.66 mm, and 4.00 mm meh to obtain the particle ize ditribution. In thi tudy, econd method wa applied only few location in Arakawa River..3. Critical hear tre etimation for d50 and d90 To evaluate the hear tre acting on the grain,, the non-dimenionalized Shield parameter that * i are uually ued for conidering the gravity force (lope direction) over the weight of the grain in water were ued a below: ρghi b HI b i = = () * ( ρ ρ) gd i ρ d i ρ where ρ and ρ are the denity of the particle and water, repectively; g i the gravitational acceleration; d i i the grain diameter at which i% volume pae through the ieve, and I b i the bed lope. The critical hear tre of d 50 for the initiation of motion, *c50 can be approximated from the Shield diagram a: * c50 = 0.06 (3) ρ ρ gd ( ) 50 To calculate the effect of the grain ize ditribution, the critical hear tre of each grain ize i, *ci, a propoed by Egiazaroff (965), wa: * ci 0. ( ) [ log ] gd = (4) ρ ρ i 09( di dm) where d m i the medium grain ize *50 and *90 are derived by ubtituting d i = d 50 or d 90 in Eq. (), repectively. *c90 i derived by ubtituting d i = d 90 in Eq. (4)..4. Definition of the Breakage or Overturning Index (BOI) and Wah Out Index(WOI) In thi tudy, BOI and WOI were defined ame with Tanaka and Yagiawa(009) a hown in below equation. BOI WOI d BH max = (5) d BH *90 = (6) * c90 Where d BH i the tree diameter at the flood event, d BHmax i the maximum d BH that the flood can break the trunk, *90, *c90 i non-dimenionalized hear tre and non-dimenionalized critical hear tre of d 90, repectively.

5 3. RESULTS 3.. Comparion of imulated and oberved water level for the September 007 flood in Arakawa River Contour map of the imulated velocity and water depth at the peak dicharge of the flood are hown in Figure (a). The inundation of flood area A (iland at KU) and B (flood plain) in Figure (c) were reproduced well in the imulation (Figure (b)). However, it wa difficult to confirm that the reult of the imulation wa good enough to evaluate the ituation of the flood a a two-dimenional expreion. Therefore, validation of the numerical imulation wa conducted by comparing the calculated and oberved peak water level (Figure (d) and (e)). The maximum water level at the flood event wa determined by the Minitry of Land, Infratructure, Tranport and Tourim of Japan (MLIT) by meauring the height at which debri wa attached. The peak water level in the flood imulation wa ued a the maximum value at each calculation grid, and the calculation agreed well with the oberved peak water level a a whole. Figure Flow ituation of Arakawa River between 76 km to 8 km at the maximum dicharge of the September 007 flood: (a) contour and vector map of imulated velocity, (b) contour map of imulated water depth, (c) aerial photo (provided by Kanto Regional Development Bureau, Minitry of Land, Infratructure, Tranport and Tourim, Japan). (d) and (e) how comparion of imulated and oberved maximum water level along the Arakawa River during the September 007 flood on the right bank and left bank, repectively. x and y repreent the axe in the orthogonal coordinate ytem. The two element in Figure 3(c) repreenting the inundated area are A (iland at KU) and B (flood plain). 3

6 3.. Effect of river bed lope and particle ize ditribution of river bed material on BOI and WOI Figure 3(a) how the comparion between BOI value obtained from drag moment by numerical imulation for Arakawa River and detruction ituation of tree due to a flood oberved from field invetigation. In thi tudy, 4 region (Region A-D) were defined depending on BOI and WOI value a hown in Figure 3(a). The mot of broken tree due to the 007 flood were categorized in Region B. In contrat, mot of tree not received damage were plotted in Region A. However, ome data repreenting broken tree were plotted in Region A. Regarding thee data, it wa confirmed by the field invetigation after the flood that thee tree were broken due to attach the large amount of debri. In numerical imulation, the effect of attached debri on the increment of drag force acting on tree wa not conidered. Therefore, it i uppoed BOI value of thee tree were underetimated. Figure 3(b) how the comparion between WOI value calculated for the flood event and wahed out ituation of tree oberved from field invetigation in the Arakawa River. Some data repreenting overturned tree were plotted in Region C and D. If WOI exceed, mot of tree can be wahed out in the region BOI >. However, not wahed out tree were alo categorized in Region C even when WOI exceed. Thi reult indicate that critical value for WOI increae with decreaing BOI in Region C (BOI <, WOI > ) Region D (BOI >, WOI > ) (a) Region A (BOI <, WOI < ) Region B (BOI >, WOI < ) (b) Figure 3 Tree damage ituation in relation to the critical value of trunk breakage(boi) and wahed out of tree(woi) baed on the reult of numerical imulation for Arakawa River (a) BOI, (b) WOI.5 Wahed out Overturned No damage WOI BOI Figure 4 Tree damage ituation in relation to the critical value of trunk breakage(boi) and wahed out of tree(woi) baed on the reult of field invetigation for Miyagawa River (Mie and Gifu Pref.), Fujigawa River, Kamanahigawa River, Ooigawa River and Abegawa River Region C. In cae of mall BOI, to break the tree root become difficult. Therefore, it i thought that the tree were not wahed out. In Figure 4, BOI and WOI value of invetigated river except for Arakawa River are plotted. In comparion with BOI value for overturned tree and not one, BOI can ditinguih well whether tree 4

7 are broken or not. Similar tendency can be obtained from Arakawa River cae (Figure 3(a)). Thee reult indicate that BOI i not affected by river bed lope and particle ize ditribution. On the other hand, unlike with reult of Arakawa River (Figure 3(b)), ome wahed out tree can be plotted In Region B. It i uppoed that large fluid force acted on upper ground part of tree and uprooting of tree-root occurred even when d 90 did not move. 4. DISCUSSION For elucidating the effect of particle ize ditribution of river bed material on critical value of WOI, relationhip between d 90 /d 50 and WOI are ummarized in Figure 5. In thi figure, WOI value plotted in Region B of Figure 4 are repreented. Dotted line and line were decided by WOI value for downward limit of wahed out tree and upper limit of remained tree, repectively. According to thee two line, it can be found that critical value of WOI increae with increaing d 90 /d 50. When the large ize particle are mixed with the mall one, movement of the mall particle hould be prevented by heltering effect of large particle. Therefore, river bed material become hard to move with the increae of d 90 /d 50. Thi reult ugget that effect of d 90 /d 50 on critical condition of wahing out tree need to be conidered in Region B. Figure 5 Effect of particle ize ditribution (d 90 /d 50 ) on the critical value of WOI KN : Kamanahigawa River, AB : Abegawa River, FJ : Fujigawa River, OI : Ooigawa River 5. SUMMARY The following concluion and recommendation were obtained by thi tudy: ) Bed lope i found to have no influence BOI, but particle ize ditribution affect the critical wahout condition for WOI. ) Critical value of WOI increae with decreaing BOI in Region C. 3) Effect of d 90 /d 50 on critical wahout condition of tree need to be conidered in Region B. 6. ACKNOWLEDGMENTS Thi tudy wa upported in part by JSPS AA Science Platform Program, Japan. Thi tudy wa partly funded by Foundation of River & Waterhed Environment Management. Dr. Kazuo Ihino, Taiei Corporation, i acknowledged for hi ueful uggetion. Mr. Keitaro Oka, Saitama univerity, i acknowledged for hi help in field invetigation. 5

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