ScienceDirect. River morphology modeling at the downstream of Progo River post eruption 2010 of Mount Merapi

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1 Available online at ScienceDirect Procedia Environmental Sciences 8 (015 ) The 5th Sstainable Ftre for Hman Secrity (SstaiN 014) River morphology modeling at the downstream of Progo River post erption 010 of Mont Merapi Pji Harsanto* *Universitas Mhammadiyah Yogyakarta, Ring Road Selatan, Tamantirto, Kasihan, Bantl Yogyakarta,55183, Indonesia Abstract Mt. Merapi is one of the most active volcanoes in Indonesia. Some of the rivers that the origin is located at Mt. Merapi have a large amont of sediment resorces after erption in October-November 010. The total volme of sediment is estimated at 130 million m 3.The deposited sediment s to the downstream area as a debris or bed load transport in high density. Few stdies considered downstream change along volcanic rivers de to a high density of bed load transport. Using nmerical simlation, the impact of high concentration of bed-load transport is applied in Progo River, Yogyakarta, Indonesia. The reslts show that the high bed-load transport rate increases the mid-channel bar grow rate and the bed degradation near the bank toe. The increase of bed degradation is an important parameter of bank erosion process. Frthermore, the bed morphology on the downstream after 010 erption of Mt. Merapi shold be considered intensively. 015 The Athors. Pblished Pblished by Elsevier by Elsevier B.V This B.V. is an open access article nder the CC BY-NC-ND license ( Peer-review nder responsibility of Sstain Society. Peer-review nder responsibility of Sstain Society Keywords:volcanic rivers;bed-load transportspply;nmerical;bank toe 1. Introdctions 1.1. Backgrond Mt. Merapi in Central Java, Indonesia had a major erption in late October and early November 010.The erptions prodced ash plmes, lahars, and pyroclastic s. Therefore, a large nmber of sediment is deposited at the pstream of several volcanic rivers. It is approximately 130 million m 3. Dring rainy season, the deposited * Corresponding athor. Tel.: ; fax: address: pji_hr@my.ac.id The Athors. Pblished by Elsevier B.V. This is an open access article nder the CC BY-NC-ND license ( Peer-review nder responsibility of Sstain Society doi: /j.proenv

2 Pji Harsanto / Procedia Environmental Sciences 8 ( 015 ) sediment s to the downstream area and prodces debris. The presence of debris increases the possibility riverbank erosion in some river reach, casing significant damage to varios infrastrctre and river strctres. Hence, the secondary disaster in term of rainfall indced debris may occr in long term period. Using nmerical model, this research is to investigate lahar occrrence as a spply of bed-load transport and its impact on riverbed deformation near the bank toe. The bed degradation at the vicinity of the bank slope which increases in the relative river bank height has a significant inflence on the stability of the bank. 1.. Stdy Area The watershed area of Progo River is arond 17,43 sqare kilometers. Several tribtaries of Progo River are located in the Mt. Merapi. The irrigation water of Sleman and Klon Progo Distric is taken from the river. Many strctres, for example, bridges, railway bridges, cross the river. Therefore, the sstainability of the river shold be monitored by Yogyakarta government. De to the major erption in October 010, the sediment spply is more than the eqilibrim condition. The river reaching of Progo River and located in Bantaris chosen in order to examine the interaction of channel geometry, sediment spply and bed deformation. Fig. 1 shows the Progo River system.. Nmerical Model Fig. 1. Location of stdy area Nmerical simlations are performed sing the horizontal two-dimensional model which the eqations are written in general coordinate system. The model ses the finite difference method to solve different eqations. Relationship between Cartesian coordinate system and General coordinate system is as follows.. 1 J x y x y (1a)

3 150 Pji Harsanto / Procedia Environmental Sciences 8 ( 015 ) y J x (1b) y J x (1c) x J y x J y (1d) (1e) Where, and are the coordinates along the longitdinal and the transverse directions in generalized coordinate system, respectively, x and y are the coordinates in Cartesian coordinate system. Comptation of srface is carried ot sing the governing eqation of the horizontal two-dimensional averaged with depth. The conservation of mass, i.e., in and ot of mass by seepage, is taken into consideration as shown in the following eqation [1]. z h h hg hg U V Ug Vg 0 tj t J t J t J t J () Where, t is the time, z is the water srface level. Srface depth is represented as h, seepage depth is h g. U and V represent the contra variant depth averaged velocity on bed along and coordinates respectively. These velocities are defined as U v x y V v x y (3a) (3b) where, and v represent the depth averaged velocity on bed along x and y coordinates, respectively. U g and V g represent the contra variant depth averaged seepage velocity along and coordinates, respectively. These velocities are defined as U v x y g g g V v x y g g g (4a) (4b) where, the depth averaged seepage velocities along x and y coordinates in Cartesian coordinate system are shown as g, v g, respectively. is a parameter related to the porosity in the soil, wherein = 1 as zz b, and = as z z b, where z b is the bed level and is the porosity in the soil. Seepage is assmed as horizontal twodimensional satration. Momentm eqations of srface water are as follows.

4 Pji Harsanto / Procedia Environmental Sciences 8 ( 015 ) hu hu hu U V t J t J t J h U V J tx t x t x hv U V J ty t y t y 1 zs 1 z s b gh J x y J x x y y J J x J x x J y x J y x h xx h xx h yx h yx hxy h h h J x y J x y J y J y y xy yy yy (5a) hv hv hv U V t J t J t J h U V J tx t x t x hv U V J ty t y t y 1 zs 1 gh J x x y y J x y J z s b J x x J x J y x J y x h xx h xx h yx h yx hxy h h h J x y J x y J y y J y xy yy yy (5b) Where, g is the gravity, is the water density. b and b represent the contra variant shear stress along and coordinates, respectively. These shear stresses are defined as x y b bx by x y b bx by (6a) (6b) where, x and y are the shear stress along x and y coordinates, respectively as follows. x b b v b b (7a) y b v b v b b (7b) b * (8)

5 15 Pji Harsanto / Procedia Environmental Sciences 8 ( 015 ) ng v R m * 1 3 (9) Where, * is the friction velocity, n m is the Manning s roghness coefficient, R is the hydralic radis, k s is the roghness height. b and v b represent velocity near the bed srface along x and y coordinates, respectively. Velocities near the bed are evalated sing crvatre radis of streamlines as follows. cos v sin b bs s bs s v sin v cos bs b bs s bs s 8.5 h vbs N* r * bs (10a) (10b) (11) (1) Where, arctan v s velocity field as follows [3].,N * is 7.0 [].r is the crvatre radis of stream lines obtained by the depth integrated 1 1 v v v v v r x x y y v 3 (13) xx, yy, xy and yx are trblence stresses as follows. xx yy x v y (14a) (14b) v xy yx x y (15) * 6 h (16) Where, is the coefficient of kinematics eddy viscosity, is the Karman constant, k t is the depth-averaged trblence kinetic energy [1]. g k gx zb zb x x (17a)

6 Pji Harsanto / Procedia Environmental Sciences 8 ( 015 ) v g k gy zb zb y y (17b) Where, k gx and k gy is the coefficient of permeability along the longitdinal and the transverse directions, respectively. When the water depth of srface becomes less than the mean diameter of the bed material, the srface is compted only in consideration of pressre term and bed shear stress term in the momentm eqation of srface [4].Grain size distribtion is evalated sing the sediment transport mltilayer model as follows[5]: ce b b fbk zb 1Fbk t J t J ce q b b fbkr b bk ce q b b fbkr b bk 0 t J J t J J (18) In the formlae above, f bk is the concentration of bed-load of size class k in the bed-load layer, f dlk is the sediment concentration of size class k in the m th bed layer, c b is the depth-averaged concentration of bed-load. E be is the eqilibrim bed-load layer thickness; it is estimated by the following eqation [6]: E d be m 1 c cos tan tan b * m (19) Where d m is the mean diameter of bed-load, is the angle of repose, and *m is the non-dimensional shear stress of mean diameter. E sd is the sediment layer thickness on cohesive sediment bed. E b is the bed-load layer thickness, q bk and q bk are the bed-load of size class k in and directions, respectively, q bxk and q byk are the bed-load of size class k in x and y directions, respectively as follows [7] [8]. q q q cos bxk bk k q sin byk bk k (0a) (0b) 3 * e * ck * ck qbk 17 1 Kc 1Kc f bk s g * * (0c) Therein, s is the sediment density, *e is the effective shear velocity; the non-dimensional critical friction velocity of size class k is evalated as follows [7]. log 19 d d d d 10 k * ck * cm log10 19 k m m (1a) Iwagaki s formla which is formlated for niform bed material is sed for evalating *cm. K c is the correction factor de to the inflence of bed inclination on sediment motion [9]. 1 Kc 1 1cos tan x sin tan y s s ()

7 154 Pji Harsanto / Procedia Environmental Sciences 8 ( 015 ) where is the angle of deviation of near-bed from the x direction. s is the coefficient of static friction. x and y are bed inclinations in x and y directions, respectively. Evoltion of bed elevation is estimated by means of the following formlae. n n ce b b zb ce q b b bk ce q b b bk 1 0 t J t J t J k1 J t J k1 J (3) In them, n represents the nmber of the size class of sediment. 3. Simlation Model 3.1. Simlation Data Figre 1 shows the grain size of riverbed material. The discharge for all simlation is 115 m 3 /s. The bondary of downstream model end is the water stage with the initial condition is at the normal depth. 3.. Simlation Scenario Fig.. Grain size distribtion of riverbed material The river bed deformations were compared by applying three conditions of bed-load transport spply at the pstream model. First condition is the bed-load spply which is same as the potential eqilibrim sediment transport rate, qb. The volme is 100% qb namely Case1. The second and third conditions are the bed-load transport that is more than qb. The bed-load transport spplies are 15% qb and 150% qb and named as Case and Case 3, respectively. The first case describes the river when there is no sediment spply from the pstream area. The second and third cases represent the river when the has sediment spply from deposited sediment at the pstream area. To evalate the bed deformation along the vicinity of bank slope, the changes of elevation near the bank toe are investigated. The grid is developed to represent the initial channel topography.

8 Pji Harsanto / Procedia Environmental Sciences 8 ( 015 ) Fig. 3. The grid of simlation (a) and initial riverbed topography (b) 4. Reslts and Discssions Figre 4, 5 and 6 show the long profile of the right bank toe in Case 1, Case and Case 3, respectively. The solid line indicates the initial elevation and the dash line indicates the elevation after 1 hor simlation. At the 00 m distance from pstream end model (see the circle dash line), comparing to Case 1, the bed degradation in Case and Case 3 is deeper. It may be de to the impact of a mid-channel bar growing at arond this station. It means that the possibility of river bank will not only collapse bt also increase. Arond station 600 m, the aggradations process de to sediment spply can be seen clearly..4 m (a) Elevation after 1 hor Fig. 4. Vertical change dring 1 hor on right bank toe with sediment spply 100 % qb 35.8 m Elevation after 1 hor Fig. 5. Vertical change dring 1 hor on right bank toe with sediment spply 15 % qb

9 156 Pji Harsanto / Procedia Environmental Sciences 8 ( 015 ) m Elevation after 1 hor Fig. 6. Vertical change dring 1 hor on right bank toe with sediment spply 150 % qb Figre 7, 8 and 9 show the long profile of the left bank toe in Case 1, Case and Case 3, respectively. On the left bank toe, the deformation is a similar phenomenon comparing to the right bank toe. Some locations are aggravated de to a large of sediment spply. Moreover, the occrrence of bed degradation is deeper than when the sediment spply is in eqilibrim condition. Elevation after 1 hor Fig. 7. Vertical change dring 1 hor on left bank toe with sediment spply 100 % qb Elevation after 1 hor Fig. 8. Vertical change dring 1 hor on left bank toe with sediment spply 15 % qb Elevation after 1 hor Fig. 9. Vertical change dring 1 hor on left bank toe with sediment spply 150 % qb

10 Pji Harsanto / Procedia Environmental Sciences 8 ( 015 ) Conclsions According to the simlation reslts, after the erption of Mt. Merapi in 010, Progo River has not only sedimentation problem bt also bed degradation. The bed degradation is the main parameter in bank erosion process. Frthermore, the changes of river morphology (bank erosion) shold be considered by the government to manage the river strctre, for example bridge abtment, revetment, and so on. Acknowledgements The athor appreciates to Prof. Masahar FUJITA, Associate Prof. Hiroshi TAKEBAYASHI and DPRI Kyoto University for their technical spport on nderstanding the nmerical model, MORPHOD. References 1. Takebayashi, H.,River Configration in Middle-Lower Reach of River Basin, Jornal of Japan Society of Flid Mechanics, Vol. 4, pp. 7-, Engelnd, F.,Flow and Bed Topography in Channel Bends, Jornal of Hydralic Div., ASCE, Vol. 100, No. HY11, Shimiz,Y. and Itakra,T., Calclation of Flow and Bed Deformation with a General Non-Orthogonal Coordinate System, Proc. of XXIVIAHR Congress, Spain, C-, pp.41-48, Nigata, N., Nmerical Analysis of the -Dimensional Unsteady Flow Using a Generalized Coordinate System, The Lectre Collection on the Compter Use in Hydralic Engineering, The Japan Society of Civil Engineers, pp , Takebayashi, H., Egashira, S. and Okabe, T.: Braided streams formed on beds with non-niform sediment, Proc. 3ndIAHR Symposim on River, Coastal and Estarine Morphodynamics, pp , Egashira, S. and Ashida, K.: Unified view of the mechanics of debris and bed-load, Advances in Micromechanics of Granlar Materials, (Edited by H.H.Shen et al.) Elsevier, pp , Ashida, K. and Michie, M.: Stdy on hydralic resistance and bed-load transport rate in allvial streams, Proc. of JSCE, No. 06, pp.59-69, Kovacs, A. and Parker, G.: A new vectorial bed-load formlation and its application to the time evoltion of straight river channels. J. Flid Mech. Vol. 67, pp , Iwagaki, Y.: Hydrodynamic stdy on critical shear stress. Proc. of JSCE, No. 41, pp. 1-1, 1956