1-D SEDIMENT NUMERICAL MODEL AND ITS APPLICATION. Weimin Wu 1 and Guolu Yang 2

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1 U-CHINA WORKHOP ON ADVANCED COMPUTATIONAL MODELLING IN HYDROCIENCE & ENGINEERING epteber 9-, Oxford, Miiippi, UA -D EDIMENT NUMERICAL MODEL AND IT APPLICATION Weiin Wu and Guolu Yang ABTRACT A one dienional edient nuerical odel UBED- ha been developed to predict the aggradation and degradation of riverbed baed on energy equation of the teady flow, nonunifor edient tranport equation for upended load and bedload, edient continuity equation and riverbed aterial copoition equation. An iproveent ethod to olve edient tranport equation of upended load ae the odel can get better reult for fat expanding or narrowing river reache and for the reache with lateral inflow. The odel ha been verified by field eaureent and the reult are generally fitted well in with the eaureent. The odel ha been ued in the deign wor of ore than 4 proect of hydropower and water reource.. INTRODUCTION To achieve the ot efficiency in reervoir deign, it i very iportant to predict the edient depoition and it affect on the engineering, and to adut the torage level and reervoir operation in accordance with the reult of prediction. Riverbed degradation downtrea of da due to large decreae of edient upply i alo conidered to alleviate poible engineering proble. A fater ore econoic and ore efficient tool, one dienional nuerical odel have been widely ued in the deign wor of reervoir with different cale to replace forer epirical prediction ethod. In preent paper, a one dienional nuerical called UBED- i developed baed on the energy equation of teady flow and edient tranport equation for both upended load and bedload. edient particle are divided into everal group according to their ize that have different etting velocity paraeter in related equation of edient tranport. Bed layer odel(wu,994 i introduced into UBED-, which can be ued to calculate edient depoition and riverbed cour, to iulate exchange between particle in flow and bed aterial. Han iwei(98 developed the equation of nonequilibriu edient tranport of upended load with nonunifor ize and got two analytical olution by the iplification of the equation repectively. Thi equation and it two olution are widely and well ued to olve edient tranport proble, but for fat expanding or narrowing river reache, the calculation of the two olution preent unreaonable reult becaue of it great difference between the iplification Aociate Profeor, National Key Laboratory of Water Reource and Hydropower Engineering, Wuhan Univerity, Wuhan, Hubei Province, 437 P.R. China. Phone: Fax: Eail: Jht@6.co Profeor, National Key Laboratory of Water Reource and Hydropower Engineering, Wuhan Univerity, Wuhan, Hubei Province, 437 P.R. China. Phone: Fax: Eail: ygl56@ina.co.cn

2 and real condition. An iproved ethod to olve the nonequilibriu edient tranport equation i developed in UBED-.. GOVERNING EUATION The baic one dienional equation for teady flow and for nonequilibriu edient tranport procee can be expreed a following(yang,994: Continuity equation for water q ( Energy equation for water Z g x A n A R 4 3 ( Continuity Equation for edient ( A G ( p q qb (3 t Nonequilibriu edient tranport Equation for upended load ( ( q αω B (4 For bedload both equilibriu nonequilibriu edient tranport Equation are conidered, the equilibriu equation i And the nonequilibriu equation i G G (5 G K t ( G G qb (6 Riverbed aterial copoition equation(wu,994 ( H P ( t ( p B G Z H [ ε P ( ε Po ] (7 t t In above equation water dicharge; Z, A, R and Bwater level, flow area, hydraulic radiu and width, repectively; xditance along channel; ggravitational acceleration ; nmanning coefficient of roughne; q l, q q b lateral water inflow, upended load and bedload dicharge in

3 3 unit length, repectively, for ingle channel ub-reache, q l, q, q b ;, edient concentration and edient capacity by volue, repectively; G and G bedload dicharge by volue for equilibriu and nonequilibriu tate, repectively; p poroity of edient in bed layer; ω etting velocity; α the aturation recovery coefficient for upended load; K t the aturation recovery coefficient for bedload; P bed layer copoition at any tie; P o original bed layer copoition; Z bed level; H thicne of bed layer; during calculation, ε when bed level lower than original river bed due to cour and ε in other cae. ubcript denote the ize group equence for nonunifor edient. For total upended load and bedload, there exit following relation: (8 (9 G G G ( ( G 3. NUMERICAL CHEME Eq. and 3 are dicretized a follow i i l ( Z xn 4 / A R g A A Z 3 [ ψ A ( A ] x ( G G t ( p ψ (3 (4 in which x length increent and ection equence along ditance, A and A are depoition or cour area in ection and repectively, weighting factor Ψ >. 5, A and R are expreed a (5 ( Ψ Ψ A (6 ( Ψ A ΨA R (7 ( Ψ R ΨR

4 4 To get A at inlet ection both for ain channel and for branche, which hould be ( deterined before the olution of Eq.4, ubtitute G and into Eq.3 with Eq.4 and 6, Eq.3 i changed to A ( p αω B( K ( G G (8 t Eq.8 decribe the relation of variable in ingle ection, o it can be directly dicretized a t γ ' [ αω B ( K ( G G ] A (9 For the calculation of depoition area of cro-ection, Eq.8 i ued at inlet ection and Eq.4 for other ection The olution(yang, 994 of Eq.6 i ψ In which G Eq.7 i dicretized a G G K t x Kt x ( G G e q ( e ( G b x K t G T ( P H B ( ψ ( P ( H B ψ εp ε x ( ψ εp ( ε P A H B [ ] ( t [ P ] ( A H B G T G G ( ( ( ( n ( P A ( P A ( P A n (3 4. UPENDED LOAD CALCULATION Eq.4 can bed written a: α Bω ( q αbω (4 It i a firt order linear differential equation and it general olution i

5 5 P e Fe P C (5 In which P ( αbω (6 And F ( q αbω (7 Ue the boundary condition to eliinate contant C, i.e. P P e F e C x x, When x (8 o, Eq.5 becoe ( P [ F ( P ] x exp P exp exp (9 x In which i the edient concentration at x. Generally it i ipoible to integrate above equation becaue of variation of river width B and edient capacity with ditance x. Han iwei(994 ha developed the iplified olution of Eq.9 for the iple ub-reache without lateral inflow, in which and q. By auing unit flow dicharge q contant and B linear variation of with x, Eq.9 i integrated a αω x αω x q q ( q ( - e e (3 αω x In which, x pace interval, and are edient carrying capacity at x and x repectively, by auing qcontant and contant, Eq.9 i integrated a ( - αω x q e (3 In which i average edient carrying capacity in ub-reach. The early verion of ubed- ue Eq.3 to calculate edient tranportation of upended load. A it i pointed out in the introduction, iproveent of Eq.3 and 3 i neceary for fat expanding or narrowing river reach, in which there exit great difference between real ituation and Han auption about q and. A new ethod i developed to iprove Han olution a well a to apply it to the ub-reach with lateral inflow.

6 Although river width B i generally uncertain for natural river, calculation ection can be choen carefully to eep it onotone variation in each ub-reach. In thi cae B can be generalized a linear variation in the reach becaue of it not very long ditance, i.e. ( B B x B B (3 x In which B and B are river width at upper and lower ection of the ub-reach repectively. o Eq.6 and 7 becoe ( B B x αω B (33 x P q ( B B x αω B x (34 F P In Eq.9 can be integrated for two cae ( For reache without lateral inflow, i.e., ql and q 6 αω B P B x B x x C (35 ( For reache with lateral inflow, i.e., ql and q In which And P B B αω ( M ln C3 (36 x M αω x( B B ( (37 ql x (38 In UBED- ipon rule i adopted to ae nuerical integration of Eq.33, becaue it i difficult to get it analytical olution for above both cae. can be calculated by the interpolation value of related hydraulic factor and Han auption of linear variation of i not longer needed. 5 UPPLEMETAY RELATION AND PARAMETER edient carrying capacity i calculated in following forula (Yang,994

7 7 β ( d ( d i unifor edient carrying capacity. According to Zhang Riin(997, ( d expreed a ( d K V 3 i (39 grω (4 V i ean ection velocity, K and are paraeter that are deterined by eaureent data, it i uggeted that K.4 and.5 baed on the calibration with field eaureent data fro Gongzui, which will be introduced in following. Coefficient β i expreed a p αω K β (4 p α ω In which p i edient copoition of ize group of bed-aterial, α for cour and α.5 for depoition. Bedload dicharge for each ize group G i calculated by G p Bgb ( d (4 In which g b (d i bed load rate by volue and i calculated by Meyer-Peter(948 and Muller forula. The value of K t in Eq.6 i.. The thicne of bed layer H i etiated a for reervoir and i calculated in other cae by In which H i water depth and H Cu H (43 C u VERIFICATION AND APPLICATION The filed eaureent data fro Gongzui i choen to verify UBED-. Gongzui Reervoir on Daduhe River, a ub-branch of upper Changiang River in ichuan Province of China, wa built up in 97 and eaureent in the reervoir wa begun in 967. Fro 977, forer Minitry of Water Reource and Electric Power choe it a ey reervoir for eaureent and cientific invetigation. Meaureent ite include ection along 4.37 long ditance, bed aterial aple and analyi, water level at poition and eaureent of outlet of water and edient fro the reervoir. In upper reach of the reervoir there exit a foral hydrological tation, which control inlet of the reervoir. The calculation period i nearly year fro May, 977 to Dec.3, 986 and the initial ection of the reervoir i eaured in April 977. The average runoff of upended load i

8 t and average concentration of upended load i.84g/ 3. Average bedload runoff 6 i etiated a.88 t baed on flue experient by forer Chengdu Intitute of Invetigation and Deign. The value of p i.47. Part of reult i given in coparion with eaureent in Table, and Figure, repectively. Calculation reult are generally well fitted in with the field data in conideration of accuracy of eaureent. Table Coparion of Yearly Depoition Volue Year Meaureent ( Calculation ( Relative Error (% -5.6%.% 6.6% 5.7% 3.9% 6.% 7.5%.% 7.6%.6% Table Coparion of Yearly Average Outlet edient ize Year Meaureent D Calculation ( Elevation ( eaureent 48 Calculation initial Ditance for Da ( 5 Figure Coparion of Longitudinal Profile in Nov. 98

9 Elevation ( eaur eent calculation Initial Ditance fro Da ( Figure Coparion of Longitudinal Profile in Nov. 986 In 996 the expert for forer Hydropower and Water Reource Planning and Deign General Intitute of the Energy Minitry of China exained calculation reult for everal proect by UBED- and gave a poitive appraial. After that the odel ha been widely ued to calculate river deforation in deigning wor for hydropower proect a a ethod to evaluate influence of edient proble on the engineering after built-up of da. A one of recoended edient nuerical odel in edient Deign tandard for Water Reource and Hydroelectric Engineering (DL/T China, a any a 5 different deign intitution up to now have ued UBED- in the deigning wor of ore than 4 proect of hydropower and water reource, including 8 in Jinhaiang River, the upper reach of Changiang River and in the upper of Yellow River UBED- i alo copiled to Dynaical Energy Deign Manual (edient ubdiviion, which i about to be publihed by Minitry of Water Reource. 7. EXAMPLE One of application of UBED- i to calculate edient depoition of three huge hydropower proect, which are Baihetan, Xiluodu and Xiangiaba fro upper to lower repectively in lower reache of Jihaiang River, and to analyze their influence on reduction of input edient of Three Gorge reervoir, which i in lower of Jinhaiang and 433 long fro Xiangiaba. The torage capacity of 4 reervoir i lited in Table 3. The calculation are carried out for year in the auption that three Proect begin to operate at the ae tie. Table 3 The torage Capacity of 4 Proect Proect Baihetan Xiluodu Xiangiaba Three Gorge Capacity of Reervoir ( The reult in Figure 3 how that depoition in Baihetan will not reach balanced tate until year later, and that for two other lower proect reervoir life can lat uch longer.

10 6 Depoition Volue ( Baihetan Xiluodu Xiangiba Tie (Year Figure 3 Depoition Volue in Three Reervoir 8 The outlet of Jinhaiang will delivery yearly.47 ton of edient to the lower river before the contruction of the three Proect. All of the edient will enter into Three Gorge 8 reervoir and 53.4% of input edient of Three Gorge, which i about ton yearly, i coe fro Jinhaiang. When the Three proect begin to operate ot of edient and nearly all of the edient with the ize greater than.5 are intercepted in the reervoir. The decreae of edient into the Three Gorge reervoir are given in Table 4 without conidering edient recovery between Xiangiaba and inlet of the Three Gorge reervoir. Table 4 Three Reervoir Delivery edient and Reduction of Three Gorge Input edient Output edient Yearly Average Reduction Fraction Accuulated Reduction of Year edient Delivery Reduction of of Tree Gorge Input Three Gorge in year Ratio Output edient Input edient edient in Year ( 年 ( 8 t (% ( 8 t (% (% ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

11 REFERENCE Han,. W, (98. A tudy on the Non-equilibriu Tranportation of upended Load, Proc. Int. yp. On River edientation, Vol. (Beiing China, pp Meyer-Peter, E. and Muller, R. 948 Forula for Bed-Load Tranport. nd IAHR Congre, tochol, 948. Wu, W. M. and Yang, G. L, et al, (994. Nuerical Modeling for the Copoition of Graded River Bed-aterial, Journal of Wuhan Univerity of Hydraulic and Electric Engineering, No.3, pp (in Chinee. Yang, G. L. and Wu, W. M, et al, (994. UBED- One Dienional Non-equilibriu edient tranport Model, Journal of Hydraulic Engineering, No.4,pp. - (in Chinee. Zhang, Riin, (997, River edient Dynaic, China Waterpower Pre, Beiing.