IMPROVED CONVERTING PERMEABILITY COEFFICIENT METHOD AND VARIABLE PERMEABILITY COFFICIENT METHOD FOR SEEPAGE CALCULATION IN KARST REGION

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1 4 8 ol.4 No Chins Journal of Rock Mchanics and Enginring April005 ( ( Colbrook ( Galrkin TU 457 A ( IMPROED CONERTING PERMEABIITY COEFFICIENT METHOD AND ARIABE PERMEABIITY COFFICIENT METHOD FOR SEEPAGE CACUATION IN ARST REGION ZHAO Jian AI Miao SHEN Zhn-zhong (. Hohai UnivrsityNanjing 0098China. Shanghai Flood Risk Inforation CntrShanghai 0000China AbstractBasd on suarizing all kinds of thods usd to calculat karst groundwatr spagaiing at th spag charactristics in karst rgion two thods considring Darcy and non-darcy fluid siultanously ar put forward( iprovd convrting prability cofficint thod. In this thoda forula suitabl for solving th stra wis had loss cofficint of thr turbulnc zons is dducd fro Colbrook C. F. forulawhich can intgrat flows in karst conduits with voids as wll as cracks and ( variabl prability cofficint thod. It prsss th prability cofficint of karst conduits as th function of watr had to b solvd and th ponnt of flow rgiwhich can intgrat th non-darcy flow in karst conduits with th Darcy flow in othr dia. To ovrco th disadvantag of convrting prability cofficints thodth forulas to calculat tnsor of karst conduit in global coordinat syst ar dducd. According to th basic diffrntial quation for karst spagth finit lnt thod(fem quations applid for calculating karst spag ar dvlopd on th basis of Galrkin FEM. rifid by aplsth two thods ar rasonabl and fasibl. y words rock chanics dynaics of spag karst spag iprovd convrting prability cofficint thodvariabl prability cofficint thod ( E-ailyangz@iwhr.co

2 4 005 H (ε (/sµ S (/st (s ( R Darcy-Wisbach l u hf ( d g [] [] h [4] f ( ( l (d (u [5] [6] (/sg (/s n nu u J hf l ( l Jl (4 ( d g gd J (5 ( ( gd (6 ( ( R Nikurads R / R (7 00R / R (8 R R [6] ((8 [6] J ( (/s (/sj ( R R [78] ( u R ( R * v ( u* u * u 8 u v u * v H u* u* ( ( R H + ε µ S ( t

3 Colbrook [8] [6] Colbrook lg + (9 d R. d Colbrook / d [9] R Colbrook [0] ( lg (0 R CJ (5 R (9 / d C Colbrook ( (5 [9].74 lg ( y z d y z h hy h C ( + + z (6 Colbrook h Colbrook (6 y z h.5 [9] y z.74 lg + ( 0. 9 d R ((7 ( (6 y z 64 ( ( R 0 ( R ( lg ( ( R 0 y z d R (4 o y o y 0 0 ( (4 (6 h hy h C( + + (7 (4 ( ( 4 ( J (8

4 { cos β } { cos cos β } { } cos cos β ( M [6] ( y ( z M ( y z ( o cos ( + ( y y + ( z z y y cos β ( ( ( + ( y y + ( z z z z ( + ( y y + ( z z o y o o o y o MM o T o y 0 T ( k ] o diag( 0 0 ( [ cos + cos β + 0 (6 o y a cos b cos β c a 0 oyz oyz [k] o b a ac a diag( 0 0 a a + b a + b a bc [ Q ] b (7 o o y o oyz a + b a + b o o y c 0 a + b o b 0 c 0 i (i ( [k [ ] ] I o o y ( i o T [ k] I[ Q] diag( ] [ o oyz [ Q ] k (0 [ k ] Q ( T I [ Q][ k] o[ ] T X 0 (5 4 ( kij i h h SS (8 j t

5 h S k t S ij (8 (8 kij ( kij ( kij (a kij (8 Galrkin h p γ + z [] P [ ]{ P} + {[ S] + [ G]} { F} (9 t [] {P} [S] [G] {F} (b y 0.5 ( Fig. Sktch ap of cor wall da t h (z 0 4 ( y C 0 y (a(c 07 h R R 00 R 0 R R 0 6 [6] 07 h 5 C.0 /s (b(d ( y.0 ( y h 4 h 07 h /s µ (c(d 0.05 SS 0 v.40 6 /s 8.0 (.0.0

6 R/0 7 R/0 6 R/0 6 R/ (a t (b t 4 h (c t 48 h (d t 7 h y/ y/ y/ (a ( (b ( Fig. Rnault nubr of karst tub (c ( 7.0 t h y/ (d ( ( y 0.5 c Fig. Maps of calculation rsults(sction of y 0.5 /s c /s C 6 C ( C

7 (Rfrncs [6]. [J]. 9950(4666.(Chn Chongi. []. [J]. 99 ( 59.(Song HanzhouWang Jianping. Study on karst lakag probl in Biankng rsrvoir[j]. Carsologica Sinica99 Groundwatr flow odl and siulation thod in tripl dia of karst tub-fissur-por[j]. Earth Scinc9950(4666.(in Chins (59.(in Chins [7]. [M]. 00.(Yu Bu. [] Hydraulics[M]. GuangzhouSouth China Univrsity of Tchnology. [J]. 984( Prss00.(in Chins 9.(Xu Yuqun Zhang Youkuan in Jiayong. Application of dual 000.(i Wi Xu Xiaoping. Hydraulics[M]. Wuhan Wuhan dia flow odl and its Ritz finit lnt solution in forcast of Univrsity of Hydraulic and Elctric Enginring Prss000.(in in groundwatr discharg[j]. Hydrogology and Enginring Chins Gology984(9.(in Chins [9]. [J]. []. [J]. 9976(758.(Ding Shiqun [8]. [M]. 990 ( (Ding iuqianxu Guoan. Finit lnt analysis of thr-dinsional non-darcy spag flow[j]. Journal of Hydraulic Fu Ruijin. Analysis on karst dvlopnt and spag in th auiliary Enginring990(04954.(in Chins da ara of th uppr rsrvoir of angyashan pupd storag hydro- [0]. [M]. plant[j]. Carsologica Sinica9976(758.(in Chins 000.(Gu Wici. Spag Calculation Thory and Its Application[M]. [4]. [J]. BijingChins Building Matrial Industry Prss000.(in Chins 996 ( 9095.(Zhou HongwnZou Chngji. Rsarch []. [M]. 987.(i on karst lakag of Mapantang rsrvoir[j]. Guizhou Gology996 (9095.(in Chins JuntingWang Yuji. Groundwatr Dynaics[M]. BijingGological [5]. [J]. Publishing Hous987.(in Chins 99 ( (Xia Riyuan Guo Chunqing. Study []. [ ][D]. on th thod of unit-ntwork athatic siulation(unms of 00.(ai Miao. Study on spag charactristics and karst groundwatr syst[j]. Carsologica Sinica99(4 calculation thods in karst rgion[m. S. Thsis][D]. NanjingHohai 6776.(in Chins Univrsity00.(in Chins

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