4 8 ol.4 No.8 005 4 Chins Journal of Rock Mchanics and Enginring April005 (. 0098. 0000 ( Colbrook ( Galrkin TU 457 A 000695(00508407 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 0006 00090 (958 98 E-ailyangz@iwhr.co
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 00 64 / R (7 00R0 000. 0.5 0.6 / R (8 R 0 000 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
4 8. 4 Colbrook [8] [6] Colbrook 4 8.7.74 lg + (9 d R. d Colbrook / d [9] R Colbrook [0] ( 8.7.74 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 (6.5.74 lg + 0.9 ( ( R 0 y z d R (4 o y o y 0 0 ( (4 (6 h hy h C( + + (7 (4 ( ( 4 ( J (8
44 005 { 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 (4 0 0 0 k ] o 0 0 0 diag( 0 0 (9 0 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
4 8. 45 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 0 4487 h (z 0 4 ( 0 69.0 y C 0 y.0 0.0 (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 0.5.0 04 h 4 h 07 h.0 5.0 7.4 0 5 /s µ 0.0500.0 (c(d 0.05 SS 0 v.40 6 /s 8.0 (.0.0
46 005 R/0 7 R/0 6 R/0 6 R/0 6.84.8.80 0 0 0 0 40 50 60 70 (a t 0 5.95 5.90 5.85 0 0 0 0 40 50 60 70 (b t 4 h.04.0.00 0 0 0 0 40 50 60 70 (c t 48 h.605.600.595 0 0 0 0 40 50 60 70 (d t 7 h y/ y/ y/ (a ( (b ( Fig. Rnault nubr of karst tub (c ( 7.0 t 0448 7 h 780.90.7645.48.90 y/ (d ( ( y 0.5 c Fig. Maps of calculation rsults(sction of y 0.5 /s 670.59.9845.8.89 c /s C 6 C ( C
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