国土技術政策総合研究所　研究資料

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1 ISSN TECHNICAL NOTE of National Institut for Land and Infrastructur Managmnt No. Marc 006 Rsarc on Groundwatr Modl Rport Rivr Dpartmnt National Institut for Land and Infrastructur Managmnt Ministry of Land, Infrastructur and Transport, Japan

2 006 * ** *** **** ***** 7

3 Tcnical Not of NILIM No. Marc 006 Rsarc on Groundwatr Modl Rport Nario Yasuda* Masaki Kawasaki** Masaiko Muras*** Yosuk Tomizawa**** Masazumi Amakata***** Synopsis Tis rport mad up contnts of rsarc on t groundwatr modl. Ky Words groundwatr, groundwatr managmnt, data bas, watr circulation ******* ******* ******* ******* ******* Had, Watr Managmnt and Dam Division, Rivr Dpartmnt, NILIM Snior Rsarcr, Watr Managmnt and Dam Division, Rivr Dpartmnt, NILIM Cif, Planning Division, Planning and Rsarc Administration Dpartmnt, NILIM Rsarcr, Watr Managmnt and Dam Division, Rivr Dpartmnt, NILIM Gust Rsarc Enginr, Watr Managmnt and Dam Division, Rivr Dpartmnt, NILIM

11 DATA(.ctl) DSET rain.dat TITLE Rain Data St UNDEF XDEF 00 LINEAR YDEF LINEAR ZDEF LINEAR TDEF LINEAR JAN000DY VARS Data Points ENDVARS + DATA(:rain.dat) X,Y,Z,Tim,RainData

23 SHER

24 ds dt imp = P D imp E imp

26 ds dt ds dt U E = s D s = P E R I U s + P a ds dt g = R D g P a

28 T + T K T R = 0 k r ( θ ) dt K 0 k r T + T K I kr( T I = 0 θ ) sdt K0I kr

29 k r kr k ( θ ) θ θ r = θ 0 θ r k K 0k r ( θ ) n = k K 0I k r ( θ ) = K 0 K 0I θ θ 0 θ r

32 K i ij j q = S S t

33 i, j :,, K : ( L / T ) : ( L) S s : ( L ) Q : (/ T ) : ( L) t : ( T )

34 control volum v z + vz z z v y + v y y y v z v + v z y v y v z y yz v control volum v Istok v Taylor ρv +! ( ρv ) + ( ρv )( ) + ( ρv )( ) +!

35 ρv + ( ρv) sinksourc q ρv y z+ ρv z + ρv y y z ρv ρv + ρq y z = t ρv y ρvz y z+ ρvy + y z ρvz z y y + + z ( ρ S n) w y z Sw q q ρv ρv y ρvz ρq = ( ) y z t ρ Swn t ( ρ ) = 0 S w n ρv ρv y y ρv z z ρq = 0 Darcy Darcy v K v K v K =, y = y, z = z y z

36 v v v K K K K K K K K K y z y z y z y yy yz z zy zz = Ky=KyKyz=KzyKz=Kz v ( ) ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ K K y K z y K K y K z z K K y K z q t S n y z y yy yz z zy zz w = ( ρ ρ ρ K q t S n i ij j w = ) ), :, : (:,,,, z y j i = ρ ρ ρ K K K i ij j i ij ij i ij j = + ρ ρ K K i ij j i ij j = /t ( ) ( ) ( ) ( w w w w S t n t n S n t S n S t ) ρ ρ ρ ρ + + = ( ) n t

37 n z = t t ( ) ( z n ) = n σ α( ) ( σ : ) n = α t ( n) σ z t σ z t n = α t n ( n) Sw t ( ρ) z z p = t p t constant βρ = ρ p ρ p = ρβ t t ( n) α = n σ z

38 t ( S w ) Sw p = 0 t t = ρg t K i ij q = j p ρg = S S t t t [ α( n) + βn] = [ α( n) + βn] n t ( ) ( ) t, = H t, H b b Kij ni = V ( i, t) j

39 V n i i K c ( c : ( lakanc) ) = ( K : d : ) d K c ( H ) = 0 : [L] H : [L] K : [L/T] (, = ) = ( ) t 0 H0

40 K i ij j q = S ( ) ( ) t, = H t, b Kij ni = V ( i, t) j (, = ) = ( ) t 0 H0 S t yz = 0 Dupuit-Forcimr z

41 u w q s q s dz = k = k sin β k β β ds d sin β tan β = qs u w d d u = k d

42 K = ij q d 0 i j 0 K d ij i j i T ij T ij ( ) qd = Kij 0 ( ) Q j = S S d dz dt d SSdz dt d = qd S 0 0 = S d S t ( ) Q( ) = S( ) T + T y + T y y y + T yy Q = S y t K T

43 y S y N S = i= b S i Si S=s y =n or S=bSs q Q q Kij d ni = V ( i, t) 0 0 T ij j ( ) ni = j 0 V (, t) V Q Tij ( ) ni = Q( i, t) j i i T ij = S + Q j t

44 ( y) = α + β + γy, (, y ) = = α + β + γy (, y ) = = α + β + γy (, y ) = = α + β + γy α β, γ, α = y / D β = y / D y y y y

45 D / = γ = = F y y y D F C y y B y y A C y y B y y A C y y B y y A = = = = = = = = = ( ) ( ) ( ) ( ) ( ) D y C B A y C B A y C B A y /, = ( ) ( ) D C C C k y k v D B B B k k v f f y f f / / + + = = + + = = S S S Q Q Q W W W 0 = + + S S S Q Q Q S S S S S S S S S Q Q Q W Q Q Q W Q Q Q W = + = = + = = + =

46 S S S Q Q Q W W W ( ) m y y v v Q y S = ( ) m y y v v Q y S = ( ) m y y v v Q y S = ( ) ( ) ( [ ] ) ( ) ( ) ( [ ] ) ( ) ( ) ( [ ] C C B B C C B B C C B B D T W C C B B C C B B C C B B D T W C C B B C C B B C C B B D T W = = = ) ( ) ( ) D T C C B B E j i j i ij / + = = = j i ij i E W

47 i k y i y k ( i) k = n, (, i) i k W i W k k = n(, i) W k A, B, C i i i A i A k B i B k C i E ij C k = n(, i) l n(, i) k E ij E kl = ( k, l) A k = B k = C k = E kl = 0 W k = n l= E kl l Wk Q E ij = 0

48 Wk M = W k Q k ( ) = 0 k =,, LN M N = l= E kl l Q k = 0 N M l= = E kl l Q k = 0 ( k =, LN) N l= a kl. l Qk = 0 ( k =, LN) L,y,t N N N, T ij Q S i j t N ( ( y, t) ) L ( (, y, t) ) 0 L N WRM R L N ( (, y, t) ) W (, y) dr = 0 W W n n,,y n W W W N Galrkin

49 W = 0 dr W t S Q T n R N j N ij i W = 0 dr W t S QW W T R n N n n j N ij i N N = 0 j N i Tij = 0 i ij T dr T W dr W T dr W T R j N ij i n R n j N ij i R n j N ij i = Gauss dl n W T dr W T i L j N ij n R n j N ij i = = R L i n j N ij n j N ij dl n W T dr W T div Q n i ( )( ) = L R n R n N R j N ij i n i n j N ij dr W Q W dr t S dr T W dl n W T 0 N y N Q Q

50 [ ] = = i= N i n N y N n i N ij n dl Q W dl Q Q W dl n t T W L L L N 0 = = = = W dr t N S QW dr dl Q W dr N T W n R R M m m m n L i N i n R j M m m m ij i n R R ( ) ( ) ( ) ( ) ( ) ( ) = Elmnts Num R N R N dr y W t y L dr y W t y L.,,,,,, 0 = = = = n R R M m m m n L i N i n R j M m m m ij i n dr W t N S dr QW dl Q W dr N T W [ ] 0. = = = = = n R R M n m m n L i N i n R j M m m m ij i n Num Elmnts dr W t N S dr QW dl Q W dr N T W m [ ]{ } [ ] { } { } m m m nm m nm D Q dt d F A = +

51 [ Anm ] = [ Anm ] = Num. Elmnts = Num. Elmnts = R W i n T ij N m j dr { Q } = { Q } m = Num. Elmnts Num. Elmnts = m Wn N m = L i= { D } = { D } = m Num. Elmnts Num. Elmnts = R = QW m m dr [ Fnm ] = [ Fnm ] = Num. Elmnts Nujm. Elmnts = R = SN m W n dr Q i dl N WGalrkin T T T T = T l N l l T Q S S = S l N l l FNuman Lumpd Mass Mtod S

52 W=N NdR NNdR NNdR N dr b N z dr c N N dr bb N N z dr bc N z N j R i j R i i R i i R i i R i j i j R i j i j R i j = = = = = = = z dr cc i j R = 4 [ ] { } j i yy i j y j i y j i R j yy i j y i j y i j i ij c c T c b T b c T b b T dr y N T y W N T y W y N T W N T W A = = 4 [ ] = 4 b c b c b c b c b c b c b c b c b c T c b c b c b c b c b c b b c b c b c T c c c c c c c c c c c c c c c c c c T b b b b b b b b b b b b b b b b b b T A y y yy ij Ty=Ty [A] [ ] = 4 b c c b b c c b b c c b b c c b b c c b b c c b b c b c b c b c b c b c T c c c c c c c c c c c c c c c c c c T b b b b b b b b b b b b b b b b b b T A y yy ij

53 { Q } W N ( Q + Q ) j ( L( Q + Q ) = i j j yj dl = L j yj j { D } j = QWi dr R Q = [ F ] ij = SN jwi R dr = S lumpd matri [ ] F ij = 4 S = 4 S

54 d + } dt m [ Anm ]{ m} [ Fnm ] = { Q n } { D n d + } dt m [ A nm ]{ m} [ Fnm ] = { C n t = t k + k + [ F ] + ω[ A ] { } nm k + { } k k k k [ F ] ( ω )[ A ] { } + ( ω ){ C } + ω{ C } nm nm nm k + m m n n k+ k+ GWAP k+/ k+/ t t/ t = t k + [ ] / k + F + ω[ A ] / { } nm k + [ ] / k + / ( )[ ] / k k + F ω A { } + { C } nm nm nm k + m k+/ t k + / m k + / m k = k m k m = t + t k m t m k m k k k k ( k m m n )

55 k + / m k + m t = k k k ( + ) + m m k m = k m t k m k k k + k t k k m = m + ( k m m t )

57 H5

59 7/90 6/70 /70 /445 6/45 5/950 5/50 4/890 4/500 4/50 /905 /00 9/60 8/85 8/75 7/765 0/050 9/860 (00m) (00m)

61 + (40)

63 E = 0.4D p 0 P t E p D0 Pt

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126 (8) (7) () () (4) () (5) (6) (7) (0) (5) (4) (6) () () () (0) (9) () () () () (9) () (8)

127 4,5 6 9 ()

128 () () () () () () () () () () () ()

129 E = 0.4D p 0 P t E p D0 Pt

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145 TECHNICAL NOTE of Marc TEL

1 (Berry,1975) 2-6 p (S πr 2 )p πr 2 p 2πRγ p p = 2γ R (2.5).1-1 : : : : ( ).2 α, β α, β () X S = X X α X β (.1) 1 2

1 (Berry,1975) 2-6 p (S πr 2 )p πr 2 p 2πRγ p p = 2γ R (2.5).1-1 : : : : ( ).2 α, β α, β () X S = X X α X β (.1) 1 2 2005 9/8-11 2 2.2 ( 2-5) γ ( ) γ cos θ 2πr πρhr 2 g h = 2γ cos θ ρgr (2.1) γ = ρgrh (2.2) 2 cos θ θ cos θ = 1 (2.2) γ = 1 ρgrh (2.) 2 2. p p ρgh p ( ) p p = p ρgh (2.) h p p = 2γ r 1 1 (Berry,1975) 2-6

国土技術政策総合研究所 研究資料

国土技術政策総合研究所　研究資料