ISSN 46-78 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
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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
DATA(.ctl) DSET rain.dat TITLE Rain Data St UNDEF -9999 XDEF 00 LINEAR YDEF LINEAR ZDEF LINEAR TDEF LINEAR JAN000DY VARS 0 99 00 Data Points ENDVARS + DATA(:rain.dat) X,Y,Z,Tim,RainData
SHER
ds dt imp = P D imp E imp
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
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
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
K i ij j q = S S t
i, j :,, K : ( L / T ) : ( L) S s : ( L ) Q : (/ T ) : ( L) t : ( T )
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 )( ) +!
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
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
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
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
V n i i K c ( c : ( lakanc) ) = ( K : d : ) d K c ( H ) = 0 : [L] H : [L] K : [L/T] (, = ) = ( ) t 0 H0
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
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
K = ij q d 0 i j 0 K d ij 0 0 0 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 0 4 5 0 4 5
y S y N S = i= b S i Si S=s y =n or S=bSs 0 4 5 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
( 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
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 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 S S S S S S S S S Q Q Q W Q Q Q W Q Q Q W = + = = + = = + =
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
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
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
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
[ ] = = 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 = +
[ 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
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 = = = = = = = 6 4 4 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
{ 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 0 0 0 4 0 0 0 = 4 S 0 0 0 0 0 0
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 )
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 )
H5
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)
+ (40)
E = 0.4D p 0 P t E p D0 Pt
0 0-0 -0-0 -40-50
(8) (7) () () (4) () (5) (6) (7) (0) (5) (4) (6) () () () (0) (9) () () () () (9) () (8)
4,5 6 9 ()
() () () () () () () () () () () ()
E = 0.4D p 0 P t E p D0 Pt
TECHNICAL NOTE of Marc 006 050804 TEL 09864675