topic 2 steady state flow through soil
DESCRIPTION
TOPIC 2 STEADY STATE FLOW THROUGH SOIL. Course: S0705 – Soil Mechanic Year: 2008. CONTENT. PERMEABILITY / CAPILARITY (SESSION 7 : F2F) SEEPAGE (SESSION 8 : F2F) FLOW NET / JARINGAN ALIRAN (SESSION 9 – 10 : F2F). SESSION 7 PERMEABILITY / CAPILARITY. INTRODUCTION. DEFINITION : - PowerPoint PPT PresentationTRANSCRIPT
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CONTENT
• PERMEABILITY / CAPILARITY (SESSION 7 : F2F)• SEEPAGE (SESSION 8 : F2F)• FLOW NET / JARINGAN ALIRAN (SESSION 9 – 10 : F2F)
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INTRODUCTION
• DEFINITION :THE VELOCITY OR THE CAPABILITY OF WATER/FLUDI PASS THROUGH POROUS MEDIA
• NOTATION : k
• UNIT :m/s, cm/s
• PURPOSE :– To evaluate the seepage through dam– To evaluate the uplift force or seepage force under hydraulic structure for
stability analysis– To control seepage velocity– To determine the consolidation time rate
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– LABORATORY• CONSTANT HEAD (TINGGI KONSTAN)• FALLING HEAD (TINGGI JATUH)
– FIELD• UNCONFINED AQUIFER (AKIFER BEBAS)• CONFINED AQUIFER (AKIFER TERKEKANG )• INCONSTANT WATER HEIGHT (TINGGI AIR TIDAK TETAP)
DETERMINATION OF PERMEABILITY COEFFICIENT
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CONSTANT HEAD (TINGGI KONSTAN)
– SUITABLE FOR SANDY SOIL, SAND OR GRAVEL WHICH HAVE BIG VOID RATIO VALUE
– BASIC EQUATION :
A.h.tQ.Lk
.tLhk. A. A.(k.i).t A.v.t Q
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FALLING HEAD (TINGGI JATUH)
– MORE ECONOMICAL FOR LONG TERM TEST– BASIC EQUATION :
2
1ln..
..-
.....
-
dtdh-v
hh
tALak
LhkA
dtdhaqq
LhkAikAvAq
dtdhaq
keluarmasuk
keluar
masuk
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UNCONFINED AQUIFER (AKIFER BEBAS)
2122
1
2
1
2
21
22
.
ln.
ln
.....2..
hhrrQ
k
rrhhkhr
drdhkQ
Q
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RANGE OF k VALUE
C is coefficient of soil roughness (published by Hazen), the value range from 40 to 150 i.e. as follow :
C Sand (one or all of the next characteristics)
40-80 Very fine, well graded or contain some fine particle
80-120 Rather rough, poor graded or clean, rough and well graded
120-150 Very rough, very poor graded, contain gravel and clean
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EQUIVALENT COEFFICIENT OF PERMEABILITY OF LAYERED SOIL
– Equivalent Coefficient of Vertical Permeability (kv’) – Equivalent Coefficient of Horizontal Permeability (kh’)
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Equivalent Coefficient of Vertical Permeability (kv’)
Basic Concept – qin = qout
– v constant
n
nn
2
22
1
11 H
h.k...Hh.k
Hh.ki'.kvv
vh
kH.....
vh
kH;
vh
kH;
vh
kH n
n
n3
3
32
2
21
1
1
n
n
3
3
2
2
1
1n321
kH...
kH
kH
kH
vh...
vh
vh
vh
LH...HHH n321
Lh'.kvv
n
n
3
3
2
2
1
1k
H...kH
kH
kH
L'kv
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Equivalent Coefficient of Vertical Permeability (kv’)
ikhLvAq average '...
i.H.k...i.H.ki.H.ki'.kh.L nn2211
LH.k...H.kH.k'kh nn2211
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EXAMPLE 1
21t hhh
1
1
1 Lh.k
Aq
SECTION 1
k.AL.qh1
11
2
2
2 Lh.k
Aq
k.AL.qh2
22
k.AL.q
k.AL.qh
2
2
1
1t
SECTION 2
TOTAL
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EXAMPLE 2
Section 11111 A.i.kq
Section 2
2222 A.i.kq
25.4050.02.01
hq 25.
405.007.02
hq
21 qq )5.(007.0)50.(02.0 hh
h = 38.33 cm
Determination of h
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EXAMPLE 2
1111 A.i.kq 2222 A.i.kq
25.4033.3850.02.0
q
Determination of water flow rate
or
q = 0.15 cc/s
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INTRODUCTION
• DEFINITIONVOLUME OF WATER/FLUID FLOW IN OR FLOW OUT AT A MEDIA OR CERTAIN SOIL MASS
• PURPOSE– TO DETERMINE THE INFLUENCE OF SEEPAGE TO THE STABILITY
OF STRUCTURE OR DAM– TO ESTIMATE THE FLOW VELOCITY AND FLOW RATE AT
DEWATERING WORK
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WATER FLOW EQUATION
– BASIC OF THEORY• DARCY LAW
• BERNOULLI LAW
• CONTINUITY EQUATION
i.kv Lhi
tconsAvAvq tan.. 2211
2w
222
1w
121 z.g
g.p
g2vz.g
g.p
g2v
= constant energy
ni.k'v
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WATER FLOW EQUATION
dxdyvdxdzvdydzvq zyxlow inf
Inflow water per time unit:
Outflow water per time unit:dxdydz
zvvdxdzdy
yv
vdydzdxxvvq z
zy
yx
xoutflow
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WATER FLOW EQUATION
dtdVdxdydz
zv
yv
xv zyx
qinflow = qoutflow
te
eo11
tW1
zv
yv
xv w
w
zyx
CONTINUITY EQUATION
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WATER FLOW EQUATION
0te
0zv
yv
xv zyx
STEADY STATE CONDITION:
WATER FLOW VELOCITY :
zhkikv
yhkikv
xhkikv
zzzz
yyyy
xxxx
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WATER FLOW EQUATION
0zhk
yhk
xhk 2
2
z2
2
y2
2
x
0zhk
zyhk
yxhk
x zyx
0zh
yh
xhh 2
2
2
2
2
22
HOMOGEN SOILk constant at x,y,z direction
ISOTROPY SOILkx = ky = kz = k
LAPLACE EQUATION
0zh
xhh 2
2
2
22
TWO DIMENSION
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WATER FLOW EQUATION
• SEEPAGE SOLUTION– CLOSED FORM SOLUTION– MODEL SOLUTIONS– APPROXIMATE SOLUTIONS
• NUMERICAL SOLUTIONS• GRAPHICAL SOLUTIONS FLOW NET
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DEFINITION
Combination of 2 line group which perpendicular each other i.e. :– Flow Line
A bundle of line or points which defined flow direction – Equipotential Line
The position of point which have same total head
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FLOW NET / JARINGAN ALIRAN
• GUIDANCE OF FLOW NET DRAWING– The water surface of upper stream and lower stream is equipotential line– The interface line of water and soil is equipotential line– The flow line perpendicular with equipotential line– The impermeable surface of boundary line is flow line– The shape area formed by flow line and equipotential line is square
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FLOW NET / JARINGAN ALIRAN
bh.k).1.a(i.k.Av.Aq
d
21
Nhhh
d
21f N
hhba.k.Nqq
21 hhH
baH.
NNkq
d
f H.NNkq
d
f a = b
h
h+h
q
a b
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SEEPAGE FORCE / GAYA REMBESAN
A).hh.(A.L.F 21wt
TOTAL FORCE
BODY FORCE (GAYA BADAN)
volumeForceTotal
FForceBody )(
L Soil weight = t.L.A
w . h2 . A
w . h1 . A
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SEEPAGE FORCE / GAYA REMBESAN
wbouyancy
wtwt
wt
iF
iLLHF
ALAhhALF
.
)1(
.)..(.. 21
w.i SEEPAGE BODY FORCE (j)=
CRITICAL CONDITION
e11Gi
0.i
s
w
bouyantc
wbouyant
bouyancy = t - w
H
h2
L
h1
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EXAMPLE 5
k = 1x10-3 cm/sn = 0.67
Questions :1. Water Flow Rate2. Flow Velocity3. Seepage Velocity4. Seepage Force at point A
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EXAMPLE 5• Water Flow Rate
• Flow Velocity
A.i.kq 144
LHi
A10x1A.1.10x1q 55
i.kv
s/m10x11.10x1v 55