Seepage Analysis by FEM (13 SEP 2011)
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Transcript of Seepage Analysis by FEM (13 SEP 2011)
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AP Harry TanCE5101 Seepage FEM
Aug 2010
1
CE5101 Lecture 4
Seepage and FEM
by
Prof Harry Tan
1
y
SEP 2011
Outline
• Seepage and 1D Slope Stability
• Seepage in FEM (Steady State Analysis)
• Case History of SICC Slope Failure
• FEM Seepage in Excavations
• Case History of One North Excavation with
2
GWT lowering
• Transient Seepage in Excavations
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AP Harry TanCE5101 Seepage FEM
Aug 2010
2
Seepage Analysis
• Simple Flow nets
L l E ti• Laplace Equation
py
xkq xx
Darcy’s Law
Groundwater Head or Potential
3
02
2
xk
x
q
y
x
w
Groundwater Head or Potential
Steady State Laplace Eqn
Seepage in Drained Slope Failure (long-term)
4
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AP Harry TanCE5101 Seepage FEM
Aug 2010
3
Equipotentials are perpendicular to slope;so piezometer will only rise by hcosb
5
tan
'tan
cos1
2
z
uF
(a) Dry Sand(b) GWT coincide with slip plane
tan
'tan
cos
cos1
2
2
z
hF w
6
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AP Harry TanCE5101 Seepage FEM
Aug 2010
4
(c) GWT below Slip Plane with Suction Pressures(d) Waterlogged Slope with Steady Parallel Seepage
tan
'tan
cos
cos1
2
2
z
hF w
7
tan
'tan
cos
cos1
2
2
z
hF w
tan
'tan
cos
cos1
2
2
z
hF w(Like DRY Soil)
tancos z
8
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AP Harry TanCE5101 Seepage FEM
Aug 2010
5
tan
'tan'
z
hzcF w
h
(With c’=0)
F
9
'tan1tan
z
hwc
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AP Harry TanCE5101 Seepage FEM
Aug 2010
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Seepage in FEM
• 2D Formulation in FEM
• Material Model and Darcy Law
• Validation with Standard Problems
• Application to SICC slope failure
• Application to excavation
11
2D Seepage Analysis (FEM)
12
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AP Harry TanCE5101 Seepage FEM
Aug 2010
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13
Why do we need a permeability function?
Can the problem be l d ith t it ti ?
14
solved without iterations?
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AP Harry TanCE5101 Seepage FEM
Aug 2010
8
TRANSITION SATURATED/UNSATURATED
rx xq K k
x
rq K k
y yq K k
y
4
4
1 saturated zone
10 unsaturated zone
410 log( )k
r
r
h hr r
K
K
hK K
15
10 log( )
0.7m (PLAXIS)k
k
K Kh
h
TYPES OF FLOW PROBLEMS
Confined flow Unconfined flow
Total head H=hz+hp = 0
16
Domain defined Domain undefined
Total head, H hz+hp 0Therefore, hp=-hzSo, Pressure head difference on phreatic surface = Elevation head drop
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AP Harry TanCE5101 Seepage FEM
Aug 2010
9
PERMEABILITY
PLAXIS allows consideration of change of permeability with void ratio
0
logk
k e
k c
There may be large contrasts of permeability between different materials in the same problem
Too much permeability contrast may cause numerical difficulties
Th ti b t th hi h t d l t bilit l
0
15Default value for is 10
k
k
k c
c
17
The ratio between the highest and lowest permeability value should not exceed 105
To simulate an almost impermeable material (e.g. concrete), a value lower by a factor 1000 is sufficient
18
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AP Harry TanCE5101 Seepage FEM
Aug 2010
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19
• InterfacesInterfaces
• ON means Seepage Cutoff
• OFF means Seepage allowed through Interface
• Drains – Zero pore pressure condition
• Wells – Prescribed flow condition; Inflow (Recharge) or
20
( g )Outflow (Discharge-Well Pumps) Q
• Boundary Conditions
• Prescribed Heads
• Closed BC – No Flow Allowed
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AP Harry TanCE5101 Seepage FEM
Aug 2010
11
Unconfined Flow in Sand
21
Equi-potential Plot of Groundwater Head
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AP Harry TanCE5101 Seepage FEM
Aug 2010
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PLAXIS Results
Dupuit’s Theory = 0.150 m3/day/m
23
Confined Flow Seepage
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AP Harry TanCE5101 Seepage FEM
Aug 2010
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Confined Flow Seepage
H=15m H=13m
25
Closed flow boundary
Groundwater Head
H=15m H 13
26
H=15m H=13m
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AP Harry TanCE5101 Seepage FEM
Aug 2010
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27
Case History of Slope Failure in Residual Soil Cut at SICC
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AP Harry TanCE5101 Seepage FEM
Aug 2010
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CIU or CID Test Should Give Same Strength Parameters
29
Slip in Cut Soil After 2 Years
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AP Harry TanCE5101 Seepage FEM
Aug 2010
16
Slip in Cut Soil After 2 Years
5 m Ht
Slip Failure ?
10 m Ht
No Failure ?
Slip Failure ?
31
Slip in Cut Soil After 2 Years
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AP Harry TanCE5101 Seepage FEM
Aug 2010
17
Soil Profile of Cut Slope
33
Stress History of Cut Slope
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AP Harry TanCE5101 Seepage FEM
Aug 2010
18
35
36
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AP Harry TanCE5101 Seepage FEM
Aug 2010
19
37Summary of Lab Test Results
SLOPE/W Analysis: FS After CUT
1.714
140
142
144
146
148
150
Description: Reddish Brown Clayey SiltSoil Model: Undrained (Phi=0)Unit Weight: 19Cohesion: 35
Description: Yellowish Brown Clayey SiltSoil Model: Mohr-CoulombUnit Weight: 20Cohesion: 20
Ele
vatio
n (m
)
120
122
124
126
128
130
132
134
136
138
140
38
Cohesion: 20Phi: 34Unit Wt. above WT: 18
Distance (m)
0 10 20 30 40 50 60110
112
114
116
118
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AP Harry TanCE5101 Seepage FEM
Aug 2010
20
SLOPE/W Analysis: FS After 2 Years
1.022
140
142
144
146
148
150
Description: Reddish Brown Clayey SiltSoil Model: Mohr-CoulombUnit Weight: 20Cohesion: 8Phi: 27Unit Wt. above WT: 18
Description: Yellowish Brown Clayey SiltSoil Model: Mohr-CoulombU it W i ht 20
Ele
vatio
n (m
)
122
124
126
128
130
132
134
136
138
140
39
Unit Weight: 20Cohesion: 20Phi: 34Unit Wt. above WT: 18
Distance (m)
0 10 20 30 40 50 60110
112
114
116
118
120
PLAXIS UnDrained Analysis: FS=1.51
Incremental Displacements Pattern
Soil Unloaded – no sign of failure mechanism
40
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AP Harry TanCE5101 Seepage FEM
Aug 2010
21
PLAXIS UnDrained Analysis: FS=1.51
Suction Excess Pore Pressures due to Soil Unloaded
41
PLAXIS Drained Analysis: FS=1.02
Incremental Displacement Vectors indicate start of shallow slip failure
42
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AP Harry TanCE5101 Seepage FEM
Aug 2010
22
PLAXIS Drained Analysis: FS=1.02
43
PLAXIS Drained Analysis: FS=1.02
GWT Heads showed seepage front exiting on slope face; this is bad g psituation for slope Phreatic surface
44
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AP Harry TanCE5101 Seepage FEM
Aug 2010
23
1.5
1.6
FS
Chart 1
5m CUT Draine...
5m CUT Undra...
10m CUT Drain
PLAXIS c/phi method FS Estimation
5m Cut Undrained FS=1.51
1.1
1.2
1.3
1.4
10m CUT Drain...
10m Cut Drained FS=1.34
5m Cut Drained FS=1 02
45
0 1 2 3 4 51
Displacement [m]
5m Cut Undrained, FS=1.51
5m CUT Drained, FS=1.02
10m CUT Drained, FS=1.34
5m Cut Drained FS 1.02
PLAXIS Drained 10m CUT
Incremental Displacements Pattern indicate stable slope – no failure mechanism
46
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AP Harry TanCE5101 Seepage FEM
Aug 2010
24
Drained 5m CUT with Internal Drains
GWT drawndown to below slope face, stable situation
47
1.5
1.6
FS
Chart 1
5m CUT Draine...
5m CUT Undra...
Drained 5m CUT with Internal Drains
1
1.1
1.2
1.3
1.4
10m CUT Drain...
5m CUT with In...
48
0 1 2 3 4 51
Displacement [m]
GWT drawn down to below slope face, stable situation, and FS increased to 1.5 (with internal drains) cf to 1.02 (without internal drains)
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AP Harry TanCE5101 Seepage FEM
Aug 2010
25
Modeling ofModeling of Ground Water in Excavation
Analysis
49
Effects of GWT on Excavation Analysis
For PLAXIS FEM Program:
• Steady State GWT Calculation is a separate program from Excess Pore Pressure and Consolidation Calculation
• This can lead to many different ways to include Effects of GWT on Excavation Analysis
• The GWT or Phreatic Surface can be determined by either
• Method A – Steady State Flow calculation (Prefered Method)
50
Method)
• Method B – User Defined Phreatic Surface, ie head is constant on a vertical section (to model hydrostatic pressure on both sides of excavation)
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AP Harry TanCE5101 Seepage FEM
Aug 2010
26
b2
Possible GWT Conditions in Excavations
wC ab
bau
2
2
b )2(
51
wG acb
acbu
2
)2(
PLAXIS Model of Full GWT
h=Ha (const)
Modeling flood conditions with heavy rainfall recharge
h=Hb(const)
Hb
Ha
52
CLOSED FLOW Boundary
Hb
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AP Harry TanCE5101 Seepage FEM
Aug 2010
27
PLAXIS Model of GWT Drawdown
h H ( )
GWT drawdownPhreatic surface, PWP=0 Modeling Steady Seepage with GWT
drawdown in Sandy Soils k>1E-6 m/s
h=Hb(const)
h=Ha(const)
HbHa
53
CLOSED FLOW Boundary
Hb
PLAXIS Model of Hydrostatic GWT
Over-estimate active pwp
h=Hb(const)
h=Ha(const)
Ha
Hb
Suppress uplift pressures
p p
54
Hb
Hydrostatic both sides but PWP not in Equilibrium
This may give problems as there are incorrect effective stresses in the mesh
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AP Harry TanCE5101 Seepage FEM
Aug 2010
28
One North Excavation in 30m Depth of Jurong Formation
•By: A/Prof Harry Tan, National University of Singapore
•At: ER2010 2‐4 Aug 2010 (Seattle USA)
55
Use of Sub-soil Drains to Lower GWT for Deep Excavation
56
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AP Harry TanCE5101 Seepage FEM
Aug 2010
29
Full Anchors not possible due to site access
57
Seepage of GWT through wall
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AP Harry TanCE5101 Seepage FEM
Aug 2010
30
GW Seepage by WSP data-Drained/Undrained Conditions
GW(S)17, 18 & 19
• GWT drawdown lags behind excavation and drains installation by 1-2 weeks• Steady-state seepage appears to be reached in about 2 weeks
• WSP showed relatively fast GW drawdown suggests Drained Soil response
105.000
110.000
115.000
120.000
nd
Wat
er L
evel
(m
)
GW(S)18
GW(S)19
GW(S)17
8m
16m
• WSP showed relatively fast GW drawdown suggests Drained Soil response
90.000
95.000
100.000
10
-Oct
-03
10
-No
v-0
3
10
-De
c-0
3
10
-Ja
n-0
4
10
-Fe
b-0
4
10
-Ma
r-0
4
10
-Ap
r-0
4
10
-Ma
y-0
4
10
-Ju
n-0
4
10
-Ju
l-0
4
10
-Au
g-0
4
10
-Se
p-0
4
10
-Oct
-04
10
-No
v-0
4
10
-De
c-0
4
10
-Ja
n-0
5
10
-Fe
b-0
5
10
-Ma
r-0
5
10
-Ap
r-0
5
10
-Ma
y-0
5
10
-Ju
n-0
5
10
-Ju
l-0
5
10
-Au
g-0
5
10
-Se
p-0
5
10
-Oct
-05
10
-No
v-0
5
10
-De
c-0
5
10
-Ja
n-0
6
10
-Fe
b-0
6
Date
Gro
u
• 16-Feb-04 Excavate to RL110.5m and Install 1st row Drains at RL112.5m• 29-Mar-04 Excavate to RL102.5m and Install Drains at RL108.5, 106.5 and 104.5m• 12-Jul-04 Excavate to RL98.0m and Install Drains at RL100.5m, then Excavate to berm top level at RL96.0m
59
Drained / Undrained Conditions
• undrained analysis
50
One North - WT7 I19after cast base slab and remove lowest anchor
0.00
0 20 40 60 80 100 120Wall Deflection (mm)
Section 2 - Stage 8
• – 50 mm
• drained analysis
• – 97 mm
• actual – 85 mm
5.00
10.00
15.00
20.00
De
pth
(m
)
• Drained Analysis
25.00
30.00
35.00
40.00
Drained
Undrained
I19
60
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AP Harry TanCE5101 Seepage FEM
Aug 2010
31
Drained / Undrained Conditions
• Simple 1D Consolidation theory: Drained requires T=1.0 (U=93%)
woedv ht
kEd
tcT
2
oed
w
w
oedv
v
kEtsocand
hT
2
,
• Assume average values for stiff Jurong soils:
• k=1E-7 m/s or 8.64E-3 m/day
• Eoed =50,000 kPa
• Drainage path length h=20m and • Unit weight of water, γw=10 kN/m3
• Therefore, Drained condition requires period of about 9.5 days (about 1 to 2 weeks per Stage of excavation, consistent with rate of Seepage observations) 61
FEM Mesh and Parameters and Stages
125 T anchor
150 T anchor75 T anchorStage Date Construction Activity
1 15-Nov-03 Install 1.8m diameter CBP wall GL at RL117.0m2 27-Nov-03 Excavate trench toRL115.0m to cast capping beam3 15-Jan-04 Install Raker Anchor with 80% of 150T preload4 16-Feb-04 Excavate to RL110.5m and install 1st row drain at RL112.5m5 29-Mar-04 Excavate to RL102.5m and
Install drains at RL108.5, 106.5 and 104.5m6 12 J l 04 F S t 1 d 2 t t RL 96 56 12-Jul-04 For Sect 1 and 2, excavate to RL 96.5m
Install drains at RL102.5m and 75 T anchors at RL96.5mFor Sect 3, excavate to RL98.5mInstall drains at RL102.5m and 100T anchors at RL100.5mExcavate to formation level at RL95.9m
7 13-Sep-04 Cut small rock berms to RL86.0m; gunnite exposed rock slope8 18-Dec-04 Cast basement wall to RL95.9m and CD slab at RL86.0m
For Sect 1 and 2, remove 75T anchors9 & 10 18-Dec-04 Cast basement wall to RL102.5m and slab at RL98.05m
For Sect 3, remove 100T anchors11 3-Mar-05 Cast basement wall and slab at RL105.0m12 26-Apr-05 Cast basement wall and slab at RL115.0m13 1-Jun-05 Excavate to capping beam and remove raker anchors14 1-Jun-05 Backfill to GL at RL117.0m
62
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AP Harry TanCE5101 Seepage FEM
Aug 2010
32
1. Influence of Preloading Force
Increasing preload force leads to more bending of wall
Section 1 - Stage 7(after cut berm)
97.5
102.5
107.5
112.5
117.5
ed L
evel
(m
)
Measured
Soil 100% - Rock 20%
Soil 100% - Rock 20%(1.2 x Preload)Soil 100% - Rock 20%(1.4 x Preload)
• 150 ton raker anchor on site is more effective than stipulated
• Preloading force
77.5
82.5
87.5
92.5
0.00 50.00 100.00 150.00
Deflection (mm)
Red
uce Soil 100% - Rock 20%
(1.6 x Preload)Soil 100% - Rock 20%(1.8 x Preload)
Soil 100% - Rock 20%(2.0 Preload)
Preloading force multiplier of 1.4 best reflects the actual deflected shape
63
2a. Influence of Horizontal Drainage System
no drains 4 drains
2 drains 6 drains2 drains 6 drains
64
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AP Harry TanCE5101 Seepage FEM
Aug 2010
33
2b. Influence of Horizontal Drainage System
no drains 4 drains117.5m
103m
6 drains2 drains
103m
108m
100m
65
2c. Influence of Horizontal Drainage System
Influence of Horizontal Drainage System• Wall deformation increase with level of
82 5
87.5
92.5
97.5
102.5
107.5
112.5
117.5
Red
uce
d L
evel
(m
)
no drains
6 drains
4 drains
2 drains
increase with level of drains which determine height of water level behind the wall
• When no drains
77.5
82.5
0 100 200 300 400
Deflection (mm)
installed, max. wall deflection is greater 300mm
Collapse of wall66
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AP Harry TanCE5101 Seepage FEM
Aug 2010
34
3a. NO Drains (switch off ) - Wall Collapsed
S M St 1
Drains in Active Zone NOT Activated
Sum M-Stage <1Anchor Force = 180 Ton >150 Ton (design)
GWT
Wall deflect > 300 mm
67
3b. WITH Drains (switch on ) – Wall OK
Drains in Active Zone Activated
GWT
M-Stage =1Anchor Force = 110 Ton <150 Ton (design)
Wall deflect = 83 mm
68
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AP Harry TanCE5101 Seepage FEM
Aug 2010
35
CBP Elastic CBP Elasto
4a. Global FOS by c/phi Reduction
CBP Elastic, Failure with no Plastic Hinge, FOS=1.75
CBP Elasto-Plastic Failure with Plastic Hinge, FOS=1.40
• Elastic wall excludes possibility of wall plastic hinge; and over-estimate FOS=1.75• Allowing for wall plastic hinge (Elasto-plastic wall) gave lower FOS=1.40 and smaller soil yielded zone behind the wall 69
4b. Wall is Stable with GWT lowered; but FOS by c/phi reduction must account for wall plastic moments
El ti DW ll FOS 1 75
70
Elastic DWall FOS=1.75
Plastic DWall FOS=1.40
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AP Harry TanCE5101 Seepage FEM
Aug 2010
36
Section 1 - Stage 3 & 4(after installing / preloading of raker anchor)
102.500
107.500
112.500
117.500
ve
l (m
)
Section 1 - Stage 1 & 2(after installation of CBP wall)
102.500
107.500
112.500
117.500
el (
m)
Measured
Section 1 - Stage 5(after excavate to RL102.5m and installation of
first 2 drains)
102.500
107.500
112.500
117.500
(m)
5. Wall Deflection Predictions
77.500
82.500
87.500
92.500
97.500
-50.00 0.00 50.00 100.00 150.00 200.00
Deflection (mm)
Re
du
ce
d L
ev
Measured
Calculated
77.500
82.500
87.500
92.500
97.500
-50.00 0.00 50.00 100.00 150.00 200.00
Deflection (mm)
Red
uce
d L
ev
Measured
Calculated
77.500
82.500
87.500
92.500
97.500
0.00 50.00 100.00 150.00 200.00
Deflection (mm)
Re
du
ce
d L
ev
el
Measured
Calculated
Section 1 - Stage 6(after excavate to berm top and installing of last
2 drains and anchors)
112.5
117.5
S ectio n 1 - S tag e 7(after cu t berm )
112.5
117.5
Section 1 - Stage 13 & 14(after removal of contingency and raker anchor)
112.5
117.5
77.5
82.5
87.5
92.5
97.5
102.5
107.5
0.00 50.00 100.00 150.00 200.00
Deflection (mm)
Re
du
ce
d L
ev
el (
m)
Measured
Calculated
77.5
82.5
87.5
92.5
97.5
102.5
107.5
0.00 50.00 100.00 150.00 200.00
D e fle ctio n (mm )
Red
uce
d L
evel
(m
)
Me as ure d
C a lcu la te d
77.5
82.5
87.5
92.5
97.5
102.5
107.5
0 50 100 150 200
Deflection (mm)
Red
uce
d L
evel
(m
)
Measured
Calculated
71
Seepage and Excavations
• GWT lowering by Steady State Seepage
• GWT lowering by Transient Seepage
72
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AP Harry TanCE5101 Seepage FEM
Aug 2010
37
GWT lowering SS Seepage
Excavate 5m, k=1e-5 m/s Excavate 10m, k=1e-5 m/s
Lower 1.3m Lower 3.0m
GWT i l
73
Excavate 15m, k=1e-5 m/s
Lower 5.6m
GWT is nearly proportional to excavation depth
GWT lowering SS Seepage
Excavate 15m, k=1e-5 m/s Excavate 15m, k=1e-7 m/s
Lower 5.6m Lower 5.6m
For SS case, GWT is not dependent on k
74
Excavate 15m, k=1e-9 m/s
Lower 5.6m
dependent on k.
Pattern of GW heads is function of geometry only and soil layer arrangements
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AP Harry TanCE5101 Seepage FEM
Aug 2010
38
GWT and Transient Seepage
Excavate 5m, k=1e-5 m/s Excavate 5m, k=1e-7 m/s
Lower 1.3m Lower 0.8m
Excavate 5m in 30 days.
75
Excavate 5m, k=1e-9 m/s
Lower 0.3m
Sands, k=1e-5 m/s is like SS case
Clays, k=1e-9 m/s very little GWT lowered
GWT and Transient Seepage
Excavate 10m, k=1e-5 m/s Excavate 10m, k=1e-7 m/s
Lower 3.0m Lower 1.8m
Excavate next 5m in 30 days.
76
Excavate 10m, k=1e-9 m/s
Lower 0.3m
Sands, k=1e-5 m/s is like SS case
Clays, k=1e-9 m/s very little GWT lowered
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AP Harry TanCE5101 Seepage FEM
Aug 2010
39
GWT and Transient Seepage
Excavate 5m, k=1e-5 m/s Excavate 5m, k=1e-7 m/s
Lower 5.6m Lower 3.6m
Excavate next 5m in 30 days.
77
Excavate 15m, k=1e-9 m/s
Lower 0.3m
Sands, k=1e-5 m/s is like SS case
Clays, k=1e-9 m/s very little GWT lowered
Science of Transient Seepage
• Governing Equations
• Hydraulic Material Models
• Boundary Conditions
78
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AP Harry TanCE5101 Seepage FEM
Aug 2010
40
Governing Equations
Steady-state continuity condition
79
Governing Equations
80
• Need to define two soil properties functions:• K as f(S) and Ksat - k function• c as f(csat, n, S(p)) - SWCC
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AP Harry TanCE5101 Seepage FEM
Aug 2010
41
Governing Equations (FEM)at element by element level
81
Governing Equations (FEM)
82
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AP Harry TanCE5101 Seepage FEM
Aug 2010
42
Hydraulic Material Model-Van Genuchten Model
83
Hydraulic Material Model-Van Genuchten Model
84
• AEV defines the suction value that must be exceeded before air enters the soil pore• Clays have very high AEV compared to Sands • ga is inversely related to AEV
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AP Harry TanCE5101 Seepage FEM
Aug 2010
43
Hydraulic Material Model-Van Genuchten Model
85
Hydraulic Material Model-Van Genuchten Model
86
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AP Harry TanCE5101 Seepage FEM
Aug 2010
44
Hydraulic Material Model-Van Genuchten Model
87
Hydraulic Material Model-Van Genuchten Model
88
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AP Harry TanCE5101 Seepage FEM
Aug 2010
45
1. Water Table
P h
Boundary Conditions
1
1
w
w
Ph y
w p wP h
2. Inflow
externalx x y yq n q n q 4. Close boundary
1
2 3
4
89
3. Outflow
externalx x y yq n q n q
0x x y yq n q n
5. Prescribed heads
1 2,h h h h
Boundary Conditions
6. Well/Drain
7. Free Seepage
Q Q
h y
5
6
78
90
8. Screen
h y
0x x y yq n q n
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AP Harry TanCE5101 Seepage FEM
Aug 2010
46
Precipitation
max
i i
if Ponding
if and
h y h
q n q n q h y h h y h
Boundary Conditions
rain max min
min
if and
if No infiltration
x x y yq n q n q h y h h y h
h y h
91
Boundary Conditions
92
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AP Harry TanCE5101 Seepage FEM
Aug 2010
47
Boundary Conditions
Eg Zone A and B
Eg. Zone C
93
Rapid Drawdown Example –Time Dependent Boundary Conditions
• A and B are Head BC drawdown from H=25m to H=5m in 50
x
y h(t)
h(t)
h(t)
0 1
23
4 5 89
B C
days• C is Free Seepage BC drawdown from H=25m to H=5m in 50 days
x
h(t)
0 14 5
6 7
89
94
A
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AP Harry TanCE5101 Seepage FEM
Aug 2010
48
Rapid Drawdown Example –Time Dependent Boundary Conditions
F H 25 t H 5 i 50 dFrom H=25m to H=5m in 50 days
H=25mH=5m
95
Rapid Drawdown Example –Time Dependent Boundary Conditions
F H 25 t H 5 i 50 dFrom H=25m to H=5m in 50 days
H=25mH=5m
96
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AP Harry TanCE5101 Seepage FEM
Aug 2010
49
Rapid Drawdown Example –Time Dependent Boundary Conditions
From H=25m to H=5m in 50 daysy
Potential Slip Surface by c/phi reduction for the Case of Slow DD in 50 days
97
1.8
Sum-Msf
Rapid Drawdown Example –Time Dependent Boundary Conditions
WL at 25m FOS=1.74
1.4
1.6
WL at 5m Very Slow DD FOS=1.63
WL at 5m Slow DD in 50 days FOS=1.47
0 0.2 0.4 0.6 0.8 11
1.2
|U| [m]
98
WL at 5m rapid DD in 5 days FOS=1.01
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AP Harry TanCE5101 Seepage FEM
Aug 2010
50
99
100
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AP Harry TanCE5101 Seepage FEM
Aug 2010
51
101
Beware of unwanted suction; better to switch off suction in design (safer)