Seepage Analysis by FEM (20 SEP 2011)

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


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


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


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


Aug 2010

5

tan

'tan'

z

hzcF w

h

(With c’=0)

F

9

'tan1tan

z

hwc

10


Aug 2010

6

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


Aug 2010

7

13

Why do we need a permeability function?

Can the problem be l d ith t it ti ?

Log_10 scale

14

solved without iterations? Normal scale


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

For Unconfined Flow:

16

Domain definedDomain undefined

For Unconfined Flow:Total head, H=hz+hp = 0Therefore, hp=-hzSo, Pressure head difference on phreatic surface = Elevation head drop


Aug 2010

9

PERMEABILITY

PLAXIS allows consideration of change of permeability with void ratio

0

logk

k e

k c

e

Ck

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

log(k/ko)

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

Flow vector Permeability Matrix

18


Aug 2010

10

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


Aug 2010

11

Unconfined Flow in Sand

21

Equi-potential Plot of Groundwater Head

22


Aug 2010

12

PLAXIS Results

Dupuit’s Theory = 0.150 m3/day/m

23

Confined Flow Seepage

24


Aug 2010

13

Confined Flow Seepage

H=15m H=13m

25

Closed flow boundary

Groundwater Head

H=15m H 13

26

H=15m H=13m


Aug 2010

14

27

Case History of Slope Failure in Residual Soil Cut at SICC

28


Aug 2010

15

CIU or CID Test Should Give Same Strength Parameters

29

Slip in Cut Soil After 2 Years

30


Aug 2010

16


5 m Ht

Slip Failure ?

10 m Ht

No Failure ?

Slip Failure ?

31


32


Aug 2010

17

Soil Profile of Cut Slope

33

Stress History of Cut Slope

34


Aug 2010

18

35

36


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


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


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


Aug 2010

22


43


GWT Heads showed seepage front exiting on slope face; this is bad g psituation for slope Phreatic surface

44


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


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)


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)


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


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


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


Aug 2010

29

Full Anchors not possible due to site access

57

Seepage of GWT through wall

58


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


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


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


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


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


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


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


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



For SS case, GWT is not dependent on k alone

74


Lower 5.6m

dependent on k alone.

Pattern of GW heads is function of geometry only and soil layer arrangements of relative permeabilities.


Aug 2010

38

SS Model of Excavation in MC Site

Soft MC k=1E-9 m/s:Prevents GWT from falling towards wall

75

SS Model of Excavation in MC Site

H=-4.0mH=-12.0mPWP on the Wall

Closed

76

Run SS Seepage analysis with Head settings and closed flow BCs as in the figure

Closed


Aug 2010

39

Simplified Hydrostatic Model of Excavation in MC Site

General phreatic level H=-4.0m

H=-12.0mPWP on the Wall

cluster DRY

Interpolate

77

Run Phreatic level analysis with General Phreatic level, Cluster Dry in Excavated Zone, Interpolate below excavated zone, results as above

GWT and Transient Seepage



Excavate 5m in 30 days.

78


Lower 0.3m

Sands, k=1e-5 m/s is like SS case

Clays, k=1e-9 m/s very little GWT lowered


Aug 2010

40




Excavate next 5m in 30 days.

79


Lower 0.3m






Excavate next 5m in 30 days.

80


Lower 0.3m




Aug 2010

41

Science of Transient Seepage

• Governing Equations

• Hydraulic Material Models

• Boundary Conditions

81

Governing Equations

Steady-state continuity condition

82


Aug 2010

42

Governing Equations

83

• Need to define two soil properties functions:• K as f(S) and Ksat - k function• c as f(csat, n, S(p)) - SWCC

Governing Equations (FEM)at element by element level

84


Aug 2010

43

Governing Equations (FEM)

85

Hydraulic Material Model-Van Genuchten Model

86


Aug 2010

44


87

• 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


88


Aug 2010

45


89


90


Aug 2010

46


91

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

92

3. Outflow

externalx x y yq n q n q

0x x y yq n q n


Aug 2010

47

5. Prescribed heads

1 2,h h h h

Boundary Conditions

6. Well/Drain

7. Free Seepage

Q Q

h y

5

6

78

93

8. Screen

h y

0x x y yq n q n

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

94


Aug 2010

48

Boundary Conditions

95

Boundary Conditions

Eg Zone A and B

Eg. Zone C

96


Aug 2010

49

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

97

A


F H 25 t H 5 i 50 dFrom H=25m to H=5m in 50 days

H=25mH=5m

98


Aug 2010

50


F H 25 t H 5 i 50 dFrom H=25m to H=5m in 50 days

H=25mH=5m

99


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

100


Aug 2010

51

1.8

Sum-Msf


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]

101

WL at 5m rapid DD in 5 days FOS=1.01

102


Aug 2010

52

103

104

Beware of unwanted suction; better to switch off suction in design (safer)

Documents

Seepage Analysis by FEM (20 SEP 2011)