2d and 3d consolidation - biot theory (oct2011)

7/26/2019 2D and 3D Consolidation - Biot Theory (OCT2011)

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CE5101 Seepage and Consolidation

Lecture 7- 2D and 3D Consolidation

Prof Harry Ta

OCT 20

CE 5101 Lecture 7 2D and

OCT 2011

1

Prof Harry Tan

Outline Biot Theory (2D and 3D Coupled

Consolidation)

FEM compare with Schiffman et. al. 1967(Mandel-Cryer Effect in 2D)

Undrained, Consolidation and DrainedResponse

2

Compare CRISP with Plaxis

Case 2 Barcelona Breakwater


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Prof Harry Ta

OCT 20

Biot Theory (2D and 3D Coupled

Consolidation)

Equilibrium Equations

Compatibility Equations

Strain/Displacements

Constitutive Equations

Continuity Equations

3

Boundary Conditions

Assume infinitesimal strain conditions

Equilibrium Equations

4


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Prof Harry Ta

OCT 20

5

6


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Prof Harry Ta

OCT 20

7

8


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Prof Harry Ta

OCT 20

9

10


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Prof Harry Ta

OCT 20

Cryer-Mandel Problem

11

Comments on True 3D

Consolidation

True 3D consolidation couples total stresses and

-

Psuedo 3D uncouples these two phenomena

When total stress distribution is constant at all

time, the rate of change of excess PP = rate of

change of volume at all points in the soil

12

s s rue on y or conso a on w erethere is a direct relationship between excess PP

and volume change


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Prof Harry Ta

OCT 20

Schiffman Strip Footing 1967

Plane-strain consolidation in 2D

resses rom e as c eory areindependent of elastic constants

Total stresses are same at start and endof consolidation

However they vary with time; they exceed

13

initial value during consolidation

So excess PP first increases before itstarts to dissipate with consolidation

FEM compare with Schiffman et. al.

1967 (Mandel-Cryer Effect in 2D)

Mean total st ress

Excess pore pressures

14

Mean effective stress


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Prof Harry Ta

OCT 20

Plaxis Biot ConsolidationSchiffman, Chen and Jordan 1967

ExcPP at x/a=1

15Strip Footing on Elastic Half-space

All round closed boundary

condition

0.6

Stress [kN/m2]

Stress at x/a=1

Mean Tot a lSt re ss

Mean Effective Stress

Plaxis Biot ConsolidationSchiffman, Chen and Jordan 1967

Mean total stress

0.2

0.3

0.4

0.5

Excess Pore Pressure

Mean excess PP

Input:

k=0.001 m/day

Eoed=10000 kPa

= *

16

1e -3 1e -2 0.1 1 10 100 1e30

0.1

Time [day]

Strip Footing on Elastic Half-space

Mean effective stress

w

cv=1 m2/day


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Prof Harry Ta

OCT 20

Plaxis Biot ConsolidationRamp Loading Schiffman 1960

1

Excess PP[kN/m2]

Chart 1

Ver 8.2

0.2

0.4

0.6

0.8Ver 7.2

17

1e-5 1e-4 1e-3 1e-2 0.1 1 10

0

Time [day]

ExcPP at Base Closed consolidation boundary

Ramp Loading with To=0.1


0

Displacement [m]

Chart 2

Ver 8.2

-6e-3

-4e-3

-2e-3er .

18

Settlement at Top Closed consolidation boundary

Ramp Loading with To=0.1

1e-5 1e-4 1e-3 1e-2 0.1 1 10

-0.01

- e-

Time [day]


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Prof Harry Ta

OCT 20


1

Excess PP[kN/m2]

At Base

Point BTo

0.2

0.4

0.6

0.8

To=0.1 To=0.5

19

Excess PP at Base Closed consolidation boundary

Ramp Loading with To=0.1 and 0.5

1e-5 1e-4 1e-3 1e-2 0.1 1 10

0

Time [day]

TYPES OF ANALYSIS Drained

Loadin /Construction/ excavation: ver slow in relation to the

soil permeability)

Undrained

Loading/Construction/ excavation: very fast (in relation to the

soil permeability)

Intermediate cases: consolidation analysis

20

o mec an ca an y rau c ow pro ems n erac More complex computations: coupled analysis


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Prof Harry Ta

OCT 20

Undrained, Consolidation and

Drained Response Defini tion drained / undrained

In terms of effective stresses with drained strengthparameters

In terms of effective stresses with undrained strengthparameters

In terms of total stresses with undrained strengthparameters

21

Example of Clay Embankment

Summary

DRAINED / UNDRAINED Drained analysis appropriate when

permeability is high

rate of loading is low

short term behaviour is not of interest for problem considered

Undrained analysis appropriate when

permeability is low and rate of loading is high

short term behaviour has to be assessed

Suggestion by Vermeer & Meier (1998) for deep excavations:

T < 0.1 (U=35%) use undrained condi tions

T > 0.40 (U=70%) use drained condit ions

22

tD

EkT

2

w

oed

k = permeability

Eoed = oedometer modulus

w = unit weight of water

D = drainage length

t = construction time

Tv = dimensionless time factor


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Prof Harry Ta

OCT 20

UNDRAINED BEHAVIOUR WITH PLAXIS

1G2EK

PLAXIS automatically adds stiffness of water when undrainedmaterial type is chosen using the following approximation

uu

total213213n

'1213

1'EK

u

utotal

assuming u = 0.495

23

- this procedure gives reasonable B-values only for < 0.35 !

- real value of Kw

/n ~ 1.106 kPa (for = 0.5)

- NB: in Version 8, B-value can be entered explicitly

UNDRAINED BEHAVIOUR WITH

PLAXISExample 1:

E = 3 000 kPa, = 0.3, u = 0.495

K = 2 500 kPa, Ktotal = 115 000 kPa Kw/n = 112 500 kPa

with = 0.978 is reasonable value for saturated so il

Example 2:

wK

nKB

'1

1

24

E = 3 000 kPa, = 0.45, u = 0.495

K = 10 000 kPa, K total = 103 103 kPa Kw/n = 93 103 kPa

B = 0.903 is poor value for saturated soil


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Prof Harry Ta

OCT 20

UNDRAINED BEHAVIOUR WITH

PLAXIS

Method A (analysis in terms of effective stresses):type of material behaviour: undrained

effective strength parameters c, ,

e ec ve s ness parame ers 50 ,

Method B (analysis in terms of effective stresses):type of material behaviour: undrained

undrained strength parameters c = cu, = 0, = 0

effective stiffness parameters E50,

25

Method C (analysis in terms of total stresses):type of material behaviour: drained

total strength parameters c = cu, = 0, = 0

undrained stiffness parameters Eu, u = 0.495

Notes on dif ferent methods:

Method A:

recommended

soil behaviour is always governed by effective stresses

increase of shear strength during consolidation included

essential for exploiting features of advanced models such as the

Hardening Soil model, the Soft Soil model and the Soft Soil

Creep model

Method B:

only when no information on effective strength parameters is

available

cannot be used with the Soft Soil model and the Soft Soil Creep

26

mo e

Method C:

NOT recommended

no information on excess pore pressure distribution (total stress

analysis)


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Prof Harry Ta

OCT 20

Consider fully undrained isotrop ic elastic behaviour

(Mohr Coulomb in elastic range)

pw = p > p = 0

'cos'c'sin2

1c

o'

y

o'

xu

27

Fig.6 Mohr Circle for evaluating undrained shear strength (plane strain)

28


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Prof Harry Ta

OCT 20

Undrained strengths of MC vs Real

NC Soils

29

Factor of Safety of Cuts/ExcavationsCritical FS is Long-

term unloading

condition,

For permanent cuts

drained strength is

key parameter for

safe design

For temporary cuts,

need to consider if

30

undrained or partiallydrained condition


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Prof Harry Ta

OCT 20

Factor of Safety of Embankments

Critical FS is Short-term loading condition,

key parameter for safe

design

31

Example of Underwater CUT Slope

(Unloading Problem)LIMIT EQUILIBRIUM ANALYSIS OF CUT SLOPES

The figures below show the results of SLOPE/W calculations

of FS for a underwater cut slope in the undrained and

', .

Drained and Undrained Parameters

The drained parameters are c'=2 kPa, '=240, =16 kN/m3

The equivalent undrained parameters are obtained from:

kPa83.124cos2cclay;oftopAt

'sincosoc'c

0u

,mu

32

kPa/m1.9424sin4.77'sin

kPa/m4.770.5916/2K12

.s n-s n

0,m

0

,v,

m

0


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Prof Harry Ta

OCT 20

Bishops FS for Drained CUTCut Slope in Clay (Drained)

1.403

Description: Clay Water

Water Level

tion(m)

14

16

18

20

22

24

26

33

o o e : o r- ou om

Unit Weight: 16

Cohesion: 2

Phi: 24

1:2 Cut

Distance (m)

0 5 10 15 20 25 30 35 40 45 50 55 60

Elev

0

24

6

8

10

Bishops FS for UnDrained CUTCut Slope in Clay (UnDrained)

2.085

Water

Water Level

ion(m)

14

16

18

20

22

24

26

34

Description: ClaySoil Model: S=f(datum)

Unit Weight: 16

C - Datum: 1.83

Rate of Increase: 1.94

Datum (elevation): 20

1:2 Cut

Distance (m)

0 5 10 15 20 25 30 35 40 45 50 55 60

Eleva

0

2

4

6

8

10


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Prof Harry Ta

OCT 20

PLAXIS Analysis Cases

Drained Analysis with c=2 kPa and =24o

Method A (analysis in terms of effective stresses):

effective strength parameters c, ,

effective stiffness parameters E50,

Method B (analysis in terms of effective stresses):

type of material behaviour: undrained

undrained strength parameters c = cu, = 0, = 0

effective stiffness arameters E50

35

Method C (analysis in terms of total stresses):

type of material behaviour: drainedtotal strength parameters c = cu, = 0, = 0

undrained stiffness parameters Eu, u = 0.495

Drained CUT, Plaxis FS=1.39 cf LE=1.40Drained Analysis with

Effective strength parameters c=2 kPa, =24, =0

Effective stiffness arameters E50=15000 kPa, =0.2

36

ONLY ONE POSSIBLE METHOD IN DRAINED

ANALYSIS ie Drained Strength and Stiffness parameters

Solutions by FEM and LE will agree very well


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Prof Harry Ta

OCT 20

Method A - UnDrained CUT plus Full Consolidation

Plaxis c/phi FS=1.37 cf LEM=1.40

Method A (undrained)

Effective strength parameters c=2 kPa, =24o, =0o

50 , .

Slip circle same as Drained Case

37

Method A - UnDrained CUT,

Plaxis FS=2.26 cf LE=2.09

Method A (in terms of effective stresses, undrained)

Effective strength parameters c=2 kPa, =24o, =0o

, .

38

Deeper slip surface than Drained Case

FEM (A) and LE not identical because undrained strength

profile in the two cases are slightly different

But slip surface of FEM (A) and LE are nearly identical


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Prof Harry Ta

OCT 20

2

Method B - UnDrained CUT,


Method B (in terms of effective stresses, undrained)

Undrained strength parameters c=1.83 kPa, c=1.94 kPa,

=0 =0,

Effective stiffness parameters E50=15000 kPa, =0.2

39

Deeper slip surface than Drained Case FEM (A and B) and LE not identical because undrained

strength profile in all three cases are slightly different

But slip surface of FEM (A and B) and LE are nearly identical

Method C - UnDrained CUT,


Method C (in terms of total stresses, Drained)

Total strength parameters c=1.83 kPa, c=1.94 kPa,

= =,

Undrained stiffness parameters E50=18625 kPa, =0.49

40

Deeper slip surface than Drained Case

FEM (A,B,C) and LE not identical because undrained strength

profile in all 4 cases are slightly different; but B and C are

nearly identical

But slip surface of FEM (A,B,C) and LE are nearly identical


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Prof Harry Ta

OCT 20

2

SUMMARY OF FS FOR CUT SLOPES

Analysis Condition PLAXIS SLOPE/W

. .

A+Consolidation 1.37 1.40

Undrained (A) 2.26 2.09

Undrained (B) 2.13 2.09

Undrained C 2.14 2.09

41

Only Drained analysis is FEM and LE identical

In Undrained analysis there are differences in strength profiles

Undrained plus Consolidation is close to Drained Case

Embankment Undrained Analysis

(Loading Problem)Embankment on Clay(Total Undrained Condition) Slope/W FS=1.029

1.029

Description: fill

Soil Model: Mohr-Coulomb

Unit Weight: 20

Cohesion: 0

Phi: 33

Piezometric Line #: 1

Description: Clay

Soil Model: S=f(datum)

Unit Weight: 16

C - Datum: 1.83

Rate of Increase: 1.94

Water Table

Height(m)

-8

-6

-4

-2

0

2

4

6

8

10

12

e o

FS=1.019

42


Distance (m)

0 10 20 30 40-10

-

For the same Undrained Strength profile,

Slip surface in FEM and LE are nearly identical


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Prof Harry Ta

OCT 20

2

Embankment Drained Analysis

2.592

Embankment on Clay(Drained Condition) Drained FS = 2.52

Description: Clay


Unit Weight: 16

Cohesion: 2

Phi: 24


Description: fill


Unit Weight: 20

Cohesion: 0

Phi: 33

Piezometric Line #: 1 Water Level

0 10 20 30 40-10

-8

-6

-4

-2

0

2

4

6

8

10

Undrained Method A+

Consolidation FS=2.11

43

Drained Analysis: FEM and LE nearly

identical results

Consolidation Analysis is not the

exactly same as Drained response

SUMMARY Undrained analysis shou ld be performed in effective stresses

and with effective stiffness and s trength parameters

Undrained Analysis wi th Full Consolidation may not agree with

Drained Analysis due to di fferent end state stress states

Note that for NC-soils in general

factor of safety against failure is lower for short term

(undrained) conditions for loading problems (e.g.

embankments)

44

factor of safety against failure is lower for long term (drained)

conditi ons for un loading prob lems (e.g. excavations)


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Prof Harry Ta

OCT 20

2

Case 1 - WCRS Excavation

Example of Deep Excavation

45

1D Closed Box Swelling

46


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Prof Harry Ta

OCT 20

2

Effects of Permeability

Heave at A (0.5m below Fmn Level)

0.03

Heave at A [m]

Uy-A(0.5...

k=1e-9

0.01

0.015

0.02

0.025UND

DRN

k=1e-7

k=1e-8

47

0 50 100 150 200

-5e-3

0

5e-3

Time [day]


Exc PP at D (1.5m below Fmn Level)

250

Excess PP at D(1.5m) [kN/m2]

EPP-D(1...

=

100

150

200

-

UND

DRN

k=1e-7

k=1e-8

48

0 50 100 150 200

0

50

Time [day]


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Prof Harry Ta

OCT 20

2


Exc PP at E (6.1m below Fmn Level)

250

Excess PP at E(6.1m) [kN/m2]

EPP-E(6...

100

150

200

k=1e-9

UND

DRN

k=1e-7

k=1e-8

49

0 50 100 150 200

0

50

Time [day]

Excavate to Formation Levelk=1e-7 m/s k=1e-8 m/s k=1e-9 m/s

50


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Prof Harry Ta

OCT 20

2

WCRS CPG Design Mesh

Compare Drained and Undrained Case

Cases at k=1e-7m/s, 1e-8m/s, 1e-9m/s

51

WCS Soil Undrained Strength Profile in Plaxis

95

100

105

Cu=Method B or C

Cu-Method A

70

75

80

85

90

Depth(m)

52

60

65

0 50 100 150 200 250 300 350

Cu (kPa)

'sin)1(2

1'cos' '

vKocCu Method A, Cu is:


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Prof Harry Ta

OCT 20

2

Drained and Undrained (Method A)

Displacements at Formation Level

Undrained Drained

53

Drained and Undrained

BMs at Formation Level

Undrained Drained

54


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Prof Harry Ta

OCT 20

2

Consolidation Analysis

assume: k=1e-7, 1e-8 and 1e-9 m/s

55

Cases of k=1e-7 to 1e-9 m/s

Displacements at Formation Level

56k = 1e-7 m/s k = 1e-8 m/s k = 1e-9 m/s


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Prof Harry Ta

OCT 20

2


BMs at Formation Level

57k = 1e-7 m/s k = 1e-8 m/s k = 1e-9 m/s


Excess PP at Formation Level

58k = 1e-7 m/s k = 1e-8 m/s k = 1e-9 m/s


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Prof Harry Ta

OCT 20

3

Wall Deflection at B (15/83.85 1.65m above FL)

0.2

Ux at B [m]

Ux at B

DRN

0.1

0.15

UND

k=1e-7

k=1e-8

k=1e-9

59

0 50 100 150 200 250

0

0.05

Time [day]

Heave at C(0/78.7 3.5m below FL)

0.03

0.035

Heave at C [m]

Uy at C

DRN

5e-3

0.01

0.015

0.02

0.025

.

UND

k=1e-7

k=1e-8

k=1e-9

60

0 30 60 90 120

-5e-3

0

Time [day]


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Prof Harry Ta

OCT 20

3

One North Station

xcava on

next to INSEAD

Is it Drained or Undrained?

61

Depth Vs. Log (Permeability, m/s) (One North and Fusionpolis Site)

0

- 1. 00 E+ 01 - 9. 00 E+ 00 - 8. 00 E+0 0 - 7. 00 E+0 0 - 6. 00 E+0 0 - 5. 00 E+ 00 - 4. 00 E+0 0 - 3. 00 E+0 0 - 2. 00 E+0 0 - 1. 00 E+ 00 0 .0 0E+0 0

Log (Permeability, m/s)

Field Permeability Tests Data from One North/Fusionpolis Site

(Jurong Formation Residual Soils)

5

10

15

20Depth,m

62

25

30

35

Single Packer Test

Falling Head Test

Variable HeadPermeability Test


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Prof Harry Ta

OCT 20

3

WT-7 next to INSEAD D1.8m CBP Wall with 30m deep cut,

20m soils, 10m rock excavation

Sandy Clay G/Sa/SC=0/25/75

Sandy Silt G/Sa/SC=0/32/68

Sandy Clayey Silt G/Sa/SC=1/17/82

63

One North - WT7 I19

after cast base slab and remove lowest anchor

0.00

5.00

0 20 40 60 80 100 120

Wall Deflection (mm) Wall Response is much closer toDrained Behavior at One North

Wall Type 7

10.00

15.00

20.00

25.00

Depth(m)

Drained

64

30.00

35.00

40.00

Undrained

I19


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Prof Harry Ta

OCT 20

3

CONCLUSIONSFrom the above study, the following conclusions can be made:

The site at WCS showed fairly consistent thick layers of sandy soils withGSD consisting of more than 60% sands and gravels.

Limited field permeability tests showed k-values in these soils ranging from1e-5 to 1e-7 m/s. .

These soils are likely to have k-values > 1e-6 m/s, therefore, they should bemodeled as drained materials.

The consolidation parametric studies showed that with soils of stiffnessesgreater than 20,000 kPa, k=1e-7 m/s will result in drained response overany reasonable construction period of 1.5 to 2 years.

Experience from the recent One North excavation supports this observation.

Undrained analysis cannot apply to this site.

Consolidation analysis must be done very carefully to reflect the true

65

stiffnesses and permeabilities of the site soils, and this will show resultsvery close to fully drained behavior.

It is more prudent to design the excavation system using fully drainedanalysis for this site

Compare CRISP with Plaxis 1D

swelling box experiment

Excavate 2m in 30 days

Excavate 3.5m in 30 days

Excavate 4m in 30 days




Set PP=0 at

each top level

66

Track PP at 1m and 6mbelow last excavated

level


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Prof Harry Ta

OCT 20

3

Swell at 1m below FML

67

Swell at 6m below FML

68


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Prof Harry Ta

OCT 20

3

PP in CRISP and Plaxis

CRISP and Abacus are formulated in terms ofactive total ore ressures i.e.

U = Uss + Uexcess

Plaxis is formulated in terms of Excess PorePressures: U = Uexcess

Uexcess is produced by Undrained loading orunloading of soil clusters specified asUndrained type

69

Steady PP is obtained from phreatic GWT orSeepage computation by Plaxis or Plaxflowprogram

Active PP = Uss + Uexcess

PP in CRISP and Plaxis In Sage Crisp, the EXCESS pore pressure always refer to the

original in-situ definition of PWP, regardless of changes of. ,

EXCESS pore pressure in typ ical soil mechanics sense.Rather, it is a reflection of the incremental variation of PWP inreference to the original in-situ PWP.

While in Plaxis, the EXCESS is exactly the same definition ofconventional definition in typ ical soil mechanics sense with the EXCESS PWP referring to the PWP in excess of the phreaticline.

Thus, there is some subtle dif ference between the two

70

compared directly. As such, the total PWP at a same point wascompared instead which expected to give roughly the samevalues, and it is a ind icator of variation o f PWP during variousstages of constructions and accompanying consolidations.


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Prof Harry Ta

OCT 20

3

Active (Total) PP at 1m below FML

71

Active (Total) PP at 6m below FML

72


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Prof Harry Ta

OCT 20

3

Case 2 - Barcelona Breakwater

73

Barcelona breakwater

y

Caisson

Rubble

x

A

A

0 1

23 45 6

78

9 10

11

12 13

Soft silty clay

20m

50m

74

Gravel


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Prof Harry Ta

OCT 20

3

Barcelona breakwater: stages (1)

re g ng

Bench

construction

75

Consolidation

Barcelona breakwater stages (2)

Caisson

Consolidation

76

Storm loading


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Prof Harry Ta

OCT 20

3

Initial pore pressures

Active pore pressures

77Groundwater head

Pore pressures after placing the bench

Active pore pressures

78Excess pore pressures


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Prof Harry Ta

OCT 20

4

Excess pore pressures during consolidation

Initial

After 30 days

79

Final

Displacements during construction and consolidation

Bench construction

80

Consolidation


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Prof Harry Ta

OCT 20

4

Caisson construction

Displacements

81Incremental shear strains

Excess pore pressures during consolidation (caisson)

Initial

After 30 days

82

Final


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Prof Harry Ta

OCT 20

Failure (factor of safety)

Incremental displacements

Factors of safety

After construction

83Incremental shear strains

FS=1.06

After 30 days

FS=1.60

End of consolidation

F=1.74

2d and 3d consolidation - biot theory (oct2011)

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