Plaxis Ho Chi Minh 2014091618 PDF [PDF]

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PLAXIS Introductory Workshop Ho Chi Minh, South Vietnam

Venue 

Date 

PTI Building, No 218 Bis   Nam Ky Khoi Nghia Street   3 District, Ho Chi Minh City.  16 to 18 September 2014 

Lecturers  Dr Phung Duc Long 

VSSMGE, Vietnam 

Dr William Cheang 

Plaxis AsiaPac, Singapore 

Organised by:  Plaxis AsiaPac   Construction Informatics and Consultancy    

 

LECTURERS    Dr. Phung Duc Long  VSSMGE, Hanoi, Vietnam 

Dr. William Cheang Wai Lum  Plaxis AsiaPac, Singapore 

William  obtained  his  PhD  from  the  National    University  of  Singapore.  His  interest  is  in  Computational Geotechnics. He has worked as a  Geotechnical  Engineer  in  Malaysia,  Singapore  and Thailand. He is involved with many seminars  and workshops around Asia for the promotion of  good and effective usage of Plaxis Finite Element  Codes. 

Dr. Phung got PhD degree at Chalmers  University of Technology, Sweden. He has  more than 30 years of international  experience, including more than 20 years with  Plaxis. His expertise areas are: deep  foundations, deep excavations, soil  improvement, pile dynamics, tunnelling, and  numerical analysis. He has worked with  projects in many countries, among other,  Sweden, Norway, Denmark, USA, England,  Russia, Germany, India, Hong Kong, China  and Vietnam, etc. 

  ORGANIZERS  Construction Informatics and Consultancy  JSC (CIC)  37 Le Dai Hanh, Hai Ba Trung Dist., Hanoi,  Vietnam,     

Plaxis AsiaPac, Singapore  16 Jalan Kilang Timor,  05‐08 Redhill Forum,  Singapore     

 

CONTENTS LECTURES & EXERCISES      Session 1: Soil Behaviour 1  CG1  Mohr‐Coulomb Model  CG2  Hardening Soil Model  CG3  Exercise 1: Calibration of soil model with Soil Lab Test  Session 2: Soil Behaviour 2  CG4  Drained & Undrained Condition   CG5  Overview of Soil Models  CG6  Geometry Idealization and Discretization  CG7  Exercise 2: Modelling of a Shallow Strip Foundation  Session 3: Modelling of Excavations‐Introduction  CG8  Modelling f Excavations in 2D  CG9  Structural Elements in PLAXIS  CG10  Exercise 3: Modelling of an Anchored Retaining Wall  Session 4: Modelling of Slopes and Embankments‐Introduction  CG11  Initial Stresses and Phi‐C’ Reduction Analysis  CH12  Modelling of Slopes and Embankments  CG13  Exercise 4: Modelling of a Soil Nailed Slope  Session 5: Modelling of Excavations and Pile Foundations in 3D  CG14  Modelling of Excavation in 3D  CG15  Modelling of Pile Group Foundations in 3D  CG16  Exercise 5: Modelling of Pile Foundations in 3D  Session 6: Modelling of Tunnels and Tunnelling   CG17  Modelling of Tunnels and Tunnelling  in 2D and 3D  CG18  Finite Element Modelling: Suggestions and Pitfalls  CG19  Exercise 6: Modelling of Shield Tunnelling in 2D   

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PLAXIS SPECIAL WORKSHOPS, 16 (Tues) – 18 (Thurs) HO CHI MINH CITY 2014

DAY 1 (16 SEPTEMBER 2014): TUESDAY Session 1: Soil Behaviour 1 8:30 8:45 Registration and Opening 8:45 9:30 CG1 Mohr-Coulomb Model 9:30 10:15 CG2 Hardening Soil Model 10:15 10:30 Tea Break 11:15 12:30 CG3 Exercise 1: Calibration of HS model 12:30 1:30 Lunch Session 2: Soil Behaviour 2 1:30 2:15 CG4 Drained and Undrained Conditions (A, B, C) 2:15 3:00 CG5 Overview of Soil Models 3:00 3:15 Tea Break 3:15 4:00 CG6 Geometry Idealization and Discretization 4:00 5:15 CG7 Exercise 2: Modelling of a Shallow Strip Foundation

Dr Phung Dr Cheang Dr Cheang

Dr Phung Dr Cheang Dr Phung Dr Phung

DAY 2 (17 SEPTEMBER 2014): WEDNESDAY Session 3: Modelling of Excavations - Introduction 9:00 9:45 CG8 Modelling of Excavations 9:45 10:30 CG9 Structural Elements in PLAXIS 2D and 3D 10:30 10:45 Tea Break 10:45 12:00 CG10 Exercise 3: Modelling of an Anchored Retaining Wall 12:00 1:00 Lunch Session 4: Modelling of Slopes and Embankments - Introduction 1:00 1:30 CG11 Initial Stresses and C-Phi’ Reduction Analysis 1:30 3:00 CG12 Modelling of Slopes and Embankments 3:00 3:15 Tea Break 3:15 5:00 CG13 Exercise 4: Modelling of a Slope and Stabilisation

Dr Cheang Dr Cheang Dr Phung

Dr Phung Dr Cheang Dr Cheang

DAY 3 (18 SEPTEMBER 2014): THURSDAY Session 5: Modelling of Excavations & Foundations in 3D 9:00 9:45 CG14 Modelling of Excavations in 3D 9:45 10:30 CG15 Modelling of Pile Group Foundations in 3D 10:30 10:45 Tea Break 10:45 12:00 CG16 Exercise 3: Modelling of Pile Foundations in 3D 12:00 1:00 Lunch Session 6: Modelling of Tunnels and Tunnelling in 2D and 3D 1:00 2:00 CG17 Modelling of Tunnels and Tunnelling in 2D & 3D 2:00 3:00 CG18 Overview of common pitfalls in FE modelling 3:00 3:15 Tea Break 3:15 5:00 CG19 Exercise 4: Modelling of a Tunnel in rock

PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

Dr Cheang Dr Phung Dr Phung

Dr Cheang Dr Cheang Dr Cheang

1

Ho Chi Minh Workshop Computational Geotechnics 1

Mohr-Coulomb Model Dr Phung Duc Long  

PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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MOHR-COULOMB MODEL Elasticity, Plasticity & Yielding of Soils Dr Phung Duc Long Dr William Cheang, Plaxis Asiapac Acknowledgement: Some slides from Dr Ronald Brinkgreve

Mohr-Coulomb model and soil stiffness Objectives: 1. To indicate features of soil behaviour 2. To formulate Hooke’s law of isotropic linear elasticity 3. To formulate the Mohr-Coulomb criterion in a plasticity framework 4. To identify the parameters in the LEPP Mohr-Coulomb model 5. To give suggestions on the selection of parameters 6. To indicate the possibilities and limitations of the MC model

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Typical results from soil lab tests Triaxial test (axial loading) F

1-3

strength

P

stiffness -1

1

v

dilatancy

1 3

-1

3

v

Typical results from soil lab tests Oedometer test (one-dimensional compression)

Pre-consolidation stress 1

1

reloading primary loading

1

1

PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

unloading

4

Typical results from soil lab tests Oedometer test (constant load; secondary compression)

1

time 1

creep

1

Typical results for soil stiffness Stiffness at different levels of strain

Modulus reduction curve after Benz (2007)

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Features of soil behaviour 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

Elasticity (reversible deformation; limited) > stiffness Plasticity (irreversible deformation) > stiffness, strength Failure (ultimate limit state or critical state) > strength Presence and role of pore water Undrained behaviour and consolidation Stress dependency of stiffness Strain dependency stiffness Time dependent behaviour (creep, relaxation) Compaction en dilatancy Memory of pre-consolidation pressure Anisotropy (directional strength and/or stiffness)

Concepts of soil modelling  yy

1. Relationship between stresses (stress rates) and strains (strain rates) 1. Elasticity (reversible deformations) d=f (d)

 yz  zy

 zz

 zx

 yx  xy  xz

 xx

1. Example: Hooke’s law

2. Plasticity (irreversible deformations) d=f (d,,h) 1. Perfect plasticity, strain hardening, strain softening 2. Yielding, yield function, plastic potential, hardening/softening rule 3. Example: Mohr-Coulomb yielding

3. Time dependent behaviour (time dependent deformations) 1. Biot’s (coupled) consolidation d=f (d,,t) 2. Creep, stress relaxation 3. Visco elasticity, visco plasticity

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Types of stress-strain behaviour 

Linear-elastic

Non-linear elastic









Lin. elast. perfectly-plast.



EP strain-hardening

EP strain-softening





Elastoplastic









Hooke’s law 1    xx        yy      zz  E    (1   )(1  2 )  0   xy   0  yz      zx   0

Inverse:   xx   1      yy     zz  1      E  0  xy    yz   0     zx   0

 1 



 

0 0

1  0 0

0

0





0

0

1 



0

0

1

0

0 0

0 0

0 2  2

0

0

0

0 2  2

0

0

0

0

0 0 1  2 0

0 0 0 1  2

0

0 0

 0   0  0   0   2  2 

PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

0  0   0  0   0  1   2

  xx     yy    zz     xy   yz     zx 

 xx     yy   zz     xy   yz     zx 

7

Hooke’s law In principal stress / strain components:

    1  1  E       1   2  (1  )(1  2 )    3     1  

 1     2  3 

In isotropic and deviatoric stress / strain components:

 p   K 0   v   q    0 3G        s

p

1 3

 1   2   3 

1 ( 1   2 ) 2  ( 2   3 ) 2  ( 3   1 ) 2 2

q

Model parameters in Hooke’s law: Two parameters:

- d1 

- Young’s modulus E - Poisson’s ratio 

d3 

- 1 Meaning (axial compr.):

E 

E

d1 d1

d  3 d1

1 

- 1 1

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Alternative parameters in Hooke’s law: dxy

Shear modulus:

G

d xy d xy



 dxy

E 21   

Bulk modulus:

K

dp

E dp  d v 31  2 

dv - d1

Oedometer modulus:

Eoed

 - d1

E 1    d  1 d1 1   1  2 

Stress definitions 1. In general, soil cannot sustain tension, only compression 2. PLAXIS adopts the general mechanics definition of stress and strain: Tension/extension is positive; Pressure/compression is negative   yy

xx

yy

xx yy

xx

xx yy

3. In general, soil deformation is based on stress changes in the grain skeleton (effective stresses) 4. According to Terzaghi’s principle: σ’ = σ - pw

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Hooke’s law for effective stress rates The modeling of non-linear soil behaviour requires a relationship between effective stress rates (d’ ) and strain rates (d)

' 1  '  '  d 'xx    ' 1  '  '  d '  yy     '  d 'zz   ' 1  ' E'    0 0  d 'xy  (1  ')(1  2 ')  0  0  d ' yz  0 0    0 0  d 'zx   0

d '  D d  e

Symbolic:



0  0 0 0  0 0 0   1 0 0  2  ' 1 0 0  2  '  1 0 0  2   ' 0

0

 

d  D

e 1

 d  xx  d   yy   d  zz     d  xy   d  yz     d  zx 

d '

Plasticity Basic principle of elasto-plasticity:

 ij   ije   ijp

(total strains)

d ij  d ije  d ijp

(strain rates)

Elastic strain rates:

d ije  D e ijkl d 'kl 1

PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Plasticity Basic principle of elasto-plasticity:

 ij   ije   ijp

(total strains)

d ij  d ije  d ijp

(strain rates)

Plastic strain rates:

d ijp  d

g  'ij

d = scalar; magnitude of plastic strains dg/d = vector; direction of plastic strains g = plastic potential function

When do plastic strains occur? Determination based on yield function f = f (’,) 1. 2. 3.

If f0  elastic volumetric contraction!  v  K (2) Isotropic hardening  plastic volumetric contraction!  vp ,cap 

  pc 

1 m

  1  m  p ref 

What contributes to the sample dilation? (1) As the stress path cut through series of shear yield line, plastic p shear strain d was generated. (2) the plastic shear strain will be accompanied by plastic volumetric strain by d vp , fric  d p , fric sin  m , and it is dilative!

q

MC line

pc

p’

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Part 2: Stiffness parameters

Part 2: Stiffness parameters 450

400

400

Deviator stress (kPa)

350 300

3’ = 100 kPa

250 200 150

Test data

100 50 0 0

0.01

E50ref 

0.02

0.013

0.03

0.04

0.05

0.06

0.07

Axial strain

400  30800 kPa  30000 kPa 0.013

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Part 2: Stiffness parameters 450

400400

Deviator stress (kPa)

350 300

3’ = 100 kPa

250 200 150

Test data

100 50 0 0

0.01

0.02

0.03

0.021 0.026

0.04

0.05

0.06

0.07

Axial strain

Eurref 

400  80000 kPa 0.026  0.021

As sand unload-reloading stiffness Eurref is generally about 3~5 times of E50ref, we may set Eurref = 90000kPa

Part 2: Stiffness parameters

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Part 2: Stiffness parameters 0 0.1 0.2

Vertical strain (%)

0.33

0.3 0.4 0.5 0.6 0.7

Test data

0.8 0.9 1 1.1 1.2 1.3 1.4 0

100

200

300

320

400

Vertical pressure (kPa)

ref Eoed 

320  29900kPa  30000kPa 1.4%  0.33%

Part 2: Stiffness parameters E50  E

Eoed 

ref 50

 c cos  ' ' 3 sin  '    ref cos '  sin ' c  p   

ref  Eoed 

c cot  ' '1  ref   c cot  ' p 

m

m

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Part 2: Stiffness parameters 0 0.1

ref Eoed 

0.2 0.3

Vertical strain (%)

0.47

0.4 0.5

320  29900kPa  30000kPa 1.4%  0.33%

400 200 kPa Eoed   43000kPa Test data 1.4%  0.47%

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 0

100

200

300

400

400

Vertical pressure (kPa)

200 kPa  c cot  ' '1 Eoed   ref ref Eoed  c cot  ' p

m

  200  43000      100 30000    m

m = 0.5

Part 3: Other parameters Jaki’s formula: K 0NC  1  sin  '  1  sin 42  0.33 400

Vertical pressure (kPa)

300

200

100

Test data 0 0

50

100

150

200

Lateral stress (kPa)

K 0NC 

 x ' 100   0.33  y ' 300

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Summary of Hardening Soil Parameters

FEM simulation using Plaxis SoilTest Facility

(1) Change of dilation angle and see its effects (2) How to simulate unload-reload step? (3) Oedometer test simulation

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Part 2: Clay

For Clay, one of the most common lab tests is Triaxial Isotropically Consolidated UnDrained (CIU) Test

A Triaxial setup in NUS Geotechnical Lab

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For Clay, one of the most common lab tests is Triaxial Isotropically Consolidated UnDrained (CIU)Test

Fa/A = q (deviatoric stress)

Close the valve = Undrained test = Excess will accumulate with shearing

a = q + r

350

Test data 300

q (kPa)

250

200 195 150

100

50

0 0

50

100

150

200

250

300

350

400

450

p' (kPa)

Test data: stress path p’~q

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CIU stress path Gradient:

350

Test data 300

6 sin  ' 195  3  sin  ' 200

q (kPa)

250

200 195 150

’ = 25

100

50

Intercept:

0 0

50

100

150

200

p' (kPa)

250

300

350

400

450

6c ' cos  ' 0 3  sin  '

c’ = 0

Another common lab test is Oedometer Test

Oedometer setups in NUS Geotechnical Lab

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Another common lab test is Oedometer Test

Typically less test points are available due to long consolidation period for each loading stage Boundary conditions

0

Test data

Vertical strain (%)

0.1

0.2

0.3

0.4

0.5 1

10

100

1000

Vertical pressure (kPa)

Typically oedometer test results are presented in SI report as logv’ ~  yy which is linear (unlike sand) which must be dealt with cautions!

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Oedometer test for clay 0

Test data

Eoed 

Vertical strain (%)

0.1

d y ' d y

0.2

Gradient _ k 

0.3

d (log  y ' ) d y

Obviously, Eoed  Gradient _ k

0.4

0.5 1

10

100

1000

Vertical pressure (kPa)

Gradient _ k 

d (log  y ' )



d yy

d(

ln  y ' 2.3

d yy

1

)



1 y'

d ( y ' )

d yy

2.3



1 d ( y ' ) 1  Eoed 2.3 y ' d yy 2.3 y '

Eoed  2.3 y ' gradient _ k

So,

Oedometer test for clay 0

Test data

ref Eoed  2.3  100  6.02  1350 kPa

Vertical strain (%)

0.1

Eoed  y '  ref Eoed pref

0.2

0.27 0.3

0.37

ref  c cot  ' '1  Eoed  Eoed  ref 

0.4

 c cot  ' p

0.5 1

10

30

100

Vertical pressure (kPa)

120

Eoed  2.3 y ' gradient _ k gradient _ k 

So,

log(120)  log(30)  6.02 0.37  0.27

m



1000

Eoed   '1   ref ref Eoed p

  

m

m=0

Eoed  2.3 y '6.02

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Oedometer test for clay Eur refers to when 3’ = 100kPa During oedometer loading, when y’ =100kPa, x’ p´ = 0  centre of Mohr Circle remains at the same point





1  x'o   y'o sin  '  c' cos  ' 2 1 cu  K 0  1 y'o sin  '  c ' cos  ' 2 cu 

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

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Factor of Safety of Cuts/Excavations Critical FS is Long-term unloading condition, For permanent cuts drained strength is key parameter for safe design For temporary cuts, need to consider if undrained or partially drained condition

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Factor of Safety of Embankments Critical FS is Short-term loading condition, undrained strength is key parameter for safe design

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Example of Underwater CUT Slope 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 condition, by Bishop's Simplified method. Drained and Undrained Parameters The drained parameters are c'=2 kPa, '=240, =16 kN/m3 The equivalent undrained parameters are obtained from: , cc c' cos φo 'm sin' m'sin  ' c ' cos  u u 

At top of clay; c u  2 cos 24 0  1 .83 kPa K 0  1  sin '  1 - sin 24 0  0.59  ,v 1  K 0   6/2 1  0.59   4.77 kPa/m 2 , m sin '  4.77 sin 24 0  1.94 kPa/m , m 

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Bishop‘s FS for Drained CUT Cut Slope in Clay (Drained)

1.403

26 24 22

Water Level

Elevation (m)

20 18 16 14

Water

Description: Clay Soil Model: Mohr-Coulomb Unit Weight: 16 Cohesion: 2 Phi: 24

12 10 8 6

1:2 Cut

4 2 0 0

5

10

15

20

25

30

35

40

45

50

55

60

Distance (m)

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Bishop‘s FS for UnDrained CUT Cut Slope in Clay (UnDrained)

2.085

26 24 22

Water Level

Elevation (m)

20 18 16 14

Water

12

Description: Clay Soil Model: S=f(datum) Unit Weight: 16 C - Datum: 1.83 Rate of Increase: 1.94 Datum (elevation): 20

10 8 6 4 2

1:2 Cut

0 0

5

10

15

20

25

30

35

40

45

50

55

60

Distance (m)

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PLAXIS Analysis Cases  Drained Analysis with c’=2 kPa and ’=24o  Method A (analysis in terms of effective stresses): type of material behaviour: undrained 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 parameters E50´, ´  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

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Drained CUT, Plaxis c/phi FS=1.35 cf LE=1.40 Drained Analysis with Effective strength parameters c´=2 kPa, ´=24, ´=0 Effective stiffness parameters E50´=15000 kPa, ´=0.2

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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 Effective stiffness parameters E50´=15000 kPa, ´=0.2

Slip circle same as Drained Case

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Method A - UnDrained CUT, Plaxis c/phi (Ignore UnDrained) FS=2.75 cf LE=2.09 Method A (in terms of effective stresses, undrained) Effective strength parameters c´=2 kPa, ´=24o, ´=0o Effective stiffness parameters E50´=15000 kPa, ´=0.2

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Method A - UnDrained CUT, Plaxis c/phi (UnDrained) FS=2.27 cf LE=2.09 Method A (in terms of effective stresses, undrained) Effective strength parameters c´=2 kPa, ´=24o, ´=0o Effective stiffness parameters E50´=15000 kPa, ´=0.2

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Method B - UnDrained CUT, Plaxis c/phi (Ignore UnDrained) FS=2.13 cf LE=2.09 Method B (in terms of effective stresses, undrained) Undrained strength parameters c=1.83 kPa, Δc=1.94 kPa, =0, =0 Effective stiffness parameters E50´=15000 kPa, ´=0.2

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Method B - UnDrained CUT, Plaxis c/phi (UnDrained) FS=2.14 cf LE=2.09 Method B (in terms of effective stresses, undrained) Undrained strength parameters c=1.83 kPa, Δc=1.94 kPa, =0, =0 Effective stiffness parameters E50´=15000 kPa, ´=0.2

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c/phi Analysis of Method A and B MC-UNDRAINED Sum-Msf 3 METHOD A (IGNORE UNDR)

A (Ignore Undrained) =2.75

METHOD A (UNDR) METHOD B (IGNORE UNDR)

2.5

METHOD B (UNDR)

A (Undrained) =2.27 B (Ignore Undrained) =2.13 B (Undrained) =2.14

2

1.5

1

0

3e3

6e3

9e3

1.2e4

|U| [m]

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SUMMARY OF FS FOR CUT SLOPES Analysis Condition

PLAXIS

SLOPE/W

Drained

1.35

1.40

A+Consolidation

1.37

1.40

A (Ignore UNDR)

2.75

2.09

A (UnDrained) 2.27 B (Ignore UNDR)

2.09 2.13

B (UnDrained) 2.14

2.09 2.09

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Compare Excess PP  of Method A Method A

Method A, c/phi - Ignore Undrained, FOS = 2.75

Exc PP unchanged, but FS not OK

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Method A, c/phi - Undrained, FOS = 2.27

Exc PP changed, but FS nearly OK

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Compare Excess PP  of Method B Method B

Method B, c/phi - Ignore Undrained, FOS = 2.13

Exc PP unchanged, but FS is OK

Method B, c/phi - Undrained, FOS = 2.14

Exc PP changed, but FS is OK

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Conclusions A. FEM analysis for Slope Stability is better than LEM as failure mechanism is  determined automatically as part of the stress equilibrium process B. FEM can handle undrained, drained and consolidation effects on slope stability,  provided we use Mohr‐Coulomb failure criteria for c/phi reduction analysis

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THANK YOU Presentation by: 1. Dr William Cheang Acknowledgment to the contributors and co-workers: 1. Dr Ronald Brinkgreve 2. Dr Lee Siew Wei

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Ho Chi Minh Workshop Computational Geotechnics 13

EXERCISE 4: MODELLING A SOIL NAILED SLOPE Dr William Cheang  

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Slope stability for a road construction project

SLOPE STABILITY FOR A ROAD CONSTRUCTION PROJECT

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Slope stability for a road construction project

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Slope stability for a road construction project

INTRODUCTION On the North Island of New Zealand a new road section has to be constructed along the shore line of a tidal bay, see figure 1.

Figure 1: Situation overview for the newly constructed road Though the easiest solution would have been to construct the road at a larger distance from the bay as the slope gradients are easier there, this is not possible as the upper land is privately owned which for historic reasons cannot be changed. The new road therefore had to be constructed along the steeper gradient just next to the shore line of the tidal bay. The hillside is mainly siltstone, weathered at the surface but intact at certain depth. Construction will take place in summer when the ground water level is low. However, in winter the hillside side almost fully saturates due to heavy rainfall, which has a significant influence on the stability. For the construction of the new road part of the slope was excavated. The excavated material is crushed and mixed with sand and gravel to make fill material to support the road. During the first winter after the road construction the road started to tilt towards the tidal bay and after assessing the winter situation the factor of safety was considered too low. The decision was taken to stabilize the fill and hillside below the road using so-called launched soil nails: long steel reinforcement bars that are shot with high speed into the ground.

Main goal of the analysis • Determine the factor of safety of the original hillside • Construct the new road under dry (summer) conditions and calculate its factor of safety • Simulate wet (winter) conditions and calculate its factor of safety • Apply stabilising soil nails and calculate the factor of safety in wet conditions Computational Geotechnics PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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INPUT Project properties Start a new project and select appropriate Dimensions according to the size of the geometry (see figure 2). After closing the Project properties window, open the Snapping options and make sure to use a snap distance of 0.25m.

(a)

(b) Figure 2: Soil model (a) and position of the road surface, construction details and soil nails (b)

Soil mode Due to the complexity of the model the geometry will not be defined using boreholes, but through soil polygons in Structures mode. Therefore, move directly to Structures mode.

Structures mode • First the intact siltstone is modelled. 4

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Slope stability for a road construction project – Select the Create soil polygon button ( select the Create soil polygon option.

) and from the submenu that opens,

– Now draw a soil polygon starting from (x y) = (0 0) and then to (0 22), (30 16), (37 11), (46.5 7.25), (58 6), (65 6) and finally to (65 0). • Secondly, the weathered siltstone layer will be added. As the bottom of weathered siltstone layer coincides with the top of the intact siltstone layer it’s not needed to draw the complete soil polygon. – From the Create soil polygon submenu now select the option Follow contour. – Click at (x y) = (0 22) and draw a line to (0 25), (25 20), (31 19.25), (35 16), (37.5 14), (43 11), (46 10.25), (58 8.25), (65 8) and finally to (65 6). – Now right click to end the drawing. A soil polygon will be created from the line that was just drawn and the upper contour of the intact siltstone layer below. • The last part of soil missing is the new fill that will be constructed for the road. – Select again the Create soil polygon option and draw a soil polygon from (x y) = (35 16) to (38 16), (43 11) and (37.5 14) • Now some additional lines must be specified in order to model the construction sequence. – From the Create line menu choose the option Create line. – Draw a line from (x y) = (25 20) to (30 16) – Draw a line from (x y) = (35 16) to (37 11) and finally to (43 11) • The road must be added, including the traffic load: – From the Create line button choose the option Create plate. – Draw a plate from (x y) = (30 16) to (38 16). – Choose the Select button (

) in order to stop drawing plates.

– Right-click on the just created plate and from the popup menu select the option Create → Line load – In the Selection explorer, make sure the line load Distribution is set to Uniform and qy,start,ref = -10 kN/m/m to create a vertical line load of 10 kN/m downwards, per meter out-of-plane. • And finally the 3 soil nails are added as well: – From the Create line button menu choose the option Create embedded pile row. – Insert 3 embedded pile rows according to the coordinates given in figure 2. Computational Geotechnics PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Material properties Soil • Enter the material properties for the three soil data sets specified in table 1. • After entering all properties for the three soil types, drag and drop the properties to the appropriate clusters, as indicated in figure 2.

Parameter Material model Type of behaviour Dry weight Wet weight Young’s modulus Poisson’s ratio Cohesion Friction angle Dilatancy angle Permeabilities Tension cut-off

Table 1: Soil material set parameters Symbol Intact Weathered siltstone siltstone Model MohrMohrCoulomb Coulomb Type Drained Drained γunsat 16.0 16.0 γsat 17.0 17.0 0 E 12000 12000 0 υ 0.3 0.3 c0ref 12 10 0 ϕ 35 19 ψ 0 0 kx , ky 1·10−3 0.01 Tension cut-off Disabled Enabled

Reinforced fill MohrCoulomb Drained 19.0 21.0 20000 0.3 8 30 0 0.1 Enabled

Units

kN/m3 kN/m3 kN/m2 – kN/m2 ◦ ◦

m/d

Road surface The road surface is modelled with a plate element. Therefore, create a new plate material set using the parameters as specified in table 2 and assign it to the plate representing the road surface. Table 2: Properties of the road surface (plate) Parameter Material model Isotropic End-bearing Axial stiffness Flexural stiffness Weight Poisson’s ratio 6

Symbol Model

EA1 , EA2 EI w ν

Road surface Elastic Yes No 2.5·105 500 3.0 0.0

Unit – – – kN/m kN m2 /m kN/m/m – Computational Geotechnics

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Slope stability for a road construction project Soil nails The 3 soil nails are modelled using embedded pile row elements. Hence, create a new embedded pile row material set with parameters as specified in table 3 and assign the material to all 3 soil nails. Table 3: Properties of the soil nails (embedded pile rows) Parameter Modulus of elasticity Material weight Pile type Predefined pile type Diameter Spacing Skin resistance Base resistance Interface stiffness factor

Symbol E γ Pile type Predefined pile type Diameter Lspacing Ttop,max , Tbot,max Fmax

Grout body 2.1*108 60 Predefined Massive circular pile 0.032 1.0 1000 0 Default values

Unit kN/m2 kN/m3 m m kN/m kN -

Mesh mode The road surface and the soil nails are automatically refined. However, as possible failure would be expected in the weathered siltstone layer, this layer has to be refined as well. The Coarseness factors as specified in figure 3 should be applied to the indicated areas. This can be done in 2 ways:

1. From the vertical toolbar select the Refine mesh button ( ) and click on the areas to be refined. For every click on an area or object its coarseness factor will become 70% of it’s current value. Hence, to reach a coarseness factor of 0.5 it’s necessary to click twice on the area, for a coarseness factor of 0.35 one has to click 3 times on the same area.

2. Select the areas and in the Selection explorer directly enter the appropriate coarseness factors.

Now select the Generate mesh button ( ) and make sure the Element distribution is set to Medium. After mesh generation, view the mesh (see figure 4) Computational Geotechnics PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Slope stability for a road construction project

Figure 3: Areas of the mesh to be refined

Figure 4: Generated mesh with refinement

Water conditions mode and Staged construction mode The calculation consists of the initial phase and 12 calculation phases more in order to model the proper construction sequence and the determination of the factors of safety at key moments in the construction process.

Initial phase The initial situation consists of the intact hill side and a phreatic level representing typical summer conditions as construction starts in summer. In order to define the initial situation, follow these steps: • Water conditions mode – From the vertical toolbar select the Create water level button ( option Create water level. 8

) and then the

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Slope stability for a road construction project – Draw a water level from (x y) = (-1 10) to (66 10). This water level will automatically become the global water level. • Staged construction mode – The geometry has a non-horizontal soil layering, hence the K0 -procedure cannot be used. Open the Phases window and for the initial phase set the Calculation type to Gravity loading. – Make sure only the clusters representing the original hillside are activated. Hence, switch off the parts of reinforced soil.

Phase 1 - Stability prior to the construction Before the construction is started the factor of safety is determined of the initial situation • Staged construction mode – Open the Phases window and change the Calculation type of this phase to Safety.

Phase 2 - Road excavation The road excavation should continue from the initial situation and not from the results of the safety factor determination. To do so: • Select the Initial phase. • Select the Add phase button ( from the initial phase.

). A new phase (phase 2) will now be created that starts

Now we will define the phase: • In Staged construction mode – In the Phases window, set the Calculation type to Plastic of loading type Staged construction. – In order to discard the displacements during gravity loading make sure the option Reset displacements to zero is selected under the Deformation control parameters. – Switch off the upper part of the road excavations, see figure 5. Computational Geotechnics PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Figure 5: Phase 2, road excavation

Phase 3 - Construction of the fill • This calculation phase that starts from Phase 2 is again a Plastic calculation, loading type Staged construction. • In Staged construction mode – Switch on the additional fill – Assign the “reinforced fill” material set to the 4 clusters of the fill area, see figure 6.

Figure 6: Phase 3, Construction of the fill

Phase 4 - Construction of the road • This calculation phase that starts from Phase 3 is another Plastic calculation, loading type Staged construction. • In Staged construction mode – Switch on the plate representing the road. Make sure the distributed load representing the traffic load remains switched off. 10

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Phase 5 - Apply the traffic load • Again a Plastic calculation of loading type Staged construction. • In Staged construction mode – Switch on both parts (left ánd right) of the distributed load representing the traffic load. The plate representing the road surface remains switched on. We are now finished with the road construction.

Phase 6 - Factor of safety of the road in summer conditions • In order to determine the factor of safety directly after constructing the road use a Safety phase starting from Phase 5.

Phase 7 - Winter conditions In winter, the water level inside the hill gradually increases due to rainfall. Only the highest water level in winter will be modelled, for which a steady-state groundwater flow analysis must be performed. The increase of water level should occur after finishing the road construction and not after determination of the factor of safety of this situation: • Select Phase 5 and press the Add phase button ( starting from Phase 5.

). Now Phase 7 will be created,

• In Water conditions mode – Select the Create water level button and draw a new water level from (x y) = (-1,20) to (5,20) and further to (20,10) and (66,10). – Choose the Select button (

) in order to stop drawing water levels.

– Right-click on the newly created water level and select the option Make global to make this new water level the global water level. – Select the bottom boundary of the model, and in the Selection explorer set the Behaviour of the boundary conditions to Closed. – Now right-click on the bottom boundary and in the menu that pops up select the option Activate in order to activate the closed boundary. • In Staged construction mode – Open the Phases window and in the General section set the Pore pressure calculation type to Steady-state groundwater flow. Computational Geotechnics PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Phase 8 - Factor of safety of the road in winter conditions • In order to determine the factor of safety directly in winter conditions create a Safety phase starting from Phase 7.

Phase 9 - Apply top level soil nails In winter conditions the factor of safety appears to be rather low and therefore it is decided to improve stability by applying launched soil nails. • The application of the first level of soil nails should occur after calculating winter conditions and not after determination of the factor of safety of this situation : select phase 7 and create a new phase • Staged construction mode – Switch on the topmost soil nail, see figure 7.

Figure 7: Phase 9, Road construction with traffic load and topmost level of soil nails

Phase 10 - Factor of safety in winter conditions with top level soil nails • In order to determine the factor of safety directly in winter conditions with the topmost level of soil nails installed create a Safety phase. Keep all default settings

Phase 11 - Apply additional soil nails • The application of the first level of soil nails should occur after installing the top level of soil nails and not after determination of the factor of safety of this situation. Therefore, create a phase starting from Phase 9 • In Staged construction mode – Switch on the 2 other soil nails 12

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Phase 12 - Factor of safety in winter conditions with all soil nails installed • In order to determine the factor of safety directly in winter conditions with the all soil nails installed create a final Safety phase. • For this Safety phase, set in the Phases window the amount of calculation steps (Max steps) to 200 in the Numerical control parameters section.

Load-displacement curves Before starting the calculation choose some points for node-displacement curves. In order to check failure for the phi/c reduction phases the chosen points should be in the expected failure zone. As there are several possible slope instabilities, chose at least points at (25,20), (35,16), (38,16) and (43,11). Now save the project and start the calculation by pressing the Calculate button.

SUCTION Beforehand, it was estimated that the factor of safety of the slope before construction should be in the order of 1.5 as there is no history of significant deformation for either low water table (summer) and high water table (winter). However, after the calculation it appears that the factor of safety before construction in summer conditions is just over 1.2 and it is doubted that the factor of safety in reality is indeed that low. Therefore the possibility of present suction is taken into account, as suction generally leads to an increased factor of safety. • Save the project under a different name • Open the Phases window and for all phases uncheck the option Ignore suction in the Deformation control parameters. Hence, we will allow for suction in all phases, • Mark all phases to be calculated. Now recalculate the project

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OUTPUT Failure mechanisms Figure 8 shows the failure mechanisms for all 5 conditions. Note that only for the winter condition with all soil nails installed, the failure mechanism is different depending on whether suction was taken into account. For all other conditions the failure mechanism is the same with or without suction, though the actual factor of safety is different.

(a) Before construction

(b) Summer conditions

(c) Winter conditions (no nails)

(d) Winter conditions (top nails)

(e) Winter conditions (all nails, no suction)

(f) Winter conditions (all nails, with suction)

Figure 8: Incremental displacements showing failure mechanisms

Factors of safety In order to check the factors of safety, strength reduction curves (ΣM sf vs. displacement of a control point) must be made in the Curves module. As can be seen from figure 8 it is not possible to use the same control point for all 6 factors of safety in case we ignore suction, as the failure mechanisms are in different locations for different situations. Therefore we choose the control points as: • (x y) = (25 20) for the winter conditions with all nails installed 14

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Slope stability for a road construction project • (x y) = (35 16) for all other conditions.

To create the curve as shown in figure 9 follow these steps:

• Open the Curves manager (

) and choose to start a new chart.

• Set the x-axis values to the total displacement of point (x y) = (35 16) and the y-axis values to the Project multiplier ΣM sf . • Right-click on the chart and choose the option Settings. • In the Settings window, on the tabsheet representing the curve, click the Phases... button and in the Select phases window that opens, deselect phase 12 (factor of safety of the winter conditions with all nails installed) so that it will not appear in the graph. To clean up the graph a bit more, one can decided to deselect all phases that are not Safety phases as well. • Close the Select phases window but do not close the Settings window. • In the Settings window now select the Add curve button and then from the popup menu select From current project. • Add a new curve, but now with the total displacements of point (x y) = (25 20) on the x-axis. The y-axis values remain the Project multiplier ΣM sf . • Back in the Settings window, on the tabsheet representing the newly added curve, click again the Phases... button. Now deselect all phases but keep phase 12 selected. • Close the Phases window • Addittionally, on the Chart tabsheet of the Settings window one can set the scaling of the axes. For instance the x-axis from 0 to 2 m. Press the Apply button to confirm this.

We now have a graph with the strength reduction curves for point (x y) = (25 20) for the final phases and for point (x y) = (35 16) for all other calculation phases. Please note that in case we do calculate with suction, all graphs can be created from point (x y) = (35 16) as this point is in the failure zone for all situations (see figure 10). Computational Geotechnics PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Figure 9: Factors of safety for key moments in the project without taking into account suction.

Figure 10: Factors of safety for key moments in the project taking into account suction. From figures 9 and 10 the effect of installing the nails on the factor of safety can be seen. It can also be seen that taking into account suction gives a factor of safety prior to construction that is more in accordance of the expected value, while suction only has a minor influence on the factor of safety in winter conditions as in winter conditions most of the soil is fully saturated.

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Ho Chi Minh Workshop Computational Geotechnics 14

MODELLING OF DEEP EXCAVATIONS IN 3D Dr William Cheang  

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Modelling of Deep Excavations in 3D Dr William Cheang Plaxis AsiaPac, Plaxis Academy

Contribution and slides from: Dr William Cheang Professor Antonio Gens Professor Helmut Schweiger A/Prof. Tan Siew An Dr Lee Siew Wei A/Prof. Boonchai Utkrichon Ir Dennis Waterman 1

CONTENTS 1. Modelling of Deep Excavations in Plaxis 2. Case Histories a. b. c.

Case 1: MCE-Influence of exacavation on adjacent piles Case 2: Performance for beam elements in the modelling of multi-strutted excavations Case 3: Back-analysis of Dragon centre excavation and reponse of piles located in excavated and retained zones.

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Geotechnical Finite Element Model The ability of finite element method to accurately reflect field conditions: 1. Ability of the constitutive model (soil and/or structural behaviour) 2. Soil Parameters 3. Correctness of boundary condition, 4. Appropriate geometry definition 5. Construction sequence

Geotechnical Finite Element Models Material Behaviour Modelling a. Soil b. Structure

Geometrical Modelling a. 2D or 3D b. Sequence of construction

3

MODELLING OF EXCAVATIONS SECTION A

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GEOMETRY‐ MODEL DISCRETIZATION & IDEALIZATION 2-D Plane Strain

3-D MODEL

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GEOMETRY‐ MODEL DISCRETIZATION Axi-symmentry

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3‐D FINITE ELEMENT MODELLING

Piled building

Tower crane

N

Strut layout Piled building 9

3-D MODEL OF AN EXCAVATION

Top of PW (70/90)

Top of Grade III or Better

N

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CASE 1 SECTION B

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365 16

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CASE 2 SECTION C

Modelling Excavations: Reponse of Struts • Model a non-symmetrical deep exc. • DWall, 6 strut layers, 24m deep exc. • Compare structural behaviour - DWall deflections/bending moments/shear forces, strut forces

20m

• Recommendation on design of reinforcement based on 3D results • Plaxis 3D Foundation V2.2 - analyses by GCG (Asia) 28m

• SAP2000 V12.0.2 (BD No. S0749) - analyses by AECOM

25m

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368 22 22

Plaxis 3D

SAP2000

Element size ~1.3m

Element size ~1m

23

Plaxis 3D

SAP2000

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Validation 3 – Deformed Mesh Plaxis 3D

SAP2000

25

Validation 3 – DWall Deflection

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Validation 3 – Strut Axial Force

27 27

DWall Bending Moment

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CASE 3: BACK-ANALYSIS OF DRAGON CENTER SECTION D

Back Analysis of Dragon Centre Deep Excavation • 9-storey RC bldg, 107×67m in plan • 5-level basement • Top-down exc. 27m deep • 1.2m thick DWall down to rockhead • GWT 1.5 mbgl • Ground conditions: Fill: ~4m thick Marine Deposits: ~3m thick CDG: ~33m thick HDG: ~25 m thick Lui & Yau (1995)

• Pumping test showed minor drawdown outside cofferdam

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HSsmall Model for CDG in Deep Excavation • HSsmall model to consider non-linear stiffness from small strain for Completely Decomposed Granite (CDG) in Hong Kong • HSsmall = Hardening Soil + Small-strain Overlay • Differentiate between shear stiffness (E50), compression stiffness (Eoed), unloading/reloading stiffness (Eur) • Two additional input parameters: G0ref and 0.7 • Calibrate HSsmall model against published CDG small strain stiffness data (Ng et al., 1998) • 3D analysis to back-analyse well-documented deep excavation at Dragon Centre, HK (Lui & Yau, 1995) • Investigate also behaviour of individual piles within and adjacent to cofferdam

HSsmall Model for CDG in Deep Excavation • Soil stiffness behaviour is non-linear from small strain • Need to model degradation of stiffness with strain

(0.01%)

(0.1%)

Benz (2007) PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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HSsmall Model for CDG in Deep Excavation • Excavation is an unloading problem • Soil stiffness in unloading is stiffer than that in loading E50: a loading stiffness Eur: Unloading stiffness Eur > E50 Eur ≈ 3 to 4 times E50

HSsmall Model for CDG in Deep Excavation • HSsmall considers non-linear unloading stiffness from small strain • Masing’s (1926) rule: 0.7 re-loading = 2×0.7 virgin-loading (Benz, 2007) Loading Re-loading

Re-loading

Un-loading

Loading

Unloading stiffness ≈ Re-loading stiffness > Loading stiffness PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Calibration of HSsmall Against Small Strain Data • Use small strain stiffness data from pressuremeter tests and drained triaxial tests by Ng et al. (1998) • CDG samples from Kowloon Bay near Dragon Centre Triaxial

Pressuremeter

Calibration of HSsmall Against Small Strain Data • Input parameters for CDG in HSsmall model Profile Upper Lower Baseline

E50ref (MPa) 50 20 39

Eoedref (MPa) 50 20 39

Eurref (MPa) 150 60 117

m 0.5 0.5 0.5

0.7 5E-5 5E-5 5E-5

G0ref (MPa) 250 100 200

pref (kPa) 200 200 200

K0nc 0.43 0.43 0.43

υur 0.2 0.2 0.2

 (°) 35 35 35

c′ (kPa) 5 5 5

1600 Triaxial_Upper

1400

Triaxial_Low er

1200

HSsmall_Upper

Gsec /p'

1000

HSsmall_Low er

800

HSsmall_Baseline

600 400 200 0 0.0001

0.001

0.01 0.1 Shear strain (%)

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1

10

375

3D Analysis by 3D Foundation • Model one-quarter of the problem • ‘Floor’ – basement slab; ‘Wall’ with interface – DWall; • ‘Volume Pile’ with interface – bored pile Slab

196 m

176 m

Fill

I3

I6

+5 mPD +1 -2

Stanchion

-35

CDG

Wall

-60

HDG

-80

Rock

33.5 m

53.5 m

symmetric plane symmetric plane

Bored pile

No. of element ≈ 31,000

3D Analysis by 3D Foundation • Input parameters for soils Soil Fill Marine Deposits CDG HDG Rock

HS

sat (kN/m3) 20

E50ref (MPa) 10

Eoedref (MPa) 10

Eurref (MPa) 30

m 0.5

0.7 -

G0ref (MPa) -

pref (kPa) 100

υur 0.2

K0nc 0.5

c′ (kPa) 0.1

 (°) 30

+1 to -2

HS

16

3

3

9

1

-

-

100

0.2

0.58

0.1

25

-2 to -35 -35 to -60 -60 to -80

HSsmall HSsmall

20 20 22

39 195 1000

39 195 -

117 585 -

0.5 0.5 -

5E-5 5E-5 -

200 988 -

200 200 -

0.2 0.2 0.2

0.43 0.36 1

5 5 -

35 40 -

Level (mPD) +5 to +1

Model

Elastic

• Wall corner effect (EI ↑) – at corner smaller wall deflection I3

I6

53.5m

33.5m

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Prediction on Wall Deflection & Surface Settlement 80

Wall deflectio n (mm) 60 40 20

(a) Pump Test

I6

0

80

Wall deflectio n (mm) 60 40 20

0

80

Wall deflectio n (mm) 60 40 20

0

0

0

0

-10

-10

-10

-20

-20

-20

-30

-30

-30

-40

(b) GWT recovery

(c) Final exc.

-40

Field

-40

Field -50

B rick

-50

Field

HSssmall

-50

B rick

HSsmall

HSsmall

-60

-60

-60

Note: Brick predictions by Malone et al. (1997) 0

10

20

Distance from exc. (m) 30 40 50 60

70

0

80

0 10

10

20

20

30

30

40

Field

50 60 70

10

Distance fro m exc. (m) 20 30 40 50

60

70

80

0

B rick

(a) Pump Test

HSsmall

40 Field

50 60 70

(c) Final exc.

B rick HSsmall

Incremental settlement due only to exc.

Behaviour of Individual Piles Near Cofferdam •

In routine design individual piles usually modelled as ‘plate’ in 2D analysis

•

2D uses equivalent EI and EA – real pile EI and EA divided by pile spacing into-the-plane

•

2D may give conservative/non-conservative predictions b’cos

1. soil not allowed to move past the piles (continuous ‘plate’ ) 2. difference in surface area between pile and ‘plate’ •

Include hypothetical piles in 3D model of Dragon Centre – piles placed outside & within cofferdam

•

Investigate difference in pile deflection and pile axial force between 3D and 2D analyses

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Individual Piles Outside Cofferdam • A row of piles 1.5 m Ø spaced at 7.5 m c/c, founded on rockhead +5 mPD A

B

C S -22 mPD

long side DWall

CDG

S

Plan view in 3D

Pile-wall (‘Plate’)

DWall

HDG

DWall

3D analysis

Close up view

2D analysis • Distance from DWall (S) = 3 m (2Ø), 7.5 m (5Ø) & 15 m (10Ø)

• Use equivalent EA and EI

Pile Deflection Between 3D and 2D Pile deflection (m)

10

Pile deflection (m)

Pile deflection (m)

10

S=3m

10

S=7.5m

0

0

0

-10

-10

-10

-20

-20

-20

-30

-30

-30

-40

-40

-40

A -50

A

B

B

-50

C

C

2D

2D

-60

-60

A

S=15m

A -50

B C 2D

-60

B

C S

long side DWall PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Individual Piles Inside Cofferdam +5 mPD DWall

Close-up view

Soil moves relative to pile -22 mPD CDG

CDG pile-wall (‘Plate’) HDG

Y X

HDG

DWall

Rock

DWall Rock

pile

3D analysis

2D analysis (EIeq & EAeq)

• A row of piles 1.5 m Ø spaced at 7.5 m c/c, founded on rockhead • Piles installed at centreline of cofferdam • Investigate tensile axial force in piles due to heaving of cofferdam

Tensile Axial Force in Piles Between 3D and 2D Load in pile (kN)

DWall -500

0

500

1000 1500 2000 2500 3000 3500 4000 4500 5000

10 X 0 -10 Level (mPD)

CDG

HDG

Y X

Rock

Y 2D

-20 -30 -40 -50 -60

• 2D predicts 4600 kN tensile axial force • 3D predicts 1250 kN (3.7 times smaller) • Main reason: 2D pile-wall (‘plate’) unrealistically large surface area for mobilisation of shaft friction PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Summary on Dragon Centre Back-analysis •

Good prediction of ground movements in all excavation stages needs to consider non-linear soil stiffness from small strain

•

HSsmall appears replicate well small strain stiffness of CDG

•

HSsmall answers engineers’ need – minimal input parameters

•

Model individual piles as continuous ‘plate’ in 2D with caution

•

2D could under-predict deflection of individual piles behind DWall → non-conservative approach

•

2D could significantly over-predict tensile axial force of individual piles installed within cofferdam → conservative approach

•

Main limitations of 2D ‘plate’ approach:

1. soil is not allowed to move past the piles 2. ‘plate’ provides too large surface area for shaft friction (end bearing area also inappropriate)

THANK YOU

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Ho Chi Minh Workshop Computational Geotechnics 15

MODELLING OF PILE FOUNDATIONS IN 3D Dr Phung Duc Long  

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Modeling of Piled Foundations in 3D Dr. Phung Duc Long

Acknowledgement: Some slides from Prof. Helmut Schweigher

Plaxis Course, 16-18 September, Ho Chi Minh City, Viet Nam

CONTENT

 Conventional pile foundation and piled-raft concept  FE-Modelling of piles: Volume piles (VP) & Embedded pile (EP)  VP concept  EP concept  Plaxis input data for EP  Validation of EP concept  Comparison of EP & VP  Deep foundation of two adjacent high-rise buildings in Vienna  Deep foundation of tower for shopping mall in Bucharest PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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FOUNDATION OPTIONS

Conentional Raft (raft only)

Piled and Raft (PRF)

Conventional piles (piles only)

PILED-RAFT & CONVENTIONAL PILES - CASE HISTORIES Phung Duc Long (2011)

• Systematic measurements of the load transfer mechanism • Designed as a pile foundation, acting as a piled-raft (cases 4, 8, 9 , 12, 13) • Piled rafts: number of piles control settlement…. • Smaller load taken by piles bigger settlement

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PILED-RAFT & CONVENTIONAL PILES - CASE HISTORIES El-Mossallamy (2008), modified by Phung Duc Long (2011)

4 = Petronas Tower, Kuala Lampur 5 = QV1 Tower, Perth, Australia 6 = Treptower, Berlin 8 = Commerzbank, Frankfurt 10 = Skyper, Frankfurt 11 = Dubai Tower, Qatar 12 = Incheon Tower, Korea 13 = Emirates Twin Tower, U.E.A.

TWO WAYS FOR MODELLING PILES IN PLAXIS

USING VOLUME PILE ELEMENTS (VP)  

Small number of piles Simulating installation effects of and the pile-soil interaction at the circumference.

USING EMBEDDED PILE ELEMENTS (EP)  

Large number of piles Piles are different in length, spacing, orientation

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MODELLING PILES USING VOLUME PILE ELEMENTS (VP)

Piles are discretized by means of volume finite elements Pile-soil interaction is modelled with interface elements

tan ´i  Rinter  tan ´

c´i  Rinter  c´

Important: Influence of dilatancy (constrained problem)

Limitations of the approach: Number of modelled piles may be limited

INFLUENCE OF MESH COARSENESS (VP)

Example by Potts & Zdravkovic (2001) Pile L= 20m, d= 1m, E= 2E7 kPa,  = 0.15 Soil: Tresca model, sat = 18 kN/m3, Eu= 1E5 kPa, cu= 100kPa,  = 0.49

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LIMITATION OF STANDARD FE APPROACH (VP)

Number of piles which can be modelled with the standard FE approach is limited, especially a reasonable fine mesh is needed to obtained reliable displacements, and even finer meshes are required to evaluate stresses.

Structural elements of a 3D FEM model with 137 volume piles

EMBEDDED PILE CONCEPT (EP) 

An embedded pile = beam elements being placed in arbitrary direction in the sub-soil with special interface elements providing the interaction between the beam and the surrounding soil (skin & foot resistance).



Although an embedded pile does not occupy volume, a particular volume around the pile (elastic zone) is assumed in which plastic soil behaviour is excluded. The size of this zone is based on the (equivalent) pile diameter according to the corresponding embedded pile material data set. This makes the pile almost behave like a volume pile.



Special interface elements are different from the regular interface elements. Therefore, at the position of the beam element nodes, virtual nodes are created in the soil volume element from the element shape functions

An embedded pile is a pile which consists of:  Beam elements • Properties: E, , d  Special interface elements • Properties: skin resistance, base resistance

Embedded pile with a 15-noded wedge element (left) and a 10-noded tetrahedral element (right)

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PILE RESISTANCE (EP)

ts

Shear stress in axial direction

tn /tt

Normal stress in n/t – direction

Ks

Elastic shear stiffness

Kn/Kt

Elastic normal stiffness in n/t - direction

up

Displacements of the pile

us

Displacements of the soil

BASIC ASSUMPTIONS Paxial Pile‐ head

Plateral soil  masses

Pile behaviour depends on: • Soil type • Stress state • Pile geometry • Pile type (Steel, concrete, timber…) • Installation procedure

Qs Qn summarized in "interface behaviour"

Pile‐ base

Fn

Fs

Qs Qn Fs Fn

: mantle/skin shear forces : mantle/skin normal forces : pile‐base shear forces : pile‐base normal forces 

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ELASTIC REGION APPROACH (EP) Elastic region: determined by diameter of pile, d  Elastic region approach •

Loop over stress points

•

Inside the elastic region (Req) plasticity is excluded

 Stiffness inside is not modified

Note: reference concept > as implemented originally in FE-code Plaxis 3D Foundation

MATERIAL DATA SETS FOR EMBEDDED PILES

A data set for EP represents type of pile, (incl. pile material & geometric properties) and the interaction properties with the surrounding soil (pile bearing capacity) In contrast to what is common in the FEM, the bearing capacity of an embedded pile is considered to be an input parameter rather than the result of the FE calculation. The parameter should be based on pile load test results. If embedded piles are used in a group, the group action must be taken into account when defining the pile bearing capacity.

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MATERIAL DATA SETS FOR EMBEDDED PILES

MATERIAL SET: • Identification • Comments • Colour

PROPERTIES:  General properties: E,   Pile type: • Predefined • Massive circular pile • Circular tube • Massive square pile • User-defined

INTERACTION PROPERTIES:  Skin resistance  Base resistance

PREDEFINED PILE

• Massive circular pile Diameter

• Circular tube: Diameter & thickness

• Massive square pile: Width Diameter determines the size of the elastic zone in the soil around the beam in which plastic soil behaviour is excluded. This makes the embedded pile almost behaves like a volume pile.

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USER-DEFINED PILE A user-defined type is defined by pile cross section area, A, and its respective moments of inertia I3 and I2 , against bending around the third and the second axis.

In this alternative, the equivalent radius for the elastic zone, Req, is determined

INTERACTION PROPERTIES (PILE BEARING CAPACITY) Interaction between the pile (beam element) and the surrounding soil (soil volume element) is modelled by a special interface element with elastic-plastic model. Linear skin resistance

Multi-linear skin resistance

Layer-dependent skin resistance The local skin resistance is related to the strength properties (cohesion c and friction angle ') of the soil layer in which the pile is located, using interface strength reduction factor, Rinter , Base resistance Fmax can be entered directly (in force unit, kN)

Skin resistance T (kN/m) & Base resistance Fmax (kN) are input data, not analysis results ! PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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DEFICIENCIES OF THE REFERENCE EMBEDDED PILE CONCEPT Mesh dependency   

Parameter study on a single pile 9.5m long Soil: slightly overconsolidated clay (HS model) Deficiencies: • Load-settlement behaviour • Convergence problems > numerical failure

3169 kN

Pile resistance R (INPUT)

IMPROVEMENTS OF EMBEDDED PILE CONCEPT Tschuchnigg (2013)

Modification of embedded pile base interface stiffness Kbase (Rsu = 0):

K base   base  Gel av Req  base

 Soil: dense sand (MC model)  Embedded pile: l = 10 m; Req = 0.4 m

 No convergence problems (Rbu = Fmax = 2300 kN)  Kbase > significant influence   25%

Increase of Kbase by a factor 5 to 10 improves performance of embedded pile concept PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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IMPROVEMENTS OF EMBEDDED PILE CONCEPT Modification of the elastic region approach  Stress flow inside the elastic region:  2D axisymmetric analyses (with elastic region)  Medium dense sand

Eur  E ur ,ref

 c´ cos ´ ´3  sin ´     c´ cos ´ p ref  sin ´   

m

Reduction of stiffness

IMPROVEMENTS OF EMBEDDED PILE CONCEPT Modification of the elastic region approach  Stress flow inside the elastic region:  2D axisymmetric analyses (with elastic region)  Medium dense sand

Change of p´ Mesh dependency  E el.R = f(p´): > Mesh dependency reduced significantly

VALIDATION OF IMPROVED EMBEDDED PILE CONCEPT Pile groups and piled raft foundations

 Geometry (Chow & Small 2008):

25 piles L = 20 m, D = 1.128 m

Load: 50 kPa

 Soil: linear elastic  Load: Vertical 50 kPa Horizontal 50 kPa

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VALIDATION OF IMPROVED EMBEDDED PILE CONCEPT Pile groups and piled raft foundations  Geometry (Chow & Small 2008):

 Settlements along cross section A-A

25 piles L = 20 m, D = 1.128 m

 Soil: linear elastic Vertical 50 kPa Horizontal 50 kPa

Cross section A-A

Cross section A-A

 Load:

  2%

VALIDATION OF IMPROVED EMBEDDED PILE CONCEPT Pile groups and piled raft foundations  Geometry (Chow & Small 2008):

 Normal force and mobilized skin friction - Pile P2

- 25 piles - L = 20 m / D = 1.128 m

 Soil: - linear elastic

 Load: - Vertical 50 kPa - Horizontal 50 kPa

Pile P2

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VALIDATION OF IMPROVED EMBEDDED PILE CONCEPT Pile groups and piled raft foundations

 Geometry (Chow & Small 2008):

 Horizontal deflection and bending moment - Pile P3

25 piles L = 20 m / D = 1.128 m

 Soil: - linear elastic

 Load: Vertical 50 kPa Horizontal 50 kPa

Pile P3

COMPARING EMBEDDED PILE (EP) TO SOLID PILE (VP) H. Tan (2007) FEM Mesh (>5000 elements)

Solid pile • Single Bored Pile of D= 1m and L= 20m • M-C soil of cu=100 kPa, =0, E= 40 MPa, =0.3, Rinter =1 • Pile under axial compressive load +Fz • Pile under axial tensile load -Fz • Pile under lateral load +Fx

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Embedded pile

395

COMPARING EMBEDDED PILE TO SOLID PILE Axial Compression Load

• Solid Pile • Embed-1, layer-dependent skin friction, end bearing limit to 9cu=900 kPa • Embed-2, layer-dependent skin friction, end bearing limit to 10000 kPa

COMPARING EMBEDDED PILE TO SOLID PILE Tension Pile Test

• Solid bored pile • Embedded pile with layer dependent skin friction distribution • Embedded pile with linear skin friction

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COMPARING EMBEDDED PILE TO SOLID PILE Lateral Load Test

• Solid Pile • Embed-1, layer-dependent skin friction, end bearing limit to 9cu=900 kPa

COMPARING EMBEDDED PILE TO SOLID PILE CONCLUSIONS

• Embedded pile is a good model of single pile response • It gives realistic results for axial compression, tension and lateral loading when compared to simple theory for a rigid plastic soil • Calibration work is needed for correct use of embedded and solid piles

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DEEP FOUNDATION FOR DC Towers (Vienna) 

Project overview



Soil conditions and its numerical modelling



Finite element models



Optimisation of the foundation concept



Results



Conclusions

DC TOWERS Concept for foundation: deep foundation with diaphragm wall panels

~220 m

~168 m

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PROJECT OVERVIEW - TWIN TOWERS Underground car parks

56.3 m

TOWER I

TOWER II 24 m

58.9 m

64.1 m

Facts:

TOWER I: 220 m high (around 60 stories) > constructed first TOWER II: 165 m high Foundation system: diaphragm wall panels

SOIL CONDITIONS AND ITS NUMERICAL MODELLING

 Constitutive model: •

Hardening Soil Model (HS)

•

Hardening Soil Small Model (HSS)

•

Consideration of overconsolidation (800 kPa) > K0 = 0.7

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SOIL CONDITIONS AND ITS NUMERICAL MODELLING

Stiffness [MPa]

Barrette length 30m

Depth [m]

Slab

 c' cot ' 3 E ur  E ref ur    c' cot ' p ref 

  

SOIL CONDITIONS AND ITS NUMERICAL MODELLING

Definition of additional parameters for the HSS model:

G0

G0: Correlation between small strain stiffness and stiffness at larger strains after Alpan (1970) 0.7: Stiffness reduction curves after Vucetic and Dobrey (1991)

0.7

Parameter E50ref (kPa) Eoedref (kPa) Eurref (kPa) pref (kPa) m (-) G0 (kPa) 0.7 (-)

Gravel 40 000 40 000 120 000 100 0.00 150 000 0.0001

Sandy silt 20 000 20 000 50 000 100 0.80 62 500 0.0002

Fine sand 25 000 25 000 62 500 100 0.65 78 125 0.0002

HS model HSS model

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m

FINITE ELEMENT MODELS - OVERVIEW

 

Both towers are modelled Models consist of around 50 000 15-noded wedge elements

FINITE ELEMENT MODELS - DETAILED MODELS

Detailed model for Tower I

Barrettes with unit dimensions of 3.6 m x 0.6 m

Detailed model for Tower II

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FINITE ELEMENT MODELS - FIRST RESULTS TOWER II

Detailed model Tower II:  Barrette length 25 m  uy,max of 80 mm  Interaction of towers  Differential settlements

Eccentric loads lead to large differential settlements

OPTIMISATION OF FOUNDATION CONCEPT Final design of deep foundation system

Arrangement of diaphragm wall panels for Tower I

Arrangement of diaphragm wall panels for Tower II

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OPTIMISATION OF FOUNDATION CONCEPT

RESULTS

 Barrette lengths between 20 m and 30 m  Maximum vertical displacements of both towers ~80 mm  Differential settlements reduced to acceptable value PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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RESULTS WITH FULL MODEL

Model details: 

No geometrical simplifications



~ 140 000 15-noded wedge elements



Mesh refinement



300 diaphragm wall panels are modelled explicitly

Expectations: 

Validate first approach



Detailed information about settlement trough between towers

_________________________________________________________ Model Nr. El. Nr.Nodes Nr.El in 2D plane _________________________________________________________ 32 bit model 49 096 131 993 2 888 64 bit model 136 710 361 243 6 510 _________________________________________________________

RESULTS WITH FULL MODEL

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RESULTS WITH FULL MODEL

 Results are similar to first approach  Maximum vertical displacements ~80 mm  More accurate with respect to interaction and settlement trough between tower

RESULTS

Contours of surface settlements

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RESULTS

Settlements / differential settlements 

B

Road – up to 40 mm > tolerable



Highway - Point A 14 mm > Inclination 1/900 > tolerable



Train - Point B 18 mm > Inclination 1/600 > tolerable

But: measurements during construction are essential

A

RESULTS - HS VERSUS HSS (TOWER I)



Up to depth of -36.6 m Distribution is similar Difference is 25%



Beneath foundation elements Difference increases



At depth of -75 m HSS predicts 51% less vertical displacements

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COMPARISON OF DIFFERENT FOUNDATION SYSTEMS Alternative foundation concept: Piled raft foundation Layout 1: 75 Piles Diameter 1.5m Spacing 6*D Pile lengths are based on executed deep foundation with panels (20 - 30m)  Piles are modelled as continuum (VP) with interfaces:    

tan  i  R inter  tan  Soil  tan  Soil c i  R inter  c Soil

 i  0 for

Rinter  1.0, otherwise  i   Soil

 Also modelled with Embedded Piles (EP)

COMPARISON OF DIFFERENT FOUNDATION SYSTEMS Alternative foundation concept: Piled raft foundation

Layout 2:  Piles modelled with Embedded Piles concept (EP)  Diameter 1.5 m  Pile spacing is reduced in high loaded regions  Pile lengths are based on executed deep foundation with panels (20 - 30 m)

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COMPARISON OF DIFFERENT FOUNDATION SYSTEMS Alternative foundation concept: Piled raft foundation

Layout 2:  Piles modelled with Embedded Piles concept (EP)  Diameter 1.5 m  Pile spacing is reduced in high loaded regions  Pile lengths are based on executed deep foundation with panels (20 - 30 m) Maximum vertical displacements:  Tower I: ~ 90 mm  Tower II: ~ 90 mm

COMPARISON OF DIFFERENT FOUNDATION SYSTEMS – TOWER I

(m)

Barrettes

Shallow foundation

Maximum settlements: • Barrettes: 7.6 cm • Layout 1 (VP): 12.0 cm • Layout 1 (EP): 12.0 cm • Layout 2 (EP): 8.7 cm • Shallow foundation: 18.7 cm

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COMPARISON OF DIFFERENT FOUNDATION SYSTEMS

 Maximum settlements 

 Kpp 

KPP:

R Pile Rtot Layout 1: 0.42 Layout 2: 0.80

~ 55 %

COMPARISON OF DIFFERENT FOUNDATION SYSTEMS – TOWER II

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CONCLUSIONS FOR THIS PROJECT

Deep foundation of DC Towers:  Same length of deep foundation elements > high differential settlements.  Final foundation concept with lengths between 20-30 m improves the settlement behaviour of the towers.  The computed maximum vertical displacements are about 80 mm. The settlements of the highway and the railway lines are in the order of 15-20 mm.  When using the HSS model the influence of the model boundary condition (in particular bottom boundary) is reduced and a more realistic settlement behaviour can be obtained.

Alternative foundation concept: Piled raft foundation 

When using embedded piles no additional geometry points are created > embedded piles do not influence the finite element discretisation.



Different modelling approaches show similar results > embedded pile option is well suitable for these types of deep foundations.



From an economical point of view a piled raft foundation (Layout 2) is a conceivable alternative.

SHOPPING MALL WITH SKY TOWER IN BUCHAREST

Sky Tower

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PROJECT OVERVIEW - SKY TOWER

•

Dimensions 93.4 x 61.7 m

•

Height more than 130 m

•

Excavation depth 20.4 m

•

Slab thickness 2.6 / 1.5 m

•

Point loads up to 14 900 kN

Results of interest: 1. Maximum differential settlements (of 2.6 m thick slab) 2. Arrangement of diaphragm wall elements

SHOPPING MALL WITH SKY TOWER

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SOIL CONDITIONS Silty Clay

~20.5 m

Soil profile: 60.0 m

~25.0 m

 Core drillings down to -60 m  Altering layers of sands and silty clays  Drained conditions are assumed

Assumption: Alternate layers continue

Sand

Constitutive models:  Diaphragm wall panels > Mohr-Coulomb  Floors > Linear elastic  Soil layers > Hardening Soil Model

FINITE ELEMENT MODELS

Core walls

Floors (Top-down method)

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SOIL CONDITIONS AND ITS NUMERICAL MODELLING

Parameter unsat (kN/m3) sat (kN/m3) E50ref (kPa) Eoedref (kPa) Eurref (kPa) ’ur (-) pref (kPa) m (-) ’(o) c’ (kPa) G0 (kPa) 0.7 (-)

Silty clay 20.5 21.0 12 000 10 000 36 000 0.2 100 0.70 22.5 25.0 45 000 0.0002

Sand 21.0 21.5 30 000 30 000 50 000 0.2 100 0.65 32.5 0.0 112 500 0.0002

Parameter  (kN/m3)  E (kPa) c‘ (kPa) ‘ (o)

HS model

Diaphragm wall 25 0.20 2.5e7 5100 45.0

HSS model

FINITE ELEMENT MODEL Layout 1 Top view

Deep foundation elements in 3D FE model Cross section

~ 62 m

2D "Plane strain" model

~ 94 m

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FINITE ELEMENT MODEL

 2D (plane strain) model overestimates differential settlements by approx. 100%  2D representation of geometry / load situation not possible uy,max~ 165 mm uy,diff.max ~ 100 mm

 2D representation of deep foundation elements not possible

> For optimisation of foundation concept full 3D modelling is required uy,max~ 95 mm uy,diff.max ~ 50 mm

OPTIMISATION OF FOUNDATION CONCEPT Final foundation concept FE discretization of panels

15 m

25 m

Top view

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OPTIMISATION OF FOUNDATION CONCEPT Final foundation concept Vertical displacements of slab

Contour lines of settlements

 Maximum vertical displacements of about 105 mm  Maximum differential settlements of about 65 mm  Between point A and C (2.6 m thick slab) differential settlements of about 47 mm

VALIDATION OF NUMERICAL MODEL (IN SITU LOAD TEST) Back-analysis of O-Cell Test FE model

Measurements vs calculation

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CONCLUSIONS FOR THIS PROJECT

 

Due to the geometrical layout 2D analysis proved to be too conservative.



The final concept of the deep foundation consists of two discontinuous circles beneath the highly loaded areas.



The computed maximum settlements are about 105 mm. The expected maximum differential displacements are about 65 mm.



The numerical back analysis of an in-situ load test shows reasonable agreement

A number of 3D calculations have been performed investigating different arrangements of diaphragm wall panels.

 The soil parameters have been estimated prior to the test and no adjustments have been made.



The analyses provide a good, yet somewhat conservative estimate of settlements for the Sky Tower.

REFERENCES



Brinkgreve, R.B.J. et al. (2012). PLAXIS 3D 2012, Finite element code for soil and rock analyses, Users Manual, Plaxis bv, Delft, The Netherlands.



Phung Duc Long (2011). Piled Raft - A New Foundation Design Philosophy for HighRises. Proc. Int. Conf. Geotec Hanoi 2011, October 2011, pp. 267-276



Schweiger, H.F., Tschuchnigg, F. (2013). Keynote lecture: Examples for successful 3D finite element analysis in geotechnical engineering. Proc. Int. Conf. Geotec Hanoi 2011, November 2013, pp. 703-712



Tschuchnigg, F. (2013). 3D Finite element modelling of deep foundations employing an embedded pile formulation. Ph.D. Thesis, Graz University of Technology.

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Ho Chi Minh Workshop Computational Geotechnics 16

EXERCISE 5: MODELLING OF PILE FOUNDATIONS IN 3D Dr Phung Duc Long  

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E5: Exercise on Pile Analysis Based on an actual project: Pile Foundations for Flieden Bridge in Germany Original exercise made by Dr Yasser El-Mossallamy (ARCADIS Consult, Germany)

Presented By RF Shen 25 November 2011 1

Briefing of the Project

2

Exercise SG-E5-Shen PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Briefing of the Project y

X = ‐35m  to 35m X

(‐4 ‐25 0) (‐.4 ‐25 ‐.8) (.4 ‐25 ‐.8) (4 ‐25 0)

z X

y = ‐25m  to 25m z = 0 to    ‐30m 3

Briefing of the Project

The subsoil consists mainly of tertiary  formations of highly plastic clay with lenses of  lignite coal (clay with brown coal). In this  analysis, a uniform clay layer was idealized with  OCR = 1.3 4

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Soil parameters

5

Simulation in Plaxis 3D Step 1:  General setting Step 2:  Add in a borehole Step 3:  Define soil properties Step 4:  Create 6 piles Step 5:  Create 1 pile cap Step 6:  Clone another pile group Step 7:  Create the trench Step 8:  Assign vertical loads Step 9:  Generate mesh with refinement Step 10: Define stages and view results

6

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Flieden bridge piled-raft foundation

FLIEDEN BRIDGE PILED-RAFT FOUNDATION

Original excercise made by Dr. Yasser El-Mossallamy ARCADIS Consult. Germany

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Flieden bridge piled-raft foundation

INTRODUCTION The foundation of the 4-span railway bridge of Flieden in Germany (figure 1) was the first railway bridge in Germany founded on piled rafts.

Figure 1: Geological conditions of the Flieden railway bridge The subsoil consists mainly of tertiary formations of highly plastic clay with lenses of lignite coal (clay with brown coal). To ascertain the adequacy of the piles and determine appropriate design values, pile load tests were first conducted on large diameter bored piles with and without post shaft grouting (El-Mossallamy et al. 2003). These results conform to the mechanical sensitivity of the organic silty clay and lignite coal lenses. It was decided to install all foundation piles applying post shaft grouting.

INPUT The bridge piers are consisted of two pillars, each founded on a separate group of 6 piles underneath a raft. The pile arrangements are shown in Figure 2. The rafts are 1.5 meters thick and are embedded in the soil with the raft base at a depth of 2.3 meters below the soil surface. The piles where designed with a diameter of 1.2 m and a length of 18 m. The pillars transfer two working loads of 20 MN and 22 MN respectively from the superstructure to the piled raft foundation.

Work flow In this excercise the model is created in a specific order that has proven to be a rather efficient way to create the model. Please note that many parts of the model can be created in any other order as well and the work flow presented here is not the only correct method to create the project. The work flow to create the project presented here is: 1. Enter dimensions of the project and some general visualisation options 2. Define the underground model using 1 borehole and the appropriate soil material sets Computational geotechnics PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Flieden bridge piled-raft foundation

Figure 2: Geometry of the piled raft foundation 3. Insert 1 pile in the model 4. Copy this 1 pile 5 times to create the 6 piles needed for 1 piled raft 5. Insert the raft, the lower column and the top load 6. Copy the complete piled-raft 1 time to create the second piled raft 7. Create an extra zone for mesh refinement around the piled-rafts 8. Generate mesh

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Geometry General settings Start the PLAXIS 3D input program. A Quick select project dialog box will appear in which you can select an existing project or create a new one; choose Start a new project so that the Project properties window appears. 1. In the Project properties window on the Model tabsheet the size of the model contour has to be set. In the Contour box fill in xmin = −35, xmax = 35, y min = −25 and y max = 25. 2. Close the Project properties window, the drawing area will now appear. 3. From the Options menu choose Visualization settings. A new window will open, containing 2 tabsheets: View and Visibility. 4. On the View tabsheet the grid point distance (Spacing) and number of snap intervals per grid distance can be set. By default the Spacing is set to 1 m with only 1 snap interval per grid distance. As can be seen from figure 2 many dimensions of this project have an accuracy of 0.1 m and therefore just 1 snap interval per 1 m is not sufficient. Therefore, set the Intervals to 10, this will results in having a snap distance of 0.1m (Spacing / Intervals). 5. Close the Visualization settings window.

Subsoil The first step in creating a model in PLAXIS 3D is the definition of the subsoil, which is done using boreholes. 1. Select the Create borehole button ( ) and move the mouse to the origin of the system of axis. Click at (x,y,z) = (0 0 0), this will open the Modify soil layers window. 2. In the Modify soil layers window click the Add button in order to define a new soil layer in this borehole. Set the top of the borehole to 0.0 m and the bottom to -30.0 m. 3. In order to assign a material set to the newly defined model it is necessary to first define ) to open the material a material set. To do so, press the Materials button ( sets database. 4. Though the model only has one soil layer (clay) we will have to define two material sets: the second material set will be used to represent the concrete needed for both raft and piles. Therefore, create two material sets according to the material parameters specified in table 1. 5. After defining the two material sets close the window by clicking OK in order to return to the Material sets window. Computational geotechnics PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Flieden bridge piled-raft foundation Table 1: Parameters for the clay layer and concrete slab Parameter Material model Type of behaviour Unsaturated soil weight Saturated soil weight Young’s modulus Drained triaxial test stiffness Primary oedometer stiffness Unloading/reloading stiffness Power for stress-dependent stiffness Poisson’s ratio Unloading-reloading Poisson’s ratio Cohesion Friction angle Dilatancy angle Permeability Interface strength Coefficient for initial lateral stress Overconsolidation ratio

Name

Clay

Concrete

Unit

Material model Drainage type γunsat γsat Eref ref E50 ref Eoed ref Eur m ν νur c’ ϕ ψ kx , k y , k z Rinter K0 OCR

Hardening Soil Drained 20.0 20.0 45.0 45.0 135.0 0.9 0.2 10 30 0 0 0.6 (Manual) Automatic 1.3

Linear Elastic Non porous 24.0 30000 0.3 Rigid Automatic -

kN/m3 kN/m3 M N/m2 M N/m2 M N/m2 M N/m2 kN/m2 o o

m/day -

6. Drag and drop the clay material set from the Material sets window onto the borehole. The mouse cursor changes shape when the material set can be dropped. After dropping the borehole should get the colour of the material set. Now close the Material sets window in order to return to the Modify soil layer window. 7. In the Modify soil layer window directly above the graphical representation of the borehole it is possible to specifty a general phreatic level for this borehole by changing the Head value. In this project the water level is 0.5 meters below ground level, therefore change the Head to -0.5 m. 8. Press OK to close the Modify soil layers window and return to the drawing area. In the drawing area there is now a block of soil with the horizontal dimensions specified in the Project properties window and a depth according to the borehole. We have now finished defining the subsoil and we will continue defining the foundation. Press ) on the mode toolbar to move to Structures mode. the Structures option (

Create foundation structures Create piles The two bridge foundations are equal with exception of the load from the bridge acting on the foundation. Therefore it’s sufficient to define 1 foundation and then make a copy of the

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Flieden bridge piled-raft foundation foundation to get the second. Similarly, each foundation is supported by six equal piles, hence it is sufficient to define 1 pile and make 5 copies to model all piles to model 1 foundation. In the current version of PLAXIS 3D the only possibility to insert a pile is by inserting a cylinderical volume using the command line. The syntax for inserting a cylinder is: cylinder ( ) ( )

In short, one specifies the radius (R) and length (L) of the cylinder, a set of 3 coordinates to indicate the starting point of the cylinder and a vector to indicate the direction of the cylinder. Special attention should be given to . In PLAXIS 3D a cylinder is modelled with a polygon cross section, hence gives the number of sides of the polygon. The higher the number the more accurate the polygon will represent the circular cross section. 9. Insert the first pile at (x,y) = (-8.4, -1.8). Note that the piles have a 1.2m diameter (hence a radius of 0.6m), are 18 meters long, start at z = -2.3m and go down vertically, that is in the negative z-direction. The number of planes is set to 15 to accurately model the cylinderical shape. This results in the following cylinder command:

cylinder 0.6 18 15 (-8.4 -1.8 -2.3) (0 0 -1) Type this command on the command line and press . The cylinder is now inserted in the model as a volume. 10. In order to assign interfaces around the pile, the pile has to be split into its separate surfaces. To do so, right click on the pile and from the popup menu choose Decompose into surfaces. 11. Now select the outer surfaces of the pile, right-click and select Create negative interface. This will create a negative interface along the outside of the pile. 12. In order to create an interface below the foot of the pile, select the bottom circular surface of the pile. It is probably necessary to rotate the model in order to see the foot of the pile from below. Right-click again and select Create negative interface to create the interface below the foot as well. Hint:

Interfaces are drawn as planes at a certain distance from the surface they belong to. Therefore, if a project requires a lot of interfaces it may become difficult to see the underlying structure as the interfaces are surrounding it. This can be solved by either reducing the distance between interface and structure or by making the interfaces invisible. The distance between interface and surface can be reduced in the Visualization settings that can be found under the Options menu. On the View tabsheet the field Interface size controls the distance. By default this value is set to 1. Reducing this value will reduce the distance between interface and surface. Alternatively, in the Object explorer it is possible to make the interfaces invisible by clicking on the small eye in front of the branch Interfaces (to make them all invisible) or in front of individual interfaces (to make only a selection of interfaces invisible).

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Flieden bridge piled-raft foundation We have now finished creating the first pile. The next step is to make 5 copies of the pile to create the group of 6 piles of the first foundation slab. 13. Click the button Select rectangle ( ), ignore the suboptions that become available. Now draw a rectangle that fits the whole pile so that all parts of the pile are selected. ) to specify the locations of the copies of the pile. 14. Now click the Create array button ( The Create array window appears, see figure 3.

Figure 3: Copy the pile by creating an 2-dimensional array of piles In x-direction we need 3 piles with an intermediate distance of 3.4 meters and in the y-direction we only need 2 piles with a distance of 3.6 meters in between. 15. Set the Shape of the array to 2D, in xy plane as we want to copy the piles in both x and y direction, keeping the z coordinate constant 16. Fill in 3 columns with a distance of x = 3.4m in between and 2 rows with a distance of y = 3.6m in between. 17. Press OK to copy the pile to the specified locations. We have now created the 6 piles for one of the bridge foundations. Create first raft After creating the 6 piles now the raft has to be modelled on top of the piles, including the lower part of the column supporting the bridge: Computational geotechnics PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Flieden bridge piled-raft foundation 1. From the horizontal button bar with general options, click the Top view button ( will show the model seen along the z-axis.

). This

2. In the Movement limitation window that appears, fix the z-coordinate to z = -0.8m by filling in -0.8 in the z-value field and clicking the Set button. 3. Select the Create surface button ( ) and draw the surface representing the top side of the raft from (x y) = (-9.6 -3.0) to (-9.6 3.0), (-0.4 3.0) and (-0.4 -3.0). 4. Select the surface that has just been created and click the Extrude button ( ). In the window that opens fill in an extrusion vector of (x,y,z) = (0 0 -1.5) in order to create the 1.5m thick raft and click OK. Now the raft has been created as volume, in order to assign interfaces to all sides of the raft, the raft volume has to be decomposed into its surfaces. 5. From the button bar with general options, click the Perspective view button (

). .

6. Right-click on one of the vertical sides of the raft and select the option Decompose into surfaces. This will created surfaces for all sides of the volume. 7. For all 6 sides, right-click on the side and add an interface. Note that all sides need a negative interface with exception of the vertical side at y = 3.0m; this side needs a positive interface. Check if all created interfaces are on the outside of the raft! 8. In order to make the lower part of the supporting column, click again the Top view button and fix the z-coordinate to ground level. 9. Create a surface from (x y) = (-6.0 -1.0) to (-6.0 1.0), (-4.0 1.0) and (-4.0 -1.0). 10. Extrude the surface 0.8 meters downwards, hence in the negative z-direction. This creates the lower part of the column from groundlevel down to the raft. 11. Decompose the column into surfaces. 12. For all 4 vertical surfaces created, create an interface on the outside. That is, negative interfaces for all vertical sides but the vertical side at y = 1.0m. The latter side needs a positive interface. The only part missing now is the load representing both the weight of the bridge and a passing train 13. Right-click on the top plane of the column, that is the plane at ground level. 14. From the popup menu that opens, select the option Create surface load to add the load. The first raft is now complete.

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Flieden bridge piled-raft foundation Create second raft The second raft is equal to the first raft, hence creating the second raft is simply making a copy of the first raft: 1. Click the button Select rectangle ( ), ignore the suboptions that become available. Now draw a rectangle that fits the whole structure of piles, raft and column so that all parts are selected. ) to specify the location of the copy of the founda2. Now click the Create array button ( tion structure in the Create array window. 3. Set the Shape of the array to 1D, in x direction as we want to copy the foundation just one time in x direction, keeping the y and z coordinates constant 4. Fill in 2 columns with a distance of x = 10m in between and press OK. Now the second raft is created as copy of the first raft. Both rafts have now been defined, see figure 4.

Figure 4: Geometry containing the two rafts

Create mesh refinement area In order to be able to refine the mesh in the area around the rafts it is needed to define a volume of soil around the rafts where a mesh refinement can be applied. To do so, follow these steps: 1. Select the Top view and fix the z-coordinate to -25.0 m Computational geotechnics PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Flieden bridge piled-raft foundation 2. Draw a rectangular surface from (x y) = (-10.0 -4.0) to (-10.0 4.0), (10.0 4.0) and (10.0 -4.0). 3. Select the Perspective view, select the newly created surface and extrude it 25m up, hence in the positive z-direction. We have now created a volume around the foundation structure that we can use for local mesh refinement.

Mesh generation In the Mesh mode we will specify global and local refinements and generate the mesh. In order to generate more accurate results a refinement of the mesh around the foundation structures will be applied. 1. In the geometry click somewhere close to the origin. This will select the body of soil that encloses the foundation structures. 2. In the Selection explorer on the left the selected soil body appears, showing a mesh refinement factor of 1.0. Change this mesh refinement factor to 0.30. 3. Select the Generate mesh button ( window appears.

) in order to generate the mesh. The Mesh options

4. In the Mesh options window choose a Very coarse element distribution and click OK to start the mesh generator. 5. After mesh generation has finished one can already see an indication of the amount of elements and nodes generated in the command line box below the draw area. For this project about 22,000 elements should be generated. 6. Click the View mesh button (

) to inspect the generated mesh.

After inspecting the mesh the output window can be closed. Mesh generation has now been finished and so creating all necessary input for defining the calculation phases has been finished.

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Flieden bridge piled-raft foundation

Figure 5: Generated mesh with local refinement

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CALCULATION The calculation consists of the initial phase and three additional phases. Since water levels will remain constant the Water levels mode can be skipped. Therefore, click on the Staged construction mode button to move to the defintion of the calculation phases.

Initial phase By default the Initial phase is set to the K0 procedure, which is fine for this example. No further changes have to be made.

First phase - construction of the foundations 1. Click on the Add phase button (

) to add the first calculation phase.

2. As the foundations are surrounded by soil they cannot be accessed directly. In order to change their properties the surrounding soil has to be made invisible. To do so, rightclick on the soil somewhere far away from the origin and from the menu that pops up choose Hide to hide the outer soil. Now only the foundations and the refinement zone is left. Make sure the soil is hidden, not deactivated! 3. Right-click on the refinement zone volume and again choose the Hide option from the popup menu. With the refinement zone hidden, only the foundations structures remain visible. 4. Open the material sets database by clicking the Show materials button ( ). Drag and drop the material set representing the concrete on all piles, the rafts and the two parts of the column. When assigning the material set, the colour changes from the colour of the material set representing the clay to the colour of the material set representing the concrete. 5. In the Model explorer, activate all interfaces by clicking on the checkbox in front of the interfaces branch so that a checkmark appears.

Second phase - working load 1. Click on the Add phase button (

) to add the second calculation phase.

2. In the Model explorer open the Surface loads branch and change the value for the two surface loads. Set the first surface load to a vertical stress of σz = −5000 kN/m2 (20 MN dived by 4 m2 cross sectional area of the column) and set the second surface load to a vertical stress of σz = −5500 kN/m2 . 3. Make sure the surface loads are activated, that is that they have a checkmark in the Model explorer. Computational geotechnics PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Third phase - ultimate limit load 1. Click on the Add phase button (

) to add the third calculation phase.

2. In the Model explorer change the values of the Surface loads to σz = −10000 kN/m2 for the first surface load and σz = −11000 kN/m2 for the second surface load. ) to start the calculation. Ignore the message "No nodes or Press the Calculate button ( stress points selected for curves" as we will not draw any load-displacement curves in this example, and continue the calculation.

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OUTPUT RESULTS Figure 6 demonstrates the calculated load settlement behaviour of the piled raft applying the GAPR (Geotechnical Analysis of Piled Raft, El-Mossallamy 1996). Due to the non-linear response of the foundation system the loads have been incrementally applied till the ultimate limit state. Another aim of the analysis under working loads was to determine the pile/soil stiffness and subgrade reaction distribution beneath the raft, which are necessary for the design of the foundation. However, within the framework of this exercise the subgrade reaction distribution will not be checked. Figure 7 shows the measured settlements in comparison to the calculated values

Figure 6: Load-settlement behaviour of the piled raft foundation (calculated by program GAPR, El-Mossallamy)

Figure 7: Measured settlements

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Ho Chi Minh Workshop Computational Geotechnics 17

MODELLING OF TUNNELS & TUNNELLING Dr William Cheang  

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Modelling of Tunnels and Tunnelling in 2D & 3D Dr William Cheang Plaxis AsiaPac, Plaxis Academy Contribution: Dr Lee Siew Wei Ir Sajjad Anwar

CONTENTS • Introduction • Section A: Modelling of Embedded Sheet‐pile Walls • Section B: Influence of Soil Models • Section C: Examples 1, 2 and 3

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2

Tunnels & Tunnelling Introduction

3

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Introduction – Main Engineering Issues 1. Settlements, ground movements 2. Complex 3D geometry 3. Lining forces 4. Face stability 5. Reinforcement design 6. Tunnel connections, galleries 7. Impact on adjacent structures (pile foundations, buildings, pipelines, …)

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3D Modelling Issues Geometry: Soil layers Boreholes Surface import (TIN)

3D Modelling Issues Geometry: 1. Tunnel model 2. Extrusion along a path 3. Import of “Volume Blocks” 4. Tunnel model 5. Shape designer

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Construction Stages of a Shield Tunnel Typical calculation process for TBM tunneling 1. Initial conditions 2. Excavation • Remove soil/water • Install TBM • Contraction 3. Tail void 4. Final lining installation

Applied by means of prescribed in‐plane strain in orthoradial direction

Either plate or volume elements

Construction Stages of a Shield Tunnel A. Practical case results

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Front Stability Front stability and related safety factor in PLAXIS 3D can be assessed 1. By means of a phi‐c reduction analysis enabling safety factor assessment from soil  resistance point of view. 2. By means of a plastic analysis with gradual reduction of face pressure when applicable.

Tunnel Connections and Galleries Shaft/tunnels connections details Shaft modelled as double solid  rings Tunnels and bottom shaft  modelled as plate Tunnels extended within the  shaft to provide rigid  connection

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Tunnel Connections and Galleries Effortless mesh generation with fully automated  unstructured mesh 1. Quadratic tetrahedral  elements 2. Support internal points, lines  and surfaces constraints 3. Possibility to prescribe local  refinement to any objects

Tunnels Connections and Galleries “Connection” feature in PLAXIS 3D – Arbitrarily release degree‐of‐ freedom along intially rigidly  connected structures – Appropriate for modeling joints and  hinges

Connections

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Tunnels Connections and Galleries A. Tunnel section local reinforcement and tunnel gallerie

Tunnels Connections and Galleries • Tunnel section local reinforcement and tunnel  gallerie

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Soil Reinforcement

• Rock bolts ̶ ̶

In practice often by means  of increase of cohesion Special elements of various  types (bars, beams,  embedded piles)

Soil Reinforcement • Stability anchors at tunnel face and forepooling

(Diaz et al, 2012) PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Interaction with Existing Structures A. Tunnel cutting existing pile foundation Building  load

Rear side Building

Tunnel Fill Front side CDG 3m Tunnel

120 m

Grouted  annulus 12m

150 m

(Lee et al., 2011)

Features in PLAXIS 3D

A. Tunnel designer

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Features in PLAXIS 3D

A. Shotcrete model 1. Softening in tension 2. Hardening/softening in  compression 3. Regularization techinque 4. Increase in stiffness and  strength in time 5. Creep deformation

Features in PLAXIS 3D Swelling rock model for Clay and Anhydrite 1. Motivation • Large invert heave even decades after  tunnel excavation • Damage and/or destruction of tunnel  lining • Claystone and anhydrite 2. Stress dependency of swelling assuming  Grob’s semi‐logarithmic law for both clay  and anhydrite.

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Example 1: Modelling of Tunnelling in 2D Section A

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Tunnelling Observations in HK • Tunnelling case histories in Hong Kong observed 1. Greenfield surface settlement profile fitted by Gaussian curve with trough width parameter (K) of 0.5 2. With good workmanship achieved greenfield volume (or ground) loss ratios were less than 1% • GCO (1985), Storry (2001), Storry (2003) & Hake & Chau (2008)

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Concept of Modelling Tunnelling in 2D 3D

2D

2D

Moller (2006)

• 3D arching around unsupported tunnel heading carries vertical load Pg by transferring them around unsupported cut stretch • 2D analysis cannot model 3D arching effect - this is compensated by including an artificial support pressure Ps (can be a pressure- or displacement-controlled approach) •

Methods Model Tunnelling in 2D  • Plaxis 2D provides 1. Lining Contraction Method 2. Stress Reduction Method (-method) • Users can specify tunnel internal support pressure manually 1. Applied Pressure Method (from Grout Pressure Method by Moller & Vermeer, 2008)

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Lining Contraction Method 1st Phase

2nd Phase

Vermeer & Brinkgreve (1993) Moller (2006)

Initial position

• 1St Phase: Lining is wished-in-place, soil elements inside tunnel deactivated – tunnel heaves • 2nd Phase: Lining is stepwise contracted until prescribed contraction % – radial displacement towards tunnel centre • Tend to give unrealistic realistic results for ground surface settlement & horizontal displacement

Stress Reduction Method () 1

Pk

2

1

Pk

=

Pk = initial ground radial pressure ΣMstage = 1 - 

• 1St Phase: Soil elements inside tunnel deactivated, internal support pressure = pk, net load acting on unsupported perimeter = (1-)pk • 2nd Phase: Lining activated, remove internal support pressure & lining takes remaining load pk

Lining

•  is Load Reduction factor, obtained from tunnelling experience • Tend to give reasonable results PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Applied Pressure Method • Based on Grout Pressure Method by Moller & Vermeer (2008) • Between Stress Reduction & Applied Pressure Methods, difference is the profile of internal support pressure

• 1st Phase: Soil elements inside tunnel deactivated, internal support pressure manually specified which is Pcrown at tunnel crown, rate of increasing with depth = grout (~15 kN/m3) • 2nd Phase: Lining activated & remove internal support pressure

FE Prediction of Greenfield Surface Settlement • Numerical

analysis with simple constitutive model cannot replicate measured greenfield (G/F) surface settlement curve • Case histories showed G/F surface settlement could be fitted with Gaussian curve • FE prediction improved by 1. Refining method of modelling tunnel excavation

2. Using advanced soil constitutive model • An exercise to investigate effects of these two factors for tunnelling in Hong Kong soils PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Modelling of Tunnelling in Hong Kong Soils 60m

0 Fill -3 Marine Deposits -6

20m Completely Decomposed Granite (CDG) 6m Ø tunnel

Rock

40m

-40

• Ground conditions: 3m Fill, 3m MD, 34m CDG & rock; GWT at surface • Tunnel 6m diameter with axis at 20 mbgl; 2700 nos of 15-noded elements

Soils Modelled by Mohr Coulomb Model Soil

g (kN/m3)

E (MPa)

ν [‐]

c' / cu (kPa)

f' (Deg)

Fill

19

20

0.3

0

30

MD (Undraine d)

16

6

0.3

15

0

CDG

20

39

0.3

5

35

Soils Modelled by HS & HSsmall Models E50ref &  Eoedref (MPa)

Eurref (MPa)

m [‐]

c' (kPa)

f' (Deg)

Pref (kPa)

νur [‐]

g0.7 [‐]

G0 (MPa)

Fill (HS)

20

60

0.5

0

30

100

0.2

‐

‐

MD (HS) (Und.)

6

18

1

0

22

100

0.2

‐

‐

CDG (HS‐ small)

39

117

0.5

5

35

200

0.2

5E‐5

200

Soil

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Pre‐failure Stress‐strain Behaviour 1: Mohr Coulomb

1: Linear elastic, perfectly plastic 2: Hyperbolic stress-strain curve (stiffness degradation for  > 1E-4) 3: Non-linear stiffness from very small strains (1E-6) 3:Hardening Soil + Small Strain Overlay

2: Hardening Soil

1e-6

1e-5

1e-4

1e-3

1e-2

1e-1

Initial Stress Equilibrium • K0 = 1 – sin'

Soil

K0

Fill

0.5

MD

0.625

' = drained effective friction angle (Fill=30˚; MD=22˚) CDG

Schnaid et al. (2000)

CDG

0.65

0.4 0.65 0.9

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Details for Analyses 1. Mohr Coulomb series analyses (i) Lining Contraction Method (ii) Stress Reduction () Method (iii) Applied Pressure Method 2.

HS & HSsmall series analyses (i) Lining Contraction Method (ii) Stress Reduction () Method (iii) Applied Pressure Method

•

Compare greenfield surface settlement curves with a ground loss ratio (VL) of 1%

•

VL = surface settlement area ÷ tunnel cross-sectional area

Comparison of MC and HS & HSsmall Models 0

10

Distance from tunnel centreline (m) 20 30 40 50

60

0

Settlement (mm)

-2 -4

Mohr Coulomb

Gaussian (K=0.5, VL 1%)

-6

Lining contraction - LC 1%, VL 0.32%

-8

Lining contraction - LC 1.7%, VL 1%

-10

Stress reduction - beta 0.68, VL 1%

-12

Applied pressure - Pcr 190 kPa, VL 1%

0

10

Distance from tunnel centreline (m) 20 30 40 50

60

0

Settlement (mm)

-2 -4 -6 -8

Gaussian (K=0.5, VL 1%)

HS & HSsmall

Lining contraction - LC 1%, VL 0.77% Lining contraction - LC 1.22 %, VL 1%

-10

Stress reduction - beta 0.66 , VL 1%

-12

Applied pressure - Pcr 186 kPa, VL 1%

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Mohr Coulomb Soil with Lining Contraction • Prescribed lining contraction 1% • Predicted greenfield surface settlement curve gives VL 0.32% only • Lining contraction is more below tunnel axis – not realistic

Lining Contraction Method: MC vs. HS & HSsmall Models Prescribed lining contraction 1% Mohr Coulomb

HS & HSsmall

Exaggeration scale 100

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Stress Reduction vs. Applied Pressure Methods  HS & HSsmall analyses, Greenfield VL 1% Applied Pressure

Stress Reduction

Exaggeration scale 100

Comparison of Radial Internal Support Pressure Radial internal support pressure (kPa) 0

17 Crown

100

200

300

400

500

Depth (m)

18 19 20

Axis

HS & HSsmall analyses

21 22 23 Invert Initial (before tunnel)

(r0=h×sin2+ v×cos2)

Stress Reduction Method

(r0, =0.66)

Applied Pressure Method (Pcrown=186

kPa, grout=15kN/m3)

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Summary of 2D Modelling of Tunnelling • Good prediction of greenfield surface settlement curve (Gaussian) in 2D requires 1. advanced soil constitutive model for nonlinear stiffness from small strains 2. refined method of modelling tunnel excavation • For HK tunnelling example investigated herein: 1. effect of advanced constitutive model is more significant than method of modelling tunnel excavation 2. Applied Pressure Method gives steeper surface settlement curve, followed by Stress Reduction Method & Lining Contraction Method • On realistic prediction of surface settlement curve & pattern of ground deformation around tunnel: 1. Mohr Coulomb model + Lining Contraction Method gives unrealistic results 2. HS & HSsmall models + Applied Pressure Method gives better results

Example 2: Tunnelling Near A Building Supported by  End‐bearing Piles Section B

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40

Tunnel‐pile Interaction • A three-dimensional problem due to 1. progressive advance of tunnel face towards piles 2. movement of piles in 3D 3. oblique orientation of building relative to tunnel alignment

• Tunnelling induced ground movements can cause 1. increase/decrease in pile axial force (negative/positive skin friction) – relative pile/soil vertical displacement 2. increase in pile bending moment – curvature of pile horizontal displacement 3. Potential reduction in pile geotechnical capacity 4. distortion of building, e.g. relative rotation & horizontal strain

Zones of Influence

Zone B

Selementas et al. (2005)

45º

Zone A

Zone B

45º

Zone C

Depth

Zone C

Pile settlement C B A

For pile toe located in Zone A: pile head settlement > soil surface settlement; decrease in pile axial force Zone B: pile head settlement ≈ soil surface settlement Zone C: pile head settlement < soil surface settlement; increase in pile axial force PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Analysis of Tunnel‐pile Interaction • Typically use the combination of 1. empirical relationships/closed-form solutions to estimate greenfield ground movements; and 2. boundary element methods to compute pile deformations stresses • Suitable for preliminary assessment, with some limitations • Alternatively, use 3D numerical analysis Pros: model tunnelling, tunnel-pile-building interaction & geotechnical entities in one single analysis Cons: complicated, relatively long analysis time & require advanced constitutive model for soil non-linear behaviour

and

Example of Tunnelling Below Piled Building 0 mbgl 2m 5 mbgl 10 mbgl

25m

P4

Pile cap Fill

9m

MD CDG 1m 4m

25m P5 Rear P6 4m

P1 10m

1m

10m P2 Front P3 6m Ø tunnel

Tunnel advance direction

20 mbgl

2m Ø pile Pile design load 15MN (~5MPa)

Tunnel 6m Ø 30 mbgl 31.5 mbgl Rock P1/P4

P2/P5

P3/P6

3m Ø bell-out

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Information for Tunnel, Piles & Ground 1. 2. 3. 4. 5. 6.

6 m diameter tunnel excavated by TBM, tunnel axis depth at 20 mbgl in Completely Decomposed Granite 15-storey building supported by 6 nos of 2 m diameter bored piles with 3 m diameter bell-outs in rock at 32 mbgl Each pile takes 15 MN design load (~5 MPa). Building plan size is 25 m by 9 m, pile cap 2 m thick Stratigraphy is 5 m Fill, 5 m Marine Deposits, 20 m CDG and rock. Groundwater table at 2 mbgl Tunnel constructed in between piles, tunnel edge to pile edge distances are 1 m, 4 m and 10 m

3D Finite Element Model (Plaxis‐GiD)  Load 15 MN

Rear

“Plate” Pile cap

Building 40m Bored pile Front Tunnel 120m

Fill MD CDG Rock

Tunnel face 149m

43,000 elements

TBM length

Bell-out

Linings

Refined mesh around tunnel & building piles PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH Ho Chi Minh City | 16 to 18 September 2014 | PLAXIS ACADEMY

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Tunnel Confinement (Face Support) Pressure  A PIII

PIV

PI

Rear 6m Ø

Front

TBM shield 9m PII

PVI PV A PIII

• Confinement (face support) pressure (PI to PII) = hydrostatic pore pressure + overpressure • Higher confinement pressure, lower ground loss • Along TBM shield, front pressure higher than rear’s to consider 1. conical shape of TBM shield / over-cutting 2. ground loss into tail void in rear

Pressure increases with depth

PV Section A-A

• Any combination of support pressure profiles can be modelled

Lining Lining

Modelling of Tunnel Face Advance  • Soil elements inside TBM shield are deactivated

1.5 1.5m

• Apply profiles of confinement pressure

Lining Lining

TBM shield (elements nulled)

TBM shield (elements nulled)

Lining Lining

1.5 1.5m

TBM shield (elements nulled)

• Shield is not modelled • For each face advance, shift confinement pressures forward & correspondingly erect new lining behind TBM • The process is repeated as tunnelling progresses

1.5 1.5m PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Prediction on Ground Surface Settlement Overpressure 20 kPa

Overpressure 20 kPa, G/F VL 1.6%

Distance from tunnel centreline (m) -60

Fill

0

MD

-40

-20

0

VL 0.31%

20

40

60

Settlement (mm)

-4

CDG Tunnel

-8 -12 -16 -20

VL 1.61% Mid-building Greenfield Gaussian

-24

• Gaussian curve with K = 0.45

• Lateral spreading of displacements in MD layer

• Close to K ≈ 0.5 from HK tunnelling experience

• Settlement trough becomes wider

Prediction on Transverse Pile Displacement Overpressure 20 kPa Transverse horizontal disp. (mm) -4 -2D Front Rear

-3

-2

-1

+10D 0 0 5

+10D

+2D

10

+2D 15 20 25 30 35

Depth (mbgl)

-5

Rear 1m

P2 Front -2D

Tunnel advance

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Prediction on Longitudinal Pile Displacement Overpressure 20 kPa +10D

Longitudinal horizontal disp. (mm) -3

-2

-1

0

1

2 0 5

+2D

15 20

-2D

Depth (mbgl)

10

Rear 1m

Tunnel advance

Front

25

P2 Front

Rear

-2D

30

+2D +10D

35

Tunnel advance

Prediction on Pile Settlement & Axial Force Overpressure 20 kPa 0 0

Settlement (mm) -1

P2

0

-2 0

-2D Front

5

Increase in axial force (MN) 1 2 3

P2

5

Rear +10D 15

7

20 25 30 35

-2D Front Rear

10

+2D Depth (mbgl)

Depth (mbgl)

10

4

15

+2D +10D

20 25

A

B C

30 35

Pile toe PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Prediction on Pile Bending Moment Overpressure 20 kPa Transverse moment (kNm) 1500 0

500

-500

Longitudinal moment (kNm) -1500

1500 0

P2

-500

-1500

P2

5

5

10

10

-2D Front

15

Rear +2D

20

+10D

Depth (mbgl)

Depth (mbgl)

500

-2D Front

15

Rear +2D

20 Tunnel advance

25

25

30

30

35

35

+10D

Check on Potential Structure Damage 

25

OP 10kPa OP 20kPa

Distance from tunnel centre (m) -10 -5 0 5 10 15

OP 10kPa

0.0

0.3

-0.4

0.2

OP 30kPa

Cat. 4 & 5

15 5

OP 40kPa

-0.8

-5

Cat. 3

0.1

=0.14 mm

-1.2

-15 -15 -10 -5 0 5 10 Moment, M (MNm)

0

0.0

15

Pile N-M Interaction Diagram

OP 20kPa OP 30kPa

OP 40kPa

/L (%)

Axial Force, N (MN)_

35

P2

Bldg. settlement (mm) _

45

0

-1.6

Building deflection

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1

2

0.1 0.2 h (%)

0.3

Burland’s chart

462

Comparison with Closed Form Solution  Greenfield subsurface settle. (mm)

-25

-15

-5

0

5

15

-15

-10

-5

0

Fill

0

Fill

5

5

MD 15 20

Depth (mbgl)

MD 10

CDG

10

CDG

15 20

25 Loganathan et al. (2001) 3D analysis

30

Rock

0

35

Depth (mbgl)

-35

Greenfield subsurface horiz. disp. (mm)

25

Loganathan et al. (2001)

Rock

3D analysis

30 35

Greenfield subsurface section corresponds to P2 location 3D analysis: Overpressure 20 kPa, G/F VL 1.61%

3D FEA vs. Analytical Solution Issues

3D FEA

Analytical Solution

Ease of use

• Complicated • Long analysis time

• Relatively easy • Less analysis time

Ground conditions

• Layered soil • Need realistic constitutive model

• Homogeneous soil • Estimated G/F deformation less good for layered soil

Tunnelling progress

• Model face advance • Pile response in transverse & longitudinal directions

• Only pile response in transverse direction

Issues

3D FEA

Analytical Solution

Ground loss, VL

• Model confinement pressure & predict VL

• Assume a certain VL

Effect on piles/building

• Model tunnel, piles, building & their interaction in one single analysis • Results from piles & building used directly in structural check

• Different boundary element programs for pile axial and lateral responses • Specific analysis for pile group effect • Dedicated modification factors account for building rigidity

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Example of Pile Toes Above Tunnel

Overpressure 20 kPa

-70

-50

Reference distance (m) -30 -10 10 30

VL 0.72%

P5 Pile group

Settlement (mm)_

0

Plan view

-5 -15

Greenfield

-20

Building

-25

VL 2.8%

-30

-2

P5

Pile axial load (MN) 0 2 4

0

Tunnel Depth (mbgl)_

-5

Pile

A

B

Tunnel axis 31 mbgl

C

70

-10

-4

3m

50

-10

6

8

10

After tunnelling

-15 -20

Before tunnelling

-25 Decrease in axial load -30

Behaviour of Cut Pile 

Pile level (mPD)

0

Pile axial force (kN) 100 200 300 400 Cut pile & tun. face 1m passing pile

-5 -10

Cut pile & tun. face 21m passing pile

-15

CDG Rock

Initial

30m

Tunnel 43m

Tunnel face 1m before pile

-25

0 Pile level (mPD)

-10 Fill -17 Marine Deposits -27

110m

-20

-2

Pile settlement (mm) -4 -6 -8 -10

0

Cut pile & tun. face 1m passing pile

-5 -10

-12

Pile Soft block

32,000 elements Greenfield VL 1%

6m Ø tunnel Tunnel face 1m

-20 before pile -25

Pile

+3

0

-15

500

Cut pile & tun. face 21m passing pile PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Conclusions 1.

Details of 3D FEA modelling tunnel advance near a piled building are given 2. Analytical solutions (empirical/closed form solution + boundary element method) are useful for preliminary assessment of pile/building response, with limitations 3. For detailed assessment of identified critical buildings, 3D FEA can offer a more rigorous & realistic assessment 4. Finally, numerical analysis needs competent analysts & predictions checked by experienced engineers & compared to case histories.

Example 4: Tunnel‐Pile Soil Interaction (C704 NEL‐Singapore) SECTION C Hartono Wu, NUS William Cheang, Plaxis Asiapac Tan Siew Ann, NUS Pang Chin Hong

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C704 NEL: Geology, Tunnels and Sensitive Structure

C704 NEL: Geotechnical Finite Element Model (s) 1.

6.5 m diameter EPB shield machine was used. The tunnel axis was 21 m. The distance of SB and NB tunnel was 16 m. SB tunnel was advancing first and later followed by NB tunnel

2.

1.9 km viaduct was being constructed along the twin tunnels of Contract 704

3.

The viaduct was supported by piers seating on bored piles

4.

Comprehensive field measurements of ground movements and pile responses were reported by Pang (2005) 62 m 30 m

0m G4a 16 m G4b

G4c

74 m

30 m

G4a NB tunnel

44 m

SB tunnel

G4b G4c

G4d

74 m

140 m 1623 of 6-noded triangular elements (Plaxis 2D v9.2.) 329,872 of 10-noded tetrahedron elements (Plaxis General PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO3D CHI MINH 2011)

G4d

466

C704 NEL: Parameters HS-small was used as a soil model. Basic soil parameters were obtained from Pang (2005).



sat (kN/m3)



E50 (MPa)

c’ (kPa)

’ (kPa)

Ko

G4a (0 < N < 15)

18

0.30

8.7

20

28

1.0

G4b (15 < N < 30)

19

0.30

40

30

30

1.0

Soil

G4c (30 < N < 60)

20

0.30

65

30

30

1.0

G4d (60 < N 105) – To simulate an fully permeable material a value increased by a factor 104 may be enough • Necessity of defining interfaces to model impermeable barriers along structural elements

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Checklist for Groundwater Definition • Check initial groundwater pressures by creating pore pressures contour plots for each individual calculation phase including initial phase • Be careful with automatic stage regeneration process when model is being reedited after calculation phases have been defined • Check carefully boundary conditions for GW flow and consolidation analyses • Check permeability values of the different constitutive materials and their respective ratio

Factor of Safety 2 – INITIAL CONDITIONS 1 – MODEL CREATION Geometry Boundary Conditions Meshing Material Model Interaction Soil Structure

Initial Stress Initial Pore Pressures

3 - CALCULATION Construction Sequence Analysis Type Groundwater Modelling Safety Factor Convergence Settings

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Safety Factor Analysis • Based on a phi-c reduction method in PLAXIS which is a strength reduction method • In Plaxis the safety factor definition is:

M

sf



available soil resistance mobilized soil resistance

M

sf



failure load working load

Phi-c Reduction Analysis

1.16

1.16

1.12

1.12

Sum-Msf

Sum-Msf

• Provide enough number of step

1.08 1.04 1.0 0.0

1.08 1.04

0.3

0.6

0.9

displacement

1.2

1.5

1.0 0.0

0.3

0.6

0.9

1.2

displacement

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Phi-c Reduction Analysis (cont.) • Influence of mesh refinement 15-noded elements 5 11 (very coarse) 38 (coarse) 82 (medium) 170 (fine) 414 (very fine) 871 3733 15749

Factor of Safety 1.90 1.62 1.52 1.51 1.50 1.45 1.43 1.43 1.43

Checklist for Phi-c Reduction Analysis • Check whether sufficiently fine mesh is used • Check sufficient number load steps • Remember – Setting the maximum structural forces for structural elements through definition of elasto-plastic behaviour gives lower factor of safety – Ignoring undrained behaviour may lead either to higher or lower safety factor depending on the failure mechanism PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Convergence Settings 2 – INITIAL CONDITIONS 1 – MODEL CREATION Geometry Boundary Conditions Meshing Material Model Interaction Soil Structure

Initial Stress Initial Pore Pressures

3 - CALCULATION Construction Sequence Analysis Type Groundwater Modelling Safety Factor Convergence Settings

Checklist for Convergence Settings • Increasing tolerated error speeds up convergence – Check the tolerated global error remains low (< 3%) – Default convergence settings does not need to be changed in principle • Converged solutions do not mean safe constructions: – Check the stiffness (CSP) parameter in the progress calculation window. A value lower than 1E-3 indicates a situation close to failure – A subsequent phi-c reduction analysis will indicate a factor of safety close to one PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Calculation Settings • Example TE = 1%

TE = 20%

Umax = 42.2 mm

Umax = 23.3 mm

References • D.M. Potts, L. Zdravkovic (2001), Finite Element Analysis in Geotechnical Engineering: Application, Thomas Telfort, London. • P.A. Vermeer, M. Wehnert (2005), Beispiele von FEAnwendungen – Man lernt nie aus in FEM in der Geotechnik, Ed Grabe et al., Hamburg,

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Ho Chi Minh Workshop Computational Geotechnics 19

EXERCISE 6: MODELLING OF A SHIELD TUNNEL IN 2D Dr William Cheang  

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Shield tunnel in Lyon

SHIELD TUNNEL IN LYON

This excercise has orginally been created by Prof. Marc Boulon University Joseph Fourier, Laboratory 3S Grenoble, France

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INTRODUCTION The subway of Lyon in the Vaise area (north of Lyon, France) consists of two tubes excavated successively by a TBM according to the mud pressure technique. Vaise is an urban area where only very small settlements are allowed, as usual in such case. The subsoil consists of several layers of alluviums, under the water table except for the upper fill layer. The tunnels are shallow, and the diameter excavated is 6 m. The lining is prefabricated in 13 circular segments whose external diameter is 6 m, and whose length is 1.00 m. Many mechanical tests (laboratory and in situ) have been performed on the soil layers. The section considered in this exercise was equipped with many systems (extensometers, inclinometers, pore pressure cells) in order to record the data during and after the construction of the tunnels. The geometry of this urban site, of the soil layers, and the position of the tubes are given in figure 1. Note that a retaining wall has been built in the past, and that the upper part of the soil consists of an artificial fill. The depth of the axis of the tubes is 16.4 m at the right side and only 11.5 m at the left side. First V1 was constructed, and then V2.

Figure 1: Subway metro of Lyon Vaise, section S1.

Many triaxial tests, pressure meter tests, SPT and CPT are available for this site. The soils are all soft soils except for the lower sandy gravel layer (« sable et graviers roux »), and the sand layer called « sable gris ». The depth of the water table, coming from the nearby river Saône is 8 m. Though the alluvium and purple clay layers have reasonably low permeabilities, all layers can be considered as drained due to the slow advancement of the tunnel (3 m/day). Computational Geotechnics PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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In situ measurements of displacements Among the various measurements of displacement realised on this site, the settlements recorded by the extensometer EX11 are remarkable, because they clearly show the mechanisms linked to each phase of construction. The history of these settlements is shown in figure 2, at several levels from the surface until the top of the tube V1. From this chart, important events accompanying the construction seem to be : • The passing of the front of the shield • Injection of grouting between the soil and the lining at the end of the TBM • Consolidation of the grouting

Figure 2: Settlemement (vertical axis) versus time (horizontal axis) recorded by the extensometer EX11, placed vertically above tunnel V1.

INPUT Project properties The situation of the shield tunnel in Lyon is to be modelled by means of a plane strain model composed of 15-noded elements. The model should be sufficiently wide to avoid influence from the boundaries, see also figure 3. 4

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Soil mode The sub soil is to be divided in 5 soil layers, as indicated in figure 3. The parameters can be found in table 1. • Create a borehole containing the 5 soil layers. • Additionally, set the Head of the borehole at 3m below ground level. • Create the material sets and assign them to the soil layers.

Figure 3: Subsoil

Structures mode In Structures mode the following must be modelled: 1. The retaining wall and its fill 2. The two tunnels 3. Additional material sets for the retaining wall and tunnel lining

Retaining wall and fill • Select the Soil button (

) and then select the option Create soil polygon.

• Draw the rectangle of fill material behind the wall. That is, over the full heigh of the wall and all the way to the right boundary of the model. • Now select the Soil button again and either select the option Create soil polygon or Create soil rectangle. Computational Geotechnics PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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6

Unsaturated weight Saturated weight Drained triaxial test stiffness Drained primary oedometer stiffness Unloading/reloading stiffness Power for stress-dependent stiffness Cohesion Friction angle Dilatancy angle Small-strain shear modulus Threshold shear strain Interface strength reduction Coefficient for lateral initial stress Overconsolidation ratio

Parameter Material model Type of behaviour

40.0·103 1.0

100.0·103 0.5 Automatic 1.0

50.0·103 150.0·103 0.5 1.0 34 4 1.0·10−4 300.0·103 Rigid Automatic 1.0

E ref ur m c0ref ϕ0 ψ γ0.7 Gref 0 Rinter K0 OCR

35.0 27 0 1.0·10−4

8.0·103

16.0 18.5 8.0·103

E ref oed

Clay HSsmall Drained

18.0 21.0 50.0·103

Gravel HSsmall Drained

Symbol Model Drainage type γunsat γsat E ref 50

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Automatic

300.0·103 0.5

5.0 35 5 1.0·10−4

0.5

120.0·103

40.0·103

18.0 21.0 40.0·103

Sand HSsmall Drained

1.0

Automatic

100.0·103 0.5

35.0 27 0 1.0·10−4

0.5

35.0·103

12.0·103

17.0 19.0 12.0·103

Silt HSsmall Drained

2.0

Automatic

250.0·103 Rigid

30.0 38 4 1.0·10−4

0.5

105.0·103

35.0·103

16.5 18.0 35.0·103

Fill HSsmall Drained

–

–

kN/m2 –

kN/m2 º º –

–

kN/m2

kN/m2

kN/m3 kN/m3 kN/m2

Unit – –

Shield tunnel in Lyon Table 1: Soil parameters for the HSsmall model

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Shield tunnel in Lyon • Draw the polygon that will form the retaining wall, see figure 4 (left). Note that the toe of the retaining wall is located one meter below ground level and 37m from the left side of the model. • Select the Geometry line button and then select the option Create interface. • Draw an interface along the contour of the retaining wall, but only for the parts where the retaining wall is adjacent to soil. • Assign the Fill soil material to the newly created retaining wall and fill areas. • See figure 4 (right) for the final result.

Figure 4: Geometry of the retaining wall (left) and complete model (right)

Tunnels The two tunnels have an outer diameter of 6 m and the lining segments are 300 mm thick. Both tunnels should have a lining and an interface, representing the TBM, and volume elements to represent the lining segments. Both tunnels centre points are located 11.5 m below ground level. The left tunnel has its centre 30 m from the left boundary of the model, the right tunnel centre is 11 m further to the right. • Select the Create tunnel button (

).

• Click in the drawing area on the location where the center point of the left tunnel should come. This is 11.5 meters below ground level and 30 m from the left boundary of the model. • In the Tunnel designer window that now opens set the following options: – In the Cross section part * On the General tabsheet · Shape type = Circular, Define a whole tunnel Computational Geotechnics PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Shield tunnel in Lyon · Offset to begin point indicates the location of the local origin relative to the bottom most point of the tunnel. Fill in Axis 1 = 0 and Axis 2 = -3 to make the centre of the tunnel the origin of the local axis. * On the Segments tabsheet · A single circular segment, Segment[0], has already been created. However, the radius of the segment is 1m and must be changed to 3 m. * On the Subsections tabsheet we will now define our thick lining ) · Select the Thick lining button ( · In the Generate thick lining window that appears, enter a thickness of 0.3 m. A subsection, Subsection[0], is created. – In the Properties part both inner and outer circle are shown as "Slicepolycurves": * Right-click on Slicepolycurve[1] that represents the outer circle of the tunnel * Select the option Create negative interface to create an interface on the outside of the lining * Similarly, create a plate element on the outer circle of the tunnel. The plate element is used to model the TBM. The plate element requires a material set representing the TBM, which can be created on the fly in the Tunnel designer, see figure 5.

Figure 5: Define a TBM material set from within the Tunnel Designer * In the properties of the polycurve, open the Plate option. The plate has only one property: Material, which is currently empty. · For the Material property now choose the option New ( plate material set. Use the date given in table 2.

) to create a new

Finally, we have to add a surface contraction needed to model the cone shape of the TBM during our construction. * Right-click again on the polycurve that already has the plate and the interface. 8

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Shield tunnel in Lyon * Select the option Create line contraction. No additional settings have to be made. • Finally, press the Generate button to generate the tunnel in the geometry • Now close the Tunnel designer. In exactly the same way the second tunnel should be entered in the geometry. The second tunnel is also located 11.5 meters below ground surface, but at a distance of 41 m from the left boundary of the model. Note that for the second tunnel it is not necessary to generate a new material set for the TBM. The same material set that was used for the first tunnel can be used. Parameter Material behaviour Axial stiffness Flexural stiffness Equivalent thickness Weight Poisson’s ratio

Symbol Material type EA EI d w ν

TBM Elastic 11.10·106 83.30·103 0.3 17.7 0.0

Units kN/m kN m2 /m m kN/m/m -

Table 2: Material properties for the TBM

Figure 6: Geometry including the tunnels

Additional material sets For both the retaining wall and for the 0.3m thick concrete lining that is applied after excavation of the tunnel an additional soil material set is needed. Table 3 shows the material properties for wall and thick lining.

Mesh mode • Select the Refine button and click on the Clay layer outside the tunnels in order to refine the layer 1 time (Coarseness factor = 0.7071) Computational Geotechnics PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Shield tunnel in Lyon Table 3: Wall and final tunnel lining properties Parameter Material model Type of behaviour Unsaturated weight Young’s modulus Poisson’s ratio

Symbol Model Drainage type γunsat E0 ν0

Wall Linear elastic Non-porous 24 25.0·106 0.2

Lining Linear elastic Non-porous 24 5.0·106 0.2

Units kN/m3 kN/m2 -

• Generate the mesh with the Element distribution set to Fine. See figure 7 for the resulting mesh.

The resulting mesh is given in figure 7.

Figure 7: Generated mesh with local refinement

10

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Staged construction modes For the excavation of both tunnels a total of 9 calculation phases (not including the initial phase) is needed.

Initial phase In the initial phase the initial stresses are being calculated using the K0 -procedure. This involves the initial stresses before the construction of the tunnels, but also before construction of the retaining wall and fill. • The Calculation type in the General section of the Phases window should be set to K0 -procedure. • In Staged construction mode deactivate the 2 clusters above the level y = 0m. Hence, the upper part of the retaining wall and the fill material behind it. • The Global water level should already be located 3m below ground level, as a result of specifying the Head in the borehole.

Phase 1: Construction of the retaining wall and fill In the first phase the wall and fill will be constructed. In reality the wall and fill were already present at the beginning of the tunnel project, so this first calculation phase will in fact generate the real initial conditions for this project. • Make sure the Calculation type is set to Plastic (default). • Now activate the upper part of the retaining wall as well as the fill material behind it. • Open the material sets database by clicking the Materials button (

).

• From the Material sets window, assign the wall material to the 2 clusters forming the upper and lower part of the retaining wall. • Make sure the interface on the outside of the retaining wall is completely activated.

Phase 2: Excavate right tunnel In Phase 2 the tunnel construction really starts. To make sure that the resulting deformations are indeed only the deformations due to tunnel construction it is necessary to reset the displacements due to the construction of the retaining wall and fill. • The Calculation type should be set to Plastic. Computational Geotechnics PLAXIS ACADEMY | 16-18 SEPTEMBER 2014| HO CHI MINH

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Shield tunnel in Lyon • In the Phases window (that opens by double-clicking on Phase 2 in the Phases explorer ) in the Defromation control parameters section, select the option Reset displacements to zero. This will assure that displacements resulting from phase 1 are discarded. • In the General section fill in a Time interval of 1 day and close the Phases window. • Now the right tunnel is excavated by the TBM: – Deactivated the 7 clusters inside the tunnel. That is 3 clusters really inside the tunnel and 4 clusters representing the final lining – Activate the complete circular plate element representing the TBM – Make sure the interface elements on the outside of the TBM are activated all around the TBM. • The soil inside the tunnel has been excavated, but the groundwater is still present and has to be removed as well: – Select all 7 clusters inside the tunnel – In the Selection explorer deactivate the option Water conditions or set its Conditions to Dry. See figure 8.

Figure 8: Cluster pore pressure distribution: set cluster dry

Phase 3: Model TBM conicity (right tunnel) Generally a TBM is not a regularly shaped tube, but has a cone shape: the tail diameter is slightly smaller than the front diameter. This results in volume loss when the TBM passes, which should be taken into account to accurately determine settlements at the soil surface. • The Calculation type of this phase is again Plastic. • In the Phases window in the General section, fill in a Time interval of 2.5 days. • Select the circular plate of the right tunnel. • In the Selection explorer activate the contraction and fill in a contraction increment of 0.4% 12

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Shield tunnel in Lyon The contraction acts on the cross-sectional area the tunnel. Hence, we assume that the cross sectional area of the tail of the tunnel is 0.4% smaller than the cross sectional area of the front of the tunnel.

Phase 4: Grout injection in the tail void (right tunnel) As the TBM passes the final tunnel lining remains as the finished tunnel. However, since the final tunnel lining was applied on the inside of the TBM, its outer diameter is smaller than the outer diameter of the TBM. This additional loss of volume may cause considerable settlements at the soil surface. In order to avoid this, grout can be pumped under pressure on the outside of the tunnel lining filling up the space left behind by the TBM shell (the so-called tail void). As said, in reality the tunnel lining is constructed inside the TBM and grout fills up the tail void. In this example the principle of grout injection will be solved in a slightly different way. Instead of applying final lining inside the TBM, we will directly after the TBM apply a grout pressure while the final lining is still switched off, and then directly after wish-in-place the final lining. • This phase is again a Plastic phase. • Enter a Time interval of 1.5 days. • Now deactivate the circular plate element that represents the TBM as the TBM is no longer there. • Also deactivate the contraction of the circular plate. • We will now apply the grout pressure directly against the soil surrounding the tunnel: – Select the 4 clusters representing the final lining (keeping Ctrl pressed) – In the Selection explorer set for the Water conditions of the selected clusters the option Conditions to User-defined – Set yref = −8.2m, pref = −220 kN/m2 and pinc = −14 kN/m2 /m, see figure 9. By setting a cluster defined pore pressure we define a grout pressure of -250 kN/m2 at the top of the tunnel, increasing with 14 kN/m2 per meter depth representing the weight of the grout.

Figure 9: Applying the grout pressure

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Phase 5: Final lining (right tunnel) After applying the grout pressure the final lining will now be installed. • Another Plastic calculation phase. • Fill in a Time interval of 2.5 days • Select the 4 clusters that represent the final lining of the right tunnel. Now in the Selection explorer do: – Activate the 4 clusters – Change the material to the Lining material – Set the Water conditions to Dry. This concludes the excavations and installation of the right tunnel. In the next 4 phases the left tunnel will be constructed.

Phase 6: Excavate left tunnel • Create another Plastic calculation phase. • Fill in a Time interval of 1 day • The left tunnel is now excavated by the TBM: – Deactivated the 4 clusters representing the final lining – Deactivate the 3 clusters inside the final lining – Remove the water from all clusters that have just been excavated. To do so, select all 7 clusters inside the left tunnel and set the Water conditions to Dry. – Activate the complete circular plate element representing the TBM – Make sure the interface elements on the outside of the TBM are activated all around the TBM.

Phase 7: Model TBM conicity (left tunnel) • Create a new Plastic calculation phase • Set a Time interval of 2.5 days • Select the circular plate of the left tunnel. • In the Selection explorer, activate the Contraction and fill in a contraction increment of 0.4% 14

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Phase 8: Grout injection in the tail void (left tunnel) In PLAXIS Calculations, make sure the Calculation type on the General tabsheet is set to Plastic. • Create a new Plastic calculation phase • Fill in a Time interval of 1.5. • Deactivate the circular plate element that represents the TBM as the TBM is no longer there. • Also deactivate the contraction of the circular plate • Select the 4 clusters representing the final lining (keeping Ctrl pressed) and in the Selection explorer do: – Set the Water conditions to User-defined – Set yref = −8.2m, pref = −180 kN/m2 and pinc = −14 kN/m2 /m. Warning: note that the grout pressure applied for the left tunnel is lower than for the right tunnel as the left tunnel is shallower than the right tunnel.

Phase 9: Final lining (left tunnel) • Create another Plastic calculation phase. • Set the Time interval of 2.5 days • Select the 4 clusters that represent the final lining of the left tunnel – activate the 4 clusters – In the Selection explorer set the material to the Lining material – Set the Water conditions to Dry. This concludes the excavations and installation of both tunnels.

Select points for curves In order to check settlements during tunnel construction, select a point straigth above the right tunnel on ground level, hence at approximately (x,y) = (41, 5). Start the calculation.

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OUTPUT Figure 10 shows the deformed mesh after installation of just the right tunnel and after installation of both tunnels.

Figure 10: Deformations after installation of the right tunnel (phase 5) and both tunnels (phase 9) Figure 11 shows the settlement of ground surface straight above the tunnel, with an indication of the different construction phases. It can be seen that most settlements occur during the passage of the TBM for construction of the right tunnel. Grout injection for the right tunnel reduces settlements just as grout injection for the left tunnel does The total settlement after construction is in the order of 5.5-6 mm. The curve as given in figure 11 can be obtained from PLAXIS Output: • Select the Curves manager (

)

• In the Curves manager on the Charts tabsheet select the New button to create a new curve. • In Curve generation window that now appears set the following: – x-axis: use Time, a Project

value

– y-axis: use Deformations → Total displacements → uy for the selected point on the ground surface – Select OK to view the chart. 16

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Shield tunnel in Lyon • It may be necessary to rescale the graph, especially the y-axis. – right-click on the graph and select the option Settings . – in the Settings window that appears go to the Chart tabsheet. – set the Scaling of the y-axis to manual and enter for instance Minimum = -0.008 and Maximum = 0.

Figure 11: Ground surface settlements above the right tunnel

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