1

Ronald B.J. Brinkgreve

Plaxis / Delft University of Technology

Efficient modelling of pile foundations

in the Finite Element Method

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Outline

• Introduction

• Embedded pile (3D)

• Embedded pile row (2D)

• Applications of embedded piles

• Ongoing research

• Conclusions

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Introduction

Finite Element Method (FEM) in geotechnical engineering:

• Numerical solution of boundary value problems:

- Deformation (stress, strain) analysis (SLS) and ULS design

- Groundwater flow analysis

- (Geo)thermal analysis

- Thermo-Hydro-Mechanical coupling

• Realistic simulation of soil, structure, soil-structure interaction and

construction process

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Introduction

Dancing Towers, Dubai

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Introduction

FEM modelling piles:

• 2D:

- Axisymmetry: Axially loaded single pile

- Plane strain: Pile (beam) becomes a wall

- New: Embedded pile row in 2D

• Most practical applications involving pile foundations require a 3D model !

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Modelling options of piles in 3D FEM:

• Solid elements:

� ‘Expensive’

� Poor mesh quality

� No structural forces

• Beam elements:

� No pile volume

� No surface area

� Unrealistic pile-soil interaction

Introduction

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Introduction

DFIMEC 2014

(Courtesy of Prof. H.F. Schweiger)

?

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Efficient 3D modelling feature: Embedded pile elements

• Pile as beam elements

• Pile-soil interaction

(shaft friction, end bearing)

• Arbitrary crossing of soil elements

Embedded pile (3D)

DFIMEC 2014

soil

pile

tskin

Ffoot

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Embedded pile (3D)

soil

pile

tskin

Ffoot

s

t

n

ks

kt

kn

ks

kt

kn

ks

kt

kn

Skin stiffness:

ks : axial stiffness

Kn ,kt : lateral stiffness

Skin tractions:

ts = qs/length = ks (uspile-us

soil) ≤ tmax

tn = qn/length = kn (unpile-un

soil)

tt = qt/length = kt (utpile-ut

soil)

kb

Base stiffness:

kb : base/foot stiffness

Base/Foot force:

Fb = kb (ubpile - ub

soil) ≤ Fmax

t

urel

k

1

tmax

(Engin et al, 2007)

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Embedded pile (3D)

Embedded pile:

• Beam nodes: Real nodes; 6 d.o.f.’s per node (ux uy uz rx ry rz)

• Interface nodes: Virtual nodes, 3 d.o.f.’s per node (ux uy uz),

expressed in volume element shape functions

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Embedded pile (3D)

Fmax

Ttop

Tbot

Lpile

Bearing capacity =½ (Ttop+Tbot)×Lpile + Fmax

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Embedded pile – Deformation behaviourPile bearing capacity is input and not result of FEM calculation

F

u

Specified bearing capacity

Global pile response

from soil modelling

and pile-soil interaction

t

urel

k

1

tmax

F

urel

k

1

Fmax

LocalGlobal

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Embedded pile –

Elastic region

Soil stress points inside elastic region are forced to remain elastic

• Around shaft

• Around foot

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Embedded pile – Output

Displacements, bending moments, axial forces, shaft friction, foot force

B AC

u N Ts

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Embedded pile – Validation by TUGraz

DFIMEC 2014

(Tschuchnigg, 2009)

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2D model: 72 mm

3D model - volume piles: 70 mm

3D model - embedded piles: 74 mm

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Embedded pile – Validation

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Lateral movement of pile in horizontal soil slice:

� Embedded pile almost behaves as volume pile due to elastic region

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Embedded pile – Validation by TUDelft (Dao, 2011)

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Embedded pile – Validation by TUDelft

Lateral force at pile top:

DFIMEC 2014

(Dao, 2011)

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Embedded pile (3D)

DFIMEC 2014

Conclusions embedded pile:

• Efficient 3D modelling of pile foundations (bored piles, piled rafts)

• Realistic pile-soil interaction (shaft friction, end bearing, group effects)

• Pile capacity is Input (not a result)

• Since 2005 many applications in practice

(pile foundations, ground anchors)

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Embedded pile row (2D)

How to model a row of piles (out-of-plane) in 2D ?

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Embedded pile row (2D)

‘Conventional’ 2D options:

• Beam (plate):

� Continuous out-of-plane

� Prevents ‘soil flow’ between piles

• Two-node spring (N2N anchor):

� No bending stiffness

� No pile-soil interaction

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Embedded pile row (2D)

New 2D modelling option:

• Embedded pile row:

� Continuous ‘soil’ mesh

� Pile as a superimposed beam element

(axial stiffness, bending stiffness)

� Pile and soil can move independently

� Pile-soil interaction (interface)

(shaft friction, end bearing)

� Out-of-plane spacing (Ls)

Ls

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Embedded pile row (2D)

(Sluis, 2012)

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Calibration of interface stiffness from 3D calculations

Embedded pile row (2D)

(Sluis, 2012)

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Calibration of interface stiffness from 3D calculations

Embedded pile row (2D)

(Sluis, 2012)(out-of-plane)

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Embedded pile row (2D)

10

m

150 kN/m N

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Case study: Bridge abudment

Embedded pile row (2D)

Soft layers (peat/clay)

Deep sand (foundation layer)

Bridge deck Piled abutment

EmbankmentRoad/railwayfreeboard

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Embedded pile row (2D)

2D

3D

detail

-20

-15

-10

-5

0

5

10

-600 -400 -200 0 200 400

ve

rtic

al h

eig

ht

[m]

First pile row: M/Q/N

Q 2d emb [kN]

M 2d emb [kNm]

N 2d emb [kN]

N 3D [kN]

M_2 3D [kNm]

Q_13 3D [kN]

Case study: Bridge abudment

Comparison 2D vs. 3D

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Embedded pile row (2D)

Conclusions embedded pile row:

• Efficient 2D modelling of pile rows (out-of-plane)

• Pile and soil can move independently

• Realistic pile-soil interaction (shaft friction, end bearing)

• Calibration of interface stiffness, based on out-of-plane spacing (Ls)

• Successful validation

• Since 2012 several applications in practice (piles and ground anchors)

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Applications of embedded piles

Quay wall

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Applications of embedded piles

Foundation of high-rise building in Frankfurt (Japan Centre)

(Courtesy of Prof. Y. El-Mossallamy)31 / 40DFIMEC 2014

Applications of embedded piles

Foundation of high-rise building in Singapore

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Applications of embedded piles

Railway station in Vienna~ 500m

~ 400m

47464 elements

~500 m

~400 m

(Courtesy of Prof. H.F. Schweiger)

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Applications of embedded piles

Railway station in Vienna

Model without soil

(bottom view)

615 Piles

� Different pile lengths

� Different pile inclinations

(Rest is modelled as blocks)

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Applications of embedded piles

Railway station in Vienna

axial force shaft friction

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Applications of embedded piles

Excavation in Monaco (Odeon Towers)

(i.c.w. Terrasol, France;

Plaxis Bulletin 29, 2011)

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Ongoing research

DFIMEC 2014

Research on installation effects of driven piles at TUDelft:

• Idea: Impose modified stress and density on ‘wished-in-place’ pile

(Engin, 2013)

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Research on large deformation analysis (MPM) due to pile installation

Ongoing research

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Conclusions

DFIMEC 2014

• Efficient modelling of piles in FEM:

- Embedded pile row (2D)

- Embedded pile (3D)

• Realistic pile-soil interaction (shaft friction, end bearing)

• Pile capacity is Input (not a result)

• Meanwhile many applications in practice (piles and ground anchors)

• Ongoing research:

- Installation effects

- Pile penetration using MPM

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References

1. Engin H.K., Septanika E.G. and Brinkgreve R.B.J. (2007). Improved embedded beam elements for themodelling of piles. In: G.N. Pande & S. Pietruszczak (eds.), Int. Symp. on Numerical Models in Geomechanics –

NUMOG X, 475-480. London: Taylor & Francis group.

2. Engin H.K., Septanika E.G., Brinkgreve R.B.J., Bonnier P.G. (2008). Modeling piled foundation by means of

embedded piles. 2nd International Workshop on Geotechnics of Soft Soils - Focus on Ground Improvement. 3-5

September 2008, University of Strathclyde, Glasgow, Scotland.

3. Septanika E.G., Brinkgreve R.B.J., Engin H.K. (2008). Estimation of pile group behavior using embedded piles,

the 12th International Conference of International Association for Computer Methods and Advances in

Geomechanics (IACMAG), 1-6 October, 2008, Goa, India.

4. Tschuchnigg F. (2009). Embedded piles – 1. Report. CGG_IR021_2009. Technische Universität Graz.

5. Tschuchnigg F. (2009). Embedded piles – 2. Report. Improvements. Technische Universität Graz.

6. Dao T.P.T. (2011). Validation of PLAXIS embedded piles for lateral loading. MSc thesis. Delft University of

Technology.

7. Brinkgreve R.B.J., Engin E., Dao T.P.T. (2012). Possibilities and limitations of embedded pile elements for lateral

loading. IS-GI Brussels.

8. Sluis J. (2012). Validation of embedded pile row in PLAXIS 2D. MSc thesis. Delft University of Technology.

9. Engin H.K. (2013). Modelling pile installation effects – A numerical approach. PhD thesis. Delft University of

Technology.

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Efficient modelling of pile foundations

in the finite element method

Ronald B.J. Brinkgreve

DFIMEC 2014