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1
Ronald B.J. Brinkgreve
Plaxis / Delft University of Technology
Efficient modelling of pile foundations
in the Finite Element Method
DFIMEC 2014 1 / 40
Outline
• Introduction
• Embedded pile (3D)
• Embedded pile row (2D)
• Applications of embedded piles
• Ongoing research
• Conclusions
DFIMEC 2014 2 / 40
2
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
3 / 40DFIMEC 2014
Introduction
Dancing Towers, Dubai
4 / 40DFIMEC 2014
3
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 !
5 / 40DFIMEC 2014
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
DFIMEC 2014 6 / 40
4
Introduction
DFIMEC 2014
(Courtesy of Prof. H.F. Schweiger)
?
7 / 40
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
8 / 40
5
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)
9 / 40DFIMEC 2014
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
DFIMEC 2014 10 / 40
6
Embedded pile (3D)
Fmax
Ttop
Tbot
Lpile
Bearing capacity =½ (Ttop+Tbot)×Lpile + Fmax
DFIMEC 2014 11 / 40
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
12 / 40DFIMEC 2014
7
Embedded pile –
Elastic region
Soil stress points inside elastic region are forced to remain elastic
• Around shaft
• Around foot
DFIMEC 2014 13 / 40
Embedded pile – Output
Displacements, bending moments, axial forces, shaft friction, foot force
B AC
u N Ts
14 / 40DFIMEC 2014
8
Embedded pile – Validation by TUGraz
DFIMEC 2014
(Tschuchnigg, 2009)
15 / 40
2D model: 72 mm
3D model - volume piles: 70 mm
3D model - embedded piles: 74 mm
DFIMEC 2014
Embedded pile – Validation
16 / 40
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Lateral movement of pile in horizontal soil slice:
� Embedded pile almost behaves as volume pile due to elastic region
DFIMEC 2014
Embedded pile – Validation by TUDelft (Dao, 2011)
17 / 40
Embedded pile – Validation by TUDelft
Lateral force at pile top:
DFIMEC 2014
(Dao, 2011)
18 / 40
10
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)
19 / 40
Embedded pile row (2D)
How to model a row of piles (out-of-plane) in 2D ?
20 / 40DFIMEC 2014
11
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
21 / 40DFIMEC 2014
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
22 / 40DFIMEC 2014
12
Embedded pile row (2D)
(Sluis, 2012)
23 / 40DFIMEC 2014
Calibration of interface stiffness from 3D calculations
Embedded pile row (2D)
(Sluis, 2012)
24 / 40DFIMEC 2014
13
Calibration of interface stiffness from 3D calculations
Embedded pile row (2D)
(Sluis, 2012)(out-of-plane)
25 / 40DFIMEC 2014
Embedded pile row (2D)
10
m
150 kN/m N
26 / 40DFIMEC 2014
14
Case study: Bridge abudment
Embedded pile row (2D)
Soft layers (peat/clay)
Deep sand (foundation layer)
Bridge deck Piled abutment
EmbankmentRoad/railwayfreeboard
27 / 40DFIMEC 2014
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
28 / 40DFIMEC 2014
15
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)
29 / 40DFIMEC 2014
Applications of embedded piles
Quay wall
30 / 40DFIMEC 2014
16
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
32 / 40DFIMEC 2014
17
Applications of embedded piles
Railway station in Vienna~ 500m
~ 400m
47464 elements
~500 m
~400 m
(Courtesy of Prof. H.F. Schweiger)
33 / 40DFIMEC 2014
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)
34 / 40DFIMEC 2014
18
Applications of embedded piles
Railway station in Vienna
axial force shaft friction
35 / 40DFIMEC 2014
Applications of embedded piles
Excavation in Monaco (Odeon Towers)
(i.c.w. Terrasol, France;
Plaxis Bulletin 29, 2011)
36 / 40DFIMEC 2014
19
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)
37 / 40
Research on large deformation analysis (MPM) due to pile installation
Ongoing research
DFIMEC 2014 38 / 40
20
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
39 / 40
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.
DFIMEC 2014 40 / 40
21
Efficient modelling of pile foundations
in the finite element method
Ronald B.J. Brinkgreve
DFIMEC 2014