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
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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DFIMEC 2014
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 rowin 2D
• Most practical applications involving pile foundations require a 3D model !
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DFIMEC 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
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 8 / 40Embedded 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-ussoil) ≤ tmax
tn= qn/length= kn(unpile-unsoil)
tt= qt/length= kt(utpile-utsoil)
kb
Base stiffness: kb : base/foot stiffness
Base/Foot force: Fb= kb(ubpile - ubsoil) ≤ Fmax
t urel k 1 tmax (Engin et al, 2007) 9 / 40 DFIMEC 2014
Embedded pile (3D)
Embedded pile:• Beam nodes: Real nodes; 6 d.o.f.’s per node (uxuyuzrxryrz)
• Interface nodes: Virtual nodes, 3 d.o.f.’s per node (uxuyuz), expressed in volume element shape functions
Embedded pile (3D)
Fmax Ttop Tbot Lpile Bearing capacity =½ (Ttop+Tbot)×Lpile+ Fmax
DFIMEC 2014 11 / 40
Embedded pile – Deformation behaviour
Pile bearing capacity is inputand not result of FEM calculationF
u
Specified bearing capacity
Global pile response from soil modelling and pile-soil interaction
t urel k 1 tmax F urel k 1 Fmax Local Global 12 / 40 DFIMEC 2014
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 A C
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
DFIMEC 2014
Embedded pile – Validation
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)
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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DFIMEC 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
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Embedded pile row (2D)
(Sluis, 2012)
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DFIMEC 2014
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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DFIMEC 2014
Embedded pile row (2D)
1 0 m 150 kN/m N 26 / 40 DFIMEC 2014
Case study: Bridge abudment
Embedded pile row (2D)
Soft layers (peat/clay)
Deep sand (foundation layer)
Bridge deck Piled abutment
Embankment Road/railway
freeboard
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DFIMEC 2014
Embedded pile row (2D)
2D 3D detail -20 -15 -10 -5 0 5 10 -600 -400 -200 0 200 400 v e rt ic a l h e ig h t [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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DFIMEC 2014
Applications of embedded piles
Quay wall30 / 40
Applications of embedded piles
Foundation of high-rise building in Frankfurt (Japan Centre)
(Courtesy of Prof. Y. El-Mossallamy)
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DFIMEC 2014
Applications of embedded piles
Foundation of high-rise building in Singapore32 / 40
Applications of embedded piles
Railway station in Vienna~ 500m ~ 400m 47464 elements ~500 m ~400 m
(Courtesy of Prof. H.F. Schweiger) 33 / 40
DFIMEC 2014
Applications of embedded piles
Railway station in ViennaModel 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 Viennaaxial force shaft friction
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DFIMEC 2014
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
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 the modelling 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.
Efficient modelling of pile foundations in the finite element method
Ronald B.J. Brinkgreve