New developments in numerical modellingof pile installationNguyen Phuong, Frits van Tol, Alexander Rohe

18 September 2014 | KIVI Geotechnical Lectures Evening | TU Delft

Displacement pilesà installation effects

Bearing capacity (vertical/lateral) depending on :• installation method

• jacking• impact driving• vibratory driving

• soil type (sand, clay)• initial soil conditions (density, OCR)• pile type, shape and size (open, closed)

Application :• onshore• offshore

2

Installation methods (displacement piles)

jacking impact driving vibratory driving

3

Testing pile capacity

static load test (SLT) rapid load test (RLT)

lateral load test

4

Current approaches

• empirical methodslimited to very specific cases and conditions

• embedded piles / volume pilesbeam/volume elements with special interfaces, no installation effects

• press and replace techniques (Engin, 2013)displacement applied + geometry update

• wished-in-place pileimposing installation field around pile

• cavity expansionexpansion of cylindrical cavity, shaft?

• advanced FE methods (large strain models, e.g. CEL, ALE)

5

How to determine capacity of displacement piles?

Numerical model would require :

• numerical method allowing for large deformations (installation)

• model incorporating coupled two-phase material behaviour(soil and water, consolidation)

• a constitutive model coupling changes in density and stress to soilstrength and stiffness properties (e.g. hypoplasticity)

• model including dynamics and cyclic behaviour (also high frequencies)

• a 3D model (e.g. lateral load test in non-symmetric conditions)

• model handling liquefaction and material softening with stable solutionalgorithm in such zero effective stress states

Modelling aspects

6

Numerical modelMaterial Point Method (MPM) with coupled two-phase behaviour

Mesh distortion in classical FEM

Material Point Method (MPM)• can model large deformation• no problems with mesh distortion• state variables are traced by

material points• no need for remeshing• enhancement of FEMà re-using established knowledge

• continuum approach

8

FEM

Basic FEM approaches

- material does not crosselements

- nodes remain onboundary

- mesh distortion ?

- material flows througha fixed mesh

- no mesh distortion- state parameters ?

Lagrangian : mesh deforms as the body deforms à SOIL MECHANICS

Eulerian : material flows through a fixed mesh à FLUID MECHANICS

9

Basic concept of MPM

Lagrangian Eulerian

initial configuration deformation after resetting the mesh

in each calculation step :

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Basic principle of MPM

initial position ofmaterial points

final position ofmaterial points

Eulerian background mesh & Lagrangian material points

material pointsmove through

mesh

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Example of MPM calculation

collapsing sand column: total displacements in [m]

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total displacements [m]

Modelling saturated soil

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Two-phase formulation (v-w-formulation)

14

strain [-]

triaxialconditions

0

100

200

300

400

500

600

700

0 0,1 0,2 0,3 0,4 0,5 0,6

Relative density = 80%

Relative density = 63%

Relative density = 30%

1s

1s

2s2s

s1–s2

[kPa

]

0.1 0.2 0.3 0.4 0.5 0.6

stress and strain (rate) dependent, density dependentà therefore correct handling of state parameters extremely important

Constitutive model: hypoplasticity

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Software tool: Material Point Method (MPM)

MPM Software is a tool for analysis of :

• large deformation problems (FEM, UL-FEM, MPM)

• 3D dynamic problems (explicit solver)

• multi-phase problems (fully coupled consolidation calculation)

• soil-structure interaction problems (no need for interface elements)

• advanced material models (continuum models as in FEM)

• soil-water interaction problems

• phase transition problems

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Pile jacking and static load test (SLT)Validation with centrifuge tests

Centrifuge tests

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modelling phases:• preparation at 1g, pile embedded 10D• spin-up to 40g, pile still embedded 10D• installation at 40g

v = 10 mm/min, Dd=10D• static load test (SLT) at 40g

v = 0.00167 mm/s, Dd=0.1D

centrifuge tests at Deltares (Huy, 2008) in a steelcontainer (0.6 m diameter and 0.79 m height) filledwith sand

Modelling approach

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12.4

D11

D25

.5D

pile

soil

D/2

numerical model:

• soil wedge of 20°

• pile diameter D = 11.3 mm

• 26,826 tetrahedral elements(including initially inactive elements)

• 152,020 material points

• side boundary at 26D distance (as in centrifuge)• bottom boundary fully fixed• side boundaries as rollers

• moving mesh concept

• frictional contact

material behaviour:

• Mohr-Coulomb• Hypoplasticity

• two initial densities- medium dense sand, RD = 54%, e0 = 0.68- loose sand, RD = 36%, e0 = 0.75

Results using Mohr-Coulomb model (1)

vertical effective stress [kPa]after spin-up at 40g

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sand RD [%] E [kPa] jmax [°] ymax [°] c [kPa] n [-]

medium dense 54 40 000 30 0 1.0 0.3

loose 36 22 000 30 0 1.0 0.3

Results using Mohr-Coulomb model (2)

horizontal effective stress [kPa] during installation at 40g

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Results using Mohr-Coulomb model (3)

installationphase

static load test(SLT)

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loose sand medium dense sand

Results using Mohr-Coulomb model (4)

horizontal effective stress [kPa] after installation

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loose sand medium dense sand

20

18

16

14

z/D

0 2 4 6 8 r/D

A A’

B

B’

20

18

16

14

z/D

0 2 4 6 8 r/D

A A’

B

B’

Results using Mohr-Coulomb model (5)

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0 2 4 6 8

A A’

B

z/D

B

B’

vertical cross section B-B’

K0-statemedium dense sandloose sand

loose sand

horizontal cross section A-A’

4000

1000

3000

2000

0

radi

alst

ress

[kPa

]

0 2 4 6 8 r/D

0 500 1000 1500 2000 2500

radial stress [kPa]

14

20

18

16

Results using hypoplastic model (1)

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installationphase

static load test(SLT)

loose sand medium dense sand

Results using hypoplastic model (2)

void ratio during installation

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determination of pile capacity

Comparison to NEN 9997-2011

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Normalised plots showing the relative stiffnessof load-displacement curve response from thenumerical simulations in comparison with thedesign curves in NEN 9997-2011. For areliable design using this code, the ultimatebase capacity is determined at 0.1Ddisplacement for a driven pile (with installationeffect) and at 0.2D displacement for a boredpile (without installation effect).

The normalised base resistance curve of theMPM simulation of the SLT is in goodagreement with curve 1 for driven piles. Thisdemonstrates the importance of using anadvanced soil model e.g. hypoplastic model inmodelling pile load tests. The curve thatsimulates the pre-embedded pile shows agood correspondence with the curvesuggested by curve 3 for a bored pile.

Pile driving

Modelling approach

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40/3D

10D

4/3D

D/2

pile

soil

4D

mov

ing

mes

hco

mpr

esse

dm

esh

numerical model:

• soil wedge of 20°

• pile diameter D = 0.3 m

• bottom and right side boundaryare full viscous boundaries

• other side boundaries are rollers

• moving mesh concept

• frictional contact

material behaviour:

• Hypoplasticity

modelling phases:• initialisation by K0-procedure• gravity loading for self-weight pile• impulse loading

Fimp = 1000 kPatimp = 0.012 stblow = 0.25 s

Fimp

timp

Results for loose sand

volumetric strain shear straindisplacement

uxuy gsev

-2.0 m

0.4 m

-0.2 m

0.2 m

-0.3

0.3

0.0

5.0RD = 30.4%, m = 0.5

each step represents one blow

displacement

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First results

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Rapid load test (RLT)

Effect of stiffness and permeability

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E = 48 300 kPaj = 40°y = 5°k = 2·10-5 m/sdamping 0.05

Comparison with centrifuge test

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Conclusions

• numerical method (MPM) presented, which is able to model• large deformations and strains• coupled two-phase behaviour (consolidation)• (quasi-)static and dynamic loading conditions• liquefying soil and material softening• advanced material behaviour (constitutive models)

• validation of MPM for jacked piles and static load testswith centrifuge experiments

• verification of MPM for impact driven piles and rapid load tests

• extension of MPM for vibratory driven piles is ongoing

• bearing capacity of displacement piles can be numerically determineddepending on installation method, soil conditions, pile specifications

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Outlook

Practical use for foundation engineering :

• simulate installation of each pile?Ø computational timeØ numerical experience

• impose stress and density state on mesh?Ø equilibrium stateØ flexibility and variation

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Thank you for your attention!