August 9, 2010

Application of a Quasi-Static Material Point Method in GeomechanicsGEO-INSTALL Modelling Installation Effects in Geotechnical

Engineering

Dipl.-Ing. Lars Beuth Deltares / University of Stuttgart

1. Quasi-Static MPM

2. Moving Block

3. Soil-Structure Interaction

4. Cone Penetration in Undrained Clay

5. Outlook

13 augustus 2010

Quasi-static MPM & Updated Lagrangian FEM with implicit integration for load step i

Iteration number

Elastic stiffness matrix

i i i ik 1 external,k internal,kK u F F

A

qLoadLoad

A

Load step number

Subincremental displacement vector

1. Quasi-Static MPM

F i

ui Displacement of point ADisplacement of point ALo

adLo

ad

1

i

k

ikuu

iku

Steps

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Particles represent the deforming solid body inside a finite element mesh

Beginningof

load step

Mesh distortionduring

load step

Resettingat end ofload step

1. Quasi-Static MPM

2. Moving Block

15-noded prismatic elementwith near-quadratic interpolation

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Active block movement

0.6 m

0.4 m

Elastic block

E = 100 MPa, = 0.0

= 20 kN/m3Full bonding with soil

Soil (Mohr-Coulomb)

E = 10 MPa, = 0.3

c = 10 kPa, = 30°

= 20 kN/m3

2. Moving Block

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Shift of block = 0 cm

Active block movement

2. Moving Block

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Shift of block = 5 cm

Active block movement

2. Moving Block

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Shift of block = 10 cm

Active block movement

2. Moving Block

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Shift of block = 15 cm

Active block movement

2. Moving Block

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Shift of block = 20 cm

Active block movement

2. Moving Block

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Shift of block = 25 cm

The block is loosing its contact to the soil, a free slope is forming. Soil isslightly heaving up in front of the block.

Active block movement

2. Moving Block

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Shift of block = 30 cm

The block is loosing its contact to the soil, a free slope is forming. Soil isslightly heaving up in front of the block.

Active block movement

2. Moving Block

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Shift of block = 35 cm

The block is loosing its contact to the soil, a free slope is forming. Soil isslightly heaving up in front of the block.

Active block movement

2. Moving Block

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Shift of block = 40 cm

A few soil particles are still sticking to the block, due to soil cohesion and adhesion between soil and block.

Active block movement

2. Moving Block

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Shift of block = 15 cm

Passive block movement

2. Moving Block

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Shift of block = 22.5 cm

Passive block movement

2. Moving Block

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Shift of block = 30 cm

Passive block movement

2. Moving Block

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Shift of block = 37.5 cm

Passive block movement

2. Moving Block

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Shift of block = 45 cm

Passive block movement

2. Moving Block

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Shift of block = 52.5 cm

Passive block movement

2. Moving Block

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Shift of block = 60 cm End of movement

Passive block movement

2. Moving Block

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-8

-7

-6

-5

-4

-3

-2

-1

0-700-600-500-400-300-200-1000

Prescribed displacement ux [mm]

F x [k

N]

FXEX

RX

Horizontal Equilibrium

Passive block movement – reaction forces

2. Moving Block

3. Soil-Structure Interaction

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... yield function ... plastic potential function

wDt BfaceAface uuw

face Aface B

Interface tractions: with

eT

ee fgd

Dtt

DDD 1Elastic-plastic stiffness matrix:

tD

tgfd e

T

tgtf

N

S

T

Application of interface elements with the MPM

3. Soil-Structure Interaction

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Activated volume elements contain particles which carry the stresses.

Activated interface elements have no particles !

New interface stresses need to be computed after mesh resetting.

Deformed mesh at end of load step

Reset mesh at end of load step

Deactivated element

Newly activated element

Application of interface elements with the MPM

3. Soil-Structure Interaction

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Supervector of internal nodal forces:interface

internalinterface T

S

dSF N t

Unknown tractions are obtained through solving system of equilibriumequations for t at (Newton-Cotes) integration points.

Supervector of external nodal forces:

= strain interpolation matrix = soil stressesBsoilsoil VV

Texternalinterface dVdV TNBF

= shape function matrix = soil weightN

external1f external

2fexternal3f external

4fexternal5f

Application of interface elements with the MPM

3. Soil-Structure Interaction

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Elastic

Load

0

20

0,0 1,0Block displacement [m]

adhesion = 10 kPa

1.0

Appl

ied

Load

[kPa

]

Sliding of elastic block

3. Soil-Structure Interaction

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+22.0

-23.5

N [kPa]

x [m]

N [kPa]

+21.5

-21.6

x [m]

s [kPa]

10.0x [m]

10.0

s [kPa]

x [m]

Low-order

x

z

x

z

High-order

Sliding of elastic block

3. Soil-Structure Interaction

4. Cone Penetration inUndrained Clay

4-noded tetrahedral elementwith linear interpolation

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In-situ site investigation with cone penetration test

4. Cone Penetration in Undrained Clay

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EU = 6 MPa U = 0.40 cU = 20 kPa U = 0°

Segment discretised with 4-noded tetrahedral elements

4. Cone Penetration in Undrained Clay

Discretisation of Cone Penetrometer

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Smooth contact: adhesion = 0

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6 7Prescribed Displacement / Cone Diameter

Rel

ativ

e Ti

p R

esis

tanc

e

tip

/ cu

Rough contact: adhesion = cu

Adhesion = cu / 2

4. Cone Penetration in Undrained Clay

Results

13 augustus 2010

Rough contact

N [kPa]

N [kPa]

s [kPa]

N [kPa]

Normal stresses Shear stresses

-500

-12

20

-20

-300

4. Cone Penetration in Undrained Clay

Results

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Principal stresses

Smooth Rough

4. Cone Penetration in Undrained Clay

Results

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Rough contact at 4 D

Incremental horizontaldisplacements

4. Cone Penetration in Undrained Clay

Results

13 augustus 2010

Accumulated shear strain at 4 D

Rough contact Smooth contact

4. Cone Penetration in Undrained Clay

Results

5. Outlook

13 augustus 2010

Pore pressure dissipation

Going beyond Mohr-Coulomb (Hardening)

Get experience in layered soil

In future also interaction between piles

1 September 2010 MPM Workshop Deltares, Delft, The Netherlands

5. Outlook

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The research leading to these results has received funding from the European Community’s Seventh Framework Programme FP7/2007-2013 under grant agreement n° PIAG-GA-2009-230638.

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Appendix

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Rough contact at 4 D

Incremental verticaldisplacements

Appendix

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results by Van den Berg

50050 100 200 350

5

10

15

20

25

Ir = G / cu

Van Den Berg (1994), ‘Analysis of soil penetration’, Technical University Delft

Nc = qc / cu

rough

smooth

Results by MPM

Range of results by Van den Berg

Appendix

13 augustus 2010

Appendix

VERMEER, P.A., BEUTH, L., BENZ, T. A New Numerical Method for Large Deformation Problems in Geomechanics, Proceedings of the International Conference of IACMAG, Goa, India, 2008; 12:55-63.

YUAN, Y., BEUTH, L., VERMEER, P.A. Frictional contact formulation for large deformation analyses in geomechanics. Proceedings of the 2nd international workshop on geotechnics of soft soil, Glasgow, 2008; 2:95-103.

STOLLE, D., JASSIM, I., VERMEER, P.A. Accurate simulation of incompressible problems in geomechanics, Proceedings of the International Conference on Computer Methods in Mechanics, Zielona Góra, Poland, 2009, 18:89-90.

VERMEER, P.A., YUAN, Y., BEUTH, L., BONNIER, P. Application of interface elements with the Material Point Method, Proceedings of the International Conference on Computer Methods in Mechanics, Zielona Góra, Poland, 2009, 18:477-478.

WIECKOWSKI, Z., BEUTH, L., JASSIM, I. Parallel computations in material point method with application to soil mechanics, Proceedings of the International Conference on Computer Methods in Mechanics, Zielona Góra, Poland, 2009, 18:491-492.

BEUTH, L., WIECKOWSKI, Z., VERMEER, P.A. Solution of quasi-static large-strain problems by the material point method, Journal for Numerical and Analytical Methods in Geomechanics, in print.