Post on 17-Oct-2021
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
13 augustus 2010
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
13 augustus 2010
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
13 augustus 2010
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
13 augustus 2010
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
13 augustus 2010
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
13 augustus 2010
+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
13 augustus 2010
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
13 augustus 2010
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
13 augustus 2010
Principal stresses
Smooth Rough
4. Cone Penetration in Undrained Clay
Results
13 augustus 2010
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
13 augustus 2010
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.
13 augustus 2010
Appendix
13 augustus 2010
Rough contact at 4 D
Incremental verticaldisplacements
Appendix
13 augustus 2010
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.