Presentatie door Alexander Rohe (Deltares) op de Geo Klantendag, tijdens de Deltares Software Dagen- Editie 2017. Donderdag 15 juni 2017, Delft.

1. Anura3D MPM for Geotechnical Engineering
Alexander Rohe
15 June 2017
Deltares Software Dagen, GeoKlantendag

2. Anura3D MPM Research Community
- 6 universities and Deltares
- Joint coordination
- research & projects
- functionality
- Regular activities
- training
- management
- workshops / conferences: www.mpm2017.eu
- website
www.anura3d.com

3. Team at Deltares – Developers & Users
+ Developers/Users
4x PhD students
2x MSc students
2x guests
+ Basic Users at Deltares
Faraz, Amine, Joost, David,
Mark, Maria Luisa, Sanjay,
Geeralt, Esther, Bernadette,
Cor, Jarno, Arjan, Remco,
Suzanne, Gijs, Hans, …

4. Product & Experimental Environment
Research Software Software Product
v2017.1 (beta)MPM Research Community
www.anura3d.com

5. Focus applications at Deltares
dikes, dams, landslides
installation, impact
flowslides, erosion, liquefaction

6. Plan for development and release
- main releases in January: v2017.1, v2018.1, etc…
- update releases in September: v2017.2, v2018.2, etc…
Upcoming functionalities for product release:
- Excavation
- CPT simulation
- Improved contact algorithm
- Improved user-defined soil models interface
- Absorbing boundaries
- Combination of FEM-MPM
- Implicit time integration
- … à What is required?

7. Anura3D v2017.1 (beta)

8. Manuals
Tutorial Scientific Validation

9. Calculation process

10. User interface for input

11. User interface for output

12. Anura3D Background

13. Basic FEM approaches as basis of MPM
- mesh deforms as the body
deforms
- material does not cross elements
- nodes remain on boundary
- mesh distortion?
- material flows through
a fixed mesh
- no mesh distortion
- state parameters in history
dependent materials?
Lagrangian : mesh deforms as the body deforms à “SOIL MECHANICS”
Eulerian : material flows through a fixed mesh à “FLUID MECHANICS”

14. Lagrangian Eulerian
initial configuration deformation after resetting the mesh
in each calculation step :
Basic concept of MPM

15. Basic idea: material points move through mesh
initial position of
material points
final position of
material points
material points
move through
mesh
total displacements [m]total displacements [m]
collapsing soil column:
total displacements in [m]

16. Soil as a multi-phase material
solid grains
liquid
gas
porous media
FTotal stresses in saturated soil are distributed
between liquid and solid grains according to
Terzaghi’s effective stress principle:
intergranular
forcesliquid
pressure
Porosity: VVn v=
n
n
VVe sv
-
==
1
Void ratio:
Saturation:
v
w
r
V
V
S =
= +
total
stress
effective
stress
pore
pressure

17. Modelling multi-phase material in MPM

18. Two-phase formulation
SOIL
(solid grains and groundwater)
SOLID
LIQUID
total representative
volume
solid
volume
liquid
volume
( 0)nÑ »
Hypotheses:
- no free-water
- negligible gradient porosity
- no shear stresses in water (only isotropic p)
- linear and laminar water flow (Darcy law)
Primary unknowns:
Lv Sv velocity field (3+3)
Lr n porosity and density field (1+1)
Derived unknowns:
S
¢s
S
&eL
&e
Lp stress field (1+6)
strain rate field (6+6)
Total = 27 unknowns

19. Two-phase MPM formulation
balance equation for the conservation of linear momentum
L
L
L L d L
D
p
Dt
r rÑ× + - =
v
g fliquid phase
mixture
balance equation for the conservation of mass
(1 ) )
) 0
(
(
0
L
L L
S
S
L
D n
n
Dt
D n
n
Dt
r
r
- - =
=
Ñ×
+ Ñ×
v
vliquid phase
solid phase
Constitutive equations
[ ], , 1
; ( ) (1 )( )
L LL
v L v LL
L L S
D DD p
K n n
Dt Dt Dt n
e e
= = Ñ× + - Ñ×v vliquid phase
solid phase ( , , )
S
S
S S
D
f
Dt
b
Ñ
¢
¢= &
s
s ,a e
Compatibility equations
1
[ ( ) ]
2
S
TS
S S
D
Dt
= Ñ + Ñ
e
v v
1
[ ( ) ]
2
L
TL
L L
D
Dt
= Ñ + Ñ
e
v vliquid phase
solid phase
3 eqs.
3 eqs.
1 eq.
1 eq.
1 eq.
6 eqs.
6 eqs.
6 eqs.
Total = 27 unknowns
(1 )
S
S
L
S
L
L
D
n
D Dt
D
n
t
r rr-= +Ñ +gs
v
g
v

20. MPM solution algorithm
• Update stress • Update Stress
• Update Material Point Volume and density
(solving mass balance equation liquid)
• Calculate new position of Material Point
• Update Material Point Volume, density and
porosity (solving mass balance equation solid)
• Calculate new position of Material Point
End of time step : t = t + Dt
• Calculation of volumetric strain liquid
• Calculation of nodal acceleration field
(solving momentum balance equation liquid)
• Calculation of nodal momentum field
• Calculation of nodal velocity field
• Calculation of nodal velocity field
(solving momentum balance equation mixture)
• Calculation of nodal momentum field
• Calculation of nodal velocity field
Liquid phase SOLID
Beginning of time step : t = t

21. MPM computational cycle
Map MP info to
nodes
Solve equilibrium
equations
Map acceleration
field to MPs
Update position
and info of MPs

22. Modelling multi-phase material in MPM

23. Dynamic equilibrium water
Dynamic equilibrium mixture
Mass balance water
Constitutive equation
Summary equations (fully coupled 2-phase problems)
( )w
w w w s w
n
p
k
g
r r= Ñ - - +v v v g&
( )1 s s w wn nr r r- + = Ñ × +v v σ g& &
(1 ) vol volw
s w
K
p n n
n
e eé ù= - +ë û& &&
=σ D εg& &g
Soil skeleton velocity
Water velocity
Porosity
Solid density
Water density
Density of the mixture
Water pressure
Total stress tensor
Strain tensor
Tangent stiffness tensor
Water bulk modulus
Gravity vector
wv
sv
n
sr
wr
r
p
σ
ε
D
wK
g
MPM is a
continuum-based
method

24. strain [-]
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%
s1–s2[kPa]
0.1 0.2 0.3 0.4 0.5 0.6
advanced material models can depend on:
plastic strain, stress and strain rates, density, …
handling the correct history of state parameters is essential
triaxial
conditions
1s
1s
2s2s
Constitutive model

25. Drainage type
Porous media
Dry Saturated Unsaturated
Fully coupledDrained Undrained
Effective stress
analysis
Total stress
analysis
1-phase: = −
1-phase: / = −
2-phase: = − −
= − −
= +
̇ = ′ ̇ ̇ = ̇
̇ = ̇
3-phase: = − − ,
= − − ,
= − − −

26. Multi-phase material in Anura3D

27. Anura3D applications: Overview

28. Modelling large deformation multi-phase problems
Unsaturated soils
• Rain effects
• Slope stability
• Collapses
Internal erosion (migration of solid particles
under action of flow)
• Internal instability (suffusion)
• Piping
• Stability of water retaining structures
Soil-water-structure interaction
• Seepage flow
• Slope liquefaction
• Submerged collapses
• Dropping geocontainers
• Erosion (macro/external)
Applications
• Slope failures
• Column collapse
• Consolidation problems
• Dike stability
• Pile installation
• Shallow foundation
• Impacts on structures
• Water reservoir
Anura3D v2017.1

29. Anura3D examples à workshop!

30. Summary
Development, validation and application of advanced Anura3D MPM Software
for modelling soil–water–structure interaction problems involving
• (very) large deformations,
• quasi-static/dynamic behaviour, cyclic loading, earthquakes,
• (very) soft soils, consolidation and creep,
• (internal) erosion, piping and scour,
• sedimentation,
• static/dynamic liquefaction and breaching,
• installation problems (piles, CPT),
• reinforcements, flood defences
Focus: applications beyond standard geotechnical or hydraulic software