1. Ingeniería

Three-node zero-thickness hydro-mechanical interface
finite element for geotechnical applications
Benjamin Cerfontaine
University of Liege
30th of January, 2015
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Outline
1
Context
2
Modelling interfaces
3
Application
4
Conclusions
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Context
Table of contents
1
Context
2
Modelling interfaces
3
Application
4
Conclusions
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Context
Suction caisson
Outer pressure
Sea level
Pumping
Reduced soil
effective
stress
Inner pressure
Sand heave
Seabed
Seepage flow
Sand
Foundation for offshore
structures
Installed by suction
Hollow cylinder open towards
the bottom
Made of steel
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Increased transient resistance to
pull and push loads
Crucial role of interfaces
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Context
Interface in geomechanics
Interface
Contact
Surface between two media (=discontinuity)
Caisson
Shearing
Sliding
Interface
Unsticking
Flow
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Soil
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Context
Interface in geomechanics
Interface
Surface between two media (=discontinuity)
Contact
Push load
Shearing
Contact pressure
Sliding
Unsticking
Flow
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Soil
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Context
Interface in geomechanics
Interface
Surface between two media (=discontinuity)
Contact
Pull load
Shearing
Sliding
Shear stresses
Unsticking
Flow
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Soil
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Context
Interface in geomechanics
Interface
Surface between two media (=discontinuity)
Pull load
Contact
Shearing
Sliding
Sliding
Unsticking
Flow
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Soil
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Context
Interface in geomechanics
Interface
Contact
Surface between two media (=discontinuity)
Unsticking
Pull load
Shearing
Sliding
Sliding
Unsticking
Flow
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Soil
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Context
Interface in geomechanics
Interface
Contact
Surface between two media (=discontinuity)
Unsticking
Pull load
Shearing
Fluid flow
Sliding
Sliding
Unsticking
Flow
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Soil
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Modelling interfaces
Table of contents
1
Context
2
Modelling interfaces
Mechanical problem
Hydraulic problem
Coupled problem
3
Application
4
Conclusions
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Modelling interfaces
Mechanical problem
Normal behaviour
Contact
pN ≥ 0
gN ≥ 0
pN gN = 0
Approaches
Regularisation
gN e11
e12
pN = f (gN )
E2
Discretisation
E1
No contact
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pN
Contact
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Modelling interfaces
Mechanical problem
Normal behaviour
Contact
pN ≥ 0
gN ≥ 0
pN gN = 0
Thin layer
Approaches
Medium 1
Thin layer
elements
Medium 3
Medium 2
Regularisation
pN = f (gN )
Zero-thickness
Medium 1
Boundary
elements
Medium 2
Discretisation
No contact
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Contact
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Modelling interfaces
Mechanical problem
Normal behaviour
Contact
pN ≥ 0
gN ≥ 0
pN gN = 0
Lagrange multiplier method
Approaches
Pressure
distribution
Regularisation
pN = f (gN )
Penalty method
No penetration
Zoom
Penetration
Discretisation
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Modelling interfaces
Mechanical problem
Normal behaviour
Contact
pN ≥ 0
gN ≥ 0
pN gN = 0
Intricate asperities
Approaches
First contact
point
pN = f (gN )
Discretisation
pN
Regularisation
Compression
Asperities
deformation
gN
pN
gN
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Modelling interfaces
Mechanical problem
Normal behaviour
Contact
pN ≥ 0
gN ≥ 0
Node to node
Approaches
pN gN = 0
Node to segment
Gap
Gap
Regularisation
Segment to segment
Penetration
pN = f (gN )
Contact domain
Gap interpolation
Gap
Discretisation
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Modelling interfaces
Mechanical problem
Tangential behaviour
Shearing
τ ≥0
g˙ T ≥ 0
τ g˙ T = 0
Criterion
gT
τ=τmax
τ
E2
Sticking
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E1
Sliding
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Modelling interfaces
Mechanical problem
Tangential behaviour
Shearing
Criterion
τ ≥0
g˙ T ≥ 0
τ g˙ T = 0
||τ||
f>0
f=0
f<0
Sliding state
No contact
Sticking
state
µ
f = kτ k − µ pN
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pN
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Modelling interfaces
Hydraulic problem
Fluid flows
Interface
Longitudinal and transversal flows
q
Discontinuity
Discretisation
Fluid flow
Fluid flow
Fluid flow
Fluid flow
pw
E2
E1
Diconstinuity = porous medium
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Modelling interfaces
Hydraulic problem
Fluid flows
Interface
Longitudinal and transversal flows
Single node
gN
Discretisation
Finite element mesh
Porous medium
Discontinuity
Double node
Triple node
gN
gN
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Modelling interfaces
Coupled problem
Couplings
Hydro-mechanical
couplings
Effective pressure
Terzaghi’s principle
Permeability
Storage
pN = p0N + pw
p0N , effective pressure (mechanical
behaviour)
pw , fluid pressure inside the
interface
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Modelling interfaces
Coupled problem
Couplings
Hydro-mechanical
couplings
Effective pressure
Permeability
Storage
Cubic law
(D0 )2
12 2
kl =

 (D0 + gN )
12



gN ≤ 0
otherwise.
kl , longitudinal permeability
D0 , residual hydraulic opening
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Modelling interfaces
Coupled problem
Couplings
Hydro-mechanical
couplings
Effective pressure
Stored water within discontinuity
Permeability
Storage
M˙ f =
L˙
ρ˙ w gN + ρw g˙ N + ρw gN
L
!
L
L, length of the discontinuity
ρw , density of water
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Modelling interfaces
Coupled problem
Summary
Mechanical problem
Zero-thickness
Segment to segment discretisation
Penalty method to enforce normal and tangential constraints
Coulomb criterion
Hydraulic problem
Three-node discretisation
Longitudinal flow
Transversal flows
Coupled problem
Effective pressure
Permeability
Storage (transient component)
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Application
Table of contents
1
Context
2
Modelling interfaces
3
Application
4
Conclusions
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Application
Statement of the problem
Inner
interface (lid)
Drained Boundary
Un
Bo dra
un ine
da d
ry
Caisson
Inner
interface
(skirt)
d
ine
dra ry
Un unda
Bo
Elastic soil and caisson
Outer
interface
(skirt)
Friction coefficient 0.57
Diameter 7.8m
Water depth 10m
Residual hydraulic aperture
1.E-5m
Soil permeability 1.E-11m2
Penalty coefficient 1.E10 N/m3
K0 = 1
Conductivity 1.E-8m/Pa/s
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Application
Drained simulation (mechanical behaviour)
ΔFtot
Shearing of the interface
900
Δy>0
800
ΔFext
∆ F [kN]
ΔFint
700
∆ Ftot
600
∆ Fext
500
∆ Fint
A
400
B
300
200
100
0
0
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0.5
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1
1.5
Displ. [mm]
2
2.5
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Application
Drained simulation (mechanical behaviour)
Shearing of the interface
0
Gapgopening
0.5
Depthg[m]
1
1.5
Displg[mm]
900
0.02
0.43
0.63
1.17
2
2.5
3
800
3.5
0.1
0.2
0.3
0.4
η ext=||τ||/p’N [−]
0.5
0.6
0.7
∆ F [kN]
4
0
700
∆ Ftot
600
∆ Fext
500
∆ Fint
A
400
B
300
Outer friction
Gap opening
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200
100
0
0
0.5
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1
1.5
Displ. [mm]
2
2.5
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Application
Drained simulation (mechanical behaviour)
Shearing of the interface
0
0.5
Depth [m]
1
Displ [mm]
1.5
900
0.02
0.43
0.63
1.17
2
2.5
800
3
3.5
0.1
0.2
0.3
0.4
η int=||τ||/p’N [−]
0.5
0.6
0.7
∆ F [kN]
4
0
700
∆ Ftot
600
∆ Fext
500
∆ Fint
A
400
B
300
Outer friction
Gap opening
Inner friction
Failure
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200
100
0
0
0.5
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1
1.5
Displ. [mm]
2
2.5
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Application
Partially drained simulation (hydraulic behaviour)
Suction effect
ΔFtot
900
∆ FB[kN]
ΔFuw
800
∆ Ftot
700
∆ Fext
600
∆ Fint
∆ Fuw
500
A
400
300
B
200
Opening∆F
of a gap
Higher
Opening oftota gap
Transversal flow
Coupling gapTransversal storage
permeability
Stationary phase
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C
100
0
0
0.5
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1
1.5
Displ.B[mm]
2
2.5
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Application
Partially drained simulation (hydraulic behaviour)
Suction effect
ΔFtot
ΔFuw
Δpw [kPa]
Opening
of a gap
∆F
tot
Opening of a gap
Transversal flow
Coupling
Coupling
0 gapp
Transversal
storage
w
N = pN + p
permeability
Transient
Stationary∆p
phase
w
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0.00
-0.84
-1.69
-2.54
-3.39
-4.24
-5.09
-5.94
-6.79
-7.64
-8.49
-9.34
E3
E2
E1
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Application
Partially drained simulation (hydraulic behaviour)
ΔFtot
Top unsticking and storage
ΔyS
0.2
ΔyC
1.4
C
ΔFuw
0.1
B
B. Cerfontaine
0.8
A
0.6
0.4
0.05
0
0
B
1
∆ ytop [mm]
ft [kg/s]
0.15
Opening
of a gap
∆F
tot
Opening
of a gap
Transversal flow
Coupling
Coupling
0 gapp
Transversal
storage
w
N = pN + p
permeability
Transient
Stationary∆u
phase
w
C
1.2
Soil
Caisson
0.2
A
1
2
Displ. [mm]
3
0
0
1
2
Displ. [mm]
3
vp = 1 mm/min
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Application
Partially drained simulation (hydraulic behaviour)
Longitudinal flow fl along the skirt
Depth [m]
Flow
Opening
of a gap
∆F
tot
Opening
of a gap
Transversal flow
Coupling
Coupling
0 gapp
Transversal
storage
w
N = pN + p
permeability
Transient
Stationary∆u
phase
w
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0
0
0.5
0.5
1
1
1.5
1.5
2
2
2.5
2.5
3
3
3.5
3.5
4
−8
−6
−4
−1
−2
−2
fl [kg.s .m ]
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0
4
−0.05
0
0.05
gN [mm]
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Conclusions
Table of contents
1
Context
2
Modelling interfaces
3
Application
4
Conclusions
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Conclusions
1
Development of a coupled hydro-mechanical interface element
Zero-thickness
Three-node flow discretisation
2
Main features of mechanical behaviour
Shearing
Sliding
3
Main features of hydraulic behaviour
Transversal flows
Longitudinal flows
4
Hydro-mechanical couplings
Suction effect (Terzaghi)
Permeability (longitudinal flow)
Storage (Unsticking)
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Conclusions
Related papers
Cerfontaine B (2014) The cyclic behaviour of sand from the Prevost
model to offshore geotechnics (2014). University of Liege.
Cerfontaine B, Collin F and Charlier R (2015) Vertical transient
loading of a suction caisson in dense sand. In Proceedings of the 14th
International Conference of International Association for Computer
Methods and Recent Advances in Geomechanics, IACMAG2014, pp.
929-934.
Cerfontaine B, Levasseur S, Collin F and Charlier R (2014). In
Proceedings of the 8th European Conference on Numerical Methods
in Geotechnical Engineering, NUMGE2014, 2, pp. 1243-1248.
Cerfontaine, B, Dieudonn´e AC, Radu JP, Collin F and Charlier R
(2015 submitted) 3D zero-thickness coupled interface finite element :
formulation and application, Computers & Geotechnics.
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