Three-node zero-thickness hydro-mechanical interface finite element - - PowerPoint PPT Presentation

▶
three node zero thickness hydro mechanical interface
SMART_READER_LITE
LIVE PREVIEW

Three-node zero-thickness hydro-mechanical interface finite element - - PowerPoint PPT Presentation

Jan 03, 2023 215 likes •587 views

Three-node zero-thickness hydro-mechanical interface finite element for geotechnical applications Benjamin Cerfontaine University of Liege 30th of January, 2015 B. Cerfontaine Groupe de contact FNRS 15/09/14 0 / 16 Outline Context 1

slide-1
SLIDE 1

Three-node zero-thickness hydro-mechanical interface finite element for geotechnical applications

Benjamin Cerfontaine

University of Liege

30th of January, 2015

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 0 / 16

slide-2
SLIDE 2

Outline

1

Context

2

Modelling interfaces

3

Application

4

Conclusions

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 1 / 16

slide-3
SLIDE 3

Context

Table of contents

1

Context

2

Modelling interfaces

3

Application

4

Conclusions

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 2 / 16

slide-4
SLIDE 4

Context

Suction caisson

Seabed Sea level

Reduced soil effective stress Outer pressure Inner pressure Sand heave Pumping Seepage flow Sand

Foundation for offshore structures Hollow cylinder open towards the bottom Made of steel Installed by suction Increased transient resistance to pull and push loads Crucial role of interfaces

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 3 / 16

slide-5
SLIDE 5

Context

Interface in geomechanics Interface Surface between two media (=discontinuity) Contact Shearing Sliding Unsticking Flow

Soil Caisson Interface

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 4 / 16

slide-6
SLIDE 6

Context

Interface in geomechanics Interface Surface between two media (=discontinuity) Contact Shearing Sliding Unsticking Flow

Push load Contact pressure

Soil

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 4 / 16

slide-7
SLIDE 7

Context

Interface in geomechanics Interface Surface between two media (=discontinuity) Contact Shearing Sliding Unsticking Flow

Pull load Shear stresses

Soil

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 4 / 16

slide-8
SLIDE 8

Context

Interface in geomechanics Interface Surface between two media (=discontinuity) Contact Shearing Sliding Unsticking Flow

Pull load

Soil Sliding

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 4 / 16

slide-9
SLIDE 9

Context

Interface in geomechanics Interface Surface between two media (=discontinuity) Contact Shearing Sliding Unsticking Flow

Pull load

Soil Unsticking Sliding

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 4 / 16

slide-10
SLIDE 10

Context

Interface in geomechanics Interface Surface between two media (=discontinuity) Contact Shearing Sliding Unsticking Flow

Pull load Fluid flow

Soil Sliding Unsticking

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 4 / 16

slide-11
SLIDE 11

Modelling interfaces

Table of contents

1

Context

2

Modelling interfaces Mechanical problem Hydraulic problem Coupled problem

3

Application

4

Conclusions

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 5 / 16

slide-12
SLIDE 12

Modelling interfaces Mechanical problem

Normal behaviour Contact pN ≥ 0 gN ≥ 0 pN gN = 0 Approaches Regularisation pN = f (gN) Discretisation

E1 E2

1

e

1 1

e2 gN pN

No contact Contact

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 6 / 16

slide-13
SLIDE 13

Modelling interfaces Mechanical problem

Normal behaviour Contact pN ≥ 0 gN ≥ 0 pN gN = 0 Approaches Regularisation pN = f (gN) Discretisation

No contact Contact Zero-thickness Thin layer

Medium 1 Medium 2 Medium 3 Medium 1 Medium 2 Boundary elements Thin layer elements

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 6 / 16

slide-14
SLIDE 14

Modelling interfaces Mechanical problem

Normal behaviour Contact pN ≥ 0 gN ≥ 0 pN gN = 0 Approaches Regularisation pN = f (gN) Discretisation

Lagrange multiplier method Penalty method

Penetration Pressure distribution No penetration

Zoom

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 6 / 16

slide-15
SLIDE 15

Modelling interfaces Mechanical problem

Normal behaviour Contact pN ≥ 0 gN ≥ 0 pN gN = 0 Approaches Regularisation pN = f (gN) Discretisation

pN

First contact point Asperities deformation Intricate asperities

pN

gN gN Compression

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 6 / 16

slide-16
SLIDE 16

Modelling interfaces Mechanical problem

Normal behaviour Contact pN ≥ 0 gN ≥ 0 pN gN = 0 Approaches Regularisation pN = f (gN) Discretisation

Node to node Node to segment Segment to segment

Penetration Gap Gap Gap

Contact domain

Gap interpolation

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 6 / 16

slide-17
SLIDE 17

Modelling interfaces Mechanical problem

Tangential behaviour Shearing τ ≥ 0 ˙ gT ≥ 0 τ ˙ gT = 0 Criterion

E1 E2

τ=τmax

Sticking Sliding

τ

gT

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 7 / 16

slide-18
SLIDE 18

Modelling interfaces Mechanical problem

Tangential behaviour Shearing τ ≥ 0 ˙ gT ≥ 0 τ ˙ gT = 0 Criterion

||τ|| p

f > f<0 f=0 Sticking state Sliding state No contact

µ

N

f = τ − µ pN

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 7 / 16

slide-19
SLIDE 19

Modelling interfaces Hydraulic problem

Fluid flows Interface Longitudinal and transversal flows Discretisation

q pw Discontinuity Fluid flow Fluid flow Fluid flow Fluid flow E

1

E

2

Diconstinuity = porous medium

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 8 / 16

slide-20
SLIDE 20

Modelling interfaces Hydraulic problem

Fluid flows Interface Longitudinal and transversal flows Discretisation

Single node Double node gN Triple node Discontinuity Porous medium Finite element mesh gN gN

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 8 / 16

slide-21
SLIDE 21

Modelling interfaces Coupled problem

Couplings Hydro-mechanical couplings Effective pressure Permeability Storage Terzaghi’s principle pN = p′

N + pw

p′

N, effective pressure (mechanical

behaviour) pw, fluid pressure inside the interface

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 9 / 16

slide-22
SLIDE 22

Modelling interfaces Coupled problem

Couplings Hydro-mechanical couplings Effective pressure Permeability Storage Cubic law kl =      (D0)2 12 gN ≤ 0 (D0 + gN)2 12

  • therwise.

kl, longitudinal permeability D0, residual hydraulic opening

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 9 / 16

slide-23
SLIDE 23

Modelling interfaces Coupled problem

Couplings Hydro-mechanical couplings Effective pressure Permeability Storage Stored water within discontinuity ˙ Mf =

  • ˙

ρw gN + ρw ˙ gN + ρw gN ˙ L L

  • L

L, length of the discontinuity ρw, density of water

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 9 / 16

slide-24
SLIDE 24

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)

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 10 / 16

slide-25
SLIDE 25

Application

Table of contents

1

Context

2

Modelling interfaces

3

Application

4

Conclusions

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 11 / 16

slide-26
SLIDE 26

Application

Statement of the problem

Undrained Boundary Undrained Boundary D r a i n e d B

  • u

n d a r y C a i s s

  • n

Inner interface (lid) Outer interface (skirt) Inner interface (skirt)

Elastic soil and caisson Diameter 7.8m Water depth 10m Soil permeability 1.E-11m2 K0 = 1 Friction coefficient 0.57 Residual hydraulic aperture 1.E-5m Penalty coefficient 1.E10 N/m3 Conductivity 1.E-8m/Pa/s

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 12 / 16

slide-27
SLIDE 27

Application

Drained simulation (mechanical behaviour)

ΔFtot ΔFint ΔFext Δy>0

0.5 1 1.5 2 2.5 3 100 200 300 400 500 600 700 800 900

  • Displ. [mm]

∆ F [kN] ∆ Ftot ∆ Fext ∆ Fint A B

Shearing of the interface

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 13 / 16

slide-28
SLIDE 28

Application

Drained simulation (mechanical behaviour)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 1 1.5 2 2.5 3 3.5 4

ηext=||τ||/p’N [−] Depthg[m] 0.02 0.43 0.63 1.17

Displg[mm]

Gapgopening

0.5 1 1.5 2 2.5 3 100 200 300 400 500 600 700 800 900

  • Displ. [mm]

∆ F [kN] ∆ Ftot ∆ Fext ∆ Fint A B

Shearing of the interface Outer friction Gap opening

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 13 / 16

slide-29
SLIDE 29

Application

Drained simulation (mechanical behaviour)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 1 1.5 2 2.5 3 3.5 4

ηint=||τ||/p’N [−] Depth [m] 0.02 0.43 0.63 1.17

Displ [mm]

0.5 1 1.5 2 2.5 3 100 200 300 400 500 600 700 800 900

  • Displ. [mm]

∆ F [kN] ∆ Ftot ∆ Fext ∆ Fint A B

Shearing of the interface Outer friction Gap opening Inner friction Failure

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 13 / 16

slide-30
SLIDE 30

Application

Partially drained simulation (hydraulic behaviour)

ΔFtot ΔFuw

0.5 1 1.5 2 2.5 3 100 200 300 400 500 600 700 800 900

Displ.B[mm] ∆ FB[kN] ∆ Ftot ∆ Fext ∆ Fint ∆ Fuw C B A

Suction effect Higher ∆Ftot Opening of a gap Transversal flow Transversal storage Stationary phase Opening of a gap Coupling gap- permeability

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 14 / 16

slide-31
SLIDE 31

Application

Partially drained simulation (hydraulic behaviour)

ΔFtot ΔFuw

0.00

  • 0.84
  • 1.69
  • 2.54
  • 3.39
  • 4.24
  • 5.09
  • 5.94
  • 6.79
  • 7.64
  • 8.49
  • 9.34

Δpw [kPa]

E1 E2 E3

Suction effect ∆Ftot Coupling pN = p′

N + pw

Transient ∆pw Opening of a gap Transversal flow Transversal storage Stationary phase Opening of a gap Coupling gap- permeability

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 14 / 16

slide-32
SLIDE 32

Application

Partially drained simulation (hydraulic behaviour)

ΔFtot ΔFuw ΔyS ΔyC

1 2 3 0.05 0.1 0.15 0.2

  • Displ. [mm]

ft [kg/s]

1 2 3 0.2 0.4 0.6 0.8 1 1.2 1.4

  • Displ. [mm]

∆ ytop [mm] Soil Caisson A B C A B C

vp = 1 mm/min Top unsticking and storage ∆Ftot Coupling pN = p′

N + pw

Transient ∆uw Opening of a gap Transversal flow Transversal storage Stationary phase Opening of a gap Coupling gap- permeability

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 14 / 16

slide-33
SLIDE 33

Application

Partially drained simulation (hydraulic behaviour)

Flow

−8 −6 −4 −2 0.5 1 1.5 2 2.5 3 3.5 4

Depth [m] fl [kg.s−1.m−2]

−0.05 0.05 0.1 0.5 1 1.5 2 2.5 3 3.5 4

gN [mm]

Longitudinal flow fl along the skirt ∆Ftot Coupling pN = p′

N + pw

Transient ∆uw Opening of a gap Transversal flow Transversal storage Stationary phase Opening of a gap Coupling gap- permeability

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 14 / 16

slide-34
SLIDE 34

Conclusions

Table of contents

1

Context

2

Modelling interfaces

3

Application

4

Conclusions

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 15 / 16

slide-35
SLIDE 35

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)

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 16 / 16

slide-36
SLIDE 36

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.

  • B. Cerfontaine

Groupe de contact FNRS 15/09/14 16 / 16