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

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Three-node zero-thickness hydro-mechanical interface

finite element for geotechnical applications

Benjamin Cerfontaine

University of Liege

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Outline

1 Context

2 Modelling interfaces

3 Application

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Context Table of contents 1 Context 2 Modelling interfaces 3 Application 4 Conclusions

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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

Installed by suction

Increased transient resistance to pull and push loads

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Context Interface in geomechanics

Interface Surface between two media (=discontinuity)

Contact Shearing Sliding Unsticking Flow Soil Caisson Interface

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Contact Shearing Sliding Unsticking Flow Push load Contact pressure Soil

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Contact Shearing Sliding Unsticking Flow Pull load Shear stresses Soil

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Contact Shearing Sliding Unsticking Flow Pull load Soil Sliding

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Contact Shearing Sliding Unsticking Flow Pull load Soil Unsticking Sliding

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Contact Shearing Sliding Unsticking Flow Pull load Fluid flow Soil Sliding Unsticking

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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 pNgN = 0 Approaches Regularisation pN = f (gN) Discretisation E1 E2 1 e1 1 e2 gN pN No contact Contact

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Modelling interfaces Mechanical problem Normal behaviour Contact pN ≥ 0 gN ≥ 0 pNgN = 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

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Modelling interfaces Mechanical problem Normal behaviour Contact pN ≥ 0 gN ≥ 0 pNgN = 0 Approaches Regularisation pN = f (gN) Discretisation

Lagrange multiplier method

Penalty method Penetration Pressure distribution No penetration Zoom

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Modelling interfaces Mechanical problem Normal behaviour Contact pN ≥ 0 gN ≥ 0 pNgN = 0 Approaches Regularisation pN = f (gN) Discretisation pN First contact point Asperities deformation Intricate asperities pN gN gN Compression

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Modelling interfaces Mechanical problem Normal behaviour Contact pN ≥ 0 gN ≥ 0 pNgN = 0 Approaches Regularisation pN = f (gN) Discretisation

Node to node Node to segment

Segment to segment Penetration Gap Gap Gap Contact domain Gap interpolation

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Modelling interfaces Mechanical problem Tangential behaviour Shearing τ ≥ 0 ˙gT ≥ 0 τ ˙gT = 0 Criterion E1 E2 τ=τmax Sticking Sliding τ gT

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Modelling interfaces Mechanical problem Tangential behaviour Shearing τ ≥ 0 ˙gT ≥ 0 τ ˙gT = 0 Criterion

||τ||

p

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

µ

N f = kτ k − µ pN

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Modelling interfaces Hydraulic problem Fluid flows

Interface Longitudinal and transversal flows

Discretisation

q

pw

Discontinuity

Fluid flow Fluid flow

E1 E2

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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

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Modelling interfaces Coupled problem Couplings Hydro-mechanical couplings Effective pressure Permeability Storage Terzaghi’s principle pN = p0N+ pw

p0_N, effective pressure (mechanical behaviour)

pw, fluid pressure inside the

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Modelling interfaces Coupled problem Couplings Hydro-mechanical couplings Effective pressure Permeability Storage Cubic law kl =      (D0)2 12 gN ≤ 0 (D0+ gN)2 12 otherwise. kl, longitudinal permeability

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Modelling interfaces Coupled problem Couplings Hydro-mechanical couplings Effective pressure Permeability Storage

Stored water within discontinuity

˙ Mf = ρ˙wgN+ ρw ˙gN+ ρwgN ˙ L 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

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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

Undra ined Bound

ary _Undrained

Bound ary Drained Boundary Caisson Inner interface (lid) Outer interface (skirt) Inner interface (skirt)

Elastic soil and caisson Diameter 7.8m

Water depth 10m

Soil permeability 1.E-11m2

Friction coefficient 0.57 Residual hydraulic aperture 1.E-5m

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Application

Drained simulation (mechanical behaviour)

ΔFtot ΔFint ΔFext Δy>0 0 0.5 1 1.5 2 2.5 3 0 100 200 300 400 500 600 700 800 900 Displ. [mm] ∆ F [kN] ∆ F tot ∆ F ext ∆ F int A B

Shearing of the interface

Outer friction Gap opening Inner friction Failure

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Application

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.5 1 1.5 2 2.5 3 3.5 4 η_ext=||τ||/p’_N[−] Depthg[m] 0.02 0.43 0.63 1.17 Displg[mm] Gapgopening 0 0.5 1 1.5 2 2.5 3 0 100 200 300 400 500 600 700 800 900 Displ. [mm] ∆ F [kN] ∆ F tot ∆ F ext ∆ F int A B

Outer friction Gap opening

Inner friction Failure

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Application

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.5 1 1.5 2 2.5 3 3.5 4 η_int=||τ||/p’_N[−] Depth [m] 0.02 0.43 0.63 1.17 Displ [mm] 0 0.5 1 1.5 2 2.5 3 0 100 200 300 400 500 600 700 800 900 Displ. [mm] ∆ F [kN] ∆ F tot ∆ F ext ∆ F int A B

Outer friction Gap opening

Inner friction Failure

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Application

Partially drained simulation (hydraulic behaviour)

ΔFtot ΔFuw 0 0.5 1 1.5 2 2.5 3 0 100 200 300 400 500 600 700 800 900 Displ.B[mm] ∆ FB[kN] ∆ F_tot ∆ F_ext ∆ F int ∆ F_uw C B A Suction effect Higher ∆Ftot Coupling pN = p0N+ pw Transient ∆uw Opening of a gap Transversal flow Transversal storage Stationary phase Opening of a gap Coupling gap-permeability

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Application

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 = p0N+ pw Transient ∆pw Opening of a gap Transversal flow Transversal storage Stationary phase Opening of a gap Coupling gap-permeability

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Application

ΔFtot ΔFuw ΔyS ΔyC 0 1 2 3 0 0.05 0.1 0.15 0.2 Displ. [mm] f t [kg/s] 0 1 2 3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Displ. [mm] ∆ y top [mm] Soil Caisson A B C A B C v = 1 mm/min

Top unsticking and storage

∆Ftot Coupling pN = p0N+ pw Transient ∆u Opening of a gap Transversal flow Transversal storage Stationary phase Opening of a gap Coupling gap-permeability

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Application

Flow −8 −6 −4 −2 0 0 0.5 1 1.5 2 2.5 3 3.5 4 Depth [m] f l[kg.s −1_.m−2_] −0.05 0 0.05 0.1 0 0.5 1 1.5 2 2.5 3 3.5 4 g N[mm]

Longitudinal flow fl along the skirt

∆Ftot Coupling pN = p0N+ pw Transient ∆uw Opening of a gap Transversal flow Transversal storage Stationary phase Opening of a gap Coupling gap-permeability

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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.