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

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 Modelling interfaces 2 Application 3 Conclusions 4 B. Cerfontaine Groupe de contact FNRS 15/09/14 1 / 16

Context Table of contents Context 1 Modelling interfaces 2 Application 3 Conclusions 4 B. Cerfontaine Groupe de contact FNRS 15/09/14 2 / 16

Context Suction caisson Outer pressure Sea level Pumping Reduced soil effective Inner pressure stress Sand heave Seabed Seepage flow Sand Foundation for offshore Installed by suction structures Increased transient resistance to Hollow cylinder open towards pull and push loads the bottom Crucial role of interfaces Made of steel B. Cerfontaine Groupe de contact FNRS 15/09/14 3 / 16

Context Interface in geomechanics Surface between two media (=discontinuity) Interface Contact Caisson Shearing Sliding Interface Unsticking Soil Flow B. Cerfontaine Groupe de contact FNRS 15/09/14 4 / 16

Context Interface in geomechanics Surface between two media (=discontinuity) Interface Contact Push load Shearing Contact pressure Sliding Unsticking Soil Flow B. Cerfontaine Groupe de contact FNRS 15/09/14 4 / 16

Context Interface in geomechanics Surface between two media (=discontinuity) Interface Contact Pull load Shearing Sliding Shear stresses Unsticking Soil Flow B. Cerfontaine Groupe de contact FNRS 15/09/14 4 / 16

Context Interface in geomechanics Surface between two media (=discontinuity) Interface Pull load Contact Shearing Sliding Sliding Unsticking Soil Flow B. Cerfontaine Groupe de contact FNRS 15/09/14 4 / 16

Context Interface in geomechanics Surface between two media (=discontinuity) Interface Pull load Contact Unsticking Shearing Sliding Sliding Unsticking Soil Flow B. Cerfontaine Groupe de contact FNRS 15/09/14 4 / 16

Context Interface in geomechanics Surface between two media (=discontinuity) Interface Pull load Contact Unsticking Shearing Fluid flow Sliding Sliding Unsticking Soil Flow B. Cerfontaine Groupe de contact FNRS 15/09/14 4 / 16

Modelling interfaces Table of contents Context 1 Modelling interfaces 2 Mechanical problem Hydraulic problem Coupled problem Application 3 Conclusions 4 B. Cerfontaine Groupe de contact FNRS 15/09/14 5 / 16

Modelling interfaces Mechanical problem Normal behaviour p N ≥ 0 g N ≥ 0 p N g N = 0 Contact Approaches Regularisation g N e 1 1 e 2 1 p N = f ( g N ) E 2 p N E 1 Discretisation No contact Contact B. Cerfontaine Groupe de contact FNRS 15/09/14 6 / 16

Modelling interfaces Mechanical problem Normal behaviour p N ≥ 0 g N ≥ 0 p N g N = 0 Contact Thin layer Medium 1 Approaches Thin layer Medium 3 elements Medium 2 Regularisation Zero-thickness p N = f ( g N ) Medium 1 Boundary elements Medium 2 Discretisation No contact Contact B. Cerfontaine Groupe de contact FNRS 15/09/14 6 / 16

Modelling interfaces Mechanical problem Normal behaviour p N ≥ 0 g N ≥ 0 p N g N = 0 Contact Lagrange multiplier method Approaches Pressure distribution Regularisation No penetration Penalty method p N = f ( g N ) Zoom Penetration Discretisation B. Cerfontaine Groupe de contact FNRS 15/09/14 6 / 16

Modelling interfaces Mechanical problem Normal behaviour p N ≥ 0 g N ≥ 0 p N g N = 0 Contact Intricate asperities Approaches First contact point p N Regularisation p N = f ( g N ) Compression g N Discretisation Asperities deformation p N g N B. Cerfontaine Groupe de contact FNRS 15/09/14 6 / 16

Modelling interfaces Mechanical problem Normal behaviour p N ≥ 0 g N ≥ 0 p N g N = 0 Contact Node to node Node to segment Approaches Gap Gap Regularisation Segment to segment Contact domain Penetration p N = f ( g N ) Gap interpolation Gap Discretisation B. Cerfontaine Groupe de contact FNRS 15/09/14 6 / 16

Modelling interfaces Mechanical problem Tangential behaviour Shearing τ ≥ 0 g T ≥ 0 ˙ τ ˙ g T = 0 Criterion g T τ = τ max τ E 2 E 1 Sticking Sliding B. Cerfontaine Groupe de contact FNRS 15/09/14 7 / 16

Modelling interfaces Mechanical problem Tangential behaviour Shearing τ ≥ 0 g T ≥ 0 ˙ τ ˙ g T = 0 0 || τ || > Criterion f f=0 Sliding state f<0 No contact Sticking µ state p N f = � τ � − µ p N B. Cerfontaine Groupe de contact FNRS 15/09/14 7 / 16

Modelling interfaces Hydraulic problem Fluid flows Longitudinal and transversal flows Interface q Discontinuity Discretisation Fluid flow Fluid flow Fluid flow Fluid flow E 2 p w E 1 Diconstinuity = porous medium B. Cerfontaine Groupe de contact FNRS 15/09/14 8 / 16

Modelling interfaces Hydraulic problem Fluid flows Longitudinal and transversal flows Interface Single node g N Finite element mesh Discretisation Porous medium Discontinuity Double node Triple node g N g N B. Cerfontaine Groupe de contact FNRS 15/09/14 8 / 16

Modelling interfaces Coupled problem Couplings Hydro-mechanical couplings Effective pressure Terzaghi’s principle Permeability p N = p ′ N + p w p ′ N , effective pressure (mechanical Storage behaviour) p w , fluid pressure inside the interface B. Cerfontaine Groupe de contact FNRS 15/09/14 9 / 16

Modelling interfaces Coupled problem Couplings Hydro-mechanical couplings Effective pressure Cubic law Permeability ( D 0 ) 2  g N ≤ 0   12 Storage k l = ( D 0 + g N ) 2  otherwise .  12 k l , longitudinal permeability D 0 , residual hydraulic opening B. Cerfontaine Groupe de contact FNRS 15/09/14 9 / 16

Modelling interfaces Coupled problem Couplings Hydro-mechanical couplings Effective pressure Stored water within discontinuity Permeability � � ˙ L ˙ M f = ρ w g N + ρ w ˙ ˙ g N + ρ w g N L Storage L L , length of the discontinuity ρ w , density of water B. Cerfontaine Groupe de contact FNRS 15/09/14 9 / 16

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

Application Table of contents Context 1 Modelling interfaces 2 Application 3 Conclusions 4 B. Cerfontaine Groupe de contact FNRS 15/09/14 11 / 16

Application Statement of the problem Inner interface (lid) D r a i n e d B o u n d a r y C a i s s o n Undrained Inner Outer Boundary Undrained interface interface Boundary (skirt) (skirt) Elastic soil and caisson Friction coefficient 0.57 Diameter 7.8m Residual hydraulic aperture Water depth 10m 1.E-5m Soil permeability 1.E-11m 2 Penalty coefficient 1.E10 N/m 3 K 0 = 1 Conductivity 1.E-8m/Pa/s B. Cerfontaine Groupe de contact FNRS 15/09/14 12 / 16

Application Drained simulation (mechanical behaviour) Δ F tot Shearing of the interface 900 Δ y >0 800 Δ F int Δ F ext 700 ∆ F tot 600 ∆ F ext ∆ F [kN] 500 ∆ F int A 400 B 300 200 100 0 0 0.5 1 1.5 2 2.5 3 Displ. [mm] B. Cerfontaine Groupe de contact FNRS 15/09/14 13 / 16

Application Drained simulation (mechanical behaviour) 0 Shearing of the interface Gapgopening 0.5 1 Displg[mm] Depthg[m] 1.5 900 0.02 2 0.43 800 0.63 2.5 1.17 3 700 ∆ F tot 3.5 4 600 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 ∆ F ext η ext =|| τ ||/p’ N [ − ] ∆ F [kN] 500 ∆ F int A 400 B 300 200 Outer friction 100 Gap opening 0 0 0.5 1 1.5 2 2.5 3 Displ. [mm] B. Cerfontaine Groupe de contact FNRS 15/09/14 13 / 16

Application Drained simulation (mechanical behaviour) 0 Shearing of the interface 0.5 1 Displ [mm] Depth [m] 1.5 900 0.02 0.43 2 0.63 800 2.5 1.17 3 700 ∆ F tot 3.5 4 600 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 ∆ F ext η int =|| τ ||/p’ N [ − ] ∆ F [kN] 500 ∆ F int A 400 B 300 200 Outer friction 100 Gap opening 0 Inner friction 0 0.5 1 1.5 2 2.5 3 Displ. [mm] Failure B. Cerfontaine Groupe de contact FNRS 15/09/14 13 / 16

Application Partially drained simulation (hydraulic behaviour) Δ F tot Suction effect 900 ∆ F tot 800 Δ F uw ∆ F ext 700 ∆ F int 600 ∆ FB[kN] ∆ F uw 500 A 400 300 B 200 C 100 Opening of a gap Higher ∆ F tot Opening of a gap 0 Transversal flow 0 0.5 1 1.5 2 2.5 3 Coupling gap- Displ.B[mm] Transversal storage permeability Stationary phase B. Cerfontaine Groupe de contact FNRS 15/09/14 14 / 16

Application Partially drained simulation (hydraulic behaviour) Δ F tot Suction effect Δ F uw Δ p w [kPa] 0.00 -0.84 -1.69 -2.54 -3.39 -4.24 -5.09 Opening of a gap ∆ F tot -5.94 Opening of a gap -6.79 Transversal flow -7.64 Coupling -8.49 Coupling gap- E 3 -9.34 p N = p ′ N + p w Transversal storage permeability E 2 E 1 Stationary phase Transient ∆ p w B. Cerfontaine Groupe de contact FNRS 15/09/14 14 / 16