Master’s dissertation

Master’s dissertation
“Formulation of a macro-element for suction caisson foundations under axial tensile load” Student: Supervisors: 8th of December, 2017 Gilles CORMAN Prof. A. BEZUIJEN UGent Prof. F. COLLIN University of Liège B. CERFONTAINE Student: Gilles CORMAN

Context Need for renewable energy Onshore vs Offshore
CORMAN Gilles Master Thesis December 2017 Need for renewable energy Introduction Context Suction caissons Description of the FE model Drained simulations Partly drained simulations Conclusion Onshore vs Offshore REN 21, 2015 Variants for OWT foundations ⟹ Suction Caissons Schaumann P et al, 2011 EWEA, 2017

Suction caissons Foundation system for OWT’s
CORMAN Gilles Master Thesis December 2017 Introduction Context Suction caissons Description of the FE model Drained simulations Partly drained simulations Conclusion Houlsby et al. 2005 Foundation system for OWT’s Hollow steel cylinder open towards the bottom Monopod or tetra/tri-pod superstructure Two-step installation by pressure differential Cheaply, silently and quickly installed, reusable

Problem statement One single caisson Part of a tripod
CORMAN Gilles Master Thesis December 2017 Introduction Description of the FE model Problem statement Geometry Interface elements Initial loading state Case studies Drained simulations Partly drained simulations Conclusion Houlsby et al. 2005 One single caisson Part of a tripod Uniaxial tensile load Use of rheological elements Approximation of the stiffness 2D axisymmetric Displacement imposed

Geometry Size Diameter 𝐷 8m 𝐿 𝐷 =1 Skirt length 𝐿 Thickness 𝑡 0.1m
CORMAN Gilles Master Thesis December 2017 Size Diameter 𝐷 8m 𝐿 𝐷 =1 Skirt length 𝐿 Thickness 𝑡 0.1m 𝑡 𝐷 =1.2% Water depth 20m Linear elastic soil and caisson Lateral earth pressure coefficient at rest 𝐾 0 1 Porosity 𝑛 0.5 Boundary conditions Mechanical Hydraulic Permeable Impermeable Introduction Description of the FE model Problem statement Geometry Interface elements Initial loading state Case studies Drained simulations Partly drained simulations Conclusion

Hydro-mechanical couplings
Interface elements Mechanical behaviour Coulomb dry friction law Flow behaviour CORMAN Gilles Master Thesis December 2017 Introduction Description of the FE model Problem statement Geometry Interface elements Initial loading state Case studies Drained simulations Partly drained simulations Conclusion Friction coefficient 𝜇 0.5 [-] Penalty coefficients 𝐾 𝑁 4× 10 9 𝑁/ 𝑚 3 𝐾 𝑇 4× 10 8 Permeability 𝑘 1× 10 −7 𝑚/𝑠 Transmissivity 𝑇 𝑤 1× 10 −3 𝑚/(𝑃𝑎.𝑠) Hydro-mechanical couplings

Initial loading state Identification of components of reaction 1.
CORMAN Gilles Master Thesis December 2017 Identification of components of reaction 1. Downward 2. Water weight 𝑊 𝑤 3a. & 3b. Friction 𝜙 𝑖𝑛 𝜙 𝑜𝑢𝑡 4. Pore water pressure Δ 𝑃 𝑝𝑤𝑝 5. Weight of the soil plug Δ 𝑊 𝑝𝑙𝑢𝑔 6a. & 6b. Buoyancy force 𝑃 𝑤,𝑙𝑖𝑑 𝑃 𝑤,𝑡𝑖𝑝 Upward 7a. & 7b. Soil pressure Σ 𝑙𝑖𝑑 ′ Σ 𝑡𝑖𝑝 ′ 8. Total reaction 𝑅 Caisson weight 𝑊 𝑐𝑎𝑖𝑠 Introduction Description of the FE model Problem statement Geometry Interface elements Initial loading state Case studies Drained simulations Partly drained simulations Conclusion State of equilibrium 𝑊 𝑐𝑎𝑖𝑠 + 𝑊 w + Φ in =0 + Φ out =0 + Δ 𝑃 𝑝𝑤𝑝 =0 + Δ 𝑊 𝑝𝑙𝑢𝑔 =0 = Ρ 𝑤,𝑙𝑖𝑑 + Σ 𝑙𝑖𝑑 ′ ≈0 + Ρ 𝑤,𝑡𝑖𝑝 + Σ 𝑡𝑖𝑝 ′ +𝑅

Case studies Simulations Scenario Sub-case Drainage condition
CORMAN Gilles Master Thesis December 2017 Simulations Scenario Sub-case Drainage condition Soil condition 1 1-1𝑏𝑖𝑠 Drained Rigid body motion 2-2𝑏𝑖𝑠 Free to move 2 3 Partly drained 4 Introduction Description of the FE model Problem statement Geometry Interface elements Initial loading state Case studies Drained simulations Partly drained simulations Conclusion Reference parameters Elastic modulus 𝑬 𝒄 =𝟏×𝟏 𝟎 𝟕 [𝑴𝑷𝒂] Poisson’s ratio 𝜈 𝑐 =0.3 [−] Tangential penalty coeff. 𝐾 𝜏 =4× 10 8 [𝑁/ 𝑚 3 ] Permeability 𝑘= 10 −7 [𝑚/𝑠] Loading rate 𝐿𝑅= 10 −6

Reaction modes Soil free to move Rigid body motion Δ 𝑅 𝑡𝑜𝑡 Δ Φ 𝑖𝑛
CORMAN Gilles Master Thesis December 2017 Δ 𝑅 𝑡𝑜𝑡 Introduction Description of the FE model Drained simulations Reaction modes Numerical-Analytical Macro-element Partly drained simulations Conclusion Δ Φ 𝑖𝑛 Δ Φ 𝑜𝑢𝑡 Δ 𝑅 𝑡𝑜𝑡 ≈Δ Φ 𝑖𝑛 +Δ Φ 𝑜𝑢𝑡 [1b] [2b] [1a] [2a]

Reaction modes (2) Rigid body motion Soil free to move Introduction
CORMAN Gilles Master Thesis December 2017 Introduction Description of the FE model Drained simulations Reaction modes Numerical-Analytical Macro-element Partly drained simulations Conclusion

Numerical vs Analytical
Rigid body motion CORMAN Gilles Master Thesis December 2017 Integration of the shear distribution 𝜏 Δ𝑦 = 0 𝑧 0 𝜏 𝑚𝑎𝑥 𝑑𝑧 𝑡𝑟𝑖𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑝𝑟𝑜𝑓𝑖𝑙𝑒 + 𝑧 0 𝑧 𝑚𝑎𝑥 𝜏 𝑚𝑜𝑏𝑖𝑙𝑖𝑠𝑒𝑑 𝑑𝑧 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑝𝑟𝑜𝑓𝑖𝑙𝑒 Introduction Description of the FE model Drained simulations Reaction modes Numerical-Analytical Macro-element Partly drained simulations Conclusion Friction components [1a & 2a] ΔΦ=2𝜋𝑅×𝜏 Δ𝑦 =2𝜋𝑅 𝐾 𝜏 Δ𝑦𝐿− 𝐾 𝜏 2 Δ 𝑦 2 𝜇 𝐾 0 Δ 𝜎 𝑣,0 ′ ΔΦ 𝑚𝑎𝑥 =2𝜋𝑅𝐿 𝐾 0 𝛾 𝑐𝑙𝑎𝑦 ′ 𝐿 2 𝜇

Numerical vs Analytical (2)
Soil free to move CORMAN Gilles Master Thesis December 2017 Expression for 𝐾 𝜏 given in the literature 𝐾 𝜏 = 1 𝑅 𝐺 ln 𝑟 𝑚 𝑅 where 𝑟 𝑚 =2.5𝐿 1− 𝜈 𝑐 𝑟 𝑚 =2.5𝐿 𝜍 𝑖𝑛,𝑑 1− 𝜈 𝑐 𝑟 𝑚 =2.5𝐿 𝜍 𝑜𝑢𝑡,𝑑 1− 𝜈 𝑐 Introduction Description of the FE model Drained simulations Reaction modes Numerical-Analytical Macro-element Partly drained simulations Conclusion Randolph & Wroth, 1978 Friction components [1b & 2b] Δ Φ 𝑜𝑢𝑡 =2𝜋 𝑅 𝑜 𝐾 𝜏 Δ𝑦𝐿− 𝐾 𝜏 2 Δ 𝑦 2 𝜇 𝐾 0 Δ 𝜎 𝑣,0 ′ Δ Φ 𝑜𝑢𝑡 =2𝜋 𝑅 𝑜 𝜉 𝑜𝑢𝑡,𝑑 𝐾 𝜏 Δ𝑦𝐿− 𝐾 𝜏 2 Δ 𝑦 2 𝜇 𝐾 0 Δ 𝜎 𝑣,0 ′ Δ Φ 𝑖𝑛 =2𝜋 𝑅 𝑖 𝐾 𝜏 Δ𝑦𝐿− 𝐾 𝜏 2 Δ 𝑦 2 𝜇 𝐾 0 Δ 𝜎 𝑣,0 ′ ΔΦ 𝑚𝑎𝑥 = 𝜉 𝑚𝑎𝑥,𝑑 ×2𝜋𝑅𝐿 𝐾 0 𝛾 𝑐𝑙𝑎𝑦 ′ 𝐿 2 𝜇

Macro-Element CORMAN Gilles Master Thesis December 2017 Δ𝑅 𝑡𝑜𝑡 =Δ Φ 𝑜𝑢𝑡 +Δ Φ 𝑖𝑛 = 𝜅 𝑜𝑢𝑡 Δ𝑦+ 𝜅 𝑖𝑛 Δ𝑦 𝑠𝑝𝑟𝑖𝑛𝑔𝑠 − 𝜍 𝑜𝑢𝑡 − 𝜍 in 𝑠𝑙𝑖𝑑𝑒𝑟𝑠 Introduction Description of the FE model Drained simulations Reaction modes Numerical-Analytical Macro-element Partly drained simulations Conclusion ΔΦ=2𝜋𝑅 𝐾 𝜏 𝐿− 𝐾 𝜏 2 Δ𝑦 𝜇 𝐾 0 Δ 𝜎 𝑣,0 ′ ×Δ𝑦 =𝜅 Δ𝑦 ×Δ𝑦 ΔΦ 𝑚𝑎𝑥 =𝜍=2𝜋𝑅𝐿 𝐾 0 𝛾 𝑐𝑙𝑎𝑦 ′ 𝐿 2 𝜇 Rigid body motion [1a & 2a] Δ Φ out =2𝜋 𝑅 𝑜 𝜉 𝑜𝑢𝑡,𝑑 𝐾 𝜏 𝐿− 𝐾 𝜏 2 Δ𝑦 𝜇 𝐾 0 Δ 𝜎 𝑣,0 ′ ×Δ𝑦 = 𝜅 𝑜𝑢𝑡 Δ𝑦 ×Δ𝑦 ΔΦ 𝑚𝑎𝑥 = 𝜍= 𝜉 𝑚𝑎𝑥,𝑑 × ΔΦ 𝑚𝑎𝑥 (𝑟𝑖𝑔𝑖𝑑 𝑏𝑜𝑑𝑦) Soil free to move [1b & 2b] → 𝜍 𝑜𝑢𝑡,𝑑 Δ Φ in =2𝜋 𝑅 𝑖 𝐾 𝜏 𝐿− 𝐾 𝜏 2 Δ𝑦 𝜇 𝐾 0 Δ 𝜎 𝑣,0 ′ ×Δ𝑦 = 𝜅 𝑖𝑛 Δ𝑦 ×Δ𝑦 → 𝜍 𝑖𝑛,𝑑

Reaction modes Rigid body motion Soil free to move Δ 𝑅 𝑡𝑜𝑡 Δ 𝑃 𝑝𝑤𝑝
CORMAN Gilles Master Thesis December 2017 Δ 𝑅 𝑡𝑜𝑡 Introduction Description of the FE model Drained simulations Partly drained simulations Reaction modes Numerical-Analytical Macro-element Conclusion Δ 𝑃 𝑝𝑤𝑝 Δ 𝑊 𝑝𝑙𝑢𝑔 Δ Φ 𝑖𝑛 Δ Φ 𝑜𝑢𝑡 Δ 𝑅 𝑡𝑜𝑡 ≈Δ Φ 𝑖𝑛 +Δ Φ 𝑜𝑢𝑡 +Δ 𝑃 𝑝𝑤𝑝 +Δ 𝑊 𝑝𝑙𝑢𝑔 Δ 𝑅 𝑡𝑜𝑡 ≈Δ Φ 𝑖𝑛 +Δ Φ 𝑜𝑢𝑡 +Δ 𝑃 𝑝𝑤𝑝 [1b] [2b] [3b] [4b] [1a] [2a] [3a]

Reaction modes (2) Rigid body motion Soil free to move Introduction
CORMAN Gilles Master Thesis December 2017 Introduction Description of the FE model Drained simulations Partly drained simulations Reaction modes Numerical-Analytical Macro-element Conclusion

Reaction modes (3) Rigid body motion Soil free to move
CORMAN Gilles Master Thesis December 2017 Introduction Description of the FE model Drained simulations Partly drained simulations Reaction modes Numerical-Analytical Macro-element Conclusion 𝑘= 10 −5 𝑚 𝑠 & 𝐿𝑅= 10 −6 𝑚 𝑠 𝑘= 10 −7 𝑚 𝑠 & 𝐿𝑅= 10 −6 𝑚 𝑠

Numerical vs Analytical
Rigid body motion CORMAN Gilles Master Thesis December 2017 PWP component [3a] Friction components [1a & 2a] 𝑣= Δy Δ𝑡 =𝑘×𝑖 ΔΦ=2𝜋𝑅 𝐾 𝜏 Δ𝑦𝐿− 𝐾 𝜏 2 Δ 𝑦 2 𝜇 𝐾 0 Δ 𝜎 𝑣,0 ′ ΔΦ 𝑚𝑎𝑥 =2𝜋𝑅𝐿 𝐾 0 𝛾 𝑐𝑙𝑎𝑦 ′ 𝐿 2 𝜇 Darcy’s law Hydraulic gradient Seepage length Δ 𝑃 𝑝𝑤𝑝 = 𝐴 𝑏𝑎𝑠𝑒,𝑖 × 𝐿 𝑠 𝛾 𝑤 𝑘 Δ𝑦 Δ𝑡 Introduction Description of the FE model Drained simulations Partly drained simulations Reaction modes Numerical-Analytical Macro-element Conclusion 𝑖= 𝑠 𝐿 𝑠 𝛾 𝑤 Similar to the drained simulation 𝐿 𝑠 = 𝐿 𝐷 −0.9 → 𝐿 𝑠 = 𝐿 𝐷 − 𝜉 𝑝𝑤𝑝,𝑢,𝐼 Δ𝑦 𝑑 0.5 Senders M. & Randolph M.F, 2009

Soil free to move CORMAN Gilles Master Thesis December 2017 Outer friction component [1b] Δ Φ 𝑜𝑢𝑡 =2𝜋 𝑅 𝑜 𝜉 𝑜𝑢𝑡,𝑢 𝐾 𝜏 Δ𝑦𝐿− 𝐾 𝜏 2 Δ 𝑦 2 𝜇 𝐾 0 Δ 𝜎 𝑣,0 ′ Δ Φ 𝑜𝑢𝑡 =2𝜋 𝑅 𝑜 𝐾 𝜏 Δ𝑦𝐿− 𝐾 𝜏 2 Δ 𝑦 2 𝜇 𝐾 0 Δ 𝜎 𝑣,0 ′ Introduction Description of the FE model Drained simulations Partly drained simulations Reaction modes Numerical-Analytical Macro-element Conclusion Expression for 𝐾 𝜏 similar to the drained simulation 𝐾 𝜏 = 1 𝑅 𝐺 ln 𝑟 𝑚 𝑅 where 𝑟 𝑚 =2.5𝐿 1− 𝜈 𝑐 𝐾 𝜏 = 1 𝑅 𝐺 ln 𝑟 𝑚 𝑅 where 𝑟 𝑚 =2.5𝐿 𝜍 𝑜𝑢𝑡,𝑢 1− 𝜈 𝑐

Soil free to move CORMAN Gilles Master Thesis December 2017 Inner friction component [2b] Expression for 𝐾 𝜏 similar to the drained simulation Δ Φ 𝑖𝑛 =2𝜋 𝑅 𝑖 𝐾 𝜏 Δ𝑦𝐿− 𝐾 𝜏 2 Δ 𝑦 2 𝜇 𝐾 0 Δ 𝜎 𝑣,0 ′ Δ Φ 𝑖𝑛 =2𝜋 𝑅 𝑖 𝜉 𝑖𝑛,𝑢 𝐾 𝜏 Δ𝑦𝐿− 𝐾 𝜏 2 Δ 𝑦 2 𝜇 𝐾 0 Δ 𝜎 𝑣,0 ′ 1− 𝑠 𝑠 𝑐𝑟𝑖𝑡 𝐾 𝜏 = 1 𝑅 𝐺 ln 𝑟 𝑚 𝑅 where 𝑟 𝑚 =2.5𝐿 1− 𝜈 𝑐 Introduction Description of the FE model Drained simulations Partly drained simulations Reaction modes Numerical-Analytical Macro-element Conclusion Senders M, 2008 Linear reduction due to plug uplift

Soil free to move CORMAN Gilles Master Thesis December 2017 PWP component [3b] 𝑣= Δy Δ𝑡 =𝑘×𝑖 Darcy’s law Hydraulic gradient Seepage length Δ 𝑃 𝑝𝑤𝑝 = 𝐴 𝑏𝑎𝑠𝑒,𝑖 × 𝐿 𝑠 𝛾 𝑤 𝑘 Δ𝑦 Δ𝑡 Introduction Description of the FE model Drained simulations Partly drained simulations Reaction modes Numerical-Analytical Macro-element Conclusion 𝑖= 𝑠 𝐿 𝑠 𝛾 𝑤 𝐿 𝑠 = 𝐿 𝐷 −0.9 → 𝐿 𝑠 = 𝐿 𝐷 − 𝜉 𝑝𝑤𝑝,𝑢,𝐼𝐼 Δ𝑦 𝑑 Senders M. & Randolph M.F, 2009

Soil free to move CORMAN Gilles Master Thesis December 2017 Plug uplift component [4b] Iterative process Romp R.H, 2013 Principle of the mechanical work : Generated work during Δ𝑡 : Δ𝑊 𝑡 =𝑠 𝑡 𝐴 𝑏𝑎𝑠𝑒,𝑖 ×Δ 𝐿 𝑝𝑙𝑢𝑔 Δ 𝐿 𝑝𝑙𝑢𝑔 → Δ 𝑊 𝑝𝑙𝑢𝑔 = 𝐴 𝑏𝑎𝑠𝑒,𝑖 𝛾 𝑐𝑙𝑎𝑦 ′ 𝐿 𝑝𝑙𝑢𝑔 Δ 𝑊 𝑝𝑙𝑢𝑔 = 𝜉 𝑝𝑙𝑢𝑔,𝑢 ×( 𝐴 𝑏𝑎𝑠𝑒,𝑖 𝛾 𝑐𝑙𝑎𝑦 ′ 𝐿 𝑝𝑙𝑢𝑔 ) Introduction Description of the FE model Drained simulations Partly drained simulations Reaction modes Numerical-Analytical Macro-element Conclusion Δ𝑊 𝑡 =Δ𝑠 𝑡 −1 ×Δ 𝑉 𝑝𝑙𝑢𝑔 𝑡 −1

Macro-element Rigid body motion
CORMAN Gilles Master Thesis December 2017 𝑅 𝑡𝑜𝑡 =Δ Φ 𝑜𝑢𝑡 +Δ Φ 𝑖𝑛 +Δ 𝑃 𝑝𝑤𝑝 = 𝜅 𝑜𝑢𝑡 Δ𝑦+ 𝜅 𝑖𝑛 Δ𝑦 𝑠𝑝𝑟𝑖𝑛𝑔𝑠 − 𝜍 𝑜𝑢𝑡 − 𝜍 𝑖𝑛 𝑠𝑙𝑖𝑑𝑒𝑟𝑠 + 𝜂Δ 𝑦 1 𝑁 𝑑𝑎𝑠ℎ𝑝𝑜𝑡 Introduction Description of the FE model Drained simulations Partly drained simulations Reaction modes Numerical-Analytical Macro-element Conclusion ΔΦ=2𝜋𝑅 𝐾 𝜏 𝐿− 𝐾 𝜏 2 Δ𝑦 𝜇 𝐾 0 Δ 𝜎 𝑣,0 ′ ×Δ𝑦=𝜅 Δ𝑦 ×Δ𝑦 Friction component [1a & 2a] Δ Φ 𝑚𝑎𝑥 =𝜍=2𝜋𝑅𝐿 𝐾 0 𝛾 𝑐𝑙𝑎𝑦 ′ 𝐿 2 𝜇 Δ 𝑃 𝑝𝑤𝑝 = 𝐴 𝑏𝑎𝑠𝑒,𝑖 × 𝐿 𝑠 × 𝛾 𝑤 𝑘 𝜂 × Δ𝑦 Δ𝑡 Δ 𝑦 1 𝑁 PWP component [3a] → 𝜉 𝑝𝑤𝑝,𝑢,𝐼

Macro-element Soil free to move
CORMAN Gilles Master Thesis December 2017 𝑅 𝑡𝑜𝑡 =Δ Φ 𝑜𝑢𝑡 +Δ Φ 𝑖𝑛 +Δ 𝑃 𝑝𝑤𝑝 +Δ 𝑊 𝑝𝑙𝑢𝑔 = 𝜅 𝑜𝑢𝑡 Δ𝑦+ 𝜅 𝑖𝑛 Δ𝑦 𝑠𝑝𝑟𝑖𝑛𝑔𝑠 − 𝜍 𝑜𝑢𝑡 − 𝜍 𝑖𝑛 𝑠𝑙𝑖𝑑𝑒𝑟𝑠 + 𝜂Δ 𝑦 1 𝑁 𝑑𝑎𝑠ℎ𝑝𝑜𝑡 + 𝜅 𝑝𝑙𝑢𝑔 𝐿 𝑝𝑙𝑢𝑔 𝑠𝑝𝑟𝑖𝑛𝑔 Introduction Description of the FE model Drained simulations Partly drained simulations Reaction modes Numerical-Analytical Macro-element Conclusion Δ Φ out = 𝜉 𝑜𝑢𝑡,𝑢 2𝜋 𝑅 𝑜 𝐾 𝜏 𝐿− 𝐾 𝜏 2 Δ𝑦 𝜇 𝐾 0 Δ 𝜎 𝑣,0 ′ ×Δ𝑦= 𝜅 𝑜𝑢𝑡 Δ𝑦 ×Δ𝑦 Friction components [1b & 2b] Δ Φ in = 𝜉 𝑖𝑛,𝑢 2𝜋 𝑅 𝑖 𝐾 𝜏 𝐿− 𝐾 𝜏 2 Δ𝑦 𝜇 𝐾 0 Δ 𝜎 𝑣,0 ′ 1− 𝑠 𝑠 𝑐𝑟𝑖𝑡 ×Δ𝑦= 𝜅 𝑖𝑛 Δ𝑦 ×Δ𝑦 Δ Φ 𝑚𝑎𝑥 =𝜍= 𝜉 𝑚𝑎𝑥,𝑢 × 2𝜋𝑅𝐿 𝐾 0 𝛾 𝑐𝑙𝑎𝑦 ′ 𝐿 2 𝜇 Δ 𝑃 𝑝𝑤𝑝 = 𝐴 𝑏𝑎𝑠𝑒,𝑖 × 𝐿 𝑠 × 𝛾 𝑤 𝑘 𝜂 × Δ𝑦 Δ𝑡 Δ 𝑦 1 𝑁 PWP component [3b] → 𝜉 𝑝𝑤𝑝,𝑢,𝐼𝐼 Plug component [4b] Δ 𝑊 𝑝𝑙𝑢𝑔 = 𝜉 𝑝𝑙𝑢𝑔,𝑢 ×( 𝐴 𝑏𝑎𝑠𝑒,𝑖 𝛾 𝑐𝑙𝑎𝑦 ′ )× 𝐿 𝑝𝑙𝑢𝑔 = 𝜅 𝑝𝑙𝑢𝑔 × 𝐿 𝑝𝑙𝑢𝑔

Conclusion Scenario Sub-case Drainage condition Soil condition
CORMAN Gilles Master Thesis December 2017 Scenario Sub-case Drainage condition Soil condition Resistance 1 1-1𝑏𝑖𝑠 Drained Rigid body motion Φ 𝑜𝑢𝑡 − Φ 𝑖𝑛 2-2𝑏𝑖𝑠 Free to move Φ 𝑜𝑢𝑡 − Φ 𝑖𝑛 −( 𝑊 𝑝𝑙𝑢𝑔 ) 2 3 Partly drained Φ 𝑜𝑢𝑡 − Φ 𝑖𝑛 − 𝑃 𝑝𝑤𝑝 4 Φ 𝑜𝑢𝑡 − Φ 𝑖𝑛 − 𝑃 𝑝𝑤𝑝 − 𝑊 𝑝𝑙𝑢𝑔 Introduction Description of the FE model Drained simulations Partly drained simulations Conclusion

Thank you for your attention
As you may know, the main purpose of this assignment is to design an artificial island and harbour in the north sea.

Master’s dissertation

Similar presentations

Presentation on theme: "Master’s dissertation"— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

Master’s dissertation

Similar presentations

Presentation on theme: "Master’s dissertation"— Presentation transcript:

Similar presentations

About project

Feedback