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ANALYSES OF STABILITY OF CAISSON BREAKWATERS ON RUBBLE FOUNDATION EXPOSED TO IMPULSIVE WAVE LOADS Burcharth, Andersen & Lykke Andersen ICCE 2008, Hamburg, Sep, 2008 1 of 12 Analyses of Stability of Caisson Breakwaters on Rubble Foundation Exposed to Impulsive Wave Loads ICCE 2008 Hamburg Burcharth, H. F., Aalborg University, Denmark Andersen, L., Aalborg University, Denmark Lykke Andersen, T., Aalborg University, Denmark Given: Wave loading determined by high frequency sampling of pressures: Design criteria for overall stability failure modes: A. No sliding and no foundation failure allowed. An equivalent static force analysis is in principle possible. B. Sliding allowed (10 – 100 cm) but no foundation failure. A dynamic analysis is necessary for determination of sliding distance.

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ANALYSES OF STABILITY OF CAISSON BREAKWATERS ON RUBBLE FOUNDATION EXPOSED TO IMPULSIVE WAVE LOADS Burcharth, Andersen & Lykke Andersen ICCE 2008, Hamburg, Sep, 2008 2 of 12 Case A, No Sliding Static analysis Failure function: Which equivalent forces F h,eq, F u,eq and F R,eq should be used? If the impulse of the force peaks cannot cause sliding or foundation failure then a lower equivalent static force can be applied. A full dynamic analysis including foundation is needed in order to study criteria for deleting/reducing force peaks in order to identify realistic equivalent static forces.

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ANALYSES OF STABILITY OF CAISSON BREAKWATERS ON RUBBLE FOUNDATION EXPOSED TO IMPULSIVE WAVE LOADS Burcharth, Andersen & Lykke Andersen ICCE 2008, Hamburg, Sep, 2008 3 of 12 Case B, Sliding Allowed Simple dynamic 1-D model analysis For a simple approximate analysis is used the equation of motion for sliding (no soil deformations and no rocking of caisson) Sliding distance:

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ANALYSES OF STABILITY OF CAISSON BREAKWATERS ON RUBBLE FOUNDATION EXPOSED TO IMPULSIVE WAVE LOADS Burcharth, Andersen & Lykke Andersen ICCE 2008, Hamburg, Sep, 2008 4 of 12 Case B, Sliding Allowed A simple slip failure analysis of foundation failure must be performed as well, but here again is the problem selection of equivalent static loading. A dynamic finite element analysis of the foundation response is needed for formulation of criteria for selection of the static loadings.

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ANALYSES OF STABILITY OF CAISSON BREAKWATERS ON RUBBLE FOUNDATION EXPOSED TO IMPULSIVE WAVE LOADS Burcharth, Andersen & Lykke Andersen ICCE 2008, Hamburg, Sep, 2008 5 of 12 2-D ABAQUS Finite Element Analysis Geometry and material parameters: SeabedBanquetCaisson MaterialDense sandRubbleConcrete and sand Mass density, ρ2000 kg/m 3 Specific weight, γ10 kN/m 3 19.64 kN/m 3 Elasticity modelLinear elastic Young’s modulus, E100 MPa 10.000 MPa Poisson’s ratio, ν0.25 Plasticity modelMohr-Coulomb N.A. Cohesion, c1 kPa N.A. Angle of friction, φ35˚45˚N.A. Angle of dilation, ψ5˚15˚N.A. Design Waves: H m0,112y = 6.2 m T p = 9-13 s

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ANALYSES OF STABILITY OF CAISSON BREAKWATERS ON RUBBLE FOUNDATION EXPOSED TO IMPULSIVE WAVE LOADS Burcharth, Andersen & Lykke Andersen ICCE 2008, Hamburg, Sep, 2008 6 of 12 2-D ABAQUS Finite Element Analysis Model description and assumptions: Finite element model with plane strain. Mohr-Coulomb modeling of soils. Fully drained conditions are assumed, i.e. no influence of pore water. Base slab friction coefficient μ = 0.6

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ANALYSES OF STABILITY OF CAISSON BREAKWATERS ON RUBBLE FOUNDATION EXPOSED TO IMPULSIVE WAVE LOADS Burcharth, Andersen & Lykke Andersen ICCE 2008, Hamburg, Sep, 2008 7 of 12 2-D ABAQUS Finite Element Analysis Pressure loadings: - P 0 : Buoyancy load (100 kPa) - P 1 : Pulsating wave load - P 2 : Impulsive wave load Static sliding failure for P 1 : P static = P 1 = 99 kPa Static tilting failure for P 1 : P 1 = 197 kPa Static soil failure for P 1 : P 1 = 83 kPa (ABAQUS). When P 2 is added combined sliding and tilting can occur. Soil failure was not observed in dynamic analyses for the combinations of P 1 and P 2 tested. Maximum permanent soil displacements 5-6 cm

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ANALYSES OF STABILITY OF CAISSON BREAKWATERS ON RUBBLE FOUNDATION EXPOSED TO IMPULSIVE WAVE LOADS Burcharth, Andersen & Lykke Andersen ICCE 2008, Hamburg, Sep, 2008 8 of 12 Example of ABAQUS Simulation Movements and plastic strains:

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ANALYSES OF STABILITY OF CAISSON BREAKWATERS ON RUBBLE FOUNDATION EXPOSED TO IMPULSIVE WAVE LOADS Burcharth, Andersen & Lykke Andersen ICCE 2008, Hamburg, Sep, 2008 9 of 12 Example of ABAQUS Simulation Movements scaled a factor 5:

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ANALYSES OF STABILITY OF CAISSON BREAKWATERS ON RUBBLE FOUNDATION EXPOSED TO IMPULSIVE WAVE LOADS Burcharth, Andersen & Lykke Andersen ICCE 2008, Hamburg, Sep, 2008 10 of 12 Comparison of ABAQUS Simulation and Simple Dynamic 1-D Sliding Model Caisson movements start earlier in ABAQUS model due to inclusion of soil elasticity. Caisson acceleration phase continues longer in ABAQUS due to tilting around rear corner which leads to an upward acceleration of the caisson (reduction of vertical load on the foundation and thus the friction force). Caisson decelerates faster due to caisson rocking back in position which increases the vertical load on the foundation. Dynamic amplification/reduction is included in ABAQUS. Caisson is vibrating.

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ANALYSES OF STABILITY OF CAISSON BREAKWATERS ON RUBBLE FOUNDATION EXPOSED TO IMPULSIVE WAVE LOADS Burcharth, Andersen & Lykke Andersen ICCE 2008, Hamburg, Sep, 2008 11 of 12 Comparison of Sliding Distances Simple dynamic 1-D model 2-D ABAQUS finite element model t 1 [s]P static / P 1 2.391.791.43 0.1 0.000 0.010 0.008 0.027 0.039 0.118 0.2 0.000 0.030 0.032 0.146 0.156 0.395 Horizontal displacements (m) for P 2 /P 1 = 4 Horizontal displacements (m) for P 2 /P 1 = 8 t 1 [s]P static / P 1 2.391.791.43 0.1 0.020 0.031 0.085 0.158 0.257 0.421 0.2 0.080 0.218 0.308 0.594 1.028 > 0.885

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ANALYSES OF STABILITY OF CAISSON BREAKWATERS ON RUBBLE FOUNDATION EXPOSED TO IMPULSIVE WAVE LOADS Burcharth, Andersen & Lykke Andersen ICCE 2008, Hamburg, Sep, 2008 12 of 12 Overall Conclusions A simple dynamic analysis method for caisson sliding distance f.ex. as proposed by Burcharth and Lykke Andersen, 2006 (COPEDEC VII, Dubai) is expected to give reasonable estimates on caisson displacements but slightly on the unsafe side due to neglecting elastic plastic deformations in the soil and rocking of the caisson. The present ABAQUS analyses gives larger displacements than the simple model. However, the calculated displacements are expected to be too large due to the assumed fully drained conditions. In reality the pore pressure will reduce rocking of the caisson. Recommendations on sampling frequencies and time averaging of recorded wave loadings given in Burcharth and Lykke Andersen (2006) is expected also to apply to ABAQUS calculations due to larger deformations. Local sampling frequency should thus be higher than 50-100 samples within a Tp-period. In case of occurrence of impulsive loads it is not possible to give simple advice on how to determine equivalent static loads to be applied in static analyses. Moreover, foundation slip failures cannot be analysed realistically by a static analysis. Static analyses generally show occurrence of foundation slip failures before sliding failures whereas dynamic analyses indicate the opposite.

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ANALYSES OF STABILITY OF CAISSON BREAKWATERS ON RUBBLE FOUNDATION EXPOSED TO IMPULSIVE WAVE LOADS Burcharth, Andersen & Lykke Andersen ICCE 2008, Hamburg, Sep, 2008 13 of 12 Setup for Finite Element Analysis in ABAQUS Model Description: Finite element model with plane strain. Quadratic interpolation with full integration. Regular mesh with quadrilateral elements with mesh size 2.5 metres. Mohr-Coulomb modeling of soils. Fully drained conditions are assumed, i.e. no influence of pore water. Effective in situ stresses in the soil are calculated (reduced gravity). Non-associated perfect plasticity, i.e. no hardening. Full density of soil applies in transient dynamic analysis. Rayleigh damping based on the stiffness only, i.e. no damping based on mass. 5 % damping in the seabed and the banquet and 1 % damping in the caisson. Added mass (in the horizontal direction) has not been included in the model.

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ANALYSES OF STABILITY OF CAISSON BREAKWATERS ON RUBBLE FOUNDATION EXPOSED TO IMPULSIVE WAVE LOADS Burcharth, Andersen & Lykke Andersen ICCE 2008, Hamburg, Sep, 2008 14 of 12 Setup for Finite Element Analysis in ABAQUS Initial conditions: 1.K 0 procedure for the subsoil due to horizontal seabed 2.Incremental gravity loading on the banquet and the caisson Interfaces (Caisson - Rubble Banquet): Base slab friction coefficient μ = 0.6 Pressure-overclosure with the linear stiffness 10 GPa/m assumed Other interfaces are rough, i.e. no sliding is allowed Iterative solver Non-linear, i.e. updated, geometry of the model Full Newton-Raphson scheme (static part) Implicit time integration (dynamic part) Automatic time step control with maximum time step 0.005 s No mass scaling

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