analyses of stability of caisson breakwaters on rubble foundation exposed to impulsive wave loads...

ANALYSES OF STABILITY OF CAISSON BREAKWATERS ON RUBBLE FOUNDATION EXPOSED TO IMPULSIVE WAVE LOADS

Burcharth, Andersen & Lykke Andersen

ICCE 2008, Hamburg, Sep, 20081 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.

Fh(t) G

Fu(t)




Case A, No Sliding

sliding , 0

sliding no , 0eq,heq,u FfFGg

Static analysis

Failure function:

Which equivalent forces Fh,eq, Fu,eq and FR,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.

FR,eq

Foundation slip failure




Case B, Sliding AllowedSimple 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)

gdt

xdMMftFGtFtF addedcaissonuh

2

2

Sliding distance:

0dtgMM

1tx

2

1

t

taddedcaisson2

0tx velocity, 2

dtdttFMM

1txtx

2

1 1

t

t

t

t addedcaisson12

F(t) = F (t) + f·F (t) - Gf = -gh u

time

t1 t1t2 t2

0

acceleration phase (g<0)

deceleration




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.




2-D ABAQUS Finite Element Analysis

Geometry and material parameters:

Seabed Banquet CaissonMaterial Dense sand Rubble Concrete and sandMass density, ρ 2000 kg/m3 2000 kg/m3 2000 kg/m3

Specific weight, γ 10 kN/m3 10 kN/m3 19.64 kN/m3

Elasticity model Linear elastic Linear elastic Linear elasticYoung’s modulus, E 100 MPa 100 MPa 10.000 MPaPoisson’s ratio, ν 0.25 0.25 0.25Plasticity model Mohr-Coulomb Mohr-Coulomb N.A.Cohesion, c 1 kPa 1 kPa N.A.Angle of friction, φ 35˚ 45˚ N.A.Angle of dilation, ψ 5˚ 15˚ N.A.

Design Waves:Hm0,112y = 6.2 mTp = 9-13 s

E = 10 Pa = 2000 kg/m³M = 638tM = 438t

10

E = 10 Pa ; = 2000 kg/m³ ; = 45 = 15 ; c =1 kPa8

E = 10 Pa ; = 2000 kg/m³ ; = 35 = 5 ; c =1 kPa8

= 0.6

5 m

15 m

5 m

15 m

20 m

1:1.51:1.5

7.5 m 7.5 m

boyancy reduced





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





Pressure loadings:

- P0: Buoyancy load (100 kPa)- P1: Pulsating wave load- P2: Impulsive wave load

• Static sliding failure for P1 : Pstatic = P1 = 99 kPa • Static tilting failure for P1 : P1 = 197 kPa • Static soil failure for P1 : P1 = 83 kPa (ABAQUS).

When P2 is added combined sliding and tilting can occur. Soil failure was not observed in dynamic analyses for the combinations of P1 and P2 tested.

Maximum permanent soil displacements 5-6 cm

P1

P1P2

P0

Thresshold of sliding static pressure Pg=0

1

time

P

t0

0

1

P + P1 2

1 t =2t2 t = 3 s3 t = 4 s41

pressure

Pstatic

P / P = 2.4 ; 1.79 ; 1.43static 1

P / P = 4 ; 82 1

t = 0.1 s ; 0.2 s1

P1

P2




Example of ABAQUS SimulationMovements and plastic strains:




Example of ABAQUS SimulationMovements scaled a factor 5:




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.




Comparison of Sliding Distances

• Simple dynamic 1-D model• 2-D ABAQUS finite element model

t1 [s] Pstatic / P1

2.39 1.79 1.43

0.10.0000.010

0.0080.027

0.0390.118

0.20.0000.030

0.0320.146

0.1560.395

Horizontal displacements (m) for P2/P1 = 4 Horizontal displacements (m) for P2/P1 = 8

t1 [s] Pstatic / P1

2.39 1.79 1.43

0.10.0200.031

0.0850.158

0.2570.421

0.20.0800.218

0.3080.594

1.028> 0.885

time0

-g

time0

-g

time0

-g

time0

-g

time0

-g

time0

-g

Pstatic

time

P

t0

0

1

P + P1 2

1 t =2t2 t = 3 s3 t = 4 s41

pressure

Pstatic

Thresshold of sliding static pressure Pg=0

1

P1

P2




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.




Setup for Finite Element Analysis in ABAQUSModel 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.




Setup for Finite Element Analysis in ABAQUSInitial conditions:1.K0 procedure for the subsoil due to horizontal seabed2.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

analyses of stability of caisson breakwaters on rubble foundation exposed to impulsive wave loads...

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