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:
G
Fh(t)
Fu(t)
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.
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
Case A, No Sliding
Foundation slip failure
Static analysis
Failure function: g  G  Fu ,eq  f  Fh ,eq
 0 , no sliding

 0 , sliding
FR,eq
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.
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 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)
F t   Fh t   G  Fu t 
d 2x
f  M caisson  M added  2   g
dt
F(t) = Fh (t) + f·Fu (t) - Gf = -g
acceleration phase (g<0)
deceleration
time
0
t1
t2
t1
velocity, x t 2   0
t2
t
2
1
x t 2  
 g dt  0
M caisson  M added t1
t2 t
Sliding distance: x t 2   x t1    
1
 Ft  dt dt
M

M
caisson
added
t1 t1
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
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.
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
2-D ABAQUS Finite Element Analysis
Geometry and material parameters:
5m
10
Design Waves:
Hm0,112y = 6.2 m
Tp = 9-13 s
E = 10 Pa
 = 2000 kg/m³
M = 638t
M boyancy reduced = 438t
15 m
 = 0.6
.5
5 m 1:1
15 m
1:1
8
E = 10 Pa ;  = 2000 kg/m³ ;  = 45 = 15 ; c =1 kPa
7.5 m
20 m
.5
7.5 m
8
E = 10 Pa ;  = 2000 kg/m³ ;  = 35 = 5 ; c =1 kPa
Material
Mass density, ρ
Specific weight, γ
Elasticity model
Young’s modulus, E
Poisson’s ratio, ν
Plasticity model
Cohesion, c
Angle of friction, φ
Angle of dilation, ψ
Seabed
Dense sand
2000 kg/m3
10 kN/m3
Linear elastic
100 MPa
0.25
Mohr-Coulomb
1 kPa
35˚
5˚
Banquet
Rubble
2000 kg/m3
10 kN/m3
Linear elastic
100 MPa
0.25
Mohr-Coulomb
1 kPa
45˚
15˚
Caisson
Concrete and sand
2000 kg/m3
19.64 kN/m3
Linear elastic
10.000 MPa
0.25
N.A.
N.A.
N.A.
N.A.
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
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
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
pressure
Pressure loadings:
- P0: Buoyancy load (100 kPa)
- P1: Pulsating wave load
- P2: Impulsive wave load
Pstatic / P1 = 2.4 ; 1.79 ; 1.43
P2 / P1 = 4 ; 8
P1 + P2
t1 = 0.1 s ; 0.2 s
P2
Pstatic
Thresshold of sliding static pressure P1
g=0
P1
P2
P1
P1
0
time
0
t1
t 2 =2t1
t 3= 3 s
t 4= 4 s
• 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
P0
P1
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
Example of ABAQUS Simulation
Movements and plastic strains:
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 scaled a factor 5:
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
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.
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 Sliding Distances
pressure
P1 + P2
• Simple dynamic 1-D model
• 2-D ABAQUS finite element model
Thresshold of sliding static pressure P1
g=0
P2
Pstatic
P1
Pstatic
P1
0
time
0
t1
t 2 =2t1
t 3= 3 s
t 4= 4 s
Horizontal displacements (m) for P2/P1 = 4 Horizontal displacements (m) for P2/P1 = 8
t1 [s]
Pstatic / P1
-g
2.39
-g
time
0
1.79
-g
time
0
t1 [s]
1.43
-g
time
0
Pstatic / P1
2.39
-g
time
0
1.79
-g
time
0
1.43
time
0
0.1
0.000
0.010
0.008
0.027
0.039
0.118
0.1
0.020
0.031
0.085
0.158
0.257
0.421
0.2
0.000
0.030
0.032
0.146
0.156
0.395
0.2
0.080
0.218
0.308
0.594
1.028
> 0.885
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
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.
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
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.
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
Initial conditions:
1. K0 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
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