three-dimensional modelling of foundations under combined loading
DESCRIPTION
z. y. Wave Load Direction. x. G.T. Houlsby (Oxford University) and M.J. Cassidy (The University of Western Australia). Three-Dimensional Modelling of Foundations under Combined Loading. - PowerPoint PPT PresentationTRANSCRIPT
Three-Dimensional Modelling of Foundations under Combined LoadingThree-Dimensional Modelling of Foundations under Combined LoadingG.T. Houlsby (Oxford University) and M.J. Cassidy (The University of Western Australia)
Purpose: to develop realistic models for shallow foundations
for offshore structures when
subjected to combined loads in three dimensions
This research is sponsored by the ARC as part of an IREX exchange programme between Oxford University and The University of Western Australia
Visit us at www-civil.eng.ox.ac.uk or www.cofs.uwa.edu.au
3
2
3
2
24
24
5
43
43
1
33
32
3
23
22
2
2
2
2
0000
0000
00000
0000
0000
00000
8
8
8
4
4
4
Ru
Ru
Rw
kk
kk
k
kk
kk
k
GRM
GRM
GRQ
GRH
GRH
GRV
012 12 2223223
23
22
223
22
vvmhmha
mmqhhf
f
THEORY
Elasticity: dimensionless stiffness factors are defined, depending on the footing geometry
Yield surface: a yield surface is defined in terms of dimensionless variables in 6-dimensional stress space
Hardening law: this defines the relationship between the size of the yield locus and the penetration of the footing into the soil
V
H
M/2R
Flow rule:
The foundation models use “non-associated” flow rules to ensure that the ratios between the plastic displacements are realistic
0
500
1000
1500
2000
2500
3000
3500
4000
0.000 0.010 0.020 0.030 0.040
wp
V0
Applications are to jack-up structures
and to caisson foundations, for
example for offshore wind
turbines
H3
H2
V
2R
1
3
2
Q
M3
M2Forces in 3 directions and moments about 3
axes are taken into account
0
50000
100000
150000
200000
250000
300000
350000
0 0.0002 0.0004 0.0006 0.0008 0.001
theta3 (radians)
M3
(kN
m)
0 degrees
30 degrees
60 degrees
90 degrees
-200000
-150000
-100000
-50000
0
-0.0004 -0.0002 0theta2 (radians)
M2
(kN
m)
Examples
The effects of horizontal loads in different directions
can be studied
A
B
D
C
D
C
B
A
H2
H3
A
B
CD
x
z(z1, r1=0)
(z4=0, r4=R)
(z3=0, r3=R)
(z2, r2)
LRP
Different geometries of foundations can be
defined
Motivation
The theoretical models are based on work-hardening plasticity theory, and have four main components. The new features for the three-dimensional models are highlighted.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 20 40 60 80 100
x an
d y
hu
ll d
isp
(m)
-0.06415
-0.0641
-0.06405
-0.064
-0.06395
-0.0639
-0.06385
-0.0638
-0.06375
-0.0637
z h
ull
dis
p (m
)x disp
y disp
z disp
-4.00E-05
-3.50E-05
-3.00E-05
-2.50E-05
-2.00E-05
-1.50E-05
-1.00E-05
-5.00E-06
0.00E+00
5.00E-06
0 20 40 60 80 100% of wave load
x an
d y
hu
ll r
ot
(m
)
-1.00E-04
0.00E+00
1.00E-04
2.00E-04
3.00E-04
4.00E-04
5.00E-04
6.00E-04
7.00E-04
8.00E-04
9.00E-04
z h
ull
ro
t (m
)x rot
y rot
z rot
x
yz
Wave Load Direction
The effects of skewed
environmental loading on three
dimensional structures can
be studied
Foundation model placed at the bottom
of each leg