three-dimensional modelling of foundations under combined loading

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