june 13 - june 15, 2012rec 2012, brno, czech republic1 different models of soil-structure...

June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 1

Different models of soil-structure interaction and

consequent reliability of foundation structure

Radim ČAJKA

Technical University Ostrava,

Faculty of Civil Engineering

http://www.vsb.cz

Czech Republic

http://www.vsb.cz/


Analyses of structures

• Reliability of the reinforced and pre-stressed concrete structure and foundation depends on a lot of factors, for example– strength and safety factors of materials (fck, gc, fyk, gs)

– static and dynamic force loads (g, q, Fg, Fq,….)

– deformation loads ( ,e g,…), for example creep, shrinkage, temperature, subsoil deformation due to undermining or flooding

• Suitable soil – structure interaction model


Application on real structure


FEM analyses of reinforced space structure


Subsoil models used in FEM

Principle condition for all subsoil models

Settlement of subsoil (s) is equal to deformation of foundation (w)

yxwyxs ,),(

Space 3D FEM modelSurface model

• Boussinesque halfspace• Winkler• Pasternak• Modification and combination of these models


Settlement calculation model and active zone determination

mEApfs defefzji ,,,,,

coefficient of structural strength

- Czech Standard ČSN 73 1001 m = 0,1 to 0,5

- Eurocode EC 7 m = 0,2 (recommended value)


Analyses of subsoil settlement

orol

z

oed

or

z

oed

z ssdzzyxE

zyxzyxmdz

zyxE

zyxyxs

zz

00 ),,(

),,(),,(

),,(

),,(),(

0),,(),(),,(),,( zorzolzz zyxyxmzyxzyx

- Condition for active zone determination

- Condition for subsoil settlement in each nodal point

- Then contact stress and contact function in all nodal points

jzijci p ,, ji

jcijzi s

C,

,,


Active zone determination with respect to ČSN or EC Standard

• The depth of compressible subsoil layers (active zone) depends on size and shape of foundation, changes of subsoil compressibility and distribution of foundation elements

• The coefficient of structural strength varies in Czech Standard ČSN 73 1001 from m = 0,1 to m = 0,5

• In accordance ČSN EN 1997-1 Design of geotechnical structures, the effective vertical stress from foundation contact pressure is equal to 20 % of effective geotechnical stress, i.s. practically for m=0,2


Explicit expression of stress under rectangular area

2222 zbyaxz

byaxarctg

p zz

222 zbyaxz

byaxarctg

222 zbyaxz

byaxarctg

222 zbyaxz

byaxarctg


2222222

222 2

zbyaxzbyzax

zbyaxbyaxz

2222222

222 2

zbyaxzbyzax

zbyaxbyaxz

2222222

222 2

zbyaxzbyzax

zbyaxbyaxz

2222222

222 2

zbyaxzbyzax

zbyaxbyaxz


Analysis of stress in subsoil

dAr

zp

A

zz

5

33

2

2222 zyxr

ddJ

r

zpzz

det3

2

),(5

31

1

1

1


Numerical integrationGauss quadrature formulae

),(),(1

1

1

1 1 1qpq

n

p

n

qp fddf

where qp , are weighting factor for interval <-1,1>, integration points of function f number of integration points

qp ,n

Numerical integration of vertical stress

),(det3

2

),(5

3

1 1qp

qpzn

p

n

qqpz J

r

zp


Shape functions of a 4-node element

)1(25,0),(1 N

)1(25,0),(2 N

)1(25,0),(3 N

)1(25,0),(4 N


Shape functions of a 8-node element

)1(25,0),( 22221 N

)1(25,0),( 22222 N

)1(25,0),( 22223 N

)1(25,0),( 22224 N

- corner nodes

- intermediate nodes

)1(5,0),( 225 N

)1(5,0),( 226 N

)1(5,0),( 227 N

)1(5,0),( 228 N


y

fx

f

J

y

fx

f

yx

yx

f

f

Jacobian of transformation

),(/),(det yxJ

r

ii

i

r

ii

i

fN

fN

Jf

f

J

y

fx

f

1

111


Contact stress course in element

zi

r

iiz pyxNyxp

),(),(1


Convergence to exact solution

• Division of loaded area into finite elements and degree of polynomial approximation (convergence of shape and size of loaded area),

• Accuracy of approximation of stress course in subsoil, i.e. number of Gauss integration points (convergence of subsoil).


Solved test examples• Square area

• Triangle area

• Circle area

• The results are practically same for exact solution and numerical integration to 6 integration points


Application of designed solution

• Analysis of stress components under arbitrary area constructed from 4-noded and 8-noded isoparametric elements

• Analysis of settlement of non-linear elastic half-space modified with soil structural strength coefficient following EC and Czech standard

• Solution of soil – foundation and soil – structure interaction problems by means of FEM


Rigidity matrix of isoparametric plate element

1

1

1

1

det ddJGDGK Te

qpqpT

qp

n

p

n

qqpe JGDGK ,det,,

1 1


Subsoil rigidity matrix

),(det),(),(),(1 1

qpqpqpT

qp

n

p

n

qqpep JNCNK

r

iziiz CNC

111 ).,(

i

cizi s

C

1

),(00

0),(0

00),(

),(

2

2

1

y

x

z

qp

C

C

C

C

Contact function

Nodal contact parameter

Matrix of contact function


Four - noded isoparametric semispace element

X

ZY

1 2

34

ZZ3

ZZ2

1'

4'

3'

2'

ZZ1

ZZ4

p2

p3=0,5p2p4

p1=2p2ol

mori

ol


Test example of circular plate on elastic halfspace

• Shallow plate foundation- modulus of elasticity of concrete Ec = 22,95.103

MPa - Poisson’s ratio mc = 0,2- plate thickness hc = 0,1 m- radius of circular plate r = 1,0 m

• Subsoil- modulus of deformation, F5 Edef = 5,0 MPa - Poisson’s ratio mp = 0,4- coefficient of structural strenght m = 0,2- density of subsoil g = 19 kN.m-3

• Load- uniformly distributed load pz = 100 kPa


Settlement s(x,y) of Halfspace under Circular Plate after 0th and

10th Iteration


Contact Stress under Centre of Circle Plate

35

40

45

50

55

60

65

70

75

1 2 3 4 5 6 7 8 9 10

Iteration

Con

tact

Str

ess

[kP

a]

IntPoints=2

IntPoints=4

IntPoints=6

IntPoints=8

IntPoints=10

Contact stress of Circular plate under Centre and Edge

Contact Stress under Edge of Circle Plate

150

200

250

300

350

400

450

1 2 3 4 5 6 7 8 9 10

Iteration

Con

tact

Str

ess

[kP

a]IntPoints=2

IntPoints=4

IntPoints=6

IntPoints=8

IntPoints=10


Test comparison with TRIMAS published example

• Shallow plate foundation- modulus of elasticity of concrete Ec = 30.103 MPa - Poisson’s ratio mc = 0,154- plate thickness hc = 0,3 m- Dimensions of rectangular plate lx = 8,0 m, ly = 12,0

m

• Subsoil- modulus of deformation, F5 Edef = 4361,5 kPa - Poisson’s ratio mp = 0,38- coefficient of structural strength m = 0,001 0,01

0,1…- density of subsoil g = 18,5 kN.m-3

• Load- uniformly distributed line load pz = 68,6 kN.m-1


Example of Foundation Plate TRIMAS (RIB software)

• Foundation plate with rigid walls in cross section

• Solution of the 2D plate on 3D space soil elements (TRIMAS software)

• Solution with proposed surface subsoil model

• Active zone in subsoil in accordance ČSN 73 1001 and EC7


Bending moments and Contact Stresses


Dependence of bending moment on subsoil stiffness, IntBody=8

-20

-15

-10

-5

0

5

10

15

20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Number of element

Be

nd

ing

mo

me

nt

[kN

m/m

']

m = 0,5

m = 0,4

m = 0,3

m = 0,2

m = 0,1

m = 0,01

m = 0,001


Design of Testing Equipment Structure


Soil – foundation interaction test


Conclusion• Original and general method for stress solution in elastic

halfspace was presented• Presented subsoil model is suitable for soil – structure

interaction task and can save 3D subsoil elements• The mentioned solution eliminates difficulties encountered up

until now, when trying to apply a soil CSN EN standard model in FEM interaction tasks.

• Comparison of various subsoil model shows great scattering results, sometimes more than 100 %

• Field soil – foundation interaction experimental tests are now performed

• Designed models will be verified and uncertainty eliminated


This paper was supported by the research project No. FR-TI2/746,

program TIP, Ministry of Industry and Trade ,

Czech Republic

Thank you for your attention

june 13 - june 15, 2012rec 2012, brno, czech republic1 different models of soil-structure...

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rectangular area slide