June 13 - June 15, 2012REC 2012, Brno, Czech Republic1 Different models of soil-structure...
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Transcript of 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
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 2
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
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 3
Application on real structure
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 4
FEM analyses of reinforced space structure
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 5
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
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 6
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)
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 7
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,
,,
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 8
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
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 9
Explicit expression of stress under rectangular area
2222 zbyaxz
byaxarctg
p zz
222 zbyaxz
byaxarctg
222 zbyaxz
byaxarctg
222 zbyaxz
byaxarctg
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 10
2222222
222 2
zbyaxzbyzax
zbyaxbyaxz
2222222
222 2
zbyaxzbyzax
zbyaxbyaxz
2222222
222 2
zbyaxzbyzax
zbyaxbyaxz
2222222
222 2
zbyaxzbyzax
zbyaxbyaxz
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 11
Analysis of stress in subsoil
dAr
zp
A
zz
5
33
2
2222 zyxr
ddJ
r
zpzz
det3
2
),(5
31
1
1
1
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 12
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
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 13
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
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 14
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
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 15
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
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 16
Contact stress course in element
zi
r
iiz pyxNyxp
),(),(1
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 17
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).
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 18
Solved test examples• Square area
• Triangle area
• Circle area
• The results are practically same for exact solution and numerical integration to 6 integration points
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 19
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
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 20
Rigidity matrix of isoparametric plate element
1
1
1
1
det ddJGDGK Te
qpqpT
qp
n
p
n
qqpe JGDGK ,det,,
1 1
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 21
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
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 22
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
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 23
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
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 24
Settlement s(x,y) of Halfspace under Circular Plate after 0th and
10th Iteration
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 25
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
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 26
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
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 27
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
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 28
Bending moments and Contact Stresses
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 29
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
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 30
Design of Testing Equipment Structure
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 31
Soil – foundation interaction test
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 32
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
June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 33
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