Different models of soilstructure interaction and consequent reliability

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 1

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 2

Application on real structure June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 3

FEM analyses of reinforced space structure June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 4

Subsoil models used in FEM Principle condition for all subsoil models Settlement of subsoil (s) is equal to deformation of foundation (w) Space 3 D FEM model Surface model • Boussinesque halfspace • Winkler • Pasternak • Modification and combination of these models June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 5

Settlement calculation model and active zone determination 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 6

Analyses of subsoil settlement - Condition for active zone determination - Condition for subsoil settlement in each nodal point - Then contact stress and contact function in all nodal points June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 7

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 8

Explicit expression of stress under rectangular area June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 9

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Analysis of stress in subsoil June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 11

Numerical integration Gauss quadrature formulae where are weighting factor for interval <-1, 1>, integration points of function f number of integration points Numerical integration of vertical stress June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 12

Shape functions of a 4 -node element June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 13

Shape functions of a 8 -node element - corner nodes - intermediate nodes June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 14

Jacobian of transformation June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 15

Contact stress course in element June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 16

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 17

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 18

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 19

Rigidity matrix of isoparametric plate element June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 20

Subsoil rigidity matrix Matrix of contact function Contact function Nodal contact parameter June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 21

Four - noded isoparametric semispace element June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 22

Test example of circular plate on elastic halfspace • Shallow plate foundation - modulus of elasticity of concrete Poisson’s ratio plate thickness radius of circular plate Ec mc hc r = 22, 95. 103 MPa = 0, 2 = 0, 1 m = 1, 0 m • Subsoil - modulus of deformation, F 5 Poisson’s ratio coefficient of structural strenght density of subsoil Edef = 5, 0 MPa mp = 0, 4 m = 0, 2 g = 19 k. N. m-3 • Load - uniformly distributed load June 13 - June 15, 2012 REC 2012, Brno, Czech Republic pz = 100 k. Pa 23

Settlement s(x, y) of Halfspace under Circular Plate after 0 th and 10 th Iteration June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 24

Contact stress of Circular plate under Centre and Edge June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 25

Test comparison with TRIMAS published example • Shallow plate foundation - modulus of elasticity of concrete Poisson’s ratio plate thickness Dimensions of rectangular plate Ec = 30. 103 MPa mc = 0, 154 hc = 0, 3 m lx = 8, 0 m, ly = 12, 0 m • Subsoil - modulus of deformation, F 5 Poisson’s ratio coefficient of structural strength density of subsoil Edef = 4361, 5 k. Pa mp = 0, 38 m = 0, 001 0, 1… g = 18, 5 k. N. m-3 • Load - uniformly distributed line load June 13 - June 15, 2012 REC 2012, Brno, Czech Republic pz = 68, 6 k. N. m-1 26

Example of Foundation Plate TRIMAS (RIB software) • Foundation plate with rigid walls in cross section • Solution of the 2 D plate on 3 D space soil elements (TRIMAS software) • Solution with proposed surface subsoil model • Active zone in subsoil in accordance ČSN 73 1001 and EC 7 June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 27

Bending moments and Contact Stresses June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 28

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Design of Testing Equipment Structure June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 30

Soil – foundation interaction test June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 31

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 3 D 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 32

Thank you for your attention This paper was supported by the research project No. FR-TI 2/746, program TIP, Ministry of Industry and Trade , Czech Republic June 13 - June 15, 2012 REC 2012, Brno, Czech Republic 33