Numerical methods for pile modeling

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Numerical methods for pile modeling

  1. 1. Mohammad Reza Falamarz-Sheikhabadi Candidacy Exam Fall 2012 Drexel University, Civil Engineering Department 1
  2. 2.  Pile foundation definition Different methods for pile modeling  Winkler method  Beam on nonlinear Winkler foundation (BNWF)  Finite element method Absorbing boundary conditions  Viscous damping boundary model  Perfectly matched layer Discussion on BNWF Conclusion References Drexel University, Civil Engineering Department 2
  3. 3. Drexel University, Civil Engineering Department 3
  4. 4. Pile usually represents aslender structural elementthat is driven into theground. However, a pileis often used as a genericterm to represent alltypes of deepfoundations.Here, I talk about normalsize piles (250-600 mm) Ref. 1 Drexel University, Civil Engineering Department 4
  5. 5. Different types of pilefoundations to carryvertical, horizontal orinclined loads fromsuperstructure. Ref. 2 Drexel University, Civil Engineering Department 5
  6. 6. Pile foundations mayconsists of an individualpile or a group of piles.Although a pile group iscomposed of a numberof individual piles, thebehavior of a pile groupis not equivalent to thesum of all the piles as ifthey were separateindividual piles Ref. 2 Drexel University, Civil Engineering Department 6
  7. 7. The behavior of a pilegroup is more complexthan an individual pilebecause of the effect ofthe combination ofpiles, interactionsbetween the piles inthe group, and theeffect of the pile cap. Ref. 2 Drexel University, Civil Engineering Department 7
  8. 8. Drexel University, Civil Engineering Department 8
  9. 9.  Continuum method Winkler method Beam on nonlinear Winkler foundation Finite element method Ref. 3 Drexel University, Civil Engineering Department 9
  10. 10. The Winkler approach is theoldest method for estimatingpile deflections and bendingmoments. The approach modelthe soil as a series ofunconnected linear springswith stiffness, Es, expressed inunits of force per length. Ref. 2 Drexel University, Civil Engineering Department 10
  11. 11. Limitations:1. The method ignores the nonlinear characteristics of soil.2. The axial load effects are ignored.3. The soil model used in the technique is discontinuous. Ref. 2 Drexel University, Civil Engineering Department 11
  12. 12. The p–y method isversatile and can be usedto solve problemsincluding different soiltypes, layeredsoils, nonlinear soilbehavior, different pilematerials, crosssections, and different pilehead connectionconditions. Ref. 4 Confining pressure Drexel University, Civil Engineering Department 12
  13. 13. Considering that both pilesand soil can behave in anonlinear manner duringextreme events, the use ofp-y methods for definingthe lateral stiffness of pile-soil model for seismicanalysis (secant stiffness asa function of piledeformation) has beenused since the seventies. Ref. 5 Why sometimes I have used p-y elements and sometimes p-y springs? Drexel University, Civil Engineering Department 13
  14. 14. In this method, the reaction of soilsurrounding the pile is modeled aslocalized springs: a series of springsalong the shaft (the t-z curves) andthe spring attached to the tip orbottom of a pile (the Q-z curve). Theload transfer or unit friction forcealong the shaft is shown by t, Q is thetip resistance of the pile incompression, and z is the settlement(for static analysis) or verticaldeformation (for dynamic analysis) ofsoil at the location of a spring. Ref. 1 Drexel University, Civil Engineering Department 14
  15. 15. Since analyzing thepile group supportedstructures underlateral loading needsincluding the effectsof rocking motions, inthe BNWF, all localizednonlinearsprings, namely, p-y, t-z and Q-z shouldbe considered Ref. 6 Drexel University, Civil Engineering Department 15
  16. 16. The bending momentsfor the corner pilesshould be increasedfor closely spacedpilesSide-by-side Corner pile spacing moment modification factor 3D 1 2D 1.2 1D 1.6 Ref. 8 Ref. 2 Drexel University, Civil Engineering Department 16
  17. 17. A popular method toaccount for shadowingeffect is to incorporatep-multipliers into the p-y method of analysis. Thep-multiplier valuesdepend on pile positionwithin the group and pilespacing. Ref. 7 Drexel University, Civil Engineering Department 17
  18. 18. Factors influencing p-multiplier: pile spacing group arrangement group size pile head fixity soil type and density Ref. 8 Drexel University, Civil Engineering Department 18
  19. 19. Limitations:1. The p-y method is based on pseudo-static loading for while lateral forces from the upper structure are only applied,2. The accuracy of the p–y method depends on the number of tests and the variety of tested parameters, such as geometry and stiffness of pile, layers of soil, strength and stiffness of soil, and loading conditions.3. The effects of pile diameter have not been considered in the primary relations of p-y curves.4. The pile cap effects are usually ignored and cap pile are considered rigid.5. For pile groups, using p-multiplier method oversimplifies the problem. Drexel University, Civil Engineering Department 19
  20. 20. The FE method has the ability of permitting toaccount for soil nonlinearity by applyingappropriate constitutive models, such as theDrucker-Prager, Cam-Clay or Mohr Coulombformulation, and to use gap-elements tomodel possible pile soil separation. Ref. 9 Too difficult and time consuming! Drexel University, Civil Engineering Department 20
  21. 21. Limitations:1. The cost of the specialized software.2. The time consuming model generation.3. The time required for the non-linear analysis.4. The difficulty in the interpretation of the result in terms of common pile (beam) variables.5. The uncertainties associated with soil non-linear modeling in 3D. Ref. 9 Drexel University, Civil Engineering Department 21
  22. 22. Drexel University, Civil Engineering Department 22
  23. 23. Bounded medium Semi-infinite mediumThe boundaries absorb the waves should be transmitted in semi-infinite medium. Bounded medium Drexel University, Civil Engineering Department 23
  24. 24.  Viscous damping boundary method Perfectly matched layer Infinite elements Consistent dashpot, spring and mass method And other numerical methods Ref. 3 Drexel University, Civil Engineering Department 24
  25. 25. The simplest local ABC isthe classical normalimpedance or standardviscous boundary. Itsperformance is known todeteriorate as the positionapproaches the source ofperturbation especially inthe low-frequency limit. Ref. 10 This method has been modified in different manners! Drexel University, Civil Engineering Department 25
  26. 26. 1. It can be only used for dynamic analyses.2. The method is able to absorb only primary and secondary waves under an angle of incidence of 90o.3. The interested medium should be elastic and linear. Ref. 10 Drexel University, Civil Engineering Department 26
  27. 27. The PML is only reflectionlesswhen the exact wave equationis solved. In practicalapplications, when theapproximate methods likefinite-difference-time-domain (FDTD) or FE areapplied for modeling, theanalytical perfection of thePML is no longer valid and souser should consider thispoint in the analysis. !!!Soil=Elastic Medium!!! Ref. 12 Drexel University, Civil Engineering Department 27
  28. 28. A newly discovered silentboundary is the perfectlymatched layer method, firstintroduced for the use ofelectromagnetic waves. Theconcept has been designeddesigned to absorbthoroughly any incident wavewithout reflection, for anyincident angle and at anyfrequency beforediscretization. Ref. 11 Drexel University, Civil Engineering Department 28
  29. 29. 1. When the approximate methods like finite-difference-time-domain (FDTD) or FE are applied for modeling, the analytical perfection of the PML is no longer valid and so user should consider this point in the analysis.2. Interested region should be elastic (such an assumption for soft or saturated soil condition and large- scale structures is absolutely unacceptable).3. Its performance depends on the type of seismic waves. Ref. 11 Drexel University, Civil Engineering Department 29
  30. 30. Drexel University, Civil Engineering Department 30
  31. 31.  In spite of the fact that the seismic responses of structures are resultant of the combined action of at least three translational components of ground motion (ignoring two rocking and one torsional earthquake components), the coupling effects of these components in the modeling of pile foundations are commonly ignored in the analytical and numerical studies. Drexel University, Civil Engineering Department 31
  32. 32. 20 50 40 40 30 15 30 20 10 20 10 a (t) cm/s/sa (t) cm/s/s a (t) cm/s/s 5 10 0 0 0 -10 R V T -5 -10 -20 -10 -20 -30 -15 -30 -40 -20 -40 -50 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 t t t Translational components 20 15 15 15 10 10 10 (t) mrad/s/s(t) mrad/s/s (t) mrad/s/s 5 5 5 0 0 -5 0 V  R  T -10 -5a a a -15 -5 -10 -20 -25 -10 -15 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 t t t Rotational components Drexel University, Civil Engineering Department 32
  33. 33. 4500 8000 8000 4000 7000 7000 3500 6000 6000 3000 5000 5000 2500A () A () A () 4000 4000 V R T 2000 3000 3000 1500 1000 2000 2000 500 1000 1000 0 0 0 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35  (Hz)  (Hz)  (Hz) Translational components 4000 1800 2500 3500 1600 1400 2000 3000 2500 1200 1500( ) ( ) ( ) 1000 2000  V T R A 800 A A 1500 1000 600 1000 400 500 500 200 0 0 5 10 15 20 25 30 35 0 0  (Hz) 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35  (Hz)  (Hz) Rotational components Drexel University, Civil Engineering Department 33
  34. 34.  Pile caps are often considered rigid and their effects in lateral resistance of pile group are considered ignorable. Both of these assumptions may cause an unknown error in estimation of actual behavior of pile foundations. Based on the size and configuration of pile group, spatial variation of strong ground motions, uncertainty in distribution of mass and stiffness of piles, unequal distribution stress on piles (shadowing effects), probable damages and torsional earthquake component; a considerable torsional moment may induce in the pile caps. This effect is usually ignored in the typical two- dimensional analyses. Although there are many recorded data on the ground surface due to various earthquakes in different site conditions, it is not the case for data recorded underground surface. Therefore, more data are required to estimate the seismic loading of deep piles. It should be pointed out that soil is more anisotropic and non- homogenous in depth. Drexel University, Civil Engineering Department 34
  35. 35. Drexel University, Civil Engineering Department 35
  36. 36. Based on the previous research on soil-pileinteraction, although it seems that the p-y method can beconsidered as an efficient technique applicable to manypractical applications, it still needs some modifications anddevelopments in order to give more reliable results in thesoil-pile interaction analyses. Drexel University, Civil Engineering Department 36
  37. 37. 1. Chen, W. F, Duan, L, Bridge Engineering Handbook, CRC press LLC (2000).2. Murthy, V. N. S, Geotechnical Engineering: Principles and practices of soil mechanics and foundation engineering, Marcel Dekker, Inc.3. Shin, H, Arduino, P, Kramer, S. L, Mackie, K, Seismic response of a typical highway bridge in liquefiable soil.4. Gazetas, G, Dobry, R, Simple Radiation Damping Model for Piles and Footings, Journal of Engineering Mechanics ASCE, Vol. 110 (1984) 937-956.5. Boulanger, R. W, Curras, C. J, Kutter, B. L, Wilson, D. W, Abghari, A, Seismic soil-pile-structure interaction experiments and analyses, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 125 (1999) 750- 759.6. Curras, C. J, Boulanger, R. W, Kutter , B. L, Wilson, D. W, Dynamic experimental and analysis of a pile-group- supported structure, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 127 (2001) 585-596.7. Comodromos, E. M, Papadopoulou, M. C, Explicit extension of the p-y method to pile groups in cohesive soils, Computers and Geotechnics, Vol. 47 (2013) 28-41.8. Mokwa, R. L, Investigation of the resistance of pile cap to lateral loading, PhD thesis, Virginia Polytechnic Institute and State University (1999).9. Yang, Z, Jeremic, B, Numerical analysis of pile behavior under lateral loads in layered elastic-plastic soils, International Journal for Numerical Methods in Geomechanics, Vol. 2 (2002) 1-31.10. Kramer, Steven L, Geotechnical earthquake engineering, Prentice Hall, Inc., Upper Saddle River, New Jersey, (1996).11. Basu, U, Chopra, A. K, Perfectly matched layers for time-harmonics elastodynamics of unbounded domains: theory and finite-element implementation, Computer methods in applied mechanics and engineering, 192 (2003) 1337-1375.12. Hasting, F. D, Schneider, J. B, Broschat, S. L, Application of the perfectly matched layer (PML) absorbing boundary condition to elastic wave propagation, Journal of Acoustic Society of America, 100 (1996) 3061- 3069. Drexel University, Civil Engineering Department 37
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