SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS

1. DOTTORATO DI RICERCA IN INGEGNERIA GEOTECNICA XXII CICLO Consorzio tra: Università di Napoli Federico II, Università di Napoli Parthenope, Seconda Università di Napoli, Università di Salerno, Università del Sannio SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS Tutore: prof. ing. Alessandro Mandolini Dottorando: ing. Raffaele Di Laora

2. AIM OF THE THESIS Tobetterunderstand the mathematical and physicalmeaningofkinematicinteraction To PROVIDE SIMPLIFIED FORMULAS FOR EVALUATING ITS EFFECTS IN TERMS OF BENDING MOMENTs (INTERFACE AND PILE head) SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS To FIND SIMPLY RULES TO ESTIMATE THE IMPORTANCE OF “FILTERING EFFECT” EXERTED BY PILES ON FOUNDATION INPUT MOTION To INVESTIGATE THE RELATIVE IMPORTANCE OF KINEMATIC VS. INERTIAL INTERACTION To PROVIDE A CRITERION TO COMBINE INERTIAL AND KINEMATIC MAXIMUM EFFECTS

3. SOIL-STRUCTURE INTERACTION SEISMIC SOIL-STRUCTURE INTERACTION FR PILE SUPPORTED SYSTEMS ONLY IN ELASTICITY

4. SOIL-STRUCTURE INTERACTION SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS

5. SOIL-STRUCTURE INTERACTION Onecouldalsodefinekinematicinteraction in a different way. Forexample, kinematicinteractioncouldbe the phenomenongenerated, under seismicmotion, whenonlysoil and piles are present, withoutanyrestraint and structure. SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS In this way, kinematicinteractionhavesensealso, forexample, in plasticity. Unfortunately, summingthiskinematicinteractionto the inertialone, onedoesn’t obtain the complete interaction. Then: Kinematicinteractionhavesenseonlywithreferencetoelasticityhypothesis and rigidrestraint at pile head

6. SIMPLIFIED FORMULAS DOBRY & O’ROURKE (1983) MYLONAKIS (2001) SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS NIKOLAOU ET AL. (2001)

7. KINEMATIC INTERACTION NUMERICAL ANALYSES • linearelasticbehaviourofpiles and soil • boundaryconditions: verticaldisplacementrestrained • modaldamping (10% forallmodes) • solutionmethod: mode superposition • frequency domain analysis • finite elements: 8-node bricks (isoparametric) HYPOTESES: SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS

8. KINEMATIC INTERACTION FREQUENCY DOMAIN ANALYSYS • Advantages of frequency domain analyses: • more accurate • very quick (about 100-200 times faster) SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS • A frequency domain analysis is performed: • performing a modal analysis extracting a certain number of modes; • applying a unit acceleration at bedrock variable with frequency; • reading the steady-state response in terms of the various parameters of interest (displacement, stress and so on); • multiplying the steady-state response by the fourier transform of the bedrock signal • perform a inverse fourier transform to obtain the results in the time domain

9. KINEMATIC INTERACTION COMPARISON WITH EERA SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS MAXIMUM ACCELERATION AGAINST DEPTH ACCELERATION TIME HISTORY AT SURFACE ACCELERATION SPECTRUM AT SURFACE HOMOGENEOUS SOIL Vs = 400 m/s RIGID BEDROCK DEPTH : 30 m INPUT SIGNAL: TOLMEZZO DAMPING b = 10%

10. KINEMATIC INTERACTION GROUP EFFECTS SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS HOMOGENEOUS SOIL Vs = 400 m/s NO DIFFERENCE AMONG PILES OF THE SAME GROUP HOMOGENEOUS SOIL Vs = 100 m/s

11. KINEMATIC INTERACTION 2-LAYERS SOIL AGAIN, LITTLE DIFFERENCE BETWEEN SINGLE PILE AND PILE IN A GROUP SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS Vs1 = 100 m/s BENDING MOMENTS MUCH LARGER WITH RESPECT TO HOMOGENEOUS SOIL FAR FROM THE INTERFACE PILE DEFORMATIONS ARE EQUAL TO SOIL DEFORMATIONS Vs2 = 400 m/s THE INTERFACE IS ONLY A SINGULARITY AND ITS EFFECTS VANISH WITH DISTANCE

12. KINEMATIC INTERACTION PARAMETRIC STUDY N. 1 FIXED PARAMETERS VARIABLE PARAMETERS SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS 288 CASES

13. KINEMATIC INTERACTION PARAMETRIC STUDY N. 2 FIXED PARAMETERS VARIABLE PARAMETERS SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS 324 CASES

14. KINEMATIC INTERACTION RESULTS – EFFECT OF DEPTH OF INTERFACE When h1 < Labending moment at pile cap increases when increasing h1. This is not due to an increase in surface acceleration, but the constraint applied by stiffer layer limits deformations the more it is close to the pile head (restrained) PILE CAP SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS h1 < La h1 > La When h1 > Laep depends only on the acceleration at surface, the shear wave velocity of the first layer, and the diameter of the pile. The second layer affects the acceleration at surface. E1 = 50 MPa, Vs2/Vs1=1.5, Ep/E1 = 300, d = 1 m LA = 1.5 d (Ep/E1)0.25

15. KINEMATIC INTERACTION RESULTS – EFFECT OF DEPTH OF INTERFACE INTERFACE When h1 < Labending moment at INTERFACE CAN DECREASE OR INCREASE BECAUSE OF THE INTERACTION WITH CAP RESTRAINT, BUT ALWAYS SMALLER THAN IN THE CASE IN WHICH h1 = La When h1 > La IT INCREASES UP TO A CERTAIN DISTANCE FROM PILE TOE, THEN IN DECREASES. h1 < La h1 > La SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS E1 = 50 MPa, Vs2/Vs1=1.5, Ep/E1 = 300, d = 1 m LA = 1.5 d (Ep/E1)0.25

16. KINEMATIC INTERACTION RESULTS – EFFECT OF STIFFNESS CONTRAST GENERALLY, INCREASING STIFFNESS CONTRAST PILE BENDING MOMENT INCREASES SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS ONLY When h1 > La IT IS ALWAYS TRUE. E1 = 50 MPa, h1/d = 16, Ep/E1 = 300, d = 1 m

17. KINEMATIC INTERACTION RESULTS – EFFECT OF STIFFNESS CONTRAST When h1 < La MOMENT AT INTERFACE CAN DECREASE WITH INCREASING STIFFNESS CONTRAST, BECAUSE EVEN IF SOIL SHEAR STRAINS GENERALLY INCREASES, TRANSMISSBILITY DROPS DUE TO INTERFERENCE BETWEEN CAP AND STIFFER LAYER RESTRAINTS SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS BENDING MOMENT AT PILE CAP DEPENDS ON SURFACE ACCELERATIONS E1 = 50 MPa, h1/d = 4, Ep/E1 = 10000, d = 1 m

18. KINEMATIC INTERACTION RESULTS – EFFECT OF PILE-SOIL STIFFNESS RATIO Bending moment alwaysincreaseswhenincreasingstiffnessratio BOTH AT PILE CAP AND AT INTERFACE. SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS IF Ep/E1 INCREASES BECAUSE OF AN INCREASE IN Ep WITH E1 CONSTANT, FREE FIELD SHEAR STRAINS REMAIN CONSTANT, RESULTING IN SMALLER STRAINS IN THE PILE DUE TO ITS GREATER STIFFNESS, BUT THEY DECREASE LESS THAN LINEARLY INCREASING STIFFNESS RATIO. Es = 50 MPa, h1/d = 16, Vs2/Vs1 = 2, d = 1 m

19. KINEMATIC INTERACTION RESULTS – EFFECT OF PILE-SOIL STIFFNESS RATIO AS BENDING MOMENT IS PROPORTIONAL TO PILE BENDING STRAIN AND ITS YOUNG MODULUS, IT INCREASES WITH INCREASING STIFFNESS RATIO. THIS IS ALSO EVIDENT IF EP IS CONSTANT AND E1 DECREASES, BECAUSE THE SOIL STRAINS INCREASE. SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS STURNO Es = 50 MPa, h1/d = 16, Vs2/Vs1 = 2, d = 1 m

20. KINEMATIC INTERACTION EFFECT OF DIAMETER AND LENGHT If the interface is located outside the active length of the pile, bending moments vary cubically against pile diameter SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS This is due to the fact that the pile bending strain at outer fiber is not dependent on pile diameter. Of course its increment increases the active length and the interface can locate inside that, so the εpcan reduce. The same happens for the pile length: if the interface remains outside the active length, the εpin not sensitive to it, but if the length decreases, the part of pile embedded in the second layer can became too short and result to a lower pile bending strain due to a lower constraint of the stiffer layer.

21. KINEMATIC INTERACTION SIMPLIFIED EVALUATION OF INTERFACE MOMENTS SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS h1 > La LA = 1.5 d (Ep/E1)0.25

22. KINEMATIC INTERACTION SIMPLIFIED EVALUATION OF INTERFACE MOMENTS SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS h1 > 0.8 La

23. KINEMATIC INTERACTION SIMPLIFIED EVALUATION OF INTERFACE MOMENTS ALTERNATIVELY, INSTEAD OF γ1, IT CAN BE REPLACED THE QUANTITY (γ1- γ2) SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS

24. KINEMATIC INTERACTION SIMPLIFIED EVALUATION OF INTERFACE MOMENTS Apparently, the last formulation has a drawback with respect to the previous one: with reference to an homogeneous soil, (γ1- γ2) tends to 0, and no bending moment is predicted along the pile, in contrast with the evidence. Actually, even if the previous formulation predicts a non-zero moment in this case, its numerical value is evidently wrong, because it becomes: SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS that is incorrect. The interface acts as a further “source of bending moment”, ruled by other parameters, and this moment adds to the moment acting when the pile is embedded in an homogeneous soil; this mechanism is ruled by different parameters (for example the bending strain is proportional to the diameter). It is evident that, when the stiffness contrast is sharp, the interface practically becomes the unique “source of bending moment” , and (γ1- γ2) tends to γ2.

25. KINEMATIC INTERACTION SIMPLIFIED EVALUATION OF INTERFACE MOMENTS ACCORDING TO THE SPEAKER, PILE BENDING STRAIN DEPENDS ALSO ON SOIL SHEAR STRAINS AROUND THE INTERFACE SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS γ1* = γ1(h1-d) γ2* = γ2(h1+d)

26. KINEMATIC INTERACTION SIMPLIFIED EVALUATION OF INTERFACE MOMENTS When h1 < la, no correlationexistsbetween pile bending strain and free fieldshear strain SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS Stiffness contrast the strains (both free-field and pile) are very small the effect of the pile stiffness is limited. The pile, in fact, has no space to deform (only 2 diameters), because constrained, and then it is anyway rigid, regardless of its Young modulus

27. KINEMATIC INTERACTION SIMPLIFIED EVALUATION OF PILE CAP MOMENTS When h1 > la, PILE FOLLOWS FREE-FIELD ALSO IN 2-LAYERS SOILS PILE CURVATURE AT PILE CAP IS EQUAL TO FREE-FIELD SOIL CURVATURE SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS No seismiclocalresponseanalysisrequired!

28. KINEMATIC INTERACTION SIMPLIFIED EVALUATION OF PILE CAP MOMENTS SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS When h1 > la, PILE bending strain at pile capisnotdependent on pile slenderness The pile follows the soilalsoifthere are more thantwolayersbelow the interface

29. KINEMATIC INTERACTION MODIFY OF THE FOUNDATION INPUT MOTION kinematic interaction between soil and piles results in two “KINEMATIC” effects: modify of the seismic signal at the base of the superstructure A ROTATIONAL COMPONENT OF MOTION RISES (IMPORTANT OLY FOR VERY TALL STRUCTURES) SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS The importance of the “filtering effect” exerted by the piles depends on various parameters; with reference to two-layers soil deposits, the primary variables influencing the phenomenon are, in analogy with bending moments: the stiffness contrast the depth of the interface the stiffness ratio between pile and soil the frequency of excitation

30. KINEMATIC INTERACTION MODIFY OF THE FOUNDATION INPUT MOTION SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS d = 0.5 m, h1/d = 16, Vs2/Vs1 = 3, Ep/Es1 = 1500 GENERALLY PILES EXERT A FILTERING EFFECT, CUTTING ONLY HIGH FREQUENCIES

31. KINEMATIC INTERACTION MODIFY OF THE FOUNDATION INPUT MOTION SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS d = 1 m, h1/d = 2, Vs2/Vs1 = 6, Ep/Es1 = 10000 IN EXTREME CASES, FILTERING EFFECT IS VERY IMPORTANT ALSO FOR LOW FREQUENCIES (IN CONTRAST WITH GAZETAS, 1984)

32. KINEMATIC INTERACTION MODIFY OF THE FOUNDATION INPUT MOTION the foundation and free-field motion tend to be more and more different: SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS increasing the stiffness ratio Increasing the stiffness contrast Increasing the importance of high frequencies of the bedrock signal decreasing the value of h1/LA

33. KINEMATIC INTERACTION MODIFY OF THE FOUNDATION INPUT MOTION Analysing the results of the two parametric studies, looking at free field and foundation signals (612 x2 = 1224 spectra), it follows that in very rare cases in which the following conditions: h1< La Vs2/Vs1> 3 Ep/Es1 ≥ 10000 SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS are contemporary present, it is possible to neglect the filtering effect (without a too large conservatism) only for structural periods T1 > 0.5 s BORGO CERRETO STURNO d = 1 m, h1/d = 2, Vs2/Vs1 = 6, Ep/Es1 = 10000

34. KINEMATIC INTERACTION MODIFY OF THE FOUNDATION INPUT MOTION In OTHER (FREQUENT) CASES, it is possible to neglect the filtering effect exerted by the piles only when the structural period is greater than 0.3 s SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS BORGO CERRETO STURNO d = 1 m, h1/d = 16, Vs2/Vs1 = 6, Ep/Es1 = 1000

35. KINEMATIC INTERACTION MODIFY OF THE FOUNDATION INPUT MOTION It’s important to clarify that the analyses have been undertaken considering the superstructure as a SDOF system. SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS These conclusions can be considered still valid if the structure (the real MDOF system) is regular, so the contribution of the other modes (CHARACTERISED BY HIGHER FREQUENCIES) is not significant Moreover, the analyses are elastic; it is evident that non linearity can increase this difference, for example, increasing the stiffness ratio. It’s anyway important to keep in mind that referring to free-field motion for inertial interaction analyses is always conservative.

36. KINEMATIC INTERACTION IT HAS BEEN HIGHLIGHTED THE ROLE PLAYED BY THE DIFFERENT PARAMETERS THAT HAVE A SIGNIFICANT INFLUENCE ON KINEMATIC INTERACTION SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS SIMPLIFIED FORMULAS HAVE BEEN PROPOSED TO SIMPLY EVALUATE KINEMATIC BENDING MOMENT AT INTERFACE AND PILE HEAD WHEN INTERFACE IS LOCATED BEYOND THE ACTIVE LENGTH OF THE PILE IN THE CASES IN WHICH H1 < LA ONE CAN ESTIMATE (CONSERVATIVELY) THESE MOMENTS PLACING THE INTERFACE AT A DEPTH EQUAL TO THE ACTIVE LENGHT IT HAS BEEN FOUND A CRITERION TO ESTABLISH IN WHICH CASES IT IS POSSIBLE TO NEGLECT THE FILTERING EFFECT EXERTED BY PILES

37. KINEMATIC VS. INERTIAL INTERACTION Recent ITALIAN Codes impose to evaluate the effects of kinematic interaction only under certain conditions, but regardingless of the amount and the distribution of masses of the structure. SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS It is evident that it should be allowable to neglect kinematic interaction when its effects are negligible with respect to inertial ones; for this reason the Codes indications appears to be incomplete, as the inertial effects are proportional to the structure mass, while kinematic ones are evidently not dependent on it. To investigate the relative importance of inertial vs. kinematic interaction (and then to verify the veracity of the indications of the Codes), once it has been estimated the effects of the latter through the formulas proposed, it has been built a simple tool for evaluating the foundation impedance and the resulting inertial effects at piles top.

38. KINEMATIC VS. INERTIAL INTERACTION SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS RANDOLPH’S EXPRESSIONS FOR BOTH PILE-SOIL COMPLIANCES AND INTERACTION COEFFICIENTS HOMOGENEOUS SOIL

39. INERTIAL VS. KINEMATIC INTERACTION EFFECT OF PILE YOUNG MODULUS SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS

40. INERTIAL VS. KINEMATIC INTERACTION EFFECT OF SOIL YOUNG MODULUS SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS

41. INERTIAL VS. KINEMATIC INTERACTION EFFECT OF SOIL YOUNG MODULUS Vs2/vs1 = 3 SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS

42. INERTIAL VS. KINEMATIC INTERACTION EFFECT OF PILE RADIUS SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS

43. INERTIAL VS. KINEMATIC INTERACTION EFFECT OF PILE SPACING SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS

44. INERTIAL VS. KINEMATIC INTERACTION EFFECT OF NUMBER OF PILES SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS

45. INERTIAL VS. KINEMATIC INTERACTION EFFECT OF M / H SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS

46. INERTIAL VS. KINEMATIC INTERACTION PHASE LAG BETWEEN KINEMATIC AND INERTIAL EFFECTS IN GENERAL, TIME HISTORIES OF KINEMATIC AND INERTIAL STRESSES ARE OUT-OF-PHASE. SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS IF KINEMATIC AND/OR INERTIAL EFFECTS ARE ESTIMATED ONLY WITH REFERENCE TO THEIR MAXIMA, IT RISES A PROBLEM: HOW TO COMBINE THEM? SUMMING THEIR MAXIMA, IN FACT, CAN BE TOO OVERCONSERVATIVE. IS IT POSSIBLE TO EVALUATE THE PHASE LAG A PRIORI?

47. INERTIAL VS. KINEMATIC INTERACTION PHASE LAG BETWEEN KINEMATIC AND INERTIAL EFFECTS KINEMATIC SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS INERTIAL (IF THE MOMENT DUE TO RAFT ROTATION PREVAILS)

48. INERTIAL VS. KINEMATIC INTERACTION PHASE LAG BETWEEN KINEMATIC AND INERTIAL EFFECTS Is important to notice that the phase lag OF EACH HARMONIC is independent of kinematic interaction, depends only on the inertial one, through the structural period SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS NEVERTHLESS, THE PHASE LAG DEPENDS ALSO ON interaction, because it depend on where are prevalent harmonics of the surface free-field signal (rigorously foundation motion). ONE CAN JUDGE A PRIORI THE PHASE LAG BETWEEN KINEMATIC AND INERTIAL INTERACTION PERFORMING A FREE-FIELD ANALYSIS LOOKING AT THE FOURIER SPECTRA OF SURFACE SIGNAL COMPARING IT WITH THE STRUCTURAL PERIOD

49. INERTIAL VS. KINEMATIC INTERACTION PHASE LAG BETWEEN KINEMATIC AND INERTIAL EFFECTS NUMERICAL ANALYSES SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS • linearelasticbehaviourofpiles and soil • boundaryconditions: verticaldisplacementrestrained • modaldamping (10% forallmodes) • solutionmethod: mode superposition • frequency domain analysis • finite elements: 8-node bricks (isoparametric) HYPOTESES:

50. INERTIAL VS. KINEMATIC INTERACTION PHASE LAG BETWEEN KINEMATIC AND INERTIAL EFFECTS In the casesshown in the figures the moment due toraft rotation prevails LOOKING AT THE SURFACE FOURIER SPECTRUM WITH REFERENCE, FOR ISTANCE, TO CASE A – STURNO SIGNAL, IT CAN BE NOTICED THAT PREDOMINANT HARMONICS HAVE LOWER FREQUENCIES (WITH RESPECT TO THE STRUCTURE). FOLLOWING THIS METHOD, THEN, KINEMATIC AND INERTIAL EFFECTS HAVE TO BE OUT-OF-PHASE. In the case b – tolmezzosignal, predominantharmonicof the surface free fieldsignal are closeto the structurefrequency (thatisequalto the groundone→ resonance). Thereshouldbe a phaselagequalto90°. SEISMIC SOIL-STRUCTURE INTERACTION FOR PILE SUPPORTED SYSTEMS