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abstractThe influence of nonlinearity on the dynamic response of cast-in-situ reinforced concrete piles subjectedto strong vertical excitation was studied. Forced vibration test of single piles (L/d=10, 15, 20) and 2 2pile groups (s/d=2, 3, 4 for each L/d) were conducted in the field for two different embedded conditions ofpile cap. From the measured nonlinear response curves, the effective pile–soil system mass, stiffness anddamping were determined and the nonlinear response curves were back-calculated using the theory ofnonlinear vibration.52537
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The test results were compared with the continuum approach of Novak withdynamic interaction factor approach using both linear and linear-equivalent numerical methods.Reasonable match between the measured and predicted response was found for linear-equivalentmethods by introducing a weak boundary-zone around the pile to approximately account for thenonlinear behaviour of pile–soil system. The test data were used to establish the empirical relationship inorder to estimate the extent of soil separation around the pile with soil under vertical vibration. 1. IntroductionDynamic pile–soil interaction is a very complex problem and ithas been a subject of broad interest. A number of solutions havebeen developed for the dynamic linear analysis of piles such as (i)using the concept of elastic subgrade reaction [1] for obtainingsoil springs, (ii) treating the pile problem as a case of onedimensional wave propagation in a rod [2], (iii) elastic half spaceapproach [3,4]; (iv) continuum methods using finite element orother numerical techniques [5]. These approximate solutions arevery useful in providing insights into the mechanism of dynamicpile–soil interaction. However, in reality both separation andslippage can appear due to the formation of weak bond at thecontact between the soil and the pile. In addition, the soil regionimmediately adjacent to the pile may experience high strain levelunder dynamic loading and consequently, the pile–soil systembehaves in a nonlinear manner.A perfect theoretical solution to dynamic pile–soil interactiondue to slippage and nonlinearity is very difficult and thereforeapproximate methods need to be used. Matlock et al. [6] introducedlumped mass models with nonlinear discrete springs, dashpot, andfriction elements. The combination of these elements makes itpossible to generate a variety of nonlinear force–displacement relationship. Another approximate approach, which includes a weakcylindrical zone or inner boundary zone around the pile, wasproposed by Novak and Sheta [7]. One of the simplificationsinvolved in the original boundary-zone concept was that the innerzone was neglected to avoid the wave reflections from the interfacebetween the inner boundary zone and the outer zone. To overcomethis problem Veletsos and Dotson [8] proposed a scheme that canaccount for the mass of the boundary zone. Mitwally and Novak [9]accounted approximately for the nonlinear behaviour of the soiladjacent to the pile by incorporating an annular weak zone withreduced soil shear modulus and a slippage element. El Naggar andNovak [10] further extended this model by accounting for loadingrate effects.
Some of the effects of the boundary-zone mass wereinvestigated by Novak and Han [11] and it was found that ahomogeneous boundary zone with a non-zero mass yields un-dulated impedances due to wave reflections from the fictitiousinterface between the near field and the far field. To solve thisproblem Han and Sabin [12] proposed a model of ideal boundaryzone with nonreflective interface. El Naggar and Novak [13,14]presented a model for the analysis of pile axial response allowing fornonlinear soil behaviour, energy dissipation through radiationdamping, soil hysteresis, and the loading rate dependency of thesoil resistance. An analytical solution to the plane strain axisym-metric problem of a vertically vibrating pile slice was presented bysome researchers [15,16] for different variation of soil shearmodulus.Although there have been a large number of analytical studieson the dynamic response of piles, relatively a few dynamic load tests on piles have been reported in the literature. Novak andGrigg [17] conducted the dynamic experiments on small-scalesingle piles and pile groups in the field. A series of dynamicexperiments were conducted with a group of 102 closely spacedpiles for all modes of vibration by El Sharnouby and Novak [18]and these experimental results were evaluated by Novak and ElSharnouby [19]. Similar field dynamic tests on small-scale pileswere conducted by Burr et al. [20]. The full scale dynamic fieldtests on pile were conducted by a few researchers [21,22]. Boththeoretical and experimental studies have shown [23–25] that thedynamic response of the piles is very sensitive to the properties ofthe soil in the vicinity of the pile shaft.The main objective of the present investigation is to study thenonlinear dynamic behaviour of piles under strong verticalvibrations. A broad study involving both model dynamic testingof pile foundation and theoretical analysis is described. In the firstpart of the paper, the methodology and the results of verticalvibration field tests are presented. The dynamic tests were carriedout on model reinforced concrete single pile and 2 2 pile groups(s=2d,3d, and 4d, where d is the diameter of the pile and s is thecentre-to-centre distance of the piles in a pile group). In thisstudy, three different pile lengths (L/d=10, 15, 20 and d=0.10m,where L is the length of the pile) were used. Soil properties at thissite were determined by conducting in-situ tests and laboratorytests. Frequency versus amplitude curves of piles were experi-mentally established in the field for different intensities ofexcitation, different static loads on pile, and different contactconditions of the pile cap with the soil.In the second part, the observed response is compared withtheoretical solutions. First the effective pile–soil system mass,stiffness and damping are determined using the methodologyproposed by Novak [26] from the measured nonlinear frequencyamplitude response curves. The nonlinear response curves areback-calculated using the theory of nonlinear vibration. Secondly,the test results are compared with Novak’s continuum approachusing both linear and linear-equivalent numerical methods. Thestiffness and damping of a single pile are computed on the basis ofa method given by Novak et al. [27] and Novak and Aboul-Ella[28,29]. To account for the pile–soil–pile interaction problem orgroup effects on the dynamic response of piles, the dynamicinteraction factors [30,31] are used. For linear-equivalent numer-ical solution, an approximate approach which includes a weakcylindrical zone around the pile proposed by Novak and Sheta [7]is used to account for the nonlinear characteristics of piles. Twodifferent linear-equivalent models are used: (1) using no separa-tion of pile with constant boundary zone parameters with depth;(2) using separation of pile with varying boundary zoneparameters with depth. The methodology involved in this studyis incorporated in the computer program DYNA 5 which isformulated by Novak et al. [32]. This program is used to presentthe dynamic behaviour of piles as frequency response curves forvertical displacement, stiffness, and damping constants.2. Site conditions and test pilesThe field tests were conducted at the site which was locatedadjacent to Hangar, at Indian Institute of Technology, KharagpurCampus, India. First soil samples were collected from three boreholes (BH) located at different places of the site. The subsurfaceinvestigation indicated that the test site was underlain by threedifferent soil layers up to a depth of 2.80m. Both laboratory andin-situ tests were performed to characterize the static anddynamic properties of the soil. The laboratory experimentsincluded natural moisture content, bulk density, triaxial test,Atterberg limits test and particle size distribution analysis of soil.In the in-situ test consisted of standard penetration tests (SPT) todetermine N value and seismic crosshole tests for determining theshear wave velocity (Vs) of soil layer. Typical S-wave arrival withtime at two bore holes of seismic crosshole tests at the depth of 0.50m is shown in Fig. 1.