Soil Dynamics and Earthquake Engineering 43 (2012) 287–299

Contents lists available at SciVerse ScienceDirect

Soil Dynamics and Earthquake Engineering

0267-72

http://d

n Corr

E-m

o.tavaso

journal homepage: www.elsevier.com/locate/soildyn

Characteristics of non-uniform cross-section piles in drivability

Mahmoud Ghazavi a,n, Omid Tavasoli b

a Civil Engineering Department, K. N. Toosi University of Technology, Tehran, Iranb Civil Engineering Department Science and Research Branch, Islamic Azad University, Tehran, Iran

a r t i c l e i n f o

Article history:

Received 21 August 2010

Received in revised form

2 September 2011

Accepted 14 July 2012Available online 25 August 2012

61/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.soildyn.2012.07.017

esponding author. Tel.: þ98 21 88779623; f

ail addresses: ghazavi_ma@kntu.ac.ir (M. Gha

li@srbiau.ac.ir (O. Tavasoli).

a b s t r a c t

A numerical analysis of pile driving for tapered piles is presented in this paper. A three-dimensional

finite difference analysis for tapered angle and geometry effects has been used on pile driving response

of tapered piles. The simulation considers an idealization for pile–soil system in drivability. The vertical

pile is assumed to have linear and elastic behavior. It is also assumed that the soil is elasto-plastic

material and its failure stage is controlled using the Mohr–Coulomb failure criterion. At the soil–pile

contact surfaces along the pile shaft and pile toe, slip is allowed to occur during the driving procedure

using interface elements. Quiet boundaries are used to prevent waves traveling in the lateral and

vertical directions for the soil. Cylindrical, fully tapered, and semi-tapered piles were analyzed.

The results obtained from numerical analyses were compared with those obtained from available

laboratory tests and also other available numerical data, resulting in a satisfactory agreement.

The results have shown that among piles of the same length and material volume, with increasing

the taper angle from zero (representing a cylindrical pile), the driving stresses decrease and the

permanent pile toe settlement (set) increases. These are interesting in pile driving and are on the safe

side for driven piles and increasing the driving efficiency. It has also been found that the geometry of

the pile can generally influence the pile drivability. Generally speaking, tapered and partially tapered

piles offer better drivability performance than cylindrical piles of the same volume and length.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

An intensive pile use is widespread in traditional areas such asbuildings and machine foundations, especially when soft depositsare present. In practice, various engineering applications may becited for piles such as machine foundations, high rise buildings,platforms and so on, where heavy dead and live loads from wind,earthquakes, nuclear power plants, airplane impact, movingtraffic, gas explosion and so on are encountered.

In practical situations, it is of interest to drive piles into theground more easily. Therefore, it is required to develop simple butaccurate model for investigation of factors affecting the piledriving procedure. In the early stage of development of the piledriving practice, Newton’s law was applied to pile driving analysison the assumption that the energy delivered by the hammerwould be immediately transmitted to the tip of pile. It is ofinterest to find a quick method to analyze the pile drivability anduse it to optimize pile driving procedure. Two important points inpile driving are the stresses developed in the pile during drivingand the amount of penetration of pile into the soil due to the

ll rights reserved.

ax: þ98 21 88779476.

zavi),

hammer impact. The former deserves the pile safety and the lattercan be useful in estimation of the pile capacity.

Pile driving analysis has been of significant interest to geo-technical engineers. The pioneer work for pile driving analyses isattributable to smith [17]. He developed a one-dimensional waveequation analysis as applied to the pile driving problems. Smith[17] presented a mathematical solution to the wave equation tosolve complicated pile driving problem. This method considersthe time-dependent events occurring as a result of a hammerimpact on the pile head. In this method, discrete non-linearsprings and dashpots were used for the pile and driving equip-ment. Chow and Smith [1] performed axisymmetric finite ele-ments analysis for solid and pipe piles driven in undrained clays.In this analysis, an elastic-perfectly plastic soil model with a VonMises yield function was used. This study showed significantdifferences in the pile behavior in comparison with one-dimen-sional analysis, especially for piles driven in stiff clays.

Coutinho et al. [2] performed analyses on pile driving foractual cases in the Brazilian coast. In this research, a parametricstudy of several factors affecting driving like pile–soil interface,damping, etc. have been incorporated. Uzag [18] investigated theproblem of open-ended steel pipe pile driven in saturated densesand by performing a finite element study on a model pile. Heverified the results with available experimental data. The soil wasmodeled using the Von Mises failure criterion with isotropic

M. Ghazavi, O. Tavasoli / Soil Dynamics and Earthquake Engineering 43 (2012) 287–299288

hardening to study of the soil plug behavior for several pile–soilinterface friction angles. Mabsout et al. [13,14] studied the piledriving problem by the use of a non-linear behavior for the soil.They studied the behavior of closed-end round concrete pileswith a conical tip driven into the soil in undrained clayey soils inthree-dimensional model.

All the above approaches considered straight-sided piles dueto the widespread use of uniform piles in routine practice. It maybe useful to distribute the pile mass along the shaft with respectto the load level and thus make the pile tapered. The advantagesof tapered piles compared to cylindrical pile have been investi-gated in recent years. For example, axial response of such pilesunder static loading has been investigated using one-dimensionalfinite element method [4] and laboratory tests using model pilesand pressure chamber [19]. The advantage of tapered pilessubjected to axial harmonic vibrations has also been investi-gated [6]. The kinematic response of such piles under earthquakeloading was also demonstrated [3,5]. Field load tests were alsoconducted on tapered piles to investigate their load-carryingcapacity [15]. Full-scale tests were performed on both cylindricaland tapered concrete piles driven into a cohesive soil profile inthe field [7,8]. These tests showed that, in long term, the taperedpile had 80% more capacity than a uniform pile of the samevolume and length.

Sakr et al. [16] have reported laboratory experimental resultsof the bearing capacity of tapered piles. They reported that bothT-C (upper tapered part connected to lower cylindrical part) andC-T (upper cylindrical part connected to lower tapered part) pilesoffer greater bearing capacity than the C (cylindrical) pile. For piledrivability analysis based on FLAC3D, the authors have chosenthese piles studied by Sakr et al. [16].

Fig. 1. Comparison between load-settlelment variation predicted by FLAC and

reported by Wei and El Naggar [19]: (a) stright-sided pile S; (b) tapered pile T1; (c)

tapered pile T2.

Ghazavi and Ahmadi [7,8] reported the results of field axialloading tests on 12 m long tapered and uniform concrete piles.Both piles were 12 m long and driven fully into cohesive satu-rated clayey ground. The results showed that when both piles

Fig. 2. Three-dimensional rod with (a) free-end conditions and (b) an elastic

support at the end.

M. Ghazavi, O. Tavasoli / Soil Dynamics and Earthquake Engineering 43 (2012) 287–299 289

were subjected to an identical load after a certain time, theuniform pile had greater settlement than the tapered pile. More-over, the tapered pile had greater capacity. They had also foundthat the long term capacity of the tapered pile was 80% greaterthat of the uniform pile of the same material volume and length.

Research work on the drivability of tapered piles is rare. Sakret al. [16] compared FRP reinforced concrete pile (FRP-SCC) andtraditional pile materials during pile driving using wave equationanalysis and laboratory tests. They concluded that the taperedgeometry have considerable effects on drivability efficiency andstatic resistance of piles.

There is an evidence in the literature which mentions the realapplications of tapered piles in practice. Rybnikov [15] reportedthe application of cast-in-place tapered piles in the constructionof some projects in the Irtysh Pavlodar region, in the formerSoviet Union. The holes for such piles were drilled by tapereddrilling rigs (end-less screws). In 1990, he believed that such pileswere not widely used because of insufficient study of theiroperating characteristics. In this connection, he performed fieldtests on 4.72 m long in the Palvador Aluminum Plant region in theformer Soviet Union. He found that tapered piles possess 20–30%more bearing capacity than conventional uniform piles of thesame volume and mean radius. He believed that for driven pilesthis increases to 250–300%, while the costs involved to erect suchfoundations were also remarkably reduced, sometimes to 50% ofthose of uniform piles [20].

Zil’berberg and Sherstnev [20] stated that on the recommenda-tion of Odessa Civil Engineering Institute and its forces in Russia,tapered piles were used widely in several projects since performedfield tests showed that the capacity of tapered piles was higher bya factor of 2.5–3 in comparison with prismatic piles.

Horvath and Trochlides [10] reported application of hot-rodsteel tapered driven piles at the well known John F. KennedyInternational Airport (JFKIA) in New York City began in late 1940s.They reported service-load capacity per such pile in excess of1780 kN, with net ultimate axial compressive geotechnical capa-cities of the order of 4450 kN.

As mentioned, there are some advantages of tapered piles tocylindrical piles of the same length and material volume. There-fore, more research work is required to quantify and qualify suchadvantages. In the present study, a three-dimensional analysis for

Table 1Properties of rod used in numerical simulation.

Constitutive model r (kg/m3) n E (MPa)

Linear elastic 2500 0.15 25,000

Fig. 3. Dynamic response of fix-end rod

pile driving is presented using FLAC3D [12]. A cylindrical drivenpile is simulated and its response in drivability is studied. Thenumerical results in this study will be compared with availableexperimental data for tapered piles and also other availablenumerical results for cylindrical piles. The driving of non-uniformconcrete piles with different geometries is simulated and theresults will be presented and discussed.

2. Analysis method

A finite difference scheme is adopted to simulate a three-dimensional model for pile driving analysis, using FLAC3D. It offersan ideal analysis tool for solution of three-dimensional problemsin geotechnical engineering. It is an explicit finite-differenceprogram for simulating the behavior of three-dimensional soilstructures constructed on rock or other materials undergoingplastic flow when their yield limits are reached. Materials arerepresented by polyhedral elements within a three-dimensionalgrid to fit the shape of the object to be modeled. Each elementbehaves according to a prescribed linear or non-linear stress/strain law in response to applied forces or boundary restraints.The material may yield and flow and thus the grid can deform atlarge strain. The explicit Lagrangian calculation scheme and themixed-discretization zoning technique are used in FLAC to ensurethat the plastic collapse and flow are modeled accurately. Thepurpose of the grid generator is to facilitate the creation of allrequired physical shapes in the model. At first, grid generator isdefined and built with different shapes to model radially thegraded mesh around cylindrical-shaped tunnel and cylindricalmesh to model the pile. One important aspect in grid generationis that all physical boundaries to be represented in the modelsimulation must be defined before the solution stepping begins.

The boundary conditions are assigned when the soil–pilemedium is generated. The boundary conditions in the numericalmodeling consist of the values of field variables such as displace-ments that are prescribed at the boundary of the numerical grid.The initials condition also is set to reproduce the in situ state ofstress in the ground. Ideally, the information about the initialstate comes from field measurements but when these are notavailable, the model can be run for a range of possible conditions.

The pile is assumed to be linear and elastic in the presentanalysis and the Mohr–Coulomb failure criterion is used for thesoil that yields when subjected to pile driving loading. The yieldstress depends on the major and minor principal stresses only andthe intermediate principal stress has no effect on yielding.

To absorb energy at the boundaries, quiet boundaries proposedby Kulhmeyer et al. [11] are used in the model. These boundariesinvolve dashpots attached independently to the boundary in the

(a) without and (b) with damping.

M. Ghazavi, O. Tavasoli / Soil Dynamics and Earthquake Engineering 43 (2012) 287–299290

normal and shear directions. The dashpots provide viscousnormal and shear traction that can be introduced directly intothe equation of motion of the grid points lying on the boundary.

There are several instances in geotechnical problems in whichit is desirable to represent planes on which sliding or separationcan occur. Thus it is important to model interfaces. Furthermore,

Fig. 5. Dynamic responses of rod with the elasti

Fig. 4. Dynamic response of free-end rod

interface elements are applied. These elements are characterizedby coulomb sliding and/or shear bonding and have the propertiesof friction, cohesion and dilation, normal and shear stiffness,tensile and shear bond strength. Interface elements are attachedto a zone surface face; two triangular interface elements aredefined for every quadrilateral zone face. Interface nodes are then

c support with variation of elastic modulus.

(a) without and (b) with damping.

Table 2

M. Ghazavi, O. Tavasoli / Soil Dynamics and Earthquake Engineering 43 (2012) 287–299 291

created at every interface element vertex. When another gridsurface comes into contact with an interface element, the contactis detected at interface node, and is characterized by normal andshear stiffness, and sliding properties.

The resistance of the cohesive soil in pile driving appears asthe skin friction and end bearing and is related to the soilundraind shear strength. The skin friction, tx, distributed alongthe pile shaft is determined using:

tx ¼ a:cu ð1Þ

where cu is the undrained shear strength and a is the adhesionfactor depending on the material and the pile installation method.

The dynamic calculation during pile driving is based on theexplicit finite difference scheme to solve the full equations ofmotion using lumped grid point masses derived from the realdensity of surrounding zones.

Properties of soil and pile used in Mabsout et al. [13,14] simulation.

Material r (kg/m3) n c (MPa) f (1) E (MPa)

Clayey soil 1600 0.35 2z 0 10

Pile 2400 0.20 – – 24.86e3

3. Verification

To ensure the validity of the numerical analysis based on FLACfor statically loaded piles, experimental data reported by Wei andEl Naggar [19] on two tapered piles tested a large laboratoryfacility were chosen. They performed tests on instrumented steeltapered piles with a length of 1.52 m, diameters ranging 0.16–0.2 m, and a slenderness ratio of 9 which represents rigid piles.

Fig. 6. (a) Pile–soil system axisymmetric model [13]. (b) Pile–soil system

axisymmetric model in FLAC3D.

The taper angles for tapered piles T1 and T2 were 0.951 and 0.61,respectively. The straight-sided pile (pile S) had a diameter of0.1683 m. The soil was sand and used at two relative densities of18.4% and 32.7%. The friction angles corresponding to thesedensities were 321 and 351, respectively, as reported by Wei andEl Naggar [19]. Fig. 1 compares the reported data from laboratory[19] and those predicted by FLAC. As seen, there is satisfactoryagreement between data.

To verify the predicted results for three-dimensional numer-ical simulation of pile drivabilty, in the first step, analysis ofwave propagation in an elastic rod with a 20 m length and0.25 m radius was preformed and different tip boundary condi-tions are considered to verify the model performance. In thecurrent study, analyses are performed on rod with three end

Fig. 7. Three-dimensional pile–soil system in FLAC3D.

Fig. 8. Force function simulating hammer blow (after [9,13,14]).

Fig. 9. (a) Comparison of top displacement result between FLAC3D and Mabsout

et al. [13,14]. (b) Comparison of tip displacement result between FLAC3D and

Mabsout et al. [13,14].

Fig. 10. Comparison of top velocity result between FLAC3D and Mabsout et al.

[13,14].

M. Ghazavi, O. Tavasoli / Soil Dynamics and Earthquake Engineering 43 (2012) 287–299292

conditions: (1) fixed-end, (2) free-end, (3) a rod with elasticsupport at the end. No soil or other supports are consideredaround the rod shaft and the rod gravity is neglected in theanalysis. Fig. 2a and b shows the three-dimensional rod in 20,301grid points and the boundary conditions of the free-end andelastic support. Rod properties are illustrated in Table 1.

The hammer blow on the rod head is simulated by a half-sinestress wave with an amplitude of 5 MPa and frequency of 320 Hz.Regarding the wave velocity of 3162 m/s in the rod, the wavelength of the half-sine signal generated in the rod is 4.94 m. Torepresent the end dynamic responses, the force and velocityrecords are picked up at 5 m below the rod head to prevent themixing up the upward stress wave and downward reflection fromthe rod head. Figs. 2 and 3 show the analysis results for a rodwithout and with damping effects for fix and free-end rod tip. Theprocedure used in this analysis is as same as PDA test outputpresentations in which the force (F) and the velocity (v) variationswith time are plotted and velocity is multiplied by the rodimpedance (Z¼EA/C) to be equivalent to force (Zv). The timerequired for stress wave to travel between the pickup records andthe rod end is L/C and because of that, the horizontal axis is scaledin it. The force sign conventions are positive and negative forcompressive and tensile waves. The downward displacement of aparticle on the rod section shows a positive velocity and theupward displacement shows a negative velocity. Figs. 3a and 4ashow that after a time equivalent to 2L/C, that is the time requiredfor stress wave to travel between the record point at 5 m belowthe rod head to rod tip and return to the same point (L¼15 m),F wave is suddenly shifted up and Zv wave is shifted down andtheir amplitudes are equal to the generated wave amplitude. Thisobservation is exactly in accordance with one-dimensional wavepropagation theory in rods without damping. The immediate F

and Zv waves shifted down after tip reflections are the reflectionsfrom the rod free head boundary condition. In fact, the downwardinitial compressive wave is reflected as compression type at rodfixed-end and reflected tension type at the rod free-top boundaryconditions.

Figs. 3b and 4b represent similar results for the same rod andloading with a 1% viscous damping ratio for the rod. The F waveand Zv wave amplitudes are attenuated with time as expecteddue to the damping presence in the rod.

As shown in Fig. 4a and b, the results for cases without andwith damping free-end rod dynamic response are similar to lastresults with opposite in sign, variations are observed, which is infact representative of the 1-D longitudinal wave propagation inthe rod with free-end boundary conditions at rod end and head.

In the third series of analyses, a 1 m elastic support wasassumed at the pile tip. The elastic support acting as spring wassimulated by using solid elements similar to ones used for the roditself with the same cross section area of the rod. The springstiffness was varied by changing its elastic modulus from 10 MPato 10,000 GPa, to see the effect on the dynamic response due tothe impact on the rod head. To absorb the portion of the wave notreflected at the tip, a quiet boundary condition was applied at thebottom of the model. The same half-sine stress wave was appliedat the rod head to simulate the dynamic impact. The results arepresented in Fig. 5a–f, for E values of 1 m segment decreasingfrom 10,000 GPa to 10 MPa. For the highest value of E in Fig. 5a,

Table 3Interface strength and deformation parameters in Mabsout et al. [1

Interface strength parameters Interface

Friction angle Cohesion (kPa) Shear sti

61 2z 0.5C

the response is identical to the fixed-end rod and for the lowestone in Fig. 5f the response is the same as the free-end rod. Agradual transition is observed between compressive to tensile

3,14] simulation.

deformation parameters

ffness, Ks (kN/m3) Normal stiffness, Kn (kN/m3)

0.5C

Fig. 11. (a) Schematic elevation of pressure chamber, tested pile and hammer [16]. (b) Oblique view of the pressure chamber, tested pile and hammer [16].

Fig. 12. Comparison of force between experiment [16] and 3D model for (a) cylindrical pile, FC and (b) tapered pile, T3.

M. Ghazavi, O. Tavasoli / Soil Dynamics and Earthquake Engineering 43 (2012) 287–299 293

Fig. 13. Typical signal-matching results for piles (a) FC and (b) T3 [16].

Fig. 14. Three-dimensional numerical model of the pile–soil system and interface

elements with FLAC3D.

M. Ghazavi, O. Tavasoli / Soil Dynamics and Earthquake Engineering 43 (2012) 287–299294

wave responses when the elastic modulus varies from high to lowmagnitudes. In cases where the elastic modulus of support isapproximately close to the elastic modulus of the rod, both forceand velocity reflections are very close to zero. This is due to thefact that at such an elastic modulus, the impedance (EA/C) of boththe rod and the segment are equivalent to each other, andtherefore, no wave is reflected. For impedances higher than therod (Fig. 5a–c), the reflections are compressive whereas it is theother way around for lower impedances (Fig. 5d–f).

The observations confirm the performance of the numericalmodel very well as a base for more complicated analyses of a realpile embedded within various soil layers below the pile tip andaround the pile shaft. The results of the three series of analysespresented above on a 20 m rod with no soil around and fordifferent boundary conditions at the rod tip indicate that thedeveloped model is capable of simulating the pile driving proce-dure and the wave propagation and reflections from the pile tipand head.

In this section, the wave propagation and pile driving analysis areconsidered with the geometry and properties of cylindrical pilesstudied numerically by Mabsout et al. [13,14]. In this study, aconcrete pile with a parabolic shaped toe was considered. This pilewas solid round concrete pile with a diameter of Dp¼50 cm andlength of 20 m. The pile–soil system has been modeled in the presentstudy using FLAC3D, as shown in Fig. 6a and b. A fine grid is used forthe model and grid definition under the tip of pile and along the pileshaft is refined. The pile properties are shown in Table 2.

Mabsout et al. [13,14] proposed that the inelastic behavior ofclays obeyed a bounding-surface plasticity model for isotropiccohesive soils, which is based on the critical state soil mechanics.In the present analysis, the soil was assumed to be elasto-plasticmaterial which obeyed the Mohr–Coulomb failure criterion. Theinitial void ratio of the soil was 0.63 and its specific gravity was2.6. The soil cohesion was a function of depth z. The soilparameters used in the present study are shown Table 2.

The three-dimensional model of the pile–soil system with517,492 grids is shown in Fig. 7. A force function is applied toidealize the hammer impact on the pile head. It is simulated bya force function introduced by Goble and Hery [9] and Mabsoutet al. [13,14]. Fig. 8 shows the force function.

For the boundary condition, a roller type support is used toresist grid displacements and allows movement in the verticaldirection. Quiet boundaries are used in the lateral and at thebottom of the model to absorb transmitting waves. In order tomodel the interface between the soil and the pile, interfaceelements are used at pile–soil border along the shaft and toeto allow slip between the pile and the soil in pile driving.The internal friction angle of the soil–pile interface is assumedto be f¼61. The interface strength and deformation parametersare presented in Table 3.

Figs. 9 and 10 show the results for the cylindrical driven pilepre-bored at 18 m in normally consolidated clay. As seen, the piletop and toe displacements are 38.82 and 38.78 mm, respectively.Also the pile top and toe maximum velocities are 1.545 and2.604 m/s, respectively. Fig. 8 presents the pile displacement andvelocity. As seen, the obtained numerical results from FLAC3D

analysis are well comparable with those reported by Mabsoutet al. [13,14].

In another experimental study, Sakr et al. [16] established alaboratory setup to characterize tapered and semi-tapered piledrivability. Numerical simulation of four piles during pile drivingwas also performed by Sakr et al. [16]. A cylindrical and threetapered piles with different taper angles were considered.The FRP–concrete composite piles named piles FC, T1, T2, andT3 had taper angles of 01, 0.531, 0.711, and 1.1311. The diametersof all piles were identical at mid-height of pile embedded lengths.

All model piles were installed to an embedded length of 1.2 m.The unit weight of 2420 kg/m3, slump of 240 mm and 58 MPa forthe 28-day compressive strength were reported for the concreteproperties. The details of piles geometry and composite materialproperties were presented in Table 4 by Sakr et al. [16].

The air-dried Fanshawe Brick sand of fine sub-round to roundparticles with D50¼ 0.26 mm was used as the soil bed prepared

Table 4Geometry and properties of model piles [16].

Pile ID Taper angle (1) Diameter (mm) Thickness

(mm)

Length (mm) Composite modulus

of elasticity (MPa)

Specific weight

(kN/m3)

dt db da

FC 0.0 162.4 162.4 162.4 6.0 1524 31,860 24.30

T1 0.53 170.0 198.0 184.0 9.8 1524 33,200 24.69

T2 0.71 159.0 197.0 178.0 7.8 1524 33,150 24.51

T3 1.13 155.0 215.0 185.0 8.2 1520 33,150 24.52

Table 5Properties of soil and Interface parameters used in Sakr et al. [16] simulation.

Soil parameters Interface parameters

Material r (kg/m3) n C (KPa) f (1) E (MPa) Normal stiffness (kN/m3) Shear stiffness (kN/m3) Friction angle (1) Cohesion (kPa)

Dense sand 2000 0.3 25 37 350 4.71e7 4.71e7 37 25

Fig. 15. Three-dimensional numerical model results of (a) velocity and

(b) displacement at 20 cm under pile head for pile FC. Fig. 16. Three-dimensional numerical model results of (a) velocity and

(b) displacement at 20 cm under pile head for pile T3.

M. Ghazavi, O. Tavasoli / Soil Dynamics and Earthquake Engineering 43 (2012) 287–299 295

using a raining technique to achieve consistent and uniformdense soil samples with relative density of about 90%. Theresidual and peak frictional angles, jr and jp, determined fromdirect shear tests were 311 and 371.

A pressure chamber with 1.52 m height and 1.34 m insidediameter was used for testing pile drivability. Fig. 10a and billustrates a schematic of the experimental arrangements and anoblique view of the test setup.

To achieve the desired radial and vertical confinement pres-sures, the chamber had radial and vertical air bladders that can bepressurized. The radial and vertical boundary pressures of 30 and60 KPa were applied to represent a soil layer at an embedmentdepth of about 4.0 m in normally consolidated sand with K0¼0.5.A single-acting hammer with a 1.0 kN ram was fallen through adistance of 1.2 m onto a 51-mm-thick plywood cushion. Theinstrumentation for dynamic load testing consisted of straingauge, accelerometers used for measuring forces at the pile head

and toe were attached at 200 mm from the pile head and theother near the pile toe (Fig. 11).

The force and velocity impedance for the cylindrical pile FCand the tapered pile T3 is illustrated in Fig. 12a and b. As seen, theforce and velocity impedance at the beginning of impact agreewell for both cases.

Also, typical signal-matching results for piles FC and T3 wereshown in Fig. 13a and b.

As shown in Fig. 14, the three-dimensional model of the pile–soil system in the pressure chamber and interface elements arementioned with 75,240 zones and 78,905 grid points. Pilegeometries and properties are illustrated in Table 4. The soilproperties and interface strength and deformation parameters arepresented in Table 5.

The force at the beginning of impact, as mentioned in Fig. 12aand b, agreed well for both tests and 3D numerical modeling.Fig. 15a and b presents the results for the cylindrical driven pile

M. Ghazavi, O. Tavasoli / Soil Dynamics and Earthquake Engineering 43 (2012) 287–299296

FC pre-bored pile at 1.2 m in dense sand. The velocity at 20 cmbelow the pile head is 2.64 m/s. In addition, if an integral is madeon velocity–time variation, the pile maximum residual displace-ment of 5.1 mm is obtained. The results for driving of pile T3 areshown in Fig. 16a and b. The maximum velocity at 20 cm belowthe pile head and the pile maximum residual displacementobtained by integration of experimental velocity–time curve are2.45 m/s and 4.2 mm, respectively. As a result, there is a wellmatching between experimental and numerical data. Further-more, the obtained numerical data from FLAC3D analysis are wellcomparable with those reported by Sakr et al. [16] forexperiments.

The above comparisons show that the constructed numericalmodel is able to simulate the soil–pile system response in piledrivability and therefore parametric study may be performed forfurther investigations on the subject confidently.

Fig. 18. Comparison of pile top displacement for various taper angles versus time.

4. Parametric study for pile tapered anngle effect

In this section, the drivability of non-uniform pile is analyzedand the results are compared with those for cylindrical pile.

Fig. 17. Three-dimensional tapered pile–soil system in FLAC3D.

Fig. 19. Comparison of pile tip displacement for various taper angles versus time.

Fig. 17 shows the pile configuration considered in this study.The pile is 20 m in length with equivalent volume with thecylinder pile. All initial and boundary conditions are same asmentioned before. The pile is assessed on a hammer blow withthe force function applied on its top shown in Fig. 8. In this study,a tapered pile is assumed to be of the same length and volume asfor the cylindrical pile (a¼0o) in three different taper angles ofa¼01, 0.51, and 11, where a is the taper angle.

The pile toe and top displacements for tapered pile withdifferent taper angles are presented in Figs. 18 and 19. Asobserved, the pile toe and head displacements increase withincreasing the taper angle. This stems from the fact that moresoil volume is present around the pile head and therefore, the rateof the load transferred to the soil grows up. Fig. 19 indicates thatthe tip displacement occurs at 0.01 s after the force function actson the pile top.

The velocities for tapered pile with various taper angles areshown in Figs. 20 and 21. As seen, when the hammer impacts thepile top, the stress waves are transferred from the top to the toe.

As presented in Fig. 22, the stresses of pile toe decrease withincreasing the taper angle during driving. This is on the safe sidefor piles in drivability. Fig. 23 shows the driving stresses atdifferent points along the pile shaft.

5. Parametric study for pile geometry effect

In this section, the drivability of four pile configurations isinvestigated and the results are compared. Fig. 24 shows the pileconfigurations considered in this study. All piles were 16 m oflength with equivalent surface area and identical materialvolumes. Pile C is cylindrical and pile T is fully tapered with

Fig. 22. Distribution of tapered pile tip stress with various taper angles versus

time.

Fig. 23. Driving stress on top, middle of pile and soil under pile toe versus taper

angle.

Fig. 24. Pile configurations.

Fig. 25. Comparison of pile top displacements versus time for various pile

geometries.

Fig. 21. Comparison of pile tip velocity for various taper angles versus time.

Fig. 20. Comparison of pile top velocity for various taper angles versus time.

M. Ghazavi, O. Tavasoli / Soil Dynamics and Earthquake Engineering 43 (2012) 287–299 297

1.11 taper angle. Pile T-C consists of a top tapered segment with8.5 m length and a lower cylindrical segment with 7.5 m length.Pile C-T has a top cylindrical part with 8.5 m followed by atapered part with 7.5 m length. All piles are fully driven to a totalpenetration depth of 16 m using an identical hammer blow with aforce function applied on their heads, as shown in Fig. 8. All initialand boundary conditions are the same as mentioned before.

Figs. 25 and 26 present the pile toe and head displacements forfour piles shown in Fig. 24. As mentioned before, the pile top and

toe displacements increase with increasing the taper angle. Pile Thas the maximum displacement and the least displacement isobserved in pile C. The displacements of pile C-T and T-C arebetween those of pile C and pile T. Pile C-T has more displacementcompared with pile T-C. This stems from the fact that the bottomconical shapes of piles T and C-T expand cavities more easily inthe soil and thus the piles penetrate more easily in the ground.

Fig. 28. Comparison of pile tip velocities versus time for various pile geometries.

Fig. 29. Distribution of pile tip stress with various geometry versus time.

Fig. 30. Distribution of pile head stress with various geometry versus time.

Fig. 27. Comparison of Pile Top velocities versus time for various pile geometries.

Fig. 26. Comparison of pile tip displacements versus time for various pile

geometries.

M. Ghazavi, O. Tavasoli / Soil Dynamics and Earthquake Engineering 43 (2012) 287–299298

Figs. 27 and 28 illustrate the velocities for four piles withdifferent geometry and shape. It is seen that when the hammerimpacts the pile top, the stress waves travel from the top tothe toe. Fig. 25 indicates that the tip displacement occurs at 0.01 safter the force function starts acting on the pile head.

The driving stresses of piles tip and head at different times areshown in Figs. 29 and 30. As shown, at their toes, pile C has the

maximum tip driving stress and pile T experiences the minimumstress. Also, the tip of pile C-T and T-C stresses are between thoseof pile C and pile T. Greater stresses are observed for the pile C-Ttoe compared with pile T-C. The same results are seen in thestresses of pile toe. This is because the radius of pile T is thebiggest one and thus for the same force, the lowest stresses isapplied. It is important to note that the stress of pile head may bemore important than the tip one. The top stress increasesimmediately because of hammer impact. Thus, it may cause pilehead failure. Therefore, by decreasing stresses in these piles, it ison the safe side for the pile upon driving.

6. Conclusions

A soil–pile system has been simulated for pile driving pheno-menon using a three-dimensional model for non-uniform cross-section piles using FLAC3D. The elastic pile has been assumed tobe driven into a Mohr–Coulomb material. The simulated pile–soilsystem response was first verified with data available from otherexperimental data for tapered and partially tapered piles andnumerical data for uniform piles. Parametric studies have beenperformed on various taper angles and pile geometries withcylindrical (C), fully tapered (T), top tapered-down cylindrical

M. Ghazavi, O. Tavasoli / Soil Dynamics and Earthquake Engineering 43 (2012) 287–299 299

(T-C), and top cylindrical-down tapered (C-T) piles. The resultsshowed that:

1.

With increasing the taper angle, the pile toe and tip displace-ments increase. This increases the pile driving efficiency.

2.

The driving stresses decrease with increasing the taper angle,resulting in the pile safety increase in pile driving.

3.

The toe and top displacements of fully tapered pile are greaterthan those of all four types of piles especially the cylindricalpile of the same volume and length.

4.

In C-T pile, for which the lower part of the pile is tapered, thepile is driven more easily than the same pile for which theupper part is tapered and the lower part is straight sided.

5.

The displacements of pile C-T and T-C are between those ofpile C and pile T.

6.

The cylindrical pile toe experiences greater driving stressduring driving than other pile toes do.

7.

The tips of piles C-T and T-C experience driving stressesbetween pile C and pile T. Generally speaking, if the drivabilityof piles is critical, fully tapered piles or at least C-T piles areadvantageous over cylindrical piles of the same volume andlength. This leads to beneficial pile driving.

References

[1] Chow, YK, Smith, IM. A numerical model for the analysis of pile drivability. In:Proceeding 2nd international conference on the application of stress waves topiles, Sweden; 1984. p. 319–25.

[2] Coutinho, ALGA, Costa, AN, Alves, JLD, Landau, L, Ebecken, NFF. Pile drivingsimulation and analysis by the finite element method. In: Proceeding 3rdinternational conference on the application of stress waves to piles, Ottawa;1988. p. 197–207.

[3] Ghazavi, M. Lateral analysis of tapered piles subjected to earthquake loadingand supporting lifelines. In: Proceedings of the 2nd Japan–Iran workshop onearthquake engineering and disaster mitigation-focusing on lifeline earth-quake engineering, Kobe, Japan; 2000. p. 127–32.

[4] Ghazavi, M, Williams, DJ, Morris, PH. Analysis of axially loaded pilesembedded in layered deposits. In: Proceedings of the 2nd international

conference on the application of numerical methods in engineering, Uni-versity Pertanian Malaysia, Selangor, Malaysia; 1997. p. 335–44.

[5] Ghazavi M. Analysis of kinematic seismic response of tapered piles. Geo-technical and Geological Engineering 2007;25(No. 1):37–44.

[6] Ghazavi M. Response of tapered piles to axial harmonic loading. CanadianGeotechnical Journal 2008;45(11):1622–8.

[7] Ghazavi, M Ahmadi, HA. Long-term capacity of driven non-uniform piles incohesive soil-field load tests. In: Proceedings of the 8th internationalconference on the application of stress wave theory to piles, Lisbon, Portugal;2008. p. 139–42.

[8] Ghazavi, M and Ahmadi, HA. Time-dependent bearing capacity increase ofuniformly driven tapered piles-field load test. In: Proceedings of the 6thinternational conference on case histories in geotechnical engineering, asymposium in honor of Professor James K. Mitchell August 11–16, 2008,Mariott Crystal City, Arlington, Virginia, USA; 2008.

[9] Goble, GG, Hery, P. Influence of residual force on pile drivability analysis. In:Proceedings 2nd international conference on the application of stress wavesto piles, Sweden; 1984. p. 162–9.

[10] Horvath, JS, and Trochlides, T. A half century taperd-pile usage at the John F.Kennedy International Airport. In: Proceedings of fifth international con-ference on case studies in Geotechnixla Engineering, New York, NY, 13–17April, 2004. Paper no. 11.02.

[11] Kulhmeyer RL, Lysmer J. Finite element method accuracy for wave propaga-tion problems. Journal of the Soil Mechanics and Foundations Division ASCE1973;99(SM5):421–7.

[12] Itasca. Fast Lagrangian analysis of continua in three dimensions (FLAC3D).Version 2.10, Itasca Consulting Group, Inc. Minnesota; 2002.

[13] Mabsout ME, Tassoulas JL. A finite element model for the simulation of piledriving. International Journal of Numerical Methods in Engineering1994;37:257–78.

[14] Mabsout ME, Reese LC, Tassoulas JL. Study of pile driving by finite-elementmethod. ASCE Journal of Geotechnical Engineering 1995;121(7):535–43.

[15] Rybnikov AM. Experimental investigations of bearing capacity of bored-cast-in-place tapered piles. Soil Mechanics and Foundation Engineering1990;27:48–51.

[16] Sakr M, El Naggar MH, Nehdi M. Wave equation analyses of tapered FRP-concrete piles in dense sand. Soil Dynamics and Earthquake Engineering2007;27:168–88.

[17] Smith EAL. Pile driving analysis by the wave equation’’. Journal of the SoilMechanics and Foundations Division ASCE 1960;86(4):35–61.

[18] Uzag, OG. An experimental and numerical study of impact driving of open-ended pipe piles in dense saturated sand. PhD thesis, University of Houston,Houston, Texas; 1988.

[19] Wei JQ, El Naggar H. Experimental study of axial behavior of tapered piles.Canadian Geotechnical Journal 1998;35:641–54.

[20] Zil’berberg SD, Sherstnev AD. Construction of compaction tapered pilefoundations (from experience of the ’’Valdespetsstroi’’ trust). Soil Mechanicsand Foundation Engineering 1990;27(3):96–101.