Bilotta, E. et al. (2015). Geotechnique 65, No. 5, 391–400 [http://dx.doi.org/10.1680/geot.SIP.15.P.016]

391

Importance of seismic site response and soil–structure interaction indynamic behaviour of a tall building

E. BILOTTA�, L . DE SANCTIS†, R. DI LAORA†, A. D’ONOFRIO� and F. SILVESTRI�

A tall public building in Naples (Italy) has recently undergone a seismic vulnerability assessment,following the new Italian code requirements. The building is about 100 m high and is founded on apiled raft floating in a thick layer of soft pyroclastic and alluvial soils. On the basis of a conventionalsubsoil classification, the inertial seismic actions on the building would lead to expensive measuresfor seismic retrofitting. By contrast, if site effects and soil–structure interaction are adequatelyaddressed the picture is completely different. First, free-field seismic response analyses highlighted thebeneficial effects of a peat layer, acting as a natural damper on the propagation of shear waves. Finite-element analyses of pile–soil kinematic interaction were then carried out to define the foundationinput motion, which was found not to be significantly affected. The effects of inertial interaction wereevaluated accounting for soil–foundation compliance; they resulted in an increase of the structuralperiod of vibration, while the overall damping did not change compared to that of the fixed-basestructure. The increased structural period led to further reduction of spectral acceleration. The resultscould lead to significant impacts on the seismic assessment of slender buildings founded on pilesembedded in deformable soils.

KEYWORDS: dynamics; footings/foundations; piles; soil/structure interaction

INTRODUCTIONSoil–structure interaction (SSI) may be an important issue inthe assessment of the seismic vulnerability of a building.Depending on the relative stiffness between the structure andthe soil–foundation system, it is generally expected that thedynamic SSI induces a significant increase of the fundamen-tal period of the structure and an increase of damping, thusreducing the seismic demand on the structure (e.g. Veletsos& Meek, 1974).

Recent studies (e.g. Han, 2002) have shown that theseismic response of a tall building supported on a pilefoundation may be difficult to predict correctly, if the com-plex dynamic interaction problem is not handled with care.Neglecting such interaction, for instance by modelling thetall building as having a fixed base, cannot represent theactual seismic response, since the overall stiffness of thesystem is overestimated and the damping is underestimated.Equally, simplifying the problem by modelling a real pilefoundation as a fictitious equivalent footing leads to nobetter prediction. Particularly in the case of large-diameterpiles, the important contribution of the foundation system tothe rocking stiffness of the building would be neglected. Asa consequence, too low natural frequencies and too largedisplacements would be calculated. In such a case, theassessment of the seismic vulnerability of the building wouldbe inaccurate, hence expensive and likely useless retrofittingcould be undertaken to meet the seismic safety requirements.

An adequate procedure to consider the soil–foundation–building interaction is based on the substructures method(Gazetas, 1984; Makris et al., 1996; Mylonakis et al., 1997)and it is implemented by subdividing the analysis into threedifferent stages

(a) assessment of the seismic input on the foundationaccounting for kinematic interaction (FIM ¼ foundationinput motion)

(b) calculation of the dynamic impedance functions asso-ciated with vertical and horizontal translation, as well aswith torsional rotation and rocking

(c) analysis of the inertial interaction of the buildingsubjected to the FIM and supported by visco-elasticsprings, characterised by the impedance functionsdetermined above.

In this paper stages (a) and (b) are described in detail, withreference to a case study of a tall building on a pile founda-tion floating in a deformable subsoil (section entitled ‘Casestudy’). The seismic actions on the building are calculated interms of response spectra by free-field seismic response(section entitled ‘Seismic site response’) and kinematic inter-action (section entitled ‘Foundation input motion’) analyses.The numerical calculation procedure of the (six-components)impedence matrix and the relevant modifications of thespectral ordinates due to the changes of the natural frequen-cies and the overall damping are finally assessed (sectionentitled ‘Influence of pile–foundation compliance’).

CASE STUDYThe analysed building, located in the eastern area of

Naples (Italy), is a 29-storey reinforced concrete tower, witha height of 107.4 m, built in the early 1980s. The tower,with a stiffening core, is rigidly connected to a pile founda-tion by a reinforced concrete box structure, made up by alower raft of thickness up to 1 m and an upper 40 cm slab,joined by vertical reinforced concrete walls 6 m high. The82 piles are unevenly distributed on a large area of 3300 m2

(Fig. 1); they were drilled in alluvial and volcanic soils witha length of 42 m and a diameter varying between 1800 mmand 2200 mm (Viggiani & Vinale, 1983; Mancuso et al.,1999).

The reconstruction of the subsoil layering was based onthe results of boreholes and cone penetration tests (CPTs)

Manuscript received 1 April 2014; revised manuscript accepted 11March 2015.Discussion on this paper closes on 1 October 2015, for further detailssee p. ii.� University of Napoli Federico II, Naples, Italy.† University of Napoli Parthenope, Naples, Italy.

Offprint provided courtesy of www.icevirtuallibrary.comAuthor copy for personal use, not for distribution

carried out in that area, during the design and constructionof the building (Vinale, 1988).

The schematic east–west stratigraphic section (Fig. 2(a))shows that the foundation subsoil profile consists of madeground (R), laying above volcanic ash (C), and pyroclasticsilty sand (cohesionless pozzolana, Ps), alternating withalluvial materials (peat, T, and sand, S). Underneath, theNeapolitan yellow tuff (NYT) is replaced in some zones byweakly cemented pozzolana (Pc), which can be viewed as aweathered and weaker kind of the same soft rock. Thisformation rests on stiff alternating layers of ash, sand andpozzolana (A) with uncertain depth.

The shear wave velocity profile, VS, shown in Fig. 2(b), isbased on interpretation of cross-hole and down-hole tests,carried out in the same area down to 60 m (Vinale, 1988).Below such a depth, no direct measurements of VS wereavailable and the profile was extrapolated to about 100 m onthe basis of the results of deep CPT by means of regionalcorrelations between qc and VS (Rippa & Vinale, 1983).

According to the national technical code (NTC, 2008),adopting similar soil classification criteria as Eurocode 8(CEN, 2003), the ground type might be classifiable betweenC and D, because the equivalent velocity VS,30 is about180 m/s. In a preliminary study carried out by Bilotta et al.(2013a), linear pseudo-static finite-element method analysisof the building was performed by assuming a fixed base andby simplifying the complex structure into main seismo-resistant elements modelled with one- and two-dimensionalelements (‘frame’ and ‘shell’, respectively).

The standard code seismic actions relevant to the life-safety limit state (SLV) were first used; in this case theycorresponded to a return period as high as 712 years and apeak reference acceleration of 0.19g at this site. A para-metric study of the seismic response of the building wascarried out by changing the input spectra according to thedifferent ground types. These first analyses showed that theseismic performance of the tall building was unsatisfactorywhen the code-specified demand spectra corresponded to themost unfavourable ground conditions, namely subsoil classC or D.

Nevertheless, it is worth remembering that the standardclassification criteria may be reliable only when VS continu-ously increases with depth: this is not the case, since a clearinversion in the velocity profile can be observed in Fig. 2(b),due to the presence of a relatively shallow layer of peatbetween 10 and 12 m.

The need for the definition of more realistic seismic

actions on the building was hence evident; therefore, theseismic site response (SSR) in ‘free-field’ conditions wasanalysed. Also, the complex SSI involving the building, theground and the pile foundation was recognised as deservingof greater insight. The former (SSR) aspect will be sum-marised briefly in the next section, whereas the latter (SSI)will be investigated in greater detail in the later sectionsentitled ‘Foundation input motion’ and ‘Influence of pile–foundation compliance’.

SEISMIC SITE RESPONSEOn the basis of the available data from geotechnical

investigation, a regular layering, characterised as shown inFig. 2, was adopted to carry out one-dimensional SSRanalyses with the linear equivalent approach in the frequencydomain, by using the code EERA (Bardet et al., 2000).

The decay of normalised shear modulus, G/G0, and thevariation of the damping ratio, D, with the shear strain, ª,were defined (Fig. 3) by resonant column tests carried outon undisturbed specimens of pozzolana (Vinale, 1988) orbased on data from literature for the other soils. Peat behav-iour was characterised by using experimental data reportedby Wehling et al. (2003).

A visco-elastic bedrock was assumed at 60 m depth, withshear wave velocity Vsb ¼ 800 m/s and damping ratioD ¼ 0.5% assigned to the stiff ‘A’ formation, based onpreliminary analyses (Bilotta et al., 2013b) showing that theamplification function of the subsoil was largely independentof any reasonable assumption about the variability of the VS

below 60 m.Seven natural accelerograms were extracted from the

European strong motion database (ESD), through the soft-ware Rexel 3.5 (Iervolino et al., 2009), compatible with thespectrum specified by the code for the life safety limit statecriteria. Fig. 4 shows with thin lines the response spectraassociated with each accelerogram, scaled to amax ¼ 0.19g.It is worth noting that at structural periods higher than 1 sthe average spectrum (thick grey line) is fully compatiblewith the code-specified reference spectrum for a ground typeA (black line).

A comparison between the profiles of the initial asopposed to the mean mobilised stiffness resulting from theone-dimensional SSR analyses is shown in Fig. 5.

The response spectra calculated at the surface for eachinput signal (thin grey lines) and their average (thick blackline) are plotted in Fig. 6. The average input spectrum(dotted line) and the code-defined spectra for any possibleground type are also shown in the figure. It may be observedthat the type C and D spectral ordinates at periods higherthan 2 s overestimate the mean values predicted by the SSRanalyses.

FOUNDATION INPUT MOTIONThe effect of kinematic interaction between the foundation

and the surrounding soil is generally of reducing the motiontransmitted to the superstructure. The amount of such areduction depends mainly on: excitation frequency, pilediameter and soil stiffness. Increasing the values of the firsttwo parameters or decreasing the soil stiffness, will lead tohigher mismatch between free field and foundation inputmotion.

The reduction of spectral acceleration due to pile–soilkinematic interaction was expressed by Di Laora & deSanctis (2013) with simplified formulations applicable to asingle pile embedded in homogeneous and two-layer subsoilmodels. For the layered subsoil at hand, such simple for-mulations cannot provide sufficiently accurate results. There-

N

Y

X

d 1·8 m�

d 2·0 m�

d 2·2 m�

70 m

Fig. 1. Piled raft – plan view

392 BILOTTA, DE SANCTIS, DI LAORA, D’ONOFRIO AND SILVESTRI

Offprint provided courtesy of www.icevirtuallibrary.comAuthor copy for personal use, not for distribution

fore the kinematic interaction problem has been analysed byway of numerical simulations in the frequency domain, byassuming a linear visco-elastic model for the soil andincluding the fixed head single pile or the pile group.

To this aim, the code Dynapile 2.0 (Ensoft, 1999) hasbeen used, based on the ‘consistent boundary matrix’ method(Kausel, 1974; Blaney et al., 1976). This is a hybridprocedure that models the soil–pile interaction through thefinite-element method in the vertical direction and appliesclosed-form solutions along the horizontal direction. Groupeffects are taken into account by means of frequency-depen-dent interaction factors, according to the superposition ap-proach. For vertical and rocking behaviour, the relationship

between displacements and forces at the heads of a coupleof piles is expressed using flexibility coefficients, by assum-ing that the presence of a second pile does not affect thedeformation of the loaded pile. For horizontal modes ofvibration, it is assumed that the deflections of both piles areidentical. Finally, the raft is assumed to be rigid and clear tothe soil.

The mobilised stiffness profile from SSR analyses (boldline in Fig. 5) has been adopted in the analyses.

Figure 7 shows the ratio between the peak accelerationsof the pile head and the free-field ground motion as afunction of the loading frequency. It can be noted that, forlow frequency, the foundation and the free-field motions are

90

75

60

45

30

15

Building H 107 m�

E WMade ground (R)

Peat (T) Sand (S)

Sand (S)

Cohensionlesspozzolana (Ps)

Cohensionlesspozzolana (Ps)

Cementedpozzolana (Pc)

Cementedpozzolana (Pc)

Alternating layers ofash, sand and pozzolana (A)

Alternatinglayers of

ash, sandand

pozzolana (A)

NeapolitanYellow tuff(NYT)

Volcanic ash (C)

Made ground (R)

Volcanic ash (C)

Peat (T)

100

80

60

40

20

0 200 400 600 800VS: m/s

Dep

th: m

(b)

(a)

Fig. 2. (a) Ground conditions and (b) shear wave velocity profile

IMPORTANCE OF SEISMIC SITE RESPONSE AND SOIL–STRUCTURE INTERACTION 393

Offprint provided courtesy of www.icevirtuallibrary.comAuthor copy for personal use, not for distribution

coincident, whereas only at high frequencies the discrepancyis noticeable; in addition, minor group effects are observed.As a matter of fact, considering that for this specific casestudy the structural fundamental frequency is of the order of

0.5 Hz, the kinematic interaction is certainly negligible. Theresults shown in Fig. 7 demonstrate that piles are unable tomodify the free-field seismic motion, which is insteadstrongly affected by the presence of the peat layer. In thefollowing the foundation input motion has been thereforeassumed coincident with the free-field ground motion.

INFLUENCE OF PILE–FOUNDATION COMPLIANCESimplified SSI model

The dynamic response of a building founded on pilesembedded in a deformable soil may be different from that ofa similarly excited, identical structure resting on a rigidground. The factors responsible for such a different behav-iour are: (a) the flexibility of the pile–foundation system; (b)the vibrational energy dissipated by the wave radiation andby the internal soil damping.

The above factors were both addressed for the case underexamination. Fig. 8 shows a simple oscillator on a flexiblefoundation, whose dynamic compliance is modelled by twosprings (K and KR) associated to translational and rotationaloscillations and a pair of dashpots (c and cR) attached in

0

0·2

0·4

0·6

0·8

1·0

10�5 10�4 10�3 10�2 10�1 100 101

G G/

0

γ: %(a)

0

5

10

15

20

25

10�5 10�4 10�3 10�2 10�1 100 101

D: %

γ: %(b)

Made ground and volcanic ashes

Peat

Sand

Pozzolana (PS, PC)

Alternating layers of ash,sand and pozzolana

Fig. 3. (a) Normalised shear modulus and (b) damping ratioplotted against shear strain

0

0·2

0·4

0·6

0·8

1·0

0 1 2 3 4

Sa:

g

Structural period, : sT

Rock input signals

Average

Code spectrum, subsoil type A (NTC)

Fig. 4. Spectra associated with the input signals

Made ground (R)

Volcanic ash (C)

Peat (T)

Sand (S)

Cohensionlesspozzolana (Ps)

Cementedpozzolana (Pc)

60

50

40

30

20

10

0 0·1 0·2 0·3

amax: g

Dep

th: m

60

50

40

30

20

10

0 100 200G: MPa

Dep

th: m

Mobilisedstiffnessfrom EERA

Initialstiffness

Back-analysisof pile load test

Fig. 5. Average profiles of initial and mobilised stiffness in SSR analyses and profile from pile load test back-analysis

394 BILOTTA, DE SANCTIS, DI LAORA, D’ONOFRIO AND SILVESTRI

Offprint provided courtesy of www.icevirtuallibrary.comAuthor copy for personal use, not for distribution

parallel to the springs. The overall system is commonlyreferred to as a ‘replacement oscillator’. In the same figure,the ratio between the mass acceleration, ast, and that of thefree-field motion, aff, is plotted against frequency. The foun-dation compliance acts as a low-pass filtering device; as aresult, the fundamental frequency of the replacement oscilla-tor is shifted far apart from the natural frequency of thefixed-base structure. In addition, the energy dissipated by thepiled foundation might lead to an increase of the dampingratio of the replacement oscillator, which is referred to as‘apparent damping’; thus, a reduction of the peak accelerationcorresponding to the natural frequency is usually expected.

From the dynamic equilibrium of the replacement oscilla-tor, the fundamental period along the i-axis, ~TT i, of a buildingmodelled as a single-degree-of-freedom (SDOF) system on acompliant base, and the associated apparent damping, ~��i, canbe expressed in the form (Veletsos & Meek, 1974; BSSC,2004)

~TTi ¼ T i

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ ki

Ki

1þ Kih2

KŁj

!vuut (1a)

~��i ¼ �0,i þ~TT i

T i

!�3

�ci (1b)

where Ti is the fundamental period of the fixed-base struc-ture; ki is the stiffness of the fixed-base structure; h is theheight of the centre of mass of the building computed fromthe top of the foundation plate; Ki is the horizontal stiffnessof the foundation; KŁj is the rotational stiffness around the j-axis perpendicular to i; �ci is the structural damping asso-ciated with oscillations along the i-axis; �0,i is the foundationdamping factor, that is, the contribution due to both radia-tion and hysteretic damping of the foundation system.

Considering that Ti is lower than ~TTi, the interactionreduces the effectiveness of the structural damping. When Ti

is small compared to ~TTi, the contribution of the structuraldamping may be significantly reduced. However, this reduc-tion is usually compensated by the increase in the apparentdamping due to the foundation. Depending on the ratio of ~TT i

over Ti, the apparent damping might be larger or smallerthan the structural damping. The expression for �0,i suppliedby Veletsos & Meek (1974) is only applicable to the case ofa shallow foundation resting on an elastic halfspace and,hence, it is not suitable for the case of a piled foundation. Anovel exact formulation for structures resting on genericsprings and dashpots has been proposed by Maravas et al.(2007, 2014).

According to this method, the damping of the overallsystem for vibration mode along the x-axis, for example,can be expressed by the following equations

~��X ¼ SX

�X

ø2X (1þ 4�2

X )þ �Łø2

ŁY (1þ 4�2ŁY )þ �CX

ø2CX (1þ 4�2

CX )

" #

(2a)

~øø2X ¼ SX=(1þ 4~��

2

X ) (2b)

with

SX ¼1

ø2X (1þ 4�2

X )þ 1

ø2ŁY (1þ 4�2

ŁY )þ 1

ø2CX (1þ 4�2

CX )

" #�1

(3)

0

0·2

0·4

0·6

0·8

1·0

1·2

1·4

0 1 2 3 4

Sa:

g

Structural period, : sT

Surface signals

Average surface signals

Average rock signals

type D

C

BA

Fig. 6. Acceleration response spectra computed at surface plottedagainst mean input spectrum and code-defined seismic actions fordifferent ground types

0 1 2 3 4 5

Acc

eler

atio

n ra

tio,

/a

ap

ff

Frequency, : Hzf

Single pile

Pile group

0

0.25

0.50

0.75

1.00

1.25

Fig. 7. Ratio between foundation and free-field accelerations as afunction of loading frequency

cKR cR

mg

UX UR Ua ast ff/

Compliantbase

Fixed base

f

h

K

Fig. 8. Replacement oscillator (left) and transfer functions of the fixed as opposed to thecompliant base structure (right)

IMPORTANCE OF SEISMIC SITE RESPONSE AND SOIL–STRUCTURE INTERACTION 395

Offprint provided courtesy of www.icevirtuallibrary.comAuthor copy for personal use, not for distribution

where

øX ¼ffiffiffiffiffiffiffiKX

m

r(4)

øŁY ¼ffiffiffiffiffiffiffiffiKŁY

mh2

r(5)

are fictitious uncoupled natural frequencies of the systemunder rocking and swaying oscillation of the base, and

øCX ¼ffiffiffiffiffiffikX

m

r(6)

is the natural oscillation frequency of the undamped fixed-base structure.

In equations (2) and (3), �X and �ŁY are the damping termsof the foundation in the vibrational modes along the x-axisand around the y-axis, respectively, while �CX is the dampingratio related to the horizontal motion of the structure alongthe x-axis.

By approximating to unity the terms expressed as(1þ 4�2), with � being any foundation or structural dampingterm, it is possible to rearrange equations (2) and (3) into

~øø2X ¼

1

ø2X

þ 1

ø2ŁY

þ 1

ø2CX

� ��1

) ~kkX ¼1

KX

þ h2

KŁY

þ 1

kX

!�1

(7a)

~��X ¼~kkX

KX

!�X þ

~kkX h2

KŁY

!�ŁY þ

~kkX

kX

!�CX

¼ ÆX�X þ ÆŁY�ŁY þ ÆCX�CX

(7b)

where ~kkX is the translational stiffness along the x-axis of theoverall system.

The same procedure may be applied to the motion alongthe y-direction.

Rewriting the expressions by Maravas et al. (2014) as inequations (7a) and (7b) has the advantage of offering aninsight into the physics of the interaction phenomenon. Theapparent damping is a linear combination of the dampingratios pertaining to the fixed-base structure, the swayingoscillation and the rocking oscillation of the foundation,weighted for the three coefficients ÆX, ÆŁY and ÆCX. It can beverified that the sum of above coefficients is 1. As a result,if damping ratios �X and �ŁY are equal to �CX, the apparentdamping must be equal to �CX. For very stiff foundationsystems, ÆX and ÆŁY are negligible, and the apparent damp-ing of the replacement oscillator coincides with that of thefixed-base structure.

Since stiffness and damping terms pertaining to the foun-dation are frequency-dependent, an iterative procedure isnecessary to obtain the apparent damping of overall system.To this aim, frequencies and damping ratios correspondingto the natural circular frequency of the structure øci can beused as starting values, thereby calculating by means ofequation (7a) a new value for the frequency ~øø2

i : Thereafter,new estimation of impedances may be obtained for ~øø2

i , untilconvergence. Generally, two or three iterations are sufficientto get accurate results. Finally, the value of the apparentdamping may be calculated from equation (7b).

Evaluation of translational and rotational impedanceThe rotational and horizontal stiffness components of the

dynamic compliance have been evaluated by means of thecode Dynapile 2.0 (Ensoft, 1999). The analyses have beenperformed by referring to a symmetric layout characterised

by a total of 76 piles (Fig. 9), all having a diameter of 2 m.Such idealisation is a reasonable approximation for engineer-ing purposes.

The Dynapile analyses have been performed by assumingthe same profile of the mobilised soil stiffness as for thekinematic interaction analysis (Fig. 5). The code allowedfirst the determination of the impedance functions of a singlepile and then those of the whole pile group.

The elastic properties of the soil representative of theresponse of single piles under vertical loads, and hence therotational impedance, are also affected by the pile installa-tion technique. In order to evalute the modification of soilproperties induced by pile installation, the procedure sug-gested by Mandolini & Viggiani (1997) was adopted. Hencethe small-strain stiffness of each layer was first evaluatedfrom cross-hole and down-hole investigations (Vinale, 1988).The stiffness profiles were then normalised by the stiffnessof the first layer to obtain a non-dimensional profile. Finally,the mobilised stiffness was calculated by performing itera-tively an elastic analysis of the single pile, until matchingthe initial slope of the experimental load–settlement curve.The initial vertical stiffness of the single pile as deduced byaveraging four load tests was KZ0 ¼ 2381 MN/m (Mandolini& Viggiani, 1997). Interestingly, the back-figured stiffnessprofile, shown in Fig. 5, is very similar to the mobilisedstiffness profile deduced from free-field SSR analyses. Thissimilarity led to the choice of the mobilised stiffness as theequivalent stiffness for the subsequent linear elastic analyses.

Figure 10 illustrates the real and imaginary part of theimpedance functions, (Kh( f ), Ch( f )) and (Kv( f ), Cv( f )), for asingle pile for horizontal (Fig. 10(a)) and vertical (Fig. 10(b))modes of vibration. The two components of the impedancefunction are plotted against frequency up to a value of 5 Hz.

The vertical static stiffness, obtained by extrapolating thedynamic stiffness function to zero frequency, meets exactlythe experimental initial stiffness KZ0 ¼ 2381 MN/m back-figured from loading test. The static horizontal stiffness ofthe fixed-head single pile is KH0 ¼ 683 MN/m.

Figure 11 shows the real and imaginary parts of theimpedance functions of the pile group associated with thehorizontal modes of vibration along the x-axis (KX) andy-axis (KY) and with rocking modes of vibration around they-axis (KŁY) and x-axis (KŁX). It is worth noting that the

Y

X

56·8 m

d 2·0 m�

Fig. 9. Simplified pile layout considered in the analyses carriedout with Dynapile

396 BILOTTA, DE SANCTIS, DI LAORA, D’ONOFRIO AND SILVESTRI

Offprint provided courtesy of www.icevirtuallibrary.comAuthor copy for personal use, not for distribution

horizontal impedance functions, KX and KY, are practicallycoincident. The same is true for the rotational components.The vertical and the torsional components of the stiffnessmatrix, KZ and KT, are not reported since they do not affectthe increase of the oscillation period and the apparentdamping.

For both directions, the value of the real part at zero-frequency is the static horizontal stiffness, corresponding to theraft restrained against rotation, that must be introduced intoequation (1) in order to evaluate the vibration period of thereplacement oscillator. From the Dynapile analyses, the follow-ing are obtained: KŁY ¼ 1.316 3 107 MNm (rotational staticstiffness around y-axis), KŁX ¼ 1.351 3 107 MNm (rotationalstatic stiffness around x-axis), KX ffi KY ¼ 6215 MN/m (hori-zontal static stiffnesses around x- and y-axes).

The natural periods of the fixed-base building along thetwo directions x and y were already calculated by Bilotta etal. (2013a). The stiffnesses ki of the fixed-base SDOFequivalent to the building were computed from the firstvibration periods assuming a seismic mass equal to 0.7W/g,with W being the weight of the building (BSSC, 2004). Theheight was assumed according to BSSC (2004) as h ¼ 0.7H,with H being the total height of the building. From suchvalues, the ratios between the fundamental periods of thebuilding on compliant and fixed bases, ~TT=T , were computedaccording to equation (1) along both directions. The result-ing ratios equalled 1.16 along the x-axis and 1.08 along they-axis, representing an appreciable increase of the structuralperiod due to foundation compliance. A reduction of theseimic action on the central core of the building and on thefoundation can be expected on the basis of such an incre-ment.

The exact solution supplied by Maravas et al. (2014) hasbeen then applied to evaluate both the modified period andthe overall damping of the complete system, in order to assessthe role of the radiation and hysteretic damping associatedwith the foundation motion. The frequency-dependent terms�i and �Łj, associated with swaying and rotational modes ofvibration of the pile foundation, can be easily obtained fromthe impedance functions by the following expression

�i ¼Ci(ø)

2Ki(ø)

�Łj ¼CŁj(ø)

2KŁj(ø)

(8)

where Ci(ø) and Ki(ø) are the imaginary and real parts of thedynamic stiffness associated with swaying along the i-axis,while CŁj and KŁj are those associated with rocking aroundthe j-axis.

For the case at hand, the method by Maravas et al. (2014)provides the results shown in Table 1.

It would be straightforward to show that the increase inoscillation period along both directions is coincident withthat evaluated by the approach proposed by Veletsos &Meek (1974); that is, by taking the static stiffness of thefoundation, in agreement with the findings by Maravas et al.(2014). This implies that the adopted procedure can beapplied without any iteration; in other words, simply bycomputing with equation (1a) the natural frequency of thereplacement oscillator. Also, the contribution of the founda-tion motion to the overall damping is very small in compari-son with that associated with the structure. For example, ÆY

and ÆŁX are only about 5% and 10%, respectively, while ÆCY

is 85%. Taking into account that �X and �ŁY are very close to�CX, the overall damping is practically coincident with thatof the structure (i.e. ~��X ¼ ~��Y ¼ 5%). This is mainly due tothe fact that the stiffness of the structure, kX, is small incomparison to the stiffness of the foundation.

Effect of soil–foundation compliance on seismic actionsThe reduction of the seismic actions achieved by taking

into account the site response and the dynamic SSI in theproblem at hand is presented in Fig. 12. The averagespectrum, computed from the SSR accelerograms by assum-ing ~��X ¼ ~��Y ¼ 5%, is compared to the spectrum for groundtype D.

By considering the effects of SSR on the fixed-basestructure, at the first vibration mode (TY ¼ 2.28 s) the spec-tral acceleration is reduced by 47.2% compared to thatpredicted by the code. An additional reduction (9.5%) of theinertial action can be achieved by accounting for the in-crease in the structural period (~TTY ¼ 2.47 s). For the secondvibration mode (TX ¼ 1.62 s), the reduction due to SSR isequal to 28.3%; a further significant reduction of 15.1% isdue to the deformability of the pile group.

Summarising, the overall reduction of inertial action dueto both seismic response and SSI is 56.8% along the y-axisand 43.5% along the x-axis.

CONCLUSIONSA tall public building in Naples (Italy) recently underwent

a seismic vulnerability assessment, following the new Italiancode requirements. After a preliminary unsatisfactory evalua-tion based on code-specified spectra, the seismic actionswere re-evaluated by a more sophisticated approach, givingcredit to seismic site effects and dynamic SSI.

Seismic site response was evaluated by one-dimensionalequivalent linear analyses, which highlighted the beneficial

0

250

500

750

1000

0 1 2 3 4 5

Sin

gle

pile

impe

danc

e,,

: MN

/mK

Ch

h

Frequency, : Hz(a)

f

Real part

Imaginary part

0

1000

2000

3000

0 1 2 3 4 5

Sin

gle

pile

impe

danc

e,: M

N/m

KC

vv

,

Frequency, : Hz(b)

f

Fig. 10. Impedance functions associated with (a) horizontal and(b) vertical modes of vibration for the single pile

IMPORTANCE OF SEISMIC SITE RESPONSE AND SOIL–STRUCTURE INTERACTION 397

Offprint provided courtesy of www.icevirtuallibrary.comAuthor copy for personal use, not for distribution

effects of a peat layer, acting as a natural damper on thepropagation of seismic waves. As a consequence, the spec-tral ordinates at the surface were reduced by as much as47% and 28%, for the first two vibration modes of thebuilding.

The attention was then focused on the role of SSI. Pile–soil kinematic interaction analyses were first carried out toassess the so-called foundation input motion (FIM): theresults showed that, in this specific case, the filtering actionexerted by the piles did not affect the FIM.

The pile foundation compliance relevant to inertial inter-action was then computed by the numerical code Dynapile,referring to mobilised stiffness profile.

The rotational and translational dynamic stiffnesses werefound to be poorly affected by the frequency in the range ofperiods corresponding to the first vibration modes of thebuilding. The swaying and rocking components of the foun-dation impedance made it possible to evaluate the increaseof the structural period of the compliant base system, whichwas found to be 1.08 and 1.16 for the first and secondmodes, respectively.

In order to evaluate the contribution of the combinedradiation and hysteretic damping, an exact solution recentlyproposed in the literature was adopted, requiring the evalua-tion of the frequency-dependent impedance components as-sociated with swaying and rocking oscillation of thefoundation. The overall damping of the compliant basesystem was found to be practically coincident with that ofthe fixed-base structure. Such a result can be attributed tothe larger foundation stiffness compared to that of thestructure.

Owing to SSR effects and dynamic SSI, the inertialactions were overall reduced by 57% and 43% for the firstand second vibration modes. It is therefore inferred that theassessment of the above factors is mandatory for reliableand sustainable predictions of the seismic performance ofbuildings like the one considered in this study.

ACKNOWLEDGEMENTSThe activity was carried out as part of WorkPackage 5

‘Soil–foundation–structure interaction’ of the sub-project on

� �2 104

� �1 104

0

1 10� 4

2 10� 4

3 10� 4

0 1 2 3 4 5

KC

XX

,: M

N/m

Frequency, : Hz(a)

f

Real part

Imaginary part

� �2 104

� �1 104

0

1 10� 4

2 10� 4

3 10� 4

0 1 2 3 4 5

KC

YY

,: M

N/m

Frequency, : Hz(b)

f

� �1 107

0

1 10� 7

2 10� 7

3 10� 7

0 1 2 3 4 5

KC

θYY

,: M

N/m

θ

Frequency, : Hz(c)

f

� �1 107

0

1 10� 7

2 10� 7

3 10� 7

0 1 2 3 4 5

KC

XX

,: M

N/m

θθ

Frequency, : Hz(d)

f

Fig. 11. Real and imaginary parts of the impedance functions associated with horizontal swaying along the (a) x-axis and (b) y-axis, and rocking around the (c) y-axis and (d) x-axis

Table 1. Results of calculations according to Maravas et al. (2014)

TX: s ~TTX: s ~ff X: Hz KX (~ff X): MN/m CX ( ~ff X): MN/m �X (~ff X) KŁY (~ff X): MN m CŁY (~ff X): MN m �ŁY (~ff X)

1.62 1.89 0.528 5.311 3 103 5.461 3 102 5.14% 1.312 3 107 1.185 3 106 4.52%

TY: s ~TTY: s ~ff Y: Hz KY (~ff Y): MN/m CY (~ff Y): MN/m �Y (~ff Y) KŁX (~ff Y): MN m CŁX (~ff Y): MN m �ŁX (~ff Y)

2.28 2.47 0.404 5.697 3 103 5.308 3 102 4.66% 1.372 3 107 1.221 3 106 4.45%

398 BILOTTA, DE SANCTIS, DI LAORA, D’ONOFRIO AND SILVESTRI

Offprint provided courtesy of www.icevirtuallibrary.comAuthor copy for personal use, not for distribution

‘Earthquake geotechnical engineering’, in the framework ofthe research programme funded by Italian Department forCivil Protection through the ReLUIS (University Network ofSeismic Engineering Laboratories) consortium.

NOTATIONaff free field acceleration

amax maximum (absolute) acceleration of the time historyap foundation accelerationast mass acceleration of the replacement oscillatorCi damping coefficient associated to the oscillation of

foundation along i-axis, with i ¼ X, YCŁj damping coefficient associated to the oscillation of

foundation around j-axis, with j ¼ Y, Xc viscous dashpot coefficient associated to the

translational oscillation of the foundationcR viscous dashpot coefficient associated to the

rotational oscillation of the foundationD soil damping ratiofi natural frequency of the fixed-base structure along i-

axis~ff i natural frequency of the compliant-base structure

along i-axisG shear modulus

G0 initial shear modulush height of the centre of mass of the buildingK horizontal stiffness of the foundation

Kh( f ), Ch( f ) real and imaginary parts of the single pile horizontalimpedance

Ki horizontal stiffness of the foundation along i-axisKR rotational stiffness of the foundation

Kv( f ), Cv( f ) real and imaginary parts of the single pile verticalimpedance

KZ0, KH0 static axial and horizontal stiffness of single pileKŁj rotational stiffness of the foundation around j-axis

ki stiffness of the fixed-base structure along i-axism massqc CPT cone resistanceSa spectral accelerationSX model parameterTi fundamental period of the fixed-base structure~TTi fundamental period of the compliant-base structure

UX, UR, U displacement components of the SDOF systemVS shear wave velocity in the soil

VS,30 equivalent shear wave velocity defined by EurocodesVsb bedrock shear wave velocity

ÆCX,ÆŁY,ÆX weighting coefficientsª shear strain~��i apparent damping ratio associated to oscillations

along i-axis�ci structural damping ratio associated to oscillations

along i-axis�i foundation damping ratio associated to oscillations

along i-axis�Łj foundation damping ratio associated to oscillations

around j-axis�0,i foundation damping factor associated to oscillations

along i-axisøCX natural circular frequency of the fixed-base structure

along x-axisøX,øŁY fictitious frequencies

~øøi natural circular frequency of the replacementoscillator

REFERENCESBardet, J. P., Ichii, K. & Lin, C. H. (2000). EERA a computer

program for equivalent-linear earthquake site response analysesof layered soil deposits. Los Angeles, CA, USA: University ofSouthern California, Department of Civil Engineering.

Bilotta, A., Sannino, D., Fretta, A., Nigro, E. & Manfredi, G.(2013a). Influenza della categoria di sottosuolo sulla vulnerabil-ita sismica di edifici alti. Proceedings ANIDIS conference attidel convegno ANIDIS 2013, Padova. Padova, Italy: PadovaUniversity Press (in Italian).

Bilotta, E., Bilotta, A., Del Prete, I., d’Onofrio, A., Nigro, E. &Silvestri, F. (2013b). Influenza delle condizioni locali di sottosuo-lo sulla risposta sismica di un edificio pubblico di notevolealtezza. Proceedings ANIDIS conference 2013, Padova. Padova,Italy: Padova University Press (in Italian).

Blaney, G. W., Kausel, E. & Roesset, J. M. (1976). Dynamicstiffness of piles. Proceedings of the 2nd international conferenceon numerical methods in geomechanics, Blaksburg, Virginia.

BSSC (2004). NEHRP recommended provisions for seismic regula-tions for new buildings and other structures, FEMA 450.Washington D.C., USA: Building Seismic Safety Council, Na-tional Institute of Building Sciences.

CEN (2003). (pr)EN 1998-1:2003: Eurocode 8: Design of structuresfor earthquake resistance – Part 1: General rules, seismic actionsand rules for buildings. Brussels, Belgium: CEN EuropeanCommittee for Standardization.

Di Laora, R. & de Sanctis, L. (2013). Piles-induced filtering effecton the foundation input motion. Soil Dynam. Earthquake Engng46, 52–63.

Ensoft (1999). Dynapile 2.0: A program for the analysis of pilesand drilled shafts under dynamic loads. Austin, TX, USA:Ensoft Inc.

Gazetas, G. (1984). Seismic response of end-bearing single piles.Int. J. Soil Dynam. Earthquake Engng 3, No. 2, 82–93.

Han, Y. (2002). Seismic response of tall building considering soil–pile–structure interaction. Earthquake Engng Engng Vibration 1,No. 1, 57–64.

Iervolino, I., Galasso, C. & Cosenza, E. (2009). REXEL: computeraided record selection for code-based seismic structural analysis.Bull. Earthquake Engng 8, No. 2, 339–362, http://dx.doi.org/10.1007/s10518-009-9146-1.

0

0·2

0·4

0·6

0·8

1·0

0 1 2 3 4

Sa:

g

Structural period, : s(a)

T

Subsoil type D (NTC)

Seismic response analysis

TY TY~

0

0·2

0·4

0·6

0·8

1·0

0 1 2 3 4

Sa:

g

Structural period, : s(b)

T

TXTX~

Fig. 12. Reduction of the inertial actions for (a) the first and(b) the second building vibration modes

IMPORTANCE OF SEISMIC SITE RESPONSE AND SOIL–STRUCTURE INTERACTION 399

Offprint provided courtesy of www.icevirtuallibrary.comAuthor copy for personal use, not for distribution

Kausel, E. (1974). Forced vibration of circular foundations. ScDthesis, Massachusetts Institute of Technology, Cambridge, MA,USA.

Makris, N., Gazetas, G. & Delis, E. (1996). Dynamic pile–soil–foundation–structure interaction: records and predictions. Geo-technique 46, No. 1, 33–50, http://dx.doi.org/10.1680/geot.1996.46.1.33.

Mancuso, C., Viggiani, C., Mandolini, A. & Silvestri, F. (1999).Prediction and performance of axially loaded piles under work-ing loads. In Pre-failure deformation characteristics of geoma-terials (eds M. Jamiolkowski, R. Lancellotta and D. Lo Presti),pp. 801–808. Rotterdam, the Netherlands: Balkema.

Mandolini, A. & Viggiani, C. (1997). Settlement of piled founda-tions. Geotechnique 47, No. 4, 791–816, http://dx.doi.org/10.1680/geot.1997.47.4.791.

Maravas, A., Mylonakis, G. & Karabalis, D. L. (2007). Dynamiccharacteristics of structures on piles and footings. Proceedingsof the 4th international conference on earthquake geotechnicalengineering, Thessaloniki, Paper 1672. Dordrecht, the Nether-lands: Springer.

Maravas, A., Mylonakis, G. & Karabalis, D. L. (2014). Simplifieddiscrete systems for dynamic analysis of structures on footingsand piles. Soil Dynam. Earthquake Engng 61, No. 62, 29–39.

Mylonakis, G. E., Nikolaou, A. & Gazetas, G. (1997). Soil-pile-bridgeseismic interaction: kinematic and inertial effects. Part I: soft soil.Earthquake Engng Structural Dynam. 27, No. 3, 337–359.

NTC (2008). D. M. 14 Gennaio 2008, ‘Norme tecniche per lecostruzioni’. Gazzetta Ufficiale della Repubblica Italiana no. 29,4 February 2008 (in Italian).

Rippa, F. & Vinale, F. (1983). Experiences with CPT in EasternNaples area. Proceedings of the 2nd European symposium onpenetration testing (ESOPT), Amsterdam. London, UK: CRCPress.

Veletsos, A. S. & Meek, J. W. (1974). Dynamic behaviour ofbuilding foundation systems. Earthquake Engng Structural Dy-nam. 3, No. 2, 121–138.

Viggiani, C. & Vinale, F. (1983). Comportamento di pali trivellatidi grande diametro in terreni piroclastici. Rivista Italiana diGeotecnica 17, No. 2, 59–84 (in Italian).

Vinale, F. (1988). Caratterizzazione del sottosuolo di un’area cam-pione di Napoli ai fini di una microzonazione sismica. RivistaItaliana di Geotecnica 22, No. 2, 77–100 (in Italian).

Wehling, T. M., Boulanger, R. W., Arulnathan, R., Harder, L. F. &Jr Driller, M. W. (2003). Nonlinear dynamic properties of afibrous organic soil. J. Geotech. Geoenviron. Engng 129, No. 10,929–939.

400 BILOTTA, DE SANCTIS, DI LAORA, D’ONOFRIO AND SILVESTRI

Offprint provided courtesy of www.icevirtuallibrary.comAuthor copy for personal use, not for distribution