Gazetas 2000-Jee_seismic Ssi. Beneficial or Detrimental

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SEISMIC SOIL STRUCTURE INTERACTION: BENEFICIAL ORDETRIMENTAL?George Mylonakisa; George GazetasaaDepartment of Civil Engineering, City University of New York, New York, NY 10031, USA

To cite this ArticleMylonakis, George and Gazetas, George(2000) 'SEISMIC SOIL-STRUCTURE INTERACTION:BENEFICIAL OR DETRIMENTAL?', Journal of Earthquake Engineering, 4: 3, 277 301

To link to this Article: DOI: 10.1080/13632460009350372URL: http://dx.doi.org/10.1080/13632460009350372

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Journal o f Earthquake Engineering, Vol. 4 No. 3 (2000) 277-301Imperial College Press

SEISMIC SOIL-STRUCTURE INTERACTION:BENEFICIAL R DETRIMENTAL?

GEORGE MYL ONAKISDepar tment o Civil E n p e e h g City University of New York

New York NY 10031 USAGEORGE GAZETAS

epartment of ivil Engzneering National Technical UniversityAthens reece

Received 1 2 November 1999Revised 14 February 2000

Accepted 3 March 2000

The role of soil-structure interaction SSI) n the seismic response of structures is reex-plored using recorded motions and theoretical considerations. Firstly, the w y currentseismic provisions treat SSI effects s briefly discussed. The deaIised design spectra ofthe odes along with t he increased fundamental period and effective damping due to SSIlead invariably to reduced forces in the structure. Reality, however, often differs fromthi s view. It s shown that, n certain seismic and soil environments, an increase in thefundamental natural period of a moderately flexible structure due to SSI may have adetrimental effect on the imposed seismic demand. Secondly, a widely used structuralmodel for assessing SSI effects on inelastic bridge piers s examined. Using theoretical ar-guments and rigorous numerical analyses it is shown th at indiscriminate use of ductilityconcepts and geometric relations may lead to erroneous conclusions in t h e assessment ofseismic performance. Numerical examples are presented which highlight critical issuesof the problem.K e y w d : Soil-structure interaction, earthquake, ductility, inelastic response, seismicregulations, bridge.

1. IntroductionIt is well known tha t established seismic design methods may involve tenets andpractices that are not always accurate. This is especially so in codified approacheswhich incorporate substantial approximations to provide simple frameworks fordesign. Several such examples, including cornerstone issues such as the relationbetween structural strength and ductility, were identified by Priestley (1993) as

myths and fallacies in earthquake engineering.Seismic soil-structure interaction SSI) is not free of misconceptions. Despite

extensive research over than 30 years in this subject [see pertinent publicationsby Jennings and Bielak, 1973; Veletsos and Meek 1974; Bielak, 975; Roesset,


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278 G Mylonakis s C aretcrs

1980; Luco, 1982; Wolf, 1985; Ciampoli and Pinto, 1995; azetas and Mylonakis,1998, Stewart e t al., 19991 here is still controversy regarding the role of SSI inthe seismic performance of structures founded on soft soil. In fact, SSI has beent raditionally considered to be beneficial for seismic response. Neglecting SSI effects is currently being suggested in many seismic codes ATC-3, NEHRP-97) as aconservative simplification that would supposedly lead to improved safety margins.Apparently this perception stems from oversimplifications in the nature of seismicdemand adopted in code provisions. The most important of these simplifications(with reference to SSI are: 1) acceleration design spectra that decrease mono-tonically with increasing structural period; 2 ) response modification coefficients(i.e. behaviour factors used to derive design forces) which are either constant(period-independent) or increase with increasing structural period; 3) foundationimpedances derived assuming homogeneous halfspace conditions for the soil, whichtend to overpredict the damping of structures on actual soil profiles.

Additional support to the belief of an always beneficial SSI has come from an-alytical studies of the seismic response of elast oplast ic oscillators. Results hornseveral such studies, performed for both fixed-base [Newmark and Hall, 1973;Ridell and Newmark, 1979; Hidalgo and Arias, 199 1 and flexibly-support ed sys-tems [Ciampoli and Pinto, 1995;Elnashai and McClure, 19961 have shown hat theductility demand imposed on an elastoplastic structure tends to decrease with in-creasing elastic structural period. Other analyses however, [Miranda and Bertero,19941 based on motions recorded on soft soil deposits, indicate t ha t in certain fre-quency ranges the trend may reverse that is, ductility demand may incre se withincreasing period. In addition, theoretical studies by Priestley and Park (1987)showed that t he additional flexibility of an elastoplastic bridge pier due to thefoundation compliance reduces the ductility c p city of the system, an apparentlydetrimental consequence of SSI.

The first objective of the paper is to evaluate the approach seismic regulationspropose for assessingSSI effects. This is done in two parts: (a) by examining the ef-fects of SSI on the response of elastic singkdegree-of-freedom SDOF) oscillators;and b) by examining the effects of increase in period due to SSI on the ductil-ity demand imposed on elustoplastic S OF oscillators. The second objective is toevaluate the model of Priestley and Park (1987) for assessing SSI effects in elasto-plastic bridge piers. To this end, the model is used to explore the role of SSI on:(i) the ductility capacity of the piers; and (ii) the corresponding ductility demandimposed on such systems, if founded on soft soil, during strong earthquake motion.It s noted that the scope of this work s to highlight rather than fully resolve theabove issues The paper focuses on SSI effects in irm nonliquefiable soil, producedby the inertia of t he superstructure ( inertial interaction). Kinematic-effects ssociated with scattering of incoming seismic waves by the foundation which mayalso be of importance in certain cases) and SSI effects in liquefiable soil, are notaddressed.


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eismic Soil Structure Intemction: Beneficial o r Detr imental? 2792 SSI and Seismic ode SpectraThe presence of deformable soil supporting a structure affects its seismic responsein many different ways, as illustrated in Fig. 1 Firstly, a flexibly supported struc-ture has different vibrational characteristics, most notably a longer fundamentalperiod, p than t he period of the corresponding rigidly-supported fixed-base)structure. Secondly, part of the energy of the vibrating flexibly-supported structureis dissipated into the soil through wave radiation a phenomenon with no counter-part in rigidly-supported structures) and hysteretic act ion, leading to n effectivedamping ratio, p which is usually larger than the darnping of the correspondingfixed-base structure.

fixed basestru ture

stm tureon flexib ebase

Fig. 1 Effect of soil-structure interaction on fundamental natural period and effective d mpingof a structure on flexible found tion according to NEWRP 97 provisions.


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Fig. 2. Reduction in design base shear due t SSI according to NEHRP-97 seismic code

tn

The seismic design of structures supported on deformable ground must properlyaccount for such an increase in fundamental period and damping. Following earlystudies by Jennings and Bielak (1973) and Veletsos and Meek (1974) , the AppliedTechnology Council's provisions for the development of seismic regulations knownwidely as ATC-3), proposed simple formulae for computing and of structuresfounded on mat foundation on a homogeneous halhpace. With these two funda-

Amental Mriables, the engineer can use t h pprdpria te design spectrum td deiiVe

IIII

the design seismic forces.With little except ion e-g . NZS4203), seismic codes today use idealized smooth

design spectra which attain constant acceleration up to a certain period (of the or-der of 0.4 s to 1.0 s at most, depending on soil conditions), and thereafter decreasemonotonically with period (usually in proportion to T- or T - ~ / ~ ) .S a conse-quence consideration of SSI leads invariably to smaller accelerations and stressesin the structure and its foundation.' For example, the reduction in base shear ac-cording to NEHRP-97 is expressed as (Fig. 2):

TRUCTUR L7: PERlOD

where C is the seismic response coefficient obtained from the spectrum and W isthe weight of the structure; the term ( ~ / g ) - ~n the right-hand side of Eq. 1) ac-counts for the difference in damping between the rigidly- and the flexibly-supportedstructure. This beneficial role of SSI has been essentially turned into a dogma.Thus, frequently in practice dynamic analyses avoid the complication of accounting'The increase in period due to SSI leads to higher relative displacements which in turn maycause an increase in seismic demand associated wi t h P-A effects. This effect however is considedto be of minor importance NEHRP-97)-


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Seismic Soil-Structure Interaction Beneficial or Detr imental? 28for SSI supposedly conservative simplification t h a t would lead to improvedsafety margins. This beneficial effect is recognized in seismic provisions. For example, th NEHRP-97 seismic code states (Commentary, p. 111 :

The s e i s m i c ) f orces c n the re f ore be evaluated conservat ive ly with rutthe a d j u s t m e n t s recommended in Sec 5 5 (i-e. for SSI effects).Since design spectra are derived conservatively, the above statement may indeed

hold for a large class of structures and seismic environments. But not always. Thereis evidence documented in numerous case histories that the perceived beneficialrole of SSI is an oversimplification t h a t may lead to unsafe design for both thesuperstructure and the foundat ion.

To elucidate this, the ordinates of a conventional design spectrum for soft deepsoil, are compared graphically in Fig. 3 against four selected response spectra:Brancea (Bucharest) 1977 Michoacan [Mexico City SCT)] 1985, Kobe (Fukiai,Takatori) 1995 presented in terms of spectral amplification. Notice that all therecorded spectra attain their maxima at periods exceeding 1.0 s. The large spectralvalues of some of these records are undoubtedly the result of resonance of the soildeposit with the incoming seismic waves (as in the case wi th t he Mexico City SCTrecord). Another phenomenon, however, of seismological rather than geotechnical

Bucharest

obe Fukiai W( 995) Kobe Takatori W

STRUCTUR L PER100 sFig. 3. Comparison of a typical seismic code design spectrum to actual spectra from catastrophicearthquakes with strong long-period components; 3 5 .


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nature, the forward fault-rupture directivity (Somerville, 1998), may be n m-portant contributing factor in the large spectral values at T 0.50 s in near-faultseismic motions e.g. in Takatori and Fukiai). As noted by Somerville, an earth-quake is a shear dislocation that egins at a point on a fault and spreads outwardalong the fault at almost the prevailing shear wave velocity. The propagation offault rupture toward a site at very high velocity causes most of the seismic energyfrom t h e rupture to arrive in a single long-period pulse of motion, at the beginningof the recording (Somerville et al. 1997). his pulse is sometimes referred t asfling .The radiation pattern of the shear dislocation on the fault causes this large

pulse of motion to be oriented in the direction perpendicular to the fault, causingthe strike-normal peak velocity to be larger than the strike-parallel velocity. Theeffect of forward rupture directivity on the response spectrum is to increase thespectral values of the horizontal component normal to the fault strike at periodslonger than about 0.5 s. Examples of this effect are the Kobe (1995) JMA Fukiai,Takatori, and Kobe University records; the Northridge (1994) Rinaldi, Newhall, Syl-mar Converter, and Sylmar Olive iew records; the Landers 1992) Lucerne Valleyrecord, and many others. Figure 4 shows the effects of rupture directivity in thetime history and response spectrum of the Rinaldi record of the 1994 Northridge

Velocity crn/sec)

- - - ault aralleZ

0 2 3Period see)

Fig. 4 Acceleration and veIocity time histories for the strike-normal and strike-parallel horizontalcomponents of ground motion, and their 5 damped response spectra, recorded at Rinaldi duringthe 1994 Northbridge earthquake. Note the pronounced high velocity/long period pulse in thefault-normal component after Somerville, 1998).


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Seismic Soil-Structure In temct ion: Beneficial or Det r imen ta l? 283earthquake. Evidently, records with enhanced spectral ordinates at large periodsare not rare in nature hether due to soil or seismological factors.

It is therefore apparent that as a result of soil or seismological factors, an increasein t h e fundamental period due to SSI may lead to increased response (despite apossible increase in damping), which contradicts the expectation incited by theconventional design spectrum. It is important to note that all three earthquakespresented in Fig. induced damage associated with SSI effects. Mexico earthquakewas particularly destructive to 10- to 12-storey buildings founded on soft clay, whoseperiod increased from about 1.0 s (under the fictitious assumption of a fixed base)to nearly 2 0 s in reality due to SSI [Resendiz and Roesset, 19851 The role of SSI onthe failure of the 630 m elevated highway section of Hanshin Expressway's Route3 in Kobe (Fukae sect on) has also been detrimental and is discussed later on [seealso Gazetas and Mylonakis, 1998;Mylonakis e t aL 20001 Evidence of a potentiallydetrimental role of SSI on the collapse of buildings in the recent Adana-Ceyhanearthquake was presented by Celebi (1998).

It should be noted that due to SSI large increases in the natural period ofstructures PIT 1.25 are not uncommon in relatively tall yet rigid structuresfounded on soft soiI [Fig 1;Tazoh t al. 1988; Mylonakis e t al. 1997; Stewart et al.19991 Therefore, evaluating the consequences of SSI on the seismic behavior of suchstructures may require careful assessmentof both seismic input and soil conditions;use of conventional design spectra and generalised/simplified soil profiles in thesecases may not reveal the danger of increased seismic demand on the structure.

To funher illustrate the above, results from a statistical study performed by theauthors using a large set of motions recorded on soft soil are presented. The set ofmotions consists of 24 actual records Appendix I); this is an extended version ofthe set used by Miranda (1991). The average acceleration spectrum obtained fromthese motions is presented in Fig. 5 , in terms of spectral amplification. The struc-tural period is presented in thr different ways: (i) actual period T ; ii) normalisedperiod TIT [T effective ground period, defmed as the period where the 5% ve-locity spectrum attains its maximum [Miranda and Bertero, 994 ; iii) normalisedperiod TIT [T period where acceleration spectrum attains its maximum.] It isseen that w i t h the actual period, the resulting average spectrum has a flat shape(analogous to that used in current seismic codes) which has little resemblance toan actual spectrum. The reason for this unrealistic shape is because t h e spectraof motions recorded on soft soil attain their maxima at different, well separatedperiods and, thereby, averaging them eliminates the peaks causing this effect. Incontrast, with the normalised periods T/T, nd T/T, he average spectrum ex-hibits a characteristic peak close (but not exactly equal) to 1 which reproduces thetrends observed in actual spectra. It is well known hat the issue of determining acharacteristic 'Ldesign period (i.e. gor T, or a given site is controversial and,hence, it has not been incorporated in seismic codes. Nevertheless, it is clear thatcurrent provisions treat seismic demand in soft soils in a nonrational way and mayprovide designers with misleading information on the significance of SSI effects.


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I I2

PERIOD T ; T /T, ; T /T,Fig. 5 . verage acceleration spectra based on 24 actual motions recorded on soft soil. The pe-riods are either normalised before averaging with a) period of peak spectral acceleration T,);b) periodof peak spectral velocity (T );or c) average without any normalisation;O = 5 .

As a h a 1 remark, it should be mentioned tha t some new methods in seis-mic design may modify some of the existing perceptions associated with SSI. For

-example,-recently developed procedures -for displacement-based- design utilise- displacement instead of acceleration) spectra, developed directly from strong motionrecords [Bommer and Elnashai, 1999; Tolis and Faccioli, 19991.Contrary to accel-eration spectra, displacement spectra exhibit increasing trends over large ranges ofperiods and, thereby, SSI effects will not appear as being invariably beneficial forseismic response. ore details on these new methods can be found in [Kowalski tal . , 1994; Calvi and Kingsley, 1995; and Bommer and Elsnashai, 19991.

2.1. Effect of period lengthening on inelastic esponseThe foregoing discussion was based on the assumption that the response of thestructure is linearly viscoelast c. However, during strong earthquake shaking astructure may exhaust its elastic strength and deform beyond its yielding pointi.e. inelastically) without collapsing. Accordingly, engineers design structures wi th

strength which is only a fraction of that required to prevent yielding elusticforce demand , provided tha t the displacement imposed to the structure by theearthquake displacement demand s smaller than the ultimate displacement thestructure can sustain displacement capacity). The foregoing can be put in a dimen-sionless form in terms of the followingwell known parameters: i) ductility demandp = displacement demand/yielding displacement); ii) response modification factorR = elastic force demand/yielding strength).


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Seismic Soil-Structure Interaction: Beneficial or D e t r im e n ta l? 285

Yielding of elastoplastic structures has some distinct similarities to t he effectsof SSI on elastic structures. Both phenomena result to an increase in the effectivenatural period and damping of t h e structure. In this section our focus is on theeffect of the increased initial period of the structure on ductility demand. To thisend, we examine the relation between ductility demand p and strength reductionfactor R as functions of structural period.In a seminal work, ewmark and Hall (1973) proposed two approximate relationships between and R. Using a limited number of recorded motions availableat that time, they observed that: 1) n the moderately-long and long period ranges,an elastic and an inelastic oscillator of the same initial period have approximatelythe same maximum relative displacement equal displacement rule ) 2) in themoderately-short period range, the energy defined by the area under a monotonicforcedisplacement diagram' is approximately the same for an elastic and an in-elastic oscillator ( equal energy rule ). Based on these assumptions it is a simplematter to show hat p and R can be related as

, moderately - hort periodsP = I7 moderately - Long to long periods.Values for the corresponding period ranges are given in Newmark and Hall 1973)and in Miranda and Bertero 1994).

In the limiting case of a very stiff elastoplastic oscillator, T t 0, nd its yieldingdisplacement u is practically zero. If the system has less strength than that requiredto remain elastic during shaking R > I ) , the ductility demand (computed bydividing the h t e displacement response of system by its zero yield displacement)will be of infinite magnitude

On the other hand, for a very flexible oscillator, T co nd the maximumrelative displacement will be equal to the peak ground displacement regardless ofyielding strength. This leads to the well-known result

Note t h a t contrary to Eqs. 2) and (3) which re approximate, the asymptoticrelations (4) and (5) are exact. [ n act, Eq. 3) is an extrapolation of Eq. (5) in themoderately-long period range.]

The trend incited by Eqs. 2) to (5) is clear: For a given R the ductility demandp will decrease with increasing structural period [i.e. from infinity at zero period, toR2+1)/2 at moderately long periods, to R at long periods]. Conversely, for a giventarget ductility the associated response modification factor R will incre se with

increasing period. This increase in R implies that the yielding strength required tachieve the prespeczfied target ductility will tend t decrease with increasing periodand accordingly the role of SS will be beneficial.


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Seismic Sod Structure Intemct ion: Beneficial or Detr imental? 287

STRUCTURAL PERIO TFig 7 Comparison of ductility demands mposed y the Fukiai and Takatori records (Kobe 1995)with those obtained from he theory of Newmark and Hall (1973). Note the strong fluctuationsofat long periods; 5 -

Miranda s curves in Fig. 6 represent the statistical average of ductility demandsderived from the analysis of a large set of records on soft soil. Apparently, in thecase of a single earthquake record, the ductility demand may fluctuate with periodmuch more strongly. This is shown in Fig. 7 in which ductility demands calculatedfrom the Kobe Fukiai and Takatori motions are plotted for three different factors.The strong fluctuation (especially for R 4) of with period is evident.The foregoing discussion considered structures tha t were perfectly fixed at thebase. The effects of SSI could only be studied indirectly (i.e. through the increase innatural period). more accurate study of the inelastic response of flexibly-supportedstructures is presented below. It will be shown that, in this case, the interpretationof ductility coefficients may involve pitfalls.

3. Ductility in Flexibly Supported StructuresT ssess the effects of soil flexibility on the inelastic response of structures (par-ticularly bridges) engineers have been using the simple structural idealization ofFig. 8: a single bridge pier connected to the deck monolithically (or through bear-ings , and subjected to a transverse seismic excitation [Priestley and Park 1987;Ciampoli and Pinto, 19951. Elastoplastic bilinear behavior is usually considered forthe pier, while the soil-foundation is modelled with translational and rotationalsprings. Moment-free (cantilever) conditions at t he deck are often (but not neces-sarily) assumed. simple approach has been proposed for evaluating th effects ofSSI on the seismic performance of the inelastic system, by subjecting the bridgepseudostatically to a lateral load.


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88 G Mylonakis G axetas

seismi

Fig. 8 The model used to investigate t h e significance o SSI in the inelastic seismic performanceof cantilever bridge piers.

The lateral displacement of the deck relative to the free-field soil, 0 can bedecomposed s [Priestley and Park 19871

in which:A and ef x H are rigid body displacements of the deck due to the swayingA and rocking Qf ) of the foundation, respectivelyA and A represent the yield and plastic displacement of the pier, respectively.[Presence of bearings is not considered for simplicity]A = F y / K c n which F is the yield shear force and c . - 3 Ec I , /H 3 ) hestifhess of the columnA is the plastic component of deck displacement due to the yielding of pier,which is concentrated at the base of the column ( plastic hinge ).

If the column were fixed at its base, Eq (6) would simplify to:and dividing by A would yield the displacement ductility factor of the wlumn

For the flexibly-supported system, the yielding displacement, u ~ ,f the bridges obtained by etting A = to Eq. 6 ) :


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e i sm i cSoil Structure Interaction: Beneficial o r Detr imental? 289

The ratio defines the socalled global or system displacement ductilityfactor of the bridge-foundation system:

Dividing y y yields t he dimensionless expression between p and p :

in which

is a dimensionless coefficient expressing the foundation to structure displacement.Equations (9) and 10) implicitly assume that the response of the foundation,

A, +ef H , s the same in oth yielding and ultimate conditions. This assump-tion holds for an perfectly el stic pl stic pier supported on a foundation with higheryielding strength than the column. For a pier with bilinear behavior, Eqs. 10) and11) should be replaced y

Equation 11) s illustrated in Fig. 9 in which p is plotted as a function of pfor different values of the flexibility coeficient c. For c 0 (a structure fixed atits base), the values of the two factors coincide ps pc . For > 0, however, pis always smaller than p decreasing monotonically wi th increasing c . In fact, in

2 6 8COLUMN DUCTILITY: PC= /A.

Fig. 9. Relation between pier ductility pc and system ductility pr [Eq l l ) ]or t h e bridge modelof Fig. 8 (elastic-perfectly plastic pier).


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29 G Mylonakis G. azetasthe limiting case of c t m (an infinitely-flexible foundation or an absolutely rigidstructure), the system ductility p , is 1 regardless of the value of p

The above trends have been widely interpreted in the following way [Priestleyand Park, 1987; Ciampoli and Pinto, 19951: iven ductility capacity pc of theco lumn p, > I) , th ductility capacity p of the SSI syst m associated with af l ex ib i l i t y m t io c > 0 is lower th n it would be for a fized base cantilever wi thc 0). As an example, for the typical values pc (a well-designed column) andc 1 (a moderately soft soil), p3 is equal to only 2.5, i.e. only 62 of the p , value.On the other hand, to achieve a certain ductility capacity for the system, sayp . 4 the ductility capacity of the column for c 1 should, according to Eq. ll),be p 7 which may require a substantial increase in deformation. This impliesthat the additional flexibility due to the foundation compliance reduces the duc-tility capacity of the system [Priestley and Park 1987; Ciampoli and Pinto, 19951.As a straightforward extension to the above statement, one may conclude thatsoi l structure interaction has a detrimental effect on t he inelastic performance of abridge foundation system y reducing its ductility capacity.b his is in apparent con-tradiction with the beneficial role of SSI discussed earlier. Although evidence fora detrimental role of SSI has already been discussed and additional such evidencewill be presented later on), it will be shown here t h a t drawing such a conclusionusing Eq. 11) is incorrect. This is done using two different approaches.

Firstly, consider a counterexample: Suppose that we are interested in the ductil-ity demand (i.e. instead of capacity) imposed to the system by a transient dynamicload. To calculate the ductility demand-one must solve the nonlinear -equation_ fmotion of the system to determine the peak plastic displacement Ap as, for in-stance, done by Ciampoli and Pinto, 1995). For any value of A however, Eq. 11)will yield smaller values than Eq. (8) due to the presence of the additional pos-itive number c in both the numerator and denominator (this is exactly what weobserve in Fig. 9). Thus, the ductility demand imposed on the SSI system will besmaller than that of a fixed-base system with the same vibrational characteristicsand, hereby, SSI will apparently have a beneficial role to the system's performance

xactly the opposite to the first interpretation.The apparent paradox stems from the fact that Eq. 11) is a kinemqt ic expres-

sion which does not distinguish between capacity and demand; it tends to reduceboth ductilities and provides no specific trend on the effect of SSI on the inelasticperformance of the system.

The second argument against the validity of p , as performance indicator is thepresence of rigid body displacements due to the foundation translation and ro-tation) which are not associated with strain in the pier. In fact, the addition ofthese displacements in both the numerator and denominator of Eq. (10) is the only

bStrictly speaking the changes in both capacity and demand should be considered to concludewhether SSI s role s beneficial or detrimental. Nevertheless the reduction in ductility capacitysuggeste by Eq 11) is obviously detrimental.


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Seismic Soil Structure Interaction: Beneficial r Detr imental? 291reason for the systematic drop in t ha t ratio. This implies that the ductility ratio p[expressed through Eqs. 10)- 12)] is not a measure of the distress of the pier, ascorrectly pointed out by Ciampoli and Pinto (1995). For example, additional rigidbody motions could be introduced t o the analysis by, say rotating the referencesystem during the response. This would reduce p but without having any phys-ical connection to the actual problem. s another example, one may introduce toEq. (10) the seismic ground displacement. Incorporation of this additional displace-ment would better reflect the absolute motion of the system, and further reducepr. s an extreme case, one may consider the translation due to the motion of theearth; the addition of such a huge displacement to both the numerator and denomi-nator of Eq. (10) will make p equal to (implying response without damage) evenfor a system that has failed

Finally, it is important to note that p in Eq. (10) was derived by examiningjust the static deflection of the system, i-e. without using time history analysisor any "dynamic" reasoning. In contrast, it is well known that seismic SSI effectsare influenced (if not governed) by dynamic phenomena such as resonance andderesonance which cannot be captured by purely static or geometric considerations.

4 Inelastic SSI AnalysesTo further investigate the role of SSI on the inelastic performance of bridge piers,nonlinear inelastic analyses were carried ou t using the model of Fig. 8. Both columnand system ductilities were obtained using different oscillators and ground excita-tions, and results were compared with corresponding demands for fixed-base conditions. similar investigation has been performed by Ciampoli and Pinto (1 95).However there are some differences between the two studies. While the foregoingstudy was based on a set of artificial ground motions matching the EC-8 (1994)spectrum for intermediate-type soils, the present study uses exclusively actual mo-tions recorded on soft soils. n addition, a two-degree-of-freedom system is adoptedhere (as opposed to a single-degree-of-freedom system in the earlier work), to bet-ter represent the dynamic response of the footing. In the present analyses, bilinearelastoplastic behavior is considered for the pier with post-yielding stiffness equaling10%of the elastic stiffness. footing mass equal to 20 of the deck mass and aRayleigh damping equal t o 5% of critical in the two elastic modes of the systemwere considered in all analyses.Figure 10 presents column ductility demands obtained using the Bucharest(1977) motion. The results are plotted as function of the fixed structural periodcomputed for four different foundation-to-structural flexibility ratios: c = 0 (whichcorresponds to fixed-base conditions), 0.25, 0.5, and 1. [Note that with c = t heperiod of the flexibly-supported system is 1+ c ) / ~ 1.4 times higher that thatof the corresponding rigid-base system.] In the period range between about 0.5 to1.5 s, the curves for c > 0 plot above that for c = which implies that SSI increasesthe ductility demand in the pier. For example, in the particular case = 0.6 S


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0 2FIXED BASE STRUCTURAL PERIOD T

Fig. lo Effect of SSI on t h e ductility demand of a bridge pier subjected to t he Buchares t Brancea1977) N-S motion; R = 2.

1 2FIXED BASE STRUCTURAL PERIOD T s

Fig 11. Effect of SSI on t h e ductility dem nd of a bridge pier subjected t the Mexico City S Tblichoacan 1985) E-W motion; R = 2.

c = 1 ductility increases from 3.5 to about 5.5 without c = 0) and with c = 1SSI, espectively. In smaller periods the increase in p , is less significant, while atlonger periods SSI ends to reduce ductility demand.

Figure 11 refers to the Mexico City SCT 1985) ecord and = 2 n this casethe effects of SSI are somewhat less sigmficant than in the previous graph Yet thetendency for increase in ductility due to SSI is evident with the curves for c 0plotting above that of = 0 or periods between 0 70 and 2 s. Incidentally, it shouldbe mentioned that most of the damage caused by this earthquake concentrated inbuildings with fundamental fixed-base periods varying from about 0.9 to 1 3 s,which coincides with the region of the maxima of this graph.


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eismic Soil Structure Interaction Beneficial r Detr imental 293

An interesting case is presented in Fig. 12 referring to the Kobe 1995) Fukiairecord. A substantial increase in ductility due to SSI is observed at periods betweenabout 0.5 and s. For example, wi th a fixed-base period of 0.6 s and c 1, heductility demand increases from 2.2 for the fixed-base pier c 0 to more than5 for the flexibly supported system. Similar trends although not as clear as nFig. 12 are shown in Fig 13 for the nearby Kobe 1995) Takatori record. It isimportant to mention here that the 18 piers a 630 m segment)of the elevated Hanshin Expressway that failed spectacularly in

Failed Fukae Section, Route 3Hanshin Ehpressway

FUKIAI

at Fukae sectionthat earthquake,

2FIXED BASE STRUCTUR L PERIOD T : s

Fig. 12. Effect of SSI on the ductility demand of a bridge pier subjected to the Kobe 1995)Fukiai E-W motion; R 2.

2FIXED BASE STRUCTUR L PERIOD T : s

Fig. 13. Effect of SSI on the ductility demand of a bridge pier subjected t o the Kobe 1995)Takatori E-W motion; R 2.


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had a fixed base natural period of about 0.6 s see Fig. 12 , located at a site havingsimilar soil conditions and located similarly with respect to the fault zone as theFukiai and Takatori sites. The role of SSI on the collapse of that s t ruc ture wasperhaps more significant than originally suspected. More details o n this failure aregiven in Gazetas and Mylonakis 1998), Anastasopoulos 1999), and Mylonakis

t al. 2000).Figures 14 and 15 present system ductility demands Eq. 13) obtained from the

Bucharest and Mexico City records. It is apparent that the us of system ductil

BUCHAREST

1 2FIXED-BASE STRUCTUR L PERIOD : s

Fig. 14. Effect of SSI on the s y s t m ductility demand of a ridge pier subjected to t h e Bucharest(1G77)N S motion; = 2. NO th reduced values as compared to Fig 10

FIXED-BASE STRUCTUR L PERIOD T sFig 15. E i k t of SSI on the system ductility demand of a bridge pi r subjected to the 985Mexico City SCT N-S motion; = 2. Note the reduction in ductility as compared to Fig 11.


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Seismic Soil Structure In temct ion: Benef ic ia l o r Detrimental 295

ity completely obscures the detrimental role of SSI observed in Figs. 10 and 11Additional insight is provided in the numerical example below.

5 Numerical ExampleThe simple bridge model of Fig. 8 having mass m 350 Mg, elastic pier stiffnessK c 48 000 kN/m and height H 6 rn is subjected to the Kobe Fukiai recordFig. 3) having a peak ground acceleration of 0.80 g. he pier is assumed to be

elastoplastic with 10 post-yielding stiffness, designed wi th a seismic coefficientC C 0.50 which is considered representative of its actual yielding strength.For simplicity, the foundation translation is ignored (Af 0, z ca the rockingstiffness of the footing s R 2 x l o 6 kN m this would be the stiffness of a groupof 4 x 5 closely-spaced piles embedded in a soil layer wi th average V of abou t200 m/s). For the sake of this demonstration, the damping ratio of the fixed-baseand the flexibly-supported system are assumed to be 5 of critical.5.1. Fixed base systemPeriod: T 2nd i 0.54 s. Displacement of the column at yield: Apm C y / K c .6 cm. The acceleration response of the bridge is calculated from thespectrum of Fig. 3 as

Using a nonlinear inelastic analysis the displacement of the column is obtained as:

from which the ductility demand is computed as

Note that if we had applied the equal displacement rule we would have obtainedthe value Eqs. 3) and 1))

which underestimates the actual ductility demand. Incidentally, applying the equalenergy rule would have yielded the almost exact value pc R2+ 1 /2 2.52 +1) /2 3.63.

5 2 Flexibly-supported systemThe flexibility coefficient c in this case is given by:


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The effective stiffness of the bridge including SSI effects, is:

providing a modified periodT T ~.74Ignoring or this demonstration and a s a first approximation the change in foun-dation input motion, leads to Fig. 3):

Note that the above acceleration response [as well as that of Eq. 141 is fictitioussince it can develop only if the structure is perfktly viscoelastic.

Applying a nonlinear inelastic analysis, the peak displacement of t h e SSI systemis determined as:

This value includes the rigid-body motion induced by the foundation rotation:8 H =[A + a ( 0 =A,)] 5 . 3 cm. 23)

Subtracting the above displacement from 8 he ductility demand in the column isobtained as:

which is much higher than the corresponding demand for the fixed-base systemp , 3.6) rather anticipated increase in view of the substantial raise in

displacement demand 23.7 vs. 13 cm in the two cases respectively). In contrast,applying Eq. 13) would have yielded a global ductility value:

This is barely higher than the ductility demand for the rigidly supported structurep c 3 . 6 , and does not reflect t he actual ductility demand in the pier.

6 ConclusionsThe main conclusions of this study are:(1) By comparing conventional code design spectra to actual response spectra, it

was shown that an increase in fundamental natural period of a structure due toSSI does not necessarily lead to smaller response, and that the prevailing viewin structural engineering of the always-beneficial role of SSI is an oversimplifi-cation which may lead to unsafe design.


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Seismic Soil Structure Interuction Beneficial r Detr imental? 297

Averaging response spectra of motions recorded on soft soil without propernormalisation of periods may lead to errors.Ductility demand in fixed-base structures is not necessarily a decreasing func-t ion of structural period, as suggested by traditional design procedures. Analysis of motions recorded on soft soils have shown increasing trends a t periodshigher than the predominant period of the motions.Soil-structure interaction in inelastic bridge piers supported on deformable soilmay cause significant increases in ductility demand in the piers, depending onthe characteristics of the motion and the structure. However, inappropriategeneralization of ductility concepts and geometric considerations may lead tothe wrong direction when assessing the seismic performance of such structures.

AcknowledgementsThe thoughtful comments of Mr Vasilis Kolias of DENCO Engineers, Greece, dur-ing the early stages of this work are gratefully acknowledged. The Authors wouldalso like to thank Mr. Dimitri Roumbas, graduate student at the City Universityof New York, for preparing some of t h e graphs.

Appendix ATable A l . Selected ground mot ions recorded at soft soil sites modified after Miranda, 1991 .

Event/ Magni- Epicentral PGA PGVStation N a m e Geology DirectionDate tude M,) istance 4 m / 4

Bucharest Romania NS 0 21 0 7 5Soft Soil 7 2 149Research Inst. 3/4/77 EW 0 18 0 33

Secretaria Comrnuni- Soft laycation Transport.Central De Abastos Michoacan NS 0 08 0 42Soft Clay 8 1 384

Oficina 9/ 19/85 E W 0 07 0 35Central De Abastos

Frigorifico oft Clay

OaklandOuter Harbor Wharf Bay Mud

Foster City Lorna Prieta S 0 26 0 32BayMud 7 1 68Redwood Shores 10/17/89 EW 0 28 0 45


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Table A l Continued)

Event/ Magni- Epicentral PGA PGVStation Name eology Direct ionDate tude (M,) Distance d b / s

San Franciscol storey

Commercial Bldg

Fill OverBay u d

N80E 0.13 0.1799 NlOW 0.16 0 16

EmeryvilleFree Field South Bay M u d

Treasure Island Lorna Prieta FillNaval Base 10/17/89San FranciscoInternational

AirportBay Mud

NlOW 0 21 0.2197 S80W 0.26 0 21

Colonia Roma Acapulco N90W 0.06 0.12Soft Clay 6 94 25 89 SOOE 0.05 0.11

K o b e SoftFukiai AlluviumKobeKobe 1/17/95 Soft o t NS 0 65 1 55Takatori Alluvium

near-field records

Appendix BLIST O F SYM OLS

damping ratio damping ratio of a rigidly-supported structure.damping ratio of flexibly-supported structure.dimensionless coefficient expressing foundation to structure flexibility ratio.seismic response coefficient.foundation displacement.plastic structural displacement.ductility demand.reduction in base shear.yield displacement.column flexural rigidity.yiel shear force.acceleration of gravity.column height.


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Seismic Sod Structure Interaction: Benef icial or Detr imental? 99

effective stiffness of flexibly-supported system.colurnn stiffness.rocking stifhess of footing.bridge mass.column displacement ductility factor.system displacement ductility factor.foundation rot ation,response modification factor.spectral acceleration.s t ruc tura l natural period, natural period of rigidly-supported structure.na tura l period of flexibly-supported structure.

effectivenearthqu ake period (where 5%-damped acceleration sp ectrumat ta ins its maximum).

effectivenearthquakeperiod (where 5%-damped velocity spectrum attainsits maximum).yielding displacement.lateral displacement of flexibly-supported structure, relative to free-fieldsoil.lateral displacement a t first yield of flexibly-supported structure .weight of structure .

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