Seismic Rocking Isolation of an Asymmetric Frame on...

Author
truongminh 
Category
Documents

view
214 
download
0
Embed Size (px)
Transcript of Seismic Rocking Isolation of an Asymmetric Frame on...

Seismic Rocking Isolation of an Asymmetric Frameon Spread Footings
I. Anastasopoulos1; F. Gelagoti2; A. Spyridaki3; J. Sideri4; and G. Gazetas, M.ASCE5
Abstract: Rocking isolation is a relatively new design paradigm advocating the intense rocking response of the superstructure as a whole,instead of flexural column deformation. This is accomplished through intentionally underdesigning the foundation to guide plastic hinging below the ground surface rather than in the columns. A 2story, 2bay asymmetric frame is used to explore the effectiveness of this novel designapproach. Finiteelement dynamic analyses are performed using as seismic excitation idealized pulses and 20 real accelerograms, taking intoaccountmaterial (soil and superstructure) and geometric (uplifting andPD effects) nonlinearities. A conventionally, Eurocodedesigned frameand its foundation are compared to a design featuring the same frame butwith substantially underdesigned (unconventional) footings. It is foundthat the performance of the unconventional system is advantageous, as not only does it escape collapse but it also suffers reparable damage.Despite their reduced width, the residual settlements of the underdesigned footings are comparable to those of the conventional ones. However,the analyses also reveal that residual rotation and differential settlement of the underdesigned footingsmay be unavoidable andmust be criticallyevaluateda need exaggerated by the asymmetry of the examined frame. Three possible ways of improvement at the foundation level arestudied: (1) a single conventional tie beam,monolithically connected to the footings; (2) two separate tie beams hinged at each footing (allowingrotation, but resisting axial deformation); and (3) a hybrid system, comprising a single continuous tie beam connecting the three footings butexternally hinged to each of them. The first solution hardly offers improvement, as it hinders rocking, and the second fails to reduce differentialsettlements. The hybrid solution provides encouraging results in terms of residual rotation and differential settlement,while it does not hinder thedevelopment of beneficial rocking isolation mechanisms and fully restrains horizontal differential movements. DOI: 10.1061/(ASCE)GT.19435606.0001012. 2014 American Society of Civil Engineers.
Author keywords:Rocking isolation; Soilstructure interaction; Foundationdesign;Tie beams; Improved foundation;Uplifting;Bearing capacityfailure; Differential settlement.
Introduction
Modern design principles advocate ductility and capacity design,where structural members aboveground are capable of bearingdeformations even beyond yielding. The formation of plastic hinging is guided to less critical structural members (beams instead ofcolumns) and brittle failure mechanisms (such as shear failure) areavoided (Park and Paulay 1975). To avoid irreparable (and uninspectable) substantial yielding belowground, the footings are overdesigned by the use of overstrength factors to ensure that neitherstructural yielding of the footing nor bearingcapacity failure mechanisms develop.
However, a new design approach has been under investigation bya growing body of researchers, according to which the foundation isallowed to rock, setting a limit on the inertia loading that may betransmitted onto the superstructure. The potential benefits of suchrocking isolation have been verified by several studies (e.g., Beckand Skinner 1974; Priestley et al. 1996; Mergos and Kawashima2005; Kawashima et al. 2007; Deng and Kutter 2012; Deng et al.2012a, b), and proposed for the retrofit of existing structures (ASCE2000; Martin and Lam 2000). Also, rocking isolation has beenapplied to a few newly constructed important bridges (Pecker 1998,2003).
A variety of analytical studies is available in the literature, rangingfrom finite element or finite differences numerical modeling of theentire soilfoundationstructure system (e.g., Paolucci and Pecker1997; Gazetas et al. 2003; Chatzigogos et al. 2009), to Winklerbased methods (e.g., Chopra and Yim 1985; Apostolou et al. 2007;Kawashima et al. 2007), and comprehensive macroelement modeling(e.g., Paolucci et al. 2008; Chatzigogos et al. 2009; Gajan and Kutter2009a). Experimental studies can be categorized broadly into largescale testing (Negro et al. 2000; Faccioli et al. 2001), centrifugemodeltesting (Kutter et al. 2003; Gajan et al. 2005; Gajan and Kutter 2008,2009b), and reducedscale testing (Fukui et al. 2005; Paolucci et al.2008; Anastasopoulos et al. 2013).
This basic idea stems from the fact that the mobilization of soilfoundation bearingcapacity failure under seismic excitation doesnot necessarily imply failure, thanks to the cyclic and kinematicnature of ground shaking. Intentionally underdesigning the foundation (to have a lower moment capacity than the correspondingstructural members to which they are attached) could lead to rockinginstead of flexural response of the superstructure. In other words,
1Professor, Division of Civil Engineering, Univ. of Dundee, Nethergate,Dundee DD1 4HN, Scotland; formerly, Assistant Professor, School of CivilEngineering, National Technical Univ. of Athens, Athens 10682, Greece(corresponding author). Email: [email protected]
2Postdoctoral Researcher, School of Civil Engineering, National Technical Univ. of Athens, Athens 10682, Greece.
3Graduate Student, Columbia Univ., New York, NY 10027; formerly,Student, National Technical Univ. of Athens, Athens 10682, Greece.
4Graduate Student, Columbia Univ., New York, NY 10027; formerly,Student, National Technical Univ. of Athens, Athens 10682, Greece.
5Professor, School of Civil Engineering, National Technical Univ. ofAthens, Athens 10682, Greece.
Note. This manuscript was submitted on September 6, 2012; approvedon July 24, 2013; published online on July 27, 2013. Discussion period openuntil June 1, 2014; separate discussions must be submitted for individualpapers. This paper is part of the Journal of Geotechnical and Geoenvironmental Engineering, Vol. 140, No. 1, January 1, 2014. ASCE, ISSN10900241/2014/1133151/$25.00.
JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2014 / 133
J. Geotech. Geoenviron. Eng. 2014.140:133151.
Dow
nloa
ded
from
asc
elib
rary
.org
by
Geo
rge
Gaz
etas
on
12/2
4/13
. Cop
yrig
ht A
SCE
. For
per
sona
l use
onl
y; a
ll ri
ghts
res
erve
d.
http://dx.doi.org/10.1061/(ASCE)GT.19435606.0001012http://dx.doi.org/10.1061/(ASCE)GT.19435606.0001012mailto:[email protected]

mobilization of soil or soilfooting failure mechanisms averts plastification of structural members.
The application of this new design concept has been exploredtheoretically and experimentally for a simple, slender, onedegree offreedom structure, representing a bridge pier (Anastasopoulos et al.2010, 2013), and for a complex 2story, 2bay symmetric frame onshallow footings (Gelagoti 2010; Gelagoti et al. 2012a, b). It wasfound that under moderately strong seismic shaking not exceedingthe design motion, the two foundation designs (conventional andunconventional) are practically equivalent, as they both sustainreparable structural damage. But, with very strong seismic shakingin excess of the design limits (hardly an impossible situation), therockingisolated (unconventional) frameperforms substantially better:damage is restricted to beams and nonstructural elements, leaving theframe columns practically unscathed and, thereby, avoiding collapse.Moreover, despite their reduced width, the underdesigned footings(i.e., intentionally designed to be weaker than the correspondingstructural members) undergo tolerable seismic settlements. This paperextends the exploration of the applicability of rocking isolation to anasymmetric, twospan, 2story framea more realistic structuralconfiguration. The external (overall) dimensions of the studied frameare the same as those of the (symmetric) frame of Gelagoti (2010).
Problem Statement
The studied problem is shown in Fig. 1. In the case of conventionaldesign, the footings are fairly wide and, hence, of larger maximummoment resistance than the bending moment capacity of the corresponding columns. Therefore, plastic hinging is guided onto thesuperstructure. On the other hand, the footings of the rockingisolated frame are intentionally underdesigned to be weaker thanthe corresponding columns, guiding plastic hinging at or below thesoilfoundation interface. At the same time, the accelerationstransmitted onto the superstructure are substantially reduced.
The RC frame has been designed in accordance with Eurocode 8[European Committee for Standardization (CEN) 2009], for aneffective design acceleration of 0.36g and a ductilitydependentbehavior factor q5 3:9 (the behavior factor q refers to the overall
ductility of the system, and is used to reduce the design seismicactions, accepting a certain degree of seismic damage). Dead load ofG5 1:5 kNm2 and live load of Q5 2 kNm2, typical of residentialbuildings, are adopted. Dimensions and reinforcement details aregiven in Fig. 2. Competent soil conditions are considered, assumingthat the foundation soil consists of stiff (overconsolidated) clay ofundrained shear strengthSu 5 150 kPa and smallstrain shearmodulusGo 5 270MPa. The structure is founded on square surface footings ofwidth B.
The conventionally overdesigned footings can mobilize a maximum moment resistance (Mu) from the underlying soil larger thanthe bending moment capacity of the corresponding column (MRD).For static vertical loads, a factor of safety FS $ 3 is required againstbearingcapacity failure. For seismic load combinations, a factor ofsafety FE 5 1 is acceptable. In the latter case, a maximum allowableeccentricity criterion is also enforced: e5M=N#B=3 (where Mand N are the overturning moment and the vertical force of the mostunfavorable load combination). For the investigated soilstructuresystem, the eccentricity criterion was found to be critical, leading tominimum required footingwidthsB5 2:7, 2.5, and 2.4m for the left,middle, and right footings, respectively. Bearing capacities andsafety factors are computed according to the provisions of Eurocode 8 (CEN 2009), which are basically the same as those typicallyused in foundation design practice.
The undersized footings of the rocking isolation design, areweaker than the superstructure, guiding the plastic hinge to or belowthe soilfooting interface instead of the base of the columns. Thesmall width of the footings promotes full mobilization of foundationmoment capacity with substantial uplifting. The eccentricity criterion is completely relaxed, while FE , 1 is allowed. FS $ 3 remainsa requirement as a measure against uncertainties regarding soilstrength. Moreover, it turns out that FS $ 5 might be desirable topromote upliftingdominated response, thereby limiting seismicsettlements (Kutter et al. 2003; Faccioli et al. 2001; Pecker and Pender2000; Kawashima et al. 2007; Chatzigogos et al. 2009; Panagiotidouet al. 2012).
More specifically, applying the methodology that has been outlined in Gelagoti et al. (2012a), the footings were designed to beadequately small to promote uplifting, but large enough to limit the
Fig. 1. (a) Conventionally designed frame compared to (b) rockingisolation design
134 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2014
J. Geotech. Geoenviron. Eng. 2014.140:133151.
Dow
nloa
ded
from
asc
elib
rary
.org
by
Geo
rge
Gaz
etas
on
12/2
4/13
. Cop
yrig
ht A
SCE
. For
per
sona
l use
onl
y; a
ll ri
ghts
res
erve
d.

settlements. Aiming to minimize differential settlements stemmingfrom asymmetry, the three footings were dimensioned in sucha manner so as to have the same FS. Based on the aforementionedcriteria, the resulting footing widths for the rockingisolated designalternative are B5 1:1, 1.8, and 1.3 m for the left, middle, and rightfootings, respectively (indeed, substantially smaller than those of thecodebased design). Footing dimensions and static factors of safetyagainst vertical loading of the two designs are summarized in Table 1.
Numerical Analysis Methodology
A representative equivalent slice of the soilfoundationstructuresystem is analyzed with the FEM, taking account of material (soiland superstructure) and geometric (uplifting and PD effects) nonlinearities. As depicted in Fig. 3, the soil and the footings aremodeled with quadrilateral plane strain continuum elements, whilebeam elements are used for the superstructure. Special interfaceelements are considered at the soilfoundation interface to realisticallysimulate detachment and sliding. The seismic performance of the
system is analyzed through nonlinear, dynamic, timehistory analysis,applying the seismic excitation at the base of the model.
Nonlinear soil behavior is modeled through a simplified kinematic hardening model with a von Mises failure criterion and associative flow rule. As discussed in detail in Anastasopoulos et al.(2011), the evolution of stresses is defined as
s s0 a (1)
where s0 5 stress at zero plastic strain; and a 5 backstress, determining the kinematic evolution of the yield surface in the stressspace. The latter is composed of an isotropic hardening component,which defines the size of the yield surface s0 as a function of plasticdeformation, and of a nonlinear kinematic hardening component,which describes the translation of the yield surface in the stressspace. The evolution of the kinematic component of the yield stressis defined as
_a C 1s0
s2a _pl 2ga_pl (2)
where C 5 initial kinematic hardening modulus C5sy=y5E5 211 vGo; and g 5 parameter determining the rate ofdecrease of the kinematic hardening with increasing plastic deformation. In the case of clay, the maximum yield stress can bedefined as
sy ffiffiffi
3p
Su (3)
And because sy 5C=g1s0, parameter g can be expressed as
Fig. 2. Geometry and member properties of the idealized asymmetric frame
Table 1. Footing Dimensions and Corresponding Factors of Safety againstVertical Loading for the Seismic Load Combination (G1 0:3Q) for the TwoDesign Alternatives
Conventional design Rocking isolation
Footing B (m) FS B (m) FS
Left 2.7 32.6 1.1 5.4Middle 2.5 10.6 1.8 5.4Right 2.4 18.1 1.3 5.4
Note: Computed following the provisions of Eurocode 8 (CEN 2009).
JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2014 / 135
J. Geotech. Geoenviron. Eng. 2014.140:133151.
Dow
nloa
ded
from
asc
elib
rary
.org
by
Geo
rge
Gaz
etas
on
12/2
4/13
. Cop
yrig
ht A
SCE
. For
per
sona
l use
onl
y; a
ll ri
ghts
res
erve
d.

g Cffiffiffi3
pSu2s0
(4)
Parameters0, which controls the initiation of the nonlinear behavior,is defined as a fraction l (typically ranging from 0.1 to 0.3) of theyield stress sy
s0 lsy (5)
Finally, parameter C corresponds to the Youngs modulus for verysmall strains. If shear wave velocity (Vs) measurements are available, it can be computed directly. Alternatively, it can be estimatedusing empirical correlations (e.g., Hardin 1978; Robertson andCampanella 1983).
The model requires calibration of three parameters only: thesmallstrain elasticity modulus, C; the ultimate strength, sy; andthe yield stress, s0. In the case of clay, the calibration requires thefollowing data: (1) undrained shear strength, Su; (2) Go or Vs(measured or assessed through the aforementioned empirical correlations); and (3) Gg curves to calibrate parameter l. For thepurposes of the current study, model parameters were systematicallycalibrated according to the experimental Gg curves of Vucetic andDobry (1991). The model has been validated thoroughly againstcentrifuge and largescale model tests, as discussed in detail previously (Anastasopoulos et al. 2011), as well as against reducedscale tests conducted at the Laboratory of Soil Mechanics of theNational Technical University of Athens (Anastasopoulos et al.2012). It has been shown to be capable of predicting with engineering accuracy the experimentalmomentrotation (Mu) loops andthe settlementrotation (wu) response, both in terms of settlementper cycle and total residual settlement.Moreover, themodel has beenvalidated against the failure envelopes of Gourvenec (2007) for
a variety of footing shapes andmomenttoshear ratios (Gazetas et al.2013); this refers to the ultimate capacity and not the entire range ofnonlinear response.Admittedly, the potential of themodel to reliablysimulate the effects ofmomenttoshear ratio, embedment, and footingshape on the settlement for any possible combination has to bedemonstrated. While there is a breadth of failure envelopes in theliterature, the experimental data dealingwith cyclic or dynamic loadingare muchmore limited. Specific cases have been tested, and only thesecan be used for validation. Table 2 summarizes the validation of themodel.
The momentcurvature (Mc) response of structural members iscomputed with static crosssectional analysis using XTRACT 3.0.3.Reasonable assumptions are made for the metaplastic regime (i.e.,c. cu): (1) the residual moment (Mres) is presumed to be 30% of theultimate moment capacity (Mult) (Vintzileou et al. 2007), and (2)Mresis reached for cmax 5 3cult. A similar kinematic hardening model isemployed, as suggested by Gerolymos et al. (2005), to simulate thenonlinearMc response of structural members. Model parameters arecalibrated against the XTRACTcomputed, Mc relationships. Fora rectangular RCmember of width db and height dh, the strengthsy isdefined as
sy 4Mydb d2h
(6)
The small strain modulus C is equal to the Youngs modulus ofRC, while the yield stress is assumed to be
s0 sy10 (7)
A user subroutine, encoded in ABAQUS 6.9, simulates the metaplastic response (i.e., the descending branch) of RC cross sections,
Fig. 3. Finiteelement model of the soilfoundationstructure system: a typical equivalent slice of the building is analyzed in planestrain, takingaccount of material (soil and superstructure) and geometric (uplifting and PD effects) nonlinearities
136 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2014
J. Geotech. Geoenviron. Eng. 2014.140:133151.
Dow
nloa
ded
from
asc
elib
rary
.org
by
Geo
rge
Gaz
etas
on
12/2
4/13
. Cop
yrig
ht A
SCE
. For
per
sona
l use
onl
y; a
ll ri
ghts
res
erve
d.

as well as stiffness degradation with deformation and cycles ofloading.
Typical results for (monotonic) static pushover loading are presented in Fig. 4(a) for ground floor column 3. Complying withEurocode 8 (CEN 2009) provisions for wellreinforced, concretecross sections, all members are capable of attaining large values ofcurvature ductility (mw 10). After exhaustion of the availableductility, i.e., for c. cu, the column enters its metaplastic regime(descending branch), reaching its residual state for c5 cmax. Resultsof cyclic response of the structural members, showing the performance and limitations of the model, have been documented in
Gelagoti et al. (2012b), with due emphasis on the effect of stiffnessdegradation. The Mu response of the corresponding footing 3 isplotted in Fig. 4(b) for the two design alternatives. The momentcapacity of the conventionally designed B5 2:4 m footing issubstantially larger (by a factor of about 1.85) than that of column3: Mult 370 kNm.McRD 200 kNm. On the contrary, themoment capacity of the rockingisolated B5 1:3m footing isclearly smaller (by a factor of about 1.5) than that of the column:Mult9 130 kNm,McRD 200 kNm. Observe that the reductionof thewidth of the footingB leadsnot only to a reduction of its capacitybut also to reduced toppling rotation (uult).
Table 2. Summary of Model Validation
Reference FS M=Q (m) B (m) Da (m) Soil type Loading type Type/scale
Model effectivenessb
Rotationalstiffness (%)
Momentcapacity (%)
Accumulatedsettlement (%)
Anastasopouloset al. (2011)c
2.8 4.6 2.7 Clay Cyclic 6 0.01 rad Centrifuge 1:20 1 8 1
2.8 4.6 2.7 Clay Cyclic 6 0.02 rad Centrifuge 1:20 3 5 12.8 4.6 2.7 Clay Cyclic 6 0.06 rad Centrifuge 1:20 5 1 6
Anastasopouloset al. (2011)d
3 0.9 1 1 Loose sand Cyclic 6 0.02 rad Real scale 1:1 4 10 5
5 0.9 1 1 Dense sand Cyclic 6 0.02 rad Real scale 1:1 6 7 8Anastasopouloset al. (2012)e
2.1 13 7 Dense sand Cyclic 6 0.03 rad Reduced 1:20 5 10 14
3.5 13 7 Dense sand Cyclic 6 0.03 rad Reduced 1:20 12 7 47.3 13 11 Dense sand Cyclic 6 0.03 rad Reduced 1:20 8 3 7
Gazetas et al. (2013)f 0.0150 010 STg Clay Monotonic ultimate Analytical 814 412 0.0150 010 SQh Clay Monotonic ultimate Analytical 917 38 0.0150 010 Ri Clay Monotonic ultimate Analytical 1020 617 0.0150 010 Cj Clay Monotonic ultimate Analytical 817 214
aEmbedment depth.bError of model prediction compared to experimental or analytical values.cUC Davis centrifuge model tests (Anastasopoulos et al. 2011).dTRISEE largescale tests (Anastasopoulos et al. 2011).eNTUA reducedscale tests (Anastasopoulos et al. 2012).fPublished failure envelopes and impedances (Gazetas et al. 2013).gStrip foundations, various widths.hSquare foundations, various widths.iRectangular foundations, 1:3 lengthtowidth ratio, various widths.jCircular foundations, various diameters.
Fig. 4. (a) Mc response of firstfloor column 3 [ductile design according to Eurocode 8 (CEN 2009)]; (b) Mu response of the correspondingfooting 3, illustrating the effect of the reduction of its width B (for combined axial and shear force at a constant lever arm)
JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2014 / 137
J. Geotech. Geoenviron. Eng. 2014.140:133151.
Dow
nloa
ded
from
asc
elib
rary
.org
by
Geo
rge
Gaz
etas
on
12/2
4/13
. Cop
yrig
ht A
SCE
. For
per
sona
l use
onl
y; a
ll ri
ghts
res
erve
d.

Effectivenessof Rocking Isolation: DynamicAnalysis
The seismic performance of the two design alternatives is investigated through nonlinear dynamic timehistory analyses. To thisend, a set of 20 real accelerograms is used as seismic excitation,applied at the base of the soilfoundationstructure model. Asdepicted in Fig. 5 and summarized in Table 3, the selected seismic
records cover a wide range of earthquake characteristics, such aspeak ground acceleration (PGA), pseudo spectral velocity (PSV),maximum spectral acceleration (maxSA), maximum spectral velocity(maxSV), frequency content, number of strongmotion cycles, andduration. Some of these records are wellrecognized as bearing thesignature of near source (directivity andflingstep) effects. They rangefrom medium intensity (e.g., El Centro 1940 and Kalamata 1986) to
Fig. 5. Acceleration time histories of the 20 real records used (without scaling) as seismic excitation for the dynamic analysis of the two designalternatives, along with their acceleration and velocity elastic response spectra
138 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2014
J. Geotech. Geoenviron. Eng. 2014.140:133151.
Dow
nloa
ded
from
asc
elib
rary
.org
by
Geo
rge
Gaz
etas
on
12/2
4/13
. Cop
yrig
ht A
SCE
. For
per
sona
l use
onl
y; a
ll ri
ghts
res
erve
d.

very strong accelerograms (e.g., Takatori 1995 and Tabas 1978). Interms of spectral accelerations (SA), many of the considered accelerograms surpass the design spectrum of the frame for all periods ofinterest.
Because all the results cannot be presented in detail within thelimits of a single paper, emphasis is placed on elucidating theperformance of the two design alternatives for the case of very strongseismic shaking, using the Takatori record, which substantiallyexceeds the design spectrum of the frame. The performance of the twodesign alternatives for moderate intensity seismic shaking has beenexplored in detail in Gelagoti et al. (2012b). It was shown that, whenthe seismic excitation is within the design limits, the performance ofthe rockingisolated frame is practically equivalent to the conventionally designed one. In both cases, the structure would survive,sustaining acceptable structural damage. With conventional design,the structural damage perhaps could be reparable (flexural cracking ofbeams and columns), but not necessarily within serviceability limits.Incontrast, the rockingisolated structurewould sufferminor structuraldamage (flexural cracking of beams), and most probably could be inservice immediately after the earthquake. In both cases, the settlementwould be reasonable, with the performance of the rockingisolatedalternative being slightly worse. Results for the complete ensemble ofmotions are shown only in summary for each design alternative.Subsequently, the idealized Tsang motion (a modulated sinusoid) ofdominant periodT 5 0:5 s and parametrically variablePGA is utilizedfor some of our studies.
Performance in Strong Seismic Shaking
The Takatori record (Fukushima et al. 2000) of theMJMA 7.2, Kobe,Japan, 1995 earthquake, with ground motion beyond the designlimits, constitutes one of the most destructive accelerograms everrecorded, with a PGA 0:70g, PGV 169 cm=s, and dominantperiods at about 1.2 and 2 s. It bears the effects of both forwardrupture directivity and soil amplification.
The performance of the two design alternatives is compared inFig. 6. The deformed mesh with superimposed, plasticstrain contours of the two alternatives is portrayed in Fig. 6(a). With suchunrelenting seismic shaking, the conventionally designed frame
collapses under its gravity load (due to excessive drift of thestructure, the moments produced by PD effects cannot be sustainedby the columns, leading to loss of stability and total collapse). Asexpected, plastic hinges firstly develop in the beams and, subsequently, at the base of the three columns, while soil under thefootings remains practically elastic. The collapse also is evidencedby the substantial exceedance of the available curvature ductility ofthe columns [Fig. 6(b)]. Conversely, the rockingisolated framewithstands the shaking, with plastic hinging taking place only in thebeams, leaving the columns almost unscathed (elastic Mc response). Instead, plastic hinging nowdevelopswithin the underlyingsoil in the form of extended soil plastification [indicated by thered regions under the foundation in Fig. 6(a) and the Mu loops ofFig. 6(c)]. Thanks to the fact that the bendingmoment capacity of thecolumn is larger than that of the footing, damage is guided belowground and at the soilfoundation interface, in the form of detachment and uplifting [evidenced in Fig. 6(c) by the zero residualrotation upon unloading, unveiling the nonlinear but elastic upliftingcomponent of rotation], instead of aboveground.
In terms of Mu foundation response [Fig. 6(c)], the situationis reversed: conventional footings behave almost elastically, experiencing negligible rotation, whereas the underdesigned footingsreach several times their moment capacity and rotate significantly,creating loops indicative of energy dissipation. Nevertheless, aspreviously mentioned, the rotation never exceeds the ultimate rotation capacity (uult) of the footing, ensuring safety against collapsedue to rotational instability of the foundation, while residual rotationis minor because of the systems inherent gravityinduced, selfcentering capability. If the footing rotation had reached uult, itsmoment capacity would have been completely lost, and the latterwould perform as a hinge. This could lead to rotational instability ofthe footing and risk of collapse.At this ultimate stage of response, theseismic loads cannot be undertaken through frame action, becausethe beamcolumn connections have failed already (plastic hinges inbeams have formed already at an earlier stage).
The time histories of interstory drift further elucidate the aforementioned behavior of the two design alternatives [Fig. 6(d)]. Whilethe horizontal deformation of the conventionally designed frameincreases uncontrollably until collapse, the residual total drift of the
Table 3. Main Characteristics of the Seismic Records Used for the Analyses
Record Event Year Ms Mechanism RJB (km) PGA (g) PGV (cm=s)
GIC090 Salvador San Salvador, El Salvador 1986 5.8 Strikeslip 4 0.7 80Kalamata Kalamata, Greece 1986 6.2 Normal 7 0.27 24Lefkada Lefkada, Greece 2003 6.4 Strikeslip 8 0.45 34Pacoima Dam 164 San Fernando, CA 1971 6.5 Thrust 3 1.06 112Pacoima Dam 254 San Fernando, CA 1971 6.5 Thrust 3 1.16 Rinaldi 228 Northridge, CA 1994 6.8 Thrust 0 0.84 148Rinaldi 318 Northridge, CA 1994 6.8 Thrust 0 0.48 65Jensen 292 Northridge, CA 1994 6.8 Thrust 0 0.6 121Sylmar 090 Northridge, CA 1994 6.8 Thrust 3 0.604 74El Centro Imperial Valley, CA 1940 6.9 Strikeslip 8 0.32 29Erzincan Erzincan, Turkey 1992 6.9 Strikeslip 2 0.5 64Treasure Island Loma Prieta 1989 6.9 Strikeslip 77 0.17 33Duzce 180 Duzce, Turkey 1999 7.2 Strikeslip 8 0.35 60Takatori 000 Kobe, Japan 1995 7.2 Strikeslip 3 0.62 127JMA 000 Kobe, Japan 1995 7.2 Strikeslip 1 0.83 81Lucerne 000 Landers, CA 1992 7.3 Strikeslip 3 0.79 32Tabas Tabas, Iran 1978 7.4 Reverse 3 0.84 98Izmit Kocaeli, Turkey 1999 7.6 Strikeslip 4 0.22 30Yarimca Kocaeli, Turkey 1999 7.6 Strikeslip 4 0.26 85TCU068east ChiChi, Taiwan 1999 7.6 Reverse 1 0.48 260
JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2014 / 139
J. Geotech. Geoenviron. Eng. 2014.140:133151.
Dow
nloa
ded
from
asc
elib
rary
.org
by
Geo
rge
Gaz
etas
on
12/2
4/13
. Cop
yrig
ht A
SCE
. For
per
sona
l use
onl
y; a
ll ri
ghts
res
erve
d.

Fig. 6. Comparison of the performance of the two design alternatives subjected to very strong seismic shaking (Takatori, Kobe, Japan, 1995):(a) deformed mesh with superimposed plastic strain contours; (b) column bending Mc response; (c) foundation Mu response; (d) time histories ofground floor drift d (flexural dC , and due to foundation rotation dR)
140 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2014
J. Geotech. Geoenviron. Eng. 2014.140:133151.
Dow
nloa
ded
from
asc
elib
rary
.org
by
Geo
rge
Gaz
etas
on
12/2
4/13
. Cop
yrig
ht A
SCE
. For
per
sona
l use
onl
y; a
ll ri
ghts
res
erve
d.

rockingisolated frame is limited to 9 cm, corresponding to a driftratio d=h 2% (where h is the height of a single story). Yet, duringseismic shaking, the maximum total drift reaches 45 cm, whichimplies serious flexural distortion of the superstructure. Althoughnonstructural members (e.g., infill walls) are affected by such lateraldisplacement, columns do not suffer any structural damage, becausethe dominant component of the total drift stems from foundationrotation (dR), while theflexural drift component (dC) isminor [for thetwo drift components, see also Priestley et al. (1996)]. Finally, undersuch severe seismic excitation, when the conventionally designedframe cannot survive, the rockingisolated frame succeeds inavoiding collapse and even structural damage to its columns, butdamage to nonstructural members and beams (which exhaust theirductility capacity) is inevitable.
The two design alternatives are compared with respect to the wuresponse of the footings in Fig. 7. As expected, before the initiationof collapse, the conventionally designed footings experience relatively small (within serviceability limits) rotations and settlements
[Fig. 7(a)]. Completely different is the wu response of the rockingisolated system [Fig. 7(b)]: the footings undergo substantially largerrotations and accumulated settlements but still within tolerablelimits. This marked increase in settlement and rotation, inextricablyconnected to the rockinginduced energy dissipation mechanism, isthe price to pay for the survival of the structure.
Despite the fact that the three footings have been dimensioned tohave the same static factor of safety FS (in an attempt to minimizedifferential settlements exacerbated by asymmetry), the centralfooting settles more than the two side footings, leading to a differential settlement of the order of 3 cm.The difference in the settlementis mainly due to their differences in width. As previously discussed,the central footing was made larger (B5 1:8m compared to 1.1and 1.3 m of the two side footings) to maintain the same FS. Becausethe latter is common for the three footings, if the loading is moreor less the same, their responses should be similar. However, suchequivalence refers to dimensionless quantities not absolute values(seeKourkoulis et al. 2012a). In otherwords,while the three footings
Fig. 7. Performance of the two design alternatives subjected to very strong seismic shaking (Takatori, Kobe, Japan, 1995); comparison of foundationwu response for (a) the conventionally designed system; (b) the rockingisolated alternative; (c) axial force time histories of the columns of the rockingisolated frame
JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2014 / 141
J. Geotech. Geoenviron. Eng. 2014.140:133151.
Dow
nloa
ded
from
asc
elib
rary
.org
by
Geo
rge
Gaz
etas
on
12/2
4/13
. Cop
yrig
ht A
SCE
. For
per
sona
l use
onl
y; a
ll ri
ghts
res
erve
d.

sustain almost the same dimensionless settlement (w=B), which isroughly equal to 0:025 3 cm=1:2 m for the two side footings and0:033 6 cm=1:8m for the central one, the latter is substantiallylarger in width and, hence, its settlement is larger in absolute terms.Naturally, the three footings are not subjected to exactly the sameloading, something which further complicates the response.
Such differential settlements may inflict additional distress ontothe superstructure and, therefore, are worthy of further investigation.Fig. 7(c) depicts the time histories of axial force N at the base of thethree columns. Observe that the axial force at the central footing doesnot fluctuate as intensely as at the two side footings. More specifically, the axial load acting on the left footing (which belongs to thenarrow span) has the lower starting value and exhibits the greatestfluctuation during seismic shaking, leading to complete instantaneousdetachment from the supporting soil (N5 0), rendering the footingprone to sliding. After a complete detachment, the footingmay land ata slightly different position where the soil is in a less disturbed (morevirgin) state, thus limiting its settlement. However, such a landing ata substantially different position also would inflict horizontal differential displacements between the neighboring footingsa potentiallydetrimental kinematic effect.
Apart from this mechanism, the observed differential settlementalso is attributed to the tendency of the central footing to accumulatemore settlement than the two side footings. In fact, this tendency isa direct outcome of the design for a common FS, thanks to which thethree footings tend to accumulate equal dimensionless settlementw=B (see Kourkoulis et al. 2012b). Thus, being the largest in width,the middle footing settles the most.
PerformanceAssessment:SynopsisofAnalysisResults
For all the investigated seismic excitations of Fig. 5, Figs. 8 and 9summarize the performance of the two design alternatives, in terms ofdrift ratio (d=h) and permanent settlement (w). The results are plottedwith respect to the maximum pseudo spectral velocity (maxPSV)evidently amore representative seismic intensitymeasure for inelasticsystems (Bertero 1976; Garini and Gazetas 2013).
In terms of total (i.e., rotational and flexural) maximum drift ratio(dmax=h), with the exception of the three cases of collapse of theconventionally designed system, the performance of the two designalternatives is practically equivalent [Fig. 8(a)]. Considering the totalresidual drift ratio, dres=h [Fig. 8(b)], the rockingisolated systemoutperforms the conventionally designed one when maxPSV exceeds150 cm=s. For moderate intensity seismic excitations, not exceedingthe design limits (maxPSV , 100 cm=s), the drift ratio d=h is almostthe same for the two design alternatives. In three extreme seismicscenarios (Takatori, Rinaldi, and JMA), during which the conventionally designed system cannot survive, the rockingisolated systemaccumulates a permanent drift ratio of up to 4% but avoids collapse.The superior performance of the rockingisolated system becomeseven more evident when examining the flexural residual drift ratio,dc,res=h [Fig. 8(c)], which is a direct indicator of column structuraldamage. In no case does the flexural drift ratio (dc=h) of the rockingisolated frame exceed 1%: the column response satisfies even strictserviceability limits (Priestley et al. 2007). For moderate seismicshaking (maxPSV , 100 cm=s), the flexural drift ratio, dC=h (whichis an indicator of structural damage), is slightly lower for the rockingisolated frame, confirming the previously mentioned conclusions(see also Gelagoti et al. 2012b). Conversely, in over 50% of the(intentionally strong) seismic excitations examined herein, the conventionally designed frame suffers irrecoverable damage and replacement is inevitable. In three cases it even reaches the state ofcollapse.
Regarding permanent settlement (w), Fig. 9 shows that the sidefootings (left and right) of the two design alternatives experiencesimilar settlements. For moderate seismic shaking [pseudo spectralvelocity (PSV, 100 cm=s], the two design alternatives are practically equivalent, with the settlement of the central footing reachingroughly 3 cm and that of the side footings not exceeding 2 cm. In thecase of strong seismic shaking, the inherent difference between the twobecomes evident at the central footings, with the underdesignedfooting of the rockingisolated frame accumulating conspicuouslylarger settlement. Hence, the previously detected problem of differential settlement for the Takatori record proves to be of fairly generalvalidity, and not just a particular case. More specifically, for the(admittedly very strong) seismic excitations used herein, the differential settlement of the rockingisolated frame ranges from0.3 to 5 cm.(The total seismic settlement of the central footing ranges from 1.5 to7.5 cm.)Although the effectiveness of the newdesign scheme remainsunquestionable in terms of life safety, it would be of interest tominimize differential settlements to improve the performance in termsof serviceability.
The Role of Asymmetry on Differential Settlement
The investigated frame resembles the one analyzed in Gelagoti et al.(2012b) but it is asymmetric. Because the performance of thesymmetric rockingisolated framewas almost immune to differentialsettlements, it can be inferred that the asymmetry plays a key role inthis respect. Hence, to gain a deeper insight on the role of frameasymmetry, an idealized modulated sinusoidal (Tsangtype) motionwas used next as seismic excitation (Fig. 10). Containing amultitudeof constantamplitude, strongmotion cycles, it is an extreme butideally symmetric seismic excitation, allowing the role of frameasymmetry to be distinguished. The analysis was conducted fordifferent acceleration amplitudes, ranging from PGA5 0:2 to 1g,aiming to shed light on asymmetrys effect on the accumulation ofdifferential settlement.
Fig. 10(a) depicts the settlement of the three footings as a functionofPGA. Evidently, the response is asymmetric despite the symmetryof loading. For small to medium intensity seismic excitations,PGA# 0:6g, the differential settlement ranged from 0.5 to 5 cm,being roughly equivalent to what was observed for real seismicexcitations. As the intensity of seismic excitation increased toPGA. 0:6g, the central footing continued to settle at the same oreven increased rate, while the settlements of the two side footingstended to stabilize or even reduce. Hence, the residual differentialsettlement increases, to the detriment of the structural behavior of theframe. For the extreme case of PGA5 1g, the differential settlementreached 18 cm. Interestingly, the settlement of the left footing wasfound to decrease from5 to 1 cmwhen thePGA increased from0.8 to1g; this prompted further investigation of the response for the extreme case of PGA5 1g.
Fig. 10(b) illustrates the wu response of the three footings. Aspreviously noticed with the Takatori excitation, the left footingexperiences sliding and complete detachment from the bearing soil.After each such complete detachment, it tends to land in a differentposition where the soil has not been disturbed with plasticdeformations; thus, its settlement is reduced. The increase of PGAleads to an aggravation of this phenomenon and a correspondingdecrease of its final settlement. At the same time, due to theaforementioned complete loss of contact, its rotation (u) becomesuncontrollable, reaching excessively large values (0.13 rad)compared to the other two footings, which do not experiencefull detachment and barely reach 0.02 rad. At the same time, thecentral footing exhibits a sinking response, accumulating a residual
142 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2014
J. Geotech. Geoenviron. Eng. 2014.140:133151.
Dow
nloa
ded
from
asc
elib
rary
.org
by
Geo
rge
Gaz
etas
on
12/2
4/13
. Cop
yrig
ht A
SCE
. For
per
sona
l use
onl
y; a
ll ri
ghts
res
erve
d.

settlement of 19 cm (for this motion with a huge number of uniformstrongmotion cycles). As a result, the frame is subjected to excessive differential settlements, in addition to differential horizontal displacement (due to the random landing of the left footing ata different location after each cycle), and significant leftfootingrotations. This leads to substantial kinematic frame distortion,partly brought about by the differential settlement and partly by thehorizontal divergence of the two footings and their differentialrotations.
To summarize, because of its geometric asymmetry, the rockingisolated frame may respond unpredictably when subjected to extremely strong seismic excitation. Nevertheless, even under suchextreme multicycle sinusoidal shaking of PGA5 1g, the isolated
structure does not collapse. However, its serviceability is notguaranteed, calling for remedial measures.
Investigation of Remedial Measures
A widely accepted practice, typically entrenched in modern seismiccodes, is the addition of tie beams between the footings (in thelongitudinal and transverse directions). Mobilizing their axial stiffness, tie beams act as a diaphragm forcing the footings to maintainthe same horizontal displacement. In addition, thanks to their flexural stiffness, they also contribute to reducing differential settlements. However, exactly because of their flexural stiffness, the (fully
Fig. 8. Synopsis of the performance of the two design alternatives with respect to the maximum PSV: (a) total maximum drift ratio for the ground floordmax=h (where h is the height of the ground floor); (b) total residual drift ratio for the ground floor dres=h; (c) residual flexural drift ratio dC,res=h; thedamage level is determined with reference to response limit states (Priestley et al. 1996)
JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2014 / 143
J. Geotech. Geoenviron. Eng. 2014.140:133151.
Dow
nloa
ded
from
asc
elib
rary
.org
by
Geo
rge
Gaz
etas
on
12/2
4/13
. Cop
yrig
ht A
SCE
. For
per
sona
l use
onl
y; a
ll ri
ghts
res
erve
d.

fixed) tie beams also would increase the moment capacity of thefoundation system, and may cancel the rocking isolation. Thus, twoadditional nonconventional solutions are explored.
Frame with a Single Fully Fixed Tie Beam
Monolithically connected to the footings, such a tie beam isdesigned according to current seismic codes to provide adequateaxial stiffness for resisting differential horizontal displacements.According to Eurocode 8 (CEN 2009), for instance, the design axialforce for a given soil category is proportional to: (1) the average,NED, of the axial loads of the two columns connected by this beam;and (2) the effective design ground acceleration, A5ag. ForEurocode 8 (CEN 2009) Soil Category C, appropriate for the systems investigated herein,
FTIE 60:40a SNED (8)
where a5A=g5 0:40; and S5 1:15. For the studied frame, theresulting tie beams have a 0:303 0:65 m rectangular cross sectionand are reinforced with 6F14quite typical for structures adheringto the provisions of Eurocode 8 (CEN 2009). Their Mc response iscomputed as describedpreviously usingXTRACT and is of theorder of
150 kNm. Tsang motions are utilized as seismic excitation, withacceleration amplitudes ranging from 0.2 to 1g and a dominant periodof 0.5 s.
Fig. 11(a) depicts the Mc response of the three groundfloorcolumns for the worstcase scenario, amax 5 1g. As suspected, theresponse of the three columns was highly nonlinear, revealing thatthe addition of the conventional (fully fixed) tie beams practicallycancelled rocking isolation. The middle and the right columnsexperienced a ductility largely exceeding their capacity. The performance of the left column was also nonlinear, but its ductilitycapacity was not completely expended. In contrast to the wholerationale of the rockingisolation concept, exactly owing to theadditionalmoment restraint provided by the fullyfixed tie beams, themoment capacity of the combined foundation system (footings andtie beams) is larger than the capacity of the columns. In other words,their effect is related to the additional resistance they provide in termsof moment capacity of the foundation system. Because the columnmoment capacity, MRD, is of the order of 200 kNm, eventhe addition of 70 kNm of moment resistance would be enoughto cancel rocking isolation: the moment capacity, Mult, of theunderdesigned footings is of the order of 130 kNm [Fig. 4(b)]. Aspreviously mentioned, the simulated tie beams have a momentcapacity of the order of 150 kNm. As a result, the middle and right
Fig. 9. Synopsis of the performance of the two design alternatives in terms of foundation settlementwwith respect to themaximum PSV of the seismicexcitation: (a) conventionally designed system; (b) rockingisolated alternative
144 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2014
J. Geotech. Geoenviron. Eng. 2014.140:133151.
Dow
nloa
ded
from
asc
elib
rary
.org
by
Geo
rge
Gaz
etas
on
12/2
4/13
. Cop
yrig
ht A
SCE
. For
per
sona
l use
onl
y; a
ll ri
ghts
res
erve
d.

footings exhibited an almost elastic response [Fig. 11(b)]. It is notedthat themoment in the footingtie beam system clearly surpassed theultimate monotonic moment capacity (gray line), which wascomputed for the rockingisolated frame without tie beams.
Fig. 11(c) illustrates the wu response of the three footings.Indeed, the tie beams reduce the differential settlement: 12 cm asopposed to 19 cm without tie beams. Regarding the previouslyobserved complete detachment of the left footing and the associatedexcessive rotation and sliding, the addition of conventional tie beamsprovided substantial but not satisfactory improvement: the leftfooting still rotated excessively, partly because of plastic hinging ofthe tie beam itself.
Thus, conventional fully fixed tie beams may eliminate thehorizontal differential displacements, reduce somewhat the differential settlements, and partially hinder the detachment of the leftfooting; but, owing to their monolithic connection to the footings,they also eliminate rocking isolation, rendering the frame performance almost identical to that of the conventionally designed framewithout tie beams.
Hinged Tie Beams
Aiming to maintain the beneficial effects of rocking isolation whilereducing the differential settlement, hinged tie beams (which would
not restrain the rotation of the footings) are considered. Indeed,thanks to their axial stiffness, the hinged tie beams restrict the lateraldifferential displacements between the footings. Such hinged connection can be materialized by placing the reinforcement at thecenter of the concrete cross section, as conceptually shown inFig. 12, or through the addition of prefabricated steel hinges.
The same analysis is repeated, subjecting the frame to the Tsangtype excitation with PGA parametrically varying from 0.2 to 1g.Fig. 12(a) illustrates theMc response of the three frame columns (attheir bases) for the worstcase scenario, PGA5 1g. As expected,the columns remained elastic, in accordance with the principles ofrocking isolation. The Mu curves of the three footings werenonlinear and consistent with their monotonic curves, which act as(approximate) envelopes for the cyclic loading [Fig. 12(b)]. Owingto their hinged connection to the footings, the tie beams did notincrease the moment capacity of the foundation system, as was thecase with fully fixed tie beams.
However, the performance in terms of differential footing settlements was not sufficiently improved [Fig. 12(c)]: the rotation ofthe left footing was reduced by almost 50% (compared to the case ofno tie beams), but the differential settlements still reached 12 cm(compared to 19 cm of the frame without tie beams). Their failure toreduce the differential settlements stems exactly from their hingedconnection to the footings. As schematically illustrated in Fig. 12
Fig. 10. Performance of the rockingisolated alternative subjected to multicycle Tsangtype pulses (top): (a) settlement of the three footings withrespect to the acceleration amplitude amax; (b) wu response of the three footings for very strong shaking with amax 5 1g, foundation wu response; themaximum differential settlement reaches 19 cm
JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2014 / 145
J. Geotech. Geoenviron. Eng. 2014.140:133151.
Dow
nloa
ded
from
asc
elib
rary
.org
by
Geo
rge
Gaz
etas
on
12/2
4/13
. Cop
yrig
ht A
SCE
. For
per
sona
l use
onl
y; a
ll ri
ghts
res
erve
d.

(top), because of their hinged connection to the footings, the twoseparate tie beams can actually rotate as rigid bodies without developing any substantial resistance in the vertical sense: theirflexural rigidity cannot be mobilized. This means that the centralfooting is free to develop its own settlement, hardly restrained by thesmaller settlement of the two side footings. Naturally, however, theiraxial rigidity is fully mobilized, leading to the reduction of settlements and the horizontal differential displacements.
Hybrid Tie Beams
Aiming to combine the advantages of conventional (fully fixed) andhinged tie beams and avoid their distinct disadvantages, a hybridconcept was conceived and investigated. As shown in Fig. 13 (top),it consists of one continuous tie beam (instead of two separate ones)placed behind the columns (i.e., in a second row) and connectedwithexternal hinges (rather than fixed) to the columns. There are various
Fig. 11. Performance of the rockingisolated alternative equipped with conventional, fully fixed tie beams, subjected to very strong seismic shaking(Tsangtype excitation of amax 5 1g): (a) Mc of the three ground floor columns; (b) Mu response; (c) wu response of the three footings; themaximum differential settlement is reduced to 12 cm, but rocking isolation is practically canceled
146 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2014
J. Geotech. Geoenviron. Eng. 2014.140:133151.
Dow
nloa
ded
from
asc
elib
rary
.org
by
Geo
rge
Gaz
etas
on
12/2
4/13
. Cop
yrig
ht A
SCE
. For
per
sona
l use
onl
y; a
ll ri
ghts
res
erve
d.

means to materialize such external hinges, with the simpler onebeing to connect the tie beamwith the columns using centrally placedsteel reinforcement as shown. Alternatively, special prefabricatedsteel components (typically used in bridges) can be utilized.
Thus, it is expected that the flexural rigidity of the tie beams canbe mobilized adequately, homogenizing the settlements of the threefootings (and, hence, reducing their differential settlements), while
at the same time allowing their rocking (and, hence, preservingthe benefits of rocking isolation for the superstructure).
Response to TsangType Excitation
To confirm the aforementioned expectations, the system wassubjected to the same Tsangtype motions, with PGA ranging
Fig. 12. Performance of the rockingisolated alternative equipped with hinged tie beams, subjected to very strong dynamic shaking (Tsangtypeexcitation of amax 5 1g): (a) Mc of the three ground floor columns; (b) Mu response; (c) wu response of the three footings; rocking isolation ismaintained, but the reduction of differential settlement still lies within unsatisfactory limits (11.5 cm)
JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2014 / 147
J. Geotech. Geoenviron. Eng. 2014.140:133151.
Dow
nloa
ded
from
asc
elib
rary
.org
by
Geo
rge
Gaz
etas
on
12/2
4/13
. Cop
yrig
ht A
SCE
. For
per
sona
l use
onl
y; a
ll ri
ghts
res
erve
d.

parametrically from 0.2 to 1g. As shown in Fig. 13(a), whichillustrates theMc response of the three columns for the worstcasescenario of PGA5 1g, the performance of the frame was consistent with the idea of rocking isolation, with all of its columnsexhibiting elastic or nearly elastic response. This is further verifiedby theMu response of the three footings, which was nonlinear and(with the exception of the left footing) consistent with their monotonicpushover response [Fig. 13(b)]. The left footing exhibited an apparent
overstrength, which is associated with the axial restraint provided bythe hybrid tie beams.
The advantageous performance of the hybrid tie beams becomesevidentwhen examining thewu response of the footings [Fig. 13(c)].The differential settlement between the middle and the side footingsdecreased impressively to just 2.5 cm, as opposed to 19 cm of thereference case (without tie beams). Given the extreme intensity of theseismic excitation (containing 10 strongmotion cycles of PGA5 1g
Fig. 13. Performance of the rockingisolated alternative equipped with hybrid tie beams, subjected to very strong dynamic shaking (Tsangtypeexcitation of amax 5 1g): (a) Mc of the three ground floor columns; (b) Mu response; (c) wu response of the three footings; rocking isolation ismaintained while a spectacular decrease in differential settlement is observed (merely 2.5 cm)
148 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2014
J. Geotech. Geoenviron. Eng. 2014.140:133151.
Dow
nloa
ded
from
asc
elib
rary
.org
by
Geo
rge
Gaz
etas
on
12/2
4/13
. Cop
yrig
ht A
SCE
. For
per
sona
l use
onl
y; a
ll ri
ghts
res
erve
d.

with a period of 0.5 s), this can be said to constitute a remarkableimprovement in seismic performance.
Response to Recorded Accelerograms
To confirm the effectiveness of the hybrid ties, the system was subjected to the previously described set of real seismic motions. Fig. 14compares the performance of the rockingisolated frame equippedwithhybrid ties to the reference case (rockingisolated frame without tiebeams), in terms of footing settlement versus peak spectral pseudovelocity,maxPSV, of the seismic excitation. The addition of the hybridtie beams led to an increase of the settlement of the two side footingsand to a decrease of the settlement of the central footing. As a result,the differential settlement was reduced substantially, by 2560%,depending on the intensity of the seismic excitation.
To shed more light on the observed performance amelioration,the response to the particular seismic excitation that induces thelargest differential settlement, namely the Tabas record, is presentedin detail in Fig. 15. While in the reference case the differentialsettlement reached 5 cm [Fig. 15(a)], the addition of hybrid tie beamsreduced it to merely 1.9 cm [Fig. 15(b)]. At the same time, theperformance in terms of drift ratio (not shown herein) remainedpractically the same, as the hybrid tie beams do not preclude therocking response of the footings. Therefore, even under such extreme seismic shaking, the performance of the frame equipped withhybrid tie beams is excellent, maintaining the advantages of rockingisolation and minimizing the differential settlements.
Conclusions
The presented nonlinear numerical analyses have verified the effectiveness of rocking isolation for an asymmetric 2story, 2bayframe. The numerical model employed herein has been validatedthoroughly against centrifuge and largescale model tests, as well asagainst published failure envelopes for a variety of footing shapesand momenttoshear ratios. The ability of the model to accuratelysimulate the effects of momenttoshear ratio, embedment, andfooting shape with respect to the accumulation of settlement havenot yet been demonstrated fully for any possible combination of theabove. Emphasis has been placed on the significance of frame asymmetry, aiming at detecting possible limitations of this new seismicdesign scheme, mainly pertaining to serviceability requirements. Thekey conclusions are summarized as follows:1. In all cases examined, the overall performance of the rocking
isolated design alternative is superior to that of the conventionally designed system. While the latter may sustain irreparablestructural damage or even collapse when subjected to verystrong seismic shaking, the rockingisolated system surviveseven the most extreme seismic excitation with minor flexuraldamage.
2. The asymmetry of the investigated frame complicates theresponse, leading to larger differential settlements than thoseexperienced by the symmetric counterpart. This differencein settlement accumulation stems from the redistribution ofaxial forces during seismic shaking, especially the substantial
Fig. 14. Synopsis of the performance of the two rockingisolated frames in terms of foundation settlement wwith respect to the maximum PSV of theseismic excitation: (a) no tie beams compared to (b) hybrid tie beams; the differential settlement between the middle and the side footings, evident in allcases, averages around 40%
JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2014 / 149
J. Geotech. Geoenviron. Eng. 2014.140:133151.
Dow
nloa
ded
from
asc
elib
rary
.org
by
Geo
rge
Gaz
etas
on
12/2
4/13
. Cop
yrig
ht A
SCE
. For
per
sona
l use
onl
y; a
ll ri
ghts
res
erve
d.

unloading of the left footing, inevitably leading to sliding andeven complete detachment from the bearing soil. The ensuinglanding onto the ground surface at a locationwhere the soil has,up to that point, undergone less intense yielding deformation,results in relatively reduced dynamic settlement. Combinedwith the inherent tendency of themiddle footing to accumulatemore settlement, as it carries a larger axial load, the resultingdifferential settlement may lead to additional (kinematicallyinduced) frame distress. Of course, in reality, such footings areusually embedded (to some extent) and such a behavior is lesslikely to be observed.
3. To alleviate the problem of differential displacements, theaddition of tie beams between the footings has been explored.Besides the conventional fully fixed tie beams, two additionalsolutions are conceived and analyzed. The key conclusions areas follows: Conventional fully fixed tie beams may reduce the differ
ential settlements and partially hinder the detachment of theleft footing, but prevent rocking isolation as their rotationalresistance is added to that of the footing, rendering the performance of the frame almost identical to that of the conventionally designed system (with overdesigned foundations).
In an attempt to maintain their beneficial effects withoutcanceling rocking isolation, two separate hinged tie beamswere placed between the footings. In contrast to conventional fully fixed tie beams and owing to their hingedconnection, these beams do not increase the capacity ofthe foundation system, allowing the frame to behaveaccording to its rockingisolation design. But, the differential settlements are hardly reduced: the hinged tie beamscan rotate as rigid bodies, without mobilizing their flexuralresistance and, hence, without offering substantial resistance in the vertical sense. Naturally, their axial rigidity is
fully mobilized, leading to a reduction of the horizontaldifferential displacements.
Aiming to combine the advantages of conventional (fullyfixed) and hinged tie beams, a hybrid concept has beenconceived and analyzed: a single (continuous) tie beamconnected with external hinges to the three footings. Thishybrid design allowsmobilization of the flexural rigidity ofthe tie beams, leading to homogenization of the settlementsof the three footings and to an impressive reduction ofdifferential settlements, without preventing rocking.
Acknowledgments
The authors are thankful for the financial support provided throughthe research project DARE, by the European Research Councils(ERCs) IDEAS Programme, in Support of Frontier Research.Contract No. ERC29AdG228254DARE. The authors also acknowledge the anonymous reviewers for their very thoughtfulcomments and suggestions.
References
ABAQUS 6.9 [Computer software]. Providence, RI, ABAQUS.Anastasopoulos, I., Gazetas, G., Loli,M.,Apostolou,M., andGerolymos,N.
(2010). Soil failure can be used for seismic protection of structures.Bull. Earthquake Eng., 8(2), 309326.
Anastasopoulos, I., Gelagoti, F., Kourkoulis, R., and Gazetas, G. (2011).Simplified constitutive model for simulation of cyclic response ofshallow foundations: Validation against laboratory tests. J. Geotech.Geoenviron. Eng., 137(12), 11541168.
Anastasopoulos, I., Loli, M., Gelagoti, F., Kourkoulis, R., and Gazetas, G.(2012). Nonlinear soilfoundation interaction: Numerical analysis.
Fig. 15. Performance of the rockingisolated alternative subjected to very strong seismic shaking (Tabas record) in terms of foundation settlementrotation (wu) response: (a) without tie beams compared to (b) with hybrid tie beams; the differential settlement is reduced from 5 to less than 2 cm
150 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2014
J. Geotech. Geoenviron. Eng. 2014.140:133151.
Dow
nloa
ded
from
asc
elib
rary
.org
by
Geo
rge
Gaz
etas
on
12/2
4/13
. Cop
yrig
ht A
SCE
. For
per
sona
l use
onl
y; a
ll ri
ghts
res
erve
d.
http://dx.doi.org/10.1007/s1051800991452http://dx.doi.org/10.1061/(ASCE)GT.19435606.0000534http://dx.doi.org/10.1061/(ASCE)GT.19435606.0000534

2nd Int. Conf. on PerformanceBased Design in Earthquake Geotechnical Engineering, Patron Editore, Bologna, Italy, Paper No. 10.03.
Anastasopoulos, I., Loli, M., Georgarakos, T., and Drosos, V. (2013).Shaking table testing of rocking2isolated bridge pier. J. EarthquakeEng., 17(1), 132.
Apostolou, M., Gazetas, G., and Garini, E. (2007). Seismic response ofslender rigid structures with foundation uplifting. Soil Dyn. EarthquakeEng., 27(7), 642654.
ASCE. (2000). Prestandard and commentary for the seismic rehabilitationof buildings. FEMA 356 Prepared for FEMA, Reston, VA.
Beck, J., and Skinner, R. I. (1974). The seismic response of a reinforcedconcrete bridge pier designed to step. Earthquake Eng. Struct. Dynam.,2(4), 637655.
Bertero, V. V. (1976). Establishment of design earthquakes: Evaluation ofpresent methods. Int. Symposium on Earthquake Structural Engineering, St. Louis, 551580.
Chatzigogos, C. T., Pecker, A., and Salencon, J. (2009). Macroelement modeling of shallow foundations. Soil Dyn. Earthquake Eng., 29(5), 765781.
Chopra,A., andYim,S. (1985). Simplified earthquake analysis of structureswith foundation uplift. J. Struct. Eng., 111(4), 906930.
Deng, L., and Kutter, B. L. (2012). Characterization of rocking shallowfoundations using centrifuge model tests. Earthquake Eng. Struct.Dynam., 41(5), 10431060.
Deng, L., Kutter, B. L., andKunnath, S.K. (2012a). Centrifugemodeling ofbridge systems designed for rocking foundations. J. Geotech. Geoenviron. Eng., 138(3), 335344.
Deng, L., Kutter, B. L., and Kunnath, S. K. (2012b). Probabilistic seismicperformance of rockingfoundation and hingingcolumn bridges.Earthquake Spectra, 28(4), 14231446.
European Committee for Standardization (CEN). (2009). Design provisionsfor earthquake resistance of structures. Part 5: Foundations, retainingstructures and geotechnical aspects. Eurocode 8, Brussels, Belgium.
Faccioli, E., Paolucci, R., and Vivero, G. (2001), Investigation of seismicsoilfooting interaction by large scale cyclic tests and analyticalmodels.Proc., 4th Int. Conf. on Recent Advances in Geotechnical EarthquakeEngineering and Soil Dynamics, San Diego, Paper No. SPL5.
Fukui, J., Shirato,M., Yoshinori, N., and Ryuichi, A. (2005). Experimentalstudy on the residual displacement of shallow foundations subjected tocyclic loads. Technical Memorandum of PWRI, 4027, Public WorksResearch Institute, Tsukuba, Japan.
Fukushima, Y., Irikura, K., Uetake, T., and Matsumoto, H. (2000).Characteristics of observed peak amplitude for strong ground motionfrom the 1995HyogokenNanbu (Kobe) earthquake.Bull. Seismol. Soc.Am., 90(3), 545565.
Gajan, S., and Kutter, B. L. (2008). Capacity, settlement, and energydissipation of shallow footings subjected to rocking. J. Geotech.Geoenviron. Eng., 134(8), 11291141.
Gajan, S., and Kutter, B. L. (2009a). Contact interface model for shallowfoundations subjected to combined cyclic loading. J. Geotech. Geoenviron. Eng., 135(3), 407439.
Gajan, S., and Kutter, B. L. (2009b). Effects of momenttoshear ratio oncombined cyclic loaddisplacement behavior of shallow foundationsfrom centrifuge experiments. J. Geotech. Geoenviron. Eng., 135(8),10441055.
Gajan, S., Kutter, B. L., Phalen, J. D., Hutchinson, T. C., and Martin, G. R.(2005). Centrifuge modeling of loaddeformation behavior of rockingshallow foundations. Soil Dyn. Earthquake Eng., 25(710), 773783.
Garini, E., and Gazetas, G. (2013). Damage potential of nearfault records:Sliding displacement against conventional intensity measures. Bull.Earthquake Eng., 11(2), 455480.
Gazetas, G., Anastasopoulos, I., Adamidis, O., and Kontoroupi, T. (2013).Nonlinear rocking stiffness of foundations. Soil Dyn. EarthquakeEng., 47(April 2013), 8391.
Gazetas,G., Apostolou,M., andAnastasopoulos, I. (2003). Seismic upliftingof foundations on soft soil, with examples from Adapazari (Izmit 1999,earthquake). BGA Int. Conf. on Foundation Innovations, Observations,Design & Practice, British Geotechnical Association, London, 3750.
Gelagoti, F. (2010). Metaplastic response and collapse of framefoundationsystems and the concept of rocking isolation. Ph.D. thesis, NationalTechnical Univ., Athens, Greece.
Gelagoti, F., Kourkoulis, R., Anastasopoulos, I., and Gazetas, G. (2012a).Rockingisolated frame structures: Margins of safety against topplingcollapse and simplified design approach. Soil. Dyn. Earthquake Eng.,32(1), 87102.
Gelagoti, F., Kourkoulis, R., Anastasopoulos, I., and Gazetas, G. (2012b).Rocking isolation of frame structures founded on separate footings.Earthquake Eng. Struct. Dynam., 41(7), 11771197.
Gerolymos,N.,Gazetas,G., andTazoh,T. (2005).Seismic responseofyieldingpile in nonlinear soil. Proc. 1st GreeceJapan Workshop on SeismicDesign, Observation, andRetrofit of Foundations,G.Gazetas, Y. Goto, andT. Tazoh, eds., National Technical Univ. of Athens, Athens, Greece, 2536.
Gourvenec, S. (2007). Shape effects on the capacity of rectangular footingsunder general loading. Gotechnique, 57(8), 637646.
Hardin, B. (1978). The nature of stressstrain behavior for soils. Earthquake Engineering and Soil Dynamics, ASCE Specialty Conf., Vol. 1,ASCE, Reston, VA, 390.
Kawashima, K., Nagai, T., and Sakellaraki, D. (2007). Rocking seismicisolation of bridges supported by spread foundations. Proc., 2ndJapanGreece Workshop on Seismic Design, Observation, and Retrofitof Foundations, Japan Society of Civil Engineers, Tokyo, 254265.
Kourkoulis, R., Anastasopoulos, I., Gelagoti, F., and Kokkali, P. (2012a).Dimensional analysis of SDOF systems rocking on inelastic soil.J. Earthquake Eng., 16(7), 9951022.
Kourkoulis, R., Gelagoti, F., and Anastasopoulos, I. (2012b). Rockingisolation of frames on isolated footings: design insights and limitations.J. Earthquake Eng., 16(3), 374400.
Kutter, B. L., Martin, G., Hutchinson, T. C., Harden, C., Gajan, S., andPhalen, J. D. (2003). Status report on study of modeling of nonlinearcyclic loaddeformation behavior of shallow foundations. PEERWorkshop, Univ. of California, Davis, CA.
Martin, G. R., and Lam, I. P. (2000). Earthquake resistant design offoundations: Retrofit of existing foundations. Proc. GeoEng 2000Conf., Melbourne, Australia.
Mergos, P. E., and Kawashima, K. (2005). Rocking isolation of a typicalbridge pier on spread foundation. J. Earthquake Eng., 9(2), 395414.
Negro, P., Paolucci, R., Pedretti, S., and Faccioli, E. (2000). Largescalesoilstructure interaction experiments on sand under cyclic loading.Proc. 12th World Conf. on Earthquake Engineering, Auckland, NewZealand, Paper No. 1191.
Panagiotidou, A. I., Gazetas, G., and Gerolymos, N. (2012). Pushover andseismic response of foundations on stiff clay: Analysis with Pdeltaeffects. Earthquake Spectra, 28(4), 15891618.
Paolucci, R., and Pecker, A. (1997). Seismic bearing capacity of shallowstrip foundation on dry soils. Soils Found., 37(3), 95105.
Paolucci, R., Shirato, M., and Yilmaz, M. T. (2008). Seismic behaviour ofshallow foundations: Shaking table experiments vs numerical modeling. Earthquake Eng. Struct. Dynam., 37(4), 577595.
Park,R., andPaulay,T. (1975).Reinforcedconcrete structures,Wiley,NewYork.Pecker, A. (1998). Capacity design principles for shallow foundations in
seismic areas.Proc., 11th European Conf. on Earthquake Engineering,Vol. 3, Balkema, Rotterdam, Netherlands.
Pecker, A. (2003). Aseismic foundation design process, lessons learnedfrom two major projects: The Vasco de Gama and the Rion Antirionbridges. ACI Int. Conf. on Seismic Bridge Design and Retrofit, Univ. ofCalifornia, San Diego.
Pecker, A., and Pender, M. J. (2000). Earthquake resistant design offoundations: New construction. Proc., GeoEng 2000 Conf., Vol. 1,Melbourne, Australia, 313332.
Priestley,M. J. N., Calvi, G.M., andKowalsky,M. J. (2007).Displacementbased seismic design of structures, IUSS Press, Pavia, Italy.
Priestley, M. J. N., Seible, F., and Calvi, G. M. (1996). Seismic design andretrofit of bridges, Wiley, New York.
Robertson, P. K., and Campanella, R. G. (1983). Interpretation of conepenetration tests. Part II: Clay. Can. Geotech. J., 20(4), 734745.
Vintzileou, E., Tassios, T. P., and Chronopoulos, M. (2007). Experimentalvalidation of seismic code provisions for RC columns. Eng. Struct.,29(6), 11531164.
Vucetic, M., and Dobry, R. (1991). Effect of soil plasticity on cyclicresponse. J. Geotech. Engrg., 117(1), 89107.
XTRACT 3.0.3 [Computer software]. Rancho Cordova, CA, Imbsen.
JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2014 / 151
J. Geotech. Geoenviron. Eng. 2014.140:133151.
Dow
nloa
ded
from
asc
elib
rary
.org
by
Geo
rge
Gaz
etas
on
12/2
4/13
. Cop
yrig
ht A
SCE
. For
per
sona
l use
onl
y; a
ll ri
ghts
res
erve
d.
http://dx.doi.org/10.1080/13632469.2012.705225http://dx.doi.org/10.1080/13632469.2012.705225http://dx.doi.org/10.1016/j.soildyn.2006.12.002http://dx.doi.org/10.1016/j.soildyn.2006.12.002http://dx.doi.org/10.1016/j.soildyn.2008.08.009http://dx.doi.org/10.1061/(ASCE)07339445(1985)111:4(906)http://dx.doi.org/10.1002/eqe.1181http://dx.doi.org/10.1002/eqe.1181http://dx.doi.org/10.1061/(ASCE)GT.19435606.0000605http://dx.doi.org/10.1061/(ASCE)GT.19435606.0000605http://dx.doi.org/10.1193/1.4000093http://dx.doi.org/10.1785/0119990066http://dx.doi.org/10.1785/0119990066http://dx.doi.org/10.1061/(ASCE)10900241(2008)134:8(1129)http://dx.doi.org/10.1061/(ASCE)10900241(2008)134:8(1129)http://dx.doi.org/10.1061/(ASCE)10900241(2009)135:3(407)http://dx.doi.org/10.1061/(ASCE)10900241(2009)135:3(407)http://dx.doi.org/10.1061/(ASCE)GT.19435606.0000034http://dx.doi.org/10.1061/(ASCE)GT.19435606.0000034http://dx.doi.org/10.1016/j.soildyn.2004.11.019http://dx.doi.org/10.1007/s1051801293970http://dx.doi.org/10.1007/s1051801293970http://dx.doi.org/10.1016/j.soildyn.2012.12.011http://dx.doi.org/10.1016/j.soildyn.2012.12.011http://dx.doi.org/10.1016/j.soildyn.2011.08.008http://dx.doi.org/10.1016/j.soildyn.2011.08.008http://dx.doi.org/10.1002/eqe.1182http://dx.doi.org/10.1680/geot.2007.57.8.637http://dx.doi.org/10.1080/13632469.2012.691615http://dx.doi.org/10.1080/13632469.2011.618522http://dx.doi.org/10.1142/S1363246905002456http://dx.doi.org/10.1193/1.4000084http://dx.doi.org/10.3208/sandf.37.3_95http://dx.doi.org/10.1002/eqe.773http://dx.doi.org/10.1139/t83079http://dx.doi.org/10.1016/j.engstruct.2006.08.013http://dx.doi.org/10.1016/j.engstruct.2006.08.013http://dx.doi.org/10.1061/(ASCE)07339410(1991)117:1(89)