rocking isolation of frames on isolated footings: design...

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Rocking Isolation of Frames on IsolatedFootings: Design Insights and LimitationsR. Kourkoulis a , F. Gelagoti a & I. Anastasopoulos aa School of Civil Engineering, National Technical University ofAthens, Athens, Greece

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To cite this article: R. Kourkoulis, F. Gelagoti & I. Anastasopoulos (2012): Rocking Isolation of Frameson Isolated Footings: Design Insights and Limitations, Journal of Earthquake Engineering, 16:3,374-400

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Journal of Earthquake Engineering, 16:374–400, 2012Copyright © A. S. Elnashai & N. N. AmbraseysISSN: 1363-2469 print / 1559-808X onlineDOI: 10.1080/13632469.2011.618522

Rocking Isolation of Frames on Isolated Footings:Design Insights and Limitations

R. KOURKOULIS, F. GELAGOTI, and I. ANASTASOPOULOS

School of Civil Engineering, National Technical University of Athens, Athens,Greece

To date, a significant research effort has been devoted attempting to introduce novel seismicprotection schemes, taking advantage of mobilization of inelastic foundation response. According tosuch an emerging seismic design concept, termed “rocking isolation,” instead of over-designing thefootings of a frame (as in conventional capacity design), they are intentionally under-designed to pro-mote uplifting and respond to strong seismic shaking through rocking, thus bounding the inertia forcestransmitted to the superstructure. Recent research has demonstrated the potential effectiveness ofrocking isolation for the seismic protection of frame structures, using a simple 1-bay frame as an illus-trative example. This article: (a) sheds light in the possible limitations of rocking isolation, especiallyin view of the unavoidable uncertainties regarding the estimation of soil properties; (b) investigatesthe potential detrimental effects of ground motion characteristics; and (c) assesses the effectivenessof rocking isolation to more complex structures. It is shown that the concept may be generalizedto 2-bay frames, and that even when foundation rocking is limited, the positive effect of foundationunder-design remains, especially when it comes to very strong seismic shaking. In contrast, its effec-tiveness may be limited when the frame is subjected to combined horizontal and synchronous verticalacceleration components — a possible scenario on the surface of alluvial basins.

Keywords Frames; Rocking Isolation; Shallow Foundations; Differential Settlement; ParasiticVertical Acceleration

1. Introduction

Current seismic foundation design principles, particularly as entrenched in the respectivecodes (e.g., EC8, 2000), prohibit the mobilisation of strength in the foundation level. Thedesigner must ensure that the below-ground support system will not even reach a numberof “thresholds” that would statically imply failure: mobilization of soil-bearing capacity,significant foundation uplifting, sliding, or any combination are forbidden or strictly lim-ited. To this end, over-strength factors and (explicit or implicit) factors of safety against allsuch possible failure modes are introduced.

However, over recent years there is a growing awareness that nonlinear foundationresponse is not necessarily detrimental but may even be beneficial [Paolucci, 1997; Pecker,1998, 2003; FEMA 356, 2000; Gazetas et al., 2003]. Under this prism, recent studies haveinvestigated the idea of exploiting the inelastic foundation action during strong seismicshaking so as to limit the stresses transmitted onto the superstructure. Such analyses mainlyexplore the seismic response of simple 1-dof systems that are assumed to be founded on

Received 15 April 2011; accepted 23 August 2011.Address correspondence to I. Anastasopoulos, School of Civil Engineering, National Technical University

of Athens, Athens, Greece. E-mail: [email protected]

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Rocking Isolation: Insights and Limitations 375

isolated footings lying on inelastic soil. The nonlinear soil-foundation-structure response,which is materialized mainly through foundation uplifting (geometric nonlinearity) or soilyielding (material inelasticity), is typically simulated by means of: (a) Winkler-based mod-els that simultaneously capture the settlement-rotation at the base of the footing [Yim andChopra, 1985; Nakaki & Hart, 1987; Chen & Lai; 2003; Houlsby et al., 2005; Hardenet al., 2005; Allotey and Naggar, 2003, 2007; Raychowdhury and Hutchinson, 2009]; (b)advanced macro-element modeling, where the entire soil-foundation system is replaced bya single element that describes the generalized force-displacement behavior of the founda-tion [Nova and Montrasio, 1991; Paolucci, 1997; Pedretti, 1998; Le Pape and Sieffert, 2001;Crémer, 2001; Crémer et al., 2001; Grange et al., 2008; Chatzigogos et al., 2009, 2011];and (c) direct methods (i.e., finite elements or finite differences) where both the structureand the foundation-soil system are modeled (e.g., Tan, 1990; Butterfield and Gottardi, 1995;Taiebat and Carter, 2000; Gourvenec, 2007; Anastasopoulos et al., 2009; 2011).

The above techniques have been applied in various studies and have helped estab-lishing the idea that allowing “plastic hinging” at the foundation (through upliftingand/or soil yielding) may act as an energy dissipation mechanism that bounds the seismicdemand exerted on the components of the superstructure, thus providing adequately largesafety margins, even for seismic motions that substantially exceed the design limits[Anastasopoulos et al., 2009]. These findings have been further corroborated by numer-ous experimental studies — centrifuge, large-scale, and reduced-scale testing [Faccioliet al., 2001; Kutter et al., 2003; Gajan et al., 2005; Mergos and Kawashima, 2005;Anastasopoulos, 2010]. Although this new concept appears to work well when the above-ground system is a single 1-dof oscillator, displacement compatibility requirements may beespecially critical for frame structures: the potential “relief” of one structural element mayresult in overstress of another.

Huckelbridge [1977] investigated the seismic performance of moment-resisting framesallowed to uplift at their base. Motivated by the need to control acceleration and inter-storyshear, he investigated the application of appropriate weakening techniques such as the useof rocking columns, to typical frame models. A rocking column is one type of a double-hinged column, or a cracked base and top column, connected at its contact surfaces onlythrough compression without any tensile capacity. More recently, Midorikawa et al. [2006]concluded that intentionally introducing column-uplifting capability into structures wouldbe both rational and economical in regions of high seismicity. The base shear appeared tobe substantially reduced, whereas the maximum roof displacements of the rocking-columnframes were about the same with their equivalent fixed-base alternatives. Yet, Roh andReinhorn [2010] pointed out that the use of such column-weakening strategies, despite theiroverall favorable response, may possess certain drawbacks: they may invoke intolerabledisplacements in the superstructure, and should therefore be supplemented with properdamping devices. Moreover, Lu [2005] indicated that when these rocking typologies areimplemented in wall-frame systems, the extensive uplifting of the wall may induce largeelongation along the wall tension chord, which subsequently may increase the rotationdemand on the beams framing the wall.

Despite their obvious usefulness, the results of the aforementioned studies do not incor-porate the interaction of the superstructure with the supporting foundation-soil system.Only recently, Chang et al. [2006] and Hutchinson et al. [2006] attempted to experimentallydemonstrate the effectiveness of the rocking-isolation concept to realistic building struc-tures, taking account of nonlinear foundation response. To this end, the performance of acombined frame-wall system (an idealized 2-story, 2-bay planar RC frame with an attachedshear wall), founded on relatively dense sand through isolated footings, was tested in theUC Davis centrifuge facility. Experimental data manifested that significant system-level

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376 R. Kourkoulis, F. Gelagoti, and I. Anastasopoulos

energy dissipation takes place, which subsequently alleviates the structural distress. A fun-damental difference between these studies compared to those previously discussed is thatpotential soil nonlinearity may now act as an energy dissipation mechanism, capable ofreducing the seismic demand (both in terms of acceleration, and displacement) exertedon the structural elements of the building. Yet, this associated nonlinearity may produceundesirable permanent deformations in the form of settlement or rotation.

Raychowdhury [2011], based on a beam-on-nonlinear-Winkler-foundation (BNWF)approach, numerically investigated the response of typical 3-bay 3-story frames. He showedthat while story displacement demand may increase when foundation nonlinearity is con-sidered, the inter-story drift is substantially decreased. Moreover, while the peak foundationsettlement was not an issue, in some cases the differential settlement exceeded the permis-sible limits, indicating the need of proper design measures (e.g., grade beams connectingthe isolated footings).

The main inspiration of the research presented herein stems from the work of Gelagoti[2010], who investigated numerically the potential effectiveness of rocking isolation (asdefined by Mergos and Kawashima, 1995) on a simple concrete frame. Rocking isolationwas accomplished through under-designing the footings of the frame, in the hope that theywill respond to strong seismic shaking through rocking, thus limiting the inertia forcestransmitted to the superstructure. It was shown that foundation rocking may be favorablefor the seismic response provided that the value of the Factor of Safety against vertical loadsFSv is maintained adequately large. Despite this quite encouraging outcome, questions stillremain as to the generalization potential of the key results to less idealized cases.

Therefore, incorporating the balance of benefit vs. consequence constitutes the funda-mental aspiration of this paper, which attempts to:

(a) shed light in the limitations contained within the concept of rocking isolation, espe-cially in view of the unavoidable uncertainties regarding the estimation of soilproperties (and hence of FSv of the foundation);

(b) investigate the potential detrimental effects of specific ground motion characteris-tics; and

(c) assess the effectiveness of the rocking isolation concept to more realistic 2-bay2-story frame structures.

2. Methodology and Initial Proof of Concept: 1-Bay Frame

The potential effectiveness of rocking isolation for the seismic protection of frame struc-tures has been explored parametrically in Gelagoti et al. [2011], using as an illustrativeexample a fairly simple 2-story 1-bay frame founded on a stiff over-consolidated uniformclay stratum of Su = 150 kPa, and Go = 40 MPa (Fig. 1a). The superstructure design fol-lowed EC8 (2000) provisions with a design acceleration Ad = 0.36 g and behavior factorq = 3.5. The seismic performance of a conventionally designed foundation was com-paratively assessed to that of a specific rocking-isolation alternative. In the former case,following EC8 [2000], the minimum acceptable footing dimension was calculated equal toB = 1.7 m (demanding that the eccentricity due to simultaneous action of axial force andearthquake moment is maintained below B/3). The resulting safety factors under static andseismic loading were FSV = 8.7 and FSE = 1.93, respectively. FSV is defined as the ratioof NCD / Nult, where NCD is the axial load calculated according to capacity design princi-ples, approximately incorporating the effect of alternately increasing vertical loading at theframe footings due to “frame action.”

On the other hand, in the rocking-isolated alternative the footing width was chosenequal to B = 1.4 m, so as to intentionally provoke significant foundation uplifting: the

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FIGURE 1 (a) Outline of finite element modeling: material (soil and superstructure) andgeometric (uplifting and second order effects) are taken into account; (b) parameters incor-porated into the formulation of the constitutive model; the latter captures effectively therocking response of footings with both high and low FSv. While in the first case theresponse is dominated by uplifting, in the second case excessive soil yielding leads tosinking-dominated response (color figure available online).

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foundation moment capacity was calculated as Mult = 100 kN (i.e., lower than the bendingmoment capacity of the corresponding column MC,RD = 165 kNm). Note that even theunder-designed foundation yields FSV = 5.9, which reflects the degree of conservatismintroduced by code requirements.

Although the superstructure design is the same for both alternatives, the structure onthe conventionally designed footings will be referred to as conventional while the one onsmaller footings is termed rocking-isolation alternative.

2.1. Analysis Methodology

The problem is analyzed utilizing the ABAQUS [2009] finite element (FE) environment.Assuming plane-strain conditions, a representative equivalent “slice” of the soil−structuresystem is simulated, with due consideration to material (soil and superstructure) andgeometric (uplifting and P-� effects) nonlinearities. Soil and footings are modeled withquadrilateral continuum elements, while nonlinear beam elements were used for the super-structure. To allow for detachment and sliding at the foundation-soil interface, appropriatecontact elements are employed. A constant coefficient of friction f = 0.7 has been assumed,considered quite common for concrete-soil interfaces. Free field boundaries, materializedthrough appropriate kinematic constraints, are incorporated at the two lateral boundaries;at the base of the model, where the seismic excitation is applied, the vertical displacementis restrained.

Nonlinear soil behavior is modeled through a simple kinematic hardening model, withVon Mises failure criterion and associated flow rule [Anastasopoulos et al., 2011]. Thefull description of the model requires knowledge of only three parameters: the Young’smodulus C, the ultimate shear strength σ y, and the yield stress σ o. The evolution of thekinematic component of the yield stress is described by the expression:

α̇ = C1

σo(σ − α)ε̇pl − γαε̇pl (1)

and is illustratively presented in Fig. 1b. Note that at large plastic strains (i.e., when σ

approaches σ y), α becomes equal to αs = C/γ , (σ–α) tends to σ o and hence·α tends to

zero. The constitutive model has been thoroughly validated against centrifuge and real scaleexperiments (for more details see Anastasopoulos et al., 2011). As indicatively displayedin Fig. 1c, the soil model employed herein may effectively capture the rocking response offoundations both in the case of uplifting-dominated (for FSV > 5), as well as for sinking-dominated response characterized by excessive soil yielding (for FSV < 3).

The same kinematic hardening model, as suggested by Gerolymos et al. [2005], is usedto simulate the nonlinear moment–curvature response of RC members of the superstructure.Model parameters are calibrated against moment–curvature relations, computed utilizingthe section analysis software X-tract [Imbsen & Assoc., 2004]. All sections are assumedto have enough hoop reinforcement thus displaying curvature ductility µφ = 10, corre-sponding to well reinforced sections according to EC8 [2000]. Reasonable assumptionsare adopted for the metaplastic response of the RC section, i.e., for curvature c exceedingcult (which is the curvature at which the ductility of the RC section has been reached): theresidual bending moment Mres is assumed equal to 30% of the bending moment capacity[Vintzileou et al., 2007]; it is considered to be attained for a curvature cmax 3 times largerthan the ultimate curvature cult (see the monotonic backbone curve of Fig. 3b).

The dynamic response of the system is simulated employing nonlinear dynamic timehistory analysis, applying the excitation time history at the base of the model. A quite

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FIGURE 2 (a) Elastic response spectra of the 24 earthquake records used (without scaling)as seismic excitation for the dynamic analysis of the frames. Note that most records overlyexceed the design spectrum (solid black line). (b) Time histories of three characteristicrecords that will be extensively discussed in the ensuing (color figure available online).

comprehensive database of 24 recorded time histories is used as an input to assess theseismic performance of the system for different earthquake scenarios. As depicted in Fig. 2,the selected records cover a wide range of strong-motion parameters such as PGA, PGV ,SA, SV , frequency content, number of strong motion cycles, duration the effect of which isstudied in this research.

2.2. Comparison of Conventional Design with Rocking Isolation

The performance of this simple (1-bay) frame on isolated footings subjected to extremeseismic shaking has been investigated systematically in Gelagoti et al. [2011]. A charac-teristic result is reproduced in Fig. 3, for the case of the frame subjected to the Takatori

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FIGURE 3 Proof of concept — comparative analysis of the 1-bay 2-story frame sub-jected to extremely strong seismic shaking (Takatori, Kobe 1995), when the foundationis designed conventionally (left) and applying rocking isolation (right). (a) Deformed meshwith superimposed plastic strains. The conventionally designed frame collapses (plastichinges are formed at the base of the two columns), while the rocking-isolated alternativesurvives despite the severity of the excitation; (b) superstucture response: moment-curvature loops at the base of the right column; (c) foundation response: settlement-rotationresponse of the two footings. The “capacity designed” (B = 1.7 m) footing responds almostelastically prior to collapse (dotted line), while the under-designed (B = 1.4 m) footingexperiences intense uplifting (color figure available online).

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(Kobe 1995) record, which has a PGA of 0.70 g and exceeds (in terms of SA) the designspectrum by a factor of at least 2 over the entire period range. As depicted in Fig. 3a,the conventionally designed system cannot withstand this level of seismic shaking. Plastichinges first develop in the beams, and later at the base of the columns. The ensuing severeaccumulation of plastic deformation surpasses the available column ductility (Fig. 3b), andthe frame eventually collapses. In stark contrast, the rocking−isolated alternative survivessuch tremendous seismic shaking, with its columns behaving almost elastically: the maxi-mum moment transmitted by the under-designed footing to the column is bounded by thelower moment capacity of the foundation (Mfooting

ult ).Naturally, in terms of foundation response the picture is reversed (Fig. 3c). In the

conventional system, the footings respond almost elastically as indicated by the minimalfooting rotation. (Note that the dashed part of the diagram corresponds to the foundationresponse following the frame collapse which is naturally accompanied by foundation rota-tion). In contrast, in the rocking−isolated alternative, the smaller (B = 1.4 m) footing issubjected to multiple uplifting cycles, leading to an appreciably large maximum rotationϑmax = 0.08 rad. Quite interestingly, the residual rotation ϑ res is practically negligible,while the settlement w does not exceed a mere 0.5 cm.

The quite favorable behavior of the rocking-isolated frame that was vividly portrayedin this specific example was also observed for all seismic motions analyzed. In principle,the conventionally designed structure experiences substantial damage beyond the limit ofrepair in most scenarios examined (and even collapses in 3 out of 24 cases). On the otherhand, the rocking−isolated alternative survives all seismic excitations sustaining minor torepairable column damage. However, the large horizontal deformations developed duringrocking may produce damage to non structural elements (infill walls, etc.), a consequencethat should be taken into account when designing rocking-isolated structures. In addition,despite the under-design of the foundation, given that the achieved FSV is greater than 5[Gajan and Kutter, 2008], the latter possesses a moment capacity that is practically insen-sitive to soil properties and more importantly does not suffer large permanent settlements,since it encompasses a self-centering mechanism which is associated with uplifting.

The aforementioned encouraging, though preliminary results could by no means beendorsed with generalized applicability, before some possible limitations inherent to theconcept are explored. To this end, the next sections attempt to illustrate potential restrictionsinduced by uncertainties regarding soil properties or ground motion characteristics, as wellas to investigate the applicability of the concept to slightly more complex 2-story 2-bayframes.

3. Uncertainties on the Estimation of Soil Properties

As summarized in the previous section, rocking-isolation may provide a fail-safe designalternative, particularly in case of extreme earthquake events substantially exceeding thedesign. Yet, to the extent explored so far, the efficiency of rocking isolation has beenshown to greatly rely on the achieved safety factor against vertical loads FSv which, inturn, strongly depends on the estimation of soil properties. Following this reasoning, theapplicability of such a concept may be questioned given that a possible over-prediction ofthe actual soil strength may lead to excessive foundation rotation (and subsequently exces-sive superstructure distortion) and/or non tolerable settlement, even in the case of moderateseismic shaking.

To shed more light on the possible effects of such uncertainties on the seismic per-formance of rocking-isolated frame structures, a rather extreme scenario is consideredhereafter. It is tactically assumed that while the undrained shear strength Su was estimated

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equal to 150 kPa (yielding FSV ≈ 5), the actual soil strength is substantially lower, notexceeding 85 kPa (and leading to a mere FSV ≈ 3).

The effects of such gross over-estimation of Su have been explored by subjecting thetwo models to the 24 acceleration time histories referred to previously. Analyses haverevealed that although the reduced factor of safety detrimentally results in increased perma-nent deformations of the rocking-isolated structure, the performance of the latter remainssuperior compared to the conventionally designed foundation. Figures 4 and 5 plot theeffect of reduced FSV on foundation performance for two earthquake scenarios: (a) moder-ately strong seismic shaking compatible with the structure’s design spectrum; and (b) verystrong seismic shaking. In the first case, the El Centro 1940 record is chosen as a represen-tative example. With a PGA of 0.31 g and maximum SA of 0.9 g (see also Fig. 2), this recordmatches quite well with the design spectrum, while it contains a multitude of strong motioncycles capable of leading to substantial accumulation of settlement. Although the record isindeed of the level of the design earthquake (as earlier explained) — which according toEC8 would justify damage on the superstructure — the performance is also (and perhapsconservatively) examined from the perspective of serviceability after the end of the earth-quake. Therefore, parameters such as the irrecoverable deformation of the foundation areexpected to be crucial in determining the effectiveness of the design. In the second case(i.e., for very strong seismic shaking), the devastating Takatori (Kobe 1995) record (seealso Fig. 2) is selected as an extreme seismic scenario, exceeding (in terms of SA) thedesign by a factor of at least 2 over the entire period range. Such seismic excitation corre-sponds to the case of an “unanticipated” event that substantially surpasses the design, andtherefore the performance is assessed on the basis of survivability.

As shown in Fig. 4, indeed, when excited by the El Centro record, the actual footingresponse (for the actual Su of 85 kPa, which yields FSV ≈ 3 instead of the FSV ≈ 5 forthe assumed Su = 150 kPa) deviates substantially from the expected response: the footingaccumulates settlement w during each strong motion cycle, reaching a peak value of 1.7 cminstead of the maximum anticipated settlement of 0.5 cm. However, although the observedincrease of w is rather substantial, the absolute magnitude of settlements remains relativelylow and should not question the structural integrity of the frame.

The most noteworthy discrepancies arise when the frame is subjected to therather extreme Takatori record (Fig. 5). While the expected response (FSV = 5) is

FIGURE 4 Investigation of the effect of uncertainties with respect to the estimation ofsoil properties. Settlement-rotation (w–θ ) response of the frame on B = 1.4 m footingssubjected to moderately strong seismic shaking (El Centro 1940 record), for: (a) assumedSu = 150 kPa (yielding FSV = 5); and (b) actual Su = 85 kPa (resulting to FSV = 3).

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FIGURE 5 Investigation of the effect of uncertainties with respect to the estimation ofsoil properties. Performance of the frame on B = 1.4 m footings subjected to very strongseismic shaking (Takatori, Kobe 1995), for the assumed Su of 150 kPa (left), which yieldsFSV = 5, compared to the actual Su of 85 kPa (right), resulting in FSV = 3: (a) deformedmesh with superimposed plastic strains; (b) foundation settlement-rotation (w–θ ) response;and (c) time histories of ground floor drift δ (color figure available online).

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uplifting-dominated, the actual response (FSV = 3) is characterized by noticeable soilyielding and accumulation of settlements – a sinking-dominated response (Figs. 5a andb). While the key mechanism is different, the footing develops significant rotation in bothcases. Although the expected uplifting-dominated response ensures self centering of thefooting, which after the shaking remains nearly horizontal, the actual response leads togradual development of permanent rotation. This brings about irrecoverable residual driftof the order of 8 cm as a result of foundation rotation as opposed to the expected 3 cm(Fig. 5c). The observed flexural drift, however, is slightly lower (although in both casesmaintained between the safe threshold of 1%) indicating a small decrease in the partic-ipation of flexural superstructure distortion. The latter is attributed to the lower momentcapacity of the footing (for the actual Su of 85 kPa) which bounds the amount of earth-quake demand transmitted to the superstructure, and thus limits the flexural distress of thecolumn. Still, it is noted that although collapse is avoided (as opposed to a conventionallydesigned frame), uplifting is definitely preferable to soil yielding since the latter may resultin unacceptable residual deformation of the structure.

Apparently, this research has not investigated the effect of tie beams, which is nonethe-less expected to restrain footing rotations and therefore further enhance the effectiveness ofrocking isolation. Yet, this topic requires further investigation.

4. Valley-Affected Ground Motions: Parasitic Vertical Component

In the preceding, the rocking-isolated frame was subjected to purely horizontal seismicexcitation. However, real seismic motions also contain a vertical component, which mayeither be due to inciting P-waves, or valley-generated: the presence of a non level sub-surface geometry may (under circumstances) not only amplify the ground motion on thesurface, but also generate a vertical component due to the refraction of waves at the inclinedinterfaces of the bedrock [Trifunac, 1971; Bard and Bouchon, 1980; Harmsen and Harding,1981; Othuki and Harumi, 1983; Fishman and Ahmad, 1995]. In general, the frequencycontent of the natural vertical component of a ground motion is quite high and therefore itseffect on structures is usually negligible. On the contrary, the “parasitic” valley-generatedvertical component can be very detrimental for overlying structures: being a direct result ofgeometry, it is fully correlated and of practically the same dominant period as the horizontalcomponent [Gelagoti et al., 2010].

In the process of exploring the validity of this statement, and aiming to explore thepossible limitations of rocking isolation, the next sections investigate the seismic per-formance of the example rocking-isolated frame founded on the surface of an alluvialvalley, i.e., simultaneously excited by a (valley-affected) horizontal acceleration compo-nent and a valley-generated (parasitic) vertical component. Instead of analyzing the coupledvalley-frame system, a simplified 2-step decoupled approach is employed below.

(i) In the first step, the valley is analyzed in 2D to compute the free-field response:horizontal and vertical acceleration time-histories at each point along the valleysurface (the model is subjected to vertically propagating SV waves, responsible forpurely horizontal acceleration at the bedrock level).

(ii) In the second step, the computed horizontal and parasitic vertical acceleration timehistories of the first step are applied as input excitation to the previously presentedsimple de-coupled model, which includes the frame and a relatively shallow soillayer beneath it.

To isolate the effect of the parasitic (valley-generated) vertical component, two sets of anal-yses are conducted: (a) the decoupled soil-structure model is subjected to the horizontal

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component AH of the ground motion produced on the valley surface (i.e., ignoring the par-asitic vertical component); and (b) the model is simultaneously subjected to the horizontaland vertical components (AH and AV) recorded at the valley model surface (at the locationof maximum AV).

4.1. Example Problem: Trapezoidal Alluvial Valley

A fairly simplified trapezoidal alluvial valley is utilized as an illustrative example.As shown in Figure 6, the valley consists of a medium clay formation of Vs = 100 m/s andundrained shear strength Su = 85 kPa, underlain by an elastic halfspace of Vs

R = 400 m/s.As for the frame-structure model, nonlinear soil response is modeled applying thepreviously discussed simplified constitutive model [Anastasopoulos et al., 2011].

To be able to clearly identify the interaction mechanisms, the analysis is conductedfor an idealized Ricker 1 pulse, scaled at 1 g. The outcome of the free-field analysis of theinitial step are summarized in Figs. 6a and 6b in terms of spatial distribution of peak hori-zontal and parasitic vertical accelerations along the valley surface. Obviously, the nonlinearsoil response not only prevents the development of any conspicuous amplification of thehorizontal component, but indeed de-amplifies the experienced ground motion. The maxi-mum AH at valley corners doesn’t exceed the input acceleration of 1 g, while the responseat the center of the valley drops to 0.6 g. In stark contrast, a noteworthy parasitic vertical

FIGURE 6 Step 1 of the decoupled approach — nonlinear dynamic time history analysisof the example trapezoidal valley (free field) excited by planar vertically propagating SVwaves — Ricker 1 seismic excitation, scaled at 1 g: (a) spatial distribution of maximumvalley–generated parasitic vertical acceleration; (b) maximum horizontal acceleration alongthe valley surface; (c) key model parameters and finite element mesh.

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FIGURE 7 Step 2 of the decoupled approach — nonlinear dynamic time history analysisof the rocking isolated frame on B = 1.6 m footings, simultaneously excited by a pairof horizontal AH and parasitic vertical acceleration AV, obtained by the free-field analysis(Step 1), at the location of peak AV (Ricker 1 seismic excitation, scaled at 1 g). Note that thetwo time histories (AH and AV) are not only correlated in time, but are also characterizedby a very similar frequency content.

acceleration may be observed, reaching a maximum value Avmax = 0.5 g near the valley

edges, and tending to zero towards the valley center.In the second step (Fig. 7), the decoupled frame-soil model (with under-designed

B = 1.6 m footings of FSV = 4.2) is simultaneously excited by a pair of horizontal AH

and parasitic vertical acceleration AV, obtained by the free-field analysis (of Step 1), at thelocation of peak AV. As witnessed by the elastic response spectra and the ground motiontime histories (Fig. 7, bottom), the two components (AH and AV) are in-phase and sharealmost the same frequency content. The analyses have revealed two main mechanisms thatluminously demonstrate the detrimental effect of the parasitic vertical acceleration. As dis-cussed in detail in the sequel, these two mechanisms either increase or decrease the axialload of the frame columns, and hence the vertical load that is transmitted onto the footings.

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4.2. 1st Mechanism: Increase of Axial Load

Figure 8 compares the behavior of the frame subjected to combined horizontal and verticalacceleration to that of the base case of horizontal component seismic excitation only. In theabsence of the parasitic vertical component, the frame responds to strong seismic shakingthrough foundation rocking, which restricts the loading that is transmitted to the superstruc-ture (rocking isolation). However, as shown in Fig. 8a, when the horizontal accelerationpulse is accompanied by a synchronous vertical acceleration pulse, the vertical load onthe foundation can be (and actually is increased in the example under study) substantiallyincreased, forcing it to stay in contact with the soil and preventing its uplifting response,thus partially negating the beneficial effects of rocking isolation.

As a result, the column is subjected to increased flexural bending, and the ductilitydemand is markedly increased. This is clearly mirrored in the curvature time histories ofthe mostly affected right column (Fig. 8b). Observe that in case of simultaneous horizon-tal and vertical seismic shaking, the curvature displays a striking increase at t = 3.5 s.Most of the curvature developed at that instant is irrecoverable afterwards, i.e., the cur-vature time history during the subsequent cycles of shaking oscillates around a highvalue of c = 0.047 m−1 (grey line), indicating a substantial permanent distortion ofthe frame. Note that when the frame is subjected to the horizontal component only,the respective residual curvature on the same column does not exceed c = 0.015 m−1

(black line).This behavior may be further clarified by analyzing footing rotations. In fact, although

the right footing does uplift under the action of the horizontal component, as seen in Fig. 8c(grey line), at t = 3.5 s the presence of the synchronous vertical acceleration producesan almost instantaneous 20% increase in the right column’s axial force N (compared tothe case of the horizontal component only), which drastically limits its capacity to uplift.At that very instant, the rotation θ of the right footing drops by almost 80% (Fig. 8d)confirming the “reluctance” of the foundation to uplift. Consequently, rocking isolation ispartially negated, and the inertial loading makes its way to the right column (as would be thecase in conventional design), which, in turn, results in a drastic increase of the curvature byalmost three times (and hence, of ductility demand) compared to the case when the verticalacceleration is ignored (Fig. 8e).

4.3. 2nd Mechanism: Decrease of Axial Load

The effect of positive vertical acceleration is briefly sketched in the deformed mesh ofFig. 9a. The main effect of a synchronous positive vertical acceleration pulse (i.e., a forcewith direction upwards) accompanying the strong horizontal pulse is associated with apotential complete loss of contact between the footing and the ground, which may result inkinematically induced permanent deformation of the frame (Fig. 9a). During the main hor-izontal acceleration pulse, the left footing whose vertical load N is already reduced due tothe frame rocking-deformation, is simultaneously subjected to a strong vertical accelerationpulse which momentarily leads to complete loss of contact with the bearing soil: the axialforce N is reduced to zero at that instant (Fig. 9b). When the footing regains contact withthe ground, at t = 4 s, its new position is slightly translated to the left. At the same time,the right footing is subjected to increased N (see previous mechanism), always maintainingcontact with the soil and not being equally translated to the left. As a result, the frame isforced to an irrecoverable kinematic deformation. The latter is reflected in the residual pos-itive curvature of the left column (Fig. 9c). During subsequent cycles of seismic shaking,the curvature oscillates around that residual value.

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FIGURE 8 Illustration of the detrimental effect of axial load increase due to valley-generated parasitic vertical component (Ricker 1 seismic excitation, scaled at 1 g):(a) snapshot of deformed mesh with superimposed plastic strain contours. Observe thatthe increased axial load N on the right footing prevents uplifting (partially negating rock-ing isolation), producing large plastic deformation at the column base. Time histories of:(b) curvature at the base of the right column; (c) axial load N of the right column; (d) rota-tion θ of the right footing; and (e) moment-curvature (M–c) loops at the base of the rightcolumn (color figure available online).

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FIGURE 9 Illustration of the detrimental effect of axial load decrease due to valley-generated parasitic vertical component (Ricker 1 seismic excitation, scaled at 1 g):(a) snapshot of deformed mesh at the time of complete loss of contact of the left foot-ing. Time histories of: (b) axial load N of the left column; and (c) curvature at the base ofthe left column.

FIGURE 10 Nonlinear dynamic time-history analysis of the valley (free field) excited bythe Tabas (Iran, 1978) record. Time histories of: (a) horizontal AH, and (b) valley-generatedparasitic vertical acceleration AV (at the point where AV is maximized).

It should be noted, however, that such mechanism would probably not develop if theframe footings were connected through tie beams, which would tend to force the twofootings to maintain common horizontal displacement. Naturally, depending on their stiff-ness, such tie beams would also tend to reduce the beneficial role of rocking isolation (sincetheir rotational resistance would be added to that of the footings).

4.4. Real Records: Natural vs. Valley-Generated Vertical Component

As previously discussed, the valley-generated parasitic vertical component is fully corre-lated and of practically the same dominant period as the horizontal component, and, hence,

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FIGURE 11 Valley-generated parasitic vs. natural vertical component — analysis of therocking isolated frame subjected to valley-affected horizontal and parasitic vertical accel-eration (left), compared to simultaneous horizontal and natural (i.e., recorded) verticalacceleration at the Tabas station (right): (a) moment-curvature loops at the column base;(b) footing rotation time histories; and (c) drift ratio at the ground floor (color figureavailable online).

it may be detrimental for structures. In contrast, the natural vertical component of an earth-quake is usually of very high frequency, and is should not be expected to pose a seriousthreat to structures. To highlight the differences between these two vertical components(natural and valley-generated), and to investigate frame response in the more realistic caseof actual seismic excitations, the frame is subjected herein to the Tabas seismic excitation,recorded during the Iran (1981) earthquake. As shown in Fig. 10, this excitation produces a0.83 g peak horizontal and 0.62 g vertical acceleration close to the valley boundaries. In theensuing, the response of the frame is discussed, comparing the parasitic valley-generatedvertical component with the natural (due to P-waves) vertical component.

As expected, in the absence of vertical acceleration both footings develop signifi-cant rotation, yet are able to sustain the imposed shaking with only limited distortion

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(cres = 0.02). On the contrary, the presence of the valley-generated vertical accelerationcomponent not only increases the developing footing rotation (Fig. 11b – left), but alsoresults in a substantial increase of ductility demand in the left column (Fig. 11a – left): cres

reaches 0.06, practically “consuming” the available ductility of the column. This combinedaction of increased foundation and superstructure distortion produces irrecoverable accu-mulation of drift, which reaches intolerably large values, indicative of complete failure ofthe frame (Fig. 11c – left). At this point, it should be stressed that a conventionally designedframe (i.e., with over-designed footings) would inevitably collapse.

To further corroborate the previously implied anticipation regarding the minimal effectof the natural (recorded) vertical component on the seismic performance of systems, theright column of Fig. 11 compares the response of the rocking-isolated frame subjectedto purely horizontal acceleration to that of the frame under horizontal and natural verti-cal component. The plots are self explanatory: in terms of moment-curvature loops andfooting rotation time histories (Figs. 11a and b – right), the high-frequency natural ver-tical component hardly modifies the response of the frame. Quite remarkably, in termsof structural drift ratio (Fig. 11c – right), the response is improved when taking accountof the high-frequency natural vertical component: the 1.8 % drift ratio almost vanishes.Certainly, this conclusion may not be generalized as it strongly depends on the specificrecord characteristics.

5. Rocking–Isolated 2-Bay Frame

Motivated by the encouraging response of the simple 1-bay frame, this section exploresthe applicability of the rocking isolation concept to a slightly more complex 2-bay 2-storyframe structure on isolated square footings, non symmetrically loaded as explained in theensuing. A schematic illustration of the frame geometry is displayed in Fig. 12. As for thepreviously discussed 1-bay frame, the superstructure conventional design was performedaccording to EC8 [2002] utilizing the computer code ETABS (AE = 0.36 g, q = 3.5).

Following EC8 [2002] code provisions, the minimum acceptable footing dimensionwas calculated equal to B = 1.8 m (demanding that the eccentricity due to simultaneousaction of axial force and moment is maintained below B/3), while for the rocking-isolatedalternative (neglecting the eccentricity criterion) the width was chosen equal to B = 1.3 m.Hence, the safety factor against vertical loads is calculated to be FSside

V ≈ 5.3 for the two-side footings and therefore — according to the previous statements — these are expected toexhibit uplifting-dominated response. The major difference between this case and the 1-bayframe, stems from the asymmetry in the distribution of axial loads on the three columns:the middle column carries double the axial load of the two side ones. Therefore, since allfootings have the same dimensions (as would typically be the case in reality), the actualsafety factor of the middle footing is substantially lower: FSmiddle

V ≈ 3.5.As for the 1-bay frame, the effectiveness of the rocking-isolation concept is firstly

evaluated through comparing the seismic performance of a conventionally and an uncon-ventionally designed frame. Next, the behavior of the rocking-isolated 2-bay frame iscompared to that of the corresponding 1-bay frame in order to highlight the implicationsstemming from the aforementioned asymmetry on the axial load distribution.

5.1. Response to Real Records: Summary of Results

Figures 13 summarizes the seismic performance of the two design alternatives (conven-tional vs. rocking isolation) subjected to the previously discussed recorded time-historiesdatabase. Results are plotted against the earthquakes’ Peak Spectral Velocity which was

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FIGURE 12 Geometry and member properties of the idealized 2-bay 2-story frame struc-ture. The superstructure is designed following the capacity design principles, as entrenchedin EC8 (AE = 0.36, q = 3.5). The minimum footing width according to conventionalseismic design requirements is equal to B = 1.8 m. For the rocking isolation alternative,under-designed footings of B = 1.3 m (for all three column) are utilized.

chosen as an indicator of the records destructiveness. Column distress is expressed in termsof ductility demand over ductility capacity ratio (µdemand/µcapacity). Based on the corre-sponding drift ratios defined by [Priestley et al., 2007], for µdemand/µcapacity ratios below0.15, the performance is considered very satisfactory, maintaining the structure withinServiceability Limits. For intermediate values, 0.15 < µdemand /µcapacity < 0.25, the per-formance falls within the Damage Control Limit State in which the structure is expectedto sustain repairable damage, with the cost of repair substantially lower than the cost ofreplacement. Finally, for 0.25 < µdemand/µcapacity < 1 the collapse of the structure maybe marginally avoided, although structural damage will be excessive and replacement willbe unavoidable. Ratios higher than 1 signify failure. Results are presented only for thecentral column of the 2-bay frame which experiences more intense loading than the twoside columns.

For the conventional frame, µdemand /µcapacity averages around 0.5, with the lateralcolumns (which are less distressed) also consuming a substantial portion of their avail-able ductility during all strong earthquake scenarios (Fig. 13a). Besides, for more than35% of the seismic excitations investigated herein, µdemand /µcapacity surpasses 1.0, imply-ing total flexural failure of the central column and probable collapse of the frame. On theother hand, the unconventional rocking-isolated alternative (Fig. 13a – right) safely sus-tains all examined earthquake scenarios, and in fact with minimal flexural distortion onthe columns: µdemand /µcapacity fluctuates around an average value of 0.1. Indeed, for thevast majority of the cases examined, the column distress index (µdemand /µcapacity ratio)falls within the damage control limit state, illustrating an overall superior response (com-pared to the conventionally designed foundation). However, two cases have been identified

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FIGURE 13 Summary of the response of the two design alternatives on the 2-bay 2-storyframe as a function of the maximum spectral velocity SV: (a) column curvature ductilitydemand over capacity ratio. Damage level is indicated with reference to Response LimitStates [Priestley et al., 1996]; (b) settlement w of the footing center (color figure availableonline).

where the distress of the rocking-isolated column marginally exceeds the damage controllimit. In these cases the frame was subjected to directivity “contaminated” motions, theeffect of which is briefly outlined in the next section.

In terms of settlement, the response of both alternatives is comparable, with therocking-isolated alternative (with under-designed footings) demonstrating a marginallyinferior behavior (Fig. 13b). Still though, the magnitude of the computed settlements (notexceeding 3 cm) is considered to be of minor importance in terms of the structural integrityof the frame.

Note that the detrimental effect of differential settlements between the center and sidecolumns may not be as augmented in case of existence of tie beams; a very common occur-rence in practice as already stated, which has not however been taken into account in thisarticle.

5.2. The Role of Ground Motion Characteristics

This section attempts to shed light on the effect of directivity contaminated ground motionssuch as those identified in the previous paragraph. To this end, Fig. 14 compares theresponse of the frame when subjected to an “asymmetric” directivity-affected seismicmotion, such as the Rinaldi (228) record to the case of a more “symmetric” motion, suchas the Takatori record. The Rinaldi is a near-field record affected by forward directivity[Abrahamson, 2000; Sommerville, 2000; Mavroeidis and Papageorgiou, 2003], contain-ing a single coherent large period (directivity) pulse, which usually results in substantial

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FIGURE 14 Illustration of the effect of ground motion characteristics – seismic perfor-mance of the rocking-isolated 2-bay frame when subjected to an “un-symmetric” (Rinaldi228 – left column), and a “symmetric” (Takatori 000, right column) seismic excitation: (a)time history of curvature at the base of the central column; (b) time history of ground floordrift; and (c) settlement-rotation response for the central footing.

impulsive deformation demand on the system [Hall et al., 1995; Anderson et al., 1999;Makris and Chang, 2000; Chopra and Chintanapakdee, 2001; Alavi and Krawinkler, 2001;Garini et.al., 2011]. Indeed, when the Rinaldi record is imposed on the frame, at the instantof the directivity pulse, a significant increase in curvature demand is clearly observed(Fig. 14a – left) which indicates substantial ductility consumption. On the other hand,when the frame is excited by the symmetric Takatori record, in each strong motion cyclethe curvature only momentarily exceeds the yield curvature of the section cy, and hence theresulting ductility demand is considerably lower (Fig. 14a – right).

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The discrepancies become even more palpable when comparing the time historiesof total drift. Although the maximum displacement demand (Fig. 14b) is comparable(30–40 cm), the “asymmetric” Rinaldi produces substantially increased residual drift (δres

≈ 15 cm), which is attributed not only to column flexural distortion, but also (if not mainly)due to permanent footing rotation. The directivity pulse generates excessive “asymmetric”soil yielding, inducing a large-magnitude rotation which is not recovered during the sub-sequent lower intensity pulses (Fig. 14c). This is not the case when the frame is subjectedto the Takatori record. Thanks to its “symmetry” (in the form of many cycles of significantduration), the footings accumulate settlement but negligible residual rotation. Therefore,the residual drift is noticeably lower.

As explained in Gelagoti et al. [2011], such phenomena are not observed in the caseof the 1-bay frame. In such symmetric systems (Fig. 15a – left), even a highly impulsivedisplacement (produced by the directivity-affected motion) can be recovered due to theinherent self-centering capability of the rocking system (Fig. 15b – left). Notice that whilein this symmetric system both footings respond identically (Fig. 15c – left), this is nottrue when referring to the asymmetric 2-bay frame (Fig. 15c – right). Since the middlefooting carries double axial load (and being of the same size, it is characterized by a sub-stantially lower FSv), when subjected to the directivity pulse its rotation is associated withsubstantial soil yielding, in contrast to the two side footings whose rotation is primarilymaterialized through uplifting. Indeed, observe that although the rotation time histories ofall three footings are very similar (Fig. 15c – right), after t = 6 s (Fig. 15d – right) themiddle footing has permanently settled by about 1 cm, which may not be retrieved duringsubsequent cycles of motion. The development of this plastic soil deformation unavoidablyproduces a permanent rotation of all three footings equal to ϑ res = 0.03 rad.

6. Conclusions

This paper has incorporated nonlinear finite element analyses with the intention of pointingout possible limitations of the rocking-isolation concept for frames supported on individ-ual footings, especially in view of the unavoidable uncertainties regarding the estimationof soil properties. The potential detrimental effects of ground motion characteristics havebeen investigated, with emphasis on valley affected motions containing a synchronous ver-tical acceleration component. Finally, the effectiveness of the rocking isolation concept tomore complex structures has been parametrically investigate, utilizing a 2-bay frame as anillustrative example. The key conclusions of the study are summarized as follows.

(1) The favorable response of rocking isolation has been shown to rely on a suffi-ciently high factor of safety against vertical loads (FSv), which largely dependson the estimation of soil properties. Since an over-prediction of the actual soilstrength may lead to excessive foundation rotation (and subsequently excessivesuperstructure distortion) and/or non tolerable settlement, the applicability of theconcept may be questioned. To account for such uncertainties, numerical analyseshave been conducted to investigate the effectiveness of rocking-isolation in casethe actually achieved FSv is substantially lower than the one initially anticipated(FSv = 3 instead of 5) — a rather extreme scenario. Subjecting the two models toan ensemble of 24 seismic excitations it is shown that:● Although the reduced FSv unavoidably leads to increased permanent defor-

mations, the performance of the rocking-isolated structure remains superiorcompared to the conventionally designed system.

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FIGURE 15 Comparison of the 1-bay with the 2-bay frame subjected to the directivityaffected Rinaldi (228) record: (a) deformed mesh with superimposed plastic strains; (b)settlement-rotation response of the left footing and the central footing (for the 2-bay struc-ture); (c) time histories of footing rotation; and (d) settlement time histories for all footings(color figure available online).

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● For seismic excitations within the design limits, although the actual footingresponse (for the actual FSV ≈ 3 instead of the assumed FSV ≈ 5) deviates sub-stantially from the expected, the settlement remains within fairly tolerable limits(of the order of 2 cm, or less), and should not be considered to pose a threat tothe structural integrity of the frame or to its serviceability.

● For extremely strong seismic excitations, substantially exceeding the designlimits, the response of the system is substantially altered: while theexpected response (FSV = 5) is uplifting-dominated, the actual response(FSV = 3) becomes sinking-dominated, leading to substantial accumulation ofsettlement and foundation rotation. As a result, the residual drift of the frame mayreach 8 cm instead of the expected 3 cm. Even in such a case, involving consider-able soil yielding underneath the footings, the effect of foundation under-designremains positive.

(2) Real seismic motions also contain a vertical component, which may either be due toinciting P-waves, or valley-generated. In contrast to the natural vertical component(which is typically of high frequency content), the “parasitic” valley-generated ver-tical component (being fully correlated and of practically the same dominant periodas the horizontal component) can be very detrimental for overlying structures.Hence, to explore the possible detrimental effects of such valley-contaminatedground motions, the seismic performance of the example rocking-isolated framefounded on the surface of an alluvial valley was further investigated. Utilizing afairly simplified trapezoidal alluvial valley as an illustrative example, it is shownthat:● When a horizontal acceleration pulse is accompanied by a synchronous negative

(i.e., upwards) vertical acceleration pulse, the vertical load on the foundation canbe substantially increased, forcing it to stay in contact with the soil and prevent-ing its uplifting response, thus partially negating the beneficial effects of rockingisolation. As a result, the frame columns may be subjected to increased flexuralbending, substantially increasing the corresponding ductility demand.

● In contrast, the effect of a synchronous positive (i.e., downwards) verticalacceleration pulse accompanying the strong horizontal pulse may result tocomplete loss of contact between the footing and the soil, which may result inkinematically-induced permanent deformation of the frame. It should be noted,however, that such mechanism would probably not develop if the frame footingswere connected through tie beams, which would tend to force the two footingsto maintain common horizontal displacement.

(3) The applicability of the rocking-isolation concept has been demonstrated for 2-bayframes. It is shown that:● The major difference with the idealized 1-bay frame stems from the asymmetry

in the distribution of axial loads on the three columns: the middle column carriesdouble the axial load of the two side ones.

● The performance of the rocking-isolated 2-bay frame is shown to be quitesatisfactory: it safely sustains all examined earthquake scenarios, and in factwith minimal flexural distortion on the columns. As for the 1-bay frame, itsperformance is always superior to that of the conventionally designed system.

● Due to its higher axial load, the middle column experiences increased settle-ment compared to the two side columns which, when the frame is excited bydirectivity-affected motions, results in a residual irrecoverable deformation (oftolerable magnitude whatsoever).

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Acknowledgment

The financial support for this article has been provided under the research project“DARE,” which is funded through the European Research Council’s (ERC) “IDEAS”Programme, in Support of Frontier Research–Advanced Grant, under contract/numberERC-2-9-AdG228254-DARE to Professor G. Gazetas.

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rocking isolation of frames on isolated footings: design...

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