eqe2198

Multiple-slider surfaces bearing for seismic retrofitting of framestructures with soft first stories

Muhannad Y. Fakhouri1,*,† and Akira Igarashi2

1Department of Urban Management, Graduate School of Engineering, Kyoto University, Kyoto 615-8540, Japan2Department of Civil and Earth Resources Engineering, Kyoto University, Kyoto 615-8540, Japan

SUMMARY

A new isolation interface is proposed in this study to retrofit existing buildings with inadequate soft storiesas well as new structures to be constructed with soft first story intended for architectural or functional pur-poses. The seismic interface is an assembly of bearings set in parallel on the top of the first story columns:the multiple-slider bearings and rubber bearings. The multiple-slider bearing is a simple sliding device con-sisting of one horizontal and two inclined plane sliding surfaces based on polytetrafluoroethylene and highlypolished stainless steel interface at both ends set in series. A numerical example of a five-story reinforcedconcrete shear frame with soft first story is considered and analyzed to demonstrate the efficiency of the pro-posed isolation system in reducing the ductility demand and damage in the structure while maintaining thesuperstructure above the bearings to behave nearly in the elastic range with controlled bearing displacement.Comparative study with the conventional system as well as various isolation systems such as rubber bearinginterface and resilient sliding isolation is carried out. Moreover, an optimum design procedure for themultiple-slider bearing is proposed through the trade-off between the maximum bearing displacement andthe first story ductility demand ratio. The results of extensive numerical analysis verify the effectivenessof the multiple-slider bearing in minimizing the damage from earthquake and protecting the soft first storyfrom excessively large ductility demand. Copyright © 2012 John Wiley & Sons, Ltd.

Received 26 August 2011; Revised 27 March 2012; Accepted 30 March 2012

KEY WORDS: seismic isolation; soft story; sliding isolator; multiple-slider bearing; sliding block motion

1. INTRODUCTION

Despite the fact that structures with soft first story are inherently vulnerable to collapse duringearthquakes, it is still in demand especially in urban areas. The soft first story offers architects anattractive model by allowing a sense of floating and bright space. The famous architect Le Corbusieris one of the pioneers who utilized the idea of soft first story by lifting the structure off the ground,supporting it by pilotis (or piers), establishing the leading principle of the modern architecture: the‘pilotis-story’ [1]. The soft first story might be functionally or commercially desirable by providingparking spaces, allowing for a grand entrance or ballrooms as in hotels and permitting a desirablecontinuous windows for display for stores located in the first story. In addition, such a building helpsin raising the inhabitant space in the building above typical storm surge levels in hurricane-prone areas.

Current design guidelines such as the International Building Code [2] classify the structure as the‘soft story’ type if the lateral stiffness of a specific story of the said structure is less than 70% of thatin the story immediately above it, or less than 80% of the average stiffness of the three stories aboveit. Moreover, the code also defines the ‘extreme soft story’ when the lateral stiffness of that story is

*Correspondence to: Muhannad Y. Fakhouri, Department of Urban Management, Graduate School of Engineering,Kyoto University, Nishikyo-ku, Kyoto 615–8540, Japan.

†E-mail: [email protected]

Copyright © 2012 John Wiley & Sons, Ltd.

EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2013; 42:145–161Published online 2 May 2012 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/eqe.2198

less than 60% of that in the story immediately above it, or less than 70% of the average stiffness of thethree stories above it.

On the basis of the ductility design concept that utilizes inelastic behavior to increase the flexibilityof the structure by lengthening the fundamental period and to provide energy absorption, somestructural engineers introduced the concept of flexible first story [3–6]. Later on, this idea wasmodified leading to the concept of the shock-absorbing soft story method [7]. This system rendersall the inelastic deformation to take place in the soft first story columns, whereas the superstructureabove the first story is designed to remain in the elastic range. The shock-absorbing soft first storycontains neoprene layers placed on top of stability walls so that the wall is separated from the slababove it. However, this attempt to reduce forces on structure by allowing the first story columns toyield during an earthquake and produce energy-absorbing action is no longer an appealing idea forstructural engineers because of the excessive drifts in the first story coupled with the P-Δ effect onthe yielded columns, increasing the risk to develop a collapse mechanism known as the soft storyfailure [8]. Failure of this type was clearly observed during many earthquakes in the past; oneexample is the damage due to the 1995 Kobe earthquake. Many reinforced concrete buildings wereseverely damaged, and most of them were buildings with soft story [9]. Another example is the caseof California’s Loma Prieta Earthquake of 1989, in which the soft story failure was responsible fornearly half of all the homes that became uninhabitable.

Chen et al. [10] proposed another modification to the soft first story concept that introducesadditional energy dissipation capacity to reduce drift and provides a mechanism to reduce P-Δeffects. In this system, Teflon sliders are placed on the top of some of the first story columns,whereas the rest of the first story columns are designed with reduced yield strength and ductilebehavior to accommodate large drifts. A similar concept with the difference that the first story shearwalls are fitted with Teflon sliders was also proposed [11]. A further extension of the concept wasproposed similar to the aforementioned philosophy with additional steel dampers to enhance theenergy dissipation during earthquakes [12].

Todorovska proposed another variation of the soft story concept using inclined rubber base isolatorsor inclined soft first story columns [13]. The system behaves as a physical pendulum pivoted above thecenter of mass and is more stable than the standard system. Briman and Ribakov [14] have developed amethod for retrofitting soft story buildings by replacing weak conventional columns with seismicisolation columns. The seismic isolation device is based on a friction pendulum principle.

Past earthquake damage examples have proven that the performance of conventionally designedcolumns in soft story structures is unsatisfactory because of the high uncertainty in the ductilitydesign concept. Although structures with soft stories may survive during earthquakes, excessivedrifts and formation of plastic hinges at critical sections could make it difficult to repair thedamaged structures. For that reason, more effective and reliable techniques are needed to enhancethe structural safety and integrity for such special type of structures. It can be noticed from theprevious studies that seismic isolation is one of the prominent alternatives that can overcome thedilemma between the need for soft story and its vulnerability to collapse.

In this study, the seismic performance of soft-first-story frame structures is upgraded by installingmultiple-slider bearings consisting of multiple sliding plane surfaces, one horizontal and twoinclined surfaces, on the top of first story columns to effectively prevent the first story damage byreducing the ductility demand to the columns and maintaining the superstructure to behave nearly inthe elastic range at the same time. The mechanism and efficiency of the proposed system areillustrated using nonlinear time history analysis of a moment resisting concrete frame subjected toseismic excitation. Comparative study with the conventional system and with various isolationsystems such as the rubber bearing interface and the resilient sliding isolation (RSI) is carried out.Finally, an optimum design procedure for the multiple-slider bearing is proposed.

1.1. Proposed system concept

The need for controlling displacement of the isolators to a minimum level is a vital issue especially inbig and crowded cities where buildings are often built closely to each other because of the limitedavailability and high cost of the land. This leads to cause pounding of adjacent buildings due to the

146 M. Y. FAKHOURI AND A. IGARASHI

Copyright © 2012 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2013; 42:145–161DOI: 10.1002/eqe

insufficient or inadequate separation and can be a serious hazard in seismically active areas.Accommodating such large displacement responses by the use of the conventional rubber bearings iscostly and may cause instability.

The proposed seismic retrofit scheme for frame structures with soft first story to solve this problem isshown in Figure 1. Isolation between the first story columns and the rest of the superstructure isincorporated by installing the multiple-slider bearings, which is described later in detail, on the top ofinterior columns and rubber bearings at the top of edge columns. The first story columns are tiedtogether by tie beams to ensure stability and enhance the safety. The orientation of the multiple-sliderbearing is chosen as shown in Figure 1 to divert P-Δ moments from weak elements below the isolationinterfaces that resemble the orientation mechanism of friction pendulum system (FPS) [15–17].

The multiple-slider bearing is a simple sliding device consisting of one horizontal and two inclinedplane sliding surfaces at both ends set in series, as shown in Figure 2.These three surfaces are based onpolytetrafluoroethylene (PTFE) and highly polished stainless steel (SUS) interface. During normal orlow intensity earthquakes, the isolator behaves as a pure friction isolator with sliding only in thehorizontal direction. However, during a severe earthquake, sliding will be activated in the inclinedsurface producing displacements in both horizontal and vertical directions.

The concept of this type of bearing was proposed to upgrade the seismic performance of multispancontinuous girder bridges with reduced horizontal displacement of the girder in case of strongearthquakes, which is referred to as the ‘Uplifting Slide Bearing’ [18–22]. Figure 3 shows photographsof sample Uplifting Slide Bearings. The concept was later extended to include multistory structuresmainly to control the maximum top floor horizontal displacement [23].

Foundation

Slab

Tie Beam

RubberBearing

Multiple-SliderBearing

Shear Key Shear Key

Figure 1. Set-up arrangement of the multiple-slider bearings in a frame structure with soft first story.

PTFE bearing material

SUSsliding plate

Figure 2. Schematic diagram of the isolator with multiple-slider surfaces.

MULTIPLE SLIDER FOR SEISMIC RETROFITTING OF SOFT STORY STRUCTURES 147


The proposed system also offers a feasible solution for seismic retrofitting of existing buildings withsoft stories in areas where clearance between adjacent buildings is limited, as will be shown in thisstudy. Commonly, the seismic rehabilitation can be carried out simply by transmitting the loadacting on the columns temporary to jacks, then columns are cut from the top at the first story level,and the isolation device is installed on the top of the columns before the removal of the temporaryjacks. Nevertheless, more neat and reliable methods without using lifting equipments also exist [24].

According to building design codes, the requirements to isolated buildings and those to nonisolatedbuildings are different. For example, fixed-base buildings are permitted a force reduction factor (R) thatrepresents global ductility up to eight, which may allow significant inelastic action. On the other hand,isolated buildings are limited to R factors no larger than two as specified in the ASCE 7–05 [25],Eurocode 8 [26], and IBC2003 [2]. Even the design force level is different for structural elementsbelow or above the interface. The first story columns in Figure 1 are to be designed for a forceequal to the maximum effective stiffness of the isolation interface times the design displacement inthe horizontal direction under consideration and for the design moment due to the shear force andthe P-Δ effect that should be considered if it exists depending on the slider orientation. In otherwords, the first story columns should be designed elastically for the maximum force that istransmitted though the isolation system at the design level earthquake [27]. Other code requirementis that isolation systems should use rigid horizontal diaphragms or bracing systems above and belowthe isolator level to provide deformation compatibility among the resisting structural elements. Inview of this requirement, the first story columns are tied together by tie beams in the proposedmodel. It is noteworthy that the device in the present status is restricted to unidirectional motionbecause it was first developed as a seismic response control device for multispan continuous girderbridges, as mentioned earlier. Currently, the device is in the process of further development andmodification to take into account the bidirectional motion that is essential in the design ofseismically isolated building structures.

1.2. Uniqueness of the multiple-slider bearing

Sliding base isolation systems have gained attention in recent years because of economic reasons aswell as their durability and stability characteristics. They are insensitive to the variation of thefrequency content of ground excitation. Moreover, sliding isolators provide a natural source ofdamping through friction because the horizontal friction force at the sliding surface offers resistanceto motion and dissipates energy. The hysteresis of PTFE–SUS interface is a rectangle that providesequivalent viscous damping of 63.7%. In addition, sliding bearings using Teflon as the slidingsurface can take much higher compressive stresses than elastomeric bearings (60MPa or more forthe former versus 15MPa or so for the latter) and are especially suitable at the ends of shear walls[27]. The main characteristics of the friction-based isolator are high initial lateral stiffness that is anattractive feature to reduce the stiffness of the isolated buildings in the large displacementrange, while resisting frequent lateral loads caused by the wind. For example, most of base isolated

Figure 3. Uplifting Slide Bearing.



high-rise buildings in Japan contain friction-type base isolated systems [28], and devices havingvarious properties have been made available in recent years [29].

Although several friction-type isolators have been developed, the FPS [30] has been extensivelyused and put into practice. The restoring force is provided by the component of the self-weighttangent to the sliding surface. However, because the restoring force varies linearly to the slidingdisplacement, effectiveness of FPS may be reduced particularly in case of long-period earthquakes,high-intensity earthquakes, or a low-friction coefficient of the sliding surface. To overcome thisproblem, several researchers have introduced modifications on the original concept of the FPS. Oneof these examples is the variable frequency pendulum isolator [31], in which the geometry of aconcave sliding surface is designed such that the oscillation frequency decreases with the slidingdisplacement amplitude and the force transmitted to the structure is limited with an upper bound. Lateron, the multiple FPS with two spherical concave surfaces and an articulated slider was proposed [32].Several isolators derived from the conventional FPS that basically represents more than onependulum systems connected together in series have been proposed and investigated [33–38].Another friction-based isolator is RoGlider that has been developed for seismic isolation of bothlight and heavy vertical loads and can be readily designed to accommodate extreme displacements[39]; it also includes elastic restoring force provided by two rubber membranes. This double actingRoGlider consists of two SUS plates with a PTFE-ended puck sitting between the plates. Tworubber membranes are attached to the puck with each being joined to the top or bottom plates.Another type of isolator that utilizes a slope surface – the sloped rolling-type bearing [40] – using asteel cylinder rolling on a V-shape surface has been proposed.

The proposed multiple-slider bearing possesses unique features essentially attributed to thegeometrical configuration and the sliding mechanism, which make it superior to other types ofbearings. Some of these special features are as follows:

1. Geometrical configuration creativity: The geometry of this device was chosen to be effective incontrolling the horizontal displacement by allowing a part of the earthquake transmitted energyto be transferred into a gravitational potential energy through the diagonal sliding.

2. Avoiding pounding effect by efficiently controlling the displacement: Pounding of adjacentbuildings due to insufficient or inadequate separation can be a serious hazard in seismicallyactive areas. The verification of the multiple-slider bearing’s efficiency to control displacementis numerically presented in an earlier study [23].

3. The multiple-slider bearing is a cost-effective solution for seismic isolation. Sliding bearingshave found more and more applications in recent years over rubber bearings for economicreasons. The multiple-slider bearing is basically made from three surfaces of SUS and PTFEinterfaces. Therefore, the ease of manufacturing adds significant reduction to its cost.

4. The hysteretic behavior of the multiple-slider bearing provides more freedom in the process ofdesign that requires determination of three parameters: clearance length (L), that is, the specifieddistance prior to the diagonal sliding; the inclination angle (θ); and the friction coefficient (m) forthe three surfaces in contact.

5. The configuration of the device has the potential of using different friction bearings for thehorizontal and inclined plane surfaces, as shown in a previous study [23]. Use of differentfriction coefficients has been found to add more reduction to the horizontal displacementresponse, especially in the cases of strong and near fault motions.

6. It is worth pointing out that the multiple-slider bearing provides an architecturally flexible andesthetic solution in terms of integration into the structural system for cases in which spaceconsideration is an important factor, rendering the conventional rubber bearing under wallsproblematic.

7. Because the multiple-slider bearing is vertically stiff, the vertical deflections of columns thatoccur during bearing installation in retrofit application is minimized, and damage to architec-tural finishes in upper stories can be avoided.

8. Contrary to the FPS that utilizes a spherical sliding surface to develop a restoring force, theslope angle of the inclined surfaces in the multiple-slider bearing is much larger than the rangeof the tangential angles of the sliding surfaces of FPS, so that the vertical component of the



structural motion is explicitly intended and a constant restoring force is generated because of theparallel component of gravity load along the sliding surfaces.

9. During large displacement response, the horizontal force in the multiple-slider bearing is keptconstant with the increase in displacement. On the other hand, the curved surface in the FPSmay result an increase in horizontal force with a larger displacement because the force isdirectly proportioned to the displacement.

10. The multiple-slider bearing is expected to be a feasible solution for seismic retrofitting ofexisting buildings with soft stories in areas where clearance between adjacent buildings is limitedbecause of its high potential in minimizing the horizontal displacement response.

1.3. Maximum displacement reduction principle

The dynamic behavior of the multiple-slider bearing and the supported superstructure can berepresented by a simplified free-body diagram shown in Figure 4.

The mechanism of the inclined surface in reducing the peak horizontal displacement in comparisonwith conventional isolation bearings is described in this section, utilizing the analogy of a dynamicsliding block on an inclined plane. The motion of a mass on a frictional inclined plane is theinterplay of different force types and the characterizing features of the incline surface. Forces actingon a block mass (m) placed on an inclined plane, which is accelerated towards left with a horizontalacceleration at the top of first story (ah), are shown in Figure 5.

The angle of incline is θ, and the friction coefficient is m at the contact surface. Assuming that theblock mass stays in contact with the inclined surface, the normal force N is expressed byN(t) =mg cos θ+mah sin θ. Therefore, when the mass is sliding upward, the net horizontal reactionforce to the block mass or the reaction force acting on the column top yields to

Fx ¼ m ah m sinθ cosθ� sin2θ� �� g sinθ cosθþ m cos2θ

� �� (1)

If the horizontal acceleration (ah) is assumed to be constant within the duration of slidingconsidered, on the basis of the energy conservation law, the maximum horizontal displacement(xmax) can be written as

1st Story Column Top Movement

L L

N

mFh

Fv

fr

0 x

y

Figure 4. Mechanical model of the isolator with multiple-slider bearing.

Figure 5. Free-body diagrams of an accelerated mass object on an inclined slope.



xmax ¼ 12v0

2 � cosθg sinθ� ah cosθþ mg cosθþ mah sinθ½ � (2)

where vο is the initial velocity. Combining Eqs (1) and (2), xmax can be expressed as

xmax ¼ 12mv0

2 � cos2θ�Fx þ mah 2m sinθ cosθ� 1½ � (3)

In the same manner, the maximum horizontal displacement for the conventional rubber bearing(xrmax) assuming the simplest case where the conventional isolation bearing’s resisting horizontalforces (Fx) are kept constant can be represented by

xr max ¼ 12mv0

2 � 1�Fx � mah

(4)

This formulation can also be seen as a flat plane when setting θ equal to zero in Eq. (3). This isuseful observation for assessing the reduction effectiveness of the inclination surface. ComparingEqs (3) and (4) reveals that xmax is always less than the xr,max, that is,

xmax

xrmax¼

�cos2θ� �Fx � mah

�F x � maha

�< 1:0 (5)

where a = [1� 2m sinθ cosθ] is a constant less than unity for any combinations of θ and m. Equation (5)implies the effectiveness of the inclined surface in reducing the peak horizontal displacement comparedwith the conventional isolation bearings for the same level of horizontal reaction force on thefirst story top column. The fraction of reduction depends mainly on the two factors simultaneously:cos 2θ and a.

1.4. Rigid body response of multiple-slider bearing under horizontal excitation

A general formulation for the equation of motion can be written depending on the direction and sectionof sliding. These have a great significance because the direction determines whether the most‘deleterious’ pulses of the excitation tend to move the block mass upward or downward [41]. Forthe flat plane section, two phases, namely the sliding and nonsliding phases, can be identified. In thenonsliding phase, the shear force at the interface is smaller than the resistance friction force, and thestructure can be treated as a fixed-base system. Once the lateral shear force exceeds the frictionforce, the structure will start to slide. The horizontal friction force at the sliding interface offersresistance to relative motion and energy dissipation during the structural response. The relativeacceleration response can be written for both cases as

€x tð Þ ¼ 0 ⇒ stick phase�mg sgn _x tð Þð Þ � ah tð Þ ⇒ sliding phase

�(6)

where sgn( ) is the signum function. The maximum absolute acceleration is €xaj j ¼ mg. For the inclinedplane section, the normal force can be written for the right-side and left-side slopes as follows:

N tð Þ ¼ m g cosθ� ah tð Þ sinθð Þ (7)

Because the critical acceleration of the mass directly depends on the direction of excitation, upwardand downward motions are expressed separately. It is clear that the horizontal acceleration ah must beeither of the following expressions, for the transition from the stick phase to the sliding phase.



ah⩽� m cosθ� sinθcosθþ m sinθ

! downward

ah⩾m cosθþ sinθcosθ� m sin θ

! upward

8>><>>:

9>>=>>;

(8)

This implies that higher inertia force is required to trigger the upward sliding than that in thedownward direction. This is another insight on the effectiveness of the proposed geometry inreducing the peak displacement. An extensive series of shaking table tests of the multiple-sliderbearing were performed by Igarashi et al. [18–22], and the effect of the maximum displacementreduction has been experimentally confirmed.

It should be noted that there are some differences in the force–displacement relationship for the caseconsidering dynamic response of the structure and that for the quasi-static equilibrium, including theimpact forces generated as a result of the transition from the horizontal to inclined surfaces, and viceversa [20–23]. However, for simplicity of the analysis, the idealized force–displacement relationshipof the multiple slider is used in the response analysis of the system in this study.

In previous studies, the validity of this simplified model is compared with past experiments on a setof sliders and sliding plates with a configuration similar to the multiple-slider bearing [20, 23, 42]. Itwas concluded that there are some differences especially in cases where excitation velocity is highand that impact forces generated at the transition point between sliding surfaces affect the response.The test results indicate that higher θ generates higher impact force. Despite these differences, thesimplified hysteresis behavior of the multiple-slider bearing is still regarded as a good approximationthat covers the essential characteristics of the device.

A proper design of the isolator is accomplished by understanding the sensitivity of the deviceparameters (L, θ, and m) and their effects in de-amplification of the input motion. The frictionalspring method has been utilized to solve the discontinuities occurring in the analysis of the slidingstructure due to repeated transition phases between stick and slip modes, which introducediscontinuity and high nonlinearity [43]. The fictitious spring stiffness is taken as zero for thesliding phase and as a very large number for the nonsliding phase. This assumption may beappropriate because sliding frictional interfaces are incapable of reproducing truly rigid-plasticbehavior as Teflon–steel interfaces undergo some very small elastic displacement before slidingprimarily due to small elastic shear deformation of the Teflon material [44].

1.5. Seismic response of five-story frame structure with soft first story

A five-story reinforced concrete shear frame with soft first story (Figure 6) is considered to demonstratethe efficiency of the proposed isolation system in reducing the ductility demand and damage in thestructure. The system is also compared with the conventional frame structure.

Table I presents the story initial stiffness (Ki) and the story yield strength to the total weight ratio(Vy /W). It is obvious that the first story property implies sharp discontinuities in strength andstiffness relative to the above stories. In this study, the foundation connected to the structure isassumed to be rigid. Girders and floor systems are assumed to be rigid bodies and the columns donot deform axially. The fundamental natural period (T1) is equal to 0.56 s for this frame structurewith equal lumped floor masses (m) of 45.34 t for each story. Rayleigh damping in the structurewith the damping ratio of 5% for the first two modes is assumed. To account for the continuallyvarying stiffness and energy-absorbing characteristics of the columns under cyclic loading, themodified Clough bilinear stiffness degrading model is used to represent the hysteretic behavior ofthe columns; see Figure 7. The post-yielding to pre-yielding stiffness ratio of 0.05 and degradationstiffness rate (a) of 10% are the parameter values used for the hysteretic model. The input groundmotions used in the simulations are 1940 El Centro record NS component (0.32 g) and 1995 KobeJMA NS record (0.82 g). Only unidirectional excitation is considered.

The clearance length of the multiple-slider bearing is L= 10mm in the case of El Centro record andL= 50mm in the case of Kobe JMA record. The inclination angle is θ= 15� for both cases. The



restoring force (Fb) of RB is modeled with linear force–displacement relationship with viscousdamping and is expressed as follows:

Fb ¼ kbxb þ cb _xb (9)

cb ¼ zb � 2obmtð Þ (10)

where cb is the effective viscous damping of RB, mt is the total mass of the superstructure above theisolation level, ob is the angular isolation frequency = 2p/Tb, and zb is the effective damping

ratio = 0.15. The period of isolation Tb ¼ 2pffiffiffiffiffiffiffiffiffiffiffiffiffimt=Kb

pis chosen to be 2.0 s. The friction coefficient of

the multiple-slider bearing for all the three sliding surfaces is assumed to be m= 0.05 in the case of

Table I. Properties of five-story frame structures.

Story Ki (kN/m) Vy /W

1 41,137 0.14512 154,220 0.53443 133,500 0.45724 96,127 0.34885 60,997 0.2084

Figure 7. Modified Clough degradation model.

m2

m3

m4

m5

m1

6.0

3.5

3.5

3.5

3.5

6.0 m6.0 m6.0 m

Figure 6. Five-story shear frame structure with soft story.



El Centro record and m= 0.15 in the case of Kobe JMA record. The peak response of the structuresusing a velocity dependent friction model was not significantly different from that predicted by aCoulomb friction model [45, 46], which is used in this study. The dynamic equation of motion forthe shear type isolated building can be written as follows:

M½ � €x tð Þ½ � þ C½ � _x tð Þ½ � þ fs tð Þf g ¼ � M½ � r1½ � €xg tð Þ �� r2½ � fh tð Þf g (11)

where [M] and [C] are the n� n mass and damping matrices, respectively; and _x tð Þ½ � and €x tð Þ½ � are n� 1relative velocity and acceleration vectors, respectively. The symbol fs(t) denotes the vector of restoringforces that are designated by the modified Clough model, €xg tð Þ is the ground acceleration, [r1] and [r2]are the force distribution loading vectors, and fh(t) represents the horizontal nonlinear isolators forces.Numerical time integration is performed using Newmark’s b method.

2. SIMULATION RESULTS AND DISCUSSION

The analysis results for seismic response of the five-story frame structure with soft first story arepresented in this section. The primary concern of these simulations is to show the effectiveness ofthe proposed system in significantly reducing the ductility demand and drift of the soft first story incomparison with the conventional structure. Figures 8 and 9 illustrate the ability of the proposedsystem to reduce both drift and ductility demand in the first story columns without significantchanges in the upper stories in comparison with the conventional design. The drift and ductilitydemand were reduced both considerably by 49% when subjected to El Centro record and by 41%when subjected to Kobe JMA record.

Figures 10 and 11 show the force–displacement relationship for the multiple-slider bearings placedon the top of the first story columns and that for the first story. As shown in Figures 10b and 11b,inelastic deformation of the first story columns is reduced, indicating less energy being absorbed bythese columns. It can be concluded that the proposed system is a practical cost-effective solutionthat can be adopted to retrofit existing buildings with soft stories and increase their seismic resistance.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.0450

5

10

15

20

Drift

h(m

)

Conventional Isolated

0 1 2 3 4 5 60

5

10

15

20

Ductility Demand Ratio

h(m

)

(a)

(b)

Figure 8. Comparison between conventional design and proposed isolation system subjected to El Centrorecord: (a) maximum story drift versus story height and (b) story ductility demand versus story height.



Installing the isolation on the top of columns rather than at the base level is a good solution toimprove the seismic performance of the existing old building, especially for cases where installationat the foundation level may be difficult or inaccessible. There exist examples of retrofit by a mid-story seismic isolation interface where it was difficult to put the isolators below the existingfoundation [24]. Furthermore, the results shown in Figures 12 and 13 indicate that the seismicperformance of the soft story frame structure in terms of ductility demand and story drift with the

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

5

10

15

20

Drift

h(m

)

Conventional Isolated

0 2 4 6 8 10 12 14 16 180

5

10

15

20

Ductility Demand Ratio

h(m

)

(a)

(b)

Figure 9. Comparison between conventional design and proposed isolation system subjected to Kobe JMArecord: (a) maximum story drift versus story height and (b) story ductility demand versus story height.

(a)

(b)

Figure 10. Hysteresis loop – El Centro record: (a) multiple-slider bearings and (b) soft first story.



seismic interface on the top of the columns is superior to the case when the same interface is allocatedat the base level.

Some researchers have studied and analyzed the effect of interstory isolation in which a seismicisolation system is installed at the middle story level [47, 48]. It is shown in those research results

(a)

(b)

Figure 11. Hysteresis loop – Kobe JMA record: (a) the multiple-slider bearings and (b) soft first story.

Figure 12. Comparison with base isolation: El Centro record case. (a) Hysteresis loop of the multiple-sliderbearings, (b) maximum story drift versus story height, (c) maximum displacement versus story height, and

(d) story ductility demand versus story height.



that the concentrated response control systems of this type reduce the response and improve the seismicperformance of the entire building.

It is indicated in Figure 14 that the displacement of the isolator at the end of seismic motion is nearlyzero, affirming the fact that the multiple-slider bearing inherits a self-centering mechanism capable ofreturning to its original position. Figure 15 shows the absolute acceleration response time history of thetop floor when the structure is subjected to the El Centro record. It is obvious that the acceleration

Figure 13. Comparison with base isolation: Kobe JMA record case. (a) Hysteresis loop of the multiple-sliderbearings, (b) maximum story drift versus story height, (c) maximum displacement versus story height, and

(d) story ductility demand versus story height.

Figure 14. Displacement time history response of the multiple-slider bearings.



responses for the fixed base, base isolation, and top story isolation are close to each other. The reasonfor the small acceleration response in the case of the fixed base can be explained by the development ofplastic hinges in the soft first columns with excessive deformation as shown in the hysteresis behaviorof Figures 10 and 11. Therefore, large amount of energy has been absorbed by these columns due totheir nonlinear deformations, hence reducing the forces that can be developed at the upper stories.Practically, these columns could not accommodate such a ductility range and would have beencollapsed, causing what is known as the soft story failure. In the previous study, a comparison ofbuilding response between the cases of the fixed base and of seismic isolation using the multiple-slider bearing has been performed [23]. Maintaining the superstructure in the elastic range, themaximum absolute top floor acceleration has been reduced significantly from 1.81 to 0.77 g,implying a reduction of approximately 60%.

2.1. Optimum design for the multiple-slider bearing

As previously mentioned, one of the distinctive characteristics of the multiple-slider bearing is itscapability to provide more freedom in the design process while defining the optimum parametersthat are required to define the bearing to obtain the most efficient seismic performance. In thissection, the optimum design for the multiple-slider bearing is discussed. This is accomplished byunderstanding the sensitivity of the bearing parameter selection and their effects in the control of thestructural response. The most appropriate design is achieved by minimizing both the maximumbearing displacement and the ductility demand ratio for the soft story. However, these two quantitiesare characterized by a trade-off relationship, making it difficult to maintain the two values minimumat the same time. For this reason, extensive analysis is carried out through various combinations ofvariation of θ, L, and m to search for the most appropriate designs. The parameters used in thesesimulations are given in Table II. A total of 441 cases are considered in this study. The sameexample of the five-story frame structure is used again in the simulation.

Figure 16 shows the relationship between the maximum horizontal displacement of the multiple-slider bearing and the ductility demand ratio of the soft first story with all the cases considered inTable II, when the frame structure was subjected to Kobe JMA record. Generally speaking, anycombination of θ, L, and m achieves a better seismic performance than the conventional design interms of the ductility demand ratio. The selection for the optimum design can simply be made bytracking the lowest points in the lower region that can be regarded as desirable in the sense that

Figure 15. Absolute acceleration time history response for the top story.

Table II. Parameters for the multiple-slider bearing.

Parameters Value

θ [degree] 5, 10, 15, 20, 25, 30, 35L [mm] 10, 20, 30, 40, 50, 60, 70, 80, 90m 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35



each point attains the minimum story ductility for a given isolator displacement, as shown in the lineconnecting these optimum design candidate points. The seismic performance represented by thosepoints is also superior to the seismic performance of the conventional bearings.

Figure 17 shows the response analysis result for another group of parameter combinations when theframe structure is subjected to El Centro record. The analysis is carried out for m= 0.05 with allcombinations of θ and L. In addition, a comparison with the RSI, which is a combination of rubberand plane sliding bearings set in parallel, is also performed. The RSI case can be considered as aspecial case of the multiple-slider bearing when either θ is zero or L is very large. Although the RSIprovides a lower story ductility demand in some cases, horizontal displacement is larger than themany cases that can be achieved by the multiple-slider bearing. In this case study, selecting θ equalto 5� and L equal to 20mm, that is, point A in Figure 17, gives better results than RSI in terms ofthe horizontal displacement while maintaining the ductility demand ratio less than unity.

As mentioned before, the maximum horizontal displacement is one of the crucial quantities in theprocess of design. Maintaining this displacement within an acceptable limit becomes a priority in case

0.1 0.12 0.14 0.16 0.18 0.20

2

4

6

8

10

12

14

16

18

Maximum Isolator Displacement xmax (cm)

Duc

tility

Dem

and

Rat

io

=5 =10 =15 =20 =25 =30 =35

Conventional Isolation

Without Isolation

Figure 16. Various design combinations for the multiple-slider bearing.

0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.0750.5

1

1.5

2

2.5

3

3.5

4

4.5

Maximum Isolator Displacement xmax

(m)

Duc

tility

Dem

and

Rat

io

=0.05:Combinations of & L

=5

=10

=15

=20

=25

=30

=35RSI

A

B

RSI

Figure 17. Comparison between multiple-slide bearing and resilient sliding isolation under variouscombinations.



where the clearance to the neighboring structure is limited or when the expansion joints in the originalconstruction turn out to be an issue for the choice of the most suitable isolator in retrofitting thestructure. For example, if the maximum displacement shall not exceed 4.5 cm in this case study, themultiple-slider bearing is applicable to achieve this criteria but with an increase in ductility demandratio at points such as B in Figure 17, whereas RSI cannot be implemented and its usage is limited.

3. CONCLUSION

Seismic retrofitting of soft-first-story frame structures by introducing a seismic interface on the top of firststory columns proves its efficiency to enhance the structural safety and integrity for the structures of thistype. The effectiveness of the multiple-slider bearing in reducing the peak horizontal displacement incomparison with the conventional isolation has been illustrated in the analogy of a dynamic slidingblock on an inclined plane. It has been shown that the multiple-slider bearing can be considered as oneof the prominent cost-effective solutions that can overcome the dilemma between the need for soft storyand its vulnerability to collapse. Moreover, the proposed system also offers a feasible solution that issimple and practical to be implemented for seismic retrofitting of existing buildings with soft stories.The results indicate the ability of the proposed system to significantly reduce the ductility demand andexcessive drift for the first story columns to the level the rubber bearing and RSI cannot achieve.

ACKNOWLEDGEMENTS

The authors would like to express their gratitude towards Dr. Hiroshige Uno, Dr. Yukio Adachi, Dr.Tomoaki Sato, Mr. Yoshihisa Kato, and Mr. Yasuyuki Ishii for their valuable advice, support, and sugges-tions on this research.

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