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

SUMMARY

A new isolation interface is proposed in this study to retrofit existing buildings with inadequate soft stories as well as new structures to be constructed with soft first story intended for architectural or functional purposes. 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 consisting of one horizontal and two inclined plane sliding surfaces based on polytetrafluoroethylene and highly polished stainless steel interface at both ends set in series. A numerical example of a five-story reinforced concrete shear frame with soft first story is considered and analyzed to demonstrate the efficiency of the proposed isolation system in reducing the ductility demand and damage in the structure while maintaining the superstructure 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 bearing interface and resilient sliding isolation is carried out. Moreover, an optimum design procedure for the multiple-slider bearing is proposed through the trade-off between the maximum bearing displacement and the first story ductility demand ratio. The results of extensive numerical analysis verify the effectiveness of the multiple-slider bearing in minimizing the damage from earthquake and protecting the soft first story from excessively large ductility demand. Copyright © 2012 John Wiley & Sons, Ltd.

1 INTRODUCTION

Despite the fact that structures with soft first story are inherently vulnerable to collapse during earthquakes, it is still in demand especially in urban areas. The soft first story offers architects an attractive model by allowing a sense of floating and bright space. The famous architect Le Corbusier is 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 providing parking spaces, allowing for a grand entrance or ballrooms as in hotels and permitting a desirable continuous windows for display for stores located in the first story. In addition, such a building helps in 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 that in the story immediately above it, or less than 80% of the average stiffness of the three stories above it. Moreover, the code also defines the ‘extreme soft story’ when the lateral stiffness of that story is less than 60% of that in the story immediately above it, or less than 70% of the average stiffness of the three stories above it.

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

Chen et al. [10] proposed another modification to the soft first story concept that introduces additional energy dissipation capacity to reduce drift and provides a mechanism to reduce P-Δ effects. 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 ductile behavior to accommodate large drifts. A similar concept with the difference that the first story shear walls are fitted with Teflon sliders was also proposed [11]. A further extension of the concept was proposed similar to the aforementioned philosophy with additional steel dampers to enhance the energy dissipation during earthquakes [12].

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

Past earthquake damage examples have proven that the performance of conventionally designed columns in soft story structures is unsatisfactory because of the high uncertainty in the ductility design concept. Although structures with soft stories may survive during earthquakes, excessive drifts and formation of plastic hinges at critical sections could make it difficult to repair the damaged structures. For that reason, more effective and reliable techniques are needed to enhance the structural safety and integrity for such special type of structures. It can be noticed from the previous studies that seismic isolation is one of the prominent alternatives that can overcome the dilemma 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 installing multiple-slider bearings consisting of multiple sliding plane surfaces, one horizontal and two inclined surfaces, on the top of first story columns to effectively prevent the first story damage by reducing the ductility demand to the columns and maintaining the superstructure to behave nearly in the elastic range at the same time. The mechanism and efficiency of the proposed system are illustrated using nonlinear time history analysis of a moment resisting concrete frame subjected to seismic excitation. Comparative study with the conventional system and with various isolation systems 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 in big and crowded cities where buildings are often built closely to each other because of the limited availability and high cost of the land. This leads to cause pounding of adjacent buildings due to the 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 is costly and may cause instability.

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

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

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

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

The concept of this type of bearing was proposed to upgrade the seismic performance of multispan continuous girder bridges with reduced horizontal displacement of the girder in case of strong earthquakes, which is referred to as the ‘Uplifting Slide Bearing’ [18-22]. Figure 3 shows photographs of sample Uplifting Slide Bearings. The concept was later extended to include multistory structures mainly to control the maximum top floor horizontal displacement [23].

Figure 3. Uplifting Slide Bearing.

The proposed system also offers a feasible solution for seismic retrofitting of existing buildings with soft stories in areas where clearance between adjacent buildings is limited, as will be shown in this study. Commonly, the seismic rehabilitation can be carried out simply by transmitting the load acting 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 temporary jacks. 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 nonisolated buildings are different. For example, fixed-base buildings are permitted a force reduction factor (R) that represents 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 elements below or above the interface. The first story columns in Figure 1 are to be designed for a force equal to the maximum effective stiffness of the isolation interface times the design displacement in the horizontal direction under consideration and for the design moment due to the shear force and the P-Δ effect that should be considered if it exists depending on the slider orientation. In other words, the first story columns should be designed elastically for the maximum force that is transmitted though the isolation system at the design level earthquake [27]. Other code requirement is that isolation systems should use rigid horizontal diaphragms or bracing systems above and below the isolator level to provide deformation compatibility among the resisting structural elements. In view of this requirement, the first story columns are tied together by tie beams in the proposed model. It is noteworthy that the device in the present status is restricted to unidirectional motion because it was first developed as a seismic response control device for multispan continuous girder bridges, as mentioned earlier. Currently, the device is in the process of further development and modification to take into account the bidirectional motion that is essential in the design of seismically 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 as well as their durability and stability characteristics. They are insensitive to the variation of the frequency content of ground excitation. Moreover, sliding isolators provide a natural source of damping through friction because the horizontal friction force at the sliding surface offers resistance to motion and dissipates energy. The hysteresis of PTFE–SUS interface is a rectangle that provides equivalent viscous damping of 63.7%. In addition, sliding bearings using Teflon as the sliding surface can take much higher compressive stresses than elastomeric bearings (60 MPa or more for the former versus 15 MPa 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 an attractive feature to reduce the stiffness of the isolated buildings in the large displacement range, while resisting frequent lateral loads caused by the wind. For example, most of base isolated high-rise buildings in Japan contain friction-type base isolated systems [28], and devices having various properties have been made available in recent years [29].

Although several friction-type isolators have been developed, the FPS [30] has been extensively used and put into practice. The restoring force is provided by the component of the self-weight tangent to the sliding surface. However, because the restoring force varies linearly to the sliding displacement, 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 this problem, several researchers have introduced modifications on the original concept of the FPS. One of these examples is the variable frequency pendulum isolator [31], in which the geometry of a concave sliding surface is designed such that the oscillation frequency decreases with the sliding displacement amplitude and the force transmitted to the structure is limited with an upper bound. Later on, 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 one pendulum 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 both light 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 acting RoGlider consists of two SUS plates with a PTFE-ended puck sitting between the plates. Two rubber 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 a steel cylinder rolling on a V-shape surface has been proposed.

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

1. Geometrical configuration creativity: The geometry of this device was chosen to be effective in controlling the horizontal displacement by allowing a part of the earthquake transmitted energy to be transferred into a gravitational potential energy through the diagonal sliding.
2. Avoiding pounding effect by efficiently controlling the displacement: Pounding of adjacent buildings due to insufficient or inadequate separation can be a serious hazard in seismically active areas. The verification of the multiple-slider bearing's efficiency to control displacement is numerically presented in an earlier study [23].
3. The multiple-slider bearing is a cost-effective solution for seismic isolation. Sliding bearings have found more and more applications in recent years over rubber bearings for economic reasons. The multiple-slider bearing is basically made from three surfaces of SUS and PTFE interfaces. 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 of design that requires determination of three parameters: clearance length (L), that is, the specified distance prior to the diagonal sliding; the inclination angle (θ); and the friction coefficient (μ) for the three surfaces in contact.
5. The configuration of the device has the potential of using different friction bearings for the horizontal and inclined plane surfaces, as shown in a previous study [23]. Use of different friction coefficients has been found to add more reduction to the horizontal displacement response, 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 and esthetic solution in terms of integration into the structural system for cases in which space consideration is an important factor, rendering the conventional rubber bearing under walls problematic.
7. Because the multiple-slider bearing is vertically stiff, the vertical deflections of columns that occur during bearing installation in retrofit application is minimized, and damage to architectural finishes in upper stories can be avoided.
8. Contrary to the FPS that utilizes a spherical sliding surface to develop a restoring force, the slope angle of the inclined surfaces in the multiple-slider bearing is much larger than the range of 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 the parallel component of gravity load along the sliding surfaces.
9. During large displacement response, the horizontal force in the multiple-slider bearing is kept constant with the increase in displacement. On the other hand, the curved surface in the FPS may result an increase in horizontal force with a larger displacement because the force is directly proportioned to the displacement.
10. The multiple-slider bearing is expected to be a feasible solution for seismic retrofitting of existing buildings with soft stories in areas where clearance between adjacent buildings is limited because 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 be represented by a simplified free-body diagram shown in Figure 4.

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

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

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

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

• (1)

If the horizontal acceleration (a_h) is assumed to be constant within the duration of sliding considered, on the basis of the energy conservation law, the maximum horizontal displacement (x_max) can be written as

• (2)

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

• (3)

In the same manner, the maximum horizontal displacement for the conventional rubber bearing (x_rmax) assuming the simplest case where the conventional isolation bearing's resisting horizontal forces (F_x) are kept constant can be represented by

• (4)

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

• (5)

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

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 section of 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]. For the flat plane section, two phases, namely the sliding and nonsliding phases, can be identified. In the nonsliding phase, the shear force at the interface is smaller than the resistance friction force, and the structure can be treated as a fixed-base system. Once the lateral shear force exceeds the friction force, the structure will start to slide. The horizontal friction force at the sliding interface offers resistance to relative motion and energy dissipation during the structural response. The relative acceleration response can be written for both cases as

• (6)

where sgn( ) is the signum function. The maximum absolute acceleration is . For the inclined plane section, the normal force can be written for the right-side and left-side slopes as follows:

• (7)

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

• (8)

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

It should be noted that there are some differences in the force–displacement relationship for the case considering dynamic response of the structure and that for the quasi-static equilibrium, including the impact forces generated as a result of the transition from the horizontal to inclined surfaces, and vice versa [20-23]. However, for simplicity of the analysis, the idealized force–displacement relationship of 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 set of sliders and sliding plates with a configuration similar to the multiple-slider bearing [20, 23, 42]. It was concluded that there are some differences especially in cases where excitation velocity is high and 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, the simplified hysteresis behavior of the multiple-slider bearing is still regarded as a good approximation that covers the essential characteristics of the device.

A proper design of the isolator is accomplished by understanding the sensitivity of the device parameters (L, θ, and μ) and their effects in de-amplification of the input motion. The frictional spring method has been utilized to solve the discontinuities occurring in the analysis of the sliding structure due to repeated transition phases between stick and slip modes, which introduce discontinuity and high nonlinearity [43]. The fictitious spring stiffness is taken as zero for the sliding phase and as a very large number for the nonsliding phase. This assumption may be appropriate because sliding frictional interfaces are incapable of reproducing truly rigid-plastic behavior as Teflon–steel interfaces undergo some very small elastic displacement before sliding primarily 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 demonstrate the efficiency of the proposed isolation system in reducing the ductility demand and damage in the structure. The system is also compared with the conventional frame structure.

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

Table 1 presents the story initial stiffness (K_i) and the story yield strength to the total weight ratio (V_y / W). It is obvious that the first story property implies sharp discontinuities in strength and stiffness relative to the above stories. In this study, the foundation connected to the structure is assumed to be rigid. Girders and floor systems are assumed to be rigid bodies and the columns do not deform axially. The fundamental natural period (T₁) is equal to 0.56 s for this frame structure with equal lumped floor masses (m) of 45.34 t for each story. Rayleigh damping in the structure with the damping ratio of 5% for the first two modes is assumed. To account for the continually varying stiffness and energy-absorbing characteristics of the columns under cyclic loading, the modified Clough bilinear stiffness degrading model is used to represent the hysteretic behavior of the columns; see Figure 7. The post-yielding to pre-yielding stiffness ratio of 0.05 and degradation stiffness rate (α) of 10% are the parameter values used for the hysteretic model. The input ground motions used in the simulations are 1940 El Centro record NS component (0.32 g) and 1995 Kobe JMA NS record (0.82 g). Only unidirectional excitation is considered.

Table 1. Properties of five-story frame structures.

Story	Ki (kN/m)	Vy / W
1	41,137	0.1451
2	154,220	0.5344
3	133,500	0.4572
4	96,127	0.3488
5	60,997	0.2084

Figure 7. Modified Clough degradation model.

The clearance length of the multiple-slider bearing is L = 10 mm in the case of El Centro record and L = 50 mm in the case of Kobe JMA record. The inclination angle is θ = 15° for both cases. The restoring force (F_b) of RB is modeled with linear force–displacement relationship with viscous damping and is expressed as follows:

• (9)

• (10)

where c_b is the effective viscous damping of RB, m_t is the total mass of the superstructure above the isolation level, ω_b is the angular isolation frequency = 2π/T_b, and ζ_b is the effective damping ratio = 0.15. The period of isolation is chosen to be 2.0 s. The friction coefficient of the multiple-slider bearing for all the three sliding surfaces is assumed to be μ = 0.05 in the case of El Centro record and μ = 0.15 in the case of Kobe JMA record. The peak response of the structures using a velocity dependent friction model was not significantly different from that predicted by a Coulomb friction model [45, 46], which is used in this study. The dynamic equation of motion for the shear type isolated building can be written as follows:

• (11)

where [M] and [C] are the n × n mass and damping matrices, respectively; and and are n × 1 relative velocity and acceleration vectors, respectively. The symbol f_s(t) denotes the vector of restoring forces that are designated by the modified Clough model, is the ground acceleration, [r₁] and [r₂] are the force distribution loading vectors, and f_h(t) represents the horizontal nonlinear isolators forces. Numerical time integration is performed using Newmark's β method.

2 SIMULATION RESULTS AND DISCUSSION

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

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

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

Figures 10 and 11 show the force–displacement relationship for the multiple-slider bearings placed on 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 by these columns. It can be concluded that the proposed system is a practical cost-effective solution that can be adopted to retrofit existing buildings with soft stories and increase their seismic resistance.

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

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

Installing the isolation on the top of columns rather than at the base level is a good solution to improve the seismic performance of the existing old building, especially for cases where installation at 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 existing foundation [24]. Furthermore, the results shown in Figures 12 and 13 indicate that the seismic performance of the soft story frame structure in terms of ductility demand and story drift with the seismic interface on the top of the columns is superior to the case when the same interface is allocated at the base level.

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

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

Some researchers have studied and analyzed the effect of interstory isolation in which a seismic isolation system is installed at the middle story level [47, 48]. It is shown in those research results that the concentrated response control systems of this type reduce the response and improve the seismic performance of the entire building.

It is indicated in Figure 14 that the displacement of the isolator at the end of seismic motion is nearly zero, affirming the fact that the multiple-slider bearing inherits a self-centering mechanism capable of returning to its original position. Figure 15 shows the absolute acceleration response time history of the top floor when the structure is subjected to the El Centro record. It is obvious that the acceleration responses for the fixed base, base isolation, and top story isolation are close to each other. The reason for the small acceleration response in the case of the fixed base can be explained by the development of plastic hinges in the soft first columns with excessive deformation as shown in the hysteresis behavior of Figures 10 and 11. Therefore, large amount of energy has been absorbed by these columns due to their 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 been collapsed, causing what is known as the soft story failure. In the previous study, a comparison of building 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, the maximum absolute top floor acceleration has been reduced significantly from 1.81 to 0.77 g, implying a reduction of approximately 60%.

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

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

2.1 Optimum design for the multiple-slider bearing

As previously mentioned, one of the distinctive characteristics of the multiple-slider bearing is its capability to provide more freedom in the design process while defining the optimum parameters that are required to define the bearing to obtain the most efficient seismic performance. In this section, the optimum design for the multiple-slider bearing is discussed. This is accomplished by understanding the sensitivity of the bearing parameter selection and their effects in the control of the structural response. The most appropriate design is achieved by minimizing both the maximum bearing displacement and the ductility demand ratio for the soft story. However, these two quantities are characterized by a trade-off relationship, making it difficult to maintain the two values minimum at the same time. For this reason, extensive analysis is carried out through various combinations of variation of θ, L, and μ to search for the most appropriate designs. The parameters used in these simulations are given in Table 2. A total of 441 cases are considered in this study. The same example of the five-story frame structure is used again in the simulation.

Table 2. Parameters for the multiple-slider bearing.

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

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 in Table 2, when the frame structure was subjected to Kobe JMA record. Generally speaking, any combination of θ, L, and μ achieves a better seismic performance than the conventional design in terms of the ductility demand ratio. The selection for the optimum design can simply be made by tracking the lowest points in the lower region that can be regarded as desirable in the sense that each point attains the minimum story ductility for a given isolator displacement, as shown in the line connecting these optimum design candidate points. The seismic performance represented by those points is also superior to the seismic performance of the conventional bearings.

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

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

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

As mentioned before, the maximum horizontal displacement is one of the crucial quantities in the process of design. Maintaining this displacement within an acceptable limit becomes a priority in case where the clearance to the neighboring structure is limited or when the expansion joints in the original construction turn out to be an issue for the choice of the most suitable isolator in retrofitting the structure. For example, if the maximum displacement shall not exceed 4.5 cm in this case study, the multiple-slider bearing is applicable to achieve this criteria but with an increase in ductility demand ratio 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 first story columns proves its efficiency to enhance the structural safety and integrity for the structures of this type. The effectiveness of the multiple-slider bearing in reducing the peak horizontal displacement in comparison with the conventional isolation has been illustrated in the analogy of a dynamic sliding block on an inclined plane. It has been shown that the multiple-slider bearing can be considered as one of the prominent cost-effective solutions that can overcome the dilemma between the need for soft story and its vulnerability to collapse. Moreover, the proposed system also offers a feasible solution that is simple 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 and excessive 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 suggestions on this research.