1. Introduction

The use of base isolators for the anti-seismic design of structures has attracted considerable interest in recent years. The main aim here [1] is to separate the structure from ground motions ensuring flexibility as well as energy dissipation’s aptitude through inserting isolation system between foundation and the superstructure. Conversely, in conventional anti-seismic design which resistance is obtained through ductility whereby the structure is allowed to deform in the non-elastic range [2]. Therefore, this type of design means that even though the collapse of the structure can be avoided, significant structural damages may be caused in the case of major earthquakes. Consequently, the new concept allowing input energy dissipation appears to have an important potential in preventing earthquake damages to structures and their internal equipments. The concept to isolate the fixed base has been suggested in last century. Early as 1909 [3], a British medical doctor had performed for a patent on separating a building from the ground by a layer of talc or sand. Nevertheless, it was only in the last three decades that this design concept has received serious attentions. Also the first modern application of this technology was carried out in 1969 by using rubber isolators in a school building in Skopje, Macedonia [4]. The basic concept of this system is to uncouple the structure motion from the soil’s one by inserting between the foundation and the superstructure isolation devices that have a very important horizontal deformability and a very high vertical stiffness [5]. Seismic isolation can be achieved by increasing the natural period of vibration of a structure via use of rubber isolation pads [6] (Fig. 1). Consequently, the seismic effects are decreased which leads to significant reductions in seismic response variables such as floor accelerations, inter-storey drifts, and base shear forces [7]. On the other hand, as the flexibility of the base dissipaters increases, base displacement becomes larger [8]. That is why it is interesting to incorporate an automatic re-centring device. Different kinds of rubber base-isolation systems can be used [9], in particular, the lead-rubber base isolator (LRB), also provides energy dissipation and re-centering capability. But above all, the elastomeric bearings filter the ground motion, leading to a low frequency in the fundamental mode and, then, to a low pseudo-acceleration spectral value for most of the expected ground motions. Thus, a significant decrease in the floor accelerations and inter-storey drifts is obtained. This dissipater and its effects on the seismic structure response are the subject of this study.

Fig.1

Last years, extensive works have investigated the performance of this device to enhance seismic response of buildings. Mkrtychev et al. [10] examined the efficiency of lead rubber bearing system with different buildings heights at multi-component seismic impact. A seismically isolated monolithic ferro-concrete with five, nine and 16-storey buildings were considered. The analysis of the problem was achieved by a direct integration of the motion equations for an explicit scheme in the software package (LS-DYNA). The calculations were conducted considering the nonlinear nature of lead rubber isolators. An analysis of the effectiveness of buildings with and without the isolation was carried out. Zordan et al. [11] proposed a new approach to reduce the required computational time, called the equivalent linear method (EL). In the aforementioned method, the nonlinear response of dissipater can be adequately modelled using a fictitious viscously damped elastic structure. An investigation of existing expressions providing the state of research was conducted and then, an improved formulation has been proposed for equivalent linearization of structures fitted with lead rubber isolators (LRB). The new presented model predicts displacements that are similar with those obtained with nonlinear time history analysis (NLTH). Some approaches based on algorithms were developed to identify the nonlinear properties of rubber devices in base isolated buildings using only partial measurements of structural dynamic responses [12]. The first algorithm is used in the case that mathematical models are available for the base dissipaters. However, a second algorithm was proposed for the general case where it is complicated to implement a mathematical model describing the nonlinear behaviour of the rubber base isolators. The nonlinear behaviour is considered as “fictitious loading” on a linear building under a strong seismic hazard. The concept is based on the sequential Kalman estimator for the dynamic responses and the least-squares evaluation of the “fictitious loading”, to identify the nonlinear strength of rubber base isolator. The results of analyses demonstrate a good accuracy of the two proposed methods. Islam et al. [13] presented a paper where they studied a design of base isolation device for multi-storey buildings under medium seismic risk. Authors examined the dynamic response through automated nonlinear models. Lead-rubber bearing and high damping rubber bearing have been considered for the study. The nonlinearities of the aforementioned isolators have been duly chosen. Linear static, linear dynamic and nonlinear dynamic analyses due to site-specific earthquake signal were achieved on buildings with and without the isolation dissipaters. In [14], the influence of the soft-storey behaviour on concrete buildings which are fitted with lead-rubber base device was studied on four different structural models. Time history analysis on these frame systems was realised using Ruaumoko software, and effect of soft-storey behaviour on the structural response in fixed base and LRB base isolated systems was examined. Estimation of the frame system’s period, storey accelerations, inter-storey drift ratio, base shear, and plastic hinges distribution and their damage conditions was performed. The results show that LRB device can be beneficial to improve both structural responses. Hedayati-Dezfuli and Allam [15] studied seismic fragility of isolated highway bridges, authors considered pier and isolation system as two major vulnerable components. An analysis of different types of rubber bearings effect as natural rubber bearing, HDRB and LRB was carried out. They concluded that the bridge isolated by natural rubber bearing is the most vulnerable system, and the bridge equipped with HDRB has the minimum risk to undergo damage. The rubber being very influenced by temperature, several works have investigated the effect of this parameter on the variation of its mechanical properties [16-17]. Casciati et Faravelli [18] conducted an experimental study where they examined the response of new base isolators compared with that of 10-year-old devices. A new base-isolation technique was investigated experimentally by OH et al. [19]. They considerate a laminated elastomeric base isolation and U-shaped hysteretic energy dissipating devices called UH dissipaters. Results obtained from a shake table tests show that the base isolated dampers provided better seismic response compared to the fixed-base frame. In [20], authors considered in their study a smart lead rubber bearing as new types of dampers which are characterized by the use of a shape memory alloy in the form of wires. These devices have the aptitude to improved performance in terms of re-centering ability and energy dissipation capacity.

This study aims to investigate the effect of the lead rubber bearing isolation on steel structure response subjected to bidirectional seismic ground motions. Fast Nonlinear time history analyses are carried out considering a Bouc-Wen nonlinear model for base isolation device. Finally, in order to identify plastic behaviour of frame elements, nonlinear dynamic analyses were applied to the structure.

2. Lead core laminated rubber bearing

The laminated rubber bearing system (Fig.2) in which a central lead core is used to reduce the base relative displacement and providing an additional mean of energy dissipation was proposed by Robinson in 1975 [21]. This device has been put in function for the first time in New Zealand. It is an isolator that present a description of a Low damper rubber bearing (LDRB) [22-25], with a bar of lead in its centre. The dissipater as shown in figure 2 is composed of alternated layers of rubber and steel, which contributes on one hand, to ensure the stability and the support to the structure and provides on the other hand, its isolation from vibrations. In addition the core lead inserted inside aims to increase the damping effect and confer a nonlinear behaviour and a flow state in shear, forced by the metal frets. The flow starts at about 10Mpa.

Fig. 2

The performance of LRB to improve dynamic response under a variety of conditions was reported in [3]. The rubber provides the flexibility for the lateral displacements of the isolator while the yielding property of the lead core works as a mechanism for dissipating energy and hence reducing the lateral displacements of the damper. The mechanical behaviour of this isolator is equivalent to a hysteretic device [26]. The schematic model of the LRB base isolation damper is presented in figure 3.. In [27], it was suggested that the restoring force generated by the hysteretic behaviour of the LRB isolator’s lead core may be approximated by wefts hysteretic model.

In [28], the influence of the base isolators hysteresis loop’s shape on the response of multi-story structure for various bi-linear systems under different seismic signals was studied. Results showed that the equivalent linear elastic-viscous damping model of a bi-linear hysteretic system overestimates the base design displacements as well as underestimates the superstructure accelerations. Therefore, response of damped structure is significantly affected by the shape of hysteresis loop of isolators. Otherwise, the analysis conducted in [29] on LRB base isolated frames under far-fault and near-fault ground motions concluded that near-fault sites induce strong ground motions with unwanted effects on the base isolation system and on the response of the superstructure. In order to reduce these effects, a reinforcing through supplemental viscous damping on the existing LRB system represents an effective design strategy.

Fig. 3

2.1 Characteristics of Lead core laminated rubber bearing

The equation governing the base displacement is given as

(1)

Where is the relative displacement between the base of the structure and the ground, is the relative acceleration and is the relative velocity. is the ground acceleration (Earthquake). N is the number of base isolators used and M is the total mass of structure. Q is the hysteretic restoring force generated by the lead core which is given as

(2)

Where is post-to-pre yielding stiffness ratio. , are linear and nonlinear stiffness of the LRB (Fig. 4) and Z is the dimensionless hysteretic displacement that satisfies nonlinear first-order differential equation:

(3)

In Eqs. (2) and (3), and represent the force and the yield displacement of the equivalent hysteretic isolator. , and are dimensionless parameters, is an integer which controls the smoothness of transition from elastic to plastic response.

The restoring total force, F, of an isolator shall be calculated as the product of effective stiffness, and response displacement, D (FEMA-356) [30]) as sown in figure 4.

(4)

The effective stiffness of an isolator is calculated as follow.

(5)

The area enclosed by the force-displacement hysteretic loop is used to calculate of the isolator.

(6)

Where the dissipated energy is

And the strain energy is .

will be then (7)

The equation of total structure motion becomes then

(8)

Where , and are displacement, velocity and acceleration of superstructure. M is structure mass; K is the superstructure stiffness and C is the damping coefficient of the structure.

Fig. 4

3. Case Study

3.1 Structure characteristics

Knowing that base isolation can be effective for a not slender building height not exceeding 20 floors [31], a twelve-storey steel building modelled as 3D moment resisting-frame is analysed considering the LRB base isolation system. [32]. Profiles of the different frame elements are illustrated in figure 5.

The Geometric characteristics of building and the mechanical properties of steel are given in table 1.

The seismic isolators in the system are simulated as link components with 0.37 m in height placed between the fixed base and the columns. The link parameters defined to simulate the utilized isolators in SAP2000 software are given in table 2.

Fast nonlinear time history analysis (FNA) of Boumerdes earthquake (Algeria May 2003) of which the magnitude is 6.69 on Richter scale is performed to represent the lateral dynamic load applied to the structure. This seismic signal is recorded at the station of Kedarra (epicentre district). The time history data of the aforementioned ground motions is given in the form of text file having 7000 points of accelerations data equally spaced at 0.05 s. L’accelerogramme is illustrated in figure6.

Otherwise, figure 7 illustrates the response spectra of the time histories of the structure with ξ=5% (no isolator) compared with the design earthquake spectra from the building from the RPA99/2003 [33].The FNA analysis method also called nonlinear modal time history (NLMTH) analysis [34] is utilized for most passively damped structures because the earthquake shakes of most civil engineering structures will involve deformation in one or more structural element beyond their yield limit. Consequently, the structure will behave according to a nonlinear relationship between force and deformation. The simulations results are given blow in the following paragraphs.

Fig. 5

Table 1

Fig. 6

Fig. 7

3.2 Results and interpretation

Table 3 summarizes the comparison between resulting periods and modal participating ratio of the fixed base of (original frame), braced structure (cross-brace with L120x13 profile) and bearing isolated models. As expected, the fundamental period of vibration for the isolated structure increases due to the added isolating device. However, in the second model, the period decreases due to the increasing in structural stiffness. It has been observed that the condition of 90% of mass participation required by RPA99/2003 (Algerian seismic code, 2003), has been satisfied in the case of the isolated alternative at the mode N° 1.

Table 3

The analysis of time history response in terms of displacement and accelerations at top of the building in the three alternatives is illustrated in curves of figure 8. Figure 8a shows no significant reduction in the structural response of the frame equipped with LRB compared to unbraced design. However, it decreases quickly over time. Hence, the maximum displacements for the three configurations are close, but present all the same a relative decrease in the responses of reinforced and isolated structures. The top displacement diminution reaches 11% for the braced frame and 19% for LRB retrofitted structure. This improvement in displacements response is achieved through a decreasing of the inter-storey drifts which reduce differences between top and bottom storeys displacements such as it will be seen later in the paper. One can also observe that the acceleration response between the two cases, braced and unbraced is almost the same unlike the case with LRB which it decreases at the peak by 14% (Fig. 8b).This can lead to mitigate the undesirable effects of acceleration for occupants of these structures, but also for non-structural parts, pipes, ceilings, etc.

Fig. 8

As the examination of structural members stability must be carried out in Algerian design code (RPA99-2003) with combinations including seismic loadings; a time history analysis of the maximal axial (N), shear (V) forces and moment (M) obtained under Boumerdes earthquake has been achieved (Fig. 9a, 9b and 9c). The results illustrated a significant reducing in isolated model compared to the two others alternatives (86% for shear force and 98% for moments). This decrease is due to the low shear stiffness generated by the LRB isolators which permitted the decoupling of superstructure motions from the ground ones. However, it is also due to the increase of damping ratio for the lead-rubber bearing model. On other hand, one can note that in the braced structure (base fixed), the cross diagonals transmit a very large axial force (Fig. 9a), estimated at 13 times the ones of the damped model.

In figure 9d, the influence of LRB base isolation on the variation of base shear forces was investigated. The figure illustrates a significant decrease of the LRB damped structure’s curve compared to the two others fixed base models. The diminution reached 45% compared to the unbraced response values and 88% to the cross-braced model ones. These results may be explained by the increase of fundamental period in the isolated structure (T=11.2 sec) which implicates reducing in structural accelerations as seen above in figure 8. One may observe that base shear forces are on one hand very low but also they disappear rapidly and completely after 15 s of motions. This is due to the ability of LRB isolators to produce a passive control system by providing the required damping forces for resistance of the frame. Otherwise, those results were confirmed by the results of table 4 which summarizes the decrease rate of the maximum structural response between the fixed and isolated base models. The results show clearly the ability of the LRB dampers to dissipate efficiently the seismic loads for different types of earthquakes.

Fig. 9

Table 4

The study of the variations of relative displacement and acceleration according to the building’s height was realised for the three configurations (Fig. 10 and Fig.11). The results obtained and represented in figures 10, demonstrate that intrusion of lead-rubber dissipaters in the frame base involves an increase in relative floor displacement at the bottom half of the building. But at the top storeys, one can see a decrease compared to the unbraced structure. The differences vary in a range of +400% in the first storey to -20% at the top storey of the structure (Fig. 10). Nevertheless the LRB model displacements remain greater than those obtained by the braced model. Likewise, in figure 11, it is observed that the curve representing the variation of the floor acceleration according to building’s height is also mitigated. Thereby, the comparison of the relative acceleration between the isolated and the braced cases shows a decrease until 57%. Furthermore, differences between damped and undamped results are very low, consequently the values of acceleration between the two models remains close. On other the hand, the inter-storey drift curve according to the height of the structure was plotted for the three configurations. Results are illustrated in figure 12. One may observe that the LRB isolated structure curve presents constant values providing a vertical line plot. Hence, the dissipaters will enable the building to behave as a single one block. Finally, the peak response analysis of shear-storey force curve according to the height of building was also achieved. Results for the three cases are shown in figure 13. The variation curve of the damped structure with LRB shows a decrease in storey shear force compared to the two other systems. Note that the storey shear forces for cross-braced model became very significant at all building height.

Fig. 10

Fig. 11

Fig. 12

Fig. 13

The force-displacement curves for LRB device are presented in figure 14 in case of real and 6 times Boumerdes ground accelerations, respectively. One can see that the bilinear behaviour assumption made in the design stage according to the UBC97 [35] is appropriate. The hysteresis loop resembles to the concept illustrated in the scheme of figure 4. Hence, it may be considered that these results justify the overall proof of the analysis concept presented in this work. As expected and shown above in Eq. (4) and (5), the restoring force induced by the isolator generates a nonlinear behaviour as it is illustrated in the curves of figures 14a and 14b. The plots represent variation of shear force versus displacement. Although, a multiplied seismic record (600%) has been considered, base displacements had increased only by 50%. The plots thus highlight the bilinear behaviour of the LRB device, of which the hysteresis loop provides an added damping ratio. Consequently, lateral flexibility allows to the isolated system greater capacity to dissipate the dynamic loading energies. The results demonstrate the validity of the analytical model versus to those in the literature review [36]. However, and as seen above, the response of base-isolated structure can significantly be influenced by the shape of hysteresis loop of dissipater [28].

Fig. 14

To conclude this study and in order to identify plastic behaviour of frame elements, nonlinear dynamic analyses were applied to the structure considering hinges elements for columns and beams.

To perform the nonlinear dynamic analysis (NLDA), the following assumptions were adopted:

• Possible plastic hinges usually form at the ends of beams and columns under earthquake actions.

• The nonlinear behaviour of the superstructure was modelled using bi-linear moment hinges without a load drop.

• For beam elements, plastic hinges are caused by uni-axial (strong-axis) bending moments.

• For column elements, plastic hinges are caused by axial loads and bi-axial bending moments (strong and weak-axis).

The material model used in the nonlinear analysis is based on the provisions of FEMA-356 [30] document defining force (moment)–displacement (rotation) criteria for the plastic hinges used in the nonlinear dynamic analysis. Figure 15 presents the typical force (moment)–displacement (rotation) relation proposed by those documents. The points A, B, C, D and E define the force–displacement relation of the hinge while the points IO, LS and CP define the performance acceptance criteria for the hinge (points IO, LS and CP stand for Immediate Occupancy, Life Safety and Collapse Prevention, respectively). The values assigned to each of these points vary depending on the type of member as well as many other parameters defined in the FEMA-356 documents. The distributions of plastic hinges in structures and their damage levels for different configurations are studied for the case of an important seismic intensity.

Fig. 15

The analysis is achieved considering a significant displacement at the top of structure. It was obtained for Boumerdes earthquake signal multiplied by 6 times. The results are shown in figure 16. One can observe the appearance of several plastic hinges in the unbraced model (Fig. 16a), some of them reach a damage levels causing a totally collapse (point E). The plastic hinges causing the collapse of columns occurs from the 5th storey and were spread until the top of the frame. At this location, the inter-storey drifts became very large as shown above in figure 12. However, in the retrofitted model by lead rubber bearing (Fig. 16b), only hinges of level B are appeared at few locations principally at the middle of frame, where we observed a collapse in the unbraced model. Consequently, there is no damage observed in the frame elements of the based isolated structure. Hence, the LRB base isolation device permitted an improvement of structural performance of building, which involves a significant effectiveness in terms of protecting the structural integrity and contributes to minimize the panic effects. These results are in good agreements with those presented in the literature [37]

Fig. 16

4. Conclusions

This work allowed studying the difference in steel structure behaviour, with and without lead rubber bearing for a seismic load. Numerical simulations with SAP2000 software was performed for the analysis of a 12-storey frame. The results show that the use of the passive control with LRB device in buildings generates a very significant diminution in the structural response compared to the unbraced ones. However, in the case of a 12-storey building, main conclusions are summarized below:

1. The fundamental period increased by 50% compared to the unbraced structure.

2. The maximum displacement decreases by 20% compared to the unbraced structure.

3. Reduction in the maximum acceleration is 14%, which reduces base shear values and its time loading.

4. The time history analysis of the most loaded member response showed a reduction by 86% in shear force (V) and 99% in bending moment (M). With the damping energy dissipation, any undesirable axial forces are transmitted to column members.

5. The relative storey displacements increase in bottom half of the building, but present a decrease in the top storeys compared to the unbraced model.

7. The floor accelerations presented no variations between different storeys which homogenize the behaviour of the global structure.

8. The inter-storey drifts became negligible, which generates block’s behaviour of the structure and reduces the effects of shear forces.

9. The use of LRB system limited the nonlinear behaviour of structural members, which generated an improvement of the structure safety against major seismic hazards.

The benefits of LRB isolators were clearly verified by the comparisons data. It can on one hand, improve substantially the structural response against moderate earthquakes without use of excessive strengthening, but also decrease the seismic hazards of major earthquakes. These systems are in general not expensive and effective supply for buildings subjected to dynamic motions.

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