The effect of LRB stiffness changes with and without supplemental viscous dampers on seismic respons

Abstract

Keywords: Base Isolation System; Earthquake; Energy Dissipation Systems; Lead Rubber Bearings; Linear Time-History Analysis; Seismic Performance of a MDOF Building; Viscous Dampers

Introduction

Türkiye is an earthquake-prone country, and there have been multiple moderate-to-large earthquakes in the last 20 years. Most of the building stock has been exposed to severe seismic forces and a great amount of seismic energy in recent earthquakes, such as 1999 Kocaeli, 2011 Van, 2020 Izmir and 2023 Kahramanmaraş earthquakes [1-3]. It follows that they will either collapse or suffer damage if this energy surpasses the lateral bearing capacity due to their inadequacy to operate in a safe manner, particularly in relation to the functional performance criteria. During the last several decades, many scientists have examined creative and attractive protection mechanisms of structure to improve the energy dissipation ability or to reduce structural seismic damages [4-6]. The innovative method for controlling structural vibration during earthquake ground motion can be divided into three systems: base isolation system (BIS), active control system (ACS), and passive energy dissipation system (PEDS) [7-10]. In consequence of this, the construction will eventually weigh less and be built at lower expenses. It is important to reduce the damage that may occur following an earthquake, which imposes many injuries, casualties, and significant structural damage. Therefore, retrofitting insufficient structural elements (e.g., beam, column, etc.) of old buildings is necessary in structural engineering. During and immediately after an earthquake, some buildings, such as hospitals and important state houses, must keep functioning and be in full operation. This can only be achieved by using the energy dissipation systems (EDSs) [11]. EDSs may be classified such as active, passive, semi-active, and hybrid (consists of both active and passive) mechanisms. Both the dampers and the BIS are considered passive devices, and are widely used by structural designers because (i) they do not need external energy, (ii) there is no need for maintenance throughout functioning, (iii) they have a cost-benefit in the long term and (iv) they are easy to apply [12, 13].

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Base Isolation BI technology is a remarkable method applied worldwide for multi-storey buildings. However, they may have some limitations on applications due to significant technical and economic issues. The implementing BI technology becomes simple and inexpensive for newly constructed structures, but it requires excavation and temporary support work for those that already exist [14]. It has become increasingly popular for seismic retrofitting existing buildings for the past two decades due to reducing the seismic effects on the structure [15, 16]. The concept of BI depends on disconnecting the building from the ground and connecting the BI to the building itself and it is widely used to decrease inter-story drifts, story accelerations and story displacements [17]. Two types of BI technology are typically used in the literature, i.e., sliding mechanisms and elastomeric bearings. The elastomer bearings are developed to mitigate lateral seismic effects by offering a layer with less lateral stiffness. The sliding systems aim to mitigate seismic loads by permitting frictional slide and reducing the quantity of shear transfer [18, 19]. In most cases, structural engineers adopt three different kinds of elastomer bearings for the building: (i) lead rubber bearings (LRBs), (ii) natural rubber bearings and (iii) high-damping rubber bearings [20, 21]. Lead Rubber Bearings (LRBS) The LRB isolation system was used in this research, and the LRB’s hysteretic behavior and typical configuration were given in Figure 1. This system is made up of many rubber layers as well. Steel lead core inserted in the center of the rubber as illustrated in Figure 1a. The LRB hysteresis loop is represented as a bilinear curve, where keff is the effective stiffness, ku and kd are the initial elastic and the post-yield stiffnesses of the bearing, respectively. Fy and du are the yield strength and yield deformation of the bearing, respectively. Fmax and di are the maximum force and displacement of the bearing, respectively, as depicted in Figure 1b.

Figure 1. The view of structural details and the mechanics of the LRB.

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The LRBs are essential elements in elastomer-based isolation technologies. In such bearings, the rubber allows lateral flexibility to have a longer service life cycle, while the lead core inside the rubber releases energy during the cyclic movement of the seismic motion [22]. One of the main characteristics of LRB is that it has a high vertical stiffness so it can carry a substantial vertical load and can move laterally with relatively lower horizontal stiffness [23, 24]. The LRB can alter a building’s natural period due to its high flexibility, preventing resonance in the structure exposed to seismic vibrations. Also, the LRB can support the structural system vertically, allowing a lateral displacement and boosting the system’s damping to the appropriate value [24]. There are several studies about the behavior of LRB-isolated buildings under the seismic movements [25-27]. For instance, Ren et al. [28] used computational and empirical approaches to study the LRB’s compressive force with different shape variables. Sesli et al. [29] compared the impacts on a seismically isolated and fixed base building of far, near, and pulse-type ground motions. Bhandari et al. [30] examined the RC building’s seismic performance, which is separated with LRB, using the capacity spectrum methodology and concluded that this method was accurate in predicting the maximum values of the BI frames as much as 0.2g. Chanda and Debbarma [31] developed fragility curves to assess the dynamic behavior of LRB-isolated multi-story RC frames under far-field and near-field seismic waves. Mousazadeh, et al. [32] studied an optimization approach to decrease the LRB’s lifetime cost. Ye et al. [33] suggested a seismic design based on displacements for analyzing multi-story LRB-building systems using response spectrum approaches and they obtained that seismic responses were within 10% of the specified values. Santhosh et al. [26] and Haque et al. [25] confront the effects of the LRB with the fixed base building under seismic forces they obtained that the LRB base-isolated building was reduced the top story horizontal displacement and acceleration, and both the base shear and the floor’s drift were lower for LRB base-isolated building. Choun et al. [34] studied the impact of alterations to the LRB’s mechanical characteristics on seismic behavior and concluded that mechanical property changes in the isolator had a substantial impact on the isolator’s shear strain

and the superstructure’s acceleration response. Kanbir et al. [35] compared multi-story frames with LRB base-isolated building exposed to NF seismic waves. The majority of LRB researches (i.e., Bhandari et al. [30], Chanda and Debbarma [31], Mousazadeh et al. [32], Wang et al. [36]) has focused on the effectiveness of the BI methodology to decrease structural seismic effects in the event of a dynamic force. Thus, BI system can lead to excessive displacements and undesirable conditions due to the inherent behaviour of the isolation material for buildings placed in adjacent or narrow locations [37]. However, it is becoming increasingly common in engineering applications to use supplemental damping devices (e.g., fluid viscous dampers (FVDs)) and LRB systems together to overcome those worst scenarios and control the structural seismic responses [38]. Viscous Dampers Viscous dampers (VDs) are one of the PED devices, and they can be applied to the new or existing structure to control the building’s seismic response. The widespread acknowledgment of viscous dampers in the literature is attributed to their capacity for operating out of phase with structural forces and their non-interference with the stiffness of a building system. They are made of highly resistant materials, and the silicone-based fluid that circulates between the piston and cylinder arrangement absorbs or dissipates energy that is imparted by the piston [39]. In this study, VDs were used to dissipate energy. Mechanical details and force-displacement relationship of VD are given in Figure 2 [40]. Politopoulos [41] revealed that viscous dampers efficiently reduce the isolator displacement and the floor acceleration close to the first mode. Higher modes, on the other hand, have a substantially greater impact on floor acceleration. Boksmati et al. [42] investigated the effect of soil conditions on the energy dissipation of bare frame and BI frame system having viscous dampers exposed to seismic loading and it was obtained that the BI frame was less influenced by the type of soil. Chang et al. [43] conducted shake table tests and developed an analytical model to analyse threestory steel buildings that had been modified with viscous dampers. In the case of El Centro earthquake striking the

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building, where viscous dampers were applied, it resulted in 68% and 30% reduction in the story displacement and shear force, respectively. Hwang et al. [44] proposed an equation, including the combined effects by considering the phase angle between the LRB and viscous damper, and the displacement of the isolation system. Ganji and Kazem [45] compared seismic behaviors of buildings with 5, 10 and 15 stories equipped with LRB or viscous dampers under the NF seismic movements. Viscous dampers with proper damping coefficient selection significantly improve the dynamic response of structures [46-50]. Domenico and Ricciardi [51] provided a dynamic configuration that consisted of the BI system and with a tuned-mass-damper situated in the building’s basement. Yaktine et al. [52] examined the combined responses of LRB or viscous dampers having irregular plan RC buildings with 3-story, 8-story, and 20-story. Hatipoglu and Duzgun [53] investigated the dynamic response of adjacent buildings with different VD distribution along building height considering soil-structure interaction. Thakur and Tiwary [54] investigated the seismic responses combined with LRB and viscous dampers. They concluded that the combined system significantly improved the behavior of the structure. An existing MDOF building (at Keio University in Japan) with different LRBs stiffnesses, and the same building with and without viscous dampers installed in the basement level were investigated in this study. For this purpose, three different stiffness ratios (i.e., the sum of the stiffnesses of the first-floor columns (k1) to the sum of the stiffnesses of LRB (kb); k1/kb=20, 40 and 80) were chosen to assess the effect of LRBs’ stiffness on the seismic response of the building. The ratio k1/kb=20 is obtained by dividing B1F by B2F

in Table 4. The remaining two ratios (k1/kb=40 and 80) are assumed, considering the potential reduction in stiffness of LRB during the lifespan of the building being studied. In addition, to investigate the effects of supplemental VD on the seismic response of the building, six different damping coefficients were adopted. One of the damping coefficients used by Dan and Kohiyama [55] is employed as a base to derive various coefficients by scaling them with different factors. The building model was developed in MATLAB language [56] and verified with experimental results of Kohiyama et al. [57].

Numerical Study

Details of the Sosokan Building Today, the base-isolation systems with low stiffness are available in many Japanese buildings. The Sosokan building, which has elliptical tower at the main gate to the campus, was also constructed in 2000 at Keio University, Japan, as illustrated in Figure 3a [57, 58]. During the 2011 Great East Japan earthquake, the building acted as a passive base isolation system as the semi-active system was out of service for maintenance work. It was observed following the earthquake that only slight damage was detected in the RC building adjacent to the Sosokan and additionally the building response in Sosokan was effectively mitigated by its base isolation system [55]. In the building with EDS, a total of 32 passive viscous dampers installed base layer of the building. Structural member details of the building were given in Table 1, while the LRB details were given in Table 2 [57]. Figure 3b depicted the isolation layer plan of the building, and in the isolation layer 65 laminated rubber bearings were used. 16

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Figure 3. a) The Sosokan building in Japan, b) Isolation layer plan, c) The viscous damper installed in the building’s isolation layer, and d) The cross-section of LRB. passive viscous dampers installed in both the EW and NS directions were utilized. The passive viscous dampers in the EW direction were shown in red rectangles, while the LRB devices were shown in blue rectangle. The passive viscous dampers and LRB illustrations, which were placed in the building’s base layer, were shown in Figure 3c-d. This building had seven floors and two basement floors for a total of nine floors The section detail of the building center line in the short axis direction was shown in Figure 4 [57]. The building structure was made of a combination of steel, steel-reinforced concrete, and concrete-filled steel tubes. For more detailed information about the building

isolated system equipped with dampers, see the work of Kohiyama et al. [57]. Mathematical Model of the Sosokan Building and Formulation In the study, a two-dimensional model of the building, which consists of one-basement floors, seven normal floors, and a roof floor (B1F + 7F + RF), is used in the dynamic analysis. B2F, B1F,1F and RF represent the 2nd basement floor, 1st basement floor, 1st floor, and roof floor, respectively. The considered building model is shown in Figure 5. The isolation layer, which is installed in B2F, is consists of

65. LRBs and 16 passive viscous dampers in EW direction.

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Figure 4. The section detail of the building center line in the short axis direction.

Figure 5. Two-dimensional model of the Sosokan building drawn by using Figure 4.

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Figure 6. Maxwell model of the VD In Figure 5, kci (i = 1,2,…,7) is the total stiffness of the ith column in the frame depth, while kbi (i = 1,2,…,7) is the total stiffness of the ith LRB in the frame depth In the study, Maxwell type viscous damper modelling is used as recommended Kohiyama et al. [57], and its mathematical model is given in Figure 6. • In the study, to investigate the building having only a BI (Base Isolation) system with different LRB stiffnesses (for the case shown in Figure 5a), three different stiffness ratios (k1/kb) were chosen, and these ratios were 20, 40, and 80. k1 is the total stiffness of all 1st basement floor columns (B1F). kb is the total stiffness of all LRBs on the 2nd basement floor (B2F). Note that there is no change in the total stiffness of columns on the 1st basement floor (B1F); instead, only the total stiffness of LRBs on the 2nd basement floor (B2F) is changed by a ratio. • The building, which had both a BI system (i.e., the stiffness ratio of k1/kb = 80 is taken) and viscous dampers, which had six different damping coefficients (shown in Table 3) at B2F level, was also investigated (for the case shown in Figure 5b). The equation of motion of the system is formulated as follows (as given in Kohiyama et al. [57]) (1) where M, C, and K are the mass, damping, and stiffness . .. matrices of the structure, respectively. x, x and x are the displacement, velocity, and acceleration vectors of the .. structure. u and z are the damping force of viscous dampers in isolation layer and ground acceleration, respectively. The E is a vector matrix, which indicates the location where the damping forces apply. The vector F shows the mass matrix for seismic force calculation. The matrices and vectors in Eq. 1 are rearranged as follows: (2)

(5) (6) (7) where mi, ci, ki are the mass, damping and spring stiffness parameters of each floor, respectively, for i = 1, 2, 3, …,10 while xi is horizontal displacement of each floor relative to ground motion. The structural parameters of mi, ci, ki were given in Table 4 [55]. These parameters are also used for the verification of the Sosokan building model in MATLAB language.

Table 3. The passive damping coefficients used in this study Abbreviation

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. From Eq. 1, velocity vector of the structure (x t) is defined as below (8) where, (9) The Maxwell-type viscous damper model for the building system, the velocity equation is defined as follow (10) where refers to the control force of passive viscous damper. From Eq. 10, (11) where cd, kd and xd denote damping coefficient, stiffness and displacement of the passive viscous damper, respectively. Bu is stated as matrix form as below (12) To model and simulate the building in MATLAB-R [56], the “ss” command, which creates a state-space model with given properties, and the “lsim” command, which plots the simulated time response of the model, are employed. In the

study, in the base isolated model (i.e., nine-story building with isolation layer), the matrix size of the mass (M), damping (C), and stiffness (K) in Eq. 9 is a twenty-by- twenty (20x20). The BI system equipped with viscous damper (BI&VD1) refers to base isolation with installed viscous damper coefficient Cd = 1.4x106 Ns/m in the isolation layer (i.e., ninestory building with both having BI and installed VDs at the same level). Eq. 10, which includes the Maxwell-type viscous damper model, is used for the model. The model has a twenty-one-by-twenty-one (21x21) matrix size in mass (M), damping (C), and stiffness (K). Total passive viscous damper stiffness kd is calculated and Kohiyama [55] as 47.0381x107 N/m. The Verification of the Building Model It is necessary to verify the code written in MATLAB before executing building simulation. Based on the above given structural details and equations, the mathematical model of the Sosokan building (having 65 LRB and 16 supplemental VDs) was written in MATLAB. The building model was subjected to the Tohoku earthquake (as given in Table 5 and Figure 7) [59]. The building model was verified by plotting acceleration time history results obtained from this study and the results given by Kohiyama et al. [57] and Dan and Kohiyama [55]. The acceleration time history of 7th floor (7F) is obtained by using Eq. 10 and the data in Table 4 and Table 5, and these results were given in Figure 8 for comparison. Figure 8a shows the results from this study, while Figure 8b shows the results of Kohiyama et al. [57]. In the results of Kohiyama et al. [57], the time-history responses of the model with

Figure 7. The time history record of 2011 Tohoku earthquake.

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Fig. 8 (a) The results of this study of the BI&VDs model, (b) The results of Sosokan building of the BI&VDs model Kohiyama et al. [57] (“updated”). “updated” structural parameters based on system parameters identification were illustrated with blue colour line. It is apparent that the results obtained from both studies are the same.

Results And Discussion

Base Isolation (BI) Model The building model with three different LRB stiffnesses (k1/kb) was simulated under the Tohoku earthquake to discuss the effect of LRBs’ stiffness on the seismic performance of the building. The results were obtained for the case where the sum of the stiffnesses of the first-floor columns (k1) and the sum of the stiffnesses of the base isolation (kb) were 20, 40, and 80. It was obtained that various LRB stiffnesses brought about different isolation layer displacements in the building, as illustrated in Figure 9. For the case the stiffness ratio (k1/kb) equals 20, the maximum displacement in the isolation layer was obtained as 45.2 cm, which was the smallest displacement among the cases considered in this study. The largest drift in the isolation layer (B2F), which is 93.4cm, was obtained at the stiffness ratio

(k1/kb) of 80 (i.e., when the total stiffness of the LRB was the smallest). Also, for the case the stiffness ratio (k1/kb) equals 40, the displacement of the isolation layer was 56.2cm. As can be seen in Figure 9, the larger the stiffness ratio (k1/ kb), the smaller the drift occurred at the above levels (from B1F to RF). The obtained results were reasonable because the small LRB stiffness in the isolation layer (B2F) resulted in large base displacement and allowed the above floors to move together without causing large inter-story drifts. Figure 10 depicted the 7th floor (7F) time-history acceleration of the building. The maximum acceleration for the considered cases were also shown in Figure 10. The bigger the ratio (k1/kb) was, the smaller the maximum acceleration observed. To put it differently, the maximum acceleration at the above floors was lessened as the stiffness of the LRB was reduced. It was reasonable to say that the smaller drift the above levels (B1F, 1F, 2F, etc.) had, the smaller maximum acceleration the building experienced. The Base Isolated Building Equipped with Viscous Dampers (BI&VDS) The building model with a stiffness ratio (k1/kb) of 80 was equipped with sixteen passive viscous dampers

Figure 9. The maximum inter-story drifts for different LRB stiffnesses under the Tohoku earthquake.

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1.0 0.5 0.0 -0.5 -1.0 k 1 / k b=80 k 1 / k b=40 k 1 / k b=20

Figure 10. The time history acceleration of 7th floor (7F) for different LRB stiffnesses under the Tohoku earthquake installed in the E-W direction in the base isolation layer (B2F). The seismic responses of the building for the case of base isolation (BI) and for the base isolation equipped with viscous dampers (BI&VDs) are given in Figure 11. The largest displacements occurred on the 2nd basement floor (B2F) in all cases. In addition, the BI system (no viscous damper) had the largest displacement (93.4 cm) among the seven model simulations. By VD instalments, a significant decrease in inter-storey drifts was observed at B2F level, where the isolation layer is located. For the case of high damping coefficient assignments, the inter-storey drifts in the 2nd basement (B2F) are reduced, yet once the damping coefficient was significantly increased (e.g., VD5 and VD6), the inter-story drift at above levels (from B1F to RF) are also increased. This showed that a proper damping coefficient assignment was needed for multi objective optimization (i.e., reducing both drift and acceleration). Figure 12 illustrated the 7th floor time-history acceleration of BI (no VDs) and BI&VDs models with a stiffness ratio of 80 for different damping coefficients of viscous dampers (from VD1 to VD6), and the values of maximum acceleration for the considered cases were also shown in

Fig. 12. Once the dynamic response of the BI&VDs (from VD1 to VD6) model was compared with the BI model, it was observed that the maximum acceleration of the building was generally reduced when viscous dampers were added to the BI building model. However, the damping coefficient of VD6 increased the maximum acceleration at above level (e.g., 7F). A similar discussion was done for Fig.

11. This showed that large damping coefficient assignment

(e.g., VD6) could increase the maximum acceleration of the building even though it reduced the drift. To assess the response of the BI&VDs model, the viscous damper’s hysteresis loop is depicted in Fig. 13. Regarding that, the force-drift loops were given for different damping coefficients. The total damper force represents the total force of the 16 viscous dampers in the building. The damper force slightly increased as the damping coefficient increased from the cases of VD1 to VD4 (except VD5 and VD6). However, a large amount of damper force was required for the cases of VD5 and VD6 compared with the other four VDs. The total damper energy dissipated by 16 viscous dampers in the building versus time was shown in Figure

Figure 11. The inter-story drift results for the BI (no viscous damper) and BI&VDs models with a stiffness ratio (k1/kb) of 80 for different damping coefficients-under the Tohoku earthquake.

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Figure 12. The maximum time history acceleration of 7th floor for the BI and BI&VDs models with a stiffness ratio of 80 for different damping coefficients-under the Tohoku earthquake.

14. The largest damper energy was observed in the case of

VD1, while the smallest damper energy was obtained in the case of VD6. It was obtained that as the damping coefficient increased (from VD1 to VD6), the maximum energy dissipation dropped. The seismic responses of the building in the case of the BI (no VDs) and the BI model equipped with 16 viscous dampers (BI&VDs) were summarized in Table 6. As compared to the BI system, the maximum displacement at the

B2F level in the use of viscous dampers reduced by up to 96%, while the maximum acceleration of 7th floor reduced by up to 71%. However, even though BI&VD6 model reduced the maximum displacement of the 2nd basement floor by 96%, it increased the maximum acceleration of the floor by 8.7%. It appears that a large VD coefficient at the base isolation layer (B2F) does not reduce acceleration. The effects of LRB stiffness were examined by employing linear time-history analysis, both with and without

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Figure 13. Hysteresis loop of the total damper force for six different damping coefficients-under the Tohoku earthquake.

Figure 14. The dissipated energy by 16 VDs versus time for six different damping coefficients-under the Tohoku earthquake.

Table 6. Main results of different models subjected to the Tohoku earthquake (Δ=reduction) Building model

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viscous dampers on the displacement of the isolation layer, inter-story drift, and acceleration of the building.

Conclusion

The present study represents an analytical investigation of a benchmark Japanese 9-story Sosokan building. The building originally had a base isolation system consisting of 65 LRBs and 16 passive viscous dampers in the EW direction. The building was modeled using the MATLAB language, and the building model was verified by generating the experimental results of Kohiyama, et al. [52]. To assess the effects of LRBs’ stiffness on the seismic performance of the building, three different stiffness ratios were chosen, and to obtain those, the 2011 Tohoku earthquake was used for each model. It was examined the effect of lead rubber bearings’s (LRBs) stiffness both with and without supplemental viscous dampers (VDs) on the seismic reactions of buildings. Also, the variation of the seismic response was investigated in case of the building has both a base isolation (BI) system and viscous dampers (BI&VDs) with different damping coefficients. To evaluate the effect of different LRB stiffnesses and viscous damper coefficients on the seismic response of the building, each building model was subjected to the Tohoku earthquake. Based on the results of the analyses, the following conclusions can be drawn: • Among the three (k1/kb) ratios (20, 40 and 80), the value of 80 experienced the largest displacement at 2nd basement floor, however it resulted in the smallest drift and acceleration at the above levels (from 1st basement floor to roof floor) compared with the ratios of 20 and 40. These findings confirmed that large stiffness ratio (k1/kb), i.e. the small LRB stiffnesses, is directly associated with large displacement at the base isolation level, and small acceleration and inter-story drift at the above levels. • The displacements and accelerations at 2nd basement floor and above levels significantly reduce in the LRB base isolated system equipped with viscous dampers (BI&VDs) as compared to BI (no VDs) model. Although a higher damping coefficient of viscous damper (e.g., VD6) reduces the maximum displacement at 2nd basement floor level, it increases the acceleration of the building and reduces its energy dissipation capacity. Therefore, an obvious finding emerging from this study is that to achieve multi-objective optimization (i.e., reduction of both displacement and acceleration at the same time) for the building’s seismic response, a proper damping coefficient (Cd) is needed. • It is obtained that the maximum displacement at the 2nd basement floor in the use of viscous dampers reduces by up to 96%, while the maximum acceleration of top floor reduces by up to 71%. Also, it appears that the using a large VD coefficient at the base isolation layer (2nd basement floor) does not reduce acceleration. • The study’s findings indicate that blindly adding damping coefficients could lead to increased structural

displacements in the upper levels (above isolation stories) and, consequently, increase the system’s acceleration. This could result in unnecessary costs and potential damage to acceleration-sensitive equipment in the building. Future Study Further research should focus on determining an optimal damping coefficient at a building’s base isolation level for the sake of multi-objective optimization of building seismic performance. It would be beneficial to expand the study to include low-, medium-, and high-rise buildings.

Acknowledgements

The first author, Adnan, expresses profound gratitude to Professor Masayuki Kohiyama for providing supplementary numerical data pertinent to this study following the first author’s visit to Keio University in Japan in 2019.

Data Availability Statement

The authors confirm that the data that supports the findings of this study are available within the article. Raw data that support the finding of this study are available from the corresponding author, upon reasonable request.

Conflict Of Interest

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

There are no ethical issues with the publication of this manuscript.

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