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Innovative baseisolated building with large massratio TMD at basement for greater earthquake resilience
Future Cities and Environment volumeÂ 1, ArticleÂ number:Â 9 (2015)
Abstract
Tuned mass dampers (TMD) have been used for the reduction of building responses to wind loading in many highrise buildings. An innovative and resilient baseisolated building with a large massratio TMD is introduced here primarily for earthquake loading in which the large massratio TMD is located at basement. This new hybrid system of baseisolation and structural control possesses advantageous features compared to existing comparable systems with a TMD at the baseisolation story. The TMD stroke can be reduced to a small level with the use of an inertial mass damper and its reaction can be limited to a lower level by detaching its connection to ground. The proposed hybrid system has another advantage that the TMD mass does not bring large gravitational effect on the building itself. It is demonstrated that the proposed hybrid system is robust both for pulsetype ground motions and longperiod, longduration ground motions which are regarded as representative influential ground motions.
Introduction
There is an increasing need and interest of construction of highrise buildings in urban areas. This trend will be accelerated in the future. Highrise buildings and super highrise buildings are required to resist for various external loadings, e.g. wind and earthquake loadings. Enhancement of resilience of such highrise and super highrise buildings after intensive wind and earthquake loadings is a major concern from the viewpoint of the business continuity plan (BCP) which is the most controversial issue in the sound development of society (Takewaki et al. 2011, 2012b).
Tuned mass dampers (TMD) are useful for the reduction of building responses to wind loading and are installed in many highrise buildings all over the world (Soong and Dargush 1997). However it is well known that TMD is not effective for earthquake responses because of its limitation on stroke and realization of large massratio TMD.
Nevertheless, some attempts have been made on the introduction of large massratio TMD mainly for earthquake loading (Chowdhury et al. 1987; Feng and Mita 1995; Villaverde 2000; Arfiadi 2000; Zhang and Iwan 2002; Villaverde et al. 2005; Mukai et al. 2005; Tiang et al. 2008; Matta and De Stefano 2009; Petti et al. 2010; Angelis et al. 2012; Nishii et al. 2013; Xiang and Nishitani 2014). Actually several projects are being planned in Japan, e.g. installation of largemass pendulum system at roof and usage of upper stories as TMD masses.
Recently large massratio TMDs are investigated for baseisolated buildings (Villaverde 2000; Villaverde et al. 2005; Angelis et al. 2012; Nishii et al. 2013; Xiang and Nishitani 2014). While usual highrise buildings exhibit large displacement around the top story, baseisolated buildings show relatively large displacement around the baseisolation story near ground surface. This property is very advantageous from the view point of mitigation of effect of excessive vertical load due to large massratio TMD (Kareem 1997; Zhang and Iwan 2002; Mukai et al. 2005; Petti et al. 2010; Nishii et al. 2013; Xiang and Nishitani 2014).
However there still exist several issues to be resolved, e.g. avoidance of excessive vertical load by large massratio TMD, reduction of TMD stroke, reduction of TMD support reactions.
The purpose of this paper is to propose an innovative system of baseisolated buildings with a large massratio TMD at basement. The most serious issue of effect of excessive vertical load due to large massratio TMD on the main building is avoided by introducing the large massratio TMD at basement which is made possible due to the large displacement of a floor in the baseisolation story near basement. Another issue of large stroke of TMD even in the large massratio TMD is overcome by introducing inertial mass dampers in parallel to the springdashpot system in the TMD system.
Baseisolated building with largemass ratio TMD at basement
FigureÂ 1(a) shows a conventional system with small massratio TMD on the roof which is effective only for wind loading. On the other hand, Fig.Â 1(b) presents a highrise building with large massratio TMD on the roof which is believed to be effective for longperiod ground motion and to cause significant vertical load on the building. Consider next a baseisolated building system, as shown in Fig.Â 1(c), with large massratio TMD on the roof which lengthens the fundamental natural period of the highrise building and also causes large vertical load on the building. The models in Fig.Â 1(b) and (c) are thought to be unrealistic because of their excessive vertical load. FigureÂ 2(a) indicates the proposed baseisolated building system with large massratio TMD at basement using sliders and rails. This model shown in Fig.Â 2(a) is called the Proposed1 model. In Fig.Â 2(a) the large massratio TMD is located on the sliders and rails and in Fig.Â 2(b) the large massratio TMD is set on the floor just above the baseisolation system.
Baseisolated building without TMD
Consider a baseisolated building without TMD. This model is called a BI model (see Ariga et al. 2006). Let k _{ I }, c _{ I }, m _{ I } denote the stiffness, damping coefficient and mass of the baseisolation story in the BI model. Furthermore let k _{1}, c _{1}, m _{1} denote the stiffness, damping coefficient and mass of the superstructure. The displacements of masses m _{1} and m _{ I } relative ground are denoted by u _{1} and u _{ I }, respectively. This model is subjected to the base ground acceleration Ã¼ _{ g }. The equations of motion for this model can be expressed by
Conventional baseisolated building with largemass ratio TMD
Recently some systems of a baseisolated building with largemass ratio TMD have been proposed. Mukai et al. (2005) proposed a newtype active response control system to improve the effectiveness of baseisolated buildings. In this system, the TMD mass is connected both to a superstructure and the basement (ground). A negative stiffness mechanism is used to amplify the response of the TMD mass which enables the avoidance of introduction of large massratio TMD. Nishii et al. (2013) revised the system due to Mukai et al. (2005) by replacing the active damper with negative stiffness with a passive inertial mass damper system. This model is called the Imass TMD model in this paper. Although their system is demonstrated to be effective for the reduction of superstructure response, the performance check on the reaction of the TMD system is not conducted. Xiang and Nishitani (2014) presented a system for a baseisolated building with a TMD mass which is located on the baseisolation story level and connected directly to the ground. This model is called the NewTMD model in this paper. They demonstrated that their system is effective for a broad range of excitation frequency and proposed an optimization method for determining the system parameters.
Consider an Imass TMD model and a NewTMD model as shown in Fig.Â 3. Let k _{2}, c _{2}, m _{2} denote the stiffness, damping coefficient and mass of the TMD system. z _{2} indicates the inertial mass capacity of the inertial mass damper installed between TMD mass and ground in the Imass TMD model.
For later comparison, the Imass TMD model and the NewTMD model are explained in the following. The equations of motion for Imass TMD model may be expressed by
On the other hand, the equations of motion for NewTMD model may be presented by
Baseisolated building with largemass ratio TMD at basement using inertial mass damper for stroke reduction
The equations of motion for a baseisolated building with largemass ratio TMD at basement may be expressed by
A baseisolated building, as shown in Fig.Â 2(c), with largemass ratio TMD at basement using an inertial mass damper for stroke reduction is called the Proposed2 model. A mechanism example of inertial mass dampers is shown in Fig.Â 2(d) (Takewaki et al. 2012a). The equations of motion for this model may be expressed by
The model parameters of BI Model, Proposed1 Model and Proposed2 Model as shown in Fig.Â 3 are specified as follows. The same model parameters are used for Imass TMD Model and NewTMD Model. The influence of the rail friction on the response of the proposed models will be discussed in SectionÂ â€˜Influence of rail friction on response of proposed systemâ€™.
The superstructure is a 20story or 50story reinforced concrete building and is modeled into a singledegreeoffreedom (SDOF) model. This modeling into an SDOF model is thought to be appropriate in a baseisolated building. The equal story height of the original building is 3.5Â m. The building has a plan of 40â€‰Ã—â€‰40Â m and the floor mass is obtained from 1.0â€‰Ã—â€‰10^{3} kg/m^{2}. The floor mass in each floor is 1.6â€‰Ã—â€‰10^{6} kg. The fundamental natural period of the superstructure with fixed base is T _{1}â€‰=â€‰1.4 s for a 20story building and T _{1}â€‰=â€‰3.5 s for a 50story building. The structural damping ratio is assumed to be h _{1}â€‰=â€‰0.02. The stiffness and damping coefficient of the SDOF model are computed by \( {k}_1={m}_1{\omega}_1^2 \), c _{1}â€‰=â€‰2h _{1} k _{1}/Ï‰ _{1} with the fundamental natural circular frequency Ï‰ _{1}â€‰=â€‰2Ï€/T _{1}.
The mass of the baseisolation story is 4.8â€‰Ã—â€‰10^{6} kg. The fundamental natural period of the BI model with rigid superstructure is T _{ I }â€‰=â€‰5.0 s for the 20story model and T _{ I }â€‰=â€‰6.0 s for the 50story model. The damping ratio of the BI model with rigid superstructure is h _{ I }â€‰=â€‰0.1. The stiffness and damping coefficient of the SDOF model are computed by \( {k}_I=\left({m}_I+{m}_1\right){\omega}_I^2 \), c _{ I }â€‰=â€‰2h _{ I } k _{ I }/Ï‰ _{ I } with the fundamental natural circular frequency Ï‰ _{ I }â€‰=â€‰2Ï€/T _{ I }. As for TMD, the mass ratio m _{2}/m _{1} is set to Î¼â€‰= 0.1 and the inertial mass damper ratio z _{2}/m _{1} is set to Î· _{ s }â€‰=â€‰0.06. The damping ratio is assumed to be h _{2}â€‰=â€‰0.3. The stiffness and damping coefficient of TMD are given by \( {k}_2=\left({m}_2+{z}_2\right){\omega}_2^2 \), c _{2}â€‰=â€‰2h _{2} k _{2}/Ï‰ _{2} in terms of the natural circular frequency Ï‰ _{2} of TMD . The process of determining Ï‰ _{2} is explained in SectionÂ â€˜Determination of stiffness and damping coefficient of TMDâ€™.
Determination of stiffness and damping coefficient of TMD
In this section, the procedure of determination of stiffness and damping coefficient of TMD for the proposed model, Imass TMD model and NewTMD model is explained. The tuning of TMD is performed by minimizing the response ratio D of the deformation of the baseisolation story to the base input (displacement amplitude) as shown in Fig.Â 4.
Let us assume the input ground acceleration as
The harmonic response of the systems may be expressed by
By solving the equations of motion, the response amplitude may be obtained as
where ()^{T} indicates the matrix transpose. The displacement response ratio D can then be defined by
where Ï‰ _{ I1} is the undamped natural circular frequency of the BI model.
Response reduction performance of proposed system for simple baseisolated building and conventional baseisolationTMD hybrid system
Simulated longperiod ground motion and simulated pulsetype ground motion
Let us assume the simulated longperiod ground motion in terms of circular frequency Ï‰â€‰=â€‰2Ï€/T (T: period) as
FigureÂ 5 shows a simulated longperiod ground motion with Tâ€‰=â€‰7.0(s).
On the other hand, let us assume the simulated pulsetype ground motion as
where C: an amplitude coefficient, a: reduction coefficient, n: envelope shape coefficient, Ï‰ _{ p }â€‰=â€‰2Ï€/T:circular frequency (see Xu et al. 2007). C is determined so as to control the maximum velocity and a is determined from aâ€‰=â€‰0.4Ï‰ _{ p }. The maximum ground velocity is set to 0.91(m/s) (the maximum velocity of JMA Kobe NS 1995). The period of the pulse wave is specified in the range of 1.0â€‰~â€‰3.0(s) with 0.1(s) as the increment. FigureÂ 6 shows the pulsetype wave of Tâ€‰=â€‰2.0(s).
Response reduction performance of proposed system for simple baseisolated building
FigureÂ 7 shows the comparison of various performances under simulated longperiod ground motion among BI model, Proposed1 model, Proposed2 model, Imass TMD model and NewTMD model. The performances to be compared are (a) Deformation of baseisolation story, (b) TMD stroke, (c) Reaction of spring supporting TMD, (d) Reaction of oil damper supporting TMD, (e) Reaction of inertial mass damper supporting TMD. The left figures are for 20story models and the right figures are for 50story models. It can be observed that Proposed1 model can reduce the deformation of baseisolation story by about 38Â % compared to BI model and Proposed2 model can decrease TMD stroke by about 27Â % compared to Proposed1 model.
On the other hand, Fig.Â 8 illustrates the comparison of those performances under simulated pulsetype ground motion. As in Fig.Â 7, the left figures are for 20story models and the right figures are for 50story models. It can be observed that the deformation of baseisolation story of Proposed1 model and Proposed2 model does not change so much from BI model and the baseisolation performance can be kept. Furthermore Proposed2 model can reduce the TMD stroke by about 38Â % compared to Proposed1 model.
Response reduction performance of proposed system for conventional baseisolationTMD hybrid system
It is meaningful to note that, while TMD is connected to the baseisolation floor in the proposed models (Proposed1 model and Proposed2 model), TMD is connected both to the baseisolation floor and ground in the conventional baseisolationTMD hybrid system (Imass TMD model and NewTMD model). For this reason the TMD reactions become relatively large in Imass TMD model and NewTMD model.
Although the proposed system (Proposed2 model) increases the building response under a longperiod ground motion slightly compared to the system without an inertial mass damper (Proposed1 model), the response is still smaller than that of a baseisolated building without TMD. In addition, the proposed system (Proposed2 model) can reduce the TMD stroke under a longperiod ground motion owing to the inertial mass damper. Furthermore, the proposed system (Proposed2 model) can also reduce the TMD stroke under a pulsetype ground motion owing to the inertial mass damper.
It can be concluded that the proposed systems (Proposed1 model and Proposed2 model) can reduce the TMD stroke and TMD reaction effectively compared to the conventional NewTMD model and Imass TMD model for both longperiod ground motions and pulsetype ground motions.
Influence of rail friction on response of proposed system
Since the friction on rail in the TMD system could affect the performance of the proposed control system, its influence has been investigated. Although the static friction behavior is usually different from the dynamic one, the static friction coefficient has been treated as the same as the dynamic one. In this paper, the friction coefficient 0.008 has been used. In order to simulate the friction on rail, an elasticperfectly plastic relation has been utilized and the initial stiffness has been specified as 1.0â€‰Ã—â€‰10^{10}(N/m).
FigureÂ 9 shows the influence of friction on rail in Proposed1 Model subjected to simulated longperiod ground motion (20story, input period Tâ€‰=â€‰5.0Â s). FigureÂ 10 illustrates the influence of friction on rail in Proposed1 Model subjected to simulated longperiod ground motion (50story, input period Tâ€‰=â€‰7.0Â s). Furthermore Fig.Â 11 presents the influence of friction on rail in Proposed2 Model subjected to simulated longperiod ground motion (50story, input period Tâ€‰=â€‰7.0Â s).
On the other hand, Fig.Â 12 shows the influence of friction on rail in Proposed1 Model subjected to simulated pulsetype motion (20story, input period Tâ€‰=â€‰2.0Â s). FigureÂ 13 illustrates the influence of friction on rail in Proposed1 Model subjected to simulated pulsetype motion (50story, input period Tâ€‰=â€‰2.0Â s). Furthermore Fig.Â 14 presents the influence of friction on rail in Proposed2 Model subjected to simulated pulsetype motion (50story, input period Tâ€‰=â€‰2.0Â s). It can be observed that, while the reactions of TMD supports and TMD stroke are affected slightly in a damped process, the superstructure response and baseisolation story response are not affected so much.
It can be concluded that, although the frictions of TMD mass on rail in the proposed systems reduce the TMD stroke for both longperiod ground motions and pulsetype ground motions, those do not affect so much on the building response.
Reduction of TMD stroke using various methods
In the large massratio TMD, the reduction of stroke of TMD is a key issue. FigureÂ 15 shows several attempts to implement it. Proposed1 model is a basic model. As its derivatives, Proposed11 model (detuning), Proposed12 model (increased damping) and Proposed13 model (increased TMD massratio) are considered. Furthermore Proposed2 model is a derivative of Proposed1 model and includes an inertial mass damper in TMD. The Imass TMD model is also a derivative of Proposed1 model and has an inertial mass damper between TMD mass and ground.
TableÂ 1 shows design conditions on TMD parameters in abovementioned several models for stroke reduction. The TMD parameters have been determined so as the reduction of TMD stroke from Proposed1 model under a longperiod ground motion to be almost equivalent.
FigureÂ 16 shows the responses ((a) deformation of baseisolation story, (b) Topfloor absolute acceleration, (c) Superstructure deformation, (d) TMD stroke, (e) TMD displacement relative to ground (f) Reaction of spring supporting TMD, (g) Reaction of oil damper supporting TMD, (h) Reaction of inertial mass damper supporting TMD) to a longperiod ground motion and Fig.Â 17 shows those responses to a pulsetype ground motion. The comprehensive comparison of the response characteristics in Fig.Â 16 will be shown in Fig.Â 20 and TableÂ 2. A similar comparison of the response characteristics in Fig.Â 17 will be shown in Fig.Â 21 and TableÂ 2.
FigureÂ 18 shows the comparison with BI model under a pulsetype motion and Fig.Â 19 indicates the comparison with Proposed1 model under a pulsetype motion. The comprehensive comparison of the response properties in Figs.Â 18 and 19 will be shown in Fig.Â 21 and TableÂ 2.
FigureÂ 20 illustrates the response comparison under a longperiod ground motion. The maximum responses with respect to the input period have been taken. It can be observed that, while Imass TMD model is superior to Proposed2 model in superstructure responses to some extent, Proposed2 model is superior to Imass TMD model in TMD reactions. On the other hand, Fig.Â 21 shows the response comparison under a pulsetype ground motion (comparison to BI Model and Proposed1 Model, comparison of inertial mass damper reaction in Imass TMD Model to Proposed2 Model). For pulsetype ground motions without peak with respect to input period, Fig.Â 21 has been derived from Figs.Â 18 and 19. It can be observed that, while Proposed2 model and Imass TMD model are almost equivalent in superstructure responses, Proposed2 model is highly superior to Imass TMD model in TMD stroke and TMD reactions.
TableÂ 2 presents the response comparison of the proposed models and conventional models with Proposed1 model under longperiod ground motion and pulsetype ground motion. Proposed11 model exhibits a good TMD stroke reduction performance under pulsetype ground motion against Proposed1 model while the structural response under longperiod ground motion increases. Proposed12 model has a good reduction performance of TMD spring reaction under longperiod ground motion and pulsetype ground motion against Proposed1 model. Proposed13 model shows a good reduction performance of structural response under longperiod ground motion against Proposed1 model while the TMDsupporting member reactions under longperiod ground motion and pulsetype ground motion cause some problems. Proposed2 model exhibits a good reduction performance of TMD stroke under pulsetype ground motion against Proposed1 model and a good reduction performance of TMDsupporting inertial mass damper reaction under longperiod ground motion and pulsetype ground motion against Imass TMD model. Imass model shows a good reduction performance of structural response under longperiod ground motion against Proposed1 model while the TMDsupporting member reactions under longperiod ground motion and pulsetype ground motion cause some problems. NewTMD model exhibits a good reduction performance of relative displacement of TMD mass to ground under longperiod ground motion against Proposed1 model while the TMDsupporting member reactions under longperiod ground motion and pulsetype ground motion cause some problems.
It is important to investigate the sensitivity of the system response to the change of the frequency of longperiod ground motions. When the input frequency of longperiod ground motions changes from the resonant situation, the TMD stroke and the reaction in the TMD decrease. Furthermore it has been confirmed that the response reduction performance in the TMD stroke and the reaction in the TMD is high in the proposed system compared to the conventional systems.
Conclusions
The following conclusions have been derived.

(1)
In order to overcome the difficulties caused by the resonance of a baseisolated building under longperiod ground motions and the ineffectiveness of TMD under pulsetype ground motions, a baseisolated building with a large massratio TMD at basement has been introduced. This new baseisolated building system is also aimed at enhancing the earthquake resilience of highrise buildings. The proposed hybrid system of baseisolation and structural control is effective for both longperiod ground motions and pulsetype ground motions. This hybrid system possesses advantageous features compared to existing comparable systems with a TMD at the baseisolation story. The TMD stroke can be reduced to a small level with the use of an inertial mass damper and its reaction can be limited to a lower level by detaching its connection to ground. The proposed hybrid system has another advantage that the TMD mass does not bring large gravitational effect on the building itself because of the placement of TMD at basement.

(2)
The proposed system (Proposed1 model) can reduce the building response under a longperiod ground motion by 38Â % compared to the baseisolated building and keeps the baseisolation performance under a pulsetype ground motion.

(3)
Although the proposed system (Proposed2 model) increases the building response under a longperiod ground motion slightly compared to the system without an inertial mass damper, the response is still smaller than that of a baseisolated building without TMD (BI model). In addition, the proposed system (Proposed2 model) can reduce the TMD stroke under a longperiod ground motion owing to the inertial mass damper. Furthermore, the proposed system (Proposed2 model) can reduce the TMD stroke under a pulsetype ground motion owing to the inertial mass damper.

(4)
The proposed system (Proposed1 model and Proposed2 model) can reduce the TMD stroke and TMD reaction effectively compared to the conventional NewTMD model and Imass TMD model for both longperiod ground motions and pulsetype ground motions.

(5)
Although the frictions of TMD mass on rails in the proposed systems reduce the TMD stroke for both longperiod ground motions and pulsetype ground motions, those do not affect so much on the building response.
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Acknowledgements
Part of the present work is supported by the GrantinAid for Scientific Research of Japan Society for the Promotion of Science (No.24246095). This support is greatly appreciated.
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Authorsâ€™ contributions
TH carried out the theoretical and numerical analysis of the proposed TMD system. KF helped the numerical analysis. MT strengthened the theoretical analysis. IT supervised the theoretical analysis and organized the research group. All authors read and approved the final manuscript.
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Hashimoto, T., Fujita, K., Tsuji, M. et al. Innovative baseisolated building with large massratio TMD at basement for greater earthquake resilience. Fut Cit & Env 1, 9 (2015). https://doi.org/10.1186/s4098401500076
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DOI: https://doi.org/10.1186/s4098401500076