Existing civil engineering structures having strategic importance, such as hospitals, fire stations, and power plants, often do not comply with seismic standards in force today, as they were designed and built based on past structural guidelines. On the other hand, due to their special importance, structural integrity of such buildings is of vital importance during and after earthquakes, which puts demands on strategies for their seismic protection. In this regard, seismic base isolation has been widely employed; however, the existing limited seismic joint between adjacent buildings may hamper this application because of the large displacements concentrated at the isolation floor. In this paper, we compare two possible remedies: the former is to provide supplemental damping in conventional base isolation systems and the latter consists in a combination of base isolation with supplemental rotational inertia. For the second strategy, a mechanical device, called inerter, is arranged in series with spring and dashpot elements to form the socalled tunedmassdamperinerter (TMDI) directly connected to an isolation floor. Several advantages of this second system as compared to the first one are outlined, especially with regard to the limitation of floor accelerations and interstory drifts, which may be an issue for nonstructural elements and equipment, in addition to disturbing occupants. Once the optimal design of the TMDI is established, possible implementation of this system into existing structures is discussed.
Passive vibration control systems of civil engineering structures and infrastructures are of utmost importance in earthquakeprone regions to mitigate or reduce damage potential due to the shaking ground. Even more importantly, seismic protection is imperative for those structures whose integrity during and after earthquakes is of vital importance for civil and social purposes, including hospitals, fire stations, schools, barracks, power plants, and so forth. Nevertheless, in many cases such structures present structural deficiency and do not comply with the requirements of seismic standards in force today, as they were designed and built according to the past structural guidelines that were not as severe as the current regulations. Consequently, seismic protection and retrofitting strategies of these structures are highly desirable, which should do not interfere with the operational and functionality aspects of the building.
In this regard, seismic base isolation [
These shortcomings have motivated the development of improved versions of the conventional base isolation scheme. The most straightforward remedy for reducing the BIS displacement is to increase the isolation damping or to provide
This paper compares the above two alternative strategies for the seismic retrofitting of existing buildings, namely, seismic base isolation with supplemental damping versus seismic base isolation with supplemental rotational inertia. Optimal tuning parameters of the TMDI are detected within a probabilistic framework, by considering the stochastic nature of earthquake ground motions and solving a nonlinear optimization problem. The earthquake ground motion is modelled as a Gaussian process in the frequency domain through the use of the power spectral density (PSD) function. The influence of soil characteristics is investigated by introducing three PSD functions representatives of firm, medium, and soft soil conditions. Based on the optimal parameters found, a possible implementation scheme with regard to existing structures is proposed. Some numerical applications demonstrate advantages and disadvantages of the two vibration control strategies with regard to the structural control of existing structures, not only in terms of displacement but also in terms of transmitted forces and other response indicators such as the base shear, the interstory drifts, and the floor accelerations, in order to evaluate the overall performance of these seismic protection systems.
The inerter element was introduced by Smith [
As schematically shown in Figure
Schematic model of the inerter with rack and pinion mechanism.
Sketch of the tunedmassdamperinerter (TMDI).
Besides the optimal design of the TMDI, which is described below in terms of its dynamic characteristics (stiffness, damping, etc.), there are a few practical considerations related to the functionality of the inerter that deserve commentary. Unlike mechanical networks involving frequent activity of the rack and pinion mechanism, in earthquake engineering, it is expected that the inerter actually works just for few seconds, that is, during the seismic event. The horizontal accelerations transmitted by the shaking ground during this short time generate resistive forces in the inerter by accelerating the internal wheels. However, there may be an issue of backfeeding energy into the structure when the building begins to slow down, unless an internal mechanism decouples the rotational mass to prevent this phenomenon. This energy is certainly transferred from the inerter to the TMD; therefore, an adequate space in the building is necessary to allow this stroke. However, this energy is not returned to the superstructure, since the inerter is not directly connected to it, but just to the TMD mass. There is an additional filter, consisting of the TMD spring and damper elements, which significantly reduce this backfeeding energy to the superstructure at the end of the earthquake. This reduction can be seen by the observation of the time history of the response at the end of the seismic event (see below). Further investigation is certainly needed to carefully analyze these phenomena in more detail, which is beyond the main scope of this paper.
In the context of hybrid control strategies, applications of BIS in conjunction with a TMD attached immediately above or below the isolation floor of the building have been extensively discussed in the literature [
Due to the proportionality of the generated force of the inerter to the relative acceleration of its two terminals as per (
Sketch of baseisolated structural SDOF with attached TMD (a) and with attached TMDI (b).
In many existing structures the actual seismic joint is insufficient or nonexisting. Indeed, although modern codes such as Eurocode 8 [
In order to mitigate the earthquakeinduced damage to such buildings, the strategy of seismic base isolation has been widely adopted. Nevertheless, while reducing the forces in the superstructure, there is an issue when the seismic joint is quite limited, as in the cases mentioned above. Indeed, the vibration control is achieved by providing flexibility at the base of the structure such that the overall displacement of the baseisolated structure may also exceed the maximum admissible displacement resulting from the actual seismic joint. Just to fix the concepts, we suppose that the actual seismic joint is a fraction of the total height of the building
Schematic representation of the displacement demand in baseisolated structures: (a) conventional BIS with medium damping; (b) lowperiod BIS with medium damping; (c) highdamping BIS.
The selection of the BIS parameters follows the conventional rules for seismic base isolation [
The TMDI is characterized by four parameters in the most general case, namely,
Owing to the stochastic nature of earthquake ground motion [
The timemodulating function by Hsu and Bernard [
In order to investigate the influence of soil characteristics in terms of frequency content, a filtered Gaussian whitenoise process is considered for the stationary PSD function
Filter parameters
Filter parameters depending on soil conditions (Der Kiureghian and Neuenhofer [
Soil type 





Firm  15.0  0.6  1.5  0.6 
Medium  10.0  0.4  1.0  0.6 
Soft  5.0  0.2  0.5  0.6 
Evolutionary PSD function as per (
Optimum design of the novel vibration control system is based on the stochastic response of the 3DOF system due to the PSD function (
It will be demonstrated that minimizing
The optimization problem dealt with in this paper is handled via a numerical search algorithm, through the builtin MATLAB
The optimal design of the TMDI to achieve a reduction of the displacement demand in a baseisolated structure is discussed here. A wide parametric study is carried out, wherein the main investigated parameters are (1) the soil condition (firm, medium, soft type, and the whitenoise process as an extremely broadband frequency content); (2) the physical mass ratio
In Figures
Optimal TMDI tuning for firm soil conditions: (a) minimum OF achieved, normalized with respect to the case without TMDI; (b) optimal frequency ratio; (c) optimal damping ratio.
Optimal TMDI tuning for medium soil conditions: (a) minimum OF achieved, normalized with respect to the case without TMDI; (b) optimal frequency ratio; (c) optimal damping ratio.
Optimal TMDI tuning for soft soil conditions: (a) minimum OF achieved, normalized with respect to the case without TMDI; (b) optimal frequency ratio; (c) optimal damping ratio.
Optimal TMDI tuning for whitenoise assumption for the earthquake: (a) minimum OF achieved, normalized with respect to the case without TMDI; (b) optimal frequency ratio; (c) optimal damping ratio.
By inspection of the OF achieved, the TMDI appears to be very effective in the displacement reduction of the baseisolated structure. In particular, depending on the soil conditions, a 60–70% reduction of the displacement variance is achieved with an inertance ratio
The optimal TMDI parameters
The influence of the BIS damping ratio
Optimal TMDI design for different BIS damping ratios and soil conditions: (a) minimum OF achieved, normalized with respect to the case without TMDI; (b) optimal frequency ratio; (c) damping ratio.
Optimal TMDI design for different BIS damping ratios and soil conditions: (a) normalized total acceleration variance and (b) normalized TMDI displacement variance, representative of the TMDI stroke.
Furthermore, this reduction is not confined to the displacement variance. In Figure
It can be noted that the reduction of the superstructure acceleration is improved when lowdamping isolators are employed (Figure
The optimal tuning of the system discussed in Section
For a possible implementation strategy of this system into existing structures, we now approach the problem of designing the base isolation system from a different perspective. The elastic and damping properties of the TMDI system,
Schematic arrangement of the proposed base isolation system comprising two sets of isolators to attach the inerter to the structure.
To summarize the basic steps of a schematic seismic retrofitting procedure via the proposed system discussed above, in Figure
Conceptual flowchart of a seismic retrofitting procedure based on the proposed system of Figure
In line with the conceptual flowchart introduced in Figure
The existing structure is a fivestory reinforced concrete (RC) building. For simplicity, we assume that the building is symmetric in plan, so that it can be analyzed through the equivalent planar frame depicted in Figure
Fivestory RC building with the seismic protection system proposed in this paper (all dimensions in m).
According to Eurocode 8 requirements [
In a seismic retrofitting procedure, the description of the seismic motion may be made by using artificial accelerograms and recorded or simulated accelerograms [
We assume that the building is installed in firm soil conditions. According to the Monte Carlo method, an ensemble of 100 artificial uniformly modulated accelerograms is generated from the firmsoil evolutionary PSD function presented in Section
Following the conceptual flowchart of Figure
Seismic retrofitting strategies analyzed and compared in this study and optimal parameters.
Seismic retrofitting label  Seismic protection strategy 





#1  Conventional BIS  0.1  2.0  —  — 
#2  BIS with rotational inertia (TMDI)  0.1  2.0  0.256  2.502 
#3  BIS with TMD  0.1  2.0  0.135  2.713 
#4  BIS with supplemental damping  0.3  2.0  —  — 
#5  BIS with supplemental damping  0.4  2.0  —  — 
The results from 100 timehistory analyses (each relevant to a given accelerograms) are averaged to obtain the mean rootmeansquare (RMS) values and the mean maximum (MAX) values of a few representative response indicators that are reported in Tables
List of results considering average RMS values of response indicators (Monte Carlo method with 100 artificial samples).
Seismic retrofitting strategy  Superstructurerelated response indicators  BIS displacement 
TMD stroke 


Lastfloor displacement 
2nd interstory drift 
4th floor acceleration 
Base shear 
Kinetic energy 
Strain energy 

#1. Conventional BIS (reference solution)  8.58  17.27  82.31  229.0  38.19  1879.8  7.92  — 
#2. BIS with rotational inertia (TMDI)  3.87  8.20  42.34  108.0  9.88  502.5  3.56  5.85 
(−54.8%)  (−52.5%)  (−48.6%)  (−53.1%)  (−74.1%)  (−73.3%)  (−55.1%)  (−26.1%)  
#3. BIS with TMD  5.61  11.02  53.95  146.0  18.18  844.9  5.19  16.41 
(−34.7%)  (−36.2%)  (−34.5%)  (−36.4%)  (−52.4%)  (−55.1%)  (−34.6%)  (  
#4. BIS with supplemental damping  5.06  10.48  52.17  138.0  15.73  772.6  4.67  — 
(−41.0%)  (−39.3%)  (−36.6%)  (−39.6%)  (−58.8%)  (−58.9%)  (−41.2%)  —  
#5. BIS with supplemental damping  4.40  10.48  52.17  122.0  15.73  772.6  4.00  — 
(−48.7%)  (−39.3%)  (−36.6%)  (−47.0%)  (−58.8%)  (−58.9%)  (−49.5%)  — 
List of results considering average MAX values of response indicators (Monte Carlo method with 100 artificial samples).
Seismic retrofitting strategy  Superstructurerelated response indicators  BIS displacement 
TMD stroke 


Lastfloor displacement 
2nd interstory drift 
4th floor acceleration 
Base shear 
Kinetic energy 
Strain energy 

#1. Conventional BIS (reference solution)  23.67  48.23  258.32  634.0  182.05  8195.1  21.81  — 
#2. BIS with rotational inertia (TMDI)  13.59  30.37  183.59  390.0  70.31  3201.7  12.39  18.47 
(−42.6%)  (−37.0%)  (−28.9%)  (−38.6%)  (−61.3%)  (−60.9%)  (−43.2%)  (−15.3%)  
#3. BIS with TMD  18.25  36.16  208.17  474.0  113.5  4512.6  16.85  48.16 
(−22.9%)  (−25.0%)  (−19.4%)  (−25.3%)  (−37.7%)  (−44.9%)  (−22.8%)  (  
#4. BIS with supplemental damping  16.32  34.89  204.5  452.3  97.65  4208.1  14.96  — 
(−31.0%)  (−27.6%)  (−20.8%)  (−28.8%)  (−46.2%)  (−48.6%)  (−31.4%)  —  
#5. BIS with supplemental damping  14.65  34.89  204.5  416.0  97.65  4208.1  13.29  — 
(−38.1%)  (−27.6%)  (−20.8%)  (−34.4%)  (−46.2%)  (−48.6%)  (−39.1%)  — 
Such performance of the system #2 is achieved without requiring large physical mass and without implying excessively large TMDI strokes: indeed, the displacements of the auxiliary isolators are reduced of around 26% and 15% (RMS and MAX values, resp.) as compared to the displacement of the conventional BIS in the uncontrolled case
In Figures
Timehistory response of the RC building shown in Figure
One possible drawback of the proposed system with rotational inertia could be the generated force, which is proportional to the relative acceleration. To assess the incidence of this force, in Figure
Timehistory for reactive forces relevant to two arbitrary artificial accelerograms.
The verification procedure of the constraints listed in (
Monte Carlo method with 100 artificial samples: average maximum distribution of horizontal displacements (a), interstory drift index (b), and floor acceleration (c) compared to threshold values as per (
The analysis discussed above has been carried out by means of uniformly modulated accelerograms, as an idealization of real accelerograms that are actually fully nonstationary in nature. To corroborate the conclusions of the present investigation, we repeat the analysis with two natural earthquake ground motions to scrutinize the effectiveness of the seismic retrofitting strategies while accounting for the fully nonstationary character of the seismic input. Two recorded accelerograms are selected from the Center for Engineering Strong Motion Data (
Lastfloor displacement timehistory response of the RC building shown in Figure
Average maximum distribution of horizontal displacements (a, d), interstory drift index (b, e), and floor acceleration (c, f) for El Centro and Loma Prieta earthquake ground motions.
The observation of realworld examples of BI solutions (see, e.g., [
Based on these observations, the assessment of the effectiveness of the proposed BIS + TMDI solution should be made by incorporating the effect of detuning, that is, by slightly varying the dynamic properties of natural frequency (thus accounting for the variation in both masses and stiffness) and damping ratio of the TMD tuned isolators. It seems of valuable importance to scrutinize and quantify the impact of tuning failure (effects of detuning) on the achieved isolation performance.
No practical implementation of the BIS + TMDI strategy in real structures is available so far; therefore, the investigation is here carried out numerically by means of a parametric analysis. In particular, the same fivestory RC building shown in Figure
This is a simplified way to simulate what happened in the CWH [
Impact of tuning failure due to imperfect knowledge of the structural TMD dynamic parameters: effect on four response indicators.
Impact of tuning failure due to imperfect knowledge of the structural TMD dynamic parameters: surface and contour plots of the lastfloor displacement (a, c) and of the base shear (b, d), respectively.
A variety of seismic retrofitting strategies exist, which are obviously not limited to the few ones discussed in this paper. Among these strategies, we mention the coupling of adjacent buildings by means of passive damping devices to reduce the risk of pounding [
The retrofitting operations are limited just to the ground floor level or to the basement level, thus not interfering with the architectural aspects of the building along its height, and the remaining parts of the structure do not have to be modified and/or altered (unlike other systems applied to the structural elements directly (see, e.g., [
It is well known that the seismic base isolation permits a strong reduction of forces to the superstructure so that the building can be designed to remain in the elastic range. Consequently, limited damage is expected in the superstructure, thus avoiding interruption of operational and functional aspects of the building, while plasticnonlinear behavior is concentrated at the isolation level. This consideration, stated for the conventional BIS, also applies to the improved BIS with supplemental rotational inertia. In other words, during and after the earthquake, the structure can, in principle, continue to hold its function, which is of extreme importance for strategic buildings having civil and social duties.
As compared to the conventional base isolation scheme, the displacements are drastically reduced in the proposed BIS with supplemental rotational inertia, which is essential in existing structures with limited seismic joints. Moreover, it has been found that also interstory drifts (related to the internal stress of the frame elements) and floor accelerations are reduced by the proposed strategy, much more than employing supplemental damping.
The inerter is a quite compact mechanical device that can be designed to provide any desired value of inertance. On the contrary, effective vibration reduction is achieved by the TMD provided that large amounts of mass are introduced into the system. Unless an architectural function is assigned to such an additional mass (e.g., a parking space and utilities room), the feasibility and costeffectiveness of this retrofitting strategy may be hampered in practical applications because of economic reasons.
The use of the TMD as a retrofitting strategy is also hindered by the TMD strokes, which may be unacceptably large, thus requiring a large space/clearance in the building in order to accommodate the displacement demand of this secondary mass/subsystem, sometimes even exceeding the maximum admissible displacement of the BIS.
As compared to alternative retrofitting strategies comprising fluid viscous dampers installed along the height of the building, the proposed system can accommodate large relative displacements without suffering from the issues of viscous heating and potential leaking that challenge the implementation of fluid dampers [
Nevertheless, all the encouraging outcomes arisen from this study should be better verified before a practical implementation of this system for seismic retrofitting purposes can be accomplished. For instance, while the assumption of linear viscous damping for the superstructure is reasonable, it would be advisable to extend this research work to incorporate a more appropriate, realistic nonlinear behavior of the isolators, thus accounting for their actual inelastic characteristics. However, it has been demonstrated that the system performs at its best when lowdamping (rubber bearing) isolators are considered; therefore, the equivalent linear viscous damping idealization dealt with in this paper could represent a reasonable assumption at least for preliminary design purposes. On the other hand, the auxiliary isolators are mediumtohigh damping isolators, which implies that a better description of their nonlinear behavior is recommended. This task is left for future research work.
Existing structures having a limited seismic joint and requiring a high level of earthquake protection, such as building with strategic importance, have been addressed in this paper. To limit the forces in the structure and to keep the functional and operational aspects of these buildings during and after earthquakes, the strategy of seismic base isolation has been assumed as the starting point of a seismic retrofitting process. On the other hand, the limited seismic joint of several existing structures built in the past requires careful considerations on the displacement demand of the baseisolated structure. In this paper, two alternative remedies are discussed and compared, the former combining a base isolation system with supplemental damping and the latter coupling the base isolation with supplemental rotational inertia via the use of the TMDI, which is a TMD with inerter. The combination of the base isolation system with a TMD has retrieved a special case of the system with the TMDI for a zero value of the inertance. Optimal design of the system and the influence of the soil characteristics on the best tuning parameters have been dealt with. A practical strategy of implementation of the proposed system into existing structures is presented, which comprises the use of two sets of isolators, namely, some conventional isolators with lowdamping properties and some auxiliary isolators that are more flexible and equipped with mediumtohigh damping characteristics. The inerter is connected in between the auxiliary isolators and the ground. Timehistory analyses for a simple multistory building subject to both artificial accelerograms and natural earthquake ground motions have been performed. The basic steps involved in a seismic retrofitting procedure via the proposed technique are outlined. A variety of response indicators are computed that are useful and of practical importance for design engineers, including the base shear, interstory drifts, floor accelerations, kinetic energy, and so forth. It is found that the BIS with supplemental rotational inertia is a more effective seismic retrofitting strategy than the BIS with supplemental damping for all the response indicators above mentioned, at least for the cases here analyzed. Advantages of the proposed techniques over a few other approaches in the literature have also been critically discussed but only from a qualitative point of view. Sensitivity analysis and the impact of tuning failures due to imperfect knowledge of the structural parameters (e.g., the TMD mass and the stiffness of the isolators) have also been discussed, motivated by the observation of a realworld case example of isolation [
Despite many simplifying assumptions adopted in this paper and the simplicity of the structural model analyzed, the authors’ opinion is that the BIS with supplemental rotational inertia can be considered as a feasible, lowmass, and efficient seismic retrofitting strategy of existing structures with limited seismic joint. However, before a practical implementation can be done, prototype testing and/or experimental findings are essential to gain a more accurate understanding of this system and to to validate the idealized models commonly adopted in the literature.
The authors declare that they have no conflicts of interest.
The financial support from the Italian Ministry of Education, University and Research (PRIN Grant 2015TTJN95—“Identification and monitoring of complex structural systems”), is gratefully acknowledged. The first author wishes to express his personal gratitude to this research fund and also to the PRIN Grant 2015JW9NJT, through which a postdoctoral scholarship was awarded.