# Seismic Response Mitigation of Base-Isolated Buildings
## 1 Introduction  
Over the last couple of decades, structural vibration control techniques have been popularized for mitigation of dynamic response caused by various environmental actions. Tuned mass dampers (TMDs) are one of the common control methods used for response mitigation of structures under dynamic loadings. Their applications in various situations and loads have been addressed by several researchers [1; 2; 3; 4; 5; 6; 7]. As single tuned mass dampers (STMDs) became popular, a more practical solution, for example, by distributing TMD mass over the structure is being investigated in recent times [8; 9; 10; 11; 12; 13; 14; 15; 16]. A detailed literature survey on passive TMDs is presented in [PERSON] and [PERSON] [17]. Base-isolation (BI) has been one of the most popular and well-established method of seismic response control. This method makes use of special devices such as friction pendulum, lead rubber bearings, etc, to isolate the main structure from the shaking of the ground. Base-isolation system works by making the isolated structure more flexible at the base, thereby reducing acceleration response of the superstructure and therefore base shear force on the structure. As a consequence of added flexibility, displacement demand on the structure gets amplified, and additional damping is provided to keep displacement demand within acceptable limits. [PERSON] et al. [18] studied the effectiveness of viscous and visco-elastic dampers on seismic response control of BI buildings. They found that there isa tradeoff between the extent to which acceleration and displacement demand can be controlled by BI system combined with additional damping devices. [PERSON] [19] investigated the use of TMD alongside BI and observed that TMD is efficient in response mitigation of BI systems if the dominant period of excitation is longer than the natural period of the structure. [PERSON] et al. [20] studied the efficiency of passive TMDs in response control of BI buildings. [PERSON] and [PERSON] [21] described the effectiveness of optimally designed non-traditional TMD for mitigation of seismic response of BI buildings. Use of TMD with inerter (TMDi) was proposed by [PERSON] et al. [22] and [PERSON] and [PERSON] [23; 24; 25] for diminishing response of BI buildings under earthquakes. [PERSON] and [PERSON] [26] reported the effectiveness of MR dampers for response mitigation of BI building under short and long period ground motions. Effectiveness of single TMD (STMD), multiple TMDs (MTMDs), and distributed MTMDs (d-MTMD) on seismic response control of BI buildings was investigated by [PERSON] et al. [27; 28]. They noticed that d-MTMDs were more efficient and practical than other schemes. Past studies on efficiency of TMDs in response mitigation of BI buildings have relied on a limited number of earthquake ground motions. As there is a large uncertainty in the frequency content, amplitude, and duration of ground shaking a structure can experience, a control scheme that is found effective for a certain type of ground motion may not be effective for other ground motions. It is therefore necessary to consider these uncertainties to have a robust understanding of the usefulness of TMDs in response mitigation of BI structures. Therefore, a probabilistic approach, for example, an examination of fragility curves of structures with and without the TMDs, can shed more light on the overall benefits of using TMDs in BI structures. Such analysis of BI buildings equipped with TMDs is lacking in the literature. Among many other methods, the incremental dynamic analysis (IDA) is one of the popular methods of estimating analytical fragility curves of structures. The idea of incremental dynamic analysis (IDA) was introduced by [PERSON] [29]. [PERSON] et al. [30] proposed the concept of fragility analysis in the field of earthquake engineering. Later, the idea was extended by many researchers including [PERSON] and [PERSON] [31; 32] and [PERSON] and [PERSON] [33; 34].