# Study on Structural Robustness of Isolated Structure Based on Seismic Response
## 1 Introduction  
Structural robustness is used to represent the ability of a structure to resist a progressive collapse due to the accidental loads. How to quantitatively analyze the robustness of the structure has been the focus of the majority of scholars in recent years. The simple and practical quantitative evaluation methods will be widely used and promoted by the engineering field. A great deal of research has been taken to work out the quantitative evaluation method of structural robustness. A technique termed 'pushdown analysis' [1,2] or 'pull down analysis' [3] was used to investigate the robustness of building systems by computing residual capacity of remaining structure. However, due to the particularity of the isolation bearing, the instability problem of rubber isolators can easily occur under large axial pressure, or much large displacement is concentrated at the isolation layer, and therefore, it is difficult to judge its robustness by applying vertical pushing force. Various quantitative evaluation methods were also proposed. A novel simplified framework for progressive collapse assessment of multi-storey buildings was suggested [4,5]. The associated concepts (redundancy and vulnerability) were discussed and interpreted in the general context of robustness such that the corresponding methodologies can be compared quantitatively using a comparable scale [6]. A methodology is developed and applied to an existing precast industrial building case study, and assumed to be prone to seismic and wind hazards [7]. The dynamic response is described using a basic substructure instead of a global frame that loses a column, and a simplified model is finally developed for the prediction of the considered system's dynamic response [8]. A new robustness definition with several robustness indicators and a framework are proposed to define more accuratelythe structural robustness concept of corroded reinforced concrete structures [9]. A reliability-based framework for quantifying structural robustness considering the occurrence of a major earthquake and subsequent cascading hazard events is proposed [10]. An experimental asymmetrical two-storey reduced-scale reinforced masonry shear walls (RMSW) building is tested to failure under simulated seismic loading, and the robustness indexes quantified for five key robustness indicators (drift ratio, strength, stiffness, strain energy, and residual drift ratio) can provide a means by which the system-level performance of RMSW buildings can be measured [11]. A quantitative analysis method of structural robustness is proposed based on mechanical characteristics of frame structure under earthquake, and the correctness and practicability of the method were verified with an example [12]. By using the developed pushdown methods, the reserve load carrying capacity of the damaged structure is evaluated; the robustness for resisting progressive collapse of the damaged structure is quantitatively assessed [13]. The influence of different plastic hinge models on the structural nonlinear behavior of reinforced concrete structures is studied by using different methods [14; 15]. The effectiveness and robustness of a pounding tuned mass damper for vibration suppression of a submerged cylindrical pipe is studied by doing experiments [16; 17]. To examine a structure in terms of its robustness, basics for the development of measures to quantify structural robustness are formulated, and a quantitative description of the robustness is proposed [18]. Some other scholars try to use other means to enhance the robustness of the structure [19; 20; 21], but whether the robustness of the original structure is really enhanced or not, and the extent of structural robustness enhancement are both difficult to evaluate and measure. There are many methods for structural robustness evaluations, but they are difficult to meet the engineering requirements [22; 23; 24; 25], because of the complex computation process and lack of practicability.