## 5 Conclusions  
A new risk-targeted method is proposed to define (a) the optimal separation gap distance \(\left(\rm d_{g,min}^{\rm P_{t}}\right)\) at a targeted value of bounding risk (probability per year) P\({}_{\rm t}\) (Decision A) and (b) the acceptable bounding risk P\({}_{\rm min}^{\rm d_{g,t}}\) at a targeted value of separation gap distance d\({}_{\rm g,t}\) (Decision B). The main goal is to guarantee the seismic performance of a structure with an acceptable (predefined) risk-targeted parameter without the need to eliminate structural bounding collisions. So, the method is based on two distinct acceptable performance objectives, the POs-\(\delta_{\rm max}\) and the POs-EDP, defined as a function of P vs. d\({}_{\rm g}\). Each pair of P\({}_{\rm i}\)-d\({}_{\rm g}\) indicates the acceptable bounding risk (probability per year) at the capacity level of an EDP when the separation distance is equal to d\({}_{\rm g}\). So, in Decision A, the acceptable POs-\(\delta_{\rm max}\) at a target probability P\({}_{\rm t}\) defines a separation distance equal to d\({}_{\rm g,min}^{\rm\delta_{\rm max,t}}\) that depicts the corresponding peak relative displacement demand \(\delta_{\rm max,t}\) without accounting for bounding. Thus, the d\({}_{\rm g,min}^{\rm\delta_{\rm max,t}}\)(\(=\delta_{\rm max,t}\)) is the minimum acceptable value of d\({}_{\rm g}\), namely the optimal d\({}_{\rm g,min}^{\rm P_{t}}\). On the other hand, the acceptable structural bounding POs-EDP at a target probability P\({}_{\rm t}\) defines a value of separation distance equal to d\({}_{\rm g,min}^{\rm PO_{t}}\) that is the optimal one \(\left(\rm d_{g,min}^{\rm P_{t}}\right)\) and indicates the peak relative displacement at the top contact point in which the capacity level of the EDP is reached. The combination of POs-\(\delta_{\rm max}\) and POs-EDP in the case of Decision A provides a calibration solution for defining the optimal d\({}_{\rm g,min}^{\rm P_{t}}\) between \(\left\{\rm d_{g,min}^{\rm\delta_{\rm max,t}};\rm d_{g,min}^{\rm PO,t};\rm d_{g, crit}\right\}\) when the structural bounding risk is set equal to P\({}_{\rm t}\). In Decision B, POs-\(\delta_{\rm max}\) and POs-EDP are also combined to determine the minimum acceptable bounding risk P\({}_{\rm min}^{\rm d_{g,t}}\) at a targeted value of separation distance d\({}_{\rm g,t}\). The structural bounding risk P\({}_{\rm min}^{\rm d_{g,t}}\) is controlled among the values of \(\left\{\rm P_{\rm dg,t}^{\rm\delta_{\rm max}};\rm P_{\rm dg,t}^{\rm PO};\rm P_{t, crit}\right\}\) to guarantee the performance of the EDP within a certain capacity level. For the needs of this attempt, a seismic hazard curve compatible with Eurocode's 8 hazard zone was adopted, and the corresponding demand hazard curves of \(\delta_{\rm max}\) and EDP were developed. Also, a variety of POs-EDPs can be used to calibrate the structural bounding risk in terms of d\({}_{\rm g,min}^{\rm P_{t}}\) and/or P\({}_{\rm min}^{\rm d_{g,t}}\). Afterward, an eight-story RC structure with the potential top contact point of colliding being the fourth story was examined (floor-to-floor interaction type). IDAs were performed, and demand hazards of \(\delta_{\rm max}\) and IDR\({}_{\rm max}\) were developed based on linear PSDMs and linear approximation of the seismic site hazard curve. Thereafter, the bounding hazard of the structure was evaluated based on the proposed frameworks taking into account different risk-target scenarios, and the following concluding remarks were deduced:* The seismic hazard imposed on the eight-story RC structure is significantly increased due to structural bounding in comparison to the case of no bounding. * Calibration of the structural bounding risk can be obtained by adjusting the separation gap distance \(\mathrm{d_{g}}\) between the adjacent structures based on the acceptable POs-\(\mathrm{\delta_{max}}\), POs-\(\mathrm{IDR_{max}}\).