## 4 Economic Analysis for the Proposed Method
### Economic Benefit Analysis  
Since the structure is retrofitted considering an increase of seismic hazard, according to Chinese seismic codes, from Region 6 to Region 8 [3], the economic benefit is calculated for both the original and the retrofitted frames under the earthquake intensity corresponding to Region 8 (PGA = 0.07 g, 0.2 g, and 0.4 g for the frequent earthquake, the occasional earthquake and the rare earthquake). Note that the results of a large number of analyses would provide a smoothed distribution for the probabilistic evaluation of earthquake results. However, with the current state of modeling capability, such a method would be infeasible for implementation in practice. Instead, the PACT software uses the Monte Carlo procedure to evaluate possible outcomes given a limited set of inputs [49]. In this procedure, limited suites of analyses are performed by using actual GMs to derive a statistical distribution of demands using many of building response states for a specific intensity of motion. In the present study, 1000 Monte Carlo realizations were conducted for a GM intensity level. The GMs selected in Section 2.1 are used here. Figure 12a-f compares the repair costs between the original frame and retrofitted frame. These figures show that the probabilities are smaller than the specific repair cost levels. Figure 13 shows the median repair costs, which are the values corresponding to a probability of 50% in Figure 12. In the figure, we added the retrofitting cost (16.7 MUD) into the total repair cost in order to compare the economic benefit. The figure also compares the repair costs of structural members and non-structural members, respectively. According to FEMA P-58 [49], when the structure is seriously damaged, as in the case shown in Figure 13c, it is necessary to demolish the structure and remove it from the site. Hence, the repair cost (or the replacement cost, which is more rational here) includes the cost to demolish the damaged structure and clear the debris in addition to replacing the structure \"in-kind\". Demolition and site clearance will increase structural repair costs by up to 20-30%. Under the rare earthquake excitation, the original frame collapses; therefore, the total repair cost increases by 20% in the calculation, i.e., 76.7 \(\times\) 120% = 92.04 MUD. Hence, the ratio between the cost of complete replacement and the cost of retrofitting is about 45%. The following observations can be made from these figures. (1) Under a frequent earthquake, for both the original and retrofitted frames, the losses are due to non-structural members, while the structural members' damages are negligible. (2) Under an occasional earthquake, losses are due to both the structural and non-structural members in the original frame, in which the loss due to non-structural members makes up a large proportion. The retrofitted frame suffers no loss due to the structural members. If the initial retrofitting cost is not considered, the loss of the retrofitted frame is smaller than that of the original frame. (3) Under a rare earthquake, for both the original and retrofitted frames, the losses are due to both the structural and non-structural members. The repair cost due to structural members accounts for a large proportion. (4) Generally, the total repair cost, repair costs of structural members and non-structural members increase with the increase of GM intensity. If the retrofitting cost is considered, the economic benefit of the retrofitting is not favorable when a future earthquake intensity, the economic benefit of the retrofitting is still not favorable (but acceptable) when a future earthquake has an occasional earthquake intensity, and the economic benefit of the retrofitting is favorable and can save life when a future earthquake has a rare or larger earthquake intensity.