## 8 Focus on Earthquake Engineering
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Topic** & **Method** & **No. Criteria** & **Notes** \\ \hline
[54] & AHP, VIKOR & 5 &
\begin{tabular}{c} Included qualitative criteria. Both \\ methods gave the same results \\ \end{tabular} \\ \hline
[55] & PROMETHEE & 7 & Includes earthquake resistance \\ \hline
[56] & AHP, VIKOR & 3 &
\begin{tabular}{c} Links MCDA with an \\ optimization technique \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Examples of MCDA applications in Bridge Design decisions. Approaches to retrofitting buildings to reduce their vulnerability to earthquakes were considered by [70; 71] who discussed the broad range of factors needed and suggested AHP as a suitable MCDA method. Subsequently, this method was used, together with TOPSIS, to rank retro-fit options to improve seismic resilience in existing buildings by [72] using seven criteria (Cost of retrofit, maintenance costs, duration of retrofit, functional compatibility (invasiveness of method), specialized labor requirements, interventions on foundations, potential loss (ratio of repair to reconstruction costs)). A general overview of issues relating to seismic resilience of buildings in Italy, [73], recommended that MCDA methods be used to select appropriate mitigation strategies. This advice was followed by [74] who used seven criteria (Installation cost, net tax refunds, risk improvement, cost of maintenance, duration of work, architectural impact and functional compatibility, and increase in force demand at the foundations). An interesting aspect of that work is a sensitivity analysis showing how decisions changed if the decision maker changed their attitude to balancing short-term vs. long-term benefits. Following on from this, [75] applied similar methods for choosing retrofitting strategies for schools in Lima. The study contains a useful list of criteria used in previous work and used a stakeholder collaborative workshop to narrow these to 6 for its own analysis (Installation cost, duration of work, seismic performance, feasibility of construction, ability to do incremental reinforcing, architectural and functional aspects). An important novelty is the integration with BIM tools for estimating the costs and durations of the options. Similarly, MCDA techniques were applied to the selection of bridge rehabilitation methods to improve seismic resilience [76], using the VIKOR method with 6 criteria (capacity, ductility, deformation, global stability, cost and duration of works). The VIKOR method was also used in selecting a passive vibration control system to use as a baseline to compare smart-passive and earthquake warning options for bridges in seismically risk areas [77]. Six technical criteria were used (peak overturning moment, peak midspan displacement, standard deviation of overturning moment, standard deviation of midspan displacement, number of earthquakes for which the smart-passive strategy gives lower overturning moment, and the number for which it gives lower midspan displacement). In [55], the PROMETHEE method was used, with weights determined by AHP, to choose a bridge construction method to reduce construction time using 7 criteria (Safety, Durability, Economy, Construction speed, Aesthetics, Serviceability, Environmental harmonization). The design and choice of material for elastomeric isolators to reduce vibration of buildings or bridges during seismic events involved both AHP and TOPSIS [78] using three criteria (vertical stiffness, horizontal stiffness and viscous damping). For foundations of buildings, in a study of the factors predicting liquifacation of soils, [79], AHP was used to consolidate the possible criteria to 5 main ones (Plasticity index, Effective vertical overburden pressure, ration of water content to liquid limit, mean particle size, and percentage clay content). Some key examples are summarized in Table 7.