Understanding the Impact of Seismic Hazard and Climate Conditions on Multi Criteria–Based Retrofitting of Existing Buildings

Abstract

A large share of the reinforced concrete (RC) building stock in Mediterranean countries faces a dual challenge of seismic vulnerability and energy inefficiency, calling for urgent renovation efforts. While energy upgrades have been the focus of previous renovation policies, recent research highlights the critical need for integrated retrofitting solutions that address both structural integrity and energy performance. Multi-criteria decision-making (MCDM) approaches are a promising tool for optimizing the combined choice of these integrated interventions, considering various decision variables (DVs) of economic, social, environmental, and technical nature. To understand the impact of climate and seismic hazard conditions on multi-criteria-based retrofitting assessment, a case-study RC school building is selected and assumed to be located in three distinct climate conditions, cold, mild, and warm, and three seismic hazard levels, low, medium and high. Moreover, given the complexity and challenges of quantifying seismic performance metrics for practitioners, an available simplified (practice-oriented) approach is compared herein with a more thorough research-based one for quantifying the seismic performance of RC buildings within the MCDM framework. Both approaches are applied to the case-study building, considering twelve possible combinations of energy and seismic interventions. The accuracy of the practice-oriented approach and its impact on the retrofitting rankings is evaluated, emphasizing the importance of accessible and efficient evaluation methods in facilitating informed decision-making for building renovation.

1. Introduction

Most of the reinforced concrete (RC) buildings of the Mediterranean countries’ stock presents a dual challenge in terms of seismic vulnerability and energy inefficiency, underlying an urgent need for renovation. These buildings have been constructed following outdated guidelines without modern seismic design considerations, rendering them susceptible to earthquake damage. Simultaneously, their energy performance is typically highly unsatisfactory. In fact, 75% of the European building stock is energy inefficient, being responsible for 40% and 36% of EU energy consumption and total CO₂ emissions, respectively [1]. Even though Italy is on track to reach the emissions reductions and energy efficiency targets set by its National Energy and Climate Plan (NECP) for 2030 [2], substantial additional efforts need to be made to reach the much more ambitious new targets for 2030 stemming from the European Union’s (EU) Fit-for-55 (FF55) package, which aims to reduce its net greenhouse gas emissions by at least 55% by 2030. Consequently, the renovation of the building sector, in terms of reducing its seismic vulnerability and increasing its energy efficiency, is highly necessary to promote well-being and economic growth and to ensure that the EU energy and climate targets are met [3,4]. Specific concerns in the Italian context include more than 55% of the RC residential buildings were constructed without seismic provisions and 88% of the Italian masonry and RC buildings do not comply with modern energy performance requirements [5]. According to Gkatzogias and Tsionis (2022) [4], when combining different indicators (seismic, energy, and socio-economic vulnerability), Italy is considered a high-priority country for building renovation.

Until recently, renovation efforts and policies were mainly directed to energy upgrades to buildings alone, without considering their structural performance, because of the immediately evident benefits from the reduced energy costs for heating/cooling. However, if the structural integrity of the retrofitted building is not guaranteed, that same investment could be completely lost in the case of seismic events. Similarly, seismic retrofitting interventions alone could compromise thermal comfort if a building’s energy efficiency is not considered. The growing need for renovation of a significant portion of EU buildings has prompted recent advancements in scientific and technical fields, which suggest that adopting an integrated approach to building renovation could lead to improved cost-effectiveness [6]. From a more global perspective, the performance upgrade process is highly influenced by the seismic hazard and vulnerability, energy performance, and socio-economic characteristics of the region where the buildings are located, as recently highlighted by Mucedero and Monteiro [7]. Such a study established a regional prioritization framework for seismic and energy efficiency performance upgrades to residential buildings in Italy, revealing that critical regions for seismic retrofitting are primarily in central-southern Italy, while those for energy upgrading are mainly in northern Italy. Although contemporary understanding recognizes that seismic retrofitting cannot be decoupled from energy renovation, the previous two scenarios highlight the need to address this combined retrofitting in a holistic way to achieve optimal results.

To address both seismic and energy performance concerns, recent research studies have aimed to minimize economic losses and environmental impacts while promoting building renovation. Most of these studies make use of optimization methodologies to identify the ideal solution when a range of several options is available. Multi-criteria decision-making (MCDM) approaches have demonstrated advantages in optimizing combined interventions [8,9,10,11,12]. The MCDM approach for selecting the optimal coupled retrofit intervention can become extremely helpful to decision-makers and practitioners because it encompasses multiple criteria when making decisions about retrofitting options. By considering different decision variables (DVs) chosen to capture the essential aspects of the decision problem (e.g., economic costs, social benefits, and technical feasibility), decision-makers can make more informed and balanced decisions.

This study evaluates the influence of climate and hazard levels on the preferential ranking of the retrofit alternatives. To do so, an RC school building is selected as a case study, given the high seismic vulnerability of school buildings in Italy demonstrated by past earthquakes [13], and twelve possible combinations of energy and seismic interventions are identified. Subsequently, the building is assumed to be located in nine different sites characterised by varying levels of seismic hazard and climate conditions. Following an energy and seismic performance assessment, the optimal combined retrofitting intervention is evaluated following a previously validated MCDM framework [11] for each location considered, resulting in nine distinct rankings.

The detailed analysis methods used to evaluate the seismic performance of different retrofitting alternatives are very computationally expensive and time-consuming; thus, they are unfeasible to implement by practitioners or general decision-makers. With such limitations in mind, this study also evaluates the implementation of a simplified approach to quantify some of the DVs required to select optimal retrofitting strategies for existing buildings. Specifically, the DVs annual probability of failure (APF) and expected annual losses (EAL) are estimated using the cloud-based capacity spectrum method (CB-CSM) and the Italian seismic risk classification procedure (Sismabonus), respectively. The goodness of the simplified approach is further gauged by comparing the MCDM rankings of combined retrofitting alternatives obtained from using both simplified and refined approaches.

2. Methodology

The MCDM framework, as employed by Clemett et al. (2023) [11] and in subsequent studies [14,15,16], is adopted herein to identify the optimal combination of seismic and energy retrofitting solutions for a building when several combination options are feasible. The overall methodology, which is concluded with the MCDM step, corresponds to a structured process for assessing, designing, and selecting retrofit solutions for buildings exhibiting both seismic and energy deficiencies. This methodology comprises five main steps: assessment, design, performance, decision, and selection, which are illustrated in Figure 1.

Initially, an assessment is conducted to identify the building deficiencies using research-based tools for seismic performance assessment and commercial energy simulation tools for energy assessment. Thereafter, the design phase involves proposing seismic and energy retrofit solutions based on the identified issues. A performance evaluation is then carried out using the same tools used in the assessment phase to quantify the effectiveness of each retrofitting option. The decision-making stage considers various DVs, including seismic and energy performance, environmental and social aspects (e.g., architectural impact and duration of works), and technical aspects (such as specialized labour or foundation interventions). The DVs chosen to assess the performance of the retrofitted building are provided in

Table 1. Decision variables considered for the MCDM framework.

Group	Decision Variables		Weight
Economic	C1	Installation cost	0.15
	C2	Expected annual costs (EAC)	0.19
Environmental	C3	Expected life-cycle environmental impacts (LCEI)	0.18
Social	C4	Annual probability of failure (APF)	0.14
	C5	Duration of works	0.13
	C6	Architectural impact	0.06
Technical	C7	Need for specialized labour/design knowledge	0.05
	C8	Required intervention at the foundations	0.10

. Finally, the MCDM process [11] is employed in the selection phase to choose the optimal retrofit alternative and to rank all the selected alternatives. Weight factors are associated with each DV, and their values are highly influenced by the preference of the decision-maker. They are used to quantify the importance of each criterion in the decision-making process, playing a crucial role in determining the relative importance or priority of different criteria or decision variables within the MCDM framework. As a result, weight factors exert a substantial influence on the ranking of the alternatives [17]. The weight factors selected in this study are based on the work of Clemett et al. [11] and shown in Table 1; more emphasis is placed on the installation cost and duration of works of the retrofit intervention, as well as the seismic performance (in terms of APF and EAL) and the energy performance of the building.

In this approach, the highest computational burden is mostly associated with the quantification of some of the DVs (obtained from the results of steps 1 and 3 in Figure 1). Such DVs are the annual probability of failure (APF), considered—C₄—the expected annual losses (EAL) and expected annual environmental impact (EAEI)—C₂ and C₃, respectively. Detailed seismic assessment is usually conducted using incremental dynamic analysis (IDA) or multiple-stripe analysis (MSA) to obtain the fragility parameters and, subsequently, the APF. In turn, within a lower-refinement level of analysis, more likely to be used in the engineering practice field, nonlinear static analysis-based procedures, such as the SPO2IDA tool [18], the SPO2FRAG tool [19] or the incremental N2 method [20] can be considered to perform collapse fragility estimation. On the other hand, comprehensive performance-based loss estimation (component-based approach—PEER-PBEE methodology [21]) or simplified tools (e.g., Storey Loss Functions [22,23], the DEAL approach [24]) are usually implemented to obtain the expected annual loss (EAL) and the expected annual environmental impact (EAEI).

This study adopts a simplified approach to estimate the aforementioned computationally onerous DVs. In particular, the APF is quantified through the results of the cloud-based capacity spectrum method (CB-CSM) [25], while, for the loss assessment, the simplified procedure outlined in the Italian guidelines for seismic risk classification of constructions (Sismabonus) [26] is chosen, replacing the cumbersome component-based approach implemented in the PACT 3.1.2 software [27]. In the following sections, a brief description of the detailed and simplified approaches employed in this study is provided.

2.1. Detailed Approach

The detailed approach for the estimation of the DVs C₂, C₃, and C₄ follows a comprehensive performance-based seismic assessment and loss analysis through the PEER-PBEE methodology. The procedure initiates with the characterisation of the seismic hazard at the selected site, followed by a selection of suitable hazard-consistent ground motion sets. Then, nonlinear time history analysis is conducted on the structure under analysis, using the previous set of selected ground motions, through multiple-stripe analysis (MSA), which allows the quantification of the structural response. Through the MSA results, collapse fragility parameters are derived. Expected damage and losses are quantified considering structural and non-structural components; thus, it is necessary to develop an inventory of damageable components in the building, together with the definition of their potential damage states, expected repair cost, and environmental impact consequences. Finally, the detailed seismic loss assessment is performed through PACT [21]. The ultimate outcomes needed for the MCDM framework are the EAL, the EAEI, and the APF.

2.2. Simplified Approach

The simplified counterpart makes use of two readily available tools to estimate the AFP and EAL, namely the cloud-based capacity spectrum method (CB-CSM) and Sismabonus, respectively. The CB-CSM is a combination of two well-established methods, the capacity spectrum method (CSM) [28] and the cloud-based (CB) procedure [29], to estimate the collapse fragility parameters of a given structure. The method starts with the identification of the performance point (PP) of the structure with the CSM. Since multiple PPs can be obtained, several recommendations on how to overcome this problem and select the most suitable PP are available in [25]. In this study, in case of multiple PPs, the adopted PP was the one for which the absolute difference between the geometric average of spectral displacements over an appropriate range of periods (AvgSdk) and each obtained PP (|AvgSdk − ΔPP|) is minimum. This procedure leads to a cloud of Engineering Demand Parameter (EDP) vs. Intensity Measure (IM) points for each analysed Single Degree of Freedom (SDoF) system. The EDP is the target displacement corresponding to the PP calculated via CSM, and the adopted IM is the geometric mean of the spectral accelerations (AvgSa) computed in the interval [0.2T_el–1.5T_el], with T_el being the elastic period of the structural system, as recommended in [25]. Based on the criteria selected to define the collapse limit state, the cloud data are divided into non-collapse (NoC) and collapse (C) points and the collapse fragility parameters are calculated through the total probability theorem.

Sismabonus is a relatively recent procedure implemented in Italy to evaluate the seismic risk of buildings and use it to classify them [26]. This guideline provides a simple method for practitioners to assess the building’s initial seismic condition and estimate its expected yearly seismic losses. This estimation can also help in evaluating the effectiveness of different retrofitting strategies in improving the building’s seismic performance, hence guiding the choice of the retrofitting strategy. Notably, the Sismabonus approach requires only nonlinear static analysis, making it a more practical and quicker method to evaluate seismic annual losses when compared to approaches like the PEER-PBEE [21]. Furthermore, when compared to other available simplified procedures for estimating the EAL of a building, Sismabonus holds additional advantages as it is already in use within the Italian engineering practice, even if recent findings show its loss estimates to be more conservative when compared to the ones obtained with more refined methodologies [30,31]. This method requires the computation of two performance indices: the Building Safety Index (SI-LS) and Expected Economic Annual Losses (EAL). The SI-LS is calculated by determining the capacity peak ground acceleration (PGA_C) and demand peak ground acceleration (PGA_D) associated with the Life Safety limit statelife (LSLS). Concurrently, the EAL is estimated by considering the building’s performance for various return periods (T_r) and repair costs expressed as a fraction of the Reconstruction Cost (%RC). The resulting loss curve, which defines the seismic risk, is represented by a point (1/T_r, %RC) for each limit state, whereas the area underneath is the EAL. The overall risk class of the building is defined as the worst between SI-LS and EAL classes. This method integrates structural and economic considerations, providing a comprehensive framework for seismic risk assessment. More details on the procedure can be found in the work by Cosenza et al. [26].

3. Application to a Case-Study Building

The selected case-study school building is a reinforced concrete (RC) moment resisting frame (MRF) with unreinforced masonry (URM) infills, located in Isola del Gran Sasso d’Italia (Abruzzo, Italy) and built between the 1960s and 1970s [32]. The building has two aboveground storeys with roughly 630 m² each and inter-story heights of 3.75 and 4.25 m on the first and second floors. Additionally, there is a small partial basement at the east end. The structural system consists of two-way RC MRFs in the longitudinal and transverse directions, along with URM infills and partitions. More details on the school building, including architectural plans and elevations, together with the material properties of structural members, can be found in Prota et al. [32]. The masonry infills were assumed to have the same geometry and material properties as the medium-strong masonry infill typology in the macro-level classification as proposed in [33]. The numerical model of the building, comprising flexural elements (for beams and columns), beam–column joints (BCJs), a staircase, and masonry infills, was developed in OpenSees [34], and a three-dimensional representation of the model is presented in Figure 2. The beam and column elements were modelled using the force-based beam–column element with a Modified Radau plastic hinge integration scheme [35]. Although the shear behaviour of RC elements was considered elastic, a post-processing analysis was carried out to determine any possible shear failure, similar to the approach adopted by Mucedero et al. [36]. To capture the nonlinear behaviour of beam–column joints, a scissor model was implemented, characterised by a zero-length spring coupled with a rotational hinge defined according to the backbone curve proposed by O’Reilly [37]. Further details on the numerical modelling of the structure can be found in [11,38].

For the purposes of this study, i.e., understanding the influence of seismic hazard level and climate conditions on the combined retrofitting, the building is assumed to be located in nine different sites in Italy. There are three sets of different hazard levels, namely high (H), medium (M), and low (L), paired with three sites characterised by different climatic conditions, namely cold (C), moderate (M), and warm (W). Choosing real locations in Italy was intended to ensure the results of this study closely reflect actual conditions. However, this decision may introduce uncertainty when assessing and comparing the results due to variations in seismic hazard curves and the corresponding selection of records.

The specific features of each site are summarized in

Table 2. Main features of selected case-study sites.

City	ID	Coordinates	Level of Seismicity	PGA (SLV) [g]	Climatic Zone	Heating Degree Days (HDD)
Città di Castello	H-C	43.4700° N, 12.2314° E	High (H)	0.30	Cold (C)	2347
Isola del Gran Sasso d’Italia	H-M	42.5056° N, 13.6592° E		0.29	Moderate (M)	2038
Catania	H-W	37.5013° N, 15.0742° E		0.29	Warm (W)	833
Vicenza	M-C	45.5455° N, 11.5354° E	Medium (M)	0.21	Cold (C)	2371
Serravalle Pistoiese	M-M	43.9059° N, 10.8330° E,		0.20	Moderate (M)	2010
Cirò Marina	M-W	39.368° N, 17.128° E		0.21	Warm (W)	845
Alessandria	L-C	44.9073° N, 8.6117° E	Low (L)	0.08	Cold (C)	2559
Genova	L-M	44.4056° N, 8.9463° E		0.10	Moderate (M)	1435
Agrigento	L-W	37.3089° N, 13.5858° E		0.08	Warm (W)	729

with the indication of the peak ground acceleration (PGA) for the life safety limit state (SLV), defined according to the Italian code (NTC-2018) [39] and the heating degree days (HDD) for each location. The latter is a measure used to estimate the heating energy demand, calculated by summing the number of degrees that the outdoor temperature falls below a certain base temperature on each day over a specified period. It is used to estimate heating energy requirements such as consumption patterns, performance, and costs. The climate and seismic maps of Italy with the indication of the selected locations is illustrated in Figure 3. Figure 4 provides the acceleration response spectrum and the hazard curve for each selected site. Even though the PGA of each location within the same seismic hazard level group is very similar, as anticipated, the corresponding hazard curves show some differences.

3.1. Preliminary Seismic Assessment

A preliminary seismic assessment of the structure was conducted through a nonlinear static procedure, using an inverted triangular load pattern and a control node located at the centre of mass on the top floor, as established in the Italian seismic code [39]. The target displacements of the structure for the collapse limit state (SLC) using the N2 method [40] were estimated and compared with the performance point displacements at which the structure attains its capacity for the SLC limit state, considered to be reached as soon as one of the following performance criteria is met:

• The shear force demand exceeds the shear capacity of one or more of the beam or column elements;
• The chord rotation of one or more of the plastic hinges in the beam, column, or wall elements exceeds the collapse limit state deformation limits;
• The shear deformation in one or more of the beam–column joints (BCJs) exceeds 0.02 rad.

The first two performance criteria are the ones prescribed by the Italian seismic code [39] for the seismic assessment of columns and beams. The last criterion, regarding the assessment of the BCJs, was adopted following experimental evidence [41], given that the one foreseen by the Italian code is very conservative. The pushover curves of the as-built structures, together with the performance points (SLC_C) and target displacements (SLC_D) of the structure for each site, are presented in Figure 5. These curves are expressed in the base shear coefficient, given by the ratio between the total base shear and the total mass of the structure.

Both directions present pushover curves with similar initial stiffness but different degradation due to the larger number of openings on the masonry infills in the longitudinal direction of the building. For both directions, the main structural weaknesses at the collapse limit state were identified as the shear failure of columns that were not designed to withstand seismic actions. Given the different demands of each set of sites, different target displacements are obtained; for the LH sites, the safety performance of the structure in its as-built condition is achieved in the X direction and almost achieved in the Y direction.

According to the Italian guidelines for the seismic risk classification of constructions [42], the safety index of the structure (SI-LS), defined as the ratio between the capacity peak ground acceleration (PGAC) and the demand peak ground acceleration (PGAD), was calculated and is summarised in

Table 3. Seismic safety index (SI-LS), in percentages, of the as-built structure as a function of the level of hazard and climate conditions (critical direction in bold).

Direction	Low Hazard			Medium Hazard			High Hazard
	L-C	L-M	L-W	M-C	M-M	M-W	H-C	H-M	H-W
X	135	115	140	55	58	54	39	40	39
Y	95	81	98	38	41	38	27	28	27

. PGAC was assumed to be the one that caused the collapse of the building, and it is calculated by scaling the code-based response spectrum to intersect the pushover curve on its capacity point for the life safety limit state (SLV). The capacity point is considered to be the one corresponding to the first element collapse within the building in terms of (i) the shear force demand exceeding the shear capacity of one or more of the beam or column elements, (ii) the chord rotation of one or more of the plastic hinges in the beam, column, or wall elements exceeds the life safety limit state deformation limits. PGAD is defined as the PGA of the code-based response spectrum for the location of interest.

The obtained SI-LS values reveal, as anticipated, variations in demand across the different sites, with direction Y emerging as the most critical. Considering the satisfactory performance of the as-built structure for the low-hazard sites, retrofitting was deemed unnecessary; hence, different retrofitting schemes were solely considered for sites with moderate and high hazard levels, as addressed in the next sections.

3.2. Seismic Retrofit Interventions

Given the structural deficiencies identified in the preliminary seismic assessment of the building, four different seismic retrofit measures (SRMs) were considered:

-

S₁: local strengthening with carbon FRP (CFRP);

-

S₂: global strengthening with concentric steel braces;

-

S₃: CFRP strengthening combined with concentric steel braces;

-

S₄: CFRP strengthening combined with viscous dampers.

Additionally, for all SRMs, a seismic gap between the URM infills and the RC frame was introduced, reducing the column-infill interaction and, thus, the shear forces acting on the columns. The design of the SRMs, conducted following the Italian building code (NTC) [39], was carried out to address the weaknesses and improve the performance of the as-built structure as much as possible, with the acknowledgment that the achieved performance was not always that required for new code-conforming buildings due to practical and cost considerations [43].

The seismic response of retrofitted structures is significantly influenced by the location and number of retrofit elements. In the case of S1, an iterative procedure was implemented wherein CFRP was initially applied to non-compliant elements, followed by successive assessments until all structural elements met safety standards. In S2, the strategic placement of braces was prioritized to minimise storey drifts. S3 modelling incorporated the methodologies of both S1 and S2. Additionally, for S4, the procedure from S1 was adopted while integrating viscous dampers at various locations within the school building. Further details on the design specifications for each retrofit alternative are available in [38].

Considering the varying seismic hazard levels across each site, the extent of retrofitting interventions implemented for the case-study building was adjusted accordingly. Due to the poor performance of the building under high seismic hazard conditions, each intervention was designed to provide the optimal contribution to the structure, meaning that it was not strictly designed for the same seismic demand. Consequently, it did not strictly achieve the same threshold in terms of capacity between the several alternatives.

Table 4. Retrofit components and corresponding amount per alternative for the considered hazard levels.

Retrofit Alternative		Units	Medium Hazard	High Hazard
S1	Column wrap	m2	245.1	352.6
	Column bar	m	2972	2972
	Beam wrap	m2	177.8	256.2
	Joint wrap	m2	138.2	186
S2	Braced bays	Nr	9	10
S3	Column wrap	m2	5.1	10.2
	Column bar	m	272.0	272.0
	Beam wrap	m2	11.7	31.22
	Joint wrap	m2	45.5	45.5
	Braced bays	Nr	10	10
S4	Column wrap	m2	-	10.2
	Column bar	m	-	456
	Beam wrap	m2	-	33.7
	Joint wrap	m2	53.4	53.4
	Viscous dampers	Nr	36	36

provides a summary of the details and quantities of the retrofit components for each retrofit alternative.

3.3. Energy Retrofit Interventions

Subsequently, with a view to improving energy performance, three different energy retrofit measures (ERMs) were considered:

-

E₁: roof insulation and installation of efficient LEDs and thermostatic valves on radiators;

-

E₂: intervention E₁ coupled with external wall insulation with expanded polystyrene (EPS) panels;

-

E₃: intervention E₂ coupled with installation of efficient windows, floor insulation, condensing boiler, lighting control system, and photovoltaic panels.

Each energy retrofitting intervention aims to simultaneously reduce heat losses to the external environment and enhance the energy efficiency of systems within the building. The level of intervention increases from E₁ to E₃, according to the Italian Ministerial Decree [44], which also corresponds to a higher degree of invasiveness.

Finally, the four seismic interventions were coupled with each energy intervention, leading to twelve possible combined retrofit alternatives. Each coupled intervention is designated by S_iE_i, where S_i and E_i correspond, respectively, to the considered seismic and energy retrofit schemes. More information on the design procedures and assumptions can be found in previous studies [11,45,46].

Table 5. Intervention cost (C₁) and duration of works (C₅) for each retrofit alternative per level of hazard.

Alt	Medium Hazard						High Hazard
	Cold		Moderate		Warm		Cold		Moderate		Warm
	C1 (EUR/m2)	C5 (Days)	C1  (EUR/m2)	C5 (Days)	C1  (EUR/m2)	C5 (Days)	C1  (EUR/m2)	C5 (Days)	C1  (EUR/m2)	C5 (Days)	C1  (EUR/m2)	C5 (Days)
S1E1	529	38	525	38	507	38	867	60	881	61	871	63
S1E2	589	38	568	38	543	38	927	60	925	61	908	63
S1E3	753	42	692	42	671	42	1091	64	1048	65	1036	67
S2E1	135	21	131	21	113	21	136	22	132	22	114	22
S2E2	196	23	175	23	150	23	196	24	175	24	150	24
S2E3	359	28	298	28	277	28	360	29	299	29	278	29
S3E1	172	23	168	23	150	23	180	37	213	42	195	42
S3E2	232	23	211	23	186	23	240	37	257	42	232	42
S3E3	396	27	335	27	314	27	404	41	380	46	360	46
S4E1	289	14	284	14	266	14	437	44	419	44	381	43
S4E2	349	27	328	27	303	27	499	44	463	44	418	43
S4E3	513	31	451	31	431	31	661	48	586	48	546	47

summarizes the intervention cost in EUR/m² and the duration of work in days corresponding to DVs C₁ and C₅, respectively. The intervention cost corresponds to the combined cost of the seismic and energy retrofit schemes for each alternative, considering efficiencies that can be gained simultaneously by implementing both retrofitting schemes. The total cost of installation of each retrofit alternative includes, in addition to the cost of the retrofit material, the removal of internal linings, partial demolition of the existing structure/infills, removal of debris, installation of the retrofit scheme, and restoration of infills and lining. More details on the energy retrofit costs can be found in [11].

3.4. Post-Intervention Seismic Assessment

The post-intervention assessment followed the same strategy outlined for the as-built structure (S₀). Nonlinear static analyses were performed for each retrofitted model, and the displacement demand and capacity (according to NTC [39]) were computed using the N2 method [40]. The results for the retrofitting scenarios are illustrated in Figure 6.

At first glance, it can be observed that the pushover curves for the same type of retrofit intervention between the different levels of hazard are very similar. This can be justified by the similarity of each retrofit intervention between the different sites, both in terms of their layout within the building structure and specific structural elements being retrofitted. When compared with the as-built scenario, all retrofitted models exhibit a decrease in the initial stiffness and lateral strength due to the seismic gap introduced between the infills and the surrounding frame. Moreover, all the retrofit interventions lead to an improvement in the structural performance of the building at the collapse limit state. Given the different design levels of the retrofitting interventions (dictated by the different seismic hazard levels), the displacement for which the structure, with the same type of intervention, reaches its capacity is distinct. Nevertheless, for most of the cases, the type of structural failure—usually a brittle failure on a column or beam as mentioned previously—that dictates the capacity performance is similar.

Table 6. Seismic safety index (SI-LS) of each structural intervention, S_i, for the different levels of hazard and climate conditions (critical direction in bold).

Alt.	Dir.	Medium Hazard			High Hazard
		M-C	M-M	M-W	H-C	H-M	H-W
S1	X	120%	123%	95%	120%	108%	99%
	Y	134%	134%	105%	120%	107%	109%
S2	X	92%	95%	73%	63%	55%	50%
	Y	113%	115%	88%	85%	76%	70%
S3	X	122%	125%	96%	82%	73%	68%
	Y	111%	113%	99%	87%	77%	76%
S4	X	125%	128%	97%	117%	105%	96%
	Y	127%	130%	99%	155%	137%	129%

summarizes the SI-LS values obtained for the retrofitted models in each hazard site. Considering the most critical direction, the effectiveness ranking of the retrofit measures is S₄ > S₁ > S₃ > S₂ and S₁ > S₄ > S₃ > S₂ for the medium- and high-hazard sites at the LSLS. Comparing the results of Table 3 with Table 6, an overall improvement is observed in the performance of the retrofitted structures with respect to the as-built structure.

After conducting the initial seismic assessment of the structure in its retrofit conditions, the estimation of all the DVs outlined in Section 2 can be carried out following the suggestions provided in [11]. The ones for which the use of simplified procedures is proposed (C₂, C₃, and C₄) are fully described in the subsequent subsections.

3.4.1. Annual Probability of Failure

The estimation of APF was assessed through different approaches, as mentioned in Section 2. To apply the detailed methodology, firstly, the characterisation of the seismic hazard at the selected site for the case-study building was carried out through probabilistic seismic hazard analysis (PSHA) using OpenQuake [47]. Then, a selection of 20 pairs of suitable hazard-consistent ground motion records was carried out for each site. The selected IM (AvgSA) is defined as the geometric mean of the pseudo-spectral acceleration in a structure-specific range of periods depending on the first-mode periods of the case studies.

Table 7. Model parameters of each retrofitted building.

Hazard Level	Model	Fundamental Period [s]		M1* [%]	TGM	0.2TGM–1.5TGM
		Longitudinal	Transverse
Medium hazard	S0	0.235	0.267	38.0	0.25	0.05–0.38
	S1	0.561	0.454	39.3	0.50	0.10–0.76
	S2	0.408	0.379	47.1	0.39	0.08–0.59
	S3	0.405	0.379	46.1	0.39	0.08–0.59
	S4	0.779	0.565	41.5	0.66	0.13–1.00
High hazard	S0	0.235	0.267	38.0	0.25	0.05–0.38
	S1	0.571	0.454	40.4	0.44	0.09–0.67
	S2	0.407	0.373	44.0	0.39	0.08–0.60
	S3	0.405	0.365	43.9	0.38	0.08–0.60
	S4	0.785	0.563	41.4	0.59	0.12–0.90

summarizes some dynamic elastic properties of the analysed models, such as the fundamental period in both directions (first mode in bold), the participation mass of the first mode of vibration (M₁^*), the geometric mean (T_GM), and the period range used in this study (0.2T_GM–1.5T_GM). MSAs were conducted, and a set of selected EDPs—absolute Peak Floor Acceleration (PFA), Peak Story Drift (PSD), and Peak Floor Velocity (PFV)—were recorded and later used as input to perform the comprehensive performance-based loss assessment (PEER-PBEE methodology). Additionally, the MSA outcomes were also used to determine the collapse fragility parameters.

Following the simplified methodology, a set of 200 ground motions covering a wide range of magnitudes were selected from the NGA-West2 ground motion database [48] and converted into the ADRS format to apply the CSM [28] outlined in Section 2.2. The intersection of the capacity curve of the SDoF system of each model with the response spectrum of the selected ground motions results in a cloud of PPs for each retrofitted model. The cloud PPs were filtered into non-collapse (NoC) and collapse (C) data by comparing the obtained PPs with the displacements at which the collapse of the structure is assumed to occur (consistently assumed as those considered for the preliminary assessment and MSA). Lastly, the regression parameters to establish the conditional probability of exceedance were estimated based on the modified cloud analysis procedure outlined in Jalayer et al. (2017) [29]. A slight modification of the CB-CSM procedure was needed to assess the structural performance of S₄ to account for the supplemental damping introduced by the viscous dampers. A supplemental damping ratio of 25%, in addition to the initial 5% damping, was considered in the time history analyses and within the CSM procedure as suggested in [38].

The collapse fragility curves computed through both approaches and accounting for the epistemic uncertainties [36,49,50] for the medium- and high-hazard sites are displayed in Figure 7.

Considering the medium hazard sites, the differences in the median collapse intensities obtained through the detailed approach are likely justified by the different hazard curves observed in Figure 4b. In contrast, the median collapse intensities for the high-hazard sites are very similar. Comparing the simplified with the detailed approach, a closer approximation of the median intensity values is achieved for the medium hazard, with a difference of about ±15% (excluding S₀ and S₄). This difference increases up to ±80% when considering the high-hazard results. For the S₄ alternative, the simplified approach results in extremely conservative results (an average difference of around 43% and 136% for the medium- and high-hazard sites).

Subsequently, the APF values were obtained, integrating the collapse fragility curve with the hazard curve of each site. Figure 8 plots the APF values as a function of the employed methodology (simplified (S) and detailed (D)) for both seismic hazard levels—medium (Figure 8a) and high (Figure 8b).

In terms of retrofitting approaches, for medium hazard, solution S₄ has the better seismic performance, followed by S₁, S₂, and S₃, with identical performance. For the high hazard, solutions S₂ and S₄ have the worst and better seismic performance, whereas the performance of S₁ and S₃ oscillates between the second and third positions.

For the medium-hazard sites, overall, both approaches lead to very similar APF results, except for solution S₄, for which the simplified APF estimates result lower than the detailed ones. On the other hand, for high hazard, regardless of the retrofitting option, the APF results can be considered in two groups, depending on the adopted approach. A general underestimation of the simplified APF values is observed with respect to the detailed ones. Among other possible reasons, it can be related to the fact that the adopted CSM procedure is the one from ATC-40 [28], which has been shown to underestimate the displacement demand [51,52], resulting in a lower number of collapses. Still, the differences are never high enough to change the corresponding ranking (when solely based on the APF values) of the different retrofit alternatives.

3.4.2. Expected Annual Losses (EAL) and Expected Annual Environmental Impacts (EAEI)

On the detailed approach side, the PEER-PBEE methodology [53] was employed to estimate the EAL and EAEI of each retrofitted model. By handling the EDP results obtained in the MSA and by adopting an inventory of damageable components in the building, their potential damage states, and expected repair cost and EI consequences, a detailed loss assessment was carried out in PACT (FEMA P-58). The presence of the ERMs was accounted for at this stage in terms of additional repair consequences to specific non-structural components due to their significant influence on the loss assessment. Regarding the simplified approach, the procedure outlined in Section 2.2 was carried out to obtain the seismic risk classification of each retrofitted structure using Sismabonus [26]. The SI-LS index, defined as the ratio between the capacity peak ground acceleration (PGA_C) and the demand peak ground acceleration (PGA_D) and used previously to compare the seismic performance of the retrofitted structures, is summarised in Table 3 and Table 6 for the X and Y directions of the as-built and retrofitted configurations, respectively. The SI-LS index and corresponding risk classification for the critical direction of the as-built and each retrofitted model are summarised in

Table 8. Sismabonus results.

Alt.	Param.	Medium Hazard									High Hazard
		M-C			M-M			M-W			H-C			H-M			H-W
		%	Class		%	Class		%	Class		%	Class		%	Class		%	Class
S1	SI-LS	120	A+	A+	123	A+	A+	95	A	A	120	A+	A	108	A+	A	99	A	A
	EAL	0.46	A+		0.48	A+		0.52	A		0.61	A		0.61	A		0.64	A
S2	SI-LS	92	A	A	95	A	A	73	B	B	63	B	B	55	C	C	50	C	C
	EAL	0.49	A+		0.51	A		0.59	A		0.80	A		0.82	A		0.60	A
S3	SI-LS	111	A+	A+	113	A+	A+	96	A	A	82	A	A	73	B	B	68	B	B
	EAL	0.46	A+		0.46	A+		0.50	A		0.63	A		0.67	A		0.65	A
S4	SI-LS	125	A+	A+	128	A+	A+	97	A	A	117	A+	A	105	A+	A	96	A	A
	EAL	0.42	A+		0.43	A+		0.47	A+		0.52	A		0.54	A		0.52	A

. The expected annual environmental impacts (EAEI) are obtained employing the detailed methodology within the loss assessment procedure through PACT. As such, when using the simplified procedure (Sismabonus), which does not enable the direct quantification of the EAEI, the results from the detailed methodology were used to fit a linear regression model between EAL and EAEI. The regression is then used to estimate, in a simplified manner, the EAEI straight from EAL [54].

The EALs of each retrofitted model, obtained through the detailed and simplified methodologies for both seismic hazard levels, are summarised in Figure 9. For all sites considered, the simplified methodology leads to greater values of EAL, when compared with those of the detailed methodology. This overestimation can be attributed to the simplifications foreseen by the procedure to make it more accessible to engineers, such as the fixed percentage of repair costs for each damage state, regardless of the building typology and their structural response [23,55]. For the high-hazard sites (H), S₂ presents the highest EAL, followed by S₃, S₁, and, finally, S₄, regardless of the approach employed and site considered. For the medium-hazard sites, the EAL values from the detailed approach exhibit the same order of magnitude (S₂ > S₃ > S₁ > S₄), while the results obtained with the simplified approach exhibit different orders of magnitude as a function of the site. The EAEI values, presented in Figure 10, are proportional to the EAL values.

3.5. Post-Intervention Energy Assessment

The energy performance of the as-built and energy-retrofitted buildings was assessed with EDILCLIMA [56]. The information regarding the energy modelling and all the assumptions made are detailed in [11]. The energy performance was assessed through different parameters, including the primary energy performance (PEC), equivalent CO₂ emissions (Eq. CO₂), annual energy costs (AEC), and Italian energy class rating. The results obtained for the as-built and energy-retrofitted buildings are summarized in

Table 9. Energy performance assessment results.

Alt.	PEC (kWh/m2)	Eq. CO2 (kgCO2e)	AEC (EUR)	Energy Class
E0	309	76,651	12,718	E
E1	221.76 (−28%)	52,476 (−32%)	8765 (−31%)	D
E2	166.63 (−46%)	40,716 (−47%)	7121 (−44%)	C
E3	64.92 (−79%)	14,982 (−80%)	3109 (−76%)	A2

Note: In brackets, the reduction (%) of PEC, Eq. CO₂, and AEC for each energy-retrofitting intervention, with respect to the as-built condition.

. As anticipated, all retrofit schemes resulted in improvements to the energy performance of the structure. Among them, E₃ demonstrated the highest performance, followed by E₂ and E₁ in a progressively incremental manner. This observation underlines the challenge of identifying the optimal energy intervention level solely through direct comparison of these variables, highlighting the necessity for additional criteria in the evaluation process. Indeed, the first level of retrofit (E₁) results in a 28% reduction in the annual PEC, while E₂ and E₃ retrofit schemes exhibit reductions of about 50% and 80%, respectively. Similar trends are observed for Eq. CO₂ and AEC.

4. Discussion

4.1. Decision Variable Assemblance

In this section, all the DVs for each combined retrofitted scheme and each site are quantified. The methods that were used to quantify the DVs, together with the assumptions made and the weight vectors assumed, are detailed in [11].

The installation cost (C₁) and duration of works (C₅) of the combined retrofit alternatives are summarized in Table 5. The expected annual cost (C₂) encompasses the EAL, the AEC, and the maintenance cost of the retrofit components. The EAL and the AEC were determined from the seismic and energy performance analyses carried out in the previous sections. The cost of the structural maintenance over the lifetime of the structure (75 years) was obtained considering the interventions outlined by Caterino et al. [9] and scaling them based on the quantity of materials used. The expected LCEI (C₃) includes the installation EI of the retrofit alternative, the EAEI of the retrofitted structure, and the total maintenance EI of the alternative over the expected service life. The EIs associated with the installation and maintenance of the retrofit alternatives were estimated using the EEIOLCA procedure (described in [46]), while the EAEI values were obtained from the loss assessment (Section 3.4.2). The values of the annual probability of failure (C₄) were determined in Section 3.4.1. The remaining DVs—architectural impact (C₆), need for specialized labour/design knowledge (C₇), and required interventions at the foundations (C₈)—were set according to [11].

The DVs directly linked to the seismic performance of the structure, namely C₂, C₃, and C₄, are the only DVs whose quantifications depend on the employed methodology. The final values for such DVs are detailed in

Table 10. DVs C₂, C₃, and C₄ for the medium-hazard sites.

	Detailed									Simplified
	C			M			W			C			M			W
Alt	C2	C3	C4	C2	C3	C4	C2	C3	C4	C2	C3	C4	C2	C3	C4	C2	C3	C4
S1E1	9.5	25.4	1.22	10.4	43.2	0.36	13.5	52.7	1.30	15.3	29.2	1.19	18.0	48.2	0.25	18.9	56.3	1.38
S1E2	9.5	21.6	1.28	9.6	35.3	0.33	12.5	42.5	1.31	15.2	25.3	1.19	17.4	40.4	0.25	18.0	46.1	1.38
S1E3	8.8	14.8	1.20	7.4	18.0	0.31	9.9	21.4	1.28	14.8	18.7	1.19	15.6	23.4	0.25	15.7	25.2	1.38
S2E1	9.0	23.5	1.14	9.5	41.1	0.26	14.2	51.8	1.95	16.8	28.9	1.33	17.1	46.2	0.35	18.8	54.8	1.49
S2E2	9.3	19.9	1.40	8.7	33.2	0.19	13.5	41.7	2.08	16.8	25.0	1.33	16.4	38.4	0.35	17.9	44.6	1.49
S2E3	8.6	13.1	1.39	6.7	16.1	0.30	11.1	20.8	2.18	16.5	18.5	1.33	14.6	21.4	0.35	15.6	23.8	1.49
S3E1	8.7	22.4	0.93	9.7	40.3	0.28	12.5	49.6	0.96	15.3	26.9	1.37	17.2	45.4	0.32	18.2	53.4	1.56
S3E2	8.6	18.4	0.95	9.2	32.6	0.37	11.4	39.3	0.92	15.2	23.0	1.37	16.6	37.6	0.32	17.2	43.3	1.56
S3E3	8.0	11.7	0.96	6.9	15.3	0.32	8.9	18.3	0.98	14.9	16.5	1.37	14.8	20.6	0.32	14.9	22.4	1.56
S4E1	8.6	21.8	0.53	10.7	40.5	0.30	12.3	49.0	0.46	16.2	26.8	0.11	17.9	45.2	0.006	18.8	53.3	0.17
S4E2	8.5	17.9	0.54	9.9	32.6	0.27	11.3	38.7	0.49	16.1	22.9	0.11	17.3	37.4	0.006	17.9	43.1	0.17
S4E3	7.8	11.1	0.54	7.9	15.4	0.31	8.5	17.5	0.44	15.8	16.4	0.11	15.4	20.4	0.006	15.6	22.2	0.17

Note: The units of C₂ and C₃ are, respectively, EUR and kgCO₂e. C₄ is unitless (×10⁻³).

and

Table 11. DVs C₂, C₃, and C₄ for the high-hazard sites.

	Detailed									Simplified
	C			M			W			C			M			W
Alt	C2	C3	C4	C2	C3	C4	C2	C3	C4	C2	C3	C4	C2	C3	C4	C2	C3	C4
S1E1	12.9	28.4	1.01	16.2	40.4	1.66	18.8	47.5	2.67	19.7	33.0	0.91	22.7	52.3	1.42	23.7	60.3	1.20
S1E2	12.9	24.5	1.08	14.3	23.4	1.87	16.5	26.6	2.90	19.6	29.1	0.91	22.1	44.5	1.42	22.8	50.2	1.20
S1E3	12.3	17.9	1.12	13.4	42.7	1.81	16.9	52.5	2.94	19.3	22.6	0.91	20.4	27.5	1.42	20.6	29.4	1.20
S2E1	13.1	25.0	2.86	18.8	38.7	4.55	19.7	44.6	4.58	20.3	30.1	1.36	22.5	48.9	2.05	22.4	56.2	1.81
S2E2	13.1	21.2	2.93	16.6	21.5	4.70	17.1	23.5	4.73	20.3	26.3	1.36	22.0	41.1	2.05	21.5	46.1	1.81
S2E3	13.3	15.1	3.30	22.3	47.2	4.37	24.2	55.9	4.69	20.2	19.9	1.36	20.5	24.3	2.05	19.5	25.3	1.81
S3E1	13.6	23.9	1.66	17.4	36.3	2.46	17.8	41.7	2.05	19.9	28.5	0.65	22.8	47.7	1.00	23.0	55.2	0.85
S3E2	13.5	20.0	1.67	15.5	19.3	2.66	15.4	20.8	2.30	19.8	24.6	0.65	22.2	40.0	1.00	22.1	45.1	0.85
S3E3	12.8	13.3	1.62	22.8	45.6	2.74	23.3	53.3	2.24	19.6	18.2	0.65	20.6	23.1	1.00	19.9	24.3	0.85
S4E1	13.7	22.6	0.43	16.3	34.2	0.79	16.9	39.8	0.52	21.2	27.6	0.027	23.8	46.6	0.06	24.8	54.7	0.03
S4E2	13.6	18.7	0.40	14.2	19.2	0.74	14.2	20.8	0.57	21.1	23.7	0.027	23.2	38.9	0.06	23.9	44.6	0.03
S4E3	13.4	14.4	0.59	2.6	1.5	0.68	2.4	1.4	0.54	20.7	19.4	0.027	21.4	24.0	0.06	21.6	25.9	0.03

Note: The units of C₂ and C₃ are, respectively, EUR and kgCO₂e. C₄ is unitless (×10⁻³).

for the medium- and high-hazard sites, respectively. The remaining DVs (C₁, C₆, C₇, and C₈), which are independent of the employed approach, are outlined in

Table 12. DVs C₆ and C₈ for the medium- and high-hazard sites.

Alt.	C6 (-)	C7 (-)	C8 (-)
			Medium Hazard			High Hazard
			M-C	M-M	M-W	H-C	H-M	H-W
S1E1	0.023	0.084	5.9	6.2	7.0	6.1	5.7	5.7
S1E2	0.023	0.084	5.9	6.2	7.0	6.1	5.7	5.7
S1E3	0.023	0.084	5.9	6.2	7.0	6.1	5.7	5.7
S2E1	0.056	0.013	10.9	11.3	12.5	16.5	16.5	16.5
S2E2	0.056	0.013	10.9	11.3	12.5	16.5	16.5	16.5
S2E3	0.056	0.013	10.9	11.3	12.5	16.5	16.5	16.5
S3E1	0.093	0.084	12.8	13.4	13.0	16.6	16.6	16.6
S3E2	0.093	0.084	12.8	13.4	13.0	16.6	16.6	16.6
S3E3	0.093	0.084	12.8	13.4	13.0	16.6	16.6	16.6
S4E1	0.162	0.151	3.3	3.5	3.9	5.1	4.8	4.8
S4E2	0.162	0.151	3.3	3.5	3.9	5.1	4.8	4.8
S4E3	0.162	0.151	3.3	3.5	3.9	5.1	4.8	4.8

.

4.2. Ranking of the Retrofit Alternatives

The DVs quantified in the previous sections were then used as input for the MCDM framework. The position of each alternative in the ranking is given by the relative closeness, which is a measure used to assess the proximity of each alternative to an ideal solution or reference point and is often expressed as a value between 0 and 1. A relative closeness value of 1 indicates that the alternative is the most desirable or closest to the ideal solution, while a value closer to 0 suggests lower desirability or greater distance from the ideal solution. This measure allows decision-makers to quantitatively evaluate and rank different alternatives, facilitating the selection of the most favourable option based on the specified criteria and their respective importance weights. According to the number of retrofit alternatives investigated herein, those occupying positions 1 and 12 are regarded as the most and least preferred options, respectively. The preferential rankings obtained for each approach and hazard level are presented in

Table 13. Classification ranking of the retrofit alternatives as a function of hazard level, employed approach, and climate site.

Rank	Medium Hazard						High Hazard
	Detailed			Simplified			Detailed			Simplified
	C	M	W	C	M	W	C	M	W	C	M	W
1	S3E3	S2E3	S3E2	S4E1	S4E1	S4E1	S3E3	S4E3	S4E2	S4E2	S4E2	S4E2
2	S4E3	S2E2	S4E1	S4E2	S4E2	S4E2	S4E3	S4E2	S4E1	S3E3	S4E3	S4E1
3	S4E2	S3E3	S2E1	S4E3	S4E3	S2E1	S4E2	S3E3	S4E3	S4E3	S4E1	S4E3
4	S3E2	S2E1	S3E1	S2E2	S2E2	S2E2	S3E2	S4E1	S3E2	S3E2	S3E3	S3E2
5	S4E1	S3E2	S4E2	S2E3	S2E1	S4E3	S3E1	S3E2	S3E3	S4E1	S3E2	S3E1
6	S3E1	S4E3	S3E3	S2E1	S2E3	S3E1	S4E1	S2E3	S3E1	S3E1	S3E1	S3E3
7	S2E3	S3E1	S2E2	S3E2	S3E2	S3E2	S2E3	S3E1	S2E2	S2E3	S2E3	S2E2
8	S2E2	S4E1	S2E3	S3E1	S3E3	S2E3	S2E2	S2E2	S2E1	S2E2	S2E2	S2E1
9	S2E1	S4E2	S4E3	S3E3	S3E1	S3E3	S2E1	S2E1	S2E3	S2E1	S2E1	S2E3
10	S1E3	S1E3	S1E3	S1E3	S1E3	S1E1	S1E3	S1E3	S1E2	S1E3	S1E3	S1E2
11	S1E2	S1E2	S1E1	S1E2	S1E2	S1E2	S1E1	S1E1	S1E1	S1E2	S1E2	S1E1
12	S1E1	S1E1	S1E2	S1E1	S1E1	S1E3	S1E2	S1E2	S1E3	S1E1	S1E1	S1E3

.

It is firstly seen that the classification ranking of the retrofit alternatives changes with the seismic hazard level. For the high-hazard sites, a clear trend is observed; the rankings of the alternatives tend to be grouped by the structural retrofit scheme option, with S₄ being the most preferred option, followed by S₃, S₂, and, lastly, S₁. This trend indicates that the seismic retrofit scheme has a more significant effect on the overall ranking of an alternative than the energy retrofit scheme, as was also highlighted in [11]. Nevertheless, inside each structural retrofit group, the energy retrofitting tends to be ranked according to the energy needs of the site, i.e., the preferential position shifts as a function of the climate conditions, favouring E₃ under cold climate and E₁ under warm climate. In contrast, for medium seismic hazard sites, the ranking is equally affected by both types of retrofit interventions. S₃ and S₄ are generally preferred as the structural retrofit, except for the moderate climate site. In fact, due to similar performance values of APF, EAL, and EAEI, the MCDM framework struggles to discern distinct benefits among alternatives.

Comparing the results obtained through both detailed and simplified approaches, for the medium-hazard sites, the simplified one aligns rankings based on the structural retrofit scheme, with S₄ being the favoured option, followed by S₂, S₃, and S₁. Overall, the main difference between the detailed and simplified approaches is the ranking positions of alternatives S₂ and S₃, which is in line with the trends highlighted by the collapse assessment results. Considering the high-hazard sites, even though the exact DV values estimated by the different approaches can be relatively different, at times, the final ranking of the different retrofit alternatives is practically the same, with only a few exceptions observed. For both detailed and simplified approaches, regardless of the hazard level, alternative S₁ is consistently ranked as the least preferred alternative, mainly due to its high installation costs, which are two to six times higher than the other alternatives. This happens because S₁ requires many CFRP bars to control the structural drifts, which are costly and labour-intensive to install.

Since the ranking is controlled by the relative closeness value obtained for each retrofit alternative, the way it changes with the level of detail of the adopted approach and the hazard level is also investigated. This can also enable more comprehensive conclusions on the reliability of the simplified methodology, regardless of some slight changes noted in the classification rankings of the retrofit alternatives. Accordingly, Figure 11 shows the relative closeness values of each alternative. In these subplots, the retrofitting alternatives along the X-axis are sorted according to the detailed approach ranking.

Regarding the medium-hazard sites, a general mismatch between the different approaches is observed, regardless of climate conditions. A closer scrutinization of these results shows a suitable alignment between the alternatives with S₁ and S₄ as structural retrofits for the cold and warm climate sites, as previously pointed out. Considering the high-hazard sites, all the alternatives demonstrate a strong alignment across all sites, with a slight variation in the relative closeness values between the detailed and simplified approaches being observed for S4 in moderate and warm climates. However, this discrepancy does not impact the overall classification.

According to the MCDM framework, the solution ranked first is considered the optimal solution. However, given the closely similar relative closeness values among certain alternatives, a group of most preferable alternatives may be identified instead of solely focusing on the top-ranked solution. To do so, the 25th and 75th percentiles of the relative closeness values were quantified for both detailed and simplified approaches, as shown in Figure 11. In this way, three groups of alternatives are obtained, allowing one to identify the less (below the 25th percentile), relatively (between the 25th and 75th percentile), and most (above the 75th percentile) preferable alternatives.

Table 14. Less, medium, and most preferable alternatives as a function of the location and employed methodology.

Medium Hazard						High Hazard
Detailed			Simplified			Detailed			Simplified
C	M	W	C	M	W	C	M	W	C	M	W
S1E1	S1E1	S1E1	S1E1	S1E1	S1E1	S1E1	S1E1	S1E1	S1E1	S1E1	S1E1
S1E2	S1E2	S1E2	S1E2	S1E2	S1E2	S1E2	S1E2	S1E2	S1E2	S1E2	S1E2
S1E3	S1E3	S1E3	S1E3	S1E3	S1E3	S1E3	S1E3	S1E3	S1E3	S1E3	S1E3
S2E1	S2E1	S2E1	S2E1	S2E1	S2E1	S2E1	S2E1	S2E1	S2E1	S2E1	S2E1
S2E2	S2E2	S2E2	S2E2	S2E2	S2E2	S2E2	S2E2	S2E2	S2E2	S2E2	S2E2
S2E3	S2E3	S2E3	S2E3	S2E3	S2E3	S2E3	S2E3	S2E3	S2E3	S2E3	S2E3
S3E1	S3E1	S3E1	S3E1	S3E1	S3E1	S3E1	S3E1	S3E1	S3E1	S3E1	S3E1
S3E2	S3E2	S3E2	S3E2	S3E2	S3E2	S3E2	S3E2	S3E2	S3E2	S3E2	S3E2
S3E3	S3E3	S3E3	S3E3	S3E3	S3E3	S3E3	S3E3	S3E3	S3E3	S3E3	S3E3
S4E1	S4E1	S4E1	S4E1	S4E1	S4E1	S4E1	S4E1	S4E1	S4E1	S4E1	S4E1
S4E2	S4E2	S4E2	S4E2	S4E2	S4E2	S4E2	S4E2	S4E2	S4E2	S4E2	S4E2
S4E3	S4E3	S4E3	S4E3	S4E3	S4E3	S4E3	S4E3	S4E3	S4E3	S4E3	S4E3

provides the less (red), relatively (yellow), and most (green) preferable alternatives as a function of the hazard level and the employed approach.

The results from Table 14 are aligned with the previous remarks. The optimal group of alternatives varies depending on the climate levels. While cold climate sites lead to a preference for the most demanding energy retrofitting and the structural retrofit with the best structural performance (in accordance with Section 3.4), warm climate sites show only a preference for the structural retrofit with the best performance. Regardless of the employed methodology, the solutions with S₁ as the structural retrofit are always the least preferred options. The shaded area between the 25th and 75th ranking percentiles from each approach (Figure 11) supports the interpretation of the differences between the application of both approaches. While minimal variations are noted in high-hazard locations among the alternatives in each preference group, greater disparities are evident in medium-hazard locations, mostly for the moderate climate, where the results obtained with the simplified approach are different from the ones obtained with the detailed counterpart. This is likely due to the difference in the hazard curves, as observed in Figure 4, which shows how the M-M hazard curve is slightly different from the other medium-hazard locations.

5. Conclusions

This study assessed the influence of different seismic hazard levels and climate conditions on the preferential ranking of combined energy and seismic retrofitting interventions through the employment of a multi-criteria decision-making (MCDM) framework, aiming at higher sustainability of existing buildings. Additionally, the accuracy of employing a simplified approach in the estimation of decision variables related to the seismic performance of a building within the MCDM framework, namely the expected annual losses (EAL), the annual probability of failure (APF), and expected annual environmental impact (EAEI), was also assessed.

To this end, a case-study school building was selected, and four seismic retrofitting solutions, combined with three energy-based interventions, were identified. The case-study building was assumed to be in six different sites in Italy, characterised by two levels of seismic hazard (moderate (M) and high (H)) and with different climatic conditions, namely cold (C), moderate (M), and warm (W). The performance of the building, in its as-built and retrofitted conditions, was then analysed considering the simplified approach and compared with a more detailed one. Finally, an MCDM framework was employed to obtain the overall ranking of the different alternatives and identify the optimal combination of retrofitting schemes, again using both detailed and simplified approaches.

The preliminary assessment of the structural retrofit models resulted in an effectiveness ranking of the retrofit alternatives as S₄ > S₁ > S₃ > S₂ and S₁ > S₄ > S₃ > S₂ for the medium and high hazard sites, respectively, for the Life Safety limit state. Regarding the APF values, notable differences were obtained. While the approaches yielded similar results for medium-hazard levels, for the high-hazard level, the simplified approach produces lower APF values than the detailed one in high-hazard sites, which needs to be considered as a trade-off for computational efficiency. Regarding the EAL and EAEI, the simplified approach tends to overestimate EAL with respect to the detailed one. Such overestimation can be attributed to the simplified nature of the Sismabonus procedure, which needed to be incorporated into the current Italian seismic risk guidelines in order to enhance its usability by practitioners. Nevertheless, the order of magnitude is kept the same between the different methodologies.

When employing the MCDM framework to obtain the overall ranking of the different alternatives and identify the optimal combination of retrofitting schemes combined with the different detailed and simplified approaches, similar relative closeness values among several alternatives pointed towards the identification of a group of preferable alternatives, instead of the most preferable one. By quantifying the 25th and 75th percentiles of the relative closeness (RC) values for both detailed and simplified approaches, three distinct groups of alternatives were identified: less preferable (RC value below the 25th percentile), relatively preferable (RC value between the 25th and the 75th percentile), and most preferable (RC value above the 75th percentile). When the relative closeness values of different alternatives are very similar, instead of selecting the optimal solution, this approach allows decision-makers to pick the solution to adopt from a group of alternatives with similar relative performance, depending on specific needs and objectives.

Globally, the results showed distinct classifications for medium- and high-seismic hazard sites. For high-hazard ones, the influence of the seismic hazard is highly present since rankings tend to be grouped by the structural retrofit scheme, and, in most cases, the most severe energy retrofit alternative was generally preferred over the other alternatives. In medium-seismic hazard sites, rankings are equally affected by both types of retrofit intervention. For both levels of hazard, S₁ is consistently the least preferable structural retrofit alternative. Even though its seismic performance is relatively better than alternatives S₂ and S₃, its high cost tends to penalize it on the MCDM framework. Comparing both approaches, results show that in high-hazard areas, rankings stay consistent, while in medium-hazard sites, detailed and simplified approaches yield different results. In the detailed one, both energy and seismic retrofit play crucial roles, leading to varied rankings, where the simplified method aligns rankings based on the structural retrofit scheme. Despite similar performance values (APF, EAL, and EAEI), the MCDM struggles to point clear preferable alternatives. Nevertheless, the results obtained through the simplified approach are promising, given that the differences observed in the optimal combination ranking, compared to the detailed counterpart, are mainly justified by the relative distance between different alternatives that affect the mathematical process of the MCDM procedure. In fact, although further investigations will support more general conclusions on the reliability of the simplified, practice-oriented approach, from an overall perspective, the employment of the detailed and simplified approaches led to similar results in the obtained ranking, showing the benefits of employing tools that require less time and computational demand.