Applied Science, Faculty of
Non UBC
Civil Engineering, Department of
DSpace
Sustainability 17 (3): 1200 (2025)
Gallegos, Marco F.
Araya-Letelier, Gerardo
Lopez-Garcia, Diego
Molina Hutt, Carlos
This study quantitatively assesses the impact of seismic design strategies on the performance of reinforced concrete (RC) dual wall–frame office buildings by comparing direct and indirect economic losses and downtime in life-cycle terms. A high-rise archetype building located in Santiago, Chile, on stiff soil was evaluated as a benchmark case study. Three design strategies to potentially enhance the seismic performance of a building designed conventionally were explored: (i) incorporating fluid viscous dampers (FVDs) in the lateral load-resisting structure; (ii) replacing conventional non-structural components with enhanced ones (ENCs); and (iii) a combination of the previous two strategies. First, probabilistic structural responses were estimated through incremental dynamic analyses using three-dimensional nonlinear models of the archetypes subjected to a set of hazard-consistent Chilean ground motions. Second, FEMA P-58 time-based assessment was conducted to estimate expected annual losses (EALs) for economic loss estimation. Finally, for downtime assessment, a novel probabilistic framework, built on the FEMA P-58 methodology and the REDi guidelines, was employed to estimate the expected annual downtimes (EADs) to achieve specific target recovery states, such as reoccupancy (RO) and functional recovery (FR). Results revealed that seismically enhancing RC dual wall–frame buildings with FVDs significantly improves resilience by reducing loss and downtime. For example, the enhanced building with FVDs achieved an EAL of 0.093% and EAL of 8.6 days for FR, compared to the archetype base building without design improvements, which exhibited an EAL of 0.125% and an EAD of 9.5 days for FR. In contrast, the impact of ENCs alone was minor, compared to the effect of FVDs, with an EAL of 0.106% and an EAD of 9.1 days for FR. With this detailed recovery modeling, probabilistic methods, and a focus on intermediate recovery states, this framework represents a significant advancement in resilience-based seismic design and recovery planning.
Academic Editor: M. AminHariri-ArdebiliReceived: 22 November 2024Revised: 25 January 2025Accepted: 31 January 2025Published: 2 February 2025Citation: Gallegos, M.F.; Araya-Letelier, G.; Lopez-Garcia, D.; MolinaHutt, C. Loss and DowntimeAssessment of RC Dual Wall–FrameOffice Buildings Toward ResilientSeismic Performance. Sustainability2025, 17, 1200. https://doi.org/10.3390/su17031200Copyright: © 2025 by the authors.Licensee MDPI, Basel, Switzerland.This article is an open access articledistributed under the terms andconditions of the Creative CommonsAttribution (CC BY) license(https://creativecommons.org/licenses/by/4.0/).ArticleLoss and Downtime Assessment of RC Dual Wall–Frame OfficeBuildings Toward Resilient Seismic PerformanceMarco F. Gallegos 1,2 , Gerardo Araya-Letelier 3,4,* , Diego Lopez-Garcia 2,5,* and Carlos Molina Hutt 61 Department of Civil & Environmental Engineering, Facultad de Ingenieria, Universidad del Bio-Bio,Concepcion 4051381, Chile; mfgallegos@ubiobio.cl2 Department of Structural & Geotechnical Engineering, Pontificia Universidad Catolica de Chile,Santiago 7820436, Chile3 School of Civil Construction, Faculty of Engineering, Pontificia Universidad Catolica de Chile,Santiago 8320165, Chile4 Concrete Innovation Hub UC (CIHUC), Pontificia Universidad Catolica de Chile, Santiago 8320165, Chile5 Research Center for Integrated Disaster Risk Management (CIGIDEN) ANID FONDAP 1523A0009,Santiago 7820436, Chile6 Department of Civil Engineering, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada;carlos.molinahutt@civil.ubc.ca* Correspondence: gerardo.araya@uc.cl (G.A.-L.); dlg@uc.cl (D.L.-G.)Abstract: This study quantitatively assesses the impact of seismic design strategies onthe performance of reinforced concrete (RC) dual wall–frame office buildings by compar-ing direct and indirect economic losses and downtime in life-cycle terms. A high-risearchetype building located in Santiago, Chile, on stiff soil was evaluated as a benchmarkcase study. Three design strategies to potentially enhance the seismic performance of abuilding designed conventionally were explored: (i) incorporating fluid viscous dampers(FVDs) in the lateral load-resisting structure; (ii) replacing conventional non-structuralcomponents with enhanced ones (ENCs); and (iii) a combination of the previous two strate-gies. First, probabilistic structural responses were estimated through incremental dynamicanalyses using three-dimensional nonlinear models of the archetypes subjected to a set ofhazard-consistent Chilean ground motions. Second, FEMA P-58 time-based assessmentwas conducted to estimate expected annual losses (EALs) for economic loss estimation.Finally, for downtime assessment, a novel probabilistic framework, built on the FEMA P-58methodology and the REDi guidelines, was employed to estimate the expected annualdowntimes (EADs) to achieve specific target recovery states, such as reoccupancy (RO) andfunctional recovery (FR). Results revealed that seismically enhancing RC dual wall–framebuildings with FVDs significantly improves resilience by reducing loss and downtime.For example, the enhanced building with FVDs achieved an EAL of 0.093% and EAL of8.6 days for FR, compared to the archetype base building without design improvements,which exhibited an EAL of 0.125% and an EAD of 9.5 days for FR. In contrast, the impactof ENCs alone was minor, compared to the effect of FVDs, with an EAL of 0.106% and anEAD of 9.1 days for FR. With this detailed recovery modeling, probabilistic methods, and afocus on intermediate recovery states, this framework represents a significant advancementin resilience-based seismic design and recovery planning.Keywords: RC dual wall–frame office buildings; fluid viscous damper; enhanced non-structural component; loss assessment; downtime assessment; resilience; subductionearthquakesSustainability 2025, 17, 1200 https://doi.org/10.3390/su17031200Sustainability 2025, 17, 1200 2 of 261. IntroductionPrescriptive seismic codes for the design of buildings are primarily aimed at avoidingcollapse under extreme earthquake loads. However, structural and non-structural damageis a latent possibility, usually not properly quantified [1]. Even without building collapse, ifthe damage is extensive, it could cause critical economic losses, long functional recoverytimes, and, consequently, significant environmental impacts due to reparation or demo-lition and reconstruction labor [2,3]. For example, recent earthquakes in Chile and NewZealand showed that the ‘life safety’ performance level has been successfully achievedwith relatively few collapsed buildings [1], which is in agreement with recent numericalstudies showing minimal probabilities of collapse even under extreme seismic events [4].However, losses and downtime due to widespread damage in modern buildings could besubstantial in earthquake-prone countries [5].Specifically, due to the Mw 8.8 2010 Chile earthquake, total losses were around USD30 billion (18% of the 2010 Chilean gross domestic product, GDP), and the internationalairports in Santiago and Concepcion were out of service for weeks due to non-structuraldamage [6]. Moreover, due to the Mw 6.3 2011 New Zealand earthquake, total losses wereestimated to be over USD 15 billion (10% of the 2011 New Zealand GDP), about 50% ofall the concrete and masonry buildings in the business district of Christchurch becameunusable due to significant damage, and the district area was closed for months [7]. Thesenumbers might not be acceptable for current societies that demand more resilient andsustainable urban built environments with limited structural damage and direct/indirectcosts resulting from seismic demands, even in the case of large earthquakes.To meet the expectations of current societies without compromising their future, build-ings need to achieve enhanced and predictable performance levels beyond the minimumrequirements of current seismic design codes [8]. Traditionally, such higher performancelevels are reached by improving the lateral load-resisting system, which can be achievedby strengthening/stiffening the structural system and/or incorporating seismic protectionsystems. An alternative strategy is to replace non-structural components with new oneswith enhanced performance levels that accommodate large displacement and accelerationdemands with minimal damage [9]. In either case, more significant initial construction costsare expected, requiring deeper cost–benefit analyses to understand the trade-off betweenhigher initial investments and future savings in earthquake-induced economic losses.The performance-based earthquake engineering (PBEE) framework enables the eval-uation of the probable seismic performance of structures over their operational life. Themethodology proposed by the Pacific Earthquake Engineering Research (PEER) Centerallows the assessment of new or existing buildings with a realistic and reliable understand-ing of the risks to life, occupancy, and economic loss that might occur in future earthquakes.In their FEMA P-58 [10] implementation, seismic performance is expressed in terms ofdecision variables (i.e., performance metrics) that can be understood by decision-makers,such as collapse probability, direct economic losses (i.e., building repair or replacementcosts), repair time, and environmental impacts.Recent investigations have proposed complementary methodologies for recovery timeassessment, extending FEMA P-58 implementation and adopting a series of assumptionsto connect building component damage to the functionality of key building systems (e.g.,structural and non-structural components). For example, Terzic et al. [11] introduced aprobabilistic framework that integrates models for evaluating post-earthquake function-ality, mobilization time, and repair time. It employs fault tree analysis to identify criticalsubsystems affecting functionality and estimates the percent loss of building functionalityfor different damage scenarios. Cook et al. [12] built a framework which described build-ing functionality at the tenant-unit level based on the performance of building systems,Sustainability 2025, 17, 1200 3 of 26relating component damage to the operation of building systems and overall functionalitythrough the use of fault trees. Molina Hutt et al. [13] estimate resilience metrics based on afour-component framework: (i) determining the post-earthquake usability, (ii) estimatingimpeding factor delays, (iii) evaluating the building repair time, and (iv) calculating therecovery time (downtime) as the combination of delays and repair time.Despite the availability of these tools, little information is available on the expectedcollapse risk and earthquake-induced losses of RC buildings equipped with FVDs, espe-cially in regions prone to subduction earthquakes, such as Chile. Consequently, the noveltyof this study is in its quantitative assessment of the impact of different design strategies onthe performance of modern code-conforming reinforced concrete (RC) buildings subjectedto subduction earthquakes. Seismic performance is evaluated in terms of decision variablesrelated to sustainability and resilience, such as expected economic losses and expected func-tional recovery times in a life-cycle framework. A high-rise dual wall–frame office buildingrepresentative of the current design and construction practice in Chile was selected as a casestudy. Three strategies to potentially improve the performance of the benchmark buildingwere explored (leading to a total of four cases, including the benchmark building designedper the current practice): (i) the incorporation of fluid viscous dampers (FVDs) into thelateral load-resisting system; (ii) the incorporation of enhanced non-structural components(ENCs); and (iii) a combination of the two previous strategies. To achieve the objectives,a fully probabilistic PBEE framework based on the FEMA P-58 [10] methodology wasintegrated with Molina Hutt et al.’s recovery time framework [13]. First, the probabilisticstructural response was estimated by incremental dynamic analyses of 3D nonlinear modelsof the archetype subjected to hazard-consistent Chilean ground motions (GMs). For lossassessment, intensity-based assessments at several ground-shaking intensity levels wereconducted to estimate the expected direct economic loss. For downtime assessment, thenovel probabilistic framework, built on the FEMA P-58 methodology and the REDi guide-lines, was utilized to predict the expected temporal recovery trajectory, robustness, andrapidity to reach specific target recovery states (e.g., reoccupancy and functional recovery).Finally, a time-based analysis was conducted, integrating the loss and downtime resultswith the respective hazard curve to estimate meaningful risk metrics, such as expectedannual loss (EAL), expected annual downtime (EAD), and expected life-cycle cost (ELCC)to evaluate the effectiveness of each strategy.To meet the above-mentioned objectives, this article is organized as follows. Section 2presents the archetype buildings used in the study, including the seismic design strategies,as well as the nonlinear modeling. The FEMA P-58 methodology and adjustments adoptedto evaluate the seismic performance of the archetypes are presented in Section 3, togetherwith the selection of hazard-consistent ground motions, incremental dynamic analyses, andloss and downtime evaluation procedures. Section 4 provides detailed results of the riskestimations of each of the design strategies. Finally, conclusions and closing remarks arediscussed in Section 5.2. Archetype Buildings2.1. Preliminary DefinitionsThe characteristics of the benchmark archetype building (BAB) were defined based onstatistical data from the Chilean RC building inventory, gathered from the Chilean nationaldatabase [14] as well as the state of design and local construction practice. According to thedatabase, from buildings of at least 3 stories built between 2002 and 2020, the number ofhigh-rise buildings (i.e., from 10 to 24 stories, 16 stories on average) has grown considerablyin recent years and there is scarce information about their seismic performance. Therefore,a high-rise office building located in Santiago (moderate seismicity zone, classified asSustainability 2025, 17, 1200 4 of 26seismic zone 2 according to the Chilean seismic design code NCh 433 [15]) on soil type B(defined as fractured rock or very dense/firm soil according to DS 61 [16]) was consideredas case study. The archetype selected has 3 underground levels surrounded by perimeterbasement walls and 16 stories above the grade level (Figure 1a depicts the elevation ofthe base archetype). The structural system consists of a dual system, i.e., core shear wallsand perimeter intermediate moment frames designed to take no more than 25% of theprescribed lateral seismic load (Figure 1b shows a plan layout of a typical floor). Ascommonly executed in Chilean practice, the thickness of the shear walls was set to beconstant along the entire height. Regarding the frames, the beams had the same cross-section for all stories. Columns from the third underground story to the second storyhad the same cross-section, and columns from the third story to the top story had thesame cross-section, as shown in Table 1. From Figure 1a,b, it is noted that the BAB hashorizontal irregularity due to the orientation of the C-shaped core walls, and it has novertical irregularity from the grade level for the upper 16 stories. These irregularities wereconsidered in the design and analysis procedures. Indeed, torsional effects in the BAB dueto horizontal irregularity were analyzed and controlled in the design procedures followingthe current Chilean seismic code for RC structures [15,16]. It is important to note that thelinear elastic model used in the code-compliant design process was, as customary in Chileanseismic design practice, a full 3D model that included all the stories of the building, bothbelow and above grade. Further details of the statistics of the national building database,archetype geometry, member cross-sections, and design issues can be found in Gallegoset al. [4].Sustainability 2025, 17, x FOR PEER REVIEW 4 of 41 performance. Therefore, a high-rise office building located in Santiago (moderate seismic-ity zone, lassified as seismic zone 2 according to th Chilean seismic design code NCh 433 [15]) on soil type B (defined as fractur d rock r very de se/firm soil according to DS 61 [16]) was considered as cas tudy. T e archetype selected ha 3 underground l vels surrounded by perimeter basement walls and 16 stories above the grade level (Figure 1a depicts the elevation of the base archetype). The structur l system consists of a dual sys-tem, i.e., core sh ar walls and perimet r inter diate moment frames designed to take no more than 25% of the prescribed lateral seismic load (Figure 1b shows a plan l yout of a typical flo r). As commonly executed in Chilean practice, the thickness of the shear walls was set to be c stant along the entire height. Regarding the frames, the beams had the same cross-section for all stories. Columns from the thir underground story to the second story had the same cross-section, and columns from the third story to the top story had the sa e cross-section, as sho n in Table 1. From Figure 1a,b, it is noted that the BA has horizontal irregularity due to the orientation of the C-shaped core walls, and it has no vertical irregularity from the grade level for the upper 16 stories. These irregularities were considered in the design and analysis procedures. Indeed, torsional effects in the BAB due to horizontal irregularity were analyzed and controlled in the design procedures follow-ing the current hilean seis ic code for R structures [15,16]. It is i portant to note that the linear elastic model used in the code-compliant design process was, as customary in Chilean seismic design practice, a full 3D model that included all the stories of the build-ing, both below and above grade. Further details of the statistics of the national building database, archetype geo etry, member cross-sections, and design issues can be found in Gallegos et al. [4]. (a) (b) (c) (d) Figure 1. Sixteen-story benchmark archetype building (BAB): (a) 3D view, (b) plan layout. Perform-3D models: (c) BAB, (d) BAB+FVD. Figure 1. Sixteen-story benchmark archetype building (BAB): (a) 3D view, (b) plan layout. Perform-3Dl : (c) , ( ) FV .Sustainability 2025, 17, 1200 5 of 26Table 1. Member cross-sections and reinforcements.ArchetypeCore Walls Beams ColumnsFlanges Webs (b × h) (b × h)l t l t us3–s2◦ s3◦–s16◦BAB 4.2 0.7 16.0 0.5 0.7 × 0.6 1.0 × 1.0 0.8 × 0.8ρlong. (%) 0.25 0.33 0.84 1.93 1.15Note: l = length; t = thickness; b = width; h = height; us3 = third underground story; s2◦ = second story; s3◦ = thirdstory; s16◦ = top story. ρlong. = ratio of area of distributed longitudinal/vertical reinforcement to gross concretearea perpendicular to that reinforcement. Dimensions in meters.Three improved design strategies are evaluated on the basis of the BAB: (i) the incor-poration of FVDs into the lateral load-resisting system (BAB+FVD); (ii) the replacement ofconventional non-structural components with ENCs (BAB+ENC); and (iii) a combinationof both strategies (BAB+FVD+ENC). Regarding the archetypes equipped with dampers,based on the expert opinion of Chilean practitioners, it was decided to include this type ofdampers without redesigning the BAB. Although not optimal (a more economical structureis possible), this approach is the most practical way to comply with the requirements of thecurrent Chilean seismic design code for buildings with energy dissipation systems NCh3411 [17] and is consistent with current Chilean practice for dual system buildings (e.g.,‘Las Condes Capital’ building).Chilean RC buildings are characterized by a stiff structural system; therefore, FVDswere placed every three stories, starting from the grade level, in the mid span of theperimeter frames along the transverse direction of the building (i.e., the critical direction)to pursue the amplification of the small relative motion at the two ends of the dampers.The FVDs were arranged in a horizontal configuration attached with inverted chevronsteel braces. A total number of 20 FVDs were required (two pairs every three stories, fivepairs per perimeter side). The location of the FVDs in the transverse perimeter frameswas considered to control possible torsional effects due to the horizontal irregularity ofthe building. In the design process, it was verified that the irregularities did not increasethe demand for axial actions in the columns and flexural actions in the shear walls. Thisverification was performed following a performance-based design with the requirementsof the current Chilean seismic design code [17]. Nonlinear dampers with a force capacityof 50 tonf and a velocity exponent (α) of 0.35 were selected [18]. A single damper typewas used in accordance with current Chilean practice. The force capacity was based onthe maximum forces that the structure could take without strengthening (i.e., withoutadditional construction costs). The behavior of the FVD was idealized as purely viscous.The relationship between force Fd and velocity.x is given by Equation (1), where cd is thedamping constant.Fd = sign( .x)cd∣∣ .x∣∣α, (1)Regarding the archetypes that consider ENCs, recent studies [19,20] have highlightedthe benefits of using the strategy of enhancing the non-structural components in the seismicperformance of mid- and high-rise steel buildings for earthquake-prone regions. For thesearchetypes, the structural systems did not need to be redesigned because the non-structuralcomponents had no impact on the strength and stiffness of the archetypes. However, thefragility and consequence functions of the original non-structure components were replacedwith those of the ENCs. More details of the non-structural components will be provided inSection 3.2.Sustainability 2025, 17, 1200 6 of 262.2. Nonlinear ModelingThe members and dampers of the structural system were modeled as nonlinear ele-ments. The 3D mathematical models of the BAB and BAB+FVD archetypes were developedin the structural analysis program Perform-3D [21]. This computational program wasselected because it provides a good balance between accuracy and computational cost.In recent research studies [22], Perform-3D was used to implement nonlinear responsehistory analyses of RC shear wall buildings, which indicates that is adequate for the seismicanalysis of the type of archetypes considered in this study.The slender shear walls of the archetypes were modeled with the ‘shear wall’ element,a fiber-based cross-section model with nonlinear concrete and steel fibers and a decouplednonlinear shear layer. The material properties of the fibers were defined using the uniaxialconstitutive relationship (i.e., stress vs. strain backbone curve) YULRX (Y: yielding, U:ultimate, L: loss, R: residual, X: maximum). Unloading and reloading stiffness degradationwas accounted for through energy dissipation and stiffness reduction factors [21]. Inaddition, a shear layer was defined by a bilinear stress–strain backbone curve. Beams andcolumns were modeled as ‘frame type’ elements. A finite-length-plastic formulation wasadopted to model plastic hinges, with fiber-based plasticity regions at both ends and alinear elastic region in between. YULRX backbone curves were also adopted to model theuniaxial stress–strain relationships of concrete and steel. Figure 1c shows a 3D view of themodel of the benchmark archetype. Further details on the calibration of the model can befound in Gallegos et al. [4].Moreover, the FVDs were modeled using the ‘viscous bar’ element, which includes alinear elastic bar component and a fluid damper component in series [21]. The bar compo-nent accounts for the in-series stiffness of the supporting brace element, the connections,and the intrinsic axial stiffness of the FVD. The fluid damper component represents themain characteristics of the FVD. As shown in Equation (1), two input values are requiredto define a FVD (cd and.x). The accuracy of the ‘viscous bar’ element was validated bycomparisons with results given by the ‘viscousdamper’ element [23], implemented inOpenSees [24], which, in turn, has been previously validated by comparisons with experi-mental results [25]. Recent studies have demonstrated the suitability of the ‘viscous bar’element of Perform-3D to model FVDs in mid- and high-rise buildings subjected to seismicloading [26]. Figure 1d shows a 3D view of the archetype equipped with FVDs, wherethe dampers (shown in red) are located at both transverse perimeter frames. The figureshows the arrangement of the set of 20 dampers in a horizontal configuration, fastenedwith inverted chevron steel braces.3. Performance Assessment MethodologyA fully probabilistic PBEE framework with FEMA P-58 [10] implementation wasadopted, considering some adjustments to adapt the methodology to the local engineeringcontext. Figure 2 illustrates the research methodology to finally evaluate the direct andindirect economic loss of each design alternative. The performance of four archetypeswas evaluated: (i) BAB; (ii) BAB+FVD; (iii) BAB+ENC; and (iv) BAB+FVD+ENC. Theprobabilistic structural responses were estimated by incremental dynamic analyses (IDAs)of the 3D nonlinear models of the archetypes subjected to sets of hazard-consistent ChileanGMs. For loss and downtime evaluations, a series of intensity-based assessments wereconducted at several ground-shaking levels until collapse. The intensities (spectral accel-eration at the fundamental period, Sa(T1), was used in this study) also include distinctivehazard intensities with probabilities of exceedance equal to 50%, 10%, 2%, and 1% in50 years, i.e., a service level earthquake (SLE), design basic earthquake (DBE), maximumconsidered earthquake (MCE), and very rare earthquake (VRE), respectively. Then, theSustainability 2025, 17, 1200 7 of 26intensity-based results were integrated with the respective hazard curve to complete thetime-based analysis, providing meaningful risk metrics for comparison purposes.Sustainability 2025, 17, x FOR PEER REVIEW 11 of 41 of the set of 20 dampers in a horizontal configuration, fastened with inverted chevron steel braces. 3. Performance Assessment Methodology A fully probabilistic PBEE framework with FEMA P-58 [10] implementation was adopted, considering some adjustments to adapt the methodology to the local engineering context. Figure 2 illustrates the research methodology to finally evaluate the direct and indirect economic loss of each design alternative. The performance of four archetypes was evaluated: (i) BAB; (ii) BAB+FVD; (iii) BAB+ENC; and (iv) BAB+FVD+ENC. The probabil-istic structural responses were estimated by incremental dynamic analyses (IDAs) of the 3D nonlinear models of the archetypes subjected to sets of hazard-consistent Chilean GMs. For loss and downtime evaluations, a series of intensity-based assessments were con-ducted at several ground-shaking levels until collapse. The intensities (spectral accelera-tion at the fundamental period, Sa(T1), was used in this study) also include distinctive haz-ard intensities with probabilities of exceedance equal to 50%, 10%, 2%, and 1% in 50 years, i.e., a service level earthquake (SLE), design basic earthquake (DBE), maximum consid-ered earthquake (MCE), and very rare earthquake (VRE), respectively. Then, the intensity-based results were integrated with the respective hazard curve to complete the ti e-based analysis, providing meaningful risk metrics for comparis n pur oses. Figure 2. Overview of research methodology. Ref: FEMA P-58 [10], Molina Hutt et al. [13]. 3.1. GM Selection and IDA As a first step within the framework, a probabilistic seismic hazard analysis (PSHA) was performed using the computational platform SeismicHazard [27], which integrates state-of-the-art seismic source models and GM models for the Chilean territory. A site-specific hazard curve was obtained for the fundamental period of the archetype (i.e., T1 = 1.93 s), assuming that the archetype was located in Santiago on stiff soil. Then, a condi-tional spectrum (CS) was rigorously constructed and used as the target spectrum to select and scale GMs. The CS calculations considered the target Sa(T1) for the 2–50 years hazard level, and the mean causal magnitude M, mean causal distance R, and mean causal epsilon ε obtained from the PSHA deaggregation. From the Chilean strong ground motion data-base SiberRisk [28], a hazard-consistent set of 44 subduction GMs was selected and scaled to match the target mean, variance, and correlations of the Sa(T1) values. The selected rec-ords incorporate actual shakings from past Chilean subduction earthquakes with M > 6.3 that occurred between 1985 and 2019, including GMs of the Mw 8.8 2010 megathrust Figure 2. vervie of research ethodology. Ref: FE P-58 [10], olina utt et al. [13].3.1. GM Selection and IDAAs a first step within the framework, a probabilistic seismic hazard analysis (PSHA)was performed using the computational platform SeismicHazard [27], which integratesstate-of-the-art seismic source models and GM models for the Chilean territory. A site-specific hazard curve was obtained for the fundamental period of the archetype (i.e.,T1 = 1.93 s), assuming that the archetype was located in Santiago on stiff soil. Then, aconditional spectrum (CS) was rigorously constructed and used as the target spectrum toselect and scale GMs. The CS calculations considered the target Sa(T1) for the 2–50 yearshazard level, and the mean causal magnitude M, mean causal distance R, and mean causalepsilon ε obtained from the PSHA deaggregation. From the Chilean strong ground motiondatabase SiberRisk [28], a hazard-consistent set of 44 subduction GMs was selected andscaled to match the target mean, variance, and correlations of the Sa(T1) values. Theselected records incorporate actual shakings from past Chilean subduction earthquakeswith M > 6.3 that occurred between 1985 and 2019, including GMs of the Mw 8.8 2010megathrust seismic event. More details about the PSHA, CS, and the set of GMs can befound in Gallegos et al. [4].The set of GMs was used to conduct the IDAs of the BAB and the BAB+FVD mod-els. Numerous nonlinear response history (NLRH) analyses were performed. Each GMwas systematically scaled until structural collapse. The adopted intensity measure (IM)was Sa(T1), which has been shown to have a good correlation with nonlinear structuralresponse [29]. The dynamic analyses were performed only along the direction of the shorterhorizontal plan dimension, which is the critical direction (i.e., the direction along whichthe collapse fragility is larger). This decision was considered by pursuing an appropriatebalance between accuracy in the results and computational burden; however, it is acknowl-edged that such an approach could restrict the capacity of the archetype model to capturethe torsional effects in the building’s response due to its horizontal irregularity. Figure 3presents the IDA results, where curves in Figure 3a,b show the relationship between theroof drift ratio (RDR) and Sa(T1) for the BAB and BAB+FVD archetypes, respectively. Thefigures also present the 50th collapse percentile (median) as well as the 16th and 84thcollapse percentiles (equal to one logarithmic standard deviation below and above themean when a lognormal distribution is assumed). For each archetype, the Sa(T1) valuesthat triggered collapse were recorded for each GM. Assuming a lognormal distribution, theSustainability 2025, 17, 1200 8 of 26median collapse capacity, θˆ, and the logarithmic standard deviation, βˆ, were computed foreach archetype. Figure 3c,d show the estimated lognormal collapse fragility curves, whichare important inputs for loss assessment. The estimated parameters θˆ and βˆ for the BABwere 0.87 g and 0.27, respectively, whereas for the BAB+FVD they were 0.97 g and 0.26, re-spectively. It is evident that the archetype equipped with FVDs (i.e., BAB+FVD) performedbetter, i.e., it had a larger value of θˆ and, consequently, a smaller collapse probability at anygiven value of Sa(T1).It is worth noting that the evaluation of the buildings that include enhanced non-structural components (BAB+ENC and BAB+FVD+ENC) required neither additional struc-tural design nor IDAs since the dynamic properties (and therefore the seismic demands onthe BAB and BAB+FVD) did not change.Sustainability 2025, 17, x FOR PEER REVIEW 8 of 29 estimated parameters θ෡ and β෡ for the BAB were 0.87 g and 0.27, respectively, whereas for the BAB+FVD they were 0.97 g and 0.26, respectively. It is evident that the archetype equipped with FVDs (i.e., BAB+FVD) performed better, i.e., it had a larger value of θ෡ and, consequently, a smaller collapse probability at any given value of Sa(T1). It is worth noting that the evaluation of the buildings that include enhanced non-structural components (BAB+ENC and BAB+FVD+ENC) required neither additional structural design nor IDAs since the dyna ic properties (and therefore the seismic demands on the BAB and BAB+FVD) did not change. (a) (c) (b) (d) Figure 3. IDA results: (a) BAB; (b) BAB+FVD. Collapse simulation results and estimated collapse fragility functions: (c) BAB; (d) BAB+FVD. 3.2. Economic Loss Assessment Following the intensity-based assessment with FEMA P-58 implementation, economic losses were estimated for the four archetypes subjected to several Sa(T1) intensities ranging from 0.05 g to 2.00 g, with increments of 0.05 g. At each shaking intensity, 2000 Monte Carlo simulations, called a realization, were performed to evaluate the mean earthquake-induced losses. It is worth noting that the number (2000) of Monte Carlo simulations was decided in order to balance accuracy (how close the results are to the true values) and efficiency (the computational cost of running simulations). The chosen number of simulations was based on a convergence. In our case, when the absolute difference between the results obtained using n simulations and using n+1 simulations was below a target error, namely 1%, the process was finished. As this happened at approximately 2000 simulations, this number was taken as the target. Figure 3. IDA results: (a) ; (b) BAB+FVD. Collapse simulation results and estimated collapsefragility functions: (c) ; (d) BAB+FVD.3.2. Economic Loss AssessmentFollowing the intensity-based assessment with FEMA P-58 implementation, economiclosses were estimated for the four archetypes subjected to several Sa(T1) intensities rangingfrom 0.05 g to 2.00 g, with increments of 0.05 g. At each shaking intensity, 2000 Monte Carlosimulations, called a realization, were performed to evaluate the mean earthquake-inducedlosses. It is worth noting that the number (2000) of Monte Carlo simulations was decidedin order to balance accuracy (how close the results are to the true values) and efficiency (thecomputational cost of running simulations). The chosen number of simulations was basedon a convergence. In our case, when the absolute difference between the results obtainedusing n simulations and using n + 1 simulations was below a target error, namely 1%, theSustainability 2025, 17, 1200 9 of 26process was finished. As this happened at approximately 2000 simulations, this numberwas taken as the target.For each realization, the losses were calculated as follows: (i) engineering demandparameters (EDPs) were estimated from the results of the NLRH analyses; (ii) fragilityfunctions were used in conjunction with the EDPs to determine the probability of reach-ing or exceeding associated damage states (DSs) for each structural and non-structuralcomponent; and (iii) consequence functions were then used to translate the DSs into re-pair/reposition costs.This process required the estimation of the EDPs, which in this study were the follow-ing: (i) peak story drift ratio, PSDR; (ii) peak story tangential drift ratio, PSDRt; (iii) peakresidual drift ratio, PRDR; and (iv) peak floor acceleration, PFA. The PSDRt, also calleddamageable story drift, eliminates rigid body rotation within wall panels and is consid-ered a better proxy than PSDR for wall damage in mid- to high-rise shear wall buildings.Lognormal probability distributions, defined by the corresponding values of θˆ and βˆ, wereassumed to characterize the aleatory nature of the EDPs at each Sa(T1) intensity. Figure 3a,bshow an example of the variability of the structural response considering the RDR asthe EDP.The building performance models were then constructed by gathering detailed char-acteristics of the structural and non-structural components of the four archetypes. Initially,fragility and consequence functions of the components were taken from the FEMA P-58database. However, some adjustments were implemented to represent the actual cost dis-tribution of components in Chilean office buildings (i.e., 40% of the total initial cost is dueto structural components and the remaining 60% is due to non-structural components, asobtained from actual RC office-building projects in Chile). This cost distribution is differentfrom that reported for office buildings in the USA and, consequently, both the total cost andthe cost of each structural and non-structural component were adjusted to reflect currentChilean RC office buildings. According to Taghavi and Miranda [30], non-structural com-ponents make up approximately 80% of the total economic investment in office buildingsin the USA. Therefore, the Chilean buildings are less susceptible to presenting high damagecosts due to the smaller relative cost of non-structural components. Moreover, even thoughthis study assumes that the DSs of each structural and non-structural component are as-sociated with the same values of θˆ and βˆ defined in the FEMA P-58 database, the repaircost of each structural and non-structural component associated with each DS followed thesame relative costs defined in FEMA P-58, but normalized by the Chilean construction costobtained from actual Chilean projects.The replacement cost for the benchmark archetype (BAB) was estimated assuming acost of USD 1660 per square meter on the basis of annual statistics for construction costsprovided by Chile’s Ministry of Housing [31]. The cost of the FVDs (including the devices,testing, and additional steel braces) was assumed to be 3% of the BAB construction cost [18].The cost of replacing the conventional non-structural components with enhanced ones waspresumed to be 3% of the BAB construction cost. The latter was estimated based on theobservation that the incorporation of non-structural components with improved seismic be-havior might represent an increment of 5% of the total non-structural cost in a typical officebuilding [19] and considering the component-cost distribution in Chilean office buildings(40–60% for structural and non-structural components, respectively) previously mentioned.The quantities of structural components were calculated based on the structural design,and the quantities of non-structural components were estimated from typical quantitiesfound in commercial buildings using the FEMA P-58 Normative Quantity EstimationTool [10]. Though the NLRH analyses were conducted in the transverse direction, lossestimation requires inputs in both orthogonal directions. Therefore, quantities in theSustainability 2025, 17, 1200 10 of 26longitudinal direction were also considered. Non-structural quantities were consistentfor all building archetypes. However, some non-structural component identifiers variedfor the buildings with ENCs. Table 2 provides a summary of the building performancemodel assumptions for the BAB and BAB+FVD archetypes, including the structural andnon-structural components adopted in each component group (i.e., super structure, interi-ors, services), their fragility identifiers, component category, quantities in both directions(d1 and d2), unit, distribution of components throughout the building, and the EDPs thefragility functions were conditioned on. Moreover, the non-structural components that aresusceptible to performance improvements have been identified with an asterisk (*).Table 2. Structural and non-structural components for BAB and BAB+FVD.Fragility ID Component Category Quant. d1 Quant. d2 Unit Location EDPSuper StructureB1041.021a b/c connection Structural 4 4 1 EA stories PSDRB1041.021b b/c connection Structural 4 8 1 EA stories PSDRB1044.093 Slender wall 12′′ Structural 24.85 45.26 144 SF undergrounds PSDRtB1044.103 Slender wall 18′′ Structural 7.65 144 SF stories PSDRtB1044.111 Slender wall 30′′ Structural 4.11 144 SF stories PSDRtB1049.032 s/c connection Structural 24 24 1 EA undergrounds PSDRB1049.032 s/c connection Structural 8 4 1 EA stories PSDRB2022.201 Curtain walls Façade 103.33 103.33 30 SF stories PSDRInteriorsC1011.001a * Wall partition (full) Partitions 5.17 5.17 100 LF stories PSDRC1011.001b Wall partition (partial) Partitions 5.17 5.17 100 LF stories PSDRC2011.011b Precast concrete stair Egress 4.42 1 EA undergroundsC2011.011b Precast concrete stair Egress 1.03 1 EA stories PSDRC3011.001a * Gypsum+wallpaper Partitions 0.78 0.78 100 LF stories PSDRC3032.001d * Suspended ceiling Ceilings 0.83 2500 SF stories PFAServicesD1014.011 Traction elevator MEP 8.06 1 EA ground level PFAD2021.012a * C/H potable (piping) MEP 1.86 1000 LF undergrounds PFAD2021.012a * C/H potable (piping) MEP 0.43 1000 LF stories PFAD2021.012b * C/H potable (bracing) MEP 1.86 1000 LF undergrounds PFAD2021.012b * C/H potable (bracing) MEP 0.43 1000 LF stories PFAD2022.012a * Heating hot water (p.) MEP 1.86 1000 LF undergrounds PFAD2022.012a * Heating hot water (p.) MEP 0.43 1000 LF stories PFAD2022.012b * Heating hot water (b.) MEP 1.86 1000 LF undergrounds PFAD2022.012b * Heating hot water (b.) MEP 0.43 1000 LF stories PFAD2031.022a * Sanitary waste (p.) MEP 1.86 1000 LF undergrounds PFAD2031.022a * Sanitary waste (p.) MEP 0.43 1000 LF stories PFAD2031.022b * Sanitary waste (b.) MEP 1.86 1000 LF undergrounds PFAD2031.022b * Sanitary waste (b.) MEP 0.43 1000 LF stories PFAD3041.011b * HVAC ducting MEP 3.32 1000 LF undergrounds PFAD3041.011b * HVAC ducting MEP 0.78 1000 LF stories PFAD3041.031a * HVAC diffusers MEP 39.80 10 EA undergrounds PFAD3041.031a * HVAC diffusers MEP 9.30 10 EA stories PFAD3041.041a * VAV box MEP 8.85 10 EA undergrounds PFAD3041.041a * VAV box MEP 2.07 10 EA stories PFAD5012.013a * Motor control center MEP 11.51 1 EA roof PFANote: b/c: beam–column; s/c: slab–column; MEP: mechanical, electrical, plumbing. d1: transverse direction;d2: longitudinal direction. *: non-structural components that are susceptible to performance improvements.Sustainability 2025, 17, 1200 11 of 26Table 3, on the other hand, provides a summary of the building performance modelassumptions for the BAB+ENC and BAB+FVD+ENC archetypes. For these buildings, thenon-structural components previously identified were replaced by those with enhancedseismic behavior. For example, conventional full-height wall partitions that are fixed belowand above (C1011.001a) were substituted with wall partitions that include a slip track abovewith returns (C1011.001c). Suspended ceilings with vertical supports only (C3032.001d)were replaced by those with vertical and lateral supports (C3032.003d). An unanchoredmotor control center that is not vibration-isolated (D5012.013a) was substituted by equip-ment that is either hard-anchored or is vibration-isolated with seismic snubbers/restraints(D5012.013c).Table 3. Structural and non-structural components for BAB+ENC and BAB+FVD+ENC.Fragility ID Component Category Quant. d1 Quant. d2 Unit Location EDPSuper StructureB1041.021a b/c connection Structural 4 4 1 EA stories PSDRB1041.021b b/c connection Structural 4 8 1 EA stories PSDRB1044.093 Slender wall 12′′ Structural 24.85 45.26 144 SF undergrounds PSDRtB1044.103 Slender wall 18′′ Structural 7.65 144 SF stories PSDRtB1044.111 Slender wall 30′′ Structural 4.11 144 SF stories PSDRtB1049.032 s/c connection Structural 24 24 1 EA undergrounds PSDRB1049.032 s/c connection Structural 8 4 1 EA stories PSDRB2022.201 Curtain walls Façade 103.33 103.33 30 SF stories PSDRInteriorsC1011.001c * Wall partition (full) Partitions 5.17 5.17 100 LF stories PSDRC1011.001b Wall partition (partial) Partitions 5.17 5.17 100 LF stories PSDRC2011.011b Precast concrete stair Egress 4.42 1 EA undergroundsC2011.011b Precast concrete stair Egress 1.03 1 EA stories PSDRC3011.001c * Gypsum+wallpaper Partitions 0.78 0.78 100 LF stories PSDRC3032.003d * Suspended ceiling Ceilings 0.83 2500 SF stories PFAServicesD1014.011 Traction elevator MEP 8.06 1 EA ground level PFAD2021.013a * C/H potable (piping) MEP 1.86 1000 LF undergrounds PFAD2021.013a * C/H potable (piping) MEP 0.43 1000 LF stories PFAD2021.013b * C/H potable (bracing) MEP 1.86 1000 LF undergrounds PFAD2021.013b * C/H potable (bracing) MEP 0.43 1000 LF stories PFAD2022.013a * Heating hot water (p.) MEP 1.86 1000 LF undergrounds PFAD2022.013a * Heating hot water (p.) MEP 0.43 1000 LF stories PFAD2022.013b * Heating hot water (b.) MEP 1.86 1000 LF undergrounds PFAD2022.013b * Heating hot water (b.) MEP 0.43 1000 LF stories PFAD2031.023a * Sanitary waste (p.) MEP 1.86 1000 LF undergrounds PFAD2031.023a * Sanitary waste (p.) MEP 0.43 1000 LF stories PFAD2031.023b * Sanitary waste (b.) MEP 1.86 1000 LF undergrounds PFAD2031.023b * Sanitary waste (b.) MEP 0.43 1000 LF stories PFAD3041.011c * HVAC ducting MEP 3.32 1000 LF undergrounds PFAD3041.011c * HVAC ducting MEP 0.78 1000 LF stories PFAD3041.031b * HVAC diffusers MEP 39.80 10 EA undergrounds PFAD3041.031b * HVAC diffusers MEP 9.30 10 EA stories PFAD3041.041b * VAV box MEP 8.85 10 EA undergrounds PFAD3041.041b * VAV box MEP 2.07 10 EA stories PFAD5012.013c * Motor control center MEP 11.51 1 EA roof PFANote: b/c: beam—column; s/c: slab—column; MEP: mechanical, electrical, plumbing. d1: transverse direction;d2: longitudinal direction. *: improved non-structural components.Sustainability 2025, 17, 1200 12 of 26Table 4 compares the median (θ) and dispersion (β) values of the damage state fragilitycurves for some conventional and enhanced non-structural components. These values arefrom the FEMA P-58 database.Table 4. Damage state definitions.Fragility ID Component DS1 (θ) β DS2 (θ) β DS3 (θ) βInteriorsC1011.001a * Wall partition (full) 0.005 rad 0.40 0.010 0.30 0.021 0.20C1011.001c * 0.004 0.45 0.011 0.35 0.019 0.25C3011.001a * Gypsum+wallpaper 0.0021 rad 0.60C3011.001c * 0.0020 0.70C3032.001d * Suspended ceiling 0.56 g 0.25 1.08 0.25 1.31 0.25C3032.003d * 1.09 0.30 1.69 0.30 1.91 0.30ServicesD2021.012a * C/H potable (piping) 1.50 g 0.40 2.60 0.40D2021.013a * 2.25 0.40 4.10 0.40D2022.012a * Heating hot water (p.) 0.55 g 0.50 1.10 0.50D2022.013a * 0.55 0.50 1.10 0.50D2031.022a * Sanitary waste (p.) 1.20 g 0.50D2031.023a * 3.00 0.50D3041.011b * HVAC ducting 1.50 g 0.40 2.25 0.40D3041.011c * 1.50 0.40 2.25 0.40D3041.041a * VAV box 1.90 g 0.40D3041.041b * 1.90 0.40D5012.013a * Motor control center 0.73 g 0.45D5012.013c * 2.50 0.4Note: Median (θ) and dispersion (β) values from FEMA P-58 database [10]. *: improved non-structural compo-nents. Units: g = gravity.PRDR values were also included in the analysis to account for cases where the build-ings are assumed to be damaged beyond repair and need to be demolished. The distributionof PRDR is highly variable since it is the result of pure nonlinear structural behavior. Hence,the probability of demolition was estimated as a function of the PSDR by a cumulativelognormal distribution with a median value of 1% and a dispersion of 0.3, following therecommendations of FEMA P-58. However, after the Chilean Mw 8.8 2010 earthquake [6],many damaged RC buildings with residual drift ratios larger than 1% were stabilized andrepaired [32]. Because of this observation, a median value of 1.5% was assumed, but furtherstudies will be needed to refine this assumption. Building-specific collapse fragilities wereadopted from the IDAs (Figure 3c,d) to determine varying probabilities of collapse at eachintensity. Quantities in the transverse and longitudinal directions were considered. TheEDPs were assumed to be the same in both directions as a conservative criterion.Using this information, the methodology implemented in the software PELICUNv2.5 [33] accounted for the fragility functions to estimate the probability of damage forindividual components (e.g., drift-sensitive or acceleration-sensitive components). Eachdamage state was associated with specific repair costs from the consequence functionsfor the economic loss, and these were aggregated to calculate the total direct economicloss, typically presented as a probabilistic distribution of repair costs, summarized by theexpected (mean) value at each Sa(T1) intensity.Finally, for the FEMA P-58 time-based assessment, economic losses for the range ofintensities (i.e., loss function), and their probabilities were weighted by the hazard curvedeveloped from the PSHA. By integrating these weighted losses over all hazard levels,the EAL was computed, providing a measure of the annualized seismic risk. The EALSustainability 2025, 17, 1200 13 of 26represents the average yearly economic loss due to earthquakes over the economic life ofthe building.3.3. Downtime AssessmentThe novel framework proposed by Molina Hutt et al. [13], which offers a probabilis-tic approach to model the post-earthquake recovery of buildings and to assess resiliencemetrics, was adopted. Downtime (i.e., recovery time) included the time for mobilizingresources after an earthquake and the time for conducting necessary repairs. The frame-work expands the FEMA P-58 [10] and the Resilience-based Earthquake Design initiative(REDi) [34] methodologies by modeling temporal buildings recovery timelines to targetrecovery states. Two target states to track the post-earthquake usability of the archetypeswere considered: (i) reoccupancy (RO) and (ii) functional recovery (FR). RO was definedas a post-earthquake recovery state where the building has ensured pre-event habitabilitycriteria. FR, on the other hand, was defined as a recovery state in which the buildingis sufficiently maintained or restored to support its pre-earthquake functionality. Thesestates provide a strategic view of recovery trajectories, offering insights into intermediatemilestones rather than focusing solely on the end state of full recovery.According to the framework, it is necessary to probabilistically model the delays thathinder the initiation or progress of repairs (i.e., impeding factors). Key factors include thetime required for inspection, stabilization, engineering and permitting, contractor mobiliza-tion, and securing financing. The delays, represented by lognormal distributions to accountfor variability and uncertainty, were calibrated with the scarce empirical information fromthe Mw 8.8 2010 Chile earthquake [6], where some buildings experienced significant dam-age and were repaired or demolished. Financing delays, which depend on factors such asthe economic loss ratio and the type of funding mechanism, were adjusted to represent thelocal politics about insurance, public loans, and private loans.Repair endeavors were organized into seven sequences (e.g., structural, interior, ex-terior, mechanical, electrical, elevator, and staircase repairs), which were grouped intoparallel repair paths. It was assumed that repairs progress in phases, with multiple floorsaddressed simultaneously to reduce downtime. This strategy is supported by observa-tions from the 1994 Northridge earthquake, where contractors typically repaired structuralelements, elevators, and staircases concurrently, followed by interior repairs [35].Using this information, the methodology, implemented in the software TREADSv2023 [13] and integrated seamlessly with PELICUN [33], provided the mean recoverytrajectories to achieve both recovery states at each Sa(T1) intensity. In particular, 2000 MonteCarlo simulations were performed to model potential recovery trajectories, integratingfragility data of damaged components and detailed repair sequencing. Each realizationprovided story-by-story downtime estimates (i.e., restoration/reconstruction over time),enabling a robust understanding of the uncertainties in recovery timelines. For collapsed orirreparable realizations, the downtime was equal to the building replacement time whichconsisted of the time for demolition and the time for reconstruction. Molina Hutt et al. [13]considered two weeks per floor to calculate the reconstruction time of US buildings. How-ever, on the basis of the Chilean engineering construction practice, it was assumed as3.5 weeks per floor.In addition, two resilience-based performance metrics were calculated: (i) robust-ness and (ii) rapidity. The former measures the ability of a building to withstand seismicdemands without significant degradation, while the latter evaluates the speed at whichrecovery milestones are achieved [36]. These resilience metrics enabled a comprehensiveevaluation of the seismic performance of the archetype. Finally, for the time-based as-sessment, recovery times for the range of intensities (i.e., downtime function) and theirSustainability 2025, 17, 1200 14 of 26probabilities were weighted by the hazard curve. By integrating these weighted times overthe derivative of all hazard levels, the expected annual downtime (EAD) was computed,providing a measure of the annualized seismic risk of the building. The EAD reflectsthe average annual recovery time caused by earthquakes over the economic lifespan ofa building.4. Results and Analysis4.1. Economic Loss Assessment ResultsThe expected loss ratio is one of the main outcomes of the intensity-based cost assess-ment. The ratio of the mean economic loss to the total construction cost defines the expectedloss ratio for a specific shaking intensity. Figure 4 shows the loss functions, which representthe expected loss ratios for a range of Sa(T1) intensities, for the benchmark archetype BAB(Figure 4a) and the archetype seismically enhanced with dampers BAB+FVD (Figure 4b).The figures also provide the loss breakdown in terms of the following: (i) the cost of build-ing collapse; (ii) irreparable damage or demolition; and (iii) repairable damage, expressedin terms of a percentage (%) of the initial construction cost of the BAB. Similarly, Figure 5shows the results for archetypes BAB+ENC (Figure 5a) and BAB+FVD+ENC (Figure 5b).According to the hazard curve from the PSHA, Sa(T1) intensities could be defined for 72-,475-, 2475-, and 4975-year return periods (i.e., SLE = 0.05 g, DBE = 0.15 g, MCE = 0.35 g,and VRE = 0.45 g, respectively).Sustainability 2025, 17, x FOR PEER REVIEW 22 of 41 average annual recovery time caused by earthquakes over the economic lifespan of a building. 4. Results and Analysis 4.1. Economic Loss Assessment Results The expected loss ratio is one of the main outcomes of the intensity-based cost assess-ment. The ratio of the mean economic loss to the total construction cost defines the ex-pected loss ratio for a specific shaking intensity. Figure 4 shows the loss functions, which represent the expected loss ratios for a range of Sa(T1) intensities, for the benchmark ar-chetype BAB (Figure 4a) and the archetype seismically enhanced with dampers BAB+FVD (Figure 4b). The figures also provide the loss breakdown in terms of the following: (i) the cost of building collapse; (ii) irreparable damage or demolition; and (iii) repairable dam-age, expressed in terms of a percentage (%) of the initial construction cost of the BAB. Similarly, Figure 5 shows the results for archetypes BAB+ENC (Figure 5a) and BAB+FVD+ENC (Figure 5b). According to the hazard curve from the PSHA, Sa(T1) inten-sities could be defined for 72-, 475-, 2475-, and 4975-year return periods (i.e., SLE = 0.05 g, DBE = 0.15 g, MCE = 0.35 g, and VRE = 0.45 g, respectively). (a) (b) Figure 4. Loss function for archetypes (a) BAB and (b) BAB+FVD. Figure 4. Loss functi n for arch types (a) BAB and (b) BAB+FVD.Sustainability 2025, 17, 1200 15 of 26Sustainability 2025, 17, x FOR PEER REVIEW 23 of 41 (a) (b) Figure 5. Loss function for archetypes (a) BAB+ENC and (b) BAB+FVD+ENC. It can be observed that the expected earthquake-induced repair costs are negligible and do not exceed 0.4% for the SLE intensity. Likewise, the expected losses are limited, with values of no more than 4.1%, for the DBE. Conversely, at MCE and VRE intensity levels, the expected costs are significantly larger. For example, the benchmark archetype BAB depicts loss ratios of 19.3% and 37.0% of the building replacement cost for the 2475 and 4975 return periods, respectively. Nonetheless, a comparison between these values and those reported in other studies on high-rise RC wall buildings under subduction seis-micity [37] for the 475-year hazard level indicate smaller losses for Chilean RC buildings than for those located in Seattle (i.e., Cascadia subduction zone) which were designed to comply with the US codes. A common characteristic of Chilean RC building is the large lateral stiffness, due to stricter inter-story drift limits and base shear requirements, which yields small lateral displacement demands and, therefore, reduced damage and economic losses. Moreover, in Chilean buildings the cost contribution of non-structural components is significantly less important than in US buildings, which is another reason why economic losses are smaller in Chilean buildings. Regarding the impact of FVDs, results indicate that the repair cost of the seismically improved Chilean RC dual wall–frame building with energy-dissipating devices (i.e., BAB+FVD) is 30–40% less than that of the conventional design (i.e., BAB). Certainly, this reduction is more meaningful at extreme intensities (MCE and VRE) than at frequent in-tensities (SLE and DBE). For instance, the repair cost drops from 19.3% to 13.1% of the Figure 5. Loss function for archetypes (a) BAB+ENC and (b) BAB+FVD+ENC.It can be observed that the expected earthquake-induced repair costs are negligibleand do not exceed 0.4% for the SLE intensity. Likewise, the expected losses are limited, withvalues of n mo e than 4.1%, for the DBE. Conversely, at MCE and VRE intensity evels, theexpected costs are significantly larger. For example, the b nchmark arch type BAB depictsloss ratios of 19.3% and 37.0% of the building replacement cost for the 2475 and 4975 returnperiods, respectively. Nonetheless, a comparison b tween thes values and those reportedin other studies on high-rise RC wall buildings n er subdu tion seismicity [37] for the475-year hazard level indicate smaller l sses for Chilean RC buildings tha for those locatedin Seattle (i.e., Cascadia s bduction zone) which were desi ned to comply with the UScodes. A common ch acteristic of Chilean RC building is the large l teral stiffness, dueto stricter inter-story drift imits and b se shear requirements, which yi l s mall lateraldisplacement demands and, therefore, reduc d damage and economic losses. Moreov r, inChilean buil ings the cost cont ibution o non-structur l compon nts is sig ificantly lessimportant han in US buildings, which is another reason why economic losses are smallerin Chilean buildings.Regarding the impact of FVDs, results indicate that repair cost of the seismi-cally improved Chilean RC dual wall–frame building with energy-dissipating devices (i.e.,BAB+FVD) is 30–40% less than that of the conventional d sign (i.e., BAB). Certainly, thisreduction is more meaningful at extr me nte sities (MCE and VRE) than at frequent inten-sities (SLE and DBE). For instance, the repair cost drops from 19.3% to 13.1% of the buildingreplacement cost at the MCE intensity, and from 37.0% to 21.1% at t e VRE intensity.Sustainability 2025, 17, 1200 16 of 26Regarding the influence of the enhanced non-structural components, results showslight reductions in repair costs at all intensity levels, revealing that the cost–benefit of thisstrategy is limited (at least for the case study considered in this study). This observationmust be regarded cautiously, since further studies will be needed to consider RC buildingswith different heights, seismicity levels, and soil types. Previous studies on commercialbuildings with more flexible structures, such as steel moment-resistant frame buildings [19],found more significant impacts due to the enhancement of the seismic performance ofnon-structural components such as partition walls.From the loss breakdown, it is identified that the major contributor to the mean loss isrepairable damage to structural and non-structural components, up to Sa(T1) = 0.80 g for theBAB and BAB+ENC archetypes and up to Sa(T1) = 0.90 g for the archetypes equipped withFVDs. For the benchmark archetype BAB, loss ratios due to irreparable damage becomemeaningful at very extreme intensities, between 0.45 g and 0.70 g, whereas collapse damageis meaningful at intensities greater than 1.0 g.Despite the scarce information available related to ground motions, it is presumedthat the 2010 Chile earthquake produced peak ground accelerations from 0.20 g to 0.25 gin the commercial district of Santiago [6]. RC high-rise buildings (T1 ~ 2.0 s, similar to thefundamental period of the archetype buildings considered in this study) could experienceSa values in the order of 0.15 g to 0.20 g. Therefore, Figure 6 and Table 5 present the explicitmetrics of the loss breakdown at the Sa(T1) intensity of 0.20 g for the base building andfor the seismically improved buildings. Some interesting observations can be pointedout, as follows. For the BAB, the major contributor to the repairable damage is non-structural damage, with a total value of 4.4% of the building replacement cost, whereas3.1% is the value for structural damage (slab–column joints, shear walls, and beam–columnjoints). Regarding the non-structural damage, the acceleration-sensitive components (e.g.,mechanical, electrical, plumbing, elevators, and ceilings) represent 2.8% of the losses, whilethe displacement-sensitive components (e.g., stairs, partitions, and façade) represent 1.6%of the losses. These results show a significant contribution of acceleration-sensitive non-structural components to losses in commercial buildings during the 2010 Chile earthquake,which is in agreement with studies that have evaluated in detail the economic losses actuallygenerated by this event [1].Sustainability 2025, 17, x FOR PEER REVIEW 25 of 41 Figure 6. Mean loss ratio for each design strategy at Sa(T1) = 0.20 g. Table 5. Loss breakdown at Sa(T1) = 0.20 g. Components BAB BAB+ENC BAB+FVD BAB+FVD+ENC Non-structural –acc. sensitive MEP 1.3 1.1 1.1 0.9 Elevator 0.5 0.5 0.5 0.5 Ceilings 1.0 0.9 0.8 0.7 Subtotal = 2.8% 2.5% 2.4% 2.1% Non-structural – drift sensitive Stairs 0.1 0.1 0.0 0.0 Partitions 1.3 0.8 0.8 0.5 Façade 0.2 0.2 0.1 0.1 Subtotal = 1.6% 1.1% 0.9% 0.6% NSC Subtotal = 4.4% 3.6% 3.3% 2.7% Structural s/c joints 2.0 2.0 0.8 0.8 Walls 0.0 0.0 0.0 0.0 b/c joints 1.1 1.1 0.3 0.3 SC Subtotal = 3.1% 3.1% 1.1% 1.1% Irreparable 0.0 0.0 0.0 0.0 Collapse 0.0 0.0 0.0 0.0 TOTAL = 7.5% 6.7% 4.4% 3.8% Note: MEP: mechanical, electrical, plumbing; s/c: slab–column; b/c: beam–column. Although comparisons at different intensity levels can be valuable, it should be con-sidered that different Sa(T1) intensities are associated with different annual exceedance rates (i.e., different probabilities of occurrence). To account for this issue, the economic losses were integrated with the absolute value of the derivative of the hazard curve to estimate the EAL, according to Equation (2). The EAL, which represents the average an-nual economic loss due to seismic damage, plays a crucial role in the evaluation of differ-ent enhancement strategies with FVDs and/or ENCs. E A L = <munderover> (2)Figure 6. Mean loss ratio for each design strategy at Sa(T1) = 0.20 g.Sustainability 2025, 17, 1200 17 of 26Table 5. Loss breakdown at Sa(T1) = 0.20 g.Components BAB BAB+ENC BAB+FVD BAB+FVD+ENCNon-structural –acc. sensitiveMEP 1.3 1.1 1.1 0.9Elevator 0.5 0.5 0.5 0.5Ceilings 1.0 0.9 0.8 0.7Subtotal = 2.8% 2.5% 2.4% 2.1%Non-structural – drift sensitiveStairs 0.1 0.1 0.0 0.0Partitions 1.3 0.8 0.8 0.5Façade 0.2 0.2 0.1 0.1Subtotal = 1.6% 1.1% 0.9% 0.6%NSC Subtotal = 4.4% 3.6% 3.3% 2.7%Structurals/c joints 2.0 2.0 0.8 0.8Walls 0.0 0.0 0.0 0.0b/c joints 1.1 1.1 0.3 0.3SC Subtotal = 3.1% 3.1% 1.1% 1.1%Irreparable 0.0 0.0 0.0 0.0Collapse 0.0 0.0 0.0 0.0TOTAL = 7.5% 6.7% 4.4% 3.8%Note: MEP: mechanical, electrical, plumbing; s/c: slab–column; b/c: beam–column.On the other hand, the building equipped with dampers (BAB+FVD) shows impor-tant loss reductions in the structural components (i.e., 60%), especially in the columnjoints, and smaller reductions for the non-structural components (i.e., reductions of 25%).The building with enhanced non-structural components (BAB+ENC) exhibits relativelysmall loss reductions in most of the non-structural components, but, as expected, impor-tant reductions in lightweight partitions (i.e., 40%, similar to that of the BAB+FVD). Thelast strategy (BAB+FVD+ENC) combines the beneficial reductions in structural and non-structural components, with significant reductions in partitions (i.e., 60%). Finally, costsrelated to demolition and collapse seem to be negligible at this specific Sa(T1) intensity, andthis observation agrees again with the empirical evidence observed after the 2010 Chileearthquake, where just one office building suffered a partial collapse in Concepcion [6].Although comparisons at different intensity levels can be valuable, it should be consid-ered that different Sa(T1) intensities are associated with different annual exceedance rates(i.e., different probabilities of occurrence). To account for this issue, the economic losseswere integrated with the absolute value of the derivative of the hazard curve to estimate theEAL, according to Equation (2). The EAL, which represents the average annual economicloss due to seismic damage, plays a crucial role in the evaluation of different enhancementstrategies with FVDs and/or ENCs.EAL =∫ ∞0E[L|IM = im ]∣∣∣∣dλ(IM)dIM∣∣∣∣ dIM, (2)where E[L|IM] represents the loss function and dλ(IM)dIM represents the derivative of thehazard curve.Figure 7 and Table 6 show the EAL as a ratio of the BAB construction cost (USD 1660per square meter). Table 6 shows EAL values in the order of 0.125, 0.106, 0.093, and 0.082%for the BAB, BAB+ENC, BAB+FVD, and BAB+FVD+ENC archetypes, respectively. Thestrategy of incorporating FVDs into the base building gives a 25% reduction in the baseEAL, while with the strategy of including ENCs a reduction of only 15% is achieved. For theSustainability 2025, 17, 1200 18 of 26strategy that combines FVDs and ENCs, the reduction is greater than 35% but at the expenseof a higher initial construction cost (106% of the BAB cost, as previously assumed). Notethat these results seem to be much smaller than those for steel office buildings in the USA,which have more flexible structural systems (and, consequently, a greater level of damage)as well as different building inventories, dominated by non-structural components thatare more susceptive to earthquake damage than structural components [19]. For instance,for a special moment-resistant-frame building with T1 = 1.86 s (similar to the fundamentalperiod of the office buildings analyzed in this study), the EAL could be as large as 1.6%.Sustainability 2025, 17, x FOR PEER REVIEW 28 of 41 components that are more susceptive to earthquake damage than structural components [19]. For instance, for a special moment-resistant-frame building with T1 = 1.86 s (similar to the fundamental period of the office buildings analyzed in this study), the EAL could be as large as 1.6%. Table 6 also shows the disaggregated EAL information for the cost of collapse, irrep-arable damage, and repairable damage. In all cases, the contribution of collapse or demo-lition to losses is relatively low. Furthermore, a significant contribution of non-structural damage is evident, especially of those components sensitive to acceleration. This would indicate that Chilean stiff RC structures have important floor acceleration demands that are just sligh ly reduc d with the incorporation of FVDs. Results revealed th incor-p ration of ENCs, FVD , and a combination of the previ us two strategies chiev EAL values of 0.106%, 0.093%, and 0.082%, r spectively, while the archetype base building wit out design improvements reached an EAL of 0.125%. The atter indicat s EAL reduc-tions (compared to the base case) of 15%, 26%, an 34% for the cases f BAB+ENC, BAB+FVD, and BAB+FVD+ENC, r spectively, whe e the largest eff ct was provided by the incorporation of FVD due to the reduced damage to both tructural components and non-structural components sensitive to story drift ratios. Figure 7. The economic loss evaluation in terms of EAL as a percentage of the BAB cost. Table 6. EAL breakdown in terms of percentage of BAB’s cost. Contributor BAB BAB+ENC BAB+FVD BAB+FVD+ENC Collapse 0.002 0.003 0.002 0.002 Irreparable 0.003 0.003 0.002 0.002 SC 0.020 0.021 0.010 0.010 NSC-DS 0.032 0.026 0.016 0.015 NSC-AS 0.067 0.054 0.064 0.054 TOTAL = 0.125% 0.106% 0.093% 0.082% [US$/m2] 2.1 1.8 1.5 1.4 Note: SC: structural components; NSC-DS: displacement-sensitive non-structural components; NSC-AS: acceleration-sensitive non-structural components. Figure 7. The economic loss evaluation in terms of EAL as a percentage of the BAB cost.Table 6. EAL breakdown in terms of percentage of BAB’s cost.Contributor BAB BAB+ENC BAB+FVD BAB+FVD+ENCCollapse 0.002 0.003 0.002 0.0 2Irreparable 0.003 0.003 0.002 0.002SC 0.020 0.021 0.010 0.010NSC-DS 0.032 0.026 0.016 0.015NSC-AS 0.067 0.054 0.064 0.054TOTAL = 0.125% 0.106% 0.093% 0.082%[US$/m2] 2.1 1.8 1.5 1.4Note: SC: structural components; NSC-DS: displacement-sensitive non-structural components; NSC-AS:acceleration-sensitive non-structural components.Table 6 also shows the disaggregated EAL information for the cost of collapse, irrepara-ble damage, and repairable damage. In all cases, the contribution of collapse or demolitionto losses is relatively low. Furthermore, a significant contribution of non-structural damageis evident, especially of those components sensitive to acceleration. This would indicatethat Chilean stiff RC structures have important floor acceleration demands that are justslightly reduced with the incorporation of FVDs. Results revealed that the incorporationof ENCs, FVDs, and a combination of the previous two strategies achieved EAL valuesof 0.106%, 0.093%, and 0.082%, respectively, while the archetype base building withoutdesign improvements reached an EAL of 0.125%. The latter indicates EAL reductions (com-pared to the base case) of 15%, 26%, and 34% for the cases of BAB+ENC, BAB+FVD, andBAB+FVD+ENC, respectively, where the largest effect was provided by the incorporationof FVDs due to the reduced damage to both structural components and non-structuralcomponents sensitive to story drift ratios.Sustainability 2025, 17, 1200 19 of 264.2. Downtime Assessment ResultsFor the intensity-based downtime assessment, the framework proposed by MolinaHutt et al. [13] was adopted to calculate the following outputs and resilience-based metrics:(i) the recovery trajectory, which shows the progress of building restoration or reconstruc-tion over time to reach a target recovery state; (ii) the robustness; and (iii) the rapidity. As anexample, Figure 8 shows the simulated recovery trajectories describing building usabilityat any time after an earthquake with Sa(T1) = 0.20 g (associated with the 2010 Chile earth-quake) for the four archetypes. Building usability ranges from 0% to 100%, where 100%indicates that all floors of the building have achieved the desired recovery state, and 0%indicates that none have. Specifically, Figure 8 displays the governing recovery trajectoriesto achieve the FR state for all 2000 realizations. The plots highlight the large uncertaintyassociated with downtime estimates (the 10th, 50th, and 90th percentiles are shown). Fromthe figures, the median FR times are 212 (BAB in Figure 8a), 206 (BAB+ENC in Figure 8b),166 (BAB+FVD in Figure 8c), and 161 (BAB+FVD+ENC in Figure 8d). Decreases in meandowntime values are noticeable when the building is equipped with FVDs (i.e., reductionsof 20%). On the other hand, minimal reductions in the order of 3% are achieved when thebuilding incorporates ENCs.Regarding the buildings’ seismic performance in terms of robustness, which describesthe probability of a building not achieving a target recovery state immediately after anearthquake, there are interesting behaviors. Results indicate that under the Sa(T1) = 0.20 gintensity, the probabilities of not achieving RO and FR immediately after the earthquake are100%, and 100%, respectively, for the BAB. Similar probabilities are reported for the otherseismically enhanced buildings. The large outputs are mostly because of the damage to non-structural components such as mechanical–electrical–plumbing, ceilings, and partitions,which need to be repaired/replaced before occupants can reoccupy the office buildings.Regarding the building performance in terms of rapidity, which describes the probabil-ity of not achieving a recovery state within a specified time, the results for the Sa(T1) = 0.20 gintensity are summarized in Figure 9. Assuming as target recovery time that the build-ings should be repaired within 4 months, the probabilities that the downtime required toachieve RO exceeds the target recovery time are 95% (BAB in Figure 9a), 90% (BAB+ENCin Figure 9b), 60% (BAB+FVD in Figure 9c), and 55% (BAB+FVD+ENC in Figure 9d). More-over, the probabilities that the downtime required to achieve FR exceeds 4 months are 98%(BAB), 97% (BAB+ENC), 87% (BAB+FVD), and 85% (BAB+FVD+ENC). It is worth notingthat these downtime assessments are related to the resilience of the built infrastructure,where more than 4 months to achieve FR implies large social impacts.As mentioned before, although comparisons at different intensity levels can be valu-able, it should be considered that each Sa(T1) intensity is associated with a different proba-bility of occurrence. Similarly to economic losses, the recovery times were integrated withthe absolute value of the derivative of the hazard curve to estimate the EAD, accordingto Equation (3). The EAD, which represents the average annual downtime due to seismicdamage, also plays a key part in the evaluation of different enhancement strategies withFVDs and/or ENCs.EAD =∫ ∞0E[DT|IM = im ]∣∣∣∣dλ(IM)dIM∣∣∣∣ dIM, (3)where E[DT|IM] represents the downtime function and dλ(IM)dIM represents the derivative ofthe hazard curve.Sustainability 2025, 17, 1200 20 of 26Sustainability 2025, 17, x FOR PEER REVIEW 30 of 41 (a) (b) (c) (d) Figure 8. Recovery trajectories to achieve FR for (a) BAB, (b) BAB+ENC, (c) BAB+FVD (d) BAB+FVD+ENC, for all realizations the Sa(T1) = 0.20 g intensity level. Note: gray lines represent single realizations, while red lines represent median values. Left and right dashed black lines rep-resent 10th and 90th percentiles, respectively. (a) (b) Figure 8. Recovery trajectories to achieve FR for (a) BAB, (b) BAB+ENC, (c) BAB+FVD(d) BAB+FVD+ENC, for all realizations the Sa(T1) = 0.20 g intensity level. Note: gray lines rep-resent single realizations, while red lines repr sent median values. Left an right dashed black linesrepresent 10th and 90th percentiles, respectively.Sustainability 2025, 17, x FOR PE R EVIEW 30 of 41 (a) (b) (c) (d) Figure 8. Recovery trajectories to achieve FR for (a) BAB, (b) BA +ENC, (c) BAB+FVD (d) BAB+FVD+ENC, for all realizations the Sa(T1) = 0.20 g intensity level. Note: gray lines represent single realizations, while red lines pres nt media values. Left and right dashed black lines rep-resent 10th and 90th percentiles, respectively. (a) (b) Figure 9. Cont.Sustainability 2025, 17, 1200 21 of 26Sustainability 2025, 17, x FOR PEER REVIEW 31 of 41 (c) (d) Figure 9. Downtime to achieve RO, and FR for (a) BAB, (b) BAB+ENC, (c) BAB+FVD, (d) BAB+FVD+ENC at Sa(T1) = 0.20 g intensity level. Note: DT: downtime. As mentioned before, although comparisons at different intensity levels can be valu-able, it should be considered that each Sa(T1) intensity is associated with a different prob-ability of occurrence. Similarly to economic losses, the recovery times were integrated with the absolute value of the derivative of the hazard curve to estimate the EAD, accord-ing to Equation (3). The EAD, which represents the average annual downtime due to seis-mic damage, also plays a key part in the evaluation of different enhancement strategies with FVDs and/or ENCs. E A D = <munderover> ∫ 0 ∞ </munderover > E <mfenced close="]" open="["> D T <mfenced close="" open="|"> I M = i m </mfenced> </mfenced><mfenced close="|" open="|"> d λ <mfenced> (3)Figure 9. Downtime to achieve RO, and FR for (a) BAB, (b) BAB+ENC, (c) BAB+FVD,(d) BAB FVD+ENC at Sa(T1) = 0.20 g int nsity lev l. Note: DT: downtime.Table 7 shows the EAD as a ratio of the BAB reconstruction time and also th time inunits of days. In thi study, the reconstructio time of the archetype building was calculatedassuming that th construction of each story takes 24.5 days. This results i a total of465.5 days for the 16-story archetypes. In addition, the median building demolition timewas estimated as 550 days based on the data from the demolition times of the Chileanbuildings that suffered s vere damag in the 2010 earthquake. Therefor , the resultanttotal building replacement time is 1015.5 days. The table shows the EAD values to achievereoccupancy RO state to be equal to 6.6, 4.0, 5.0, and 2.6 days for the BAB, BAB+ENC,BAB+FVD, and BAB+FVD+ENC archetypes, respectively. In addition, the EAD values toachieve FR state are equal to 9.5, 9.1, 8.6, and 8.3 days for the BAB, BAB+ENC, BAB+FVD,and BAB+FVD+ENC, respectively. A co parison between EAD values to achieve FRindicates that the strategy of incorporating FVDs gives a 10% reduction in the base EAD,while the strategy of including ENCs gives a reduction of only 4%. For the strategy thatcombines FVDs and ENCs the reduction is about 13% of the base EAD. These results, whichcorrespond to median predictions of downtime, highlight how damage that requires onlymoderate repair costs could result in excessive downtimes, leading to the displacement ofoccupants with associated indirect costs.Table 7. EAD in terms of percentage of building replacement time in absolute days.BAB BAB+ENC BAB+FVD BAB+FVD+ENCRO state [%] 0.65 0.39 0.49 0.26[days] 6.6 4.0 5.0 2.6FR state [%] 0.94 0.90 0.85 0.82[days] 9.5 9.1 8.6 8.34.3. Earthquake-Induced Life-Cycle CostTime-based assessments were performed to evaluate the probable performance ofthe four archetypes over a specified period of time (e.g., t = 50 years, assumed equal tothe building economic life in this study) considering all earthquakes that could occurin that time period, and the probability of occurrence associated with each earthquake.Mean annual values such as EAL and EAD were taken from the analysis described inthe former paragraphs. These annual values were useful for a benefit–cost study becausethey can be associated with reasonable insurance premiums. From the EAL, the annualdirect economic costs were USD 2.1, USD 1.8, USD 1.5, and USD 1.4 per square meter forthe BAB, BAB+ENC, BAB+FVD, and BAB+FVD+ENC archetypes, respectively. It wasassumed that the cost associated with each day of downtime was USD 0.5 per squaremeter in lost rent. This results in annual indirect economic costs of USD 4.8, 4.6, 4.3, and4.2 per square meter for the BAB, BAB+ENC, BAB+FVD, and BAB+FVD+ENC archetypes,respectively. Combining direct and indirect costs results in a total expected annual lossSustainability 2025, 17, 1200 22 of 26(EALt) of USD 6.9, 6.4, 5.8, and 5.6 per square meter for the BAB, BAB+ENC, BAB+FVD,and BAB+FVD+ENC archetypes, respectively.The benefit–cost study involved a comparison between the net present value of averageannual losses that are avoided through enhanced seismic performance and the initialconstruction costs associated with providing enhanced seismic performance. Using thediscount rate (DR) concept, according to Equation (4), the EALt of the next 50 years can bebrought to present value (PV) and combined with the initial construction cost (CC).PV(EALt) =∑ti=1EALt(1+ DR)i, (4)The expected life-cycle cost (ELCC), a parameter with which decisions can be made, iscalculated as shown in Equation (5). The ELCC facilitates the economic evaluation of thebase archetype BAB and of each seismic performance improvement strategy.ELCC = CC + PV(EALt), (5)Given the variations in interest rates worldwide as well as in the Chilean econ-omy in recent years (post-pandemic era), a parametric study was carried out taking DRsaround 6% ± 3%. The initial CCs of the BAB, BAB+ENC, BAB+FVD, and BAB+FVD+ENCarchetypes were assumed equal to USD 1660, 1710, 1710, and 1755 per square meter, respec-tively. Figure 10 shows the variation in the ELCC at different DRs for the four archetypebuildings. Moreover, Table 8 presents a summary of the costs. Regarding the outcomes, forall the range of DRs the BAB base building has the lowest ELCC, while the highest costsbelong to the building that incorporates both FVDs and ENCs. For the BAB+FVD strategy,the ELCCs were slightly lower than those of the BAB+ENC strategy. For the largest DRs,costs were very similar for both the BAB+FVD and BAB+ENC strategies.It is worth mentioning that even though the previous ELCCs have been analyzedbased on varying levels of DRs (0% to 9%) and a reasonable number of ownership years(50 years, which is common for office building occupancy), the BAB base building alwayspresented the lowest ELCC. This can be explained by the already-high seismic performanceof code-conforming RC buildings in Chile (particularly due to their high stiffness, whichreduces losses from damage to non-structural drift-sensitive components) and the lowercost fraction of non-structural components compared to other locations (e.g., California).Sustainability 2025, 17, x FOR PEER REVIEW 37 of 41 Figure 10. Expected life-cycle costs at different discount rates. Table 8. Initial construction cost and expected life-cycle cost. Cost [US$/m2] BAB BAB+ENC BAB+FVD BAB+FVD+ENC CC 1660 1710 1710 1755 ELCC (DR = 9%) 1734 1778 1772 1818 (DR = 6%) 1767 1809 1799 1845 (DR = 3%) 1836 1873 1857 1901 Note: CC: construction cost; ELCC: expected life-cycle cost; DR: discount rate. Finally, since current Chilean seismic design provisions primarily focus on life safety and structural integrity during seismic events, with limited emphasis on recovery times, the resilience-based seismic design insights obtained in this study could play a crucial role in updating these provisions in Chile and other seismically active regions. In the future, seismic design provision in Chile might include considerations for di-rect economic losses and downtime (it is worth noting that still Chilean codes do not in-clude consideration for maximum probabilities of collapse, which are already included in ASCE 7-2022). As an initial step, quantifying economic losses and downtime for high-im-portance or high-occupancy buildings, such as hospitals, could become a requirement. This process would enable the establishment of future performance limits that balance enhanced resilience with reduced economic impacts and manageable initial construction costs. By integrating these resilience-based principles into seismic design provisions, Chile and other seismically active regions can transition toward more comprehensive frame-works that address both immediate safety and long-term resilience, ensuring economic sustainability and faster recovery after seismic events. 5. Conclusions This research evaluated the influence of three alternative design strategies to improve the seismic performance of code-conforming dual wall–frame buildings subjected to sub-duction seismicity. In particular, the impacts of the following strategies for the benchmark archetype building (BAB) were assessed: (i) fluid viscous dampers (FVDs); enhanced non-structural components (ENCs); and (iii) a combination of strategies (i) and (ii). The study estimated and compared the seismic performance of typical, representative Chilean RC dual wall–frame buildings in terms of economic losses and downtime, which are quanti-ties that are meaningful to improve the resilience of the built environment towards Figure 10. Expected life-cycle costs at different discount rates.Sustainability 2025, 17, 1200 23 of 26Table 8. Initial construction cost and expected life-cycle cost.Cost [US$/m2] BAB BAB+ENC BAB+FVD BAB+FVD+ENCCC 1660 1710 1710 1755ELCC (DR = 9%) 1734 1778 1772 1818(DR = 6%) 1767 1809 1799 1845(DR = 3%) 1836 1873 1857 1901Note: CC: construction cost; ELCC: expected life-cycle cost; DR: discount rate.However, it is important to note that the decision to choose between these designstrategies is not solely based on the ELCC; it might also involve stakeholders’ risk pref-erences and indirect costs (e.g., downtime) during the decision-making process. For ex-ample, a risk-averse stakeholder might still choose the strategy of BAB+FVDs to avoidlow-probability/high-consequence losses and reduce the expected downtime, whereas arisk-neutral stakeholder would choose the BAB strategy. Further research is needed toincorporate these preferences.Finally, since current Chilean seismic design provisions primarily focus on life safetyand structural integrity during seismic events, with limited emphasis on recovery times,the resilience-based seismic design insights obtained in this study could play a crucial rolein updating these provisions in Chile and other seismically active regions.In the future, seismic design provision in Chile might include considerations for directeconomic losses and downtime (it is worth noting that still Chilean codes do not includeconsideration for maximum probabilities of collapse, which are already included in ASCE7-2022). As an initial step, quantifying economic losses and downtime for high-importanceor high-occupancy buildings, such as hospitals, could become a requirement. This pro-cess would enable the establishment of future performance limits that balance enhancedresilience with reduced economic impacts and manageable initial construction costs.By integrating these resilience-based principles into seismic design provisions, Chileand other seismically active regions can transition toward more comprehensive frame-works that address both immediate safety and long-term resilience, ensuring economicsustainability and faster recovery after seismic events.5. ConclusionsThis research evaluated the influence of three alternative design strategies to improvethe seismic performance of code-conforming dual wall–frame buildings subjected to sub-duction seismicity. In particular, the impacts of the following strategies for the benchmarkarchetype building (BAB) were assessed: (i) fluid viscous dampers (FVDs); enhanced non-structural components (ENCs); and (iii) a combination of strategies (i) and (ii). The studyestimated and compared the seismic performance of typical, representative Chilean RCdual wall–frame buildings in terms of economic losses and downtime, which are quantitiesthat are meaningful to improve the resilience of the built environment towards sustainabledevelopment. As a case study, a reinforced concrete (RC) high-rise (16-story) office buildingwas considered. Following the FEMA P-58 and REDi methodologies, loss and downtimeassessments were conducted to calculate seismic performance metrics such as expectedannual loss (EAL), expected annual downtime (EAD), recovery trajectories, robustness, ra-pidity, and expected life-cycle cost (ELCC) for each strategy. The summary of the outcomesis as follows:• For all archetypes, expected direct economic losses are negligible at the SLE intensitylevel (≤0.4% of the building replacement cost) and are minimal (≤4.1%) at the DBElevel. For the benchmark archetype, losses are considerable at the MCE and VRESustainability 2025, 17, 1200 24 of 26levels (19.3% and 37.0%, respectively). For the archetype with FVDs, there are lossreductions of approximately 40% at most Sa(T1) intensities.• The archetype equipped with FVDs showed EAL reductions in the order of 25%with respect to a conventional design (from 0.125% to 0.093%). In contrast, slightdecreases in the order of 12% were found for the archetypes that incorporate ENCs(from 0.125% to 0.106%, and from 0.093% to 0.082%). This reveals that there may be alimited cost–benefit trade-off when applying this latter strategy, at least for this typeof RC building.• Regarding the building performance in terms of robustness at the Sa(T1) = 0.20 gintensity level (i.e., the 2010 Chile earthquake), the probabilities of not achievingRO and FR states immediately after the earthquake are equal to 100% for all thearchetypes. The large outputs are mostly because of damage in non-structural compo-nents such as mechanical–electrical–plumbing, ceilings, and partitions, which need tobe repaired/replaced before residents can reoccupy office buildings.• Regarding the building performance in terms of rapidity at the same intensity, theprobabilities that the downtime required to achieve FR exceeds 4 months are 98%(BAB), 97% (BAB+ENC), 87% (BAB+FVD), and 85% (BAB+FVD+ENC). It is worthnoting that these downtime assessments are related to the resilience of the builtinfrastructure, where more than 4 months for FR implies large social impacts.• The archetype equipped with FVDs showed EAD reductions in the order of 10%with respect to a conventional design (from 9.5 to 8.6 days) to achieve the functionalrecovery (FR) state. On the other hand, slight reductions in the order of 4% are reportedfor the archetypes that incorporate ENCs (from 9.5 to 9.1 and from 8.6 to 8.3 days).This reveals that there may be a limited cost–benefit trade-off when applying this latterstrategy, at least for this type of RC building.• Results indicate that in Chilean RC dual wall–frame buildings, incorporation of aseismic protection system such as FVDs could lead to higher levels of resilience.Nevertheless, the observations made in this study must be judged with caution sincefurther studies will be needed to consider buildings with different heights, seismicitylevels, soil types, and possibly a more refined review of the initial assumptions.• Finally, the resilience-based insights from this study could guide updates to includeconsiderations for direct economic losses and downtime in current Chilean seismicdesign provisions (that focus solely on life safety and structural integrity, lackingperformance-based objectives, including resilience). As first step, quantification oflosses and downtime for critical buildings, such as hospitals, could establish per-formance limits that balance resilience, economic impact, and construction costs.Incorporating these principles would enable Chile and other regions to adopt com-prehensive frameworks that address both safety and long-term recovery, ensuringeconomic sustainability and faster post-earthquake recovery.All these conclusions are based on results obtained from a large number of nonlinearresponse history analyses. In order to make possible such large amount of analyses, somesimplifying assumptions had to be made, and some features of the seismic response (e.g.,the torsional response) were not taken into account. The simplifying assumptions adoptedin this study were carefully evaluated in order to minimize their impact on the results.However, although not expected to be significant, such an impact will nevertheless beevaluated in future studies.Author Contributions: Conceptualization, M.F.G., G.A.-L., D.L.-G. and C.M.H.; methodology, M.F.G.,G.A.-L., D.L.-G. and C.M.H.; software, M.F.G. and C.M.H.; validation, M.F.G., G.A.-L., D.L.-G. andC.M.H.; formal analysis, M.F.G., G.A.-L., D.L.-G. and C.M.H.; investigation, M.F.G., G.A.-L., D.L.-G.Sustainability 2025, 17, 1200 25 of 26and C.M.H.; resources, G.A.-L. and D.L.-G.; data curation, M.F.G.; writing—original draft preparation,M.F.G. and G.A.-L.; writing—review and editing, G.A.-L., D.L.-G. and C.M.H.; visualization, M.F.G.and C.M.H.; supervision, G.A.-L., D.L.-G. and C.M.H.; project administration, G.A.-L.; fundingacquisition, G.A.-L. All authors have read and agreed to the published version of the manuscript.Funding: This research was funded by Agencia Nacional de Investigación y Desarrollo (ANID)de Chile, ANID Doctorado Nacional 2018 Folio 21181157, ANID FONDECYT de Iniciación, Grant11191194, Research Center for Integrated Disaster Risk Management (CIGIDEN) ANID FONDAP1523A0009, and UBB-FAPEI FP2460533.Institutional Review Board Statement: Not applicable.Informed Consent Statement: Not applicable.Data Availability Statement: Data are available upon reasonable request.Acknowledgments: Valuable comments on the Chilean seismic design practice were provided by IanWatt (VMB Structural Engineering) and Mario Lafontaine (Rene Lagos Engineers). The strong motiondatabase was provided by the SIBER-RISK project: Simulation Based Earthquake Risk and Resilienceof Interdependent Systems and Networks. Funding for the APC was provided by ANID FONDECYTde Iniciación, Grant 11191194. 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Vancouver : University of British Columbia Library
Multidisciplinary Digital Publishing Institute
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Faculty
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RC dual wall–frame office buildings
fluid viscous damper
enhanced non-structural component
loss assessment
downtime assessment
resilience
subduction earthquakes
Loss and Downtime Assessment of RC Dual Wall–Frame Office Buildings Toward Resilient Seismic Performance
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