Seismic Retrofitting of RC Buildings Using a Performance-Based Approach for Risk Resilience and Vulnerability Assessment

Abstract

This paper presents a framework for evaluating the impact of seismic retrofitting alternatives on seismic risk, specifically focusing on economic losses, social losses, environmental losses, resilience, and vulnerability of reinforced concrete (RC) structures. From a cost-effectiveness perspective, this study concentrates on the retrofitting of ground story columns, which has proven to be highly effective in enhancing the performance of the structure, particularly when its behavior is mainly governed by column capacities and story response. The methodology is divided into three main parts. The first part involves a global damage evaluation, which is estimated using a seismic vulnerability assessment based on the collapse fragility function. This function is derived from capacity curves obtained through nonlinear pushover analysis. The second part focuses on assessing seismic risk for various earthquake intensities, where fragility functions and consequence functions are derived and evaluated for structural components. This allows for the calculation of losses in terms of social, economic, and environmental impacts. The third part addresses the functionality and recovery of the structure, along with its resilience, by considering repair times and associated delays. Indices are developed for all direct and indirect losses, and weightage factors are assigned to each category to optimize the selection of the most suitable retrofitting alternative for specific scenarios. To illustrate this framework, a five-story hospital building is used as an example, as hospitals are critical structures that need to remain operational after earthquakes. Four retrofitting alternatives are proposed to identify the optimal choice that effectively meets all desired functions.

1. Introduction

Earthquake studies confirmed that the expected life safety level can be provided by the customary strength design methods satisfactorily. However, huge structural and nonstructural damage can take place, thus triggering a great amount of direct and indirect losses as a result of downtime and repair actions [1,2,3,4,5,6,7,8], evidenced by 1994 Northridge, 1995 Kobe [9], and, most recently, 2023 Turkey earthquakes [5,7]. Recent destructive earthquakes throughout the world have exposed the vulnerability of existing infrastructure, including (non-code-conforming) RC frame structures. These structures are more vulnerable to structural failures than modern code-compliant frame structures [10,11,12,13] because of poor structural and seismic detailing adopted during the execution phase of these structures [14,15]. These RC frame structures often possess the soft-story mechanism that makes them vulnerable to earthquakes. Since these kinds of structures consist of a large portion of the existing infrastructure, particularly in seismic areas, effective assessment techniques are desirable to calculate the potential collapse and to compare various retrofit strategies for these existing structures [16,17,18]. Various researchers have investigated the response of RC frame structures [19,20,21,22,23,24,25,26,27,28,29] and highlighted the response of these structures to various earthquakes. One such finding from those studies, as outlined by Gautam et al. [29], describes the significance of timely retrofitting of such structures that are vulnerable to earthquake damage as one of the key attempts to ensure the safety of such structures in seismically prone regions. Various traditional retrofit approaches [30,31,32,33,34], like steel or concrete jacketing of the columns, provision of shear walls, etc., have been offered [35,36,37,38] and can be utilized for certain performance levels as well as requirements by adopting modern seismic codes to decrease the potential collapse, optimize the performance, and mitigate the losses. These losses can be further subcategorized into social, economic, and environmental losses, e.g., casualties and fatalities, property damage, occupants’ relocation and rent charges, missing revenues, business interruption, etc. [1]. An illustration of these earthquake-induced losses is presented in Figure 1.

The performance-based assessment has been a continued research subject over the last two decades among the engineering community to create seismic fragilities [39,40,41] and earthquake loss assessment [42,43,44,45]. The performance-based paradigm permits engineers to evaluate an explicit structural performance level for a specified earthquake hazard level at any local site. Nonlinear structural analysis methods can be employed to determine the structure’s response subjected to various types of loading [46,47,48,49,50]. These techniques can be applied to approximate factors essential for explicit probabilistic evaluation criteria, like demand and capacity factor design (DCFD) [51], and also to perform direct probabilistic performance evaluation using numerical methods [39,52,53,54,55]. In a nonlinear static pushover (NSP) analysis, a numerical model integrating the nonlinear load-displacement response of several building components is exposed to escalating lateral loads, signifying inertia forces during an earthquake, until a target displacement is surpassed. The ease of its formulation makes it a fast and efficient analysis procedure for capacity assessment and/or performance-based safety-checking [56,57,58,59,60,61,62,63,64,65,66,67,68]. Accordingly, FEMA 356 [69] endorses the use of no less than two lateral load patterns for the NSP to include the extent of forces that the structure may experience in the real dynamic excitation. Therefore, the NSP analysis method is adopted in this study for its accuracy and cost-effectiveness to quantify the structural damage of the reference model along with the retrofitting strategies.

Both structural elements (SEs) and nonstructural elements (NSEs) are equally important in the functionality of a structure, and a structure will be considered functional only if it fulfills the desired performance level [70]. The effects of damages in buildings extend from economic losses (due to repair activities and business disruption) to social and environmental losses like casualties, fatalities, homelessness, and discharge of harmful materials, among others. Structures are conventionally designed for the so-called ‘‘maximum considered earthquake”, and it is expected that this design will minimize the losses due to earthquakes. Thus, in this study, the damages to both the SEs and NSEs are considered; however, the NSEs depend on the type of facility and vary considerably with the usage of the building. Thus, the list of NSEs will be different for a residential building as compared to a commercial or office building. However, all the NSEs can be broadly classified into two main categories: acceleration-sensitive and drift-sensitive. Therefore, to make this study more appealing and adaptive, both the acceleration- and drift-sensitive components are considered in the damage estimation and loss calculations; therefore, the functionality of both the SEs and NSEs is considered in this study. Especially, resilience herein is defined as the recovery of complete functionality of the structure; therefore, the non-functionality is measured in terms of resilience of the structure, i.e., the loss of functionality due to an earthquake and recovery of the functionality, with and without the retrofit alternatives. Various researchers [39,71,72,73,74,75] offered resilience calculation methodology based on a probabilistic approach, and Burton et al. [76] offered a PBEE methodology for the recovery phase related to the building infrastructure. Lin and Wang [77,78] proposed a procedure for the recovery phase by combining structure-level restoration through probabilistic damage evaluation, also used for recovery estimation [79,80]. It should be noted that the impedance factor has been ignored in the current study due to its subjective nature and can be taken as a limitation [81,82]. The repair cost related to the damage of SEs as well as NSEs due to any hazard level can be estimated using the well-established performance-based earthquake engineering (PBEE) methodology [83]. It also estimates the downtime of the structures, but the related social, economic, and environmental losses to downtime still need to be investigated in-depth. The huge economic losses due to the seismic events in the past are coupled with the immediate repercussions of that event to the recovery stage of the structures [84,85]; however, the indirect losses demand further analysis [3,4,86,87,88]. Thus, to accomplish a resilient structure, the seismic resilience should be considered while selecting the retrofitting strategy and determining the loss.

The earthquake studies have revealed that the inadequate performance of structures may cause excessive damage, and since losses associated with the NSEs mainly rely on the facility usage and vulnerability and the intensity of the earthquake; thus, most of the studies ignore the damages to NSEs and the resulting losses and focus more on the damages to SEs. Thus, a more complete performance-based seismic retrofit assessment framework of structures is still essential, which quantifies various combinations of damage levels for SEs and NSEs, to estimate the resulting direct and indirect losses in terms of social, economic, and environmental consequences, considering enhancing structural performance and seismic resilience based on retrofitting. This study proposes a performance-based assessment of reinforced concrete (RC) frame buildings by evaluating various retrofitting strategies, as demonstrated through a case study. The purpose of these retrofitting strategies is to enhance the overall seismic response of the structure. Four specific retrofitting techniques are examined: steel plate jacketing (SPJ), steel angles jacketing (SAJ), reinforced concrete jacketing (RCJ), and engineered cementitious composite jacketing (ECCJ). ECC is a relatively new material as compared to steel and RC jacketing, and there is very little/no literature available on its application as a retrofit material. The effectiveness of these retrofitting strategies is measured by their ability to improve the structure’s seismic performance, as well as to reduce direct losses through component-level damage calculations and indirect losses related to the restoration of functionality, which is associated with resilience. The assessment of direct and indirect losses relies on the damage inflicted on structural elements (SEs) and nonstructural elements (NSEs), and it is presented in terms of social, economic, and environmental impacts. The NSEs are categorized based on their sensitivity to either drift or acceleration. For instance, elements such as partition walls and curtain walls are sensitive to inter-story drifts, while sprinklers, HVAC systems, and ceilings are more vulnerable to floor acceleration. The key contributions of this study include

• A novel performance-based seismic retrofit assessment methodology is proposed to enhance the resilience of structures and reduce the associated risk and vulnerability.
• The effectiveness of the proposed retrofit strategies in enhancing the structure’s global performance by increasing column capacities and story response is proved.
• A comparative assessment of four retrofit strategies (SPJ, SAJ, RCJ, and ECJ) is performed by quantifying all the losses in a normalized manner, and the weightage factor is specified for each loss to select the optimum retrofit solution.
• The proposed performance-based framework recognizes the most efficient retrofit alternative that ensures structural safety and reduces direct and indirect costs by minimizing structural and nonstructural damages.

2. Performance-Based Seismic Retrofit Assessment

The proposed framework initiates by choosing a structure and retrofitting strategies aimed at studying and determining the structure’s response, damages to SEs and NSEs, and quantification of direct and indirect losses. The detailed description of the framework by identifying its main steps is discussed in detail in the subsequent sections. The first part of the methodology focuses more on quantifying the global response of the structure by using the accurate and cost-effective method of lateral load assessment (i.e., NSP method) because, to make the approach more appealing, the computation time should be minimal without compromising the accuracy of results. The nonlinear finite element models are generated for the structure (pre- and post-retrofit conditions), and NSP is performed to generate the capacity curves. The global damage of the structure is quantified from the capacity curve. The capacity curves obtained from the NSP are then used to determine the effectiveness of retrofitting strategies in reducing the overall vulnerability of the structure. Collapse fragility functions are determined to filter the initial selection of the retrofitting options. After assessing the structure’s global response and the effect of retrofitting numerically, the second part of the methodology focuses on the component-level damages (i.e., SEs and NSEs), for which the fragility curves and consequence functions for these components are defined in a building information model. Using various hazard levels, the direct loss assessment (i.e., social, economic, and environmental) is performed for each hazard level. The third part of the methodology follows the consequence assessment and uses the downtime/repair time along with potential delays in starting the recovery action, the functionality loss and recovery of functionality are estimated, and the resulting indirect social and economic losses are then calculated in terms of the system’s resilience. Both the direct and indirect losses are then normalized in the simplest possible way, and a weightage factor is defined based on the importance of each factor to determine the most efficient retrofit alternative. The detailed layout of the framework is presented in Figure 2.

2.1. Modeling Description and Retrofitting Strategies

For the reference building model and the proposed retrofitting strategies, 21 models were created and analyzed using the commercially available software ETABS V21. ETABS is a finite element software specifically designed for the modeling, analysis, and design of building structures [89]. The material models available in ETABS can accurately describe the nonlinear responses of various materials, such as concrete, steel, and rebar, in both unidirectional and cyclic testing scenarios. Additionally, ETABS allows users the flexibility to define new materials as needed; for this study, an engineered cementitious composite (ECC) material model was generated using the user-defined option [90], as it is not included in the software’s material library [91].

The concrete material model utilized is based on Mander’s model. In this analysis, the concrete slab is modeled as a rigid diaphragm at each floor level to account for axial stiffness and to uniformly apply lateral displacements across all columns within a specific story. Structural members, such as beams and columns, are modeled using distributed plasticity. For lateral load analysis—specifically, the nonlinear static procedure (NSP)—lumped plasticity or concentrated plasticity in the form of plastic hinges is employed to determine the flexural behavior of the lateral load-resisting system. A brief description of the analysis procedure used is provided in the following section.

2.2. Nonlinear Pushover Analysis

The FEMA-356 [69] and ATC-40 [92] have established modeling limitations, acceptance measures, and methods of NSP analysis. The NSP analysis is used for the evaluation of the actual/ultimate strength and seismic response of the structure. The load-deformation response established from NSP in both the principal orthogonal directions (i.e., longitudinal and transverse) of the structure is used to calculate the weaknesses in the lateral load-resisting system of a structure. While generating the load-deformation curves, the lateral displacements are applied at the top of the structure with increasing magnitude, and the base shear is recorded accordingly [93]. The NSP analysis accounts for the failure of the structure; therefore, it can be taken as a technique for evaluating the collapse load as well as ductility capacity.

After defining the material models, geometric non-linearities, loadings assigned, and meshing details, the boundary conditions were defined for the model. For that purpose, another commercially available software, SeismoBuild [94], was used to verify the results of the ETABS model. The material models and other modeling assumptions were kept the same, and boundary conditions of the ETABS model were defined to match and validate the results of the SeismoBuild model. Once the model was validated, the analysis was performed for the reference model, and the capacity curve was plotted. The model was then retrofitted (only the ground floor columns) with the various alternatives, and the analysis was performed. For each retrofitting option, the capacity curve was plotted relative to the reference structure to compare the efficiency of retrofitting on the global response of the structure. The infill walls were not considered in the analysis and, hence, can be considered as one of the limitations of the current study.

2.3. Quantification of Structural Damage

The structure’s global response obtained in the form of a capacity curve is then used to quantify the damages experienced by the structure. The effect of various retrofit alternatives on lateral load enhancement and total deformation enhancement can be easily assessed from the capacity curves. Apart from that, a very well-known and most accurate technique to date is used to quantify the structural damage, i.e., collapse fragility functions.

To establish the collapse fragility functions for the reference structure along with all the retrofit alternatives, the methodology proposed by Vamvatsikos and Cornell [95] is adopted in which they developed a method signifying that NSP can be employed to approximate the nonlinear dynamic behavior. As a result of that study, an Excel sheet was generated with the name of Static Pushover to Incremental Dynamic Analysis (SPO2IDA), which is freely available along with other resources of FEMA P-58 [83]. In this study, the nonlinear pushover curve is used for quantifying the IDA results by employing the SPO2IDA tool. FEMA [83] recognizes that this tool can generate collapse fragility functions for structures primarily governed by their fundamental mode of vibration. The procedure for generating collapse fragility is described below:

• Import the results of the capacity curve to the SPO2IDA tool and fit it into a quadrilinear function by classifying given limit points, each representing the start- and end points of the distinct segments.
• Apart from the capacity curve, the tool also requires other important data (e.g., height, weight, and fundamental period) of the structure to obtain the median value.
• Create the collapse fragility using lognormal distribution.

2.4. Estimation of Losses Based on Component-Level Damages

To determine the structure’s performance, various parameters (or engineering responses) like capacity curve, shear load distribution among the stories, stresses, strains, and other associated factors are analyzed, but it is tough to associate these parameters directly with the damages to SEs and NSEs [96,97]. On the contrary, engineering demand parameters (e.g., inter-story drifts, peak floor acceleration, etc.), referred to as EDPs, are the responses of the structure to estimate the earthquake-induced damages, but these parameters are hard to understand by the decision-makers [98,99]. Thus, more expressive performance measures can be acquired by calculating the direct losses (in terms of economic, social, and environmental consequences) and indirect losses (in terms of downtimes or repair times and functionality of structures subjected to seismic events) [100,101]. This section focuses on the determination of component-level damages and the resulting direct losses (i.e., as a result of the repair activities), whereas the quantification of indirect losses (i.e., supplementary losses when the structure is not functional) is presented in Section 2.5.

The information provided by the collapse fragility study links the potential damage with an intensity measure. To get more expressive details for stakeholders, the collapse fragility, along with the component’s fragility functions and consequence functions, is used to determine direct losses [16,102,103]. For this reason, the building information model is convened, and all the damageable components in the building are considered by properly defining the consequence and fragility functions. Fragility curves control the potential of assumed damage for each element, while the consequence function utilizes the possibilities of elements being in distinct failure conditions and defines the economic, social, or environmental losses. The social losses are defined by assembling the population model, as well as specifying the casualty function and the population at risk. A population model is defined to account for a specific time in a particular day of the week, for estimating the time effect on the total consequences. The exact quantity of various NSEs can also be estimated by using another tool provided by FEMA [83], named the normative quantity estimation tool, which determines the types of NSEs required for specific usage of the building, and their quantity based on floor area. The subsequent steps define economic, social, and environmental losses for a given hazard situation.

• Identify a hazard curve for which results (losses) need to be defined.
• Assess the EDPs from the established nonlinear numerical model.
• Describe the potential exceeding of various damages for all components.
• Employ the probability of exceeding various damage states, along with collapse fragility to find losses.

The social losses (i.e., casualties, fatalities) are found as [83]:

$$S_{\left.m\right|IM}={\varphi }_C{T}_{rand}f\left(p|T_{rand}\right)p_T{p}_R{p}_{\left.C\right|IM}$$

(1)

where $S_{\left.m\right|IM}$ is the social criterion of seismic vulnerability; ${\varphi }_C$ is the casualty function, depending on facility usage, and can be determined from previous data (e.g., population model); $T_{rand}$ is the random time generated for a specific realization; $f\left(p|T_{rand}\right)$ is the population model depending on time; $p_T$ is the total building population; $p_R$ is a population at risk; and $p_{\left.C\right|IM}$ is the potential collapse probability for a given intensity measure (IM).

The economic and environmental losses are described as [83]:

$$C_{L_{\left.T\right|IM}}=\sum _{DS}\underset{0}{\overset{\infty }{\int }}{C}_{L_{\left.R\right|DS}}{p}_{\left.DS\right|EDP}{f}_{\left.EDP\right|IM}dEDP.\left(1-p_{\left.C\right|IM}\right)+C_{L_{\left.C\right|C}}.p_{\left.C\right|IM}$$

(2)

where $C_{L_{\left.T\right|IM}}$ is the total losses at IM; $C_{L_{\left.R\right|DS}}$ is the random loss function value of the component for a particular damage state; $p_{\left.DS\right|EDP}$ is the damage probability of a given damage state at EDP; $f_{\left.EDP\right|IM}$ is the probability density function of EDP for IM; and $C_{L_{\left.C\right|C}}$ is the consequence of potential collapse probability $p_{\left.C\right|IM}$.

2.5. Quantification of Indirect Loss Based on Recovery of Functionality

The functionality of a structure during a seismic event and its complete recovery after the earthquake can be opted for functionality indicator while evaluating the recovery function. The functionality curve offers the level of performance at the considered time and its recovery to complete functionality after the earthquake. To evaluate the indirect losses of structure, functionality function for reference building, as well as various retrofitting alternatives, was obtained using the defined recovery function. The recovery function used comprises of trigonometric recovery path, as proposed by Bruneau et al. [104] and Kumar et al. [105]. The functionality function Q(t) in terms of resilience is described as follows:

$$Q\left(t\right)=1-\left\{L\left(1, T_{RE}\right)\times \left[H\left(t-t_{OE}-t_{Oi}\right)-H\left(t-\left(t_{OE}+T_{RE}\right)-t_{Oi}\right)\right]\times f_{rec}\left(t, t_{OE}, T_{RE}, t_{Oi}\right)\right\}$$

(3)

The occurrence time of the event (i.e., earthquake in this case) is termed as t_OE, the structure’s recovery time is termed as T_RE, the Heaviside step function is designated as H (), and t_oi is the initial delay in the recovery process. In this study, t_OE is assumed at 10 days and T_RE as 365 days with a total control time (t) of 400 days. The rational equation for the recovery function is

$$f_{rec}\left(t, t_{OE}, T_{RE}, t_{Oi}\right)=0.5 \{ 1+\mathit{cos}\left[\pi {\displaystyle \frac{\left(t-t_{OE}-t_{oi}\right)}{T_{RE}}}\right]\}$$

(4)

Finally, the seismic resilience can be calculated by the integration of the functionality curve w.r.t time.

$$R=\underset{t_{OE}}{\overset{T_{RE}}{\int }}{\displaystyle \frac{Q\left(t\right)dt}{T_{RE}}}$$

(5)

where R is the seismic resilience of the structure.

The downtime for all the functionality levels can be calculated by taking into account the repair plan (i.e., repair sequence taken from the repair times), obstructing delays (i.e., financial constraints, expert review and allowing, contractor deployment, etc.), and utility accessibility. The repair time can be calculated from the consequence assessment (Section 2.4), which considers the damages to both the SEs and NSEs, depending upon the intensity of various hazard levels. The obstructing delays and the accessibility of utility are taken into account in this study using the lognormal distribution function established by Almufti and Willford [106]. The performance function can be generated by finding the downtime for each performance level, after which the seismic resilience of the structure can be estimated.

Different from most existing studies, the resilience measured by this method accounts for both structural and nonstructural damages (obtained from consequence assessment) and calculates the social and economic losses by defining the recovery of functionality function. Therefore, it accounts for all the indirect losses associated with the SEs and NSEs.

3. Case Study

3.1. Modeling Description and Retrofitting Strategies

The reinforced concrete (RC) frame structure chosen for this purpose is a five-story hospital building having an approximate height of 65 ft, as a representative of a large class of buildings in the area. The numerical model generated for the said building is presented in Figure 3. The plan of the building is presented in Figure A1. The complete hospital building is comprised of six blocks separated by extension joints or seismic joints; thus, each block acts separately under the action of forces (gravity and lateral); therefore, only one block (highlighted in the figure) is modeled and analyzed as a representative of the whole building since all the data used is similar for other blocks. The hospital building was designed before the modern seismic codes; therefore, many structural deficiencies were encountered. For instance, no shear wall was provided in the building for lateral load resistance mechanism, which made the ground floor more vulnerable, as there is a demand for more open spaces on the ground floor usually. Thus, a soft story mechanism is encountered in the analysis, and for this reason, the retrofitting was applied at the ground floor columns, only to account for the effectiveness of the retrofitting in terms of the cost of retrofitting. Concrete with 3000 psi strength and steel of 40,000 psi yield strength are considered in the modeling assumptions. The material assumption is made on the recommendations given in ASCE/SEI-41-13 (Tables 4.2 and 4.3) [107]. The retrofitted columns considering all four retrofitting strategies, i.e., RCJ, SPJ, SAJ, and ECJ, are also shown in Figure 4. Various parameters were studied in detail among these four retrofitting options to find the optimum retrofitting solution. In RCJ, the concrete quality in the jacket, the number and size of longitudinal bars in the jacket, and the number and spacing of transverse bars in the jacket are kept constant; however, the thickness of the jacket is varied. The concrete strength used was 4000 psi, 8#5 rebars were used as longitudinal steel, and #3 rebars @ 6″ were used as transverse steel. In the case of SPJ, the thickness of steel plates/jackets is investigated. Similarly, in the case of SAJ, various angle sizes available in AISC14 [108] were investigated along with various thicknesses. And lastly, in the case of ECJ, the thickness of the ECC jacket is considered in the optimization study. The ECC material used in jacketing possesses a compressive strength of 8000 psi, an ultimate strain of 0.1, a tensile strength of 80 psi, and a tensile strain of 0.05. A detailed description of the material can be found in [90].

Table 1. Detail of all the retrofitting alternatives along with different parameters used for each alternative.

Retrofitting Alternatives		Parameters for Each Alternative
Steel Plate Jacketing	Plate Thickness (in)	0.12	0.16	0.20	0.24	0.28
	Designation	SPJ-1	SPJ-2	SPJ-3	SPJ-4	SPJ-5
Steel Angle Jacketing	Angle Dimension (in)	5 × 5 × 5/8	5 × 5 × 3/4	6 × 6 × 1/2	6 × 6 × 9/16	6 × 6 × 5/8
	Designation	SAJ-1	SAJ-2	SAJ-3	SAJ-4	SAJ-5
RC Jacketing	Jacket Thickness (in)	1.5	2.0	2.5	3.0	3.5
	Designation	RCJ-1	RCJ-2	RCJ-3	RCJ-4	RCJ-5
ECC Jacketing	Jacket Thickness (in)	1.5	2.0	2.5	3.0	3.5
	Designation	ECJ-1	ECJ-2	ECJ-3	ECJ-4	ECJ-5

presents the details of the parameters considered for the four retrofitting strategies. The aforementioned retrofit strategies necessitate altering the current lateral force-resisting system (i.e., columns of the ground floor only, in this case). The improvement of the cross-sections is assumed by the FEMA-547 [109] guidelines and ASCE/SEI-41-13 [107] suggestions, which emphasize the detailing approach, construction methods as well as seismic assessment of existing structures. In total, 21 models are generated, including the reference model and 20 retrofitted models (i.e., five options for each alternative as presented in Table 1). Infill walls are very important to incorporate into the numerical model as their presence affects the overall behavior of the structure [110,111]. However, given the necessity for open spaces on the ground floor, the amount of infill in that area will be limited compared to the upper floors. This condition will also contribute to a soft story effect on the ground floor due to its reduced lateral stiffness relative to the other levels. Moreover, due to various complexities and the variations associated with the material of infill walls used in various parts of the world, it was decided not to model the infill elements, an approach that is also adopted by various other researchers [65,112,113,114,115,116,117,118,119].

As already mentioned in the previous section, the FE models are generated in the commercially available finite element analysis program “ETABS V21.2” [89], and the material models already available in the software are used for rebars, concrete, and steel; however, the material model was defined for the ECC material, as per Bora and Elnashai [99]. The material models used for the definition of retrofitting materials, i.e., steel, concrete, rebars, and ECC, are presented in Figure 5.

3.2. NSP Analysis Results

NSP analysis was conducted, lateral deformation was applied at the top of the structure, and the resulting base share was noted for each corresponding deformation. Signifying structural deformation in fundamental mode and calculating the response parameters even after the yielding since the deformation-controlled environment was adopted. Initial stiffness, ultimate strength, and ductility of the structure can be obtained from the resulting load-deformation curve of the structure to estimate the performance of the structure [120]. Figure 6 and Figure 7 present the capacity curve of the reference building, along with the proposed intervention strategies, in the longitudinal and transverse directions, respectively. The load-deformation curve offers significant details regarding the stiffness, ductility, and ultimate strength of the building. In general, it can be concluded that all the retrofitting alternatives have enhanced the structural performance (in terms of lateral load- and deformation-enhancement) considerably in both the principal directions, given that retrofitting was applied only to the columns of the ground floor, which makes the results very interesting since the cost of retrofitting is minimal. Moreover, the pushover curves were saturated and dropped in both directions for all the models; however, the drop was more obvious in the longitudinal direction.

To make the results more conclusive, the lateral load- and deformation-enhancement are normalized for each retrofit strategy w.r.t the reference structure (in both the principal directions) and are presented in Figure 8. It can be seen that for lateral load enhancement in the transverse direction (Figure 8b), the ultimate strength of the structure for SPJ1, SPJ2, SPJ3, SPJ4, and SPJ5 has been increased by 55.9%, 65.3%, 84.7%, 103.1%, and 105.8%, respectively. Similarly, in the case of SAJ alternative, the ultimate strength for SAJ1, SAJ2, SAJ3, SAJ4, and SAJ5 has been increased by 68.7%, 83.1%, 63.4%, 72.1%, and 80.2%, respectively. It can be seen that all the SAJ options give the strength enhancement that lies between the values provided by SPJ2 and SPJ3 so that SPJ2 can be compared directly with SAJ1 and SAJ3; however, SPJ3 can be compared directly with SAJ2 and SAJ5 in terms of strength enhancement. In the case of the RCJ alternative, the structure’s ultimate strength for RCJ1, RCJ2, RCJ3, RCJ4, and RCJ5 is increased by 57.7%, 66.2%, 73.1%, 80.0%, and 86.2%, respectively. Here, the results of RCJ1 and RCJ2 match very closely to those of SPJ1 and SPJ2; however, the % enhancement by RCJ3, RCJ4, and RCJ5 matches with the SAJ4, SAJ5, and SPJ3 (and SAJ2), respectively. In the case of the ECJ alternative, the structure’s ultimate strength for ECJ1, ECJ2, ECJ3, ECJ4, and ECJ5 is increased by 39.6%, 49.2%, 57.8%, 66.3%, and 74.3%, respectively.

Similarly, the lateral load enhancement in longitudinal direction and deformation capacity enhancement in both longitudinal and transverse direction can be compared among the various retrofit strategies. It can be simply stated that the retrofit strategies enhanced the load and deformation capacity of the structure, thus increasing their ductility and energy dissipation capacity and making them less vulnerable to earthquake demand. Figure 8 clearly shows that the SPJ alternative shows better performance as compared to the other three alternatives, followed by SAJ and RCJ alternatives, where SAJ gives better strength enhancement; however, the RCJ performs better in enhancing the total deformation capacity. ECJ alternatives also depicted decent results on par with RCJ and SAJ alternatives.

Figure 9 presents the story shear at peak lateral response of the structure. When Figure 9 is studied together with Figure 7, important outcomes can be drawn as follows: First, the story shear value is enhanced the same amount for all the stories above as for the retrofitted story, regardless of the retrofitting strategy adopted. This gives a very important result that enhances the ground floor column’s strength, which also affects the load distribution and makes the columns of the above stories take more load and utilize their capacity, hence increasing the overall strength of the whole structure and making it less vulnerable to seismic loads. Second, the % enhancement in the story shear is the same for all the stories. For instance, if the story shear of the first story is doubled with SPJ-5, then the story shear of all other stories is also doubled, and the same kind of response is observed for all kinds of retrofitting alternatives.

Third, the ultimate lateral load and story shear values are enhanced with the same percentage for all the retrofitting options apart from SPJ-1, where the ultimate lateral load is enhanced by 56% and the story shear for all the stories is enhanced by 45%. The enhancement in ultimate lateral load and story shear for SPJ-2, SPJ-3, SPJ-4, and SPJ-5 are 65%, 84%, 102%, and 105%, respectively. Similarly, for SAJ-1, SAJ-2, SAJ-3, SAJ-4, and SAJ-5, the enhancement in ultimate lateral load and story shear is 68%, 82%, 63%, 71%, and 79%, respectively. In the case of RCJ-1, RCJ-2, RCJ-3, RCJ-4, and RCJ-5, the enhancement in ultimate lateral load and story shear is 58%, 66%, 73%, 80%, and 86%, respectively. The enhancement in ultimate lateral load and story shear in the case of ECJ-1, ECJ-2, ECJ-3, ECJ-4, and ECJ-5 are 40%, 49%, 58%, 66%, and 74%, respectively. Fourth, the enhancement in ultimate lateral load and story shear is maximum in the case of SPJ retrofitting where SPJ-5 showed an increment of 105% of enhancement. The maximum enhancement in the case of SAJ, RCJ, and ECJ are 82%, 86%, and 74%, respectively. Thus, a combined study of Figure 8 and Figure 9 makes it very clear that the application of retrofitting is proven to be very effective in enhancing the structure’s global performance, most importantly when behavior is primarily controlled by column capacities and story response. And since no shear wall was provided in the case study building, it was very clear that the behavior will be governed by the column capacities, and that too will be directed by the ground floor since it exhibits the soft story mechanism. Thus, enhancing the strength of ground story columns resulted in better performance of the whole structure, thus proving retrofitting to be an effective methodology.

3.3. Quantification of Structural Response Based on Collapse Fragility Function

Determining the response of the building from the numerical model necessitates generating collapse fragility and developing a performance model for the building. In this case study, a suite of 22 earthquake records was used to create the collapse fragility, performing THA on generated numerical models and chronologically raising the IMs of earthquakes following an IDA procedure. The details of the chosen earthquakes are provided in

Table A1. Details of selected ground motions.

No.	Name	Station	Year	Mag.	PGAdir-1 (g)	PGAdir-2 (g)
1	Northridge	Beverly Hills-Mulhol	1994	6.7	0.416	0.516
2	Northridge	Canyon Country-WLC	1994	6.7	0.41	0.482
3	Imperial Valley	Delta	1979	6.5	0.238	0.351
4	Imperial Valley	El Centro Array #11	1979	6.5	0.364	0.38
5	Loma Prieta	Capitola	1989	6.9	0.529	0.443
6	Loma Prieta	Gilroy Array #3	1989	6.9	0.555	0.367
7	Kobe, Japan	Nishi-Akashi	1995	6.9	0.509	0.503
8	Kobe, Japan	Shin-Osaka	1995	6.9	0.243	0.212
9	Chi-Chi, Taiwan	CHY101	1999	7.6	0.353	0.44
10	Chi-Chi, Taiwan	TCU045	1999	7.6	0.474	0.512
11	Kocaeli, Turkey	Duzce	1999	7.5	0.312	0.358
12	Kocaeli, Turkey	Arcelik	1999	7.5	0.219	0.15
13	Landers	Yermo Fire Station	1992	7.3	0.245	0.152
14	Landers	Coolwater	1992	7.3	0.283	0.417
15	Duzce, Turkey	Bolu	1999	7.1	0.728	0.822
16	Hector Mine	Hector	1999	7.1	0.266	0.337
17	Manjil, Iran	Abbar	1990	7.4	0.515	0.496
18	Superstition Hills	El Centro Imp. Co.	1987	6.5	0.358	0.258
19	Superstition Hills	Poe Road (temp)	1987	6.5	0.446	0.3
20	Cape Mendocino	Rio Dell Overpass	1992	7	0.385	0.549
21	San Fernando	LA—Hollywood Stor	1971	6.6	0.21	0.174
22	Friuli, Italy	Tolmezzo	1976	6.5	0.351	0.315

[102]. The peak floor response is denoted as a point in Figure 10a,b. A total of 22 points are presented for each floor denoting inter-story drifts (IDRs) and peak floor acceleration (PFA) under chosen earthquake histories with an IM of 0.4 g. Then, the IMs are modified, and THA is conducted to get IDRs for building models considering IDA methodology. Figure 11 presents the collapse fragilities generated by following the method defined in Section 2.1.

Figure 11a shows IDA outcomes on the reference model with IMs up to 2 PGA. The IDA procedure is employed to estimate the total collapses for the IM. The structure is assumed to collapse due to numerical instability or extensive drifts experienced. The total collapses for the IMs for the reference model with distinct retrofit strategies were determined, and it was noticed that by increasing the IMs, the collapse ratio rises. Moreover, the collapse ratio is maximum for the reference model, and with the application of distinct retrofit strategies, the number of collapses is reduced, subject to the retrofit option. Lastly, a lognormal cumulative distribution function is tailored contrary to the total collapses for the IMs employing the maximum probability method precisely given in Equations (1) and (2), and the fragilities are calculated for all retrofit models as presented in Figure 11b–e.

Before proceeding to the estimation of component-level damages, it was decided to select one out of five options for each retrofit alternative. For this purpose, the retrofit option that gives the result closer to the mean values of the whole group was considered.

Therefore, the four retrofitting alternatives used for further analysis are SPJ-3, i.e., steel plate jacketing with a plate thickness of 0.2 in (5 mm); SAJ-5, i.e., steel angle jacketing with an angle size of 6 × 6 × 5/8 in; RCJ-3, i.e., reinforced concrete jacketing with jacket thickness of 2.5 in; and ECJ-3, i.e., ECC concrete jacketing with jacket thickness of 2.5 in. These strategies will be considered in the quantification of direct and indirect losses, and the most effective option will be selected as the optimal solution.

3.4. Quantification of Losses Based on Component-Level Damages

To perform the consequence assessment, the first step is the selection of seismic hazard levels and the construction of a building information model. The seismic hazard levels selected in this study are presented in

Table 2. List of seismic hazard details used for the consequence assessment.

Seismic Hazards
No.	Return Period (Years)	Sa (g)	Title
1	40	0.124	EQ-1
2	100	0.271	EQ-2
3	250	0.419	EQ-3
4	420	0.566	EQ-4
5	775	0.714	EQ-5
6	1250	0.861	EQ-6
7	2475	1.009	EQ-7

. To study the impact on component damage level (thus resulting in economic, social, and environmental losses) by changing intensity level, seven hazard levels are considered.

The building information model contains fragility curves along with consequence functions. The fragility curves associate certain demands with the probability of damage; however, consequence functions interpret those damages into economic, social, and environmental losses. The component-level damages, i.e., damage/collapse of NSCs, are presented in

Table 3. Damage states defined for various nonstructural components.

No	Non-Structural Components	Damage States
		DS1	DS2	DS3
1	Curtain Walls	Glass Cracking	Glass Fall from Frame	-
2	Wall Partition, Type: Gypsum with metal studs	Screw pop-out, wallboard cracking, small crushing of panel corners	Trivial cracking of walls. Corner gap openings and bending of studs.	Buckling of studs. Bending of the top track. Large gap openings.
3	Suspended Ceiling	5% of grid and tile damages	30% of grid and tile damages.	50% of grid and tile damages.
4	HVAC Galvanized Sheet Ducting	1 failed support per 300 m	Numerous in-line supports fail, and 18 feet of duct fail per 300 m.	-
5	Fire Sprinkler Drop Standard Threaded Steel	0.01 leaks per drop	Drop Joints Break—Major Leakage—0.01 breaks per drop.	-
6	Access Floor	Minor damage to the flooring. Damage to the equipment of the flooring.	-	-
7	Pendant Lighting	Disassembly of rod system at connections. Low cycle fatigue. Failure of the rod.	-	-
8	Control Panel	Damaged. Inoperative but anchorage is OK.	-	-

. The component fragility curves (shown in Figure 12) and consequence functions opted for the case study (presented in

Table 4. Consequence functions for various NSCs.

Components	Quantity per Floor	Damage State	Consequence Functions
			Economic (USD)		Environmental (KgCO2)		Repair Time (Day)
			Median	CoV.	Median	CoV.	Median	CoV.
Curtain walls	2.79 m2 × 24.50	DS1	2055	0.17	406	0.3	0.905	0.48
		DS2	2055	0.17	406	0.3	0.48	0.30
HVAC	305 m × 0.58	DS1	715	0.37	181.8	0.44	0.84	0.44
		DS2	6985	0.10	2372	0.27	2.99	0.27
Partition	30.5 m × 6.20	DS1	2160	0.15	756	0.29	2.02	0.29
Ceiling	23.22 m2 × 21.0	DS1	290	0.55	217.5	0.60	0.28	0.60
		DS2	2270	0.52	2132.5	0.57	2.16	0.57
		DS3	4670	0.20	8155	0.32	4.46	0.32
Sprinklers	305 m × 1.16	DS1	550	0.37	75	0.44	0.65	0.44
		DS2	550	0.37	75	0.44	0.17	0.44
Access Floor	1 EA	DS1	110	1.28	6	1.31	0.1	1.31
Pendant Lighting	1 EA × 758	DS1	1.6	0.64	51.81	0.68	0.002	0.68
Control Panel	1 EA	DS1	4252	0.18	865.45	0.31	5	0.31

EA = each, m² = square meter of area.

) are obtained from [82,83,121]. The component fragility curve and consequence function for several kinds of retrofitted elements are absent from the published literature. Thus, in this study, retrofitting of the NSEs is not considered; therefore, normal fragility curves and consequence functions are employed. The population model signifies several persons existing at a specific time during the day and a specific day in the week for a certain realization. The fatality rate and injury rate for the proposed RC frame was 0.9 and 0.1, respectively, which specifies that 90% will endure fatalities during the failure and the remaining 10% will face major injury [83].

Details of damage states for NSCs, obtained by numerical simulations, are shown in

Table 5. Total non-structural damages (elements become nonfunctional due to damage beyond repair or collapse).

Floor	NSCs	Sa (g)
		0.124	0.27	0.42	0.57	0.71	0.86	1.01	1.16
1st	D-S	36.36	45.45	81.82	100.00	100.00	100.00	100.00	100.00
	A-S	0.00	15.38	38.46	69.23	53.85	69.23	76.92	76.92
	All	16.67	29.17	58.33	83.33	75.00	83.33	87.50	87.50
2nd	D-S	36.36	72.73	100.00	100.00	100.00	100.00	100.00	100.00
	A-S	7.69	23.08	46.15	53.85	53.85	53.85	53.85	76.92
	All	20.83	45.83	70.83	75.00	75.00	75.00	75.00	87.50
3rd	D-S	36.36	81.82	100.00	100.00	100.00	100.00	100.00	100.00
	A-S	0.00	38.46	38.46	53.85	53.85	53.85	53.85	46.15
	All	16.67	58.33	66.67	75.00	75.00	75.00	75.00	70.83
4th	D-S	36.36	63.64	100.00	100.00	100.00	100.00	100.00	100.00
	A-S	0.00	30.77	46.15	46.15	46.15	53.85	46.15	53.85
	All	16.67	45.83	70.83	70.83	70.83	75.00	70.83	75.00
5th	D-S	18.18	54.55	81.82	81.82	81.82	81.82	81.82	81.82
	A-S	0.00	37.50	66.67	58.33	62.50	66.67	62.50	66.67
	All	5.71	42.86	71.43	65.71	68.57	71.43	68.57	71.43

A-S refers to acceleration-sensitive; D-S refers to story drift-sensitive NSCs.

. At lower values of S_a, approximately all the damages are due to NSCs since they are more vulnerable and they were not retrofitted. As the intensity level rises, the ratio of structure to nonstructural damages also increases, reaching the maximum threshold value at S_a of 0.861 g for the reference structure; however, for the retrofitted case, the threshold value does not reach until the last considered intensity level, i.e., 1.156 g, thus indicating that all the structural elements do not completely damage. Thus, it can be concluded that NSCs are vulnerable components that can be damaged at even low-intensity levels and, therefore, can cause disruption of the functionality of the building.

In addition to the distribution of components in SC and NSC categories, the NSCs were further distributed into drift- and acceleration-sensitive elements. The damages associated with the nonstructural elements only are presented in Table 5, where storywise % damages of each category (i.e., drift-sensitive and acceleration-sensitive) of NSCs are determined for various intensity levels (i.e., S_a (g)). For example, on the first floor with S_a of 0.71 g, 100% of story drift-sensitive NSCs were damaged, 53.85% of acceleration-sensitive NSCs were damaged, and 75% of all NSCs on that floor were damaged, considering both drift- and acceleration-sensitive elements. A relation of nonstructural damages with the S_a is shown in Figure 13.

The social losses in terms of several expected fatalities, the economic losses in terms of expected repair cost, and environmental consequences in terms of expected CO₂ emission and embodied energy for all seven hazard scenarios are presented in Figure 14. The case study building before retrofitting exhibited a maximum number of probable fatalities. However, these losses decrease considerably after employing retrofitting strategies, with SPJ, SAJ, and RCJ showing the most efficient results in mitigating the social losses. In the case of financial and environmental losses, the engineering demand parameters (i.e., story drifts and accelerations) obtained are associated with damage via fragility curves and losses via consequence functions.

The total economic, social, and environmental losses obtained from Equations (2) and (3) are presented in Figure 14. All the losses intensify with rising IM levels. The original structure before retrofitting bears the maximum losses decreased via retrofit strategies. All three losses are plotted against the PGA level to show the effect of hazard level on the consequences. Hazard levels with PGA of 0.124, 0.271, and 0.419 do not show any fatalities for all the structures. However, the economic losses (for reference structure and the considered retrofitting alternatives) turn out to be the same. Increasing the hazard level tends to change the pattern, and at PGA of 0.566, the reference structure possesses 10 fatalities, while all the retrofitting alternatives showed 0 fatalities at this hazard level. Similarly, the repair costs for reference structure, SPJ, SAJ, RCJ, and ECJ, are 5.2, 2.1, 2.8, 3.1, and 3.7 million USD, respectively. The pattern continues for the following hazard levels of PGAs 0.714 and 0.861, and details can be obtained from the results presented in Figure 14. For a hazard level with a PGA of 1.009 that has a return period of 2475 years, the fatality number rises to 45 for reference structure. However, these fatalities are reduced considerably by retrofitting alternatives, and several expected fatalities for SPJ, SAJ, RCJ, and ECJ are 12.5, 12.5, 15.5, and 18.5, respectively, thus making an immense impact on the social consequences and making retrofitting an inevitable option. Nevertheless, the repair cost of all the retrofitting alternatives becomes equal to that of the reference building, indicating the irreparability of the structure primarily due to the damage of NSEs since the NSEs are not considered to be seismically enhanced in this study. Still, the casualties and fatalities are reduced considerably by retrofitting the columns of ground floor only.

Based on the results presented in Figure 14, loss indices were estimated by the relative normalization method, where for a specific intensity level, the maximum performance is taken, and the performance of all the retrofitting alternatives, along with the reference structure, was divided by the maximum performance value. In this way, a normalized relative index value is obtained for each case at all considered intensity levels by referring to 1 as the greatest value and showing the best relative performance in terms of that specific loss. The same methodology was adopted to determine the direct social losses (

Table 6. Normalized direct social losses (injuries + deaths) at all considered intensity levels.

EQ-Level	REF	SPJ-3	SAJ-5	RCJ-3	ECJ-3
EQ-1	1.00	1.00	1.00	1.00	1.00
EQ-2	1.00	1.00	1.00	1.00	1.00
EQ-3	0.35	1.00	0.91	0.89	0.84
EQ-4	0.04	1.00	1.00	0.95	0.80
EQ-5	0.11	1.00	1.00	0.91	0.21
EQ-6	0.39	1.00	1.00	0.97	0.82
EQ-7	0.35	1.00	1.00	0.85	0.74

) and direct economic losses. For EQ-4 and EQ-5, the maximum losses are encountered. It is because at these intensity levels, the retrofitted structures perform very well and, therefore, the relative difference in maximum in these cases. However, in the subsequent intensity levels, i.e., EQ-6 and EQ-7, the retrofitted structures also experienced damages; therefore, the relative performance of the reference structure seems to enhance (

Table 7. Normalized direct economic (direct) losses at all considered intensity levels.

EQ-level	REF	SPJ-3	SAJ-5	RCJ-3	ECJ-3
EQ-1	0.99	1.00	1.00	1.00	1.00
EQ-2	0.94	1.00	1.00	1.00	0.99
EQ-3	0.89	1.00	0.99	0.99	0.98
EQ-4	0.41	1.00	0.76	0.69	0.58
EQ-5	0.42	1.00	0.87	0.77	0.63
EQ-6	0.67	1.00	0.89	0.84	0.79
EQ-7	1.00	1.00	1.00	1.00	1.00

) direct environmental losses. These tables provide the data (based on rigorous calculations) in the simplest possible way so it can be used for further processing to determine the optimized retrofitting alternative (

Table 8. Normalized direct environmental losses (embodied energy + CO₂ emission) at all considered intensity levels.

EQ-Level	REF	SPJ-3	SAJ-5	RCJ-3	ECJ-3
EQ-1	1.00	1.00	1.00	1.00	1.00
EQ-2	0.96	1.00	1.00	1.00	0.99
EQ-3	0.56	1.00	1.00	0.99	0.99
EQ-4	0.52	1.00	1.00	0.99	0.98
EQ-5	0.61	1.00	0.98	0.89	0.80
EQ-6	0.70	1.00	0.93	0.87	0.78
EQ-7	1.00	1.00	1.00	1.00	1.00

), and indirect social and economic losses (

Table 9. Normalized seismic resilience (indirect losses) values at all considered intensity levels.

EQ Title	Ref	SPJ-3	SAJ-5	RCJ-3	ECJ-3
EQ-1	0.88	1.00	0.97	0.95	0.92
EQ-2	0.76	1.00	0.97	0.94	0.84
EQ-3	0.68	1.00	0.98	0.93	0.83
EQ-4	0.51	1.00	0.95	0.89	0.84
EQ-5	0.28	1.00	0.94	0.88	0.85
EQ-6	0.00	1.00	0.96	0.90	0.84
EQ-7	0.00	0.00	0.00	0.00	0.00

). It should be noted that social, economic, and environmental losses need sensitivity analysis and, therefore, are recommended for future studies in the field.

Table 6, Table 7, Table 8 and Table 9 reveal the impact of retrofitting strategies more clearly on direct and indirect losses that the structure may face under any given earthquake intensity. For EQ-1 and EQ-2, the reference structure shows better responses, and the losses are not significant and can be comparable to the retrofitting cases. So it can be stated that up to PGA of 0.271 g, the reference structure does not need any retrofitting intervention, and it performs well. Retrofitting might only increase the cost. However, for PGA beyond 0.271, retrofitting becomes inevitable, and the structure faces great losses (both direct and indirect) in each following intensity level with increasing PGA.

For EQ-4 and EQ-5, the maximum losses are encountered. It is because at these intensity levels, the retrofitted structures perform very well and, therefore, the relative difference in maximum in these cases. However, in the subsequent intensity levels, i.e., EQ-6 and EQ-7, the retrofitted structures also experienced damages; therefore, the relative performance of the reference structure seems to enhance.

These tables provide the data (based on rigorous calculations) in the simplest possible way so it can be used for further processing to determine the optimized retrofitting alternative.

3.5. Quantification of Indirect Losses Based on Functionality Recovery

To estimate the seismic resilience, the initial step is to obtain the downtime for every damageable assembly in a structure. Table 8 of Almufti and Willford framework [115] presents the downtime functions for the assumed damage state, employed to estimate downtimes for all the elements in a specified story. After estimating the downtime, the following step is to generate a rational sequence of repair for the repair time of a structure. The structure’s repair begins by fixing the SEs in sequence, i.e., the first story’s elements are repaired first before going to the higher stories. It is to be noted that the nonstructural assemblies cannot be repaired concurrently, i.e., the fire sprinklers should be repaired before the repair of ceilings. Similarly, partitions should be repaired to do finishes. In the case study, it is assumed that sprinklers, partitions, and HVAC will be repaired side by side, and after that, the ceilings and curtain walls will be done. Other impeding delays, i.e., inspection and permission, project mobilization, and financing, and utility availability are taken into account through lognormal distribution functions. The restoration of the structure’s utilities can be taken from the utility disturbance functions, which can be verified from past earthquake records and respective simulation investigations [115]. The utility disturbances rely on the level of damage to the supply chain system (at the local level within a structure and global level throughout the distribution system) and, hence, are calculated by repair rate (RR), which is calculated based on the peak ground velocity at the structure’s site. Then associated lognormal distribution function is chosen for RR, as per Figure 19 of Almufti and Willford framework [115].

Before the hazard, the structure is assumed to perform its proposed function and is fully efficient, i.e., facilities are completely serviceable and no damage (either structural or non-structural) obstructs the usual proposed function. Following the hazard, the structure could be in any performance state, as shown in Figure 15, depending on damage to the systems and utilities. The functionality curves show the loss of functionality of the reference structure (Figure 15a) for all the seven hazard levels and retrofitting alternatives (Figure 15b) for EQ4 and EQ6 hazard levels (as per Table 2) for comparing the loss of functionality among various options. The recovery times could be estimated, and a performance recovery function is made that provides the dissemination of performance states to complete functionality under the considered time period. The function could be employed to generate resilience using Equation (5). Figure 16 presents the resilience of the case study structure for the considered hazard scenarios. It can be noted that at the hazard level with a return period of 40 years, the structure exhibited better performance in terms of resilience; however, for other hazard states, it exhibited deprived performance as resilience is considered.

Retrofitting decreases the damages, hence enhancing the performance and resilience of the structure. The enhancement in seismic resilience for ECC intervention is less as compared to the other strategies, but it is because the ECC jacketing assumed in this study is without any longitudinal and transverse reinforcement; thus, the cost comparison might make it more feasible and useful as compared to the other alternatives, but the considered performance was less in this scenario, whereas substantial enhancement is noted for the SPJ, SAJ, and RCJ retrofit alternatives. By considering the functionality of the structure subjected to various hazard levels and then estimating the seismic resilience over the given period, it is concluded that SPJ is the most effective retrofitting alternative followed by SAJ and RCJ. The ECJ also enhances seismic resilience considerably, but its impact is relatively less as compared to the other alternatives.

To get an optimal solution based on structural and nonstructural damages and considering the direct and indirect losses, it is important to define the weightage factors for all the parameters presented in Table 6, Table 7, Table 8 and Table 9 to select the option that is suitable for specific seismic intensity levels. For this reason, weightage factors of 0.40, 0.20, 0.20, and 0.20 were assigned to direct social losses, direct economic losses, environmental losses, and indirect (social and economic) losses, respectively. The weightage factors selected are subjective and depend on several factors defined by the decision-makers, designers, evaluators, and other stakeholders. In this study, a higher weightage is assigned to direct social losses since, under any given circumstance, the loss of human life is the most serious consequence, which should be avoided at any cost. Hence, a higher weightage means that the retrofitting alternative that offers more safety will have more impact on decision-making as compared to the other parameters.

Table 10. Performance of retrofitting alternatives considering direct and indirect losses at all considered intensity levels.

EQ-Level	Ref	SPJ-3	SAJ-5	RCJ-3	ECJ-3
EQ-1	0.97	1.00	0.99	0.99	0.98
EQ-2	0.93	1.00	0.99	0.99	0.97
EQ-3	0.56	1.00	0.96	0.94	0.90
EQ-4	0.30	1.00	0.94	0.89	0.80
EQ-5	0.31	1.00	0.96	0.87	0.54
EQ-6	0.43	1.00	0.96	0.91	0.81
EQ-7	0.54	0.80	0.80	0.74	0.69

presents the details of optimized values based on the methodology discussed above. It can be seen that for any given earthquake, different alternatives are performing in different ways. Since the results are based on normalized values, the relative performance of these options can be checked very easily. At EQ-1 and EQ-2, almost all the alternatives, along with reference structure, perform relatively well. However, from EQ-3 onwards, the difference in performance is becoming more obvious. Hence at EQ-3, the reference structure performs 56% to that of SPJ-3, which makes a huge impact considering both direct and indirect losses. Similarly, at EQ-4 and EQ-5, the performance of the reference structure is 30% and 31%, respectively, as compared to that of SPJ-3. Results of EQ-7 are somewhat different than the pattern discussed above because, at this intensity level, the functionality of all structures was also non-recoverable; hence, the indirect losses at EQ-7 are not included, and only direct losses are calculated and presented. Based on these results, the SPJ-3 retrofitting alternative turns out to be the most effective solution to minimize the direct and indirect losses from both SEs and NSEs in the form of social, economic, and environmental consequences. SAJ-5, RCJ-3, and ECJ-3 also performed very well at all intensity levels, with the performance above 94%, 87%, and 80%, respectively, apart from EQ-5, where ECJ-3 yielded 54% performance relative to SPJ-3.

Since the hospitals are provided with delicate and fragile equipment that can be drift- or acceleration-sensitive, the damage to that equipment is not considered in this study. Damages of SEs and NSEs were calculated, which led to the estimation of direct and indirect losses (in terms of economic, social, and environmental losses). It will also be worth mentioning here that since the retrofitting costs, i.e., initial costs and maintenance costs, along with many other parameters, i.e., fire protection, durability aspects of retrofitting material, etc., are not considered in this study, which could have a huge impact on the decision-making. Thus, the optimized retrofitting option should be evaluated under the limitations of the current study. However, the authors aim to address the issues mentioned here in the next study to bring together all the parameters that could affect the decision-making process. Finally, optimization reveals that SPJ-3 is the best retrofit alternative under the limitations of the current study; however, it is subject to many factors and the weightage of those factors and depends on the stakeholders and decision-makers to consider all or some of those factors partially or completely.

4. Conclusions

This study proposes a performance-based method for estimating direct and indirect losses based on both structural and nonstructural damages, considering various retrofitting alternatives to reduce these damages and enhance performance in terms of vulnerability, risk, and resilience. A hospital building is taken as reference, and nonlinear pushover analysis is used to determine the structural response. The capacity curves are generated and used to quantify the structural vulnerability and impact of retrofitting on performance enhancement. The economic, social, and environmental, both direct and indirect, losses are estimated and compared for the said reference structure before and after the retrofitting, considering four different techniques. It should be noted that retrofitting was applied to the columns of the ground floor only, and all other SEs and NSEs are not altered; nevertheless, the losses are considered for both the SEs and NSEs of the whole building. It is determined from the results that retrofitting lessens the probability of collapse, economic, social, and environmental losses. The repair times of the components are also decreased, thus increasing the seismic resilience. In the end, optimization of the retrofitting strategies is done by defining the seismic risk and resilience indices and assigning them weightage factors to select the most suitable retrofitting option.

Based on the study performed, the following conclusions are made:

• The proposed framework can efficiently assess the resilient enhancement of structure for various retrofit alternatives. Various seismic hazard levels can be considered to determine the damage level of SEs and NSEs to estimate the direct and indirect losses.
• The application of retrofitting has proven to be very effective in enhancing the structure’s global performance, most importantly, when behavior is primarily controlled by column capacities and story response. Four retrofit alternatives, namely, RCJ, SPJ, SAJ, and ECJ, were opted to enhance the performance of the structure. In terms of structural damage quantification, the SPJ alternative showed the most effective performance, followed by SAJ, RCJ, and ECJ.
• The quantification of component-level damage reveals that under the increasing value of PGA, the direct losses also increase for reference structure; however, these losses reduce considerably in the case of SPJ-3 jacketing, followed by RCJ-3 and SAJ-5 alternatives. In the case of ECP-3 retrofit, the reduction in direct losses is also significant but relatively less. For example, at hazard level with a return period of 2475 years, the reference structure shows the direct social losses to be 50 casualties, which was reduced to 23.8, 20.5, 17.5, and 17.5 by ECJ-3, RCJ-3, SAJ-5, and SPJ-3 alternatives, respectively.
• In quantifying the indirect losses, all the retrofitted alternatives showed better resilience as compared to the reference structure; however, SPJ-3 showed relatively superior performance followed by SAJ-5 and RCJ-3 alternatives and ECJ-3 last. For example, at a hazard level of 1250 years return period, the reference structure shows 0 recoveries, hence showing the indirect losses to be 100%; however, at the same hazard level, the seismic resilience shown by SPJ, SAJ, RCJ, and ECJ were 52%, 49%, 47%, and 43%, respectively.
• An optimization study highlights the significance of seismic retrofitting, especially at higher intensity levels, to improve the overall performance of structures. In normalized terms, the SPJ-3 alternative showed comparatively strong performance relative to the other alternatives, followed by SAJ-5, RCJ-3, and ECJ-3. The performance differences among the various alternatives become more pronounced as the intensity of the seismic hazard increases.