Comparative benefit-cost analysis for a resilient industrial power plant building with isolation system and energy dissipating devices

ABSTRACT While the use of innovative seismic control strategies has become widespread in industrial plants, assessment of benefits derived from these measures in a quantifiable form can significantly contribute to a more rational risk-informed decision-making of essential infrastructures. In this paper, a benefit–cost analysis is used to examine three retrofit design schemes of an actual thermal power plant building equipped with different seismic control systems, i.e. buckling-restrained brace (BRB), the hybrid shape memory alloy-buckling restrained brace (SMA-BRB), and the partial mass isolation of heavy industrial equipment. The original design scheme having concentrically braced frames as lateral resisting systems is considered as a benchmark model for comparison purposes. For each mitigation alternative, the benefits against seismic effects were quantified in terms of repair cost and recovery time. The results showed that the retrofit system using SMA-BRB leads to the best performance achieving average reduction in residual drift, peak story drift, resilience index, repair time, and average annual loss by 71%, 27%, 48%, 83%, and 89% compared to the original system, respectively. The proposed benefit–cost analysis framework for industrial power plant buildings can be considered as a practical approach of supporting decision-making for non-technical stakeholders and motivating practicing engineers.


Introduction
With the rapid development and integration of carbon-capture technology in fossil fuel power plant (IEA 2018), power plant now plays a significant role in the energy production for sustainable economic growth (Figure 1).Great attentions have been devoted to the evaluation of seismic performance of energy infrastructures.However, major earthquakes such as the 2011 Christchurch earthquake in New Zealand (Uckan et al. 2015), the 2011 Great Sendai and the 1995 Kobe earthquakes in Japan (Fujisaki et al. 2014), the 1999 Kocaeli and the 2011 Van earthquakes in Turkey (Uckan et al. 2015), and the 2008 Wenchuan earthquake in China (Aida et al. 2014) have raised a great concern for the need of incorporating resilience concept into the seismic design of infrastructural systems.Post-earthquake surveys of recent earthquakes revealed that the damages and subsequent operational interruption of electric power facilities would lead to severe, unexpected social and financial consequences (Fujita et al. 2012;Rahnama and Morrow 2000).The resulting consequence includes direct loss due to repair and replacement costs for building functional recovery (Fujita et al. 2012) and indirect losses due to inadequate electrical power supply and Natech disasters (Caputo et al. 2019).Resilience is usually regarded as the ability of a system to quickly recover from the disaster disruption to the initial state and regain its functionality (Fang and Wang 2020).Thus, minimizing the loss of resilience is essential for industrial structures.To facilitate operational recovery, the performance-based earthquake engineering (PBEE) framework developed by the Pacific Earthquake Engineering Research (PEER) has been receiving increasing attention (FEMA 2012) and the design objective for such critical structures is not only to protect the structural system but also to limit the non-structural damage to be repairable within a reasonable shutdown period.
As a result of technological advancements in geographic information systems (GIS), and the availability of computational GIS-oriented and multifunctional applications, researchers are now able to perform more accurate and timely assessments of residential, sensible, and strategic structures.For example, Leggieri, Mastrodonato, and Uva (2022) proposed GIS model for estimating the seismic fragility of residential buildings which is faster and capable of improving overall estimation accuracy.Another regional seismic risk assessment framework was developed by Gentile et al. (2019) based on 85 RC school buildings in Indonesia.The results demonstrate the effectiveness of the proposed framework in providing a rational method to derive seismic risk prioritization schemes for more detailed evaluations.Similar advances are occurring in the area of artificial intelligence making vulnerability databases readily accessible.For this reason, Stefanini et al. (2022) used a large dataset representing RC-building stock to develop a vulnerability assessment framework based on artificial neural network (ANN) capable of reliably predicting the seismic behaviour of existing RC structures.Despite recent developments in earthquake evaluation and mitigation technology, annual losses due to global hazards of power plants are approximately $15 billion, which is equivalent to 0.2% of the constructing cost of power generation infrastructure (Nicolas et al. 2019).
By using supplemental energy dissipation devices, base isolation, and innovative systems, several solutions have been proposed to improve the seismic performance of sensible and strategic structures.They include the resilience improvement through self-centering systems (Pham 2013;Miller, Fahnestock, and Eatherton 2012), the enhancement of lateral forceresisting systems (Stefanini et al. 2022;Gentile et al. 2019;Giordano, De Luca, and Sextos 2021), and minimizing damage using mixed concrete-steel frames (Pnevmatikos, Papagiannopoulos, and Papavasileiou 2019).Power plant structures are preferred to be constructed by steel materials compared to other materials due to their versatility, lightweight properties, and speed of construction and recovery.Concentrically braced frame is the most commonly used primary lateral force-resisting system in industrial structures (e.g.Imanpour and Tremblay 2017;Vela, Brunesi, and Nascimbene 2019).Although it exhibits a sound seismic performance when designed strictly following modern design codes, experimental studies and previous earthquakes demonstrated that braces have a poor energy dissipation capacity due to their buckling behaviors and resulting in unrepairable post-earthquake damages (Kiggins and Uang 2006;Sabelli, Mahin, and Chang 2003).Therefore, bucklingrestrained brace (BRB) has been developed to provide sufficient and consistent cyclic response both in tension and compression (Xu et al. 2018).However, due to the low post-yielding stiffness, BRBs have the drawback of causing large post-earthquake residual deformation which increases difficulties related to the repair work (Asgarkhani, Yakhchalian, and Mohebi 2020).For this reason, self-centering braced frames have been proposed to eliminate residual drift due to provision of both self-centering and energy dissipation capabilities (Christopoulos et al. 2008).
Applications of innovative-damping techniques in thermal power plants have been investigated in the past few years.A heavy coal-scuttle housed in coalfired thermal power plants was found to deteriorate structural seismic performance due to its significant concentrated weight.As an alternative to conventional tuned mass dampers (TMDs), Dai et al. (2018) utilized coal scuttles as a non-conventional tuned mass damper (TMD) to minimize their adverse effects on the seismic performance of supporting structure.They demonstrated that the isolation system reduces the inertial forces imposed on heavy coal scuttles.Furthermore, a reliability-based optimization design framework was proposed for multiple coal-scuttles housed in a thermal power plant working as multiple TMD (MTMD) (Li et al. 2019).The coal scuttles were utilized as MTMD by Li et al. (2019), Shu et al. (2017) and Peng et al. (2018), and the results proved that the MTMD mitigates seismic responses of thermal power plant buildings.Kang et al. (2020) investigated the effectiveness of MTMD system used for coal scuttles by utilizing a combination of bearings and viscous dampers.The analysis results showed an improvement in seismic performance.Besides numerical studies, Wang et al. (2021) conducted shake table tests on a scaled thermal power plant building equipped with metallic dampers (Figure 2a) and isolation systems used for heavy coal scuttles (Figure 2b).Meanwhile, groundbreaking seismic mitigation technologies continue to be developed rapidly to enhance the seismic performance of power plants in an ever-challenging seismic environment.However, in previous studies, the effectiveness of damping and isolation techniques was evaluated in terms of decreasing the seismic responses of structures.The cost-benefit induced by the retrofit strategy has not been reported so far.Thus, the present study considers four common mitigation techniques to represent the general classification of seismic control techniques that have been applied to industrial buildings.Detailed descriptions of this classification are available in Alfanda, Dai, and Wang (2022).Additionally, other, not yet used, techniques can be applied to the proposed framework provided they fall into the class of supplementary damping, equipment isolation, hybrid system, or innovative combination of both.
From a structural safety and economic perspective, stakeholders and professional engineers always prefer a sound benefit-cost ratio (BCR).Numerous studies investigated the benefit-cost analysis (BCA) and economic-related consequences of the seismic design of building structures (Carofilis et al. 2020;Smyth et al. 2004;Zerbe and Falit-Baiamonte 2002) to minimize economic loss and post-earthquake operational downtime.However, there is still a lack of a comprehensive evaluation framework of BCA performance for industrial power plant systems.Efforts are required to make a cost-effective comparison among available seismic mitigation options.
In this paper, a BCA framework applicable to power plant industrial buildings is studied.The main motivation of this study is to optimize the selection of innovative damping techniques and control the repair costs that are not disproportionately high compared to the costs of seismic control techniques.An overview of the proposed BCA framework is shown in Figure 3.It has the following key stages: (1) performance-based earthquake engineering, (2) structural analysis and performance assessment, and (3) decision variables (DVs) in the form of expected losses and downtime for benefit cost analysis.The subsequent sections illustrated the procedures step by step.It is worth noting that the purpose of this paper is not to develop novel mitigation strategies.The goal is to investigate the effectiveness of mitigation strategies not considered in previous studies by implementing the BCA framework

Prototype building description
In this study, a 2 × 650 MW thermal power plant building described by Wang et al. (2018Wang et al. ( , 2021) ) is considered as a benchmark industrial structure.The elevation and plan view of case example power plant are shown in Fig. 4(a,b), respectively.The column has a 66.1 m × 92 m layout (Figure 4b).The functional units of the power plant consisting of a turbine hall and a deaerator bay are designed as a moment resisting frame due to highstory clearance requirements, while the bunker bay is designed as a concentrically braced frame.The primary lateral-force resisting systems in both directions are designed as of special concentrically braced frame (SCBF) and moment-resisting frame (MRF) according to AISC 360-16 (AISC 2016), AISC 341-16 (AISC 2016), and ASCE/SEI 7-16 (ASCE 2016) provisions.As thermal power plant building is a lifeline system, a risk category III and an importance factor of 1.25 are considered for the seismic design of structural components as recommended by ASCE/SEI 7-16 (ASCE, 2016).According to ASCE/SEI 7-16 (ASCE, 2016), design load combinations include dead load due to the self-weight of structural members, as well as live loads to account for equipment, pipelines, cranes, wind, and seismic loads.The structural components include columns and beams with wide-flange W-shape sections and braces with rectangular hollow structural sections.The sectional strengths (e.g.compression, flexure, and buckling) of each structural member were examined based on the AISC 360-16 (AISC 2016) provision.A planer frame in the transverse direction (Figure 4b) is focused because of the presence of the vertical and mass irregularities (Wang et al. 2018;Shu et al. 2017).Consequently, three retrofit techniques using buckling-restrained braces, shape-memory alloy braces, and lead rubber bearing isolators are considered to improve the seismic performance of the industrial building.
To compare effectiveness of three retrofit techniques, four design schemes using different structural systems are considered: (1) Case 1: special concentrically braced frame (SCBF) system; (2) Case 2: bucklingrestrained braced frame (BRBF) system; (3) Case 3: hybrid SMA-BRB frame system; (4) Case 4: coal scuttle isolation system.The four design schemes are evaluated with the help of SAP2000 V20 (SAP 2019), and their finite element models are built with OpenSees (McKenna et al. 2010) for nonlinear response history analysis.Note that the nonstructural components (NSCs) housed in the power generation operation should be designed using equivalent lateral force procedure as stipulated in ASCE/SEI 7-16.Seismic demands on NSCs are calculated using the parameters design-based spectral acceleration, component weight, and importance factor.Using retrofit techniques does not affect the design of general NSCs.Therefore, the design of NSCs is not described in detail, but structural design information and finite element model for the four systems are presented in the following subsections.

Structural system design and numerical modeling
Prior to developing finite element models in OpenSees, structural components are designed and checked by using SAP2000.The design information for the four design cases are separately presented in the following subsections.In the OpenSees numerical models of the four cases, all beams and columns are modeled as nonlinear beam-column elements with fiber sections.Fully restrained beam-column connections are modelled in accordance with the prototype building.To consider nonlinear geometry under large displacements of columns, a co-rotational geometric transformation is included to account for local and global geometric nonlinearities.The Steel02 material model is used to simulate the Bauschinger effect, in which the kinematic and isotropic strain hardening is considered with the yield stress F y = 345 MPa, Young's modulus E = 200 GPa, and strain hardening rate b = 0.1% (accounting for the kinematic hardening of the steel material).The required parameters, namely, R 0 = 20, cR 1 = 0.925, and cR 2 = 0.25, and parameters related to isotropic hardening (a 1 = 0.4, a 2 = 10, a 3 = 0.4, and a 4 = 10) were assigned to account for the transition from elastic phase to inelastic phase as well as the isotropic hardening of the steel, respectively.For each modeling case, leaning columns are simulated to consider the second-order P-Δ effects.Detailed modeling techniques for each design case are separately illustrated in the following subsections.According to AISC 360-16 (AISC 2016), the lateral stiffness and strength for i th story are calculated using Eq. ( 1) and ( 2), respectively.
where V BFi and K BFi are the lateral strength and lateral stiffness of braced frame, respectively.A is the total sectional area of braces per story, α is the angle between the diagonal brace and horizontal direction, and ϕP is the brace flexural strength.K b and L b are effective length factor and of brace per story, respectively.n b denotes the number of brace per story.

Case 1: conventional SCBF system
Table 1 shows the cross-sectional area of structural components for Case 1 evaluated by SAP2000.The brace components used for the numerical simulation are made up of ASTM A500 grade C (F y = 335MPa).For each element, the number of integration points is determined based on a previous parametric study (Uriz and Mahin 2005) with a co-rotational geometric transformation to account for local and global geometric nonlinearities.Each brace is sub-divided into 10 force-based beam-column elements.The fiberbased section is used for elements to model the nonlinear behaviors of brace components.The effects of lateral buckling of braces are explicitly considered with an initial mid-span imperfection of 1/1000 of the component length based on the maximum allowable out of straightness suggested by AISC 360-16 (2016).A zero-length hinge element is used to model gusset plates at the ends of brace elements, and its mechanical properties are determined following suggestions of Hsiao, Lehman, and Roeder (2012).In addition, lowcycle fatigue fracture in braces is simulated with fatigue material available in OpenSees and the associated material parameters required for the fatigue model (ɛ 0 ) are determined according to suggestions of Hsiao, Lehman, and Roeder (2012).

Case 2: buckling-restrained braced frame (BRBF) system
Case 2 is retrofitted by BRB instead of conventional steel braces, and the structural design is performed according to the BRBF requirements stipulated in AISC 341-16 (AISC 2016) and the AISC 360-16 (AISC 2016) seismic provisions.The cross-section area (A sc ) of the core of BRB component is determined based on the axial force demands.Specifically, the axial strength is calculated as ϕA sc F y , in which ϕ = 0.9 and the nominal yield stress,F y = 290MPa.The yield strength, P y , is determined by using Eq. ( 3), as specified in AISC 360-16 (AISC 2016).The cross-sectional area is calculated according to Eq. ( 4), and parameters ω and β are determined by Eq (5).
where E u is the axial force demand primarily determined by load combinations, C max and T max denote maximum compression and tension forces, respectively.Two factors ω and β are to account for overstrength of the brace.β =1:05 and ω = 1.3 are taken from the experimental results of Christopulos (2005).The cross-sections of BRBs and the stiffness and strength ratios between adjacent stories are summarized in Table 2.
In the numerical model developed for Case 2 (i.e.BRBF system), the BRB component is modeled by nonlinear force-based elements (Zsarnoczay 2013).The cyclic behavior of BRB is simulated by using the Steel04 material available in OpenSees.The Steel04 material considers the Bauschinger effect, and it is capable of simulating different hardening characteristics under both tension and compression responses by a set of independent parameters.Miner's rule-based fatigue material proposed by Zsarnoczay (2013) is used to adjust the inelastic strains in the yielding zone.To ensure the accuracy of the numerical model, the parameters summarized in Table 3 are verified by the experimental results of a single-bay braced frame tested by Christopulos (2005).Figure 5 shows a reasonable agreement between the experimental and simulation results.

Case 3: SMA-BRBF system
The SMA-BRB normally consists of a BRB core and a SMA rod that provide energy dissipation capacity and self-centering ability, respectively.Similarly, the analysis and design procedures of SMA-BRBF are comparable to those of standard BRBF and SCBF (Miller, Fahnestock, and Eatherton 2012).The cross-sectional area of BRB core and SMA rods (Table 4) is determined by using Eqs.( 6) and (7), respectively.
where F ysc and A sc are the yielding strength and the cross-sectional area of the BRB core, respectively.A SMA , F SMA , and σ SMA are the cross-sectional area, the initial strength, and the forward transformation stress of SMA component, respectively.With these parameters, the nominal strength P n of the SMA-BRB component is determined by Eq. ( 8).
Note that A sc and A SMA obtained from Eqs. (6)-and ( 7) are used to compute the self-centering ratio defined in Eq. ( 9).The resulting α sc for SMA-BRB components of each story is greater than 1, as presented in Table 4. Miller, Fahnestock, and Eatherton (2012) and Pham (2013) proved that self-centering ability is achieved when α sc ≥1.0.Hence, the prescribed condition is satisfied.
To compare four cases, the SMA-BRB frame is designed to resist the same load combinations as the other cases.The SMA and BRB components are modelled using self-centering and Steel04 materials in OpenSees, respectively.The parameters of Steel04 material model, as well as the strength and stiffness  ratios are given in Table 4.The super-elastic behavior of SMA is simulated by the uniaxial self-centering model reported by DesRoches, McCormick, and Delemont (2004).Table 5 provides the parameters of the SMA material model.The SMA-BRB hybrid model is a paralleling combination of these two material models.The hysteresis behavior of each component and hybrid model under cyclic loading is shown in Figure 6.

Case 4: coal scuttle isolation system
Coal scuttles are essential equipment positioned at a height of 32.2 m in the bunker bay of the benchmark power plant building (Figure 7).Such equipment has significant weight which may increase demand on the supporting structure under seismic loadings (Kang et al. 2020).Therefore, in Case 4, a coal-scuttle isolation system is used to replace the rigid support connections of coal scuttles to improve the seismic performance of the main structure (Wang et al. 2021).Under normal service conditions, the mass of the scuttle includes the self-weight of an empty scuttle and the full weight of fossil materials.Based on this assumption, the entire seismic mass of the coal bunker is approximately 520 tons.In the numerical model, the coal-scuttle is simplified as a concentrated mass at the top of the support nodes.Depending on the stiffness of the selected isolator and the seismic weight of a coal bunker, a single coal bunker has a fundamental period of 0.05 s when its base is fixed, and 2.01 s when using isolation technique.The lead-rubber bearing (LRB) devices used for the isolation of coal-scuttle are modelled using Elastomeric Bearing (Bouc-Wen) element available in   OpenSees.The LRB component connects every mass node and the support node on the girder.Body constraints are also assigned to the support nodes to ensure that they act as coal-scuttle equipment.The primary mechanical properties of the isolator are considered as K 1 = 7.1kN/mm, K 2 = 0.71kN/mm, Q d = 63kN, α = 0.1, and K v = 1800kN/mm, corresponding to initial stiffness, yield stiffness, yield strength, post-yield stiffness ratio, and vertical stiffness, respectively.These parameters are determined based on the design procedure proposed by Dai et al. (2018).A schematic view of the simplified model can be seen in Figure 7.

Ground motions selection
The example thermal power plant building is situated in a seismically active region of China.The building site is classified as a soft soil with a reference shear wave velocity (179 m/s < V s30 <280 m/s).To perform response history analyses, three suites of 15 ground motions are selected and scaled to match the uniform hazard spectrum at three levels: service level earthquake (SLE), design-based earthquake (DBE), and maximum considered earthquake (MCE).The DBE hazard level (Figure 8b) refers to an earthquake with 10% probability of occurrence in 50 years (i.e.475-year return period).The earthquake ground motions are scaled in such a way that the mean squared error between the target hazard spectrum and the average spectrum of selected ground motions is less than 10%.Detailed information on the selected ground motions and the hazard consistency to the target hazard spectrum can be found in Wang et al. (2018).

Seismic demand and development of fragility curves
The concept of risk assessment has been developed in the first-generation PBEE design codes (ASCE-41 2013) focusing mainly on conventional buildings and bridges.Its application to industrial plants and critical components (e.g.boiler, pressure vessels, silo, and piping systems) is still limited.Basically, seismic risk analysis could be classified into two approaches.The first alternative is to use building-based approach by integrating hazard curves with fragility models to assess the seismic risk.A typical example of such approach is HAZUS (FEMA 2003) which covers fragility models of industrial facilities, like oil system, communication system, and water system.An alternative approach is to use the next-generation PBEE framework, which has been in FEMA P58 (FEMA 2012) with more details.However, the companion software, PACT, has few special industrial equipment and nonstructural components.As PBEE advances from risk-based to resilience-based approaches, several projects such as   2020) performed building-based fragility models for a typical thermal power plant to quantify the detrimental and beneficial effects induced by retrofit strategies.This study does not go beyond vulnerability analysis with little consideration of seismic-induced losses and downtime.The following sections put a step forward to estimate the seismic loss risk in a way that incorporates economic loss and downtime.

Drift demands
With the selected ground motions and developed numerical models, nonlinear time history analyses are performed.The resulting peak story drift ratio and residual drift ratio along the transversal axis marked in Figure 4b are plotted in Figs. 9 and 10, respectively.It is clear that the effectiveness of the retrofit technique increases with increasing the intensity of ground motions.Specifically, the drift ratios of Case 1 are comparable to those of Cases 2, 3, and 4 under SLE and DBE levels.This is because all braces remain elastic under low-intensity ground motions.In contrast, the difference between the drift ratios of Case 1 and other cases becomes more evident below MCE level.In particular, the SMA-BRB and BRB components provide an additional damping ratio for the structure, and consequently reduce the drift response of Case 2 and Case 3 below MCE level.
Compared with the response of Case 2 equipped with BRB, the residual drift of Case 3 is smaller due to the self-centering capability provided by the SMA component (Figure 10).Further, the results showed that under all hazard levels, Case 3 has the lowest residual drift, followed by Case 2 and Case 4, and the corresponding average residual drifts are 0.09%, 0.19%, and 0.24%, respectively.FEMA P-58 (2012) suggested that a residual drift higher than 0.5% indicates significant difficulty in post-earthquake repair.The residual drifts of the retrofitted frame structures for all cases meet the residual drift requirements under SLE and DBE levels.Under MCE level, only Case 3 has a residual drift smaller than 0.5%, while the residual drifts of the first story of the other cases are beyond this limit.

Fragility and risk analyses
Establishing the probabilistic seismic demand model (PSDM) is the first step of development of fragility functions.Due to the lack of peer-reviewed component fragility applicable to thermal power plant, the global seismic fragility of the considered four cases is developed using the cloud analysis approach (Jalayer 2003).Specifically, a non-linear regression is used to derive the relationship between the seismic intensity measure (IM) and the engineering demand parameter (EDP).The peak story drift θ max is considered as an EDP, mainly because of its correlation with the global damage states of thermal power plants.This has been proven based on the results of recent studies (Shu et al. 2017;Kang et al. 2020) and past earthquake surveys (Rahnama and Morrow 2000;Uckan et al. 2015).Also, the peak story drift is suggested by performance assessment guidelines to quantify the global damage of braced frames (FEMA 2003).Although the peak ground acceleration (PGA) and the spectral acceleration at the fundamental period (Sa(T 1 )) are the most popular intensity measures regarding their efficiency and effectiveness, the results of Wang et al. (2018) showed that Sa(T 1 ) is suitable for planer and irregular braced frames.Therefore, a regression analysis between θ max and Sa(T 1 ) is carried out based on Eq. (10). Figure 11 shows the results of regression for the four cases.
To define fragility function, the probability of exceeding a certain EDP conditioned on a given  hazard level, the drift response obtained from Section 3.1 is taken as the EDP and along with damage states predefined in Table 6, the seismic fragilities are developed following Eq.( 11), and the results are shown in Figure 12.
where Φ � ½ � is the standard normal cumulative distribution function, edp 0:5 is the median capacity of the structural demand for a given seismic intensity measure (IM) and β is the logarithmic standard deviation of the demand conditioned on the IM.
Three commonly adopted damage states (DS) in steel frames and industrial buildings (Kang et al. 2020;Wang et al. 2018), namely slight (DS 1 ), moderate (DS 2 ), and extensive (DS 3 ) damage states, are considered in this study.The threshold values of the damage states indicated in Table 6 are used to classify the overall severity of damage to both structural and nonstructural components.Accordingly, the description of damage states for Cases 2 and 3 is judgmental with consideration of the findings of recent studies on performance assessment of hybrid SMA frames, such as Pham (2013), Christopoulos et al. (2008), and Fang and Wang (2020).These studies have shown that SMA hybrid frames have higher deformation limit states compared to BRBF and SCBF but still remain functional.It should be mentioned that the present study only considers three repairable damage states.If a power plant suffers more severe damage like total collapse, its demolition and replacement are highly recommended.
Figure 12 compares seismic fragility curves for slight, moderate, and extensive damage states of four cases.It can be seen that seismic intensity increases with the probability of exceeding more intense damage states, i.e. for the states of extensive damage (see Figure 12c) and moderate damage (see Figure 12b), while increases slightly with the probability of exceeding slight damage state (see Figure 12a).The reference case and the one retrofitted with equipment isolation system have a considerably higher probability of exceeding slight damage state as compared to the cases retrofitted by BRB and SMA-BRB retrofit.The difference is more pronounced for probability exceeding the extensive damage states (differences with respect to Case 1) as follows: Case 2: 24% (64%), Case 3: 8% (88%), and Case 4: 29% (57%).
As mentioned earlier, the considered power plant building is located in a seismically active region of China.The hazard curves of the four cases were obtained from the local geological bureau (Wang  et al. 2018), as shown in Figure 13.The annual probability of exceedance of θ max for the four cases is obtained by convoluting the corresponding seismic hazards (Figure 13) and fragility curves (Figure 12), according to Eq. ( 12).
where λ (x) is the mean annual frequency that drift θ exceeds the value x, P θ 12) donates the probability that drift θ exceeds the value x for the given spectral acceleration, and the absolute value of the derivative of the hazard curve with respect to Sa (T 1 ).As the prototype power plant building is expected to provide a service life of 50 years, the probability of exceeding DS 1 , DS 2 , and DS 3 in 50 years is computed using Eq. ( 13) and Figure 12 as follows: The probability of exceedance over a period of 50 years for the four cases is shown Table 7.It is clear that Case 3 has a probability of exceedance of DS 2 and DS 3 smaller than 10% in 50 years.The probability of exceedance of DS 3 for Case 3 is smaller than those of Cases 2 and 4 by 2.8% and 3.4%, respectively.For Case 1, which represents the original power plant building, the probability of being in extensive damage (DS 3 ) is 7.6%.As for probability of exceeding DS 1 , the difference between these four cases is more pronounced, especially between Cases 1 and 3.Besides Case 1, Case 4 has the highest probability of exceedance among three retrofit schemes, where the probability of exceeding DS 1 (i.e.72%) for this case is about 10% smaller than that for Case 1.

Seismic loss estimation
Unlike common residential (Smyth et al. 2004;Stefanini et al. 2022) and strategic and commercial buildings (Carofilis et al. 2020) with relatively high human occupancy, industrial buildings have large financial losses due to equipment damage and interruption of operations (Wang et al. 2018(Wang et al. , 2020)).Therefore, this study is limited to quantifying expected repair cost and downtime as decision variables (DVs) obtained by considering probability propagation as: where λ is the average annual rate of seismic events with IM ≥ im, im is a threshold of IM, the DM is the damage measure which is categorized into three discrete damage states DS as described in Sec.3.2, P(DM| EDP) is the probability of exceedance of a damage measure given an engineering demand parameter, and P(EDP|IM) is the probability of exceedance of an EDP parameter for a given intensity measure, IM.The expected economic loss for each design case is appraised following the recommendations by FEMA P-58 (FEMA 2012, HAZUS (FEMA 2003), EIA (EIA 2018), Schröder et al. (2013), andKumar, Sharma, andTewari (2015).Economic loss from potential repair activities that are not provided by these references, such as cost of material supply, skilled labor, and installation and other additional costs, are assumed to be the same for the four design schemes and hence this part of cost is exempted in benefit-cost analysis.To further compensate the limitation of global-based analysis, the approximate replacement costs were estimated by summing up the cost values associated with structural components, non-structural components, and equipment as indicated in Table 8.Note that the replacement cost encompasses construction cost, demolition cost, and replacement of damaged components, as well as costs of recovery due to impending factors (Bradley et al. 2009).Therefore, additional costs are included to account for building demolition and site clean-up.Specifically, 118% of the total cost in Table 8 was considered to arrive at the average replacement cost (C Rep ) for the power plant.
In addition, the retrofit costs attributed to material usage for retrofit implementation were estimated as (Babaei and Zarfam 2019): where Q m = the quantity of material required and C m = unit cost of material (Alibaba Group Holding Limited.2020), and C is the cost of labor and installation.The total additional cost due to retrofit actions and the corresponding replacement cost for Cases 2-4 are presented in detail in Table 9.Note that the cost values for all considered items are based on the production capacity and economic development level of China (Alibaba 2022).The cost-benefit analysis results presented are thereby more suitable for industrial buildings located or invested by China.
Figure 14(a,b) shows the expected loss and ratios with respect to replacement values under each of the four cases considered.It is observed that the expected losses increase with increasing seismic intensity.At the intensity of DBE (i.e., Sa(T1) = 0.6 g), the loss ratios are estimated to be 0.46, 0.06, 0.02, and 0.14 for Case 1, Case 2, Case 3, and Case 4, respectively.And at the intensity of MCE (i.e.Sa (T 1 ) = 0.9 g), the loss ratios increase to 0.65, 0.11, 0.04, and 0.25 for Case 1, Case 2, Case 3, and Case 4, respectively.
For further comparison of the four cases in terms of economic loss, the average annual loss (AAL) is calculated using Eq. ( 16): where C Rep is the replacement value, P[DS i |Sa(T 1 )] is the probability of a given damage state given Sa T 1 ð Þ; is the absolute value of the derivative of the hazard curve with respect to Sa T 1 ð Þ (Figure 12) and L Ri [DS i ] denotes loss ratio of 0.1, 0.4, and 0.8 (FEMA  2020) for DS 1 , DS 2 , and DS 3 , respectively.The AAL values were computed to be $186,283 (Case 2), $73,579 (Case 3), and $227,863 (Case 4) with the corresponding reduction of 75%, 89%, and 69% relative to $731152 (Case 1), respectively.Similarly, the recovery time for the four cases was evaluated using Eq. ( 17) and the associated average annual recovery time is derived following Eq.( 16) and presented in Figure 14(d).
where E(Days|DS i ) is the DS i recovery time given DS 1 (10 days), DS 2 (90 days), and DS 3 (240 days) as suggested by HAZUS (FEMA 2020).MOD DSi is the construction time modifiers with 0.5, 1, and 1 assigned to DS 1 , DS 2 , and DS 3 , respectively (FEMA 2020).When compared to Case 1, the reduction in the downtime by different retrofit schemes are 58%, 83%, and 52% for Case 2, Case 3, and Case 4, respectively.

Benefit-cost analysis
The resulting benefits are considered in terms of AAL reduction (with respect to the AAL of the Case 1) due to different retrofit actions.It is worth pointing out that earthquake losses do not occur in annual increments, the AAL could be accumulated to the total loss over the service lifespan, 50 years (FEMA 2020).As a result, the benefits of the retrofit design cases (abbreviated as B) were estimated using Eq.( 18) where the difference in AAL values between the original design and the retrofit designs is considered divided by the discount rate (r = 3%) over time t, within a useful lifespan T of 50 years.Then, given B, the BCR is calculated using Eq. ( 18).
Based on Eq. ( 16), the effectiveness for each seismic mitigation option is compared with AAL.Again, the AALs reported in Table 10 were approximately $186,283 (Case 2), $73,579 (Case 3), and $227,863 (Case 4) with the corresponding reduction of 75%, 89% and 69% relative to $731152 (Case 1), respectively.This further indicates the effectiveness of the three retrofit strategies as AAL values obtained with both retrofit alternatives are lower than the values of the original building (Case 1).However, after taking the cost of each retrofit strategy into account, the BCR for case 4 with isolated coal scuttle is derived as 1.70, while for case 2 with BRB, the value goes up to 1.79.Better results can be seen for case 3 with SMA-BRB which has a BCR of 1.83.Based on the BCRs, the use of SMA-BRB as a resilient improving solution is the more economically beneficial, followed by strategies of BRB and then coal-scuttle isolation.Given that the retrofitted power plant has 50 service years at a discount rate of 3%, the BCRs corresponding to Case 2, Case 3, and Case 4 are in the ranges of 1. 79-46.45, 1.83-47.3, and 1.7-44.1,respectively.The highest BCR was achieved for SMA-BRBF followed by BRBF and then coal scuttles isolation.
Downtime and repair cost are complementary and should be used in an integrated perspective.To further demonstrate the benefit of the retrofit cases in terms of business downtime, a resilience index (R-index) as a function of the recovery time, is estimated based on Eq. ( 20): where Q (t) is the functionality of the facility, T LC is the control time-horizon assuming that a retrofit is completed in a given year,T RE is the recovery time from disruption, event and t O is the time of occurrence of an earthquake event.
With the estimated downtime, the resilience index (R-index) of the design cases is computed using Eq. ( 18).The resulting R-index values are classified according to the USRC (US Resiliency Council) rating system (Table 10).The results show that Case 1 has the lowest seismic resilience of 62% compared to the other three retrofit strategies.When the retrofitting actions of Case 4 and Case 3 are considered, the resilience index increases slightly by 33% and 37%, respectively.Despite the high retrofitting costs ($360,023) compared to Case 2 ($303,767) and Case 4 ($295,740), Case 3 (R-index = 92%) would be highly recommended because it yields the shortest recovery time and the largest BCR.In principle, the time required for retrofitting and the expected losses usually decide which retrofitting option to be chosen.Although there are few indicators estimated to guide the retrofit scheme selection, it is important to recognize that decisionmaking solely depends on the facility owner's top priorities, such as recovery time, reduced economic losses, short payback period, retrofit feasibility, and the remaining life span of the facility.They are also important indicators for insurance companies to cover seismic loss in the event of an earthquake and/or business interruption.Although SMA-BRBF achieves a sound performance and is relatively cost-effective, the availability of suitable retrofitting materials, financing, and availability of skilled workmanship are the factors that would define the suitability of retrofitting schemes.High cost of hybrid BRB-SMA installation in terms of machining and fabrication which required highly skilled workmanship (Miller, Fahnestock, and Eatherton 2012).
Despite the above-mentioned factors, SMA-BRBF remains the most cost-effective retrofit strategy.It is important to note that the proposed framework adopts BCAs that are based on a single criterion (repair costs) and corresponding recovery times.The analysis does not consider the combined effects of multiple criteria, such as the payback period, the feasibility of retrofitting, and the availability of skilled labor.This framework can be further improved by integrating multi-criteria decision-making tools such as TOPSIS (technique for ordering preference by similarity to ideal solution), which can be used to identify and select the optimal alternative among a variety of options that meet a specific set of criteria to match the profiles of different owners.

Discussion
As observed from the response history analysis results in terms of drift demands, Case 1 is prone to large residual story drifts after severe earthquakes due to the low post-yield stiffness of the bracing components.This explains why the cost of repair would be higher compared to the other three options.Moreover, Cases 2 and 3 were found to be more effective than lead rubber bearing isolators of Case 4 in reducing seismic drift demands.As indicated in a shaking table test (Wang et al. 2021) of a scaled thermal power plant building, failure of isolators, and permanent displacement of coal bunkers were observed.Therefore, the residual displacement of the LRB devices may become an obstacle to recovery operations if Case 4 is adopted.The isolation effect can be further enhanced by employing hysteretic viscous damping or hybrid self-centering bearings.
In this study, the peak story drift is taken as the engineering demand parameter to quantify the damage state of the building system.The development of PBEE provides another approach to estimate seismic loss based on the damage of individual structural and nonstructural components.However, such approach requires a database of fragility models for critical NSCs in the thermal power plant building.At present, there are few studies performed to verify the intensity measure of special NSCs such as deaerator, turbines, ash handlings, etc. and much less to propose adequate fragility models.Therefore, for the sake of estimating seismic loss based on damage of components, more efforts are required in the future for the development of fragility models of NSCs that are particularly essential in industrial process.Although Cases 2 and 3 have similar drift ratios, the most significant finding is that the BRBF does not reduce significantly the residual story drifts.Such permanent deformations provide another justification for self-centering framing system as an incentive for design options to be investigated in our future research.Furthermore, SMA-BRB hybrid-frame experienced relatively lower peak story and residual drifts along the building height, compared to the BRBF, SCBF, and coal scuttles isolation implying less damage concentration due to its re-centering capabilities not possessed by other bracing systems as well as the reduced functionality and maintenance requirements.
At a lower discount rate with a longer service life of the retrofitted structures, a higher benefit can be obtained.By comparing the benefits of different retrofit alternatives, stakeholders, facility owners, and relevant decision-makers can express retrofit feasibility more clearly.In this way, decision-makers may be interested in losses in a particular payback period, for example, in this case, a 50-year loss at a discount rate of 3%.The owner may be willing to invest up to the value of this loss in the form of earthquake mitigation to avoid recurring losses in the future during this period.This helps to show the reasonable value of insurance premiums due to business interruption.Tackling the following limitations is worth recommending: • In this study, the planner frames are considered with the purpose of comparing benefit-cost ratios of using various retrofit strategies.As per a determined retrofit design scheme, 3D structural analysis and component-based seismic loss analysis is recommended since it is capable of quantifying the exact damage states and capturing the irregularities and torsional effects typically associated with industrial buildings.• On improving efficiency and practicality of the IM, instead of the spectral acceleration at the fundamental period of the structure Sa(T 1 ), better IMs such as the recently proposed average spectral acceleration could be used which is capable of producing more accurate results, especially for higher modal effects and periods in the inelastic response range.• Since saving direct investment costs is the main focus of this study, further improvement and active participation of relevant decision-makers can be encouraged by including detailed monetary losses for secondary components, recovery time and other environmental impacts.
• SMA hybrid brace is relatively expensive, there might be reasonable sources of cost savings in the fabrication and repair phases by employing potential substitutes available in the form of SMA wires, SMA-cables, spring-rings, SMA bolts, or SMA-plates requiring less fabrication and installation efforts.
• It is noted that in the seismic design of damping devices and isolators following ASCE/SEI 7, the property modification factors shall be considered to account for variation of the nominal design parameters of components caused by dynamic loading features, production bearing properties, temperature, aging, environmental exposure, and contamination, etc.For retrofit strategy selection based on BCR analysis, such seismic examination at every single component is not considered in this study and once the retrofit design scheme is determined, the detailed design efforts should be further developed.

Conclusions
The present study compared the cost-effectiveness of different design options in terms of AAL reduction for retrofitting an industrial thermal power plant building using techniques of BRB, SMA-BRB, and isolation of heavy equipment.The response history analysis results under ground motions at intensities of SLE, DBE, and MCE show that SMA-BRB hybrid system can be a promising option for enhancing the seismic performance of the lateral seismic resistance system of the power plant building.Compared with the other two seismic control options, SMA-BRBF has the lowest average residual drift and peak drift demands achieving 71% and 28% reduction rates, respectively.The seismic fragilities of the original design and the three retrofit designs were developed.Convolved with seismic hazard, the AALs of the four design cases were calculated and compared.The results show that Case 1 has the highest AAL with the lowest R-index of 62% compared to the other three retrofit strategies.When the retrofitting actions of Case 2 and Case 4 are considered, the R-index increases to a value around 84%.Despite the high retrofitting costs of Case 3 ($360,023) compared to Case 2 ($303,767) and Case 4 ($295,740), Case 3 (R-index = 92%) would be highly recommended because it yields the shortest recovery time as well as the highest BCR.Similarly, the average annual repair time is reduced to 30, 75, and 86 days for Cases 3, 2, 4 with respect to Case 1, respectively.These values match very well with the USRC (US Resiliency Council) rating system (Table 10).A good balance is achieved between cost and savings as a result of reduced damage from the self-centering ability of the SMA-BRB bracing members.
Overall, this study offers some practical insights into the use of common seismic mitigation strategies in determining the most economical option for preliminary risk assessment and insurance premiums of industrial facilities.This is required by decision-makers to have full knowledge of all the available options and estimates that must be paid today or benefits in the future for adequate recovery plans of essential facilities.Clearly, the AAL could serve as a useful decision variable as well as a performance measure for determining a rational investment cost, accounting for the possible future benefit of a seismic control action when selected from a wide range of options.
Furthermore, for different mitigation actions considered and the loss evaluation at the specified performance levels is a conservative estimate based on a global (building-based) level approach, not a component-based due to the lack of some technical data.However, other contributors of seismic-induced losses, i.e., accelerative sensitive component losses accounting for about 17% of the overall power plant cost, were neglected.As an alternative, the component-based seismic loss approach can be used.Presently, there are few studies performed to verify the intensity measure of NSCs such as deaerator, turbines, ash handlings, etc., and much less to propose adequate fragility models.In sum, refined component-based seismic loss estimation approaches and fragility models specific for special industrial equipment housed in power plants need to be comprehensively investigated in the future.

Figure 1 .
Figure 1.Age structure of existing coal power capacity by region (IEA 2020).

Figure 2 .Figure 3 .
Figure 2. Illustrations of a thermal power plant building with damping and isolation devices (Wang et al. 2021).

Figure 4 .
Figure 4. Schematic views of the case study thermal power plant building.

Figure 5 .
Figure 5.A comparison between the numerical simulation and the experimental test for a BRB braced frame.

Figure 6 .
Figure 6.Typical hysteresis curves of SMA-BRB model used in Case 3: (a) SMA model, (b) BRB model, (c) SMA-BRB hybrid model, and (d) Illustration of the hybrid model.

Figure 7 .
Figure 7.A schematic view of partial coal scuttle isolation system used in Case 4.

Figure 8 .
Figure 8. Target hazard spectrum with response spectrum of selected ground motions.

Figure 13 .
Figure 13.Hazard curves of alternative seismic mitigation cases: Probability of exceeding at Sa(T 1 ) level.

Figure 14 .
Figure 14.Loss estimation results for the considered retrofit alternatives.

Table 1 .
Cross-sectional area and relevant design information evaluated by SAP2000 for Case 1.

Table 2 .
Cross-sectional area and relevant design information evaluated by SAP2000, for Case 2.

Table 3 .
Parameters used for the Steel04 material model in OpenSees.

Table 4 .
Summary of the design of SMA-BRBF model.

Table 6 .
Performance levels and corresponding story drift limit states for fragility development.

Table 7 .
Probability of exceeding different damage states for four mitigation strategies over a service life of 50 years.

Table 8 .
Unit costs of components and materials.

Table 9 .
Additional cost due to retrofit actions for cases.

Table 10 .
Comparison of decision variables for BCA of different mitigation options.