Seismic performance-based design and risk analysis of thermal power plant building with consideration of vertical and mass irregularities

Engineering Structures 164 (2018) 141–154

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Seismic performance-based design and risk analysis of thermal power plant building with consideration of vertical and mass irregularities

T

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Jianze Wanga, Kaoshan Daib,a, , Yexian Yinc, Solomon Tesfamariamd a

State Key Laboratory of Disaster Reduction in Civil Engineering and College of Civil Engineering, Tongji University, Shanghai 200092, China Department of Civil Engineering, Sichuan University, Chengdu 610065, China c SEPCOIII Electric Power Construction Corporation, 882 Tong'an Rd, Qingdao 261061, China d School of Engineering, The University of British Columbia, Okanagan Campus, 3333 University Way, Kelowna, BC V1V 1V7, Canada b

A R T I C LE I N FO

A B S T R A C T

Keywords: Thermal power plant Mass irregularity Vertical irregularity Risk assessment Special concentrically braced frame

Industrial buildings often have irregularities due to operational and complex industrial process. In this paper, a thermal power plant with mass and vertical irregularities was designed with the 2010 ASCE and AISC design codes. Subsequently, a parametric study was undertaken on simplified braced frames to quantify the impact of mass and vertical irregularities, as well as their combined effect. Detailed numerical models were developed in Open System for Earthquake Engineering Simulation platform. With a high seismicity level in China, ground motions were selected and nonlinear time-history analyses were performed. Subsequently, probabilistic seismic demand models, seismic fragilities, and risks were developed for different performance levels. The results show that the vertical irregularity generated larger detrimental effect than mass irregularity, and need more attention in structural design. Collapse risk increased the most due to the combined effect of mass and vertical irregularities. Furthermore, under small earthquake intensities, the thermal power plant with the combined irregularities had higher risk in functional disruption.

1. Introduction Electric power is an important lifeline system for any country. Past earthquakes, however, have highlighted the vulnerability of such system with impact on financial losses (e.g. [1,2]) and other cascading effects (e.g. water supply, telecommunications [3]). In developing countries, major electricity generation is using thermal power plants operated with fossil fuels [4]. The thermal power plant buildings carry heavy equipment and machinery needed for operation. Such plants have complex and irregular geometries, and significant mass concentrations on specific floors. The current seismic design procedures for such irregular industrial buildings still follow conventional methods [5,6], however, if the effects of irregularities were not considered properly, would probably result in vulnerable structures [7]. Structural irregularities reported in different codes, e.g. ASCE/SEI 710 [8], Eurocode 8 [9] and National Building Code of Canada (NBCC) [10], primarily include mass irregularity (MI) and vertical irregularity (VI) (stiffness and strength irregularities are categorized under VI). Under moderate to high seismic hazards, buildings with one or more of these irregularities sustained severe damage (e.g. [11,12]). Several studies were undertaken to quantify the effect of each irregularity or

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their combined effects on structural performance (e.g. [13–16]). Letrung et al. [17] designed 20-story steel frame buildings with mass, stiffness and strength irregularities (24 buildings in total) using equivalent static force procedure, and performed nonlinear static and dynamic analyses. Based on the drift values, they discussed that the design criteria in IBC 2000 [18] are conservative for irregular structures. Similarly, Tremblay and Poncet [19] evaluated the effect of MI on a steel braced building and compared two analysis procedures available in NBCC [10] for irregular structural design. They reported that the equivalent static force procedure is inadequate to design a building with 300% MI and the dynamic analysis method is better suited. By using incremental dynamic analysis method, Michalis et al. [20] compared influences of different VIs on the seismic capacities of a 9-story steel frame. They found that the effects of VIs are highly dependent on the selected ground motion records. With consideration of record-torecord variability, Pirizadeh and Shakib [21] adopted the probabilistic design method to evaluate the effect of different VIs on steel moment frames in terms of the exceedance probabilities and confidence levels of various performance objectives. Reported analytical studies focused on residential/commercial buildings (e.g. [13,20–22]), but limited studies were reported on

Corresponding author at: Department of Civil Engineering, Sichuan University, Chengdu 610065, China. E-mail address: [email protected] (K. Dai).

https://doi.org/10.1016/j.engstruct.2018.03.001 Received 27 August 2017; Received in revised form 28 February 2018; Accepted 2 March 2018 0141-0296/ © 2018 Elsevier Ltd. All rights reserved.

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bracing in the first story was unsymmetrical. It is a “half” chevron type bracing and there is a lack of brace member that connects the column bottom of Axis-C to the mid-span of the girder on the first story floor. Similarly, for the roof story (i.e. sixth story), lateral loads are resisted by a moment frame. Thus, the discontinuities in lateral force-resisting structural members lead to VIs. A total of 7 coal scuttles, which are shaped like silos, were installed at the 32.2 m level of the bunker bay (Fig. 1a, d). The coal scuttle, using 12-fixed supports, were rigidly connected to the girders. The mass of each scuttle was assumed to include the self-weight of an empty scuttle combined with the full weight of fossil coals (each coal scuttle weighs 1040 tons) under normal service conditions. Thus, for the 7 coal scuttles, the total weight was 7280 (7 × 1040) tons, which is 5 times to that of the adjacent story. Such large mass concentration on one story introduces significant MI. Although the structure is featured with complex configurations and irregularities, based on conventional building design codes, practicing engineers have options to examine strength capacities of structural members as well as deformation of the structural system by using elastic analysis methods. However, with performance-based design approach, inelastic structural responses of such special and complex building under earthquake loads should be checked [34]. The performance levels can be defined with consideration of the required operational performance of critical equipment [35]. In this study, three performance limit states of SCBF structural systems as proposed by FEMA 356 [36] were adopted: Immediate Occupancy (IO), Life Safety (LS) and Collapse Prevention (CP). The structural performance levels can be combined with nonstructural performance levels as shown in Table 1. Unlike residential/commercial buildings with a relatively larger population density, industrial buildings may have limited human loss but higher financial loss due to equipment damage as well as operational interruptions.

industrial buildings. Thermal power plants, as an important lifeline facility, are designed with stringent performance objectives. Engineers should ensure the thermal power plant meet collapse prevention performance limit under severe intensity earthquakes; and under small and moderate intensity earthquakes, it is allowed to have limited structural damage and normal operational functionality should not be disrupted [23]. Recently, performance-based design framework provided engineers and stakeholders options of quantifying prevalent risk and making an informed decision [24]. Due to operational constraints, MI and VIs are prevalent in thermal power plant building. In this paper, within the framework of performance-based design, seismic risk analysis (SRA) of the thermal power plant was carried out to investigate impacts of MI and VIs. The SRA entails the integration of seismic hazard, structural demand evaluation, and vulnerability [25,26]. The vulnerability assessment, which is generally represented by fragility curves (e.g. [27,28]), can be used to quantify the effect of irregularities (e.g. [13,29,30]). The paper is outlined as follows. In Section 2, the design of a typical thermal power plant building and corresponding performance levels were introduced. In Section 3, three groups of ground motions based on hazard levels of service-level, design-based, and maximum considered earthquakes were selected. Three simplified irregular structural models and a regular structural model based on the complex thermal power plant building were analyzed in Section 4. In Section 5, seismic risks were computed, presented and discussed, followed by discussion and conclusion sections. 2. Thermal power plant building design A three-dimensional view of a typical thermal power plant and the corresponding columns layout are shown in Fig. 1a and b, respectively. The main portion of the plant is 66.1 m × 92 m in plan. Based on functionality, the plant can be grouped into three parts: turbine hall (Axis A–B, 31.5 m high), deaerator bay (Axis B–C, 38.4 m high) and bunker bay (Axis C–D, 53.3 m high). The building also includes three extensions, one in the north-east corner of the bunker bay with a 6 mtall penthouse at the top (Axis 01–1), other two annex in the south-east and south-west corners of the turbine hall (Axis 0A–A). The design loads considered were dead load (due to self-weight of structural members), live load (to account for equipment, pipelines, and cranes), wind load and seismic load. Quantification of the loads and their combinations were performed using ASCE/SEI 7-10 standard [8]. The structural members consist of columns and beams with wide flange Wshape sections, and braces with rectangular hollow structural sections. The beam-column connections were designed to be fully restrained. The sectional strengths (e.g. compression, flexure, buckling) of each structural member were examined with the AISC 360-10 design code [31]. The primary lateral force-resisting systems were concentrically braced frames in both directions. As the building was designed for Chinese high seismic hazard zone, the structural system is expected to have a highlyductile capacity and therefore, criteria associated with special concentrically braced frame (SCBF) system in AISC 341-10 provision [32] were followed. The structural design examination of the entire thermal power plant was carried out using SAP2000 V18 [33] commercial software. The three parts of the thermal power plant have different functionalities, and as a result, the corresponding structural configurations and lateral force-resisting systems were altered along the Y-direction. Fig. 1c shows a typical elevation view of the structure in Y-Z plane (i.e. Axis-6 frame). The turbine hall and deaerator bay were designed as moment frames due to high-story clearance requirements while the bunker bay was designed as a concentrically braced frame system. In order to provide enough space for equipment or large-caliber pipelines that extend through the building, the corresponding lateral force-resisting system in bunker bay could not be designed with continuous bracing arrangement and balanced strength hierarchy. Specifically, the

3. Ground motion selection The seismic risk analysis involves consideration of site-specific seismic hazard [37], and for each of three different hazard levels, an ensemble of 15 ground motion records was selected. The three hazard levels are: (i) service-level earthquake (SLE), (ii) design-based earthquake (DBE), and (iii) maximum considered earthquake (MCE). The corresponding exceedance probabilities for these three levels are 63%, 10% and 2% in 50 years, respectively. The ground motion selection criteria are: moment magnitude (Mw) ranges from 5 to 8; source-to-site distance (Rrup) is 0 ≤ Rrup ≤ 120 km; and as the soil site is classified as stiff soil, average shear velocity in 30 m upper soils, Vs30, ranges from 179 to 280 m/s. Each ensemble of ground motion records was scaled to match target uniform hazard spectrum of SLE, DBE, and MCE, respectively. The scaling was done when less than 10% mean squared error (MSE) for each record was achieved. The target spectrum and spectra of scaled records for each hazard level are shown in Fig. 2. The details of the selected ground motions were summarized in Tables 2–4 for SLE, DBE, and MCE, respectively. 4. Simplified structures with consideration of irregularities 4.1. Structural simplification The X-Z planar frames of the thermal power plant were designed with continuous and paired bracing systems, which provide uniform strength and stiffness distributions. However, as shown in Fig. 1, the MI and VIs exist simultaneously in the bunker bay and make the Y-Z planar frames vulnerable. The lateral force-resisting system in Y-Z planar frames consists of one bay braced frame in bunker bay and moment frames in the rest structural part. To quantify the lateral stiffness provided by the braced frame and moment frames, the frame along Axis-6 without braces (FB1, Fig. 3a) was used for comparison with the original 142

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Fig. 1. Thermal power plant building in this study.

Table 1 Performance levels and damage considered for the thermal power plant building [36] Building Components

Immediate Occupancy (IO)

Life Safety (LS)

Collapse Prevention (CP)

Structural elements

Minor yielding or buckling of braces Units secure and most operable if power and utilities available

Many braces yield or buckle but do not totally fail. Many connections may fail Units slide, but do not overturn, utilities not available; some realignment required to operate

Minor leaks develop at a few joints

Minor damage at joints, with some leakage. Some supports damaged, but systems remain suspended

Extensive yielding and buckling of braces. Many braces and their connections may fail Units slide and overturn; utilities disconnected. Heavy units require reconnection and realignment. Sensitive equipment may not be functional Some lines rupture. Some supports fail; some piping falls

Nonstructural elements

Manufacturing Equipment

Piping

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Fig. 2. Target spectrum and spectra of selected records.

(i.e. 45 for bidirectional excitations and 45 for unidirectional excitations) were performed. The roof drift and base shear responses of the Axis-6 frame were used as the engineering demand parameters. The symbols of θR,BI and θR,UNI were used to represent roof drift responses under bidirectional and unidirectional excitations, respectively; the symbols of FBS,BI and FBS,UNI were used to represent base shear responses under bidirectional and unidirectional excitations, respectively. A total of 45 values of θR,BI/θR,UNI and FBS,BI/FBS,UNI were plotted in Fig. 4a and b, respectively. From Fig. 4, it can be seen that the mean values of θR,BI/θR,UNI and FBS,BI/FBS,UNI are nearly 1.0 and the standard deviations (SD) are around 6.2%. Therefore, from this result, it can be concluded that, the seismic behaviors of Axis-6 frame are primarily affected by MI and VIs while the torsional effect is negligible. Thus, to simplify the analysis, the frame along Axis-6 (Fig. 1b and c) which is close to the middle of the structure was adopted as the baseline frame.

braced frame (FB2, Fig. 3b). A static horizontal force of 100 kN was applied at the top of Axis-A column and the displacements at eight locations (i.e. labeled and marked in Fig. 2) were obtained (Table 5). The average displacement ratio of FB1/FB2 is 3.2 and thus the lateral stiffness provided by bracing elements approximately accounts for 76%. Therefore, the braced bay between Axis-C and Axis-D was selected for further investigation. Details of the actual structure within the bunker bay (Axis C–D) were considered and the rest of the structural parts are simplified as a leaning column. The torsional effect on the seismic behaviors of Axis-6 frame was first examined by comparing responses of the 3D complex structural model in SAP2000 (Fig. 1a) under bidirectional and unidirectional excitations. The ground motion components listed in Section 3 were used as inputs along Y-Z plane for both bidirectional and unidirectional excitations. The other horizontal component for each pair of ground motions was used as input along X-Z plane for bidirectional excitation cases. Structural nonlinear behaviors were achieved by assigning plastic rotational hinges to beams and columns; and axial hinges to braces in the SAP2000 V18 [33]. A total of 90 nonlinear time-history analyses

4.2. Cases considered for the parametric study To investigate the effect of MI, VIs, and their combination, four

Table 2 Ground motions for service-level earthquake (SLE). No.

Earthquake Name

Year

Station Name

Mw

Rrup (km)

Vs30 (m/s)

Scaling Factor

MSE

ID

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Imperial alley-08 Victoria Mexico Superstition Hills-01 Kobe Japan Dinar Turkey Darfield New Zealand Christchurch New Zealand Friuli Italy-01 Imperial Valley-06 Taiwan SMART1(45) Loma Prieta Imperial Valley-06 Christchurch New Zealand Taiwan SMART1(25) Loma Prieta

1979 1980 1987 1995 1995 2010 2011 1976 1979 1986 1989 1979 2011 1983 1989

Westmorland Fire Sta Chihuahua Imperial Valley Wildlife Liquefaction Array Shin-Osaka Dinar Christchurch Cashmere High School Styx Mill Transfer Station Codroipo El Centro Array #1 SMART1 M01 Hollister Differential Array El Centro Array #12 SBRC SMART1 I01 Richmond City Hall

5.6 6.3 6.2 6.9 6.4 7.0 6.2 6.5 6.5 7.3 6.9 6.5 6.2 6.5 6.9

9.8 19.0 17.6 19.2 3.4 17.6 11.3 33.4 21.7 56.9 24.8 17.9 44.2 96.2 87.9

193.7 242.1 179.0 256.0 219.8 204.0 247.5 249.3 237.3 268.4 215.5 196.9 263.2 275.8 259.9

1.73 0.80 1.23 0.58 0.36 0.47 0.69 1.76 1.36 0.76 0.47 0.93 2.59 3.72 1.25

0.09 0.06 0.05 0.06 0.10 0.05 0.06 0.10 0.07 0.09 0.04 0.04 0.08 0.07 0.08

WSM180 CHI102 IVW090 SHI000 DIN090 CMHSN10E SMTCN88W COD000 E01140 45M01EW HDA165 E12140 SBRCS31E 25I01NS RCH280

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Table 3 Ground motions for design-based earthquake. No.

Earthquake name

Year

Station name

Mw

Rrup (km)

Vs30 (m/s)

Scaling factor

MSE

ID

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Imperial Valley-06 Victoria Mexico Superstition Hills-01 Christchurch New Zealand Christchurch New Zealand Christchurch New Zealand Friuli Italy-01 Imperial Valley-06 Taiwan SMART1(45) Loma Prieta Loma Prieta Christchurch New Zealand Kobe Japan Taiwan SMART1(25) Christchurch New Zealand

1979 1980 1987 2011 2011 2011 1976 1979 1986 1989 1989 2011 1995 1983 2011

El Centro Array #12 Chihuahua Imperial Valley Wildlife Liquefaction Array Christchurch Hospital Papanui High School Styx Mill Transfer Station Codroipo El Centro Array #1 SMART1 M01 Hollister City Hall Hollister Differential Array SBRC Shin-Osaka SMART1 I01 Christchurch Cathedral College

6.5 6.3 6.2 6.2 6.2 6.2 6.5 6.5 7.3 6.9 6.9 6.2 6.9 6.5 6.2

17.9 19.0 17.6 4.9 9.1 11.3 33.4 21.7 56.9 27.6 24.8 44.2 19.2 96.2 3.3

196.9 242.1 179.0 194.0 263.2 247.5 249.3 237.3 268.4 198.8 215.5 263.2 256.0 275.8 198.0

2.78 2.41 3.70 0.94 1.65 2.07 5.28 4.09 2.28 1.59 1.42 7.76 1.75 12.72 0.87

0.04 0.06 0.05 0.04 0.08 0.06 0.10 0.07 0.09 0.06 0.04 0.08 0.06 0.07 0.07

E12140 CHI102 IVW090 CHHCN01W PPHSS33W SMTCN88W COD000 E01140 45M01EW HCH090 HDA165 SBRCS31E SHI000 25I01EW CCCCN26W

chevron and inverted-V type braces, similar to the original thermal power plant building structure. However, unlike the prototype structure, symmetrical bracing configurations were considered for both first and sixth stories for a structural system with a well-tailored load path. Also, a uniform mass distribution was achieved by assigning 105 tons of the effective seismic mass to each floor. As stated in Section 4.1, the second-order P-delta effect induced by the structural parts of Axis A–C on the bunker bay was considered. This was achieved by means of a leaning column and rigid links that connect the leaning column to the braced frame. The concentrated gravity loads on leaning column were defined based on the ratio of the tributary mass of Axis A–C to the mass of Axis C–D in the original thermal power plant building.

cases were considered (Fig. 5). And the definitions of MI and VIs were borrowed from ASCE/SEI 7-10 standard [8] which are specified as follows: (1) Mass irregularity: It shall be considered to exist where the effective mass of any story is more than 150% of the effective mass of an adjacent story. A roof that is lighter than the floor below need not be considered. (2) Stiffness-soft story irregularity: It shall be considered to exist where there is a story in which the lateral stiffness is less than 70% of that in the story above or less than 80% of the average stiffness of the three stories above. (3) Stiffness-extreme soft story irregularity: It shall be considered to exist where there is a story in which the lateral stiffness is less than 60% of that in the story above or less than 70% of the average stiffness of the three stories above. (4) Strength-weak story irregularity: It shall be considered to exist where the story lateral strength is less than 80% of that in the story above. (5) Strength-extreme weak story irregularity: It shall be considered to exist where the story lateral strength is less than 65% of that in the story above.

4.2.2. Case 2: mass irregularity (MI) Case 2 was designed to represent a structure with MI (Fig. 5b). Due to the presence of 7 coal scuttles installed on the third story (at the level of 32.2 m) of the bunker bay (marked with wave lines in Fig. 1c), the power plant building was subject to MI. The mass of the third story was approximately 7280 tons (i.e. 5 times to that of the adjacent story), which is greater than the 150% limit prescribed in ASCE/SEI 7-10 standard [8]. Based on the mass distribution of the base structure (Case 1), the seismic mass on the third story floor was increased to 525 tons, which is 5 times to that of the adjacent stories as well as a half of the weight of a coal scuttle (1040 tons). The remaining conditions of Case 2 (e.g. geometry, configuration, mass assigned to other stories) were consistent with Case 1.

4.2.1. Case 1: regular structure The base structure (Case 1) was designed with regular configuration (i.e. no VIs) and uniform mass distribution (i.e. no MI) (Fig. 5a). This structure was a single-bay six-story braced frame. The height and span were 54 m and 10 m, respectively. The first story height was 16 m and heights of above stories were 8 m. The brace configurations were Table 4 Ground motions for maximum considered earthquake. No.

Earthquake name

Year

Station name

Mw

Rrup (km)

Vs30 (m/s)

SF

MSE

ID

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Imperial Valley-08 Victoria Mexico Superstition Hills-01 Kobe Japan Dinar Turkey Parkfield-02 CA Christchurch New Zealand Coalinga-01 Imperial Valley-06 Taiwan SMART1(45) Loma Prieta Christchurch New Zealand Christchurch New Zealand Chi-Chi Taiwan-02 Northridge-01

1979 1980 1987 1995 1995 2004 2011 1983 1979 1986 1989 2011 2011 1999 1994

Westmorland Fire Sta Chihuahua Imperial Valley Wildlife Liquefaction Array Shin-Osaka Dinar Parkfield - Gold Hill 1 W Christchurch Cathedral College Cantua Creek School El Centro Array #1 SMART1 M01 Hollister City Hall Christchurch Botanical Gardens SBRC ILA002 Anaheim - W Ball Rd

5.6 6.3 6.2 6.9 6.4 6.0 6.2 6.4 6.5 7.3 6.9 6.2 6.2 5.9 6.7

9.8 19.0 17.6 19.2 3.4 2.7 3.3 24.0 21.7 56.9 27.6 5.6 44.2 117.8 68.6

193.7 242.1 179.0 256.0 219.8 214.4 198.0 274.7 237.3 268.4 198.8 187.0 263.2 219.8 269.3

7.92 3.68 5.64 2.66 1.62 9.13 1.33 2.84 6.23 3.47 2.42 1.15 11.82 39.37 8.62

0.09 0.06 0.05 0.06 0.09 0.10 0.07 0.08 0.07 0.10 0.07 0.06 0.07 0.10 0.07

WSM180 CHI102 IVW090 SHI000 DIN090 PG1090 CCCCN26W CAK270 E01140 45M01EW HCH090 CBGSN89W SBRCS31E ILA002W WBA090

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Fig. 3. 2D frames of Axis 6 with/without braces under horizontal loads.

stiffness of the three stories above and the lateral strength 51.6% of that in the second story, which are classified as stiffness-extreme soft story irregularity and extreme weak story irregularity, respectively. The detailed design examinations are presented in the following section.

Table 5 Displacement responses of the frames with/without braces. Number

Axis-6 frame without braces (FB1) (mm)

Original Axis-6 frame (FB2) (mm)

Ratio (FB1/FB2)

1 2 3 4 5 6 7 8 Average

20.73 20.14 11.64 17.27 18.55 19.86 21.00 21.35 ⧹

8.34 6.21 4.18 5.23 5.48 5.81 6.09 6.28 ⧹

2.5 3.2 2.8 3.3 3.4 3.4 3.4 3.4 3.2

4.2.4. Case 4: vertical irregularities (VIs) and mass irregularity (MI) One additional simplified structure (Case 4) featured with both VIs and MI was also considered (Fig. 5d). It is a case that was designed to represent the original power plant building. For comparison purpose, the mass distribution was kept consistent with that of Case 2. A total of 525 tons of seismic mass was used on the third story to account for the coal scuttle and 105 tons assigned to the rest floors. The structural configurations were designed same with Case 3, where discontinuous braces were present in the first and roof stories.

4.2.3. Case 3: vertical irregularities (VIs) Case 3 was designed to represent a structure with VIs (Fig. 5c). On the first story, the brace configuration was same as the original thermal power plant building, where only one diagonal bracing connecting the column base of the first story to the mid-span of the beam. A knee brace configuration was employed as well to connect the mid-length of the diagonal brace and the beam-column connection on the first story floor. Similarly, for the sixth story, braces were removed and the lateral forceresisting force system was replaced by the corresponding moment frame. According to the definitions of stiffness and strength irregularities as specified in ASCE/SEI 7-10 standard [8], the “half” chevron bracing in the first story results in the lateral stiffness 68.3% of the average

4.3. Structural design Designs of all four cases were carried out in accordance with the requirements associated with SCBF system using ASCE/SEI 7-10 [8], AISC 360-10 [31] and AISC 341-10 [32] design codes. Modification factor R and deflection amplification factor Cd considered were 6.0 and 5.0, respectively. As the power plant was constructed as a lifeline system, for seismic loads, Risk Category III was considered with an importance factor of 1.25. The modal response spectrum analysis procedure was used to calculate the design seismic loads. Based on the site of the original thermal power plant building, the design spectral accelerations for the simplified structures are Sds = 1.0 g and Sd1 = 0.6 g. The structural designs of the four cases were carried out using

(a) Roof drift

(b) Base shear

Fig. 4. Responses of Axis-6 frame in 3D model under bidirectional and unidirectional excitations.

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Fig. 5. Cases with consideration of irregularities.

checks, and with the introduction of MI and VIs to the base structure, the braced frames of other cases (i.e. Cases 2–4) were not re-designed. The four cases are composed of structural members with identical crosssectional properties as presented in Table 6. Gusset plate connections at the bracing ends were fabricated with ASTM A572 Gr. 50 steel (Fy = 345 MPa) and they were designed with an elliptical gusset plate clearance equal to eight times the thickness of the gusset plate [38]. The beam-column connections were designed as fully moment restrained connections. The braced columns and leaning column were designed to

SAP2000 V18 [33] commercial software. The brace members were selected from cold-formed square tubing (HSS members) conforming to ASTM A500 grade C, with a minimum yield stress, Fy = 345 MPa, and expected yield stress, RyFy = 483 MPa. As prescribed in AISC 341-10 [32], the brace slenderness ratio is limited to 200 and the local slenderness has to meet the limitations specified for highly-ductile members. The wide-flange columns and beams in the frame were specified as ASTM A992 steel with a nominal yield strength of 345 MPa. It should be noted that the design of the base structure (i.e. Case 1) passed all 147

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Table 6 Cross-sectional information of structural members.

Table 8 Story strength distributions.

Structural member

Story

Cross section

Area (mm2)

Material

Fy (MPa)

Story number

Cases 1 and 2 (kN)

Min (Vn Vn+1, Vn/Vn−1)

Cases 3 and 4 (kN)

Min (Vn/Vn+1, Vn/Vn−1)

Column

1 2–3 4–5 6 1–2, 4–6 3 1 2–3 4–6

H900 × 750 × 20 × 52 H800 × 666 × 24 × 48 H700 × 583 × 16 × 40 H600 × 500 × 16 × 35 H600 × 240 × 8 × 13 H1000 × 400 × 12 × 22 HSS380 × 380 × 25 HSS240 × 240 × 18 HSS210 × 210 × 14

93,920 80,832 56,560 43,480 10,832 29,072 35,500 15,984 10,976

ASTM A992

345

ASTM A992 ASTM A500, grade C

345

1 2 3 4 5 6

3274 3172 3172 2460 2460 1815

103.2% 96.9% 100.0% 77.6% 100.0% 73.8%

1637 3172 3172 2460 2460 938

51.6% 100.0% 100.0% 77.6% 100.0% 38.1%

Beam Brace

345

51.6% of that of the second story. Also, although the lateral stiffness and strength of the sixth story is 3.0% and 38.1% of those in the story below (i.e. fifth story), respectively, such sudden changes are not classified as weak and soft stories as required in ASCE/SEI 7-10 standard [10].

be pin connected to their bases. The braced frames were assumed to act as truss structure [39], and the lateral strength and stiffness were mainly provided by diagonal braces in the projection of the horizontal direction. As for the roof story of Cases 3 and 4 with VIs, the flexural capacity of the moment frame was considered to provide the lateral strength and stiffness. Hence, Eqs. (1a) and (1b) were used to calculate the story stiffness of braced frame and moment frame, respectively. Eq. (1b) was used with the assumption that the inflection point for bending moments is at the mid-point of the column.

KBF = EAtotal,bcosα /(kb Lb)

(1a)

KMF = nc ·12EIc /(kc Lc )3

(1b)

5. Seismic risk assessment of simplified structures with irregularities 5.1. Numerical modeling Numerical models were developed using the Open System for Earthquake Engineering Simulation (OpenSees) platform [40] to assess the nonlinear seismic response of the four simplified structures. The beams, columns, and braces were modeled by using the force-based beam-column elements with fiber discretization of the cross section to reproduce the inelastic responses under dynamic loadings. The forcebased formulation was used to model structural members as it offers higher accuracy compared to the displacement-based formulation [41]. The selected force-based beam-column element uses the Gauss-Lobatto quadrature rule for the numerical integration within each segment. Five integration points were considered for this element to obtain a smooth spreading of the inelastic deformation along the members as recommended by [42]. Since the force-based beam-column element uses local coordinates with small deformation assumptions, a co-rotational formulation was chosen for the braces to account for large displacements [43]. P-delta and linear formulations were adopted for columns and beams, respectively. Rayleigh damping was considered by assigning 3% of mass and stiffness proportional damping to the numerical models. In order to simulate inelastic flexural buckling behaviors of the columns and braces, as shown in Fig. 6, bi-directional initial sinusoidal out-of-straightness was applied to the columns to simulate in-plane and

where KBF and KMF are the lateral stiffness of braced frame and moment frame, respectively; E is Young’s modulus of steel material; Atotal is the total sectional area of braces per story; α is the angle between the diagonal brace and horizontal level; nc is the number of columns per story; Ic is the inertia module of column cross section, kb and kc are the effective length factors of brace and column members, respectively; Lb and Lc are unbraced lengths of brace and column members. The story lateral strength of braced frame and moment frame can be calculated as:

VBF = nb (ϕc Pn )cosα

(2b)

VMF = nc (φc Mn )/ He

(2c)

where VBF and VMF are lateral strengths of braced frame and moment frame, respectively; nb is the number of brace members per bay; He is the story height; ϕc Pn and ϕc Mn are the compression and flexural strengths prescribed in AISC 360-10 [31]. According to the selected cross sections shown in Table 6, the story lateral stiffness and strength for each case, which were calculated with Eqs. (1) and (2), were summarized in Tables 7 and 8, respectively. As shown in Tables 7 and 8, as expected, Cases 1 and 2 have uniform stiffness and strength distributions. In contrast, for Cases 3 and 4, the lateral stiffness and strength of the first and sixth stories are significantly lower than those of the adjacent stories (i.e. second and fifth stories, respectively). Specifically, the lateral stiffness of the first story is 64.6% of that of the second story and 68.3% of the average stiffness of the second to fourth stories; the lateral strength of the first story is Table 7 Story stiffness distributions. Story number

Cases 1 and 2 (kN/m)

Min (Kn/Kn+1, Kn/Kn-1)

Cases 3 and 4 (kN/m)

Min (Kn/Kn+1, Kn/Kn-1)

1 2 3 4 5 6

875,000 677,720 677,720 567,141 567,141 465,381

129.1% 77.5% 100.0% 83.7% 100.0% 82.1%

437,500 677,720 677,720 567,141 567,141 17,151

64.6% 100.0% 100.0% 80.4% 79.9% 3.0%

Fig. 6. Numerical model development.

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out-of-plane buckling modes. According to AISC 360-10 code [31], a maximum amplitude of 1/1000 of the unsupported member length was considered. Similarly, the braces were assigned an initial sinusoidal outof-plane imperfection with maximum amplitude of 1/1000 of the unsupported member length. Ten elements were specified for each of the brace and column members. For the wide-flange column and beam sections, a 4 (along thickness) by 8 (along flange or web length) fiber discretization was used. For the HSS bracing members, 10 and 4 fibers were used along the cross-sectional width and through the thickness, respectively. A uniaxial stress-strain relationship was assigned to each fiber in order to obtain the cross-section behavior of the element. The Giuffré-Menegotto-Pinto (Steel02) material model was adopted to account for the Bauschinger effect and simulate both kinematic and isotropic strain hardening responses [44]. The material was defined by specifying the yield stress, Fy, Young’s modulus, E = 200 GPa, the strain-hardening ratio, b = 0.1% (to consider kinematic hardening of the steel material), and three parameters including R0 = 20, cR1 = 0.925, and cR2 = 0.25 (to simulate the transition from the elastic to inelastic phases); four isotropic hardening parameters, a1 = 0.4. a2 = 10, a3 = 0.4, and a4 = 10 were used to model the isotropic hardening of the steel material. Fracture induced by low-cycle fatigue was considered by using the fatigue material model [45]. The fatigue material model is based on a linear strain accumulation rule in accordance with the Coffin-Manson relationship [46] in the logarithmic domain as:

εi = ε0 (Nf )m

Fig. 7. Comparison between test result and numerical simulation.

convergence on the norm of the displacement increment vector with a tolerance of 1 × 10−12 and a maximum number of iterations of 1000. A Newmark acceleration time integration method with gamma and beta of 0.5 and 0.25 [51], respectively, was adopted. The integration equations were formed using UmfPack system [52] and numbered using RCM [53]. The constraints were enforced with a transformation constraint handler and a small time step of 0.001 s was used. The modal analysis was performed first to calculate the fundamental periods of the four cases, which are Tc1 = 0.97 s for Case 1, Tc2 = 1.15 s for Case 2, Tc3 = 1.35 s for Case 3 and Tc4 = 1.66 s for Case 4. The increased mass on third story floor (525 tons) in Case 2 enlarge the period compared to the base structure (105 tons on third story floor in Case 1). Similarly, Case 3 with soft stories has a larger fundamental period than Case 1 as well as Case 2. Since Case 4 was designed with MI and VIs, it has the largest period of the four cases.

(3)

where ε0 is a material parameter that indicates the strain amplitude εi at which one complete cycle of an undamaged material causes fracture. The exponent m is a material parameter that relates the sensitivity of the total strain amplitude of the material to the number of cycles to fracture Nf. The fiber-based low cycle fatigue model would predict rupture within individual fibers, and a gradual, or complete failure of the brace would be simulated. The material stress in the corresponding fiber element drops to zero when fracture is initiated. This fiber is then removed from the element that was originally used for the brace crosssection discretization. According to test calibrations performed by [47], the material parameter required in fatigue model (ɛ0) was evaluated by using Eq. (4) and m = −0.3.

kL −0.484 w −0.613 ⎛ E ⎞ ε0 = 0.291·⎛ ⎞ ·⎛ ⎞ ·⎜ ⎟ ⎝t⎠ ⎝ r ⎠ ⎝ Fy ⎠

5.2. Structural responses For each case, a total of 45 time-history analyses were performed. The structural responses of peak interstory drift ratio (θmax) and shear demand/capacity ratio (DCR) were considered as primary damage indicators. Fig. 8 shows the time histories of the first story θmax values of the four cases for SMART 1 ground motion as recorded in Taiwan on 9/ 21/1983. From Fig. 8, it can be clearly seen that Cases 3 and 4 have the largest interstory drift and residual drift values. For different ground motions, the largest values between Cases 3 and 4 are interchanged. For Case 4, structural collapse was observed under few MCE simulations. Fig. 9 shows the mean θmax distributions of the four cases under different seismic hazard intensities. In general, the base structure (i.e. Case 1) has uniform drift distributions for all hazard levels. This result highlights that, as expected, a well-designed structure without any irregularities has good seismic performance. For SLE (Fig. 9a), the differences in θmax values among the four cases are minimal. For DBE, the θmax values of Cases 3 and 4 for the first and sixth stories are larger than those of Cases 1 and 2. The difference becomes evident for DBE (Fig. 9b) and MCE (Fig. 9c) hazard levels. The largest θmax values are predominantly observed in the first story, and subsequent discussions

0.303

(4)

where kL/r is the brace global slenderness ratio, k is the effective length factor, L is the full length of the brace and r is the moment of gyration with respect to the buckling axis; w/t is the local slenderness ratio, w is the width of the rectangular HSS cross section, t is the cross sectional thickness; E and Fy are Young’s modulus and the measured yield stress of the steel brace, respectively. Rigid elements were assigned at both ends of each structural member to simulate the joint zones. Nonlinear rotational springs were used between the rigid end links and brace elements to simulate the out-of-plane flexural strength and flexibility of the gusset plates. These springs were modeled by zero-length element using Steel02 material model and 1% hardening ratio. The yield moment capacity, My, and the initial out-of-plane flexural stiffness, Kgusset that are required to be assigned to the corresponding material model, were defined with empirical equations proposed by Hsiao et al. [48]. A static cyclic test performed on a single-bay braced frame [49] was used to validate the modeling techniques as mentioned above. The corresponding numerical model of the tested braced frame was developed and a comparison was made between the numerical results and the test results (Fig. 7), which shows a good agreement. To achieve good convergence in the time-history dynamic analysis, a Krylov-Newton solution algorithm [50] was used. This algorithm tests

Fig. 8. First story drift response time-histories of different cases.

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Fig. 9. Maximum drift distributions under different seismic hazard levels.

Fig. 10. Story shear DCR values under different hazard levels.

are for this story. For the DBE (Fig. 9b), with respect to Case 1, the θmax values for Cases 2 to 4 have increased by 105%, 310%, and 543%, respectively. Similarly, for the MCE (Fig. 9c), the θmax values for Cases 2–4 have increased by 106%, 250%, and 385%, respectively. Under the two high-intensity earthquake levels, the second stories of Cases 3 and 4, which are adjacent to the soft/weak story (i.e. first story), also have higher θmax values. Fig. 10 shows the story shear DCR values for the four cases. Generally, the first story of each case has the largest shear DCR value under any hazard levels. Also, for SLE, the DCR values of all cases are less than 1.0, i.e. elastic responses, and uniform from second to sixth stories. Under DBE excitations, the differences of the first story shear DCR values for the four cases are significant but they diminish under MCE excitations. Compared to the result of SLE (Fig. 10a), the distribution patterns of the four cases are different under two higher intensity excitations. Specifically, for results of DBE (Fig. 10b), with consideration of MI only (at the third story floor in Case 2), the shear DCR values from the first to third stories are greater than those of Case 1 by 33.3–40.6%. For structure configured with VIs only (i.e. Case 3), majority shear demands concentrate in the first story and the corresponding shear DCR values suddenly decrease by 31.1–48.5% in the upper stories (i.e. second to fifth stories) as compared to Case 1. It is worth noting that, the shear DCR values of the second to fifth stories for Cases 1 and 2 with no VIs are evidently larger than those of Cases 3 and 4 with VIs as well as the value of 1.0, which indicates that the whole structures of Cases 1 and 2 go into plastic to dissipate the input energy.

5.3. Demand model development Seismic risk assessment deals with the probabilistic estimation of the performance of buildings exceeding unacceptable limit states under uncertain future seismic events [28]. Probabilistic seismic demand model (PSDM) is a mathematical expression used to evaluate the relation between seismic demands (D) and ground motion intensity measure (IM). The seismic demand model can be represented by a power model as [54]:

D = a·IM b

(5)

where a and b are regression coefficients. In this study, the IM and D are expressed with the spectral accelerations at the fundamental period of the structure, Sa(T), and the peak interstory drift, θmax, respectively. Using the “Cloud Analysis” method [55], the Sa(T) and θmax results of the 45 nonlinear dynamic analyses were used to build the PSDM (Fig. 11). By taking the logarithms of Sa(T) and θmax to linearize Eq. (5), the PSDM parameters were obtained and plotted in Fig. 11 (coefficients of the regression are also inserted in Fig. 11). For each case, the dispersion of the demands (i.e. θmax) about its median on the condition of Sa(T), which is expressed with βD|Sa, are also provided in Fig. 11. The small dispersion in terms of βD|Sa of Case 1 (i.e. 0.10) indicates that the seismic demands of the well-designed base structure (Case 1) are not overly sensitive to the record-to-record variability. For Cases 2 to 4 with consideration of MI and VIs, values of βD|Sa are higher. Also, the parameter, a, shows an increasing trend with an increase in case number. It shows again that the detrimental effect generated by irregularities following the order of MI + VIs > VIs > MI. 150

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Fig. 11. Demand models with θmax of Cases 1 to 4.

5.4. Seismic fragility

exceedance (POE) for a designated performance level (PL) as [56]:

The seismic fragility is generally used to provide the probability of the structure attaining beyond a designated performance level as a function of IM. It can be modeled by a lognormal cumulative distribution function as [26]:

λPL =

⎤ ⎡ ln(C /̂ D )̂ P [C < D|IM = x ] = 1−Φ ⎢ ⎥ 2 2 2 + βC + βM ⎥ β ⎢ ⎦ ⎣ D | IM

∫0

∝

P (DPL > CPL |IM = x )·

dH (x ) ·d (x ) d (x )

(7)

where P (DPL > CPL |IM = x ) is the fragility function or probability of exceedance for a designated PL when the intensity measure IM is equal to x; H(x) represents the seismic hazard, which is the mean annual frequency of an earthquake with the IM larger than x. Based on the site-specific information of the original thermal power plant building, the seismic hazard curves of the four cases in terms of 5%-damped Sa(T1) were obtained [37] at their fundamental periods (Fig. 13). The annual probabilities of exceedance of θmax (Fig. 14) for the four cases were computed by convoluting their corresponding seismic hazards (Fig. 13) and fragility curves (Fig. 12). Case 1 has a better risk performance than other cases. For Case 2 with MI, the corresponding drift hazard curve is close to the curve of Case 1 when the drift demand is less than the IO limit value (i.e. θmax < 0.5%). Similarly, there is no appreciable difference between Cases 3 and 4 even up to LS limit value (i.e. θmax < 1.5%). The contribution of MI is less than VIs but it becomes higher with increase of θmax value. As the thermal power plant building was expected to provide 50-year service life (t = 50 years), the probabilities of exceeding IO, LS and CP performance levels in 50 years were computed using Eq. (8) which is expressed as:

(6)

where Φ[·] is standard normal probability integral; C ̂ is median structural capacity associated with a certain limit state; βC and βM donates the aleatoric uncertainty in seismic capacity (C) and epistemic uncertainty in modeling, respectively. The fragilities of Cases 1 to 4 were computed at three performance levels: Immediate Occupancy (IO, θmax = 0.5%), Life Safety (LS, θmax = 1.5%), and Collapse Prevention (CP, θmax = 2%) [36]. The capacity and epistemic uncertainties, βC and βM, were both assumed to be 0.20 [26]. The fragility curves of Cases 1 to 4 were obtained by using Eq. (6) and plotted in Fig. 12. The base structure (Case 1), as expected, has the best seismic performance as it has the least exceeding probabilities for any Sa value. Also, the fragility curves in Fig. 12 show similar trends with the seismic drift responses (Fig. 9). Specific comparisons can be made in terms of the median capacities summarized in Table 9 (i.e. Sa values at 50% probability of exceedance, Sa,50%). From Table 9, compared to the IO results of Case 1, the Sa,50% values decreased by 32%, 83% and 88% for Cases 2 to 4, respectively. Similar trends are observed for LS and CP performance levels, the corresponding Sa,50% values approximately decreased by 46%, 71%, 82% for Cases 2 to 4 relative to Case 1, respectively. Also, it can be seen that the median capacities of Case 4 have minimal difference to those of Case 3 for all performance levels, which indicates that the seismic capacity is predominantly controlled by the VIs. Convoluting the fragility curves with the site-specific hazard, seismic risk can be expressed with the mean annual probability of

PPL (T = t ) = 1−exp(−λPL t )

(8)

The results of the four cases are summarized in Table 10. From Table 10, the likelihoods that represent the structural damage of Case 1 exceed LS and CP in 50 years are less than 1.0%, which provide a highlevel safety confidence. Configured with MI and VIs, the exceedance probability values increase to 0.81% and 7.56% for Cases 2 and 3, respectively. For Case 4, which was designed with intention to represent the original power plant building, the probability of collapse prevention exceedance is 16.79%. As for the exceedance probabilities of IO performance level, the differences among these four cases are significant especially between Cases 2 and 3. And Case 4 has the maximum 151

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Fig. 12. Fragility curves of Case 1 to Case 4 for different performance levels.

Table 9 Median capacities (Sa,50%) of each case for different performance levels (g). Performance level

Case 1

Case 2

Case 3

Case 4

IO LS CP

0.59 1.65 2.17

0.40 0.92 1.15

0.10 0.45 0.67

0.07 0.29 0.42

Fig. 14. Drift hazard levels for different cases.

Table 10 PPL (T = 50 years) for Case 1 to Case 4.

Fig. 13. Hazard curves of four cases.

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Performance objective

Case 1

Case 2

Case 3

Case 4

IO LS CP

15.40% 0.19% 0.02%

25.98% 2.23% 0.81%

75.58% 18.73% 7.56%

77.49% 30.39% 16.79%

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Fig. 15. Normalized θmax distribution comparisons.

Equipment and piping need realignment and inspections. The probability of the operational system failure occurrence is 16.79%. However, stakeholders and societies have different perceptions of what represents a tolerable risk. Hence, it is imperative to involve stakeholders in the definition of the risk-based performance objective.

probability value for IO (i.e. 77.49%). It is clear that the majority of attention should be devoted to reducing the effect of VIs to fulfill a stringent performance objective. 6. Discussion

7. Conclusion

As assumed in simplified structural design (i.e. Section 4.2), Case 4 was considered with intention to represent the original thermal power plant. To validate that the findings as obtained above can be used in the thermal power plant building design for practicing engineers, a comparison was made between the seismic responses of Case 4 braced frame and the original thermal power plant building. As stated in Section 4.1, a total of 45 nonlinear time-history analyses were conducted with the 3D structural model (Fig. 1a) under unidirectional excitations. The excitations used for these two models were same. For each model, distributions of the θmax normalized by the maximum θmax value along the height (i.e. θmax/MAX(θmax)) under SLE, DBE and MCE excitations are shown in Fig. 15. It can be seen that, the distribution shapes of these two models are similar: the first story and roof stories are more critical than the second to fifth stories. For the 3D detailed model, the roof story experienced a larger drift than its first story. It is worth noting that, as prescribed in ASCE/SEI 7-10 standard [8], VIs are identified just by the stiffness or strength ratio of any story to the story above. The roof story of the bunker bay actually cannot be regarded as VIs although the lateral stiffness and strength are much smaller than those of the fifth story (Tables 7 and 8). However, in the NBCC code [10], it states that stiffness irregularity is considered to exist where the lateral stiffness of the lateral force-resisting system in a story is less than 70% of any adjacent story instead of the adjacent story above. As the roof story sustained more severe damage than the middle stories (Figs. 9, 10 and 15) and therefore, the roof story should be classified as VIs as well. From the viewpoint of engineers, the seismic responses of Case 4 satisfied the requirements as prescribed in conventional building design codes (i.e. ASCE/SEI 7-10 [8], AISC 360-10 [31] and AISC 341-10 [32]). For example, under DBE excitations, θmax is less than the limit value of 1.5% required in Section 12.12.1 of ASCE 7-10/SEI standard [8]. With the attained risk results (Fig. 14) and the performance levels for nonstructural elements (Table 1), the post-earthquake operational conditions can be predicted and be easily understood by stakeholders. For example, for Case 4, there is a value of 77.49% exceedance probability in 50 years for IO performance level (Table 10), the consequence of which is that piping has minor leaks and most equipment maintain intact. The operation work can be continued immediately. The probability for suspended operation (i.e. LS performance level) is 30.39%.

Industrial plants are used to be featured with irregularities. In this study, a typical thermal power plant in practice was selected to be studied. Due to the existence of heavy concentrated masses – coal scuttles, the power plant building has significant mass irregularity. Also, the difficult communications between structural configuration and operational process lead to extreme vertical irregularities (i.e. soft story and weak story). To study the effect of each irregularity as well as their combined effect, a parametric study was undertaken with four simplified braced frames. The frames represent well-designed structure, structure with MI, structure with VIs, and structure with both of MI and VIs. Structures were examined with newly design standards. Finite element models were built with OpenSees. And nonlinear time-history analyses were performed. With performance-based design theory, the seismic responses of each case as well as their corresponding fragilities and risks were obtained and discussed. From the comparison between the base structure (Case 1) and structure with MI (Case 2), the results indicate that, (i) the effect of MI on drift demands is minimal under small intensity earthquake (i.e. SLE) and it becomes evident as the excitation intensity increases, particularly on the stories below the MI story; (ii) The effect of MI on the shear force demands are observed on the lower stories; (iii) the decrease in median seismic capacities caused by MI is approximately in the range of 32–45.6%. From the comparison between the base structure (Case 1) and structure with VIs (Case 3), it is found that, (i) the VI story is most critical along the height and their θmax and shear DCR values are significantly larger than those of Case 1; (ii) in contrast, the rest regular stories have elastic responses under any level of earthquake as their shear DCR values are less than 1.0; (iii) according to the fragility results, the median seismic capacities of Case 3 decrease by 70.9–83.0% relative to Case 1. As for the structure with MI and VIs (Case 4), it has similar θmax and shear DCR distribution patterns for the structure with VIs (Case 3), which is most vulnerable to severe damage under any intensity earthquake. The seismic demands of Case 4 are more sensitive to record-torecord variability than Cases 2 and 3 with single irregularity feature. With the attained risk results and pre-defined performance levels for 153

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nonstructural elements, stakeholders can be involved in decisionmaking. Therefore, as for irregular thermal power plant building design, performance-based design and SRA method are recommended to be employed. From a viewpoint of practicing engineers, to effectively mitigate the seismic risk, it is suggested that, (i) in the phase of structural configuration decision-making, a comprehensive communication with other discipline engineers should be undertaken to reduce the potential detrimental effect of VIs as much as possible; (ii) reducing MI effect helps little for seismic performance improvement; (iii) critical stories where VIs exist and their corresponding adjacent stories are essential to the whole structure, which need carful examinations in structural design.

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Acknowledgements The authors would like to acknowledge the support from International Collaboration Program of Science and Technology Commission of Shanghai Municipality (Grant No. 16510711300), National Natural Science Foundation of China (Grant No. U1710111), International Collaboration Program of Science and Technology Commission of Ministry of Science and Technology, China (Grant No. 2016YFE0105600), Power Construction Corporation of China (Grant No. KJ-2016-095) and China Scholarship Council. References [1] Kongar I, Esposito S, Giovinazzi S. Post-earthquake assessment management for infrastructure systems: learning from the Canterbury (New Zealand) and L’Aquila (Italy) earthquakes. Bull Earthq Eng 2015:1–32. [2] Schiff AJ. Guide to Improved Earthquake Performance of Electric Power Systems. Electric Power and Communications Committee, Technical Council on Lifeline Earthquake Engineering; 1999. [3] Didier M, Sun L, Siddhartha G, et al. Post-earthquake recovery of a community and its electrical power supply system. In: Proceedings of 5th ECCOMAS thematic conference on computational methods in structural dynamics and earthquake engineering, Crete Island, Greece; 2015. [4] Erdem H, Akkaya AV, Cetin B, et al. Comparative energetic and exergetic performance analyses for coal-fired thermal power plants in Turkey. Int J Therm Sci 2009;48(11):2179–86. [5] Rolfes JA, MacCrimmon RA. Industrial building design – seismic issues. Iron Steel Tech 2007;4(5):282–98. [6] Hidalgo P, Montecinos R. Chilean seismic design provisions for industrial structures. In: Proceedings of 16th World conference on earthquake engineering, Santiago, Chile; 2017. [7] Richard J, Koboevic S, Tremblay R. Seismic response of irregular industrial steel buildings. In: Lavan O, Stefano MD, editors. Seismic behaviour and design of irregular and complex civil structures. Netherlands: Springer Inc; 2013. p. 73–85. [8] ASCE. Minimum design loads for buildings and other structures. ASCE/SEI 7–10, Reston, VA; 2010. [9] CEN. EN 1998–1, Eurocode 8: design of structures for earthquake resistance Part 1: general rules, seismic actions and rules for buildings. European Committee of Standardization, Brussels; 2004. [10] NRCC. National building code of Canada. Institute for Research in Construction, National Research Council of Canada, Ottawa, Canada; 2010. [11] Tesfamariam S, Saatcioglu M. Risk-based seismic evaluation of reinforced concrete buildings. Earthq Spec 2008;24(3):795–821. [12] Tezcan SS, Alhan C. Parametric analysis of irregular structures under seismic loading according to the new Turkish Earthquake Code. Eng Struct 2001;23:600–9. [13] Rajeev P, Tesfamariam S. Effects of vertical irregularities and construction quality in seismic fragilities for reinforced concrete buildings. Int J Earthq Imp Eng 2017;2(1):1–31. [14] Chintanapakdee C, Chopra AK. Seismic response of vertically irregular frames: response history and modal pushover analyses. Struct Eng 2004;130(8):1177–85. [15] Das S, Nau JM. Seismic design aspects of vertically irregular reinforced concrete buildings. Earthq Spec 2003;19(3):455–77. [16] Lee H, Ko D. Seismic response characteristics of high-rise RC wall buildings having different irregularities in lower stories. Eng Struct 2007;29(11). 3149-1367. [17] Letrung K, Lee K, Lee J, Lee DH. Evaluation of seismic behavior of steel special moment frame buildings with vertical irregularities. Struct Des Tall Spec 2012;21(3):215–32. [18] ICC. International building code. International Code Council, VA; 2000. [19] Tremblay R, Poncet L. Seismic performance of concentrically braced steel frames in multistory buildings with mass irregularity. Struct Eng 2005;131(9):1363–75. [20] Michalis F, Dimitrios V, Manolis P. Evaluation of the influence of vertical irregularities on the seismic performance of a nine-storey steel frame. Earthq Eng Struct Dynam 2006;35(12):1489–509. [21] Pirizadeh M, Shakib H. Probabilistic seismic performance evaluation of non-

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