Seismic Vulnerability Assessment of Wood-frame Buildings in Southwestern British Columbia

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1 Seismic Vulnerability Assessment of Wood-frame Buildings in Southwestern British Columbia K. Goda University of Bristol, United Kingdom G.M. Atkinson University of Western Ontario, Canada ABSTRACT: The seismic performance of typical wood-frame structures in south-western British Columbia is analytically investigated through incremental dynamic analysis by utilizing available UBC-SAWS models. To reflect complex seismic hazard contributions from different earthquake sources (i.e., crustal, interface, and inslab events), we construct conditional mean spectra for three earthquake types, and use them to select adequate sets of ground motion records for scaling. The results indicate that the record selection procedures have significant influence on the probabilistic relationship between spectral acceleration at the fundamental vibration period and maximum inter-story drift ratio, highlighting the importance of response spectral shapes in selecting and scaling ground motion records. Subjected to 2%-in-50-years ground motions, House 1 is expected to experience very limited damage; Houses 2 and 3 may be disturbed by minor damage; whereas House 4 may suffer from major damage occasionally. Keywords: Incremental dynamic analysis, Wood-frame building, Conditional mean spectrum 1. INTRODUCTION South-western British Columbia (BC) is inhabited by a large population and is a centre of business and industrial activities in western Canada. The regional seismicity is relatively high, and hence, potential urban seismic risk is a serious concern. Residential wood-frame buildings are the most prevalent construction type; the majority of the buildings are non-engineered and may lack sufficient post-yield seismic resistance. Thus, vulnerability assessment of wood-frame buildings is important for home owners and emergency officials in local municipalities. The main objective of this study is to assess the seismic vulnerability of typical wood-frame houses in south-western BC. We adopt structural models for wood-frame houses, UBC-SAWS models, which were developed by White and Ventura (2006) based on the computer program SAWS (Folz and Filiatrault, 2004), and carry out incremental dynamic analysis (IDA) (Vamvatsikos and Cornell, 2004). IDA involves the selection and scaling of ground motion records, which could induce bias in assessing the nonlinear response potential. Careful selection of ground motion records, focusing on seismic characteristics as well as response spectral shapes, is particularly important (Luco and Bazzurro, 2007; PEER GMSM Working Group, 2009). Recently, Baker (2010) proposed a record selection procedure based on the conditional mean spectrum (CMS), which can be used in tandem with uniform hazard spectra (UHS) that are obtained from probabilistic seismic hazard analysis (PSHA). The use of the CMS as a target response spectrum produces a reasonable ensemble representation of ground motion records and is pertinent for evaluating the seismic vulnerability of a structure. We carry out IDA of the UBC-SAWS models using two extensive ground motion datasets: the PEER-NGA database for worldwide shallow crustal earthquakes and the K-NET/KiK-NET database for Japanese earthquakes that occur in a subduction environment. In this study, two different databases are considered, as seismic activities in south-western BC are contributed by three distinct types of

2 seismic events: shallow crustal earthquakes, interface Cascadia subduction earthquakes, and deep inslab subduction earthquakes (Goda et al., 2010). Thus, for different earthquake types, we define and adopt different CMS as a target response spectrum, as based on a recent seismic hazard assessment in south-western BC. In the following, a brief summary of the UBC-SAWS models is given in Section 2. Then, methodologies for the seismic vulnerability evaluation based on UHS, IDA, and CMS are discussed in Section 3. In Section 4, the impacts of record selection procedures and of using different shear-wall types on the assessment are investigated. 2. UBC-SAWS MODEL The seismic performance of typical single-family residential wood-frame houses in south-western BC has been investigated by researchers at the University of British Columbia. Nonlinear characteristics of wall assemblies with different sheathing and finishing materials were tested quasi-statically as well as dynamically, and full-scale shake-table tests of one/two-story wood-frame houses with different shear-wall types were conducted (Ventura et al., 2002). Moreover, White and Ventura (2006) calibrated parameters of the SAWS model based on the static and dynamic test results of shear-walls and full-scale houses, and developed the UBC-SAWS models for typical two-story residential wood-frame houses in south-western BC. There are four house models: 1) House 1 with stucco/engineered oriented strand board and gypsum wallboard (OSB/GWB), 2) House 2 with engineered OSB/GWB, 3) House 3 with non-engineered OSB/GWB, and 4) House 4 with horizontal boards/gwb. The natural vibration periods of the four models in the direction of seismic excitation were obtained as about 0.25, 0.3, 0.35, and 0.4 sec for Houses 1-4, respectively. The pushover analysis of the UBC-SAWS models indicates that the installation of exterior stuccos leads to higher stiffness and displacement capacity, whereas the use of blocked or unblocked OSB/GWB does not affect seismic capacity significantly. White and Ventura (2006) concluded that the UBC-SAWS models are capable of predicting the maximum inter-story drift ratios of about 1-4 reasonably well. 3. INCREMENTAL DYNAMIC ANALYSIS AND RECORD SELECTION 3.1. Seismic Hazard Analysis and Target Scenarios PSHA is a standard procedure for seismic hazard assessment. PSHA results are often presented in terms of UHS; scenario events that are associated with the UHS are identified by seismic hazard deaggregation. In this study, we use an updated seismic hazard model for western Canada, developed by Goda et al. (2010). Using the updated model, seismic hazard curves and deaggregation results can be flexibly obtained for different soil conditions and for different return period levels. The sensitivity analysis indicates that the use of a suite of recent ground motion prediction equations (GMPEs) with proper distance measure conversion has significant impact on seismic hazard estimates. PSHA is carried out for Vancouver using the updated seismic hazard model. The obtained UHS for a soft soil condition having the average shear-wave velocity in the uppermost 30 m V s30 of 200 m/sec are shown in Figure 1a. The assessment considers annual non-exceedance probabilities ranging from to To investigate the characteristics of seismic events that contribute to a selected probability level, seismic hazard deaggregation for spectral acceleration at 0.3 sec is conducted at the annual non-exceedance probability of (i.e., 2% probability of exceedence in 50 years), and the results are shown in Figure 1b, in terms of [M, R, ε] and [M, R, Event type] (note: M is the moment magnitude, R is the distance measure, and ε is the epsilon). Percentages of seismic events contributing to different annual non-exceedance probability levels and mean values of identified earthquake scenarios in terms of M, R, and ε (i.e., M, R, and ε ) are summarized in Table 1. In Table 1, three sets of M, R, and ε are listed for shallow crustal events, interface subduction events, and inslab subduction events, respectively. We observe that as the non-exceedance probability level increases, more contributions come from inslab earthquakes, rather than shallow crustal and interface subduction

3 earthquakes, and that each event type has distinct characteristics. For example, the interface Cascadia events are associated with almost fixed values of M and R, as they can be regarded as a characteristic event that occurs at a specific plate boundary; consequently, the value of ε increases significantly with the non-exceedance probability level to attain a higher seismic intensity level. The results shown in Figure 1 and Table 1 suggest that to define physically meaningful expected ground motions, one should utilize appropriate scenarios for each earthquake type. Table 1. Seismic deaggregation results for Vancouver Non-exceedance Percentage of contribution: Crustal events probability [Crustal, Interface, Inslab] [M, R, ε ] [46.0, 9.7, 44.3] [6.16, 33.7, 1.39] [41.2, 9.9, 48.9] [6.26, 28.3, 1.55] [31.9, 9.7, 58.4] [6.36, 22.4, 1.75] [3, 8.6, 61.4] [6.44, 18.2, 1.87] [24.0, 1, 66.0] [6.44, 16.9, 2.13] Interface events [M, R, ε ] [8.55, 144.4, 1.08] [8.57, 144.5, 1.42] [8.59, 143.9, 1.86] [8.62, 144.9, 2.14] [8.61, 143.9, 2.34] Inslab events [M, R, ε ] [6.72, 71.4, 1.15] [6.79, 67.3, 1.31] [6.86, 63.2, 1.56] [6.89, 60.7, 1.72] [6.93, 55.9, 1.82] Figure 1. PSHA results for Vancouver: a) uniform hazard spectra and b) seismic hazard deaggregation at the annual non-exceedance probability of Figure 2. Response spectra of 50 ground motion records selected using the CMS-based procedures at the annual non-exceedance probability of : a) CMS-Event-based approach and b) CMS-All-based approach 3.2. Record Selection and Conditional Mean Spectrum One of the key issues related to IDA is the impact of using scaled ground motion records on the nonlinear structural response. The scaling of records is needed to reach high seismic intensity levels, as available ground motion records that match various record characteristics of target scenarios are very limited. Luco and Bazzurro (2007) showed that the use of an excessive scaling factor could

4 induce significant bias in the estimated nonlinear structural response, and suggested that the similarity of the response spectral shape of a record to the target response spectrum is an important criterion in selecting records. Moreover, Baker (2010) proposed that in case record selection is implemented with reference to UHS, the use of the CMS is adequate to represent a target response spectrum. In this study, the CMS-based record selection procedure is considered; the adopted seismic intensity measure is the spectral acceleration at the vibration period T n with T n = 0.3 (sec). The procedure begins by specifying a target spectral acceleration and representative scenario(s) based on UHS and [ M, R, ε ]. By adopting an adequate GMPE and a suitable inter-period correlation model of spectra accelerations at different vibration periods, one can construct the CMS (see Baker (2010) for details). A complicated aspect in constructing a CMS for south-western BC is that three earthquake types, having distinctly different characteristics, contribute to overall seismic hazard significantly. Therefore, three CMS must be constructed for record selection. To highlight this point, two sets of CMS are considered in this study: 1) CMS-Crustal, CMS-Interface, and CMS-Inslab (or CMS-Event-based approach) are based on the weighted average of the CMS that are computed by using applicable GMPEs and the corresponding scenarios for each earthquake type, in proportion to relative influences of the scenarios, whereas 2) CMS-All is the weighted average of CMS-Crustal, CMS-Interface, and CMS-Inslab by considering relative influences of the individual earthquake types. The CMS at the annual non-exceedance probability of based on the two approaches are illustrated in Figure 2. All CMS approximately equal the ordinate of UHS at T n = 0.3 (sec). We observe that CMS-Interface records have distinctly different characteristics, in particular a much richer spectral content in the long vibration period range, in comparison with CMS-Crustal and CMS-Inslab records. Thus, for the purpose of selecting a representative set of ground motion records that are consistent with the expected ground motion characteristics, the use of three CMS for different earthquake types is recommended. The final step of the CMS-based record selection is to identify a set of ground motion records whose response spectra match the target CMS over a range of vibration periods in a least-squares sense. It is important to select a suitable vibration period range over which response spectra are matched, because it is related to the extent of structural nonlinearity under the considered earthquake scenario. Based on the CMS-Event-based and CMS-All-based procedures, 50 ground motion records are selected considering a vibration period range from 0.1 to 1.0 sec, and the average response spectra of the selected 50 ground motion records for the two approaches are shown in Figure 2. The CMS-Event-based procedure reflects spectral characteristics of different earthquake scenarios commensurate with their relative contributions based on deaggregation results, whereas the CMS-All-based procedure does not distinguish different spectral characteristics for different earthquake types. Consequently, variability of elastic response spectra for the former is greater than that for the latter. It is argued that greater variability for the former is desirable for assessing the seismic performance of a structure, accounting for realistic uncertainty, because a tight match to a CMS leads to the underestimation of uncertainty of the nonlinear structural response (Baker, 2010) Preliminary Record Selection Ground motion records that are used for IDA are selected from two extensive databases, the PEER-NGA database (see and the K-NET/KiK-NET database (see Goda and Atkinson (2009a)). We carry out record selection in two steps. The intention of the first-step record selection is to establish a pool of ground motion records that may possess some important characteristics of damaging ground motions, whereas more detailed second-step record selection is discussed in Section 4. For both PEER-NGA and K-NET/KiK-NET databases, the following criteria are applied: 1) two horizontal components are recorded on the ground surface (for the PEER-NGA database, free-field observations in the one-story building of light construction are also considered); 2) magnitude-distance cut-off limits considered by Goda and Atkinson (2009b) are applied with the minimum moment magnitude equal to 6.0; 3) V s30 is between 100 and 360 m/sec (site class D or E); and 4) geometric means of peak ground acceleration (PGA) and peak ground velocity (PGV) of two horizontal components are greater than 0.1 g and 10 cm/sec, respectively. The

5 application of the first-step criteria leads to 368 records from 51 events: 179 records from 28 events for the PEER-NGA database, and 189 records from 23 events for the K-NET/KiK-NET database. To prepare a dataset of the maximum inter-story drift ratio of the UBC-SAWS models (Houses 1-4) for different seismic intensity levels, IDA is carried out using the preliminary record set. In IDA, the seismic intensity level is varied from 0.1 to 8.0 g (109 levels). For each record, two analyses are conducted by alternating two horizontal components along the two structural axes. In scaling a record, the scaling factor is calculated as the target seismic intensity level divided by the geometric mean of spectral accelerations due to two horizontal components, and the same scaling factor is applied to both horizontal components. In total, 336,592 runs of nonlinear dynamic analysis are implemented. 4. SEISMIC VULNERABILITY EVALUATION We evaluate the seismic vulnerability of typical wood-frame houses in south-western BC by developing a probabilistic relationship between the seismic intensity measure (IM), spectral acceleration at 0.3 sec, and the seismic demand measure (DM), maximum inter-story drift ratio at the first story level. In Section 4.1, we investigate the impact of using different record selection procedures on the assessment, focusing on House 2. In Section 4.2, we investigate the impact of considering different shear-wall types (Houses 1-4) on the seismic vulnerability. More specifically, to facilitate the comparison of IDA results for different cases, we set up a base case: a structure is subjected to 50 ground motion records (i.e., 100 runs), and record selection is implemented using the CMS-Event-based procedure by considering the annual non-exceedance probability of. The IDA results for different cases are discussed by comparing three IM-DM curves that correspond to different fractile values (0.16-, 0.50-, and 0.84-fractile) Impact of Record Selection Criteria on Nonlinear Structural Response House 2 First, we investigate the impact of the vibration period range that is used for the CMS-Event-based procedure. For the base case, the lower and upper bounds are set to 0.1 and 1.0 sec, respectively. To consider narrower and wider ranges, two additional cases are investigated: 0.1 to 0.6 sec and 0.1 to 1.5 sec. Results for the three cases are shown in Figure 3; 0.16-, 0.50-, and 0.84-fractile IM-DM curves are compared in Figure 3a, whereas average response spectra of the selected records are compared in Figure 3b. Inspection of Figure 3 indicates that the use of the longer upper vibration period leads to less nonlinear structural response. This can be explained by pointing out that significant nonlinearity of the structural model leads to an elongated vibration period and is thus affected by spectral content in the long vibration period range. The results shown in Figure 3 highlight the importance of the vibration period range for the CMS-Event-based procedure. We adopt the upper vibration period equal to 1.0 sec as the base case, although this value is selected somewhat arbitrarily. We note that the secant vibration period corresponding to the maximum inelastic ductility demand μ is given by T n [μ/(1+α(μ-1))] 0.5, where α is the ratio of post-yield stiffness to initial stiffness; a substitution of T n = 0.3 to 0.4 (sec), μ = 10, and α = 5 into the above equation leads to the secant vibration period equal to about 0.8 to 1.0 sec. Next, we investigate the impact of using different record selection procedures: CMS-All-based procedure, MR-based procedure, and ε-based procedure. The difference between the CMS-Event-based procedure and the CMS-All-based procedure was discussed in Section 3.2 (see Figure 2). The MR-based procedure selects a record that has similar characteristics in terms of M and R to those of target scenario earthquakes, whereas the ε-based procedure selects a record that has a ε value close to that of target scenario earthquakes (Baker and Cornell, 2006). Both MR-based and ε-based procedures are implemented by taking earthquake type into account. To show the impact of using different record selection procedures, results for the four procedures are compared in Figure 4. We observe that the median curves for the CMS-Event-based procedure and for the CMS-All-based procedure are similar, whereas variability of the IM-DM relationship for the former is greater than that

6 for the latter. At the chosen probability level, nonlinear response potentials estimated by the MR-based and ε-based procedures are greater and less, respectively, than that by the CMS-Event-based procedure; the differences can be explained by noting different average response spectra of the selected record sets (Figure 4b). Figure 3. Impact of the vibration period range for the CMS-Event-based procedure: a) 0.16-, 0.50-, and 0.84-fractile curves and b) average response spectra Figure 4. Comparison of the CMS-Event-based, CMS-All-based, MR-based, and ε-based procedures: a) 0.16-, 0.50-, and 0.84-fractile curves and b) average response spectra Finally, we examine the impact of considering different annual non-exceedance probability levels on the nonlinear response potential. For this, three IM-DM curves for the CMS-Event-based, MR-based, and ε-based procedures are shown in Figures 5a, 5b, and 5c, respectively, for the annual non-exceedance probabilities of, 0.996, and In addition, average response spectra of the selected records for the three procedures are presented in Figure 5d. We observe that: (i) IM-DM curves for the CMS-Event-based procedure are not sensitive to the annual non-exceedance probability level; (ii) IM-DM curves for the MR-based procedure are slightly dependent on the annual non-exceedance probability level; and (iii) IM-DM curves for the ε-based procedure are significantly affected by the annual non-exceedance probability level. These observations are consistent with average response spectra (shapes) at different annual non-exceedance probability levels (Figure 5d). The results discussed above highlight the impact of different record selection procedures on the nonlinear structural response; the effects can be predicted by examining average response spectra (shapes) of the record sets. This is in agreement with past studies (Luco and Bazzurro, 2007; PEER GMSM Working Group, 2009). We recognize that the CMS-based procedure is not necessarily the

7 only suitable method. Nevertheless, it has some foundation based on statistical characteristics of response spectra in specifying target scenario earthquakes and is advantageous when the target seismic intensity level is specified in terms of UHS (Baker, 2010). Figure 5. Comparison of 0.16-, 0.50-, and 0.84-fractile curves at different annual non-exceedance probability levels: a) CMS-Event-based procedure, b) MR-based procedure, c) ε-based procedure, and d) comparison of average response spectra at different annual non-exceedance probability levels Table 2. Probability of reaching the maximum inter-story drift ratio of 1, 3, 5, or 0.10 at the annual non-exceedance probabilities of and Probability of reaching a target inter-story drift ratio Shear-wall Non-exceedance type probability DM = 1 DM = 3 DM = 5 DM = 0.10 House House House House Impact of Shear-wall Types We investigate the impact of different shear-wall types (i.e., Houses 1-4) on the nonlinear response potential. To examine the impact of different shear-wall types quantitatively, the probability of reaching the maximum inter-story drift ratio equal to 1, 3, 5, or 0.10 subjected to ground motions corresponding to the annual non-exceedance probabilities of and is summarized

8 in Table 2. The maximum inter-story drift ratios of 1 and 3 may be considered as a performance limit corresponding to immediate occupancy and collapse prevention, respectively, while the maximum inter-story drift ratios of 5 and 0.10 may be considered as an ultimate capacity limit corresponding to major damage and collapse. The results shown in Table 2 indicate that at the annual non-exceedance probability of : 1) structural damage to House 1 will be very limited; 2) minor structural damage may occur to Houses 2 and 3, but major damage and collapse are unlikely to occur; and 3) minor damage is almost certain, and major damage and collapse may be concerned for House CONCLUSIONS The seismic vulnerability of typical wood-frame houses was evaluated quantitatively by employing various methods/techniques (UHS, IDA, and CMS) and by accounting for complex seismic hazard contributions from three earthquake types. We adopted the CMS-Event-based method for record selection, and investigated the impacts of using different record selection criteria and of using different shear-wall types on the seismic vulnerability evaluation. The IDA results highlight the importance of response spectral shapes in selecting and scaling ground motion records. In particular, diversity of target CMS reflecting different types of seismic events and record selection criteria (CMS-Event-based method versus MR-based method versus ε-based method) have important impact on the assessment. At a seismic excitation level specified in the current building codes, House 1 is expected to experience very limited structural damage; Houses 2 and 3 may suffer from minor damage but no major damage/collapse; whereas House 4 may be subjected to major damage/collapse. AKCNOWLEDGEMENT The financial support and the postdoctoral fellowship award provided for the first author by the Natural Sciences and Engineering Research Council of Canada are gratefully acknowledged. Japanese ground motion data were obtained from the K-NET and KiK-NET databases at and California ground motion data were obtained from the PEER-NGA database at The financial support by the University of Bristol is appreciated. REFERENCES Baker, J.W. and Cornell, C.A. (2006). Spectral shape, epsilon and record selection. Earthquake Engineering and Structural Dynamics 35:9, Baker, J.W. (2010). The conditional mean spectrum: a tool for ground motion selection. Journal of Structural Engineering 136 (in press). Folz, B. and Filiatrault, A. (2004). Seismic analysis of woodframe structures I: model formulation. Journal of Structural Engineering 130:9, Goda, K. and Atkinson, G.M. (2009a). Probabilistic characterization of spatially-correlated response spectra for earthquakes in Japan. Bulletin of the Seismological Society of America 99:5, Goda, K. and Atkinson, G.M. (2009b). Seismic demand estimation for inelastic SDOF systems for earthquakes in Japan. Bulletin of the Seismological Society of America 99:6, Goda, K., Hong, H.P. and Atkinson, G.M. (2010). Impact of using updated seismic information on seismic hazard in western Canada. Canadian Journal of Civil Engineering 37 (in press). Luco, N. and Bazzurro, P. (2007). Does amplitude scaling of ground motion records result in biased nonlinear structural drift responses? Earthquake Engineering and Structural Dynamics 36:13, PEER Ground Motion Selection and Modification (GMSM) Working Group (2009). Evaluation of Ground Motion Selection and Modification Methods: Predicting Median Interstory Drift Response of Buildings. PEER Report 2009/01, University of California at Berkeley, Berkeley, CA. Vamvatsikos, D. and Cornell, C.A. (2004). Applied incremental dynamic analysis. Earthquake Spectra 20:2, Ventura, C.E., Taylor, G., Prion, H., Kharrazi, M. and Pryor, S. (2002). Full-scale Shake Table Studies of Woodframe Residential Construction. 7 th U.S. Conference on Earthquake Engineering, Boston, MA. White, T.W. and Ventura, C.E. (2006). Seismic Performance of Wood-frame Residential Construction in British Columbia. Earthquake Engineering Research Facility Report No , University of British Columbia, Vancouver, Canada.