Variability of seismic demands according to different sets of earthquake ground motions

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1 See discussions, stats, and author profiles for this publication at: Variability of seismic demands according to different sets of earthquake ground motions Article in The Structural Design of Tall and Special Buildings September CITATIONS 3 READS 12 3 authors, including: Sang Whan Han Hanyang University 16 PUBLICATIONS 539 CITATIONS SEE PROFILE All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. Available from: Sang Whan Han Retrieved on: 13 September 16

2 THE STRUCTURAL DESIGN OF TALL AND SPECIAL BUILDINGS Struct. Design Tall Spec. Build. 16, (7) Published online in Wiley Interscience ( DOI:1.12/tal.318 VARIABILITY OF SEISMIC DEMANDS ACCORDING TO DIFFERENT SETS OF EARTHQUAKE GROUND MOTIONS SANG WHAN HAN*, EUNG SOO KIM AND SOO MIN HWANG Department of Architectural Engineering, Hanyang University, Seoul, Korea SUMMARY It is a challenging task to predict seismic demands for earthquake resistant design, particularly for tall buildings. In current seismic design provisions, seismic demands are expressed as a design base shear of which the key components are linear elastic design response spectra, force reduction factor ( R factor ), and building weight. For tall buildings, response spectrum analysis or response history analysis is recommended in current design provisions. In recent years, new methods for predicting seismic demands have been developed, such as the capacity spectrum method (CSM) and displacement coefficient method. This study investigates the effect of different earthquake ground motion (EQGM) sets on seismic demands. Key components of the base shear and performance points in the CSM are considered as the seismic demands to be tested. For this purpose three EQGM sets are collected independently at rock sites. This study found that seismic demands can vary significantly according to different EQGM sets even though those sets were obtained at sites with similar soil conditions. This study also attempts to provide a criterion for reducing the variability in seismic demands according to different EQGM sets. Copyright 7 John Wiley & Sons, Ltd. 1. INTRODUCTION It is very difficult to predict future seismic demands because they are random in nature. Many research studies have been conducted to predict the seismic demands on structures based on past seismological and geological data. Seismic active regions have relatively more historical information than low and moderate seismic regions. Since there are few reliable data in low and moderate seismic regions, seismic design procedures as well as earthquake ground motion records have been adopted from seismic active regions. Particularly when a time history analysis or response spectrum analysis is performed for tall buildings, earthquake ground motion (EQGM) data collected in the western USA or Japan have been commonly used. This study attempts to investigate the variability of seismic demands according to different EQGM sets. As a seismic demand, this study considers performance points in the capacity spectrum method (CSM) and key components of base shear such as linear elastic response spectra (LERS), R factor, and inelastic response spectra (IRS). Three different EQGM sets are considered that were independently collected at rock sites. Furthermore, this study attempts to reduce the variability in seismic demands according to different EQGM sets. 2. SELECTION OF EQGM SETS This study adopts three EQGM sets independently collected at rock sites (Hwang, 2). The three independent sets are called, M and R, respectively. contains 28 strong motion data at rock sites in the western part of the USA that has a peak ground acceleration (PGA) greater than 5 g. *Correspondence to: Sang Whan Han, Department of Architectural Engineering, Hanyang University, Seoul , Korea. swhan@hanyang.ac.kr Copyright 7 John Wiley & Sons, Ltd.

3 322 S. W. HAN, E. S. KIM AND S. M. HWANG Table 1(a). EQGMs for Researcher/ Date Magnitude Soil PGA PGV set name Station name Earthquake (M/D/Y) (Ms) type (g) (cm/s) Federal Building Helena 1/31/35 6 Rock Taft Kern County 7/21/ Rock Golden Gate Park San 3/22/ Rock 83 4 Francisco 15 5 Wrightwood, CA Lytle Creek 9/12/7 5 4 Rock Temblor Parkfield 6/27/ Rock SCE Power Plant, San Borrego Mtn 4/8/ Rock 41 4 Onofre 46 6 Devils Canyon, San Lytle Creek 9/12/7 5 4 Rock Bernardino Cal. Tech. Seism. Lab San Fernando 2/9/ Rock Santa Felicia Dam San Fernando 2/9/ Rock Lake Hughes Sta. 4 San Fernando 2/9/ Rock Pacoima Dam San Fernando 2/9/ Rock Santa Anita Dam San Fernando 2/9/ Rock Lake Hughes Sta. 12 San Fernando 2/9/ Rock Lankershim Blvd San Fernando 2/9/ Rock Griffith Park Observatory San Fernando 2/9/ Rock Thirty-seven free field EQGMs in California are included in Set-M. Set-R has 18 EQGMs obtained from 1985 Chilean earthquake (Ms = 7 8). In general, rock site is defined as the stiffest soil site according to the classification of current seismic provisions such as rock, stiff soil, cohesionless soil and soft soil. It is noted that no clear definition is provided for rock site in the current seismic design provisions (UBC, 1997; IBC, ). In Korea, designers have often used those three sets to conduct response history analysis for estimating seismic demand for tall buildings located at a rock site without considering the variability according to different sets. Table 1(a c) contains 28, 37 and 18 EQGM records for, Set-M, and Set-R, respectively. 3. EFFECTS OF DIFERENT EQCM SETS ON BASE SHEAR In most seismic design provisions (NEHRP, 1997; UBC, 1997; IBC, ), base shear is defined as the following form: V = CW R (1)

4 VARIABILITY OF SEISMIC DEMANDS 323 Table 1(b). EQGMs for Set-R Researcher/set Magnitude PGA (g) PGV name Station name Earthquake Date (M/D/Y) (Ms) Soil type (cm/s) Set-R Papudo Chile 3/3/ Rock Los Vilos Chile 3/3/ Rock Zapallar Chile 3/3/ Rock Valparaiso Chile 3/3/ Rock (UTFSM) Valparaiso Chile 3/3/85 7 Rock (UTFSM) Quintay Chile 3/3/ Rock Quintay Chile 9/4/ Rock Rapel Chile 3/3/ Rock Rapel Chile 9/4/ Rock Pichilemu Chile 3/3/ Rock where V = the base shear, C = the linear elastic design response spectrum (LEDRS), R = the force reduction factor and W = the weight of a structure. In Equation (1), C/R is the inelastic design response spectrum (IDRS), which allows a structure to behave in an inelastic range during a design-level EQGM. Since each lateral force-resisting system may provide a different ductility capacity and overstrength, a different R factor has been assigned to each system. The relationship among LEDRS, IDRS and R factor can be found in ATC-19 (1998). This study evaluates the effect of different EQGM sets on major components of base shear such as linear elastic response spectra (LERS), R factor and inelastic response spectra (IRS). 3.1 Effect of different EQGM record sets on LERS LERS are a set of maximum acceleration response of a single degree of freedom system with respect to different frequencies and damping ratios for a given EQGM. This study calculates LERS for a system with a damping ratio of 5%. In each EQGM set, LERS is calculated for all records and is normalized by its PGA of 15 g, which is a design earthquake intensity used in Korean. The mean normalized LERS of each EQGM set is then calculated. This study compares mean normalized LERS obtained from three different EQGM sets (, Set-M, and Set-R). Note that all records of these three sets were recorded at rock sites. Figure 1(a) shows the mean normalized LERS obtained from three different EQGM sets. Within a period of 5 s, the LERS of Set-R is slightly larger than that of. At a period range of 5 3 s, Set-M has a larger value of LERS compared with the LERS of the other two sets. This indicates that normalized elastic demand can vary according to different EQGM sets even if they were obtained at sites with similar soil conditions. At each period, the deviation of mean normalized LERS of Set-R and M from that of is calculated using the following equation:

5 324 S. W. HAN, E. S. KIM AND S. M. HWANG Table 1(c). EQGMs for Set-M Researcher/ Date Magnitude PGA PGV set name Station name Earthquake (M/D/Y) (Ms) Soil type (g) (cm/s) Set-M Golden Gate San Francisco 3/22/ (ML) Siliceous 8 4 Park sandstone 11 4 Cholame Parkfield 6/27/ (ML) Rock Shandon No Castaic Old San Fernando 2/9/ (ML) Sandstone Ridge Road Llolleo Central Chile 3/3/ Sandstone and volcanic rock Valparaiso Central Chile 3/3/ Volcanic rock La Union Michiacan 9/19/ Metavolcanic rock La Villita Michiacan 9/19/ Gabbro rock Zihuatanejo Michiacan 9/19/ Tunalite rock Natl Geogr. San Salvador 1/1/ Balsamo Institute formation Inst. Urban San Salvador 1/1/ Fluviate Construction pumice rock pumice Geotech. San Salvador 1/1/ Fluviate 42 6 Invest. Center pumice rock Mt Wilson Whittler- 1/1/ Quartz diorite 19 5 Caltech Narrows Seismic station Mt Wilson Whittler- 1/1/ Quartz diorite 13 3 Caltech Narrows Seismic station Corralitos Loma Prieta 1/17/ Landslide Eureka deposits Canyon Road Santa Cruz Loma Prieta 1/17/ Limestone UCSC San Francisco, Loma Prieta 1/17/ Franciscan Cliff House sandstone 7 11 San Francisco, Loma Prieta 1/17/ Franciscan 5 9 Pacific Heights sandstone 6 13 San Francisco, Loma Prieta 1/17/ Serpentine 32 Presidio 1 13 San Francisco, Loma Prieta 1/17/ Franciscan 9 1 Rincon Hill sandstone 8 7 Yerba Buena Loma Prieta 1/17/ Franciscan 6 14 Island sandstone 3 4 x: a EQGM having a PGV less than a given PGV.

6 Acceleration (g) VARIABILITY OF SEISMIC DEMANDS 325 Set-M Set-R UBC 97 (a) (b) Figure 1. Mean normalized LERS. (a) Mean normalized LERS of different EQGM sets. (b) Deviation of mean normalized LERS of Set-M and R from that of XSet-i - X d X - i = X 1(%) (2) where d X-i = the deviation of mean response value of each set from that of, X Set-i = the mean response value of Set-i (i can be either R or M), and X = the mean response value of. Response values are mean normalized LERS here. Figure 1(b) shows the deviation of mean normalized LERS of Set-R and M from that of. According to this figure, the difference between Set-M and becomes larger in a period region greater than 5 s. The maximum deviation reaches almost 1%. In contrast, the difference is small in acceleration-sensitive regions ( 1 5 s). The difference between Set-R and is not large compared with the difference between Set-M and. The maximum deviation of mean normalized LERS between Set-R and S is about 38%. Comparing the difference of mean normalized LERS between and R, and and Set-M, the general shape and maximum values are quite different, as shown in Figure 1(b). This may be possible since earthquake records are calibrated by PGA rather than peak ground velocity (PGV) or peak ground displacement (PGD). In the period range longer than 5 s, the response spectrum may be more sensitive to PGV or PGD. However, it is noted that PGA-based calibration of EQGMs are commonly used in design practice. 3.2 Reducing variability in mean normalized LERS In order to reduce the variability in mean normalized LERS according to different EQGM sets, this study attempts to refine the EQGM sets by removing some EQGMs having PGV > cm/s from EQGM sets. After removing EQGMs from EQGM sets, median LERS and the difference in LERS between two sets are recalculated. This criterion removes 3,, and 16 EQGMs from, Set-R, and Set-M, respectively. Using this criterion, maximum difference in mean LERS between Set-M and Set- S is reduced to 5% (see Figure 2). From this test, it is found that the PGV-based criterion can reduce the variability in response spectrum according to different EQGM sets. Thus, the PGV-based criterion can be used for classifying EQGMs with soil conditions.

7 326 S. W. HAN, E. S. KIM AND S. M. HWANG Acceleration (g) (a) Set-M Set-R (b) Figure 2. Mean normalized LERS after removing EQGMs having PGV > cm/s. (a) Mean LERS of different EQGM Sets. (b) Deviation of mean LERS between EQTM sets 3.3 Effect of different EQGM sets on R factor The force reduction factor (R factor) was first introduced in ATC 3-6 (1978). This is one of the major components of base shear. In ATC 19 and 34 (1995), R factor is broken down into three components as follows: R= Rm RS RR (3) where R m = the ductility factor, R S = the strength factor, and R R = the redundancy factor. In this study, only the ductility factor (R m ) is considered. This factor is defined as the ratio of LERS (elastic strength demand) to the IRS (inelastic strength demand) for a target ductility ratio (m = m t ) subject to a given EQGM. The R m factor can be represented by the following equation: R m Fy ( m = 1) = F ( m = m ) y t (4) where F y (m = 1) = the elastic strength demand (e.g., LERS) and F y (m = m t ) = the inelastic demand to attain a target ductility ratio (m t ) (e.g., IRS). The average R m factors of, M, and R for a given target ductility (m t = 4, 6) are shown in Figure 3. Figure 4(a) shows the deviation of mean R m factor of Set-M and from that of, which is calculated using Equation (2), where X = R m. As shown in Figure 4(a), the deviation of mean R m factor between Set-M and S, and Set-R and S is smaller than that of LERS. From these figures it is seen that deviation of the mean R m factor does not vary with respect to a target ductility ratio. The maximum deviation of the mean R m factor between and R for a ductility ratio of 4 and 6 is 68% and 8%, respectively, which is larger than those between and M. In a period range longer than 2 s the deviation is less than 3% with respect to target ductility ratios. Figure 4(b) also shows the mean R m factor and difference of mean R m factor for a target ductility ratio of 4 between and Set-R, and and Set-M after removing EQGMs that exceed a PGV of from EQGM sets. No discernible change can be found in Figure 4 except that the difference between and Set-R is reduced in short period range.

8 R (a) VARIABILITY OF SEISMIC DEMANDS 327 Set-M Set-R Ru Figure 3. Mean R m factor: (a) m t = 4; (b) m t = 6 (b) Set-M Set-R Difference(%) µ = 4 µ = 6 t Set-Rl vs Difference(%) (a) t mt = 4 mt = 6 (b) Figure 4. Difference of mean R m factor for m t = 4: (a) before removing EQGMs; (b) after removing EQGMs having a PGV > cm/s

9 328 S. W. HAN, E. S. KIM AND S. M. HWANG Accelration (g) Set-M Set-R Accelration (g) Set-M Set-R. (a). (b) Figure 5. Mean IRS: (a) m t = 4; (b) m t = (a) Period(sec) (b) Figure 6. Difference between of mean IRS: (a) m t = 4; (b) m t = Effect of different EQGM sets on IRS Inelastic response spectra (IRS) for a given target ductility ratio, m t, can be obtained by dividing LERS by the R m factor: IRS LERS = Rm (5) Figure 5 shows mean IRS of, Set-M, and Set-R for a target ductility ratio of 4 and 6. It is noted that all EQGMs are calibrated to have a PGA of 15 g. The difference of mean IRS between and M, and and R is shown in Figure 6. As shown in Figure 6, there is a large difference in a period range greater than 5 s. Maximum deviation reaches 1%. For Set-R and S deviation is relatively small. Maximum deviation is less than 3%. From Figure 6 it is observed that the difference is not sensitive to target ductility ratios, which is a similar observation with mean R m factors. As done for LERS and R factor, this study calculates mean IRS for each EQGM set after removing EQGMs having PGV >. Figure 7 shows the difference in mean IRS between and Set-R,

10 VARIABILITY OF SEISMIC DEMANDS Figure 7. Deviation of mean IRS of Set-M and R from that of for m = 4 (after removing EQGMs according to PGV > cm/s) Table 2. Properties of SDOF systems System T n (s) f y w u y (cm) and and Set-M, for a target ductility ratio of 4. As seen in this figure, the difference in mean IRS decreases significantly between and Set-M. 4. EFFECT OF DIFFERENT EQGM SETS ON PERFORMANCE POINTS The capacity spectrum method (CSM) was developed by Mahaney and Freeman (1993) and was adopted in ATC 4 (1996). This method adopts the acceleration displacement response spectrum (ADRS) format, which uses spectral acceleration and displacement (S a and S d ). In the CSM, a seismic demand is determined by calculating a performance point that is an intersecting point between the capacity and demand curve in the S a and S d domain. The capacity curve can be obtained by nonlinear pushover analysis. For the demand curve real EQGMs or LEDRS can be used. This study used four different SDOF systems. The properties of each system are shown in Table 2. It is assumed that all systems behave in a perfectly elasto-plastic manner. This study adopts the procedure for calculating a performance point using the R m relationship rather than equivalent damping (Hwang, 2). All EQGM records in, Set-M, and Set-R are calibrated to make their PGA 3, 45, and 6 g. This study calculates mean performance points of each system for each set with calibrated EQGMs. Tables 3 and 4 show average performance points of each system to each set of EQGMs. These tables also show the deviation of the mean performance point of each EQGM set from that of.

11 33 S. W. HAN, E. S. KIM AND S. M. HWANG (a) System 1 Table 3. Comparison of performance points PGA = 3 g PGA = 45 g PGA = 6 g (b) System 2 PGA = 3 g PGA = 45 g PGA = 6 g (c) System 3 PGA = 3 g PGA = 45 g PGA = 6 g (d) System 4 PGA = 3 g PGA = 45 g PGA = 6 g As shown in Table 3, there is large difference in mean performance points of different EQGM sets. The largest difference is 144%, which results from system 4 for Set-M and S with EQGMs calibrated to have a PGA of 6 g. As done for other seismic demands, PGV-based criteria (PGV > ) are applied to reduce the variability in mean performance points according to different EQGM sets. After removing EQGMs that exceed a PGV of from the sets, mean performance points of the systems are recalculated for each set of EQGMs. In system 4, the largest difference was reduced from 144% to 38% (see Table 4d). 5. CONCLUSIONS AND RECOMMENDATIONS This study investigates the effect of different EQGM sets obtained at rock sites on key components of base shear (LERS, ductility factor R m, and IRS) and performance points in the CSM. Furthermore, this study proposes PGV-based criteria to reduce the variability in seismic demand according to EQGM sets. The following conclusions are drawn: (1) Special care must be made to adopt EQGMs or EQGM sets obtained from other sites when evaluating seismic demands on structures particularly located in low to moderate seismic zones, even though those EQGMs were recorded on sites with similar soil conditions. (2) Comparing mean normalized LERS of three different EQGM sets, there is a large difference (maximum = 1%), particularly in a period range greater than 5 s. Mean LERS varies according to different EQGM sets even though they were obtained at sites with similar soil conditions.

12 (a) System 1 VARIABILITY OF SEISMIC DEMANDS 331 Table 4. Comparison of performance points (after removing EQGMs having PGV > cm/s) PGA = 3 g PGA = 45 g PGA = 6 g (b) System 2 PGA = 3 g PGA = 45 g PGA = 6 g (c) System 3 PGA = 3 g PGA = 45 g PGA = 6 g (d) System 4 PGA = 3 g PGA = 45 g PGA = 6 g The variability in LERS between the sets are significantly reduced by removing EQGMs having PGV > cm/s from the sets. (3) Mean R m factor varies with different EQGM sets. However, the difference in mean R m factor between two EQGM sets is not significant as that of mean LERS. Also, the difference does not change according to different target ductility ratios. Furthermore, PGV-based criterion does not reduce the difference except for the difference in the short period range. (4) Mean IRS varies with different EQGM sets as well. This is more prominent in Set-M and, particularly in a period range greater than 5 s. The difference is significantly reduced by removing EQGMs having PGV >. It is more prominent that the difference is much reduced by removing EQGMs having PGV > 1 cm/s from the sets. (5) A larger difference is observed in the mean performance point according to different EQGM sets. The maximum difference is 144%, which results from system 4 under EQGMs of and Set- M. By removing EQGMs that exceed a PGV of and 1 cm/s from EQGM sets, the maximum difference is reduced to 38% and 29%, respectively. (6) According to the above investigations, seismic demand can vary according to EQGM sets even though all EQGMs were recorded at sites having similar soil conditions. The difference is more than expected, particularly in the case of performance points. However, the difference can be reduced by removing EQGMs from the sets using PGV-based criteria (PGV > and 1 cm/s). Thus, PGV-based criteria can be used to classify EQGMs with soil conditions. (7) For constructing the response spectrum used in response spectrum analysis or adopting EQGMs used in response history analysis for estimating the seismic demand for tall buildings located in a moderate seismic zone, the variability of different EQGM sets should be considered.

13 332 S. W. HAN, E. S. KIM AND S. M. HWANG ACKNOWLEDGEMENT This study is supported by the ERC program of MOST / KOSEF (R ). It is greatly appreciated. REFERENCES ATC Structural Response Modification Factors. Applied Technology Council: Redwood City, CA. ATC A Critical Review of Current Approaches to Earthquake Resistant Design. Applied Technology Council: Redwood City, CA. ATC Seismic Evaluation and Retrofit of Concrete Buildings. Applied Technology Council: Redwood City, CA. FEMA 32, NEHRP Recommended Provisions for Seismic Regulations for New Building. Building Seismic Safety Council: Washington, DC. Hwang SM. 2. Seismic demand for moderate seismic regions. Thesis, Hanyang University. International Code Council. 3. International Building Code. Falls Church, VA. International Conference of Building Officials Uniform Building Code: Whittier, CA. Mahaney JA, Paret TF, Kehoe BE, Freeman SA The Capacity Spectrum Method for Evaluating Structural Response During the Loma Prieta Earthquake. National Earthquake Conference, Memphis, TN.