ANALYTIC STUDIES OF THE MAXIMUM DISPLACEMENTS OF SEISMIC ISOLATION UNDER MANY OBSERVED STRONG EARTHQUAKES Abstract KIMOTO Koichiro SAI Structural Design Co., Ltd. FUKUOKA, Japan Seismic response analysis of the seismically isolated structures which have various characteristics under many observed strong ground motions are examined in order to estimate the maximum displacements of the isolation. As results, with case of Tf=4. second (post yield period) and μ=.4 (damper ratio) that chosen frequently in design in Japan, more than 5cm of maximum displacements of isolation are estimated by 8 time histories of 94. Dominant period T1 which corresponding with deep soil structure and maximum displacements have some correlation. The correlations between damper ratio μ and displacement are looked over by plotting μ- displacements curves for every earthquake and every Tf. Various tendencies are found. Some have peak or some have dip on μ- displacements curves, and some do not change displacements so much even if μ changes, though we are apt to think intuitively generally that when μ increases, maximum displacements decreases. 1. Introduction After the Great Hanshin Earthquake brought the serious damages around Kobe of January 17, 95, the planned observation networks of the strong earthquakes have been equipped eagerly in Japan from 96. Many strong ground motions that give the building damage were observed. In those, some of them are felt uneasy with regard to affecting the withstanding stress of the seismically isolated structures 1) 2). In this report, seismic response analysis of the seismically isolated structures which have various characteristics under many observed strong ground motions are examined in order to estimate the maximum displacements of the isolation. There are existing studies to predict the maximum displacement of isolation by indexes such as PGA,PGV,PGD, spectrum intensity of seismic ground motion itself 3). The peculiarity of this examination is to suppose maximum displacements of isolation with the information of the hypo-center's conditions(magnitude, distance) or soil conditions (deep and shallow) mainly, if possible, without using observed time histories or spectrum. In particular, it is useful that the conditions which give excessive displacements of isolation is found. The following words are used in this paper. Menshin means Seismically isolated, it is called in Japanese. JMA means Japan Meteorological Agency. PGV means Peak Ground Velocity. 2. K-NET and J-SHIS In this study, data of K-NET 4) and J-SHIS 5) are used. The outline of them will be introduced. Both K-NET and J-SHIS are operated by Natl. Res. Inst. for Earth Sci. and Disaster Prevention (NIED). K-NET covers the Japanese whole land approximately every 2km with an earthquake observation network started from 96, and has about 2, observation points by the present. Observed strong motion data are opened within one day by Web Site, and anyone can search favorite data by information such as epicenter, Richter scale magnitude, seismic intensity scale, PGA, and so. K-NET is used for academic study, structural design, and recently is used as a part of the JMA's Earthquake Early Warnings system. And the ground survey results of the shallow ground below the stations are also opened by Web Site.
J-SHIS is Japan Seismic Hazard Information Station, and started from 25 based on the results 6) of research of the section Headquarters for Earthquake Research Promotion with the Japanese government. For all over Japan meshed in 25m, the following are easily obtained. They are mainly applied in disaster prevention plans, infrastructures and the seismic design of structures. Predicted PGV on ground surface and the engineering bedrock with 6m/s in shear wave velocity and JMA's seismic intensity scale of ground surface For known epicenter or active faults By probabilistic supposition or by fault rapture mathematics model. Profiles of shallow soil (layer upper than the engineering bedrock with 6m/s) Topography classification. Shear wave velocity. Amplification of seismic motion. Structure of deep soil (layer upper than the bedrock with 31m/s) Depth of each shear wave velocity and soil density The soil information of deep and shallow are used for calculation of above predicted PGV and seismic intensity scale. Though the dimension of the mesh is fine, the value of most points are interpolated from values of a few actual survey points. Therefore it is necessary to be careful to errors. In this study, observed acceleration time histories by K-NET and digital data of deep and shallow soil are used. 3.Model for Analysis About response analysis SDOF model with a bi-linear shear spring for isolator are adopted as shown in figure 1. 63 cases of parametric k studies that varied 9 damper ratio μ (damper's yielding force / μ weight of building) and 7 Tf (tangent period by post-yielding stiffness) as property values of the Menshin structure are performed. The yielding deformation is set to 3cm in all case. Recentry, sliding 3cm δ isolator spreads and pile top sliding isolator is put to practical use. Figure 1 Model for Analysis Because long period Menshin is realized easily in those way, Tf more than 6 seconds are included for longer period Menshin. In addition, Tf=99 second ( ) is included to simulate "Only Putting Menshin that consist of only sliding isolator without restoring spring, and it is regarded as an inexpensive Menshin system. Table 1. Parameters of the study Parameter Values Tf sec (tangent period by post-yielding stiffness) 3, 4, 5, 6, 7, 8, 99 damper ratio μ.2,.3,.4,.5,.6,.7,.8,.9,.1 4.Input Ground Motion Tf = 2π W k As input earthquakes for this examination, records of "K-NET" were used. For a criterion of the intensity of the ground motion, JMA's seismic intensity scale was used. And from January 96 to July 29, 47 earthquake records were picked up by searching their Web Site, that have more than 5.5 of JMA's seismic intensity scale (three directions composition) - This level causes the structural damage for buildings where seismic capacity is low -, then, 94 horizontal components (, direction) were considered to be input ground acceleration time histories. Chosen input ground motion data are shown in table 2. The PGV in the table was calculated by integral calculus from the acceleration, but baseline correction and filtering (passing.1 to 1 second) were done only for finding the maximum value. 5 >PGV > 1cm/s : 21 components, PGV > 1cm/s : 5 components are included. W Q/W
Table 2 Input Ground Motions Maximum Value, the hypo-center, Soils No Recorded File Name PGA() PGV() PGA() PGV() Magnit Epicent Depth T1 T2 AVS3 Station Station-Code Date Time cm/s 2 cm/s cm/s 2 cm/s ude er km km sec sec m/s 1 TCG9 9621 9 524 2.9 422 17.5 5.8 68 53.51. 6 IMAICHI 2 SZO2 9733 239 36 13.7 587 31.2 5. 6 3 1.87.99 6 ITOH 3 KGS4 973 1731 293 43.8 132 17.7 6.3 17 8 1.49.68 6 AKUNE 4 KGS5 973 1731 434 28.9 493 35.7 6.3 13 8 2.33 1.1 279 MIYANOJOH 5 OKY4 133 527 14.3 8.9 7.3 38 11.. 4 NIIMI 6 TTR7 133 7 42. 573.4 7.3 13 11.51.22 318 KOHFU 7 TTR8 133 314 35.7 384 53.5 7.3 17 11 1.79.84 YONAGO 8 EHM3 1324 1528 325 21.4 459 3.5 6.4 51 2.7 1.23 189 TOHYO 9 HRS9 1324 1528 6.7 828 3.4 6.4 57 51.. 776 YUKI 1 HRS14 1324 1528 36 3.1 4 32. 6.4 43 51.4.15 253 OHNO 11 MYG11 35 1824* 111 51.1 1114 36.5 7. 59 71.4.15 2 OSHIKA HKD66 39 45 43 43.5 492 52. 8. 2 42 6.35 2.94 SHIBETSU 13 HKD7 39 45 476 36.5 35 32.6 8. 24 42 7.96 3.48 134 HONBETSUKAI 14 HKD77 39 45 311 35.4 47 4.3 8. 136 42 6.43.86 KUSHIRO 15 HKD84 39 45 351 43.2 354 46.3 8. 148 42 5.57 2.51 4 AKAN 17 HKD91 39 45 391 57.2 374 69.6 8. 1 42 1.56.81 283 URAHORO 18 HKD92 39 45 433 55. 69 57. 8. 138 42 5.17 2.39 6 IKEDA HKD98 39 45 366 73.9 346 74. 8. 13 42 5.71 2.67 432 TAIKI 2 HKD1 39 45* 81.8 97 48.1 8. 84 42 1.31.49 398 HIROO 21 HKD 39 68 592.4 49 47.5 7.1 92 21 4.7.79 253 URAKAWA 22 NIG17 23 1756 468 48.3 369 23.2 6.8 17 13 15.11 7.15 218 NAGAOKA 23 NIG 23 1756** 11 98.5 1314 7.2 6.8 7 13 17.35 7.51 428 OJIYA 24 NIG2 23 1756 522 3.8 48.6 6.8 11 13 1.9.53 393 KOIDE 25 NIG21 23 1756* 17 53.8 849 49.8 6.8 21 13.29 7.51 352 TOHKAMACHI NIG28 23 1756* 871 4.6 76 9.7 6.8 15 13 13.4 6. 321 NAGAOKA-SHISHO 27 NIG 23 1834 794 63. 637 53.6 6.5 14 17.35 7.51 428 OJIYA 28 NIG2 23 1834 527.6 525 34.9 6.5 9 14 1.9.53 393 KOIDE 29 NIG21 23 1834* 8 58.2 8 49.6 6.5 14.29 7.51 352 TOHKAMACHI 3 NIG24 23 1834 521 25.1 398 22. 6.5 47 14 8.51 3.71 6 YASUDUKA 31 NIG 23 46 28 15.6 432 39.4 5.7 8 17.35 7.51 428 OJIYA 32 NIG 24 1421 398 21.3 36.7 5. 7 11 17.35 7.51 428 OJIYA 33 NIG2 27 14 523 37.6 388 18.8 6.1 9 1.9.53 393 KOIDE 34 HKD74 9 332 493 21.6 55 28.6 7.1 64 48.84.46 2 NOSAPPU 35 HKD2 214 1456 536 39.8 18 73.6 6.1 9 9 7.48 2.83 399 MINATOMACHI 36 FKO6 532 153 277 59. 239 32.3 7. 9 1.49.74 218 FUKUOKA 37 ISK3 7325 942 5 39.3 396 21.5 6.9 28 11 3. 1.7 28 WAJIMA 38 ISK4 7325 942 622 23.6 589 18.9 6.9 42 11 2.49.79 346 NOTO 39 ISK5 7325 942* 473 34.7 78 98.6 6.9 11 1.75.24 28 ANAMIZU 4 ISK6 7325 942 717 38. 849 5.6 6.9 7 11 3.5 1. TOGI NIG18 77 113* 668.6 511 83.7 6.8 21 17 13.65 5.75 5 KASHIWAZAKI 42 NIG 77 113 391 21.3 455 45.8 6.8 32 17 17.35 7.51 428 OJIYA 43 MYG4 8614 843 74 45.2 678 39.1 7.2 35 8 3.25 1.67 9 TSUKIDATE MYG5 8614 843 69.7 521 33.2 7.2 32 8 2.43 1. 5 NARUKO 45 MYG6 8614 843 238 35.1 233 4.8 7.2 5 8 5.27 2.69 3 FURUKAWA 46 AOM 8724 6.7 534 22.1 6.8 88 18 6.57 2.78 181 HACHINOHE 47 IWT1 8724 827.6 65 29.2 6.8 76 18 1.39.65 46 TANEICHI HKD86 39 45* 728 65.1 81 1.9 8. 42 6.72 2.45 9 CHOKUBETSU BCJL2, KOB BCJL2: PGA=356, PGV=58, KOB: PGA=818, PGV=91 Mark *, ** means more than measurement seismic intensity 6., 6.5 respectively. T1,T2 are dominant periods of the deep ground above bedrock (Vs=31m/s)
From depths and shear wave velocities and densities of the deep ground with bedrock (Vs=31m/s) of J-SHIS, soil column model were made and furthermore it converted to mass-spring model in order to obtain the dominant periods (natural periods) of the ground by eigenvalue analysis. An extreme liquefaction of soil is watched in record of No in the table. Then the records of No have strong surface wave with intense peak in 3 seconds. The Japan Society of Seismic Isolation is studying these. Author judged that records of No should be treated just for reference because they seems to have electric or mechanical malfunction with showing the shift of the acceleration baseline in the middle of main shock. For comparison, BCJL2 and 95 JMA KOBE are also included for examination. BCJL2 is devised as design recommendation strong motion such as super high-rise structures by Building Center of Japan, and it is artificial earthquake having the constant pseudo-velocity spectrum with value of 1cm in more than.63 second period. 95 JMA KOBE (KOB) was observed at the Great Hanshin Earthquake in Kobe in 95. Both are available for unique digital acceleration. Correction of the waves performed only the vertical The number in Table 2 baseline shift so that the average of first one second of Tf=4. μ=.4 the record became zero. The damping of the system 1 gave 1% as proportional damping coefficient for instantaneous stiffness, and the numerical integration was performed by Newmark-β method (β =1/4,.5second for integration time step). 8 5.Results of the examination 5.1 Result of the case of Tf=4second and μ =.4 The examination result of the case of Tf=4. second (Post yield period) and μ=.4 (damper ratio) will be explained. Around this case is chosen frequently in Menshin design in Japan. Dmax means the maximum displacement of Menshin. (1) Relation between PGV and maximum displacement(dmax) When PGV increases, Dmax increases to easily imagine. Dmax are less than 4cm in PGV<6cm/s. 8 components of 94 make Dmax more than 5cm. (2)Shallow soil profile and Dmax From shallow soil profile data of J-SHIS, AVS3 (average shear wave velocity of 3m in depth) were searched. Relation between AVS3 and Dmax is shown in figure 3, but clear correlation can not be found. More than 4m/s is regarded as the considerably hard ground, but it does not make Dmax small. Tf= 4. μ=.4 1 3 2 4 6 8 (3)Deep ground structure and Dmax Relation between 1 st Average Shear Verocity of 3m AVs3 m/s dominant period T1 from deep soil data of J- SHIS and Dmax is shown in figure 4(1). When T1<2 figure 3 Relation between AVS3 and Dmax second, Dmax<3cm without one exceptional as component of No. In 5<T1<7 second, Dmax have large value of No and. Dmax were normalized by PGV to find tendency in detail. Relation between 1 st dominant period T1 and normalized Dmax shows Maximum Displacement Dmax cm 6 4 2 5 1 15 Peak Ground Velocity PGV cm/s 1 8 6 4 2 18 39 17 7 45 18 36 17 45 37 39 22 74 13 14 21 837 22 3634 1 4 46 34 23 2343 35 15 43 15 6 29 24 27 33 25 28 35 29 33 2 4 38 31 42 6 38 47 1131 32 5 23 39 3 3 23 23 figure 2 Relation between PGV and Dmax 9
Maximum Displacement Dmax cm Tf= 4. μ=.4 1 8 6 4 2 17 39 43 7 36 17 3 43 24 39 37 33 7 24 4 6 4 28 37 1 33 2 8 2 36 38 5 32 6 4 34 11 9 47 372 38 18 18 35 4515 4515 14 14 21 3513 13 46 3 3 22 22 23 23 27 29 29 42 25 31 31 32 32 1.6 Tf= 4. μ=.4 1 5 1 15 5 1 15 1st Dominant Period of Deep Soil T1 sec 1st Dominant Period of Deep Soil T1 sec (1) Dmax (2) Normalized Dmax by PGV in figure 4(2). In T1<2 second, normalized Dmax are less than.5. When T1 increases in T1<4second, the normalized Dmax increases and the lower bound is in proportion linearly. Around T1=6 (No,18, ) and around T1=13 (No,) second they are large. Around T1>15 second they are small The 1 st dominant period T1 that corresponding with deep soil structure and Dmax have some correlation. 5.2 Relation between damper ratio μ and maximum displacement(dmax) Relations between damper ratio μ and Dmax shows in figure 5(1~4) about earthquake of No,,, in Table 2. In the upper section of the figure time history of velocities are shown, in the middle section pseud-velocity spectrum (psv) are also shown. In the lower section of the figure relation between μ and Dmax are shown. When μ increases Dmax increases in No, No, No. Menshin design would be difficult unless μ make too large. In No Dmax become small when Tf become small in the range of large μ, but it is a reverse tendency in No. In No Dmax does not change very much when μ change, and it is difficult to design of Menshin even if any μ is chosen. And about Tf, Dmax grow largest in Tf=4 seconds with the both, direction. Note that the long period surface wave influences No and liquefaction of the ground influences No. Relations between μ and Dmax shows in figure 5 (5) about BCJL2 and KOB. Because BCJL2's value of psv is constant in more than.63 second in period, It is easy to understand that Dmax shrinks when μ grows larger. In addition, Dmax increases when Tf grows larger. When μ increases, Dmax increases slightly in KOB. In figure 6 shows μ-dmax curve of No, 17, 18, 23, 39. Shapes are different each earthquake such as peak (No, 17) or dip (No17). There is as No39, when μ increases Dmax increases. And shapes changes in, components by the same earthquake. In the case of Tf=99 second simulated to Only Putting Menshin, Dmax are larger than the other Tf and are not stable in many case. So Tf=99 does not seem to be suitable for practical use in the range of these μ. Maximum Displacement Normalized by PGV (Dmax/PGV) cm/(cm/s) 1.4 1.2 1.8.6.4.2 43 17 43 24 37 33 2439 7 28 4 36 37 333 7 38 17 39 4 134 28 8 362 59 2 384 6 2 2 4 9 47 1134 47 1 18 45 15 45 18 15 14 13 35 21 13 21 3 46 3 figure 4 Relation between 1 st dominant period T1 and Dmax 22 22 42 23 27 31 23 27 29 42 31 29 25 32
1 5-5 -1 No HKD98 39 45 TAIKI, Tokachi-Oki Vmax=:73.9 :74. cm/s -73.9cm/s No MYG5 8614 843 NARUKO, IwateMiyagi Vmax=:69.7 :33.2 cm/s 1 5 69.7cm/s -5-1 1 5-5 -1 3 25 2 15 1 74.cm/s 4 6 8 1 h=.5 h=.2 h=.4 4 2-2 -4 35 3 25 2 15 1-33.2cm/s 2 4 6 8 1 14 h=.5 h=.2 h=.4 5 5 1-1 1 1 1 No HKD98 39 45 Station=TAIKI EQ=Tokachi-Oki M=8. Δ=13km Depth= 42 T1=5.71s,T2=2.67s AveVs3=432m/s 1-1 1 1 1 No MYG5 8614 843 Station=NARUKO EQ=IwateMiyagi M=7.2 Δ= 32km Depth= 8 T1=2.43s,T2=1.s AveVs3=5m/s 1 1 Tf= 3. Tf= 4. Tf= 5. Tf= 6. Tf= 7. Tf= 8. Tf=99. 8 6 4 2 Tf= 3. Tf= 4. Tf= 5. Tf= 6. Tf= 7. Tf= 8. Tf=99. 8 6 4 2.2.4.6.8.1.2.4.6.8.1 (1) No (2) No figure 5 Relations between damper ratio μ and Dmax
No NIG18 77 113 KASHIWAZAKI, Niigata-Chuetsu-Oki No NIG28 23 1756 NAGAOKA-SHISHO, Niigata-Chuetsu Vmax=:.6 :83.7 cm/s Vmax=:4.6 :9.7 cm/s 1 1-1 -.6cm/s -1-4.6cm/s -2-2 1 5-5 -1 5 4 3 2 1-83.7cm/s 2 3 4 5 6 h=.5 h=.2 h=.4 1-1 1 1 1 No NIG18 77 113 Station=KASHIWAZAKI EQ=Niigata-Chuetsu-Oki M=6.8 Δ= 21km Depth= 17 T1=13.65s,T2=5.75s AveVs3=5m/s 2 1-1 -2 4 35 3 25 2 15 1 5 9.7cm/s 4 6 8 1 h=.5 h=.2 h=.4 1-1 1 1 1 No NIG28 23 1756 Station=NAGAOKA-SHISHO EQ=Niigata-Chuetsu M=6.8 Δ= 15km Depth= 13 T1=13.4s,T2=6.s AveVs3=321m/s 1 1 8 6 4 2 Tf= 3. Tf= 4. Tf= 5. Tf= 6. Tf= 7. Tf= 8. Tf=99. 8 6 4 2 Tf= 3. Tf= 4. Tf= 5. Tf= 6. Tf= 7. Tf= 8. Tf=99..2.4.6.8.1 (3) No (4) No figure 5 Relations between damper ratio μ and Dmax.2.4.6.8.1
BCJL2 : Vmax=58. cm/s KOB : Vmax=91. cm/s 1 5-5 -1 1 5-5 -1 3 25 2 15 1 5-58.cm/s 2 4 6 8 1 91.cm/s 5 1 15 2 25 3 35 4 1-1 1 1 1 8 7 6 5 4 3 2 1 h=.5 h=.2 h=.4 KOB Tf= 3. Tf= 4. BCJL2 / KOB Tf= 5. Tf= 6. Tf= 7. Tf= 8. Tf=99. BCJL2 KOB BCJL2 KOB BCJL2.2.4.6.8.1 (5) BCJL2 and KOB figure 5 Relations between damper ratio μ and Dmax Tf= 3. Tf= 4. Tf= 5. No HKD66 39 45 Station=SHIBETSUTf= 6. 4 Tf= 7. Tf= 8. 3 Tf=99. 2 1.2.4.6.8.1 No17 HKD91 39 45 Station=URAHORO 6 5 4 3 2 1.2.4.6.8.1 6 5 4 3 2 1 No18 HKD92 39 45 Station=IKEDA.2.4.6.8.1 6 5 4 3 2 1 No23 NIG 23 1756 Station=OJIYA.2.4.6.8.1 No39 ISK5 7325 942 Station=ANAMIZU 6 5 4 3 2 1.2.4.6.8.1 (1) No (2) No17 (3) No18 (4) No23 (5) No39 figure 6 Relations between damper ratio μ and Dmax
6. Conclusion For 47 strong motions more than measurement seismic intensity 5.5 observed in K-NET for 13 years, 94 horizontal components are used for input ground motions for time history analysis of 63 cases of Menshin structure to calculate the maximum displacement. As results, with case of Tf=4. second and damper ratio μ =.4, more than 5cm of Dmax (maximum displacements of Menshin) are estimated by 8 time histories of 94. About deep soil structure, in the case above, The 1 st dominant period T1 that corresponding with deep soil structure and Dmax have some correlation. When T1 decreases, Dmax decreases. About shallow soil deposit, it seems that there are no relation between AVS3 and Dmax. It seems that the characteristics of the earthquake sources (hypo-center parameter - such as fault shape or sliding velocity or stress descent) may have more influence over Dmax than the factors argued above. The correlations between damper ratio μ and displacement Dmax are looked over by plotting μ- Dmax curves for every earthquake and every Tf. As a result, various tendencies are found. Some have peak or some have dip on μ- Dmax curves, and some do not change Dmax so much even if μ changes, though we are apt to think intuitively generally that when μ increases, Dmax decreases. For Menshin, it is important to pay attention to the ground. By the record with liquefaction of the soil, the record with long period surface wave make design of Menshin almost impossible. In this study, SDOF system is chosen for Menshin structure and shear force of upper structure is not argued, but furthermore, multi-stories models would be considered to examine shear force distributions. And focusing the same earthquake data set - for example,23 Tokachi-Oki Earthquake -, difference of the response by strong motions of every observation points would be considered to clarify what kind of factor affected the response. In addition, simulation analysis also would be perform for the base-fixed structure (non Menshin) under the strong motions in this study. It seems that the base-fixed structure with short period in eigenvalue would be superior to Menshin in some ground conditions and some earthquake source characteristics. It would be examined what kind of condition does short period structure favorable. Lastly the high-density seismograph network and earthquake information system helped this study. And they may be effective for improvement of the aseismic design technology. Also the research and development of the strong motion prediction technology is important. Reference 1) NAMITA Hiroyuki, et al., 29, Change of Isolated Building Response by Additional Amount of Non-linear Viscous Dampers, Architectural Institute of Japan Summaries of technical Papers of annual Meeting, Japan, pp.97-98 2) Japan Society of Seismic Isolation, 29.4.23, Summary of No. 5 Technical Report (in Japanese) 3) TAKAYAMA Mineo, et al., 27, Relationship between Maximum Story Drift of Base Isolated Buildings and Intensity Indexes of Seismic Ground Motions Architectural Institute of Japan memoir. Architectural Institute of Japan, Kyushu branch office, Japan, pp.349-352 4) http://www.k-net.bosai.go.jp/k-net/ (Japanese and English) 5) http://www.j-shis.bosai.go.jp/ (Japanese only) 6) Report: 'National Seismic Hazard Maps for Japan (25)' http://www.jishin.go.jp/main/chousa/6mar_yosoku-e/index-e.htm