CHYI-TYI LEE, SHANG-YU HSIEH

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Presentation transcript:

EMPIRICAL ESTIMATION OF NEWMARK DISPLACEMENT FROM ARIAS INTENSITY AND CRITICAL ACCELERATION CHYI-TYI LEE, SHANG-YU HSIEH Institute of Applied Geology, National Central University

Newmark’s cumulative displacement for a sliding block can be calculated by double integration of an earthquake acceleration time history data above certain critical acceleration value (Newmark, 1965)

Newmark method need? Critical acceleration Strong motion data Ac=(FS-1)sinα

Use Newmark method to build landslide potential map in Taiwan? Critical acceleration for each grid---YES Strong motion data for each grid---NO

Empirical formula Base on peak ground acceleration Ambraseys and Menu (1988) use PGA calculate the critical acceleration ratio

Base on Arias intensity Jibson (1993) choose 11 earthquakes magnitude range between Mw 5.3~7.5 and use regression method to build an empirical formula. logDn=1.460logIa-6.642Ac+1.546 Jibson et al.(1998) used 13 earthquakes and 555 data to regress Ia、Ac and Dn , and get a new empirical formula logDn=1.521logIa-1.993logAc-1.546

Peak ground acceleration? Or Arias intensity? Build landslide potential map by Newmark method. Are the empirical formula proposed in 1993 and 1998 were suitable for Taiwan?

Data Collection After the occurrence of the 1999 Chi-Chi, Taiwan earthquake (Mw7.6), huge strong-motion data sets, especially near field data, have been accumulated. Duzce、Kocaeli 、Kobe 、 Northridge and Loma Prieta earthquake strong motion data sets were chosen to be assured the results will not be only a local phenomenon.

All the strong-motion data are processed by Pacific Earthquake Engineering Research Center (PEER). The processing includes baseline correction and band-pass filtering. Ias are calculated for each strong-motion record and each horizontal component. Dns calculated for different Ac level for each of the record.

The five analysis steps include: 1. Pick 15 Chi-Chi earthquake strong motion data in central Taiwan. Compare formula and form made in 1993, 1998. 2. Fixing Ia and check out the relation between Ac-Dn . 3. Fixing Ac and check out the relation between Ia-Dn . 4. Set more candidate form for comparison. 5. Regressing each candidate form with present data and find out a better form.

1993 formula 1998 formula logDn=1.460logIa-6.642Ac+1.546 logDn = 1.46logIa-6.642logAc+1.546 1.052 logDn=1.521logIa-1.993logAc-1.546 0.925 logDn=1.460logIa-6.642Ac+1.546 logDn=1.521logIa-log1.993Ac-1.546 Ac =0.15 Ac =0.6 Ac =0.55 Ac =0.5 Ac =0.45 Ac =0.4 Ac =0.35 Ac =0.3 Ac =0.25 Ac =0.2 Ac =0.1 Ac =0.05 =1.052 Goodness of fit = 0.802 = 0.925 Goodness of fit = 0.86 1993 form 1998 form logDn =2.265logIa-7.032logAc+0.458 logDn=2.306logIa-3.931logAc-4.056 = 0.6178 Goodness of fit =0.8291 = 0.6575 Goodness of fit =0.8707

Chi-Chi (logDn-logAc) Chi-Chi Earthquake TCU072(NS) Random sampling:100 Dn logDn logDn R2=0.90 R2=0.66 R2=0.99 logAc Ac Ac Chi-Chi (Dn-Ac) Chi-Chi (logDn-Ac) Chi-Chi (logDn-logAc) R2=0.6~0.7 R2=0.98~0.99 R2=0.89~0.97

CHI-CHI (logDn-logIa) Chi-Chi Earthquake Ac=0.05 Dn logDn logDn R2=0.38 R2=0.26 R2=0.72 Ia Ia logIa CHI-CHI (Dn-Ia) CHI-ChI (logDn-Ia) CHI-CHI (logDn-logIa) R2=0.3~0.5 R2=0.2~0.5 R2=0.7~0.9

Dn versus Ac Dn versus Ia Earthquake (Dn- Ac) (logDn- Ac) (logDn-log Ac) Chi-Chi R2=0.6~0.7 R2=0.98~0.99 R2=0.89~0.97 Duzce & Kocaeli R2=0.7~0.87 R2=0.82~0.93 Kobe R2=0.67~0.82 R2=0.89~0.96 Loma prieta R2=0.64~0.88 R2=0.88~0.96 Northridge R2=0.61~0.88 R2=0.81~0.97 Dn versus Ia Earthquake (Dn- Ia) (logDn- Ia) (logDn-log Ia) Chi-Chi R2=0.3~0.5 R2=0.2~0.5 R2=0.7~0.9 Duzce & Kocaeli R2=0.76~0.8 R2=0.8~0.87 R2=0.88~0.98 Kobe R2=0.7~0.89 R2=0.78~0.87 R2=0.9~0.98 Loma prieta R2=0.6~0.8 R2=0.32~0.5 R2=0.77~0.85 Northridge R2=0.4~0.75

New form I logDn=C1log Ia Ia Ac +C2Ac+C3 New form II logDn=15.4689logIaAc-20.4415Ac+2.3464　 logDn =2.265logIa-7.032logAc+0.458 Ac =0.15 Ac =0.6 Ac =0.55 Ac =0.5 Ac =0.45 Ac =0.4 Ac =0.35 Ac =0.3 Ac =0.25 Ac =0.2 Ac =0.1 Ac =0.05 = 0.6178 Goodness of fit =0.8291 = 0.3862 Goodness of fit =0.9449 New form I logDn=C1log Ia Ia Ac +C2Ac+C3 New form II logDn=C1logIa+C2Ac +C3 +C3logIaAc +C4 1993 formula 1998 form New formI New formII 0.8540 0.9072 0.5284 0.4722 0.3862 0.3765 R2 0.8644 0.9004 0.8927 0.9153 0.9449 0.9475

CHI-CHI EARTHQUAKE Ac =0.15 Ac =0.6 Ac =0.55 Ac =0.5 Ac =0.45 Ac =0.4 =1.0520 Goodness of fit =0.8029 =0.9249 Goodness of fit =0.8605 =0.6718 Goodness of fit =0.8291 Ac =0.15 Ac =0.6 Ac =0.55 Ac =0.5 Ac =0.45 Ac =0.4 Ac =0.35 Ac =0.3 Ac =0.25 Ac =0.2 Ac =0.1 Ac =0.05 1993 formula 1998 formula 1993 form =0.5911 Goodness of fit =0.8707 =0.6575 Goodness of fit =0.8370 =0.5768 Goodness of fit =0.8777 1998 form New form I New form II

KOBE EARTHQUAKE 1993 formula 1998 formula 1993 form Ac =0.15 Ac =0.3 =0.3437 Goodness of fit =0.9186 =0.3876 Goodness of fit =0.9401 =0.2829 Goodness of fit =0.9361 1993 formula 1998 formula 1993 form Ac =0.15 Ac =0.3 Ac =0.25 Ac =0.2 Ac =0.1 Ac =0.05 =0.2660 Goodness of fit =0.9437 =0.2660 Goodness of fit =0.9437 =0.2138 Goodness of fit =0.9640 1998 form New form I New form II

TURKEY EARTHQUAKE 1993 formula Ac =0.15 Ac =0.3 Ac =0.25 Ac =0.2 =0.5164 Goodness of fit =0.8874 =0.3942 Goodness of fit =0.8941 =0.3715 Goodness of fit =0.8874 1993 formula Ac =0.15 Ac =0.3 Ac =0.25 Ac =0.2 Ac =0.1 Ac =0.05 1998 formula 1993 form =0.3530 Goodness of fit =0.8990 =0.3928 Goodness of fit =0.8731 =0.3544 Goodness of fit =0.8981 1998 form New form I New form II

Loma Prieta EARTHQUAKE =0.4384 Goodness of fit =0.8971 =0.3679 Goodness of fit =0.8810 =0.3009 Goodness of fit =0.9131 Ac =0.15 Ac =0.3 Ac =0.25 Ac =0.2 Ac =0.1 Ac =0.05 1993 formula 1998 formula 1993 form =0.2993 Goodness of fit =0.9141 =0.3017 Goodness of fit =0.9126 =0.2847 Goodness of fit =0.9226 1998 form New form I New form II

Northridge EARTHQUAKE =0.4178 Goodness of fit =0.9173 =0.3637 Goodness of fit =0.9278 =0.3115 Goodness of fit =0.9247 Ac =0.15 Ac =0.3 Ac =0.25 Ac =0.2 Ac =0.1 Ac =0.05 1993 form 1993 formula 1998 formula =0.3043 Goodness of fit =0.9282 =0.3310 Goodness of fit =0.9145 =0.2869 Goodness of fit =0.9365 1998 form New form I New form II

Six earthquake data sets =0.4381 Goodness of fit =0.9098 =0.3707 Goodness of fit =0.9102 =0.3332 Goodness of fit =0.9099 Ac =0.15 Ac =0.6 Ac =0.55 Ac =0.5 Ac =0.45 Ac =0.4 Ac =0.35 Ac =0.3 Ac =0.25 Ac =0.2 Ac =0.1 Ac =0.05 1993 formula 1998 formula 1993 form =0.3280 Goodness of fit =0.9129 =0.3418 Goodness of fit =0.9055 =0.3111 Goodness of fit =0.9220 1998 form New form I New form II

1993 formula 1998 form New form I New form II Chi-Chi 1.0520 0.9249 0.6718 0.5911 0.6575 0.5768 Kobe 0.3437 0.3876 0.2829 0.2660 0.2138 Loma Prieta 0.4384 0.3679 0.3009 0.2993 0.3017 0.2847 Northridge 0.4178 0.3637 0.3115 0.3043 0.3310 0.2869 Turkey 0.5164 0.3942 0.3715 0.3530 0.3928 0.3544 Whole 0.4381 0.3707 0.3332 0.3280 0.3418 0.3111 Goodness of Fit 1993 formula 1998 form New form I New form II Chi-Chi 0.8029 0.8605 0.8291 0.8707 0.8370 0.8777 Kobe 0.9186 0.9401 0.9361 0.9437 0.9640 Loma Prieta 0.8971 0.8810 0.9131 0.9141 0.9126 0.9226 Northridge 0.9173 0.9278 0.9247 0.9282 0.9145 0.9365 Turkey 0.8874 0.8941 0.8990 0.8731 0.8981 Whole 0.9098 0.9102 0.9099 0.9129 0.9055 0.9220

Residual Distribution Chi-Chi Kobe Turkey count count count Residual Residual Residual Loma Prieta Loma Prieta地震 Northridge Six earthquake data sets count count count Residual Residual Residual

Rock site Chi-Chi Northridge Ac =0.15 Ac =0.3 Ac =0.25 Ac =0.2 Ac =0.1 =0.5184 Goodness of fit =0.9032 =0.2990 Goodness of fit =0.9255 Loma Prieta Six-earthquake data sets =0.2971 Goodness of fit =0.9198 =0.4441 Goodness of fit =0.8616

Soil site Chi-Chi Northridge Ac =0.05 Ac =0.1 Ac =0.15 Ac =0.2 =0.5687 Goodness of fit =0.8833 =0.2574 Goodness of fit =0.9519 Loma Prieta Six-earthquake data sets =0.2772 Goodness of fit =0.9224 =0.2884 Goodness of fit =0.9363

CONCLUSION We tested new form with each of the data set from the six, and got a smaller estimation error and a better goodness of fit for each set. However, for the whole data set, this new form has only a little better than the old form proposed by Jibson. This new form may be tested by more different data set to make sure its stability in the future. The estimation error is smaller and the goodness of fit is higher for either soil site formula or rock site one. Because landslide is usually occurred on hillside, rock site formula may be more valid in this case. Soil site formula may be used at slope of landfills.

Thanks for your attention!