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

2. 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)

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

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

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

6. 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

7. 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?

8. 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.

9. 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.

10. 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.

11. 1993 formula 1998 formula logDn=1.460logIa-6.642Ac+1.546
logDn = 1.46logIa-6.642logAc
logDn=1.521logIa-1.993logAc
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 =
Goodness of fit =0.8291 =
Goodness of fit =0.8707

12. 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

13. 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

14. 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

15. New form I logDn=C1log Ia Ia Ac +C2Ac+C3 New form II
logDn= logIaAc Ac 　
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 =
Goodness of fit =0.8291 =
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

16. CHI-CHI EARTHQUAKE Ac =0.15 Ac =0.6 Ac =0.55 Ac =0.5 Ac =0.45 Ac =0.4
= Goodness of fit =0.8029
= Goodness of fit =0.8605
= 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
= Goodness of fit =0.8707
= Goodness of fit =0.8370
= Goodness of fit =0.8777
1998 form
New form I
New form II

17. KOBE EARTHQUAKE 1993 formula 1998 formula 1993 form Ac =0.15 Ac =0.3
= Goodness of fit =0.9186
= Goodness of fit =0.9401
= 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
= Goodness of fit =0.9437
= Goodness of fit =0.9437
= Goodness of fit =0.9640
1998 form
New form I
New form II

18. TURKEY EARTHQUAKE 1993 formula Ac =0.15 Ac =0.3 Ac =0.25 Ac =0.2
= Goodness of fit =0.8874
= Goodness of fit =0.8941
= 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
= Goodness of fit =0.8990
= Goodness of fit =0.8731
= Goodness of fit =0.8981
1998 form
New form I
New form II

19. Loma Prieta EARTHQUAKE
= Goodness of fit =0.8971
= Goodness of fit =0.8810
= 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
= Goodness of fit =0.9141
= Goodness of fit =0.9126
= Goodness of fit =0.9226
1998 form
New form I
New form II

20. Northridge EARTHQUAKE
= Goodness of fit =0.9173
= Goodness of fit =0.9278
= 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
= Goodness of fit =0.9282
= Goodness of fit =0.9145
= Goodness of fit =0.9365
1998 form
New form I
New form II

21. Six earthquake data sets
= Goodness of fit =0.9098
= Goodness of fit =0.9102
= 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
= Goodness of fit =0.9129
= Goodness of fit =0.9055
= Goodness of fit =0.9220
1998 form
New form I
New form II

22. 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

23. 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

24. 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

25. 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

26. 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.

27. Thanks for your attention!