EMPIRICAL ESTIMATION OF NEWMARK DISPLACEMENT FROM ARIAS INTENSITY AND CRITICAL ACCELERATION
CHYI-TYI LEE, SHANG-YU HSIEHInstitute 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
])()1log[(90.0log 09.1
max
53.2
max
a
A
a
AD cc
n
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?
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.
Data Collection
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.
logDn=1.521logIa-1.993logAc-1.546 0.925logDn = 1.46logIa-6.642logAc+1.546 1.052
logDn=1.460logIa-6.642Ac+1.546 logDn=1.521logIa-log1.993Ac-1.546
Ac =0.15
Ac =0.6Ac =0.55Ac =0.5Ac =0.45Ac =0.4Ac =0.35Ac =0.3Ac =0.25Ac =0.2
Ac =0.1Ac =0.05
=1.052
Goodness of fit = 0.802
= 0.925
Goodness of fit = 0.86
= 0.6178
Goodness of fit =0.8291
= 0.6575
Goodness of fit =0.8707
logDn=2.306logIa-3.931logAc-4.056logDn =2.265logIa-7.032logAc+0.458
1993 formula 1998 formula
1993 form 1998 form
Chi-Chi Earthquake TCU072(NS)
Random sampling:100
0.05 0.1 0.15 0.2 0.25 0.3
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0.05 0.1 0.15 0.2 0.25 0.3
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60
-1.4 -1.2 -1 -0 .8 -0.6 -0.4
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Ac AclogAc
Dn logDn logDn
R2=0.66 R2=0.99 R2=0.90
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 Earthquake Ac=0.05
0 2 4 6 8 10
0
200
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600
800
0 2 4 6 8 10
-1
0
1
2
3
-2 -1 0 1
-1
0
1
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Ia Ia logIa
Dn logDn logDn
R2=0.38 R2=0.72R2=0.26
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
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=0.98~0.99 R2=0.82~0.93
Kobe R2=0.67~0.82 R2=0.98~0.99 R2=0.89~0.96
Loma prieta R2=0.64~0.88 R2=0.98~0.99 R2=0.88~0.96
Northridge R2=0.61~0.88 R2=0.98~0.99 R2=0.81~0.97
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=0.6~0.8 R2=0.4~0.75 R2=0.77~0.85
Dn versus Ac
Dn versus Ia
logDn=C1logIa+C2Ac
IaIa AclogDn=C1log +C2Ac+C3
+C3+C3logIaAc +C4
Ac =0.15
Ac =0.6
Ac =0.55
Ac =0.5Ac =0.45
Ac =0.4
Ac =0.35
Ac =0.3Ac =0.25
Ac =0.2
Ac =0.1Ac =0.05
New form I
New form II
= 0.6178
Goodness of fit =0.8291
logDn =2.265logIa-7.032logAc+0.458
logDn=15.4689logIaAc-20.4415Ac+2.3464 = 0.3862
Goodness of fit =0.9449
1993formula
1998 formula
1993form
1998form
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
nDlog
CHI-CHI EARTHQUAKE
1993 formula 1998 formula 1993 form
1998 form New form I New form II
Ac =0.15
Ac =0.6
Ac =0.55
Ac =0.5Ac =0.45
Ac =0.4
Ac =0.35
Ac =0.3Ac =0.25
Ac =0.2
Ac =0.1Ac =0.05
=1.0520 Goodness of fit =0.8029 =0.9249 Goodness of fit =0.8605
=0.5911 Goodness of fit =0.8707
=0.6718 Goodness of fit =0.8291
=0.6575 Goodness of fit =0.8370 =0.5768 Goodness of fit =0.8777
KOBE EARTHQUAKE =0.3437 Goodness of fit =0.9186 =0.3876 Goodness of fit =0.9401
=0.2660 Goodness of fit =0.9437
=0.2829 Goodness of fit =0.9361
=0.2660 Goodness of fit =0.9437 =0.2138 Goodness of fit =0.9640
Ac =0.15
Ac =0.3Ac =0.25
Ac =0.2
Ac =0.1
Ac =0.051993 formula 1998 formula 1993 form
1998 form New form I New form II
TURKEY EARTHQUAKE =0.5164 Goodness of fit =0.8874 =0.3942 Goodness of fit =0.8941
=0.3530 Goodness of fit =0.8990
=0.3715 Goodness of fit =0.8874
=0.3928 Goodness of fit =0.8731 =0.3544 Goodness of fit =0.8981
Ac =0.15
Ac =0.3Ac =0.25
Ac =0.2
Ac =0.1
Ac =0.051993 formula 1998 formula 1993 form
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
=0.2993 Goodness of fit =0.9141
=0.3009 Goodness of fit =0.9131
=0.3017 Goodness of fit =0.9126 =0.2847 Goodness of fit =0.9226
Ac =0.15
Ac =0.3Ac =0.25
Ac =0.2
Ac =0.1
Ac =0.051993 formula 1998 formula
1993 form
1998 form New form I New form II
Northridge EARTHQUAKE =0.4178 Goodness of fit =0.9173 =0.3637 Goodness of fit =0.9278
=0.3043 Goodness of fit =0.9282
=0.3115 Goodness of fit =0.9247
=0.3310 Goodness of fit =0.9145 =0.2869 Goodness of fit =0.9365
Ac =0.15
Ac =0.3Ac =0.25
Ac =0.2
Ac =0.1
Ac =0.05
1993 formula 1998 formula 1993 form
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
=0.3280 Goodness of fit =0.9129
=0.3332 Goodness of fit =0.9099
=0.3418 Goodness of fit =0.9055 =0.3111 Goodness of fit =0.9220
Ac =0.15
Ac =0.6
Ac =0.55
Ac =0.5Ac =0.45
Ac =0.4
Ac =0.35
Ac =0.3Ac =0.25
Ac =0.2
Ac =0.1Ac =0.05
1993 formula 1998 formula 1993 form
1998 form New form I New form II
1993formula
1998formula
1993 form
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 0.2660 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
1993formula
1998formula
1993 form
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 0.9437 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 0.8874 0.8990 0.8731 0.8981
Whole 0.9098 0.9102 0.9099 0.9129 0.9055 0.9220
nDlog
nDlognDlog
nDlog
-3 -2 .5 -2 -1 .5 -1 -0 .5 0 0.5 1 1.5 2 2.5 3
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200
300
400
-3 -2 .5 -2 -1 .5 -1 -0 .5 0 0.5 1 1.5 2 2.5 3
0
20
40
60
80
-3 -2 .5 -2 -1 .5 -1 -0 .5 0 0.5 1 1.5 2 2.5 3
0
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-3 -2 .5 -2 -1 .5 -1 -0 .5 0 0.5 1 1.5 2 2.5 3
0
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-3 -2.5 -2 -1 .5 -1 -0 .5 0 0.5 1 1.5 2 2.5 3
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coun
t
Residual Residual Residual
ResidualResidualResidual
Chi-Chi Kobe Turkey
Loma Prieta地震 Northridge Six earthquake data sets
nDlog
nDlog
nDlog-3 -2 .5 -2 -1 .5 -1 -0 .5 0 0.5 1 1.5 2 2.5 3
0
20
40
60
80
Residual Distribution
Loma Prieta
coun
t
coun
t
coun
t
coun
t
coun
t
Rock site
Chi-Chi Northridge
Loma Prieta Six-earthquake data sets
=0.5184
Goodness of fit =0.9032
=0.2990
Goodness of fit =0.9255
=0.2971
Goodness of fit =0.9198
=0.4441
Goodness of fit =0.8616
Ac =0.15
Ac =0.3Ac =0.25
Ac =0.2
Ac =0.1
Ac =0.05
Soil site
Chi-Chi Northridge
Loma Prieta Six-earthquake data sets
=0.5687
Goodness of fit =0.8833
=0.2574
Goodness of fit =0.9519
=0.2772
Goodness of fit =0.9224
=0.2884
Goodness of fit =0.9363
Ac =0.15
Ac =0.3Ac =0.25
Ac =0.2
Ac =0.1
Ac =0.05
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.
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