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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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

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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

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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

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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.

Thanks for your Thanks for your attention!attention!