** EARTHQUAKES**

**2.1 INTRODUCTION**

**2.3.3 P ROPOSED M ETHODOLOGY FOR S ELECTING R EPRESENTATIVE E ARTHQUAKE S UITES**

Based on the previous selection of the far- and near-fields, the procedure can be

summarised into steps that would be followed endeavouring a credible selection of

representative earthquake suites and scenarios. The steps are as follows:

1. Identify the level of PGA and Sa(T1) for the considered structure at the elected

percentage of damping, e.g. 5-percent.

2. From local faulting and seismology, and also informed by the governing loading code,

[NZS1170.5 (2004)] and seismic hazard maps identify whether near-, medium- and/or

far-field seismic events would be the representative scenario for the site of the

considered structure.

3. Obtain or calculate *k0* and *k* seismic hazard coefficients of the site of the considered

structure in order to identify representative earthquakes from geographic area that

matches the considered seismic hazard.

4. Set the initial search parameters of the elected strong motion database, e.g. PEER

(2000), by moment magnitude (M) > 6.5 and closest distance to the rapture surface (R)

to be: R ≤ 8km, 8km ≤ R ≤ 40km and R ≥ 40km for near-, medium- and far-field events respectively. Also enforce damped PGA ≥ 0.2g and ≥ 0.4 for far- and near-field events respectively. Further, select representative soil classification albeit for credible

earthquake scenario it is preferable to choose at least C for USGS, D for Geomatrix or 1

for CWB classifications. Consequently, site-specific soil amplifications can be avoided.

5. Download the above-mentioned criteria-matched earthquakes including all their

component accelerograms and spectral accelerations, if available, else compute them.

7. Build an information table listing the properties of all components for each initially

selected earthquake. These data include accelerogram information including recording

station, component type and direction, M, R, damped PGA and Sa(T1) values.

8. Select earthquakes, including their components, that at least one of their horizontal

components has high value of Sa(T1). Consequently, limit the number of selected

earthquakes to a little more than 20, say about 25, that achieve the highest available

values of Sa(T1).

9. For far-field suites, plot spectral accelerations of the horizontal components between

the maximum and minimum spectral acceleration bounding values obtained from the

above-developed far-field suite. Subsequently, cull earthquakes that exceed 1/T or

have a component significantly exceeding the maximum bound in order to remove

earthquakes that breach the guidelines.

10. For near-field events, plotting spectral accelerations of the horizontal components

between the maximum and minimum spectral acceleration bounding values of the

above-developed near-field may be helpful. It would show whether the newly selected

near-field suite is relatively of lower or higher magnitude in comparison with the

above-developed one.

11. Scale and plot the spectral accelerations of the remaining horizontal components by

setting the value of PGA = 1g. Subsequently inspect the plot and eliminate any

earthquake with peculiar large peak values around a specific period value, as

highlighted previously in the case of Mexico City (1985) records, see Figure 2-2.

12. Moreover, scale and plot the remaining spectral accelerations by setting the values of

Sa(½T1) and Sa(T1) to 1g. Afterwards, inspect the plots for any peculiarities or marked

exceedance of the maximum bounding values in order to remove breaching

earthquakes. Note that scaling with the spectral acceleration values of one-third or

13. If the total number of earthquakes drops below 20, repeat the above detailed procedure

with slightly reduced thresholds of M, R and PGA. Repeat this procedure until 20

earthquakes are acquired. For near-field events, it is expected to later relax the rule of

selecting earthquakes only from geographic areas with matching seismic hazard due to

the scarcity of these records.

Note that for two-dimensional analysis, the same proposed procedure applies where both

horizontal accelerogram can be used along with the vertical one if considered. Consequently,

this methodology can be applied to both two- or three-dimensional studies of structures.

**2.4 ** **CONCLUSIONS AND RECOMMENDATIONS **

The employed methodology in selecting both the far- and near-field proved credibility by

their reported reduced randomness (βEQ). Chapters four, five and six later show that marked reduced

randomness in the structural response and behaviour that assures the credibility of their findings. The

proposed stepwise procedure is portable and can be easily followed in selecting representative one-,

two- or three-dimensional earthquake suites and scenarios. Finally, it is worthwhile to mention that

South Californian strong motion records can be implemented in New Zealand, and vice versa, due to

the confirmed large resemblance in their seismic hazard characteristics.

It is highly recommended to follow the proposed procedure in selecting and/or verifying

the selection appropriateness of representative earthquake suites and scenarios. Earthquakes

recorded on soft soils should be strictly avoided to avoid site-specific amplification as depicted

in the case of the earthquake records of Mexico City (1985), see Figure 2-2.

**2.5 ** **REFERENCES **

Abrahamson, N. A., and Silva, W. J. (1997). “Empirical response spectra attenuation relations for

shallow crustal earthquakes”, Seismological Research Letters (SRL), Vol. 68, pp94-127.

Federal Emergency Management Agency (FEMA) (2002). “Seismic rehabilitation pre-standard.”

DOE (1994). “Natural phenomena hazards design and evaluation criteria for Department of

Energy Facilities”, DOE-STD-1020-94, U. S. Dept. of Energy, Washington DC.

Federal Emergency Management Agency (FEMA) (2000). “FEMA 350 – Recommended

Seismic Design Criteria for New Steel Moment-Frame Buildings.” Report No. FEMA-

350, Washington DC.

Han, S.W., and Wen, Y.K. (1997). “Method of Reliability-Based Seismic Design. I: Equivalent

Nonlinear Systems. II: Calibration of Code Parameters”, Journal of Structural

Engineering, ASCE, Vol. 123. No. 3, pp. 256-270.

Kircher, C. A., Nassar, A. A., Kustu, O. and Holmes, W. T. (1997). "Development of Building

Damage Functions for Earthquake Loss Estimation", Earthquake Spectra, Vol. 13, No. 4,

pp. 663-682, Earthquake Engineering Research Institute, Oakland, California.

Luco, N., and, Cornell, C. A., (1998A). “Seismic drift demands for two SMRF structures with

brittle connections”, Structural Engineering World Wide 1998, Elsevier Science Ltd.,

Oxford, England, Paper T158-3.

NZS1170.5 and Supp 1 (2004). “Structural design actions – Earthquake actions – New Zealand”,

Standards New Zealand, 2 parts, Wellington, New Zealand.

PEER Strong Motion Database (2000). Complied by Dr. Walt Silva of Pacific Engineering,

Pacific Earthquake Engineering Research Center (PEER), University of California at

Berkeley. http://peer.berkeley.edu/smcat/.

Penzien, J. and Watabe, M. (1975). “Characteristics of 3-dimensional earthquake ground

motions”, Earthquake Engineering and Structural Dynamics, Vol. 3, pp. 365-373.

Shome, N., and Cornell, C. A. (1999). “Probabilistic seismic demand analysis of nonlinear

structures”, Report No. RMS-35, RMS Program, Stanford University, Stanford, CA.

http://www.stanford.edu/group/rms/Thesis/NileshShome.pdf. (Last time accessed: 08

January 2007).

motion time histories for phase 2 of the FEMA/SAC steel project.” SAC Background

Document SAC/BD-97/04, SAC Joint Venture, Richmond, California.

Stirling, M. W., McVerry, G. H. and Berryman, K. R. (2002). “A New Seismic Hazard Model

for New Zealand”, Bulletin of the Seismological Society of America, Vol. 92. No. 5, June

2002, pp. 1878-1903.

USGS (2002). “USGS national seismic hazard maps”, United States Geological Survey

http://geohazards.cr.usgs.gov/eq/.

Vamvatsikos, D., and Cornell C. A. (2002). “Incremental Dynamic Analysis”, Earthquake

Engineering and Structural Dynamics, Vol. 31, pp. 491–514.

Vamvatsikos, D., and Cornell, C. A. (2004). “Applied incremental dynamic analysis”,

Earthquake Spectra, Earthquake Engineering Research Institute (EERI), Vol. 20, No. 2,

**Table 2-1.** **The Initial Earthquake Suite. **
**EQ **

**No. **

**Suite **

**No. ** **Event Station **φ

(1) _{Soil}(2)

**M(3)** **R(km)(4)** **PGA(g)**

**1 ** 1 Imperial Valley, 1940 El Centro 90 C,D 7 8.3 0.214

2 Imperial Valley, 1940 El Centro 0 C,D 7 8.3 0.348

**2 ** 3 Imperial Valley, 1979 Imperial County Services Bldg _{90 ? 6.5 } _{? 0.236 }

4 Imperial Valley, 1979 Imperial County Services Bldg _{0 ? 6.5 ? 0.213 }

**3 ** 5 Kobe, 1995 Kobe JMA Observatory _{90 ? 6.9 19.163 }_{0.631 }

6 Kobe, 1995 Kobe JMA Observatory _{0 ? 6.9 }_{19.163 }_{0.837 }

**4 ** 7 Mexico City, 1985 CDAO, D3-115 _{0 D,E 8.1 400 0.071 }

8 Mexico City, 1985 CDAO, D3-115 90 D,E 8.1 400 0.082

**5 ** 9 Mexico City, 1985 SCT1, D3-144 0 D,E 8.1 400 0.100

10 Mexico City, 1985 SCT1, D3-144 90 D,E 8.1 400 0.171

**6 ** 11 San Fernando, 1971 Pacoima Dam _{164 } –,B 6.6 8 1.221

12 San Fernando, 1971 Pacoima Dam _{254 } –,B 6.6 8 1.246

**7 ** 13 Parkfield, 1966 Temblor _{295 ? 6.1 } _{61 0.281 }

14 Parkfield, 1966 Temblor _{205 ? 6.1 } _{61 0.410 }

**8 ** 15 Northridge, 1994 Pacoima Dam - Upper Left Abutment 194 A,A 6.6 18.573 1.284

16 Northridge, 1994 Pacoima Dam - Upper Left Abutment 104 A,A 6.6 18.573 1.584

**9 ** 17 Northridge, 1994 Sylmar-6 Storey C. Hosp., Ground, E. Wall 0 C,– 6.6 15.057 0.799

18 Northridge, 1994 Sylmar-6 Storey C. Hosp., Ground, S. Wall 90 C,– 6.6 15.057 0.383

**10 ** 19 Loma Prieta, 1989 Corralitos - Eureka Canyon Road _{90 B,}_{–}_{ 7 7.167 }_{0.478 }

20 Loma Prieta, 1989 Corralitos - Eureka Canyon Road _{0 B,– 7 7.167 0.630 }

**11 ** 21 Loma Prieta, 1989 Treasure Island _{90 Fill 7 67.700 0.159 }

22 Loma Prieta, 1989 Treasure Island _{0 Fill 7 67.700 0.100 }

**(1)**

Component.

**(2)**

USGS, Geomatrix soil class.

**(3)**

Moment magnitude.

**(4)**

**Table 2-2.** **Linear regression coefficients (k****0**** and k) of Seismic hazard on intensity measure (S****a) for **

**Christchurch and Wellington, based on Stirling et al (2002). **

**Linear regression coefficients (k****0 **** and k) of New Zealand **

**Seismic Hazard **** Wellington Christchurch ****PGA T=2s PGA T=2s ****k****0****3 x 10****-4****5 x 10****-5****5 x 10****-5****8 x 10****-7****Median k********0****0.0001 ****k****-2.74 -2.43 -2.81 -3.58 ****Median k******** -2.78 **

**Table 2-3.** **Sorted Vamvatsikos and Cornell (V&C) Far-Field Suite (May 2004). **
**EQ **

**No. **

**Suite **

**No. (1)** **Event Station ** φ

(2) _{Soil}(3)

**M(4)** **R(km)(5)** **PGA(g)**

**1 ** 13 Imperial Valley, 1979 Chihuahua 282 C,D 6.5 28.7 0.254

**2 ** 8 Imperial Valley, 1979 El Centro Array #13 140 C,D 6.5 21.9 0.117

14 Imperial Valley, 1979 El Centro Array #13 230 C,D 6.5 21.9 0.139

**3 ** 2 Imperial Valley, 1979 Plaster City 135 C,D 6.5 31.7 0.057

18 Imperial Valley, 1979 Plaster City 45 C,D 6.5 31.7 0.042

**4 ** 9 Imperial Valley, 1979 Westmoreland Fire Station 90 C,D 6.5 15.1 0.074

15 Imperial Valley, 1979 Westmoreland Fire Station 180 C,D 6.5 15.1 0.11

**5 ** 1 Loma Prieta, 1989 Agnews State Hospital 90 C,D 6.9 28.2 0.159

**6 ** 4 Loma Prieta, 1989 Anderson Dam Downstream 270 B,D 6.9 21.4 0.244

**7 ** 5 Loma Prieta, 1989 Coyote Lake Dam Downstream 285 B,D 6.9 22.3 0.179

**8 ** 19 Loma Prieta, 1989 Hollister Diff. Array 165 –,D 6.9 25.8 0.269

3 Loma Prieta, 1989 Hollister Diff. Array 255 –,D 6.9 25.8 0.279

**9 ** 10 Loma Prieta, 1989 Hollister South & Pine 0 –,D 6.9 28.8 0.371

**10 ** 7 Loma Prieta, 1989 Sunnyvale Colton Ave 270 C,D 6.9 28.8 0.207

11 Loma Prieta, 1989 Sunnyvale Colton Ave 360 C,D 6.9 28.8 0.209

**11 ** 16 Loma Prieta, 1989 WAHO 0 –,D 6.9 16.9 0.37

20 Loma Prieta, 1989 WAHO 90 –,D 6.9 16.9 0.638

**12 ** 12 Superstition Hills, 1987 Wildlife Liquefaction Array 90 C,D 6.7 24.4 0.18

17 Superstition Hills, 1987 Wildlife Liquefaction Array 360 C,D 6.7 24.4 0.2

**13 ** 6 Imperial Valley, 1979 Cucapah 85 C,D 6.5 23.6 0.309

**(1)**

The component’s original number V&C suite.

**(2) **

Component.

**(3)**

USGS, Geomatrix soil class.

**(4)**

Moment magnitude.

**(5)**

Closest distance to fault rupture.

**Table 2-4.** **Statistical properties of the V&C Far-Field Suite. **
**Criterion M(3)** **R(km)(4)** **PGA(g)**

**Max ** 6.9 31.7 0.638

**Min ** 6.5 15.1 0.042

**Std Deviation ** 0.189 5.059 0.133

**Table 2-5.** **The Far-Field Suite: The Populated V&C Far-Field Suite, **
**plus the Added 8 Far-Field Earthquakes. **

**EQ **
**No. **

**Suite **

**No. (1)** **Event Station ** φ

(2) _{Soil}(3)

**M(4)** **R(km)(5)** **PGA(g)**

**1 ** 13-b Imperial Valley, 1979 Chihuahua 12 C,D 6.5 28.7 0.27

13 Imperial Valley, 1979 Chihuahua 282 C,D 6.5 28.7 0.254

**2 ** 8 Imperial Valley, 1979 El Centro Array #13 140 C,D 6.5 21.9 0.117

14 Imperial Valley, 1979 El Centro Array #13 230 C,D 6.5 21.9 0.139

**3 ** 2 Imperial Valley, 1979 Plaster City 135 C,D 6.5 31.7 0.057

18 Imperial Valley, 1979 Plaster City 45 C,D 6.5 31.7 0.042

**4 ** 9 Imperial Valley, 1979 Westmoreland Fire Station 90 C,D 6.5 15.1 0.074

15 Imperial Valley, 1979 Westmoreland Fire Station 180 C,D 6.5 15.1 0.11

**5 ** 1-b Loma Prieta, 1989 Agnews State Hospital 0 C,D 6.9 28.2 0.172

1 Loma Prieta, 1989 Agnews State Hospital 90 C,D 6.9 28.2 0.159

**6 ** 4-b Loma Prieta, 1989 Anderson Dam Downstream 270 B,D 6.9 21.4 0.244

4 Loma Prieta, 1989 Anderson Dam Downstream 360 B,D 6.9 21.4 0.24

**7 ** 5-b Loma Prieta, 1989 Coyote Lake Dam Downstream 195 B,D 6.9 22.3 0.16

5 Loma Prieta, 1989 Coyote Lake Dam Downstream 285 B,D 6.9 22.3 0.179

**8 ** 19 Loma Prieta, 1989 Hollister Diff. Array 165 –,D 6.9 25.8 0.269

3 Loma Prieta, 1989 Hollister Diff. Array 255 –,D 6.9 25.8 0.279

**9 ** 10 Loma Prieta, 1989 Hollister South & Pine 0 –,D 6.9 28.8 0.371

10-b Loma Prieta, 1989 Hollister South & Pine 90 –,D 6.9 28.8 0.177

**10 ** 7 Loma Prieta, 1989 Sunnyvale Colton Ave 270 C,D 6.9 28.8 0.207

11 Loma Prieta, 1989 Sunnyvale Colton Ave 360 C,D 6.9 28.8 0.209

**11 ** 16 Loma Prieta, 1989 WAHO 0 –,D 6.9 16.9 0.37

20 Loma Prieta, 1989 WAHO 90 –,D 6.9 16.9 0.638

**12 ** 12 Superstition Hills, 1987 Wildlife Liquefaction Array 90 C,D 6.7 24.4 0.18

17 Superstition Hills, 1987 Wildlife Liquefaction Array 360 C,D 6.7 24.4 0.2