Citation: Díaz, V., S. Kataoka (2020), Proposal of ground motion prediction equation (GMPE) for
Chilean ground motion records and its application, Synopsis of IISEE-GRIPS master report.

PROPOSAL OF GROUND MOTION PREDICTIONEQUATION (GMPE) FOR CHILEAN GROUNDMOTION RECORDS AND ITS APPLICATION
Víctor Pablo Díaz Gómez1,2Supervisor: Shojiro KATAOKA3
ABSTRACT

After the 2010 Chilean Earthquake, buildings design code was upgraded in topics related to spectrum
design and soil classification; however, the bridge's code was not. The main target of this research is to
propose a Ground Motion Prediction Equation (GMPE) in order to predict seismic intensity in Chile andto analyze the current spectrum design of the Road Manual code and use on it to evaluate the Seismic
Risk Inform. I use an existing Japanese GMPE (Dr. KATAOKA Shojiro from NILIM) but modified by
Chilean records using modification factors. These modification factors multiply the parameter “b” inside
the original GMPE and become the geometric mean value (ratio between observed acceleration response
spectrum over predicted acceleration response spectrum) to one (1). The results show excellent
performance of GMPE Modified. Also, it shows that the peak of acceleration response spectrum andacceleration value at 1 second period of the current spectrum design for bridges must be examined.
Keywords: Ground Motion Prediction Equation (GMPE), Seismic Intensity, Bridge Spectrum Design,
PGA.

1. INTRODUCTION
Chile is over the South American plate. Whileon its western edge, the Nazca and Antarctic
plates converge and generate subduction
zones, the Scotia plate slides horizontallyconcerning the South American plate, on apassing plate edge. These interactions produce
a great deformation of the South American
continent
andgenerateearthquakes
throughout Chile. Due to the high speed ofconvergence between Nazca and SouthAmerica, the seismicity in that area is the mostintense and produces the most massive
earthquakes in the country. Also, Chile is oneof the most prone countries to suffer from Figure 1. Road Manual Spectrum Design. Seismic Zone 3.
earthquakes in the world. Most of them areinterplate subduction earthquakes, except for the one in 1939 that corresponds to the Chillán earthquake,
which is an intraplate-oceanic earthquake, and the 1949 Punta Arenas earthquakes (M ~ 7.8), whichcorrespond to earthquakes with a passing edge in the Magallanes fault zone. The massive earthquakes

1

Ministry of Public Works, Chile.
IISEE-GRIPS master course student.
3
Research Department Chief, National Institute for Land and Infrastructure Management.
2

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in recent years are the 2010 (8.8 Mw), 2014 (8.2 Mw), and 2015 (8.4 Mw). After these large earthquakes,
the bridge’s design code was not upgraded or modified related to the spectrum design method.
On the other hand, The Road Manual of the Road Direction is a technical document thatserves as a guide for the bridge’s design in Chile. It defines three seismic zones. These are divided byimaginary lines almost parallel between them. Besides, the Road Manual describe five (5) bridges design
method; one of them is the Spectrum Design method including a Seismic Risk Inform (SRI). The SRI
is a technical research which target is develop an acceleration response spectrum in function of thebridge’s location, to use it in the bridge design. However, inside Road Direction, there is not any
professional with the skills to revise this inform.
Then, the target of this research is checking the current spectrum design with the GMPE
Modified and get the skills to be able to review the spectrum design included in the Seismic Risk Inform
for special bridges.

2. THEORY AND METHODOLOGY
2.1. The Ground Motion Prediction Equation (GMPE)
The GMPE was developed by Dr. KATAOKA Shojiro in order to predict seismic intensities, PGA, andan acceleration response spectrum. In this case, include acceleration data of interplate earthquakes inJapan from the year 1978 to 2003, using more than 11.000 data records. From the beginning, the original
GMPE shows an excellent correlation with the Chilean records. However, the geometric mean value did
not show a good dispersion; in higher frequencies, the tendency value is over one (1), and for lower
frequencies, the tendency value is lower than one (1). The Eq. (1) is the GMPE.
𝑌 = 𝑎1 ∗ 𝑀𝑤 = 𝑎2 ∗ 𝐷 − 𝑏 ∗ 𝑋 + 𝑐0 − 𝑙𝑜𝑔10(𝑋 + 𝑑 ∗ 100,5∗𝑀𝑤 )(1)

The inputs of the GMPE are (a) the soil type of the target point according to Japaneseclassification (I, II, III), (b) the shortest distance from the target point to the rupture area (X value), (c)the depth of the hypocenter (D value), and (d) the earthquake magnitude (Mw value).
2.2. The Ground Motion Prediction Equation Modified (GMPE Modified)
The GMPE Modified is the original
GMPE multiplied by some values(modification factors) to parameter“b” for each period. These
modification factors make thegeometric mean value of thespectrum ratio, a trend to 1.
The spectrum ratio is theratio between the observed data
(using Chilean records) over thepredicted data (using GMPE
Modified).
The GMPE Modified
has excellent behavior with Chilean
acceleration records and has a correct
Figure 2. The original GMPE and Chilean acceleration
performance compare it with therecords. Dots are acceleration records with different
Chilean attenuation equation.
magnitudes. This GMPE is at 1 second period.

22.3. Analysis of the current Spectrum Design
The current Spectrum Design was developed in 2002; at that time, the Road Manual was created. The
earthquake base, of the current spectrum design, is the San Antonio Earthquake (1985). It is an interplate
earthquake, magnitude 8.0 Mw, and 33 km of depth. For this research, I use only the seismic zone 3 ofthe current Road Manual for the analysis.

Figure 3. Road Manual Spectrum Design. Seismic
Zone 3. Soil Type I, II, III , and IV in Chile.
The seismic zone 3 is the coastal area in Chile and corresponds to the zone with a higher
acceleration demand (Ao = 0.4g) in the country. The seismic zone 1 is in the Los Andes Mountainlocation and corresponds to the lower acceleration demand (Ao = 0.2g), and the seismic zone 1 is thecentral valley zone (Ao = 0.3g). The target analysis area is the Metropolitan Region in the middle partof Chile. Therefore, the dip angle of the trench is around 23 degrees. With this information, I calculated
the lower acceleration response spectrum possible in seismic zone 3, and the higher acceleration
response spectrum possible in seismic zone 3. These two (2) spectrums I compare with the current
spectrum design of bridge code.

3. DATA
3.1. Acceleration Data
All the acceleration data used in this research were obtained from the seismic Network in Chile(www.csn.cl). In total, I used 77 acceleration records of 10 earthquakes from 67 different seismic
stations. However, the seismic station network is more extensive.
3.2. Soil Classification
The soil classification in Chile is quite similar to Japan; I (Ts > 0,2 sec), II (0,2 > Ts > 0,5), III (1,0 >Ts > 0,5); however, in Chile there is one more category of soil, IV (Ts > 1,0). Therefore, I assumed
category III and IV in Chile, as III in Japan. The parameter to classify the soil is the Shear Velocity(Vs30) and Nakamura Method was used to transform the Vs30 to a natural period. All the Vs30
information was obtained from each seismic station that I used.
3.3. Hypocenter Distance
The hypocenter distance is the shortest distance between the target position to the rupture area. Thisrupture area is related to the dip angle of the trench. In Chile, the dip angle is according three zones, (1)the north location with the longitude of 15 degrees to the longitude of 27 degrees where the dip angle
value is between 25 degrees to 30 degrees, (2) location with the longitude of 26 degrees to the longitude3

of 33 degrees where dip angle value is 10 degrees, and (3) from longitude 33 degrees to the south where
dip angle is almost 30 degrees.

4. RESULTS AND DISCUSSION
4.1. Modification Factors
Although the original GMPE surprising correct performance, the geometric mean value of the spectrum
ratio (accelerations response spectrum of Chilean records over GMPE acceleration response spectrum)
is not adequate, as I explained before. It is why, through the iterative process, I found some Modification
Factors that fix that issue.
Table 1. Modification Factors.

Multiplying these modification factors to parameter b inside GMPE, the dispersion of thespectrum ratio value change and fix the trend of the geometric mean value. The geometric mean value
tendency now is correct.

Figure 4. The spectrum ratio dispersion in 5 second period. On the left side is the GMPE and shows thatfor high frequency, the spectrum ratio trend towards valuing over 1, on the other hand, for lower
frequency, the trending value is less than 1. On the right side, GMPE Modified, and show that thetendency to 1 is more homogeneous.

Figure 5. The geometric mean value dispersion in 5 seconds period. On the left side is the GMPE
distribution, on the right side is the GMPE Modified dispersion. In this last, the dispersion is fixed dueto the Modification Factors.

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There are no relevantchanges between the GMPE curve and
the GMPE Modified curve. However,
due to the modification of the parameter“b”, the shape of the curve changes. One
acceleration value is obtained with ahypocenter distance shorter than using
the original version. The GMPE
Modified keeps the adequate behavior
using Chilean acceleration records andcorrelates correctly comparing withother attenuation equation developed in
Figure 6. The GMPE is the solid line, and the GMPE
Chile like the developed by professor
Modified is the broken line.
Boroschek from the University of Chile.
4.2. Current Spectrum Design in Chile
The higher acceleration response
spectrum possible, occur when the
hypocenter distance (X value) is equal
to 37 km (San Antonio city in the
coastal area). The lower acceleration
response spectrum possible, occur
when the hypocenter distance (Xvalue) is equal to 71 km, in the border
between the seismic zone 3 andseismic zone 2 (near Santiago city). In
this research, I am only analyzing theseismic zone 3 and the type of soil III.
Then, it is easy toconclude that the peak of the current Figure 7. Spectrum Design. In segmented line spectrum foracceleration design spectrum is lower soil type III and IV (correlated as III in Japan). Orange line
than that is predicted by GMPE the lower acceleration spectrum possible inside seismic zone
Modified. However, at 1 second 3, and in blue line the highest acceleration spectrum possible
period, the current spectrum design inside seismic zone 3.
amount is near to lower case value.
Quite different is comparison with the higher case; in this case, the acceleration amount isalmost double. Therefore, the current spectrum design must be upgraded according to more significant
earthquakes that occurred in Chile in recent years.

5. CONCLUSIONS AND RECOMMENDATIONS
5.1. GMPE Modifieda) GMPE Modified has an excellent performance with Chilean records.
b) I recommend to include more acceleration data in the database from the south part of Chile (notcontained in this research) and find new modifications factors. Besides, I recommend analyzing the typeof soil and modify it if necessary. However, the correct behavior of the GMPE Modified using Chilean
data records should be maintained.
c) Also, I recommend the GMPE Modified as a tool to review the Spectrum Design proposed in the
Seismic Risk Inform for unique bridges design. This revision should be overseen by the engineersinside the Project Department of the Road Directions in the Ministry of Public Works in Chile.

55.2. Current Spectrum Designd) After the 2010 earthquake, 2014 earthquake, and 2015 earthquake, the current spectrum design of theRoad Manual has not been analyzed or upgraded. However, the Chilean building code has been
upgraded.
e) This research proves the need to analyze the current Spectrum Design and evidence that it must be
modified. According to the result, it is necessary to use a hypocenter distance (X value) between 37 km
and 71 km in order to define a new spectrum. However, the choice of the final amount will be
determinded by the authority.
f) I propose to change the current spectrum design in two-period ranges, (a) at high frequencies (from 0
to 1,3 seconds) to increase the PGA and the peak value of the spectrum, and (b) for low frequencies(from 1,4 to 5 seconds) keep the current spectrum amount.

ACKNOWLEDGEMENTS
This research was conducted during the individual study period of the training course “Seismology,
Earthquake Engineering and Tsunami Disaster Mitigation” by the Building Research Institute, JICA,
and GRIPS. I would like to express my sincere gratitude to Dr. KASHIMA for supervising me andgiving me very useful advice and suggestions during my study and also all the other staff members at
IISEE/BRI for their support and encouragement during this training program. Further, I am incredibly
thankful to Dr. KATAOKA Shojiro, Road Structures Department of NILIM, for permitting me to use
his Ground Motion Prediction Equation and also for support and constructive comments regarding thiswork. I would like to express my gratitude to JICA for giving me a chance to follow this course throughfinancial support.
Moreover, I would like to express my sincere gratitude to my family and all people thatlove me, for supporting me at any time and any moment, and forgiving me tools to face life with effort,
work, and love. Special thanks to Ms. Chavarria for helping me with the maps.
Finally, I would like to express my gratitude to all JICA members for believing in me and my skills andall Japanese people to make me feel so comfortable this year.

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