THE ESTIMATION OF NONLINEAR SITE EFFECTFROM THE SURFACE MOTIONKyi Kyi Swe ∗MEE10506

Supervisor:Toshiaki, YOKOI ∗∗ABSTRACT
We have conducted a case study for recently proposed parameter of non-linear site response DNLs.
The data are used the accelerograms of the 2011 off the Pacific coast of Tohoku earthquake and its
aftershocks, mainly, recorded at three KiK-Net stations that have vertical arrays.
Besides DNLs PGA amplification is considered as a reference parameter. In FKSH14 andIBRH13, a significant de-amplification is observed in the range of PGA at the borehole bottom greaterthan 10 gals; also in the range of PGA at the ground surface greater than 100 gals, whereas in IBRH18,
it is not observed with the only exception, i.e., the main shock. It is observed that DNLs increases with
the PGA both at the ground surface and borehole bottom in the range as mentioned above for all threestations. DNL based on the horizontal to vertical spectral ratio of the surface record (DNL S-H/V ) wellfollows the behavior of that based on the spectral ratio of the surface records to those obtained at theborehole bottom (DNL SB ) and shows a possibility to use the former in place of the latter if only surface
records are available. We may expect that these DNLs will be useful for the future strong motion study
in Myanmar.
Keywords: Nonlinear site effect, Vertical array, DNLs, PGAs, PGA-amplification.
1. INTRODUCTION
In this study we cannot use any strong motion data obtained in Myanmar due to lack of a digitalstrong motion seismograph network. We use the data of the Off the Pacific Coast of TohokuEarthquake on March 11/14:46, 2011 (Mw=9.0, Event 2 in Table 1), which occurred near thenortheast coast of Honshu, Japan. The hypocenter depth of the earthquake is 20 km and is located inthe subduction zone of plate boundary between the Pacific and North American plates. Thisearthquake generated strong ground motions over a wide region of Tohoku in Japan. We investigate
the influences of nonlinear site responses on these strong motion data. The purpose of this study is toconduct a case study using real strong motion data for the recently proposed parameters that describe
the non-linear response of soil layers DNLs (Noguchi and Sasatani 2008; 2010): to verify their capacity
to characterize the non-linearity; to verify the applicability to the cases where only surface records areavailable.
2. DATAWe use the strong motion data obtained by the KIK-Net stations, NIED, Japan, at which they haveboth surface sensor and another at the bottom of a borehole that reaches to the basement composed of
the hard rock. The vertical array data is available at KiK-Net stations. These vertical arrays provided
us the possibility to verify the DNL approach. In this study we mainly use the main shock’s andaftershock’s records of this earthquake and a few other earthquakes additionally.

*The author works for Department of Meteorology and Hydrology, Ministry of Transport, Myanmar.
**International Institute of Seismology and Earthquake Engineering, Building Research Institute, Tsukuba,
Japan.

We select the records obtainedat IBRH13, IBRH18 andFKSH14 stations. The events
parameters are listed in Table 1.
These records are selected using
criteria: the focal depth lessthan 40Km and epicentral
distance shorter than 100Km,mostly.
Thegeologicalcondition and the location ofthree stations are; IBRH13 hasweatheringrockattheshallowest part and is located inthe northern part of IbarakiPrefecture. IBRH18 has shallow
sandy gravel layer and locatedin the middle Ibaraki Prefecture
and FKSH14 has sand layer andLocated in the southern part ofFukushima Prefecture.
3. METHOD OF STUDY
3.1. Degree of Nonlinear Site Response
Noguchi and Sasatani (2010) have proposed new indicators DNL (Degree of non-linearity)
for a non-linear behavior of shallow soil layers as follows. The response of a shallow layer is directlygiven by the spectral ratio of a horizontal component of the surface record to that obtained at thebottom of a borehole. At a low strain level, i.e., weak ground shaking, this gives a linear amplification(hereafter denoted as a function of the frequency RSB
weak (f) ). At a strong ground shaking, theamplification will be changed due to a non-linear behavior of soils and becomes different from theoriginal linear one (hereafter denoted as a function of the frequency RSB
strong (f)). They define anindicator of a non-linear behavior DNL SB using the ratio of these spectral ratios of surface to borehole
records. They also define another indicator DNL S-H/V using the spectral ratio of a horizontal component
to a vertical one of surface records based on the observation reported by Wen et al. (2006): thisS−H/V
spectral ratio at a ground shaking, strong enough for non-linear response R strong (f), differs from that
S−H/Vat a weak ground shaking R weak (f).
DNL is defined as follows

Rstrong (f)DNL = ∑ �log Rweak (f)� ∆f,(2)where the summation is taken over the frequency from 0.5 Hz to 20 Hz (Figure 6 right). This denotes
the area between the two spectral ratio curves in full logarithmic graph. For DNL SB , R weak (f) andSBR strong (f) are replaced with RSB
weak (f) and R strong (f), respectively, whereas for DNL S-H/V with
S−H/VS−H/V

R weak (f) and R strong (f), respectively. DNL SB requires both of surface and borehole records,
whereas DNL S-H/V requires only surface records of three components.

4. RESULTS OF ANALYSIS
4.1 De-Amplification EffectWe analyzed the relation of PGA (Peak Ground Acceleration) amplification at the ground surface andat the bottom of a borehole in order to investigate the influence of nonlinear site responses on strong
motion records (Figure 1). Here, PGA amplification means the ratio of PGA at the surface to that at
the bottom of a borehole; PGA is calculated as the vector sum of the maximum absolute value ofNorth-South and that of East-West components.
The value of PGA amplification is limited to below 12 gals for all of these three stations. A
de-amplification is observed clearly at FKSH14 (Figure 11 a) and b)) and IBRH13 (Figure 11 c) andd)): the bigger PGA both at the ground surface and the borehole bottom correspond to the lower PGA
amplification, therefore to the stronger non-linearity. In these two stations a significant
de-amplification of the strong motion is observed in the range of PGA at a borehole bottom greaterthan 10 gals; also in the range of PGA at the ground surface greater than 100 gals.
On the other hand, in IBRH18 a de-amplification effect is not observed as clearly as in others(Figure 1 e) and f)). Only the mark of the maximum PGA that is of the main shock (Event 2) shows
the graph slightly decaying, but others’ PGA amplifications are aligned almost constant. This seems toimply a linear response of IBRH18 except for the Event 2. However, the limitation of PGA
amplification implies non-linearity. It’s better to verify another parameter of non-linearity, DNLs.

Figure 1. Relations of PGA amplification factor to PGA: a) FKSH14, to PGA at the surface, b)
FKSH14, to PGA at the borehole, c) IBRH13, to PGA at the surface, d) IBRH13, to PGA at theborehole, e) IBRH18, to PGA at the surface, f) IBRH18, to PGA at the borehole.
4.2 Change of Spectral Ratio Curve due to Non-Linearity
We calculated (1) the spectral ratio of surface records to the corresponding one recorded at theborehole bottom (surface/borehole or S/B), (2) the ratio of a horizontal component at the surface to avertical component at the surface (S-H/V) and (3) the ratio of these spectral ratios of a strong groundmotion to that of a weak ground motion in order to observe the degree of nonlinear behavior, or DNLs.

Examples are shown in Figure 2. In Figure 2, the records at FKSH14 due to Event 2 (Mw=9.0) andEvent 14 (M=4.4) are compared as examples to explain the procedure of this analysis. In panels a) andd) the spectral ratios (surface/borehole) of Event 2 and 14 are shown with solid curves, respectively,
while the dotted curve shows that of Event 15 (M=4.4), i.e., the reference event in this study.
For a linear response case, panel d) shows the solid curve almost identical to the dotted curve.
DNL SB of the panel d) is 2.107. Panel e) shows the spectral ratio (S-H/V) and its quite similar tendency
as panel d) with DNL S-H/V 2.862. The solid curve of panel f) shows the ratio of the spectral ratio(surface/borehole) of Event 14 to that of Event 15 shown by the solid and dotted curves in panel d),respectively. Due to the similarity of these ones, the solid curve in the panel f) deviates around 1.0. A
similar procedure is taken to draw the dotted curve in panel f) from the solid and dotted curves in panele).
For a non-linear response case, panel a) shows a significant reduction of amplification and thepeak shift toward lower frequency for the solid curve (Event 2) in comparison with the dotted curve(Event 15). DNL SB of panel a) is calculated to be 8.179. Panel b) shows the spectral ratio (S-H/V),
which shows a quite similar tendency as that of panel a). DNL S-H/V of panel b) is calculated to be 8.052.
In panels a) and b) the difference between the solid and dotted curves appear in the frequency range
from 1 Hz to 3Hz and 5Hz to 15Hz. This is reflected to panel c). The solid curve in panel c) shows
the ratio of the spectral ratio (surface/borehole) of Event 2 to that of Event 15 shown by the solid anddotted curves in panel a), respectively. Due to the strong non-linearity, the solid curve in the panel c)has a systematic decay from 1.0 in the above mentioned frequency range. A similar procedure is taken
to draw the dotted curves in panel c) from the solid and dotted curves in the panel b).
The behavior of the dotted curves in panels c) and f) is quite similar to that of thecorresponding solid curves and shows a possibility to use the spectral ratio S-H/V in place of thespectral ratio (surface/borehole).The same procedure as these examples is applied for all other eventsand for all stations. The result will be described in the following.
Surface/Borehole

S-H/VStrong/WeakFigure 2. Example of change of spectral ratios at FKSH14 due to Event 2: a) Spectral ratio(surface/borehole), b) Spectral ratio (S-H/V), c) Ratio of spectral ratios (strong/weak). Those due toEvent 14: d) Spectral ratio (surface/borehole), e) Spectral ratio (S-H/V), f) Ratio of spectral ratios(strong/weak).

4.3 Degree of Non-Linearity: DNL SB and DNL S-H/V
We compared the relation of DNLs to PGA at the ground surface and at the borehole bottom in orderto confirm the influence of nonlinear site responses on the strong motion (Figure 3).
It is observed that DNL SB increases with the PGA both at the ground surface and the boreholebottom in the range PGA (surface) bigger than 100 gals and PGA (borehole) bigger than 10 gals. The
behaviors of FKSH14, IBRH13 and IBRH18 look similar. Below this threshold, any clear trend
cannot be found. It is also observed that DNL S-H/V follows the change of DNL SB . Above the thresholdmentioned, DNL S-H/V takes close value of DNL SB , whereas below it DNL S-H/V tends to differ fromDNL SB . This may be due to a fluctuation of observed spectra or other disturbance.
Figure 3 shows a clear relation of DNLs to PGAs and possibility to use DNL S-H/V in place ofDNL SB above the threshold value of PGA (surface) bigger than 100 gals.

abcde

f

Figure 3. Relation of DNLs to PGA: a) FKSH14, to PGA at the surface, b) FKSH14, to PGA at theborehole, c) IBRH13, to PGA at the surface, d) IBRH13, to PGA at the borehole, e) IBRH18, to PGA
at the surface, f) IBRH18, to PGA at the borehole.

5. DISCUSSION AND CONCLUSIONS
We have conducted a case study for DNLs recently proposed by Noguchi and Sasatani (2010). The
data are used the accelerograms of the 2011 off the Pacific coast of Tohoku earthquake (Mw=9.0) and
its aftershocks, mainly, recorded at three KiK-Net stations in Fukushima and Ibaraki Prefectures:
FKSH14 sandy site; IBRH13 weathering rock site; and IBRH18 sand and gravel site. In FKSH14 andIBRH13, smaller PGA amplification corresponds to bigger PGA at the ground surface and also at theborehole bottom. Namely, a significant de-amplification of the strong motion is observed in the rangeof PGA at borehole bottom greater than 10 gals; also in the range of PGA at the ground surface greaterthan 100 gals, whereas in IBRH18 de-amplification is not observed with the only exception, i.e., themain shock (Event 2).
It is observed that DNLs increases with the PGA both at the ground surface and boreholebottom in the range of PGA at the ground surface bigger than 100 gals and PGA at the boreholebottom bigger than 10 gals. The behaviors of FKSH14, IBRH13 and IBRH18 look similar. Below thisthreshold, any clear trend cannot be found.
S−H/v

S−H/V

For the above two, DNL S-H/V well follows DNL SB . The curve R strong (f)�R weak (f) fits well to theSBcurve RSBstrong (f)�Rweak (f). This shows a possibility to use the former in place of the latter when only
surface records are available.
All these results of analysis support Noguchi and Sasatani (2010). We may expect thatDNLs and methods of Noguchi and Sasatani (2010) will be useful for the future strong motion study inMyanmar.
Nonlinear site effect is one of the key issues to investigate past ground shakings and toestimate future ones. It is a common sense that a detailed study of underground structures is necessary
to improve the understanding of nonlinear site effects which is indispensable for the earthquake hazard
and risk assessment and further earthquake disaster mitigation. The current strong motion observation
in Myanmar, however, has accelerographs on the ground surface only. A way to estimate nonlinear
behaviors of shallow soil layers using only records obtained at the ground surface is desired. In thisstudy, we analyzed nonlinear site effects of a strong ground motion obtained by the KiK-net verticalarray, by checking the relation between the site responses and the strength of a ground motion. A trendthat is not very clear but visible is observed in the plots of DNLs against PGA amplification and thoseagainst PGA at the surface. These may allow us to estimate, roughly, PGA at the engineering bedrockfrom the data obtained at the ground surface.
Nowadays, Myanmar is planning to improve new seismic stations. So, I hope that seismic
data of Myanmar can be used to investigate nonlinear site effects of a strong ground motion, after
installation of new seismic stations.

AKNOWLEDGEMENT
I am sincerely thankful to the National Research Institute for Earth Science and Disaster Prevention(NEID), Japan for providing the waveform data for my study and to Dr. Toshihide Kashima (IISEE,BRI) for the software View Wave.
REFERENCES
Noguchi, S. and Sasatani, T., 2008, Proc. of 14th WCEE.
Noguchi, S., and Sasatani, T., 2010, Proc. of 13th Japan Earthquake Engineering Symposium, PS3.
Wen, K., et al. (2006), Terrestrial Atmospheric and Ocean Sciences, 17, 533-546.
Kashima, T., 2009, View Wave software (version 1.56),
http://iisee.kenken.go.jp/staff/kashima/software_e.html
KIK-NET web site, http://www.kik.bosai.go.jp/kik/index_en.shtml