Pure appl. geophys. 165 (2008) 1–24
DOI 10.1007/s00024-008-0401-1

 Birkhäuser Verlag, Basel, 2008

Pure and Applied Geophysics

Characteristics of Soil Response in Near-Fault Zones during the 1999
Chi-Chi, Taiwan, Earthquake
O. V. PAVLENKO

Abstract—Distribution of parameters characterizing soil response during the 1999 Chi-Chi, Taiwan,
earthquake (Mw = 7.6) around the fault plane is studied. The results of stochastic finite-fault simulations
performed in PAVLENKO and WEN (2008) and constructed models of soil behavior at 31 soil sites were used forthe estimation of amplification of seismic waves in soil layers, average stresses, strains, and shear moduli
reduction in the upper 30 m of soil, as well as nonlinear components of soil response during the Chi-Chi
earthquake. Amplification factors were found to increase with increasing distance from the fault (or, withdecreasing the level of ‘‘input’’ motion to soil layers), whereas average stresses and strains, shear moduli
reduction, and nonlinear components of soil response decrease with distance as *r -1. The area of strong
nonlinearity, where soil behavior is substantially nonlinear (the content of nonlinear components in soil
response is more than *40–50% of the intensity of the response), and spectra of oscillations on the surface
take the smoothed form close to E(f) * f -n, is located within *20–25 km from the fault plane (*1/4 of its
length). Nonlinearity decreases with increasing distance from the fault, and at *40–50 km from the fault(* 1/2 of the fault length), soil response becomes virtually linear. Comparing soil behavior in near-fault
zones during the 1999 Chi-Chi, the 1995 Kobe (Mw = 6.8), and the 2000 Tottori (Japan) (Mw = 6.7)
earthquakes, we found similarity in the behavior of similar soils and predominance of the hard type of soil
behavior. Resonant phenomena in upper soil layers were observed at many studied sites; however, during the
Chi-Chi earthquake they involved deeper layers (down to *40–60 m) than during lesser-magnitude Kobe andTottori earthquakes.
Key words: The 1999 Chi-Chi earthquake, nonlinear soil behavior, seismic wave amplification, stresses,
strains, shear moduli reduction, nonlinear components of soil response.

1. Introduction
The Chi-Chi earthquake (Mw = 7.6) that occurred in central Taiwan on September 21,
1999 was recorded by more than 400 strong motion devices island-wide. The majority ofnear-fault records were obtained at soil sites, and at present they apparently represent themost complete database allowing a study of soil behavior during a strong earthquake innear-fault zones at various distances from the fault.

Institute of Physics of the Earth, Russian Academy of Sciences, B. Gruzinskaya 10, Moscow 123995,
Russia. E-mail: olga@ifz.ru
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In the paper by PAVLENKO and WEN (2008) we simulated acceleration time historiesof the Chi-Chi earthquake at rock and soil sites and constructed models of the behaviorof upper *80 m of soil at 31 soil sites located within *50 km from the fault. At sevensites, such as, TCU065, TCU072, TCU138, CHY026, CHY104, CHY074, and CHY015,
information on the profiling data down to *70–140 m was available. For the othertwenty four sites, the profiling data were known down to *30–40 m, and to constructmodels of soil behavior, we assumed approximate values of the profiling parameters at
depths of *30–80 m based on shallow S-wave velocity structures obtained by LIN et al.
(2006) for western Taiwan (PAVLENKO and WEN, 2008). To construct models of soil
behavior, we used a method similar to that developed for the estimation of soil behavior
based on vertical array records (PAVLENKO and IRIKURA, 2003; 2006). As input for soil
layers, we used acceleration time histories of the Chi-Chi earthquake, simulated bystochastic finite-fault modeling with a slip distribution over the fault plane obtained by
CHI et al. (2001). First, we simulated the acceleration time histories of the Chi-Chi
earthquake at 18 rock sites, and comparing them with the observed ones, calibrated thecalculation program, i.e., found input parameters for the stochastic simulation, such as,parameters of radiation of seismic waves from the source and parameters of theirpropagation: Geometrical spreading, Q(f), kappa operator describing additional attenuation of the spectra, parameters defining the shape of the time window and someothers. The earthquake source (119 km by 35 km) was represented as a set of 85
subfaults of 7 km by 7 km. At the second stage, we simulated acceleration time
histories at soil sites, at the bottoms of soil layers. These signals were used as ‘‘inputs’’to soil layers, i.e., prescribed motion at the base of soil columns (that is, we assumed
infinity rigidity in the underlying medium). The technique and the constructed models
of soil behavior at 31 soil sites are described in detail in PAVLENKO and WEN (2008). The
models represent vertical distributions of hysteretic relations of stresses and strains,
induced in the upper tens of meters of soil and changing in time during the strong
motion.
Models of soil behavior are constructed for 31 soil sites located at various distancesfrom the fault plane within a wide range of azimuthal directions, and they allow us toobtain a general representation of soil behavior during the Chi-Chi earthquake. With
these models, we can investigate some regularities in soil behavior during a strong
earthquake at various distances from the fault plane.
In this paper, the constructed models of soil behavior are applied to estimate someparameters, characterizing soil response during the Chi-Chi earthquake, such as,
amplification of seismic waves by soil layers, stresses and strains induced by the strong
motion in soil layers at different depths, reduction of shear moduli in soil layers due tostrong motion, and nonlinear components of soil response. The distribution of theseparameters around the fault plane is analyzed.
As shown in the paper by PAVLENKO and WEN (2008), soil behavior during the Chi-Chi
earthquake was essentially nonlinear in the near-fault zones, and in this paper, theinfluence of nonlinearity of soil response on the studied parameters is discussed.
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2. Data and Methods
In this paper, numerical models of soil behavior during the Chi-Chi earthquake at 31
soil sites are used that were constructed and described in PAVLENKO and WEN (2008).
Figure 1 shows the locations of the studied soil sites, identifies liquefaction zones, andthe area of basin-induced surface waves. Information on the soil sites, such as, thedistances to the fault plane and site classification according to LEE et al. (2001), as well as
estimated parameters of soil response, are given in Table 1. Seven sites, such as,
TCU065, TCU072, TCU138, CHY026, CHY104, CHY074, and CHY015, for which

Figure 1
Locations of the studied soil sites around the fault plane of the Chi-Chi earthquake. Dotted lines indicate areas
showing signs of soil liquefaction; area of basin-induced surface waves is marked by gray color.
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Table 1
Characteristics of soil response at 31 soil sites during the 1999 Chi-Chi earthquake
Station
Code

r, km

Vs-30, m/sFaFv

s30, Pa

c30, 10-5

DG/Gmax-30, %Nl, %Site Class(LEE et al., 2001)

CHY101
TCU110
TCU116
TCU138
TCU082
CHY025
TCU054
TCU065
CHY036
TCU102
CHY092
CHY104
TCU115
CHY074
TCU072
CHY002
CHY026
TCU033
CHY039
CHY094
CHY032
CHY015
CHY082
TCU017
CHY027
CHY033
CHY004
CHY093
CHY055
CHY044
CHY012

1.9
2.4
3.4
3.8
5.7
5.9
6.1
6.9
7.5
7.8
9.5
9.5
11.4
12.8
14.9
15.0
16.1
16.9
20.8
24.9
25.6
25.9
26.6
29.7
32.1
33.6
38.2
41.2
41.5
43.0
46.6

260
207
483
605
478
277
454
300
282
735
260
225
190
546
563
231
226
448
198
227
202
234
209
601
221
194
279
199
240
193
202

1.5
0.7
1.0
1.1
1.0
1.2
1.1
2.5
2.4
1.4
1.3
2.2
1.4
1.6
2.7
1.9
1.2
2.3
2.0
1.6
3.1
2.2
2.2
2.2
3.9
3.0
2.8
2.8
3.7
3.0
3.5

2.0
2.9
1.8
1.6
1.7
2.7
1.7
2.9
2.1
2.2
2.5
2.9
3.1
2.1
2.1
2.6
2.0
1.9
2.2
2.7
3.2
2.6
3.0
2.3
3.4
3.6
3.0
3.4
3.0
2.9
2.8

1817
1013
852
2140
1162
1487
1494
1677
1995
2325
440
1435
654
1824
3481
420
530
1642
450
1048
780
361
211
227
645
970
1342
1145
1234
576
276

18.0
32.0
0.3
0.54
0.3
11.5
0.8
9.3
9.6
3.4
1.2
5.7
17.0
3.5
6.2
0.7
8.0
0.5
5.8
4.1
2.9
1.0
0.8
0.2
4.9
5.3
3.5
4.7
3.8
2.2
1.0

81
46
32
10
15
41
21
63
73
51
37
13
34
44
37
16
22
12
86
9
9
19
13
28
13
7
7
5
5
5
2

75
57
16
24
15
62
11
54
61
56
11
28
50
25
48
28
33
22
27
16
33
31
25
8
24
13
11
11
12
30
28

D
E
E
D
D
E
D
D
D
D
E
E
E
C
D
E
E
D
E
E
E
D
E
?
E
E
E
E
E
E
E

more complete information on the profiling data down to *70–140 m was available, aremarked by bold face.
Parameters, characterizing soil response during the Chi-Chi earthquake, were
estimated based on the constructed models of soil behavior. Four groups of parameters
were studied, such as, (1) characteristics of amplification of seismic waves by soil layers;(2) stresses and strains induced in soil layers by the Chi-Chi earthquake; (3) reduction ofshear moduli in soil layers due to strong motion; and (4) contents of nonlinear
components in soil response.
Coefficients of amplification of seismic waves by soil layers represent the ratio of theintensity of an observed ground motion to a reference value of that intensity for aparticular site condition (intact rock or rock-average). In this paper, amplification factors
were estimated separately for acceleration and velocity (from accelerograms andJournal : 24

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Characteristics of Soil Response

5velocigrams) as the ratios of root mean-square (rms) accelerations and velocities on thesurfaces and at the bottoms of soil thicknesses. Values of rms accelerations and velocities
were calculated for 50-second time intervals of strong motion; estimates obtained for NS
and EW components averaged. Amplification was estimated for the same acceleration
time histories that were previously used for constructing models of soil behavior (whichwere taken as one of the series of accelerograms calculated by the stochastic method).
Accelerograms of the Chi-Chi earthquake possess a fairly uniform intensity during thestrong motion, and rms values should give us rather reliable estimates of the square roots of
the ratios of intensities of oscillations on the surfaces and at the bottoms of soil layers. The
selected 50-second time intervals correspond to the largest duration of records, observed atsouthern stations (as mentioned in the paper by PAVLENKO and WEN (2008), directivity
effects are clearly seen as decreased durations of acceleration time histories in forward(northern) directions and increased durations in backward (southern) directions; eastern
and western directions represent intermediate cases). At stations, located to the north, east
and west of the fault plane, the duration of records is smaller, however, these differences (aswell as the increase of duration with distance) can only slightly influence amplification
estimates, because the ratios are taken of rms values of oscillations on the surfaces and at
the bottoms of soil layers. Generation of surface basin waves does not change our estimatesof amplification, because the estimates are based on the simulated records on the surfaces
and at the bottoms of soil layers and basin waves are not simulated in our one-dimensional
problem. In this work, the dependence of amplification on frequency is not studied, because
the nonlinearity of soil response was high in near-fault zones and quickly decreased withthe distance from the fault. Nonlinear effects change the dependences of amplification
coefficients on frequency, and analysis of frequency-dependent amplification would becomplicated. We will likely study this problem in the future. Since amplification factors are
considered to be functions of the amplitude of shaking, their dependencies on the distancefrom the fault plane (i.e., on the level of input motion) are studied.
Maximum and average (averaged over the duration of the strong motion) stresses andstrains induced by the strong motion in soil layers were estimated. To obtain theseestimates, at each site, for each soil layer, maximum (during the strong motion) stresses
and strains were found; to find their average estimates, absolute values of ‘‘limiting’’ (forloading and unloading cycles) stresses and strains corresponding to final points of loading
and unloading on the hysteretic curves were averaged for each site and for each soil layer;
then, averaging was performed over two horizontal components, NS and EW. Averagevalues of stresses and strains were estimated for the upper 30 m of soil mostrepresentative from the viewpoint of engineering seismology.
Shear moduli reduction values were assessed for soil layers within the upper 30 m in thefollowing way. For each site, average shear moduli were calculated as the ratios of stresses
and strains averaged in time (over the strong motion duration), in depth (over the upper30 m), and over two horizontal components; stresses and strains were taken as theirabsolute values corresponding to final points of loading and unloading cycles of thehysteretic curves. Shear moduli reduction was calculated as the difference between
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O.V. Pavlenko

Pure appl. geophys.,maximum values of shear moduli, calculated within small time intervals at the
beginning parts of the strong motion records, and their average values, normalized by
the average values and expressed in percent. As mentioned in PAVLENKO and WEN (2008),
due to averaging and smoothing of the models of soil behavior, the obtained shear
moduli reduction values could be slightly underestimated. At sites where soil behavior was
not adequately simulated in the middle and final parts of the strong motion because of basin
effects (Fig. 1), shear moduli reduction estimates should be treated as very approximate.
To estimate the contents of nonlinear components in soil response, methods ofnonlinear system identification and the white-noise approach (MARMARELIS and
MARMARELIS, 1978) were applied. Application of these methods to seismic data analysis
is described in PAVLENKO (2001) and PAVLENKO and IRIKURA (2005). In system analysis,
the nonlinear identification of a system implies determination of linear and nonlinear
domains of the system response and construction of such a mathematical model of asystem that its seismic response coincides with the response of the real physical system.
Soil profiles can be represented as nonlinear systems, transforming input seismic signals
into the ground response. The quickest and most effective method for nonlinear system
identification is testing the studied system with the Gaussian white noise and calculating
the Wiener kernels. If an input is the Gaussian white noise, an output can be represented
as the Wiener series (MARMARELIS and MARMARELIS, 1978):1XyðtÞ ¼Gm ½hm ðs1 ; . . .; sm Þ; xðt0 Þ; t0  t;
ð1Þ
m¼0

where Gm are orthogonal functionals, if x(t) is the Gaussian white noise with a zeromean, {hm(s1,…,sm)} is a sequence of the Wiener kernels, and s1,…,sm are time delays.
The first four Wiener functionals are:G0 ½h0 ; xðtÞ ¼ h0 ;G1 ½h1 ; xðtÞ ¼

Z1

ð2Þ

h1 ðsÞxðt  sÞ ds;

ð3Þ

0

G2 ½h2 ; xðtÞ ¼

Z Z1

h2 ðs1 ; s2 Þxðt  s1 Þxðt  s2 Þ ds1 ds2  P

0G3 ½h3 ; xðtÞ ¼

Z1

h2 ðs1 ; s1 Þ ds1 ;ð4Þ

0Z Z1 Zh3 ðs1 ; s2 ; s3 Þxðt  s1 Þxðt  s2 Þxðt  s3 Þ ds1 ds2 ds3

0

 3P

Z Z1

ð5Þ
h3 ðs1 ; s2 ; s2 Þxðt  s1 Þds1 ds2 ;0where s is time delay, P is the intensity of the Gaussian white noise not depending on
frequency.
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Terms in the Wiener series are orthogonal with respect to the input signal in the formof the Gaussian white noise, so the Wiener kernels can be determined mutuallyindependent. Effective methods can be used in estimating the Wiener kernels, based ondetermination of cross-correlation functions, and knowledge of a limited number of thesekernels allows the best approximation for a real system from the viewpoint of theminimal mean square error (MARMARELIS and MARMARELIS, 1978). By analogy with an
ordinary impulse characteristic h(t), the series of the Wiener kernels {hm} can be treatedas a generalized, composed impulse characteristic of a nonlinear system. The first-orderkernel defines the linear part of the system response, whereas higher-order kernels
describe nonlinear corrections related to quadratic, cubic, and higher-order nonlinearitiesof the system. The nonlinear corrections express interactions between the values of the
input signal in the past with respect to their influence on the response at present.
Analyzing the nonlinear components in the output, we can judge regarding the types andquantitative characteristics of the system nonlinearity: If the second Wiener functional G2
provides the largest contribution to the system response, the system possesses mostly
quadratic nonlinearity; if the third functional G3 contributes more, the system is cubic
nonlinear, etc. (MARMARELIS and MARMARELIS, 1978).
Knowledge of stress–strain relations in soil layers in strong ground motion allows
calculation of the propagation of testing signals in the studied soil profiles and thenonlinear identification of the soil behavior (PAVLENKO, 2001). Thus, to estimate
nonlinear components of soil response, soil profiles were tested by the Gaussian white
noise, and estimates of the zero-, first-, second-, and third-order Wiener kernels wereconstructed based on input and output signals of 500,000 points of duration (more than
40 minutes). Since Wiener kernels and functionals depend on the intensity of an input
signal P, the intensity of testing noise signals was chosen so that average stresses andstrains induced in soil layers during the propagation of testing signals were close to thoseinduced in the layers by seismic waves from the Chi-Chi earthquake. Based on theestimated Wiener kernels, the response of the linear model and nonlinear corrections
accounting for quadratic and cubic nonlinearities of soil response was constructedaccording to formulas (3)–(5). Zero-order Wiener kernels h0 describe quasi-static
deformations of the surface (related to even-order nonlinearities); they can be interpreted
as a result of accumulation of residual shift deformations on the surface (ZVOLINSKII,
1982). They were evaluated as constant parts of soil response; the obtained estimates
were averaged over NS and EW components.
Nonlinear components were estimated in percent of the intensity of soil response. The
entire nonlinear component of soil response was estimated as the deviation of the real soil
response from the response of the linear model constructed by zero- and first-orderkernels. The nonlinear quadratic and cubic components were estimated as nonlinear
corrections due to quadratic and cubic nonlinearities predicted by kernels {h2} and {h3},respectively. Then the residual part of the soil response was estimated, which is related tohigher-order (4th-, 5th-, etc.) nonlinearities, as well as to inaccuracies in estimating
kernels (MARMARELIS and MARMARELIS, 1978; PAVLENKO, 2001).
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O.V. Pavlenko

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In this paper, the dependence of the above described parameters of soil response
during the Chi-Chi earthquake on the distance from the fault plane is analyzed. All
studied soil sites are located in near-fault zones, and their distances from the fault plane
are comparable with the fault length. Generally speaking, two values can be considered as
the distance of a site from the earthquake source, such as, the shortest distance of a sitefrom the fault plane and the average distance of a site from all subfaults of the fault plane(or weighted average distance with weights being proportional to subfault radiation
intensities). It was found that the dependencies of the studied parameters on their distancefrom the source can be approximated by power functions, and these approximations are
more exact (scattering of the obtained estimates is smaller), when we define ‘‘distancefrom the source’’ as the shortest distance of a site from the fault plane. Therefore, later on
distance from the fault r designates the shortest distance of a site from the fault plane.
Inaccuracies in the obtained estimates of soil response parameters are mainly caused
by deviations of the constructed models of soil behavior from real soil behavior, byinaccuracies in the profiling data, and by errors in the obtained estimates of the Wiener
kernels and functionals.

3. Results
Table 1 summarizes information of the studied soil sites (closest distances to the fault
plane, average S-wave velocities in the upper 30 m of soil, Vs-30, site classificationaccording to LEE et al. (2001) and the obtained estimates of soil response parameters,such as amplification factors for acceleration and velocity, average stresses, strains, andshear moduli reduction in the upper 30 m of soil, as well as the contents of nonlinear
components in soil response.
As seen from the Table, the majority of sites (22 sites) possesses soft soils in theupper 30 m: Vs-30 is less than 300 m/s, whereas at the other 9 sites possessing denser
subsurface soils Vs-30 varies within 448–735 m/s. Thus in many cases it was foundreasonable to consider separately these two groups of sites, such as sites with ‘‘softer’’subsurface soils (Vs-30 B 300 m/s) and sites with ‘‘harder’’ subsurface soils (Vs30 C 450 m/s). Simultaneously, the whole number of the studied sites is not large andvirtually all of them are located in valleys to the west of the fault, so that further divisionof them into smaller groups considering the age and composition of soil layers is notreasonable.
3.1. Ampliﬁcation of Seismic Waves in Subsurface Soils in Near-Fault Zones during
the Chi-Chi Earthquake
The constructed models of soil behavior allowed a rather detailed study of
amplification of seismic waves by subsurface soils during strong ground motion.
Amplification factors were estimated for acceleration and velocity (Fa and Fv); the results
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are presented in Figure 2 and in Table 1. In Figure 2, in the upper raw, the distributionsof root-mean-square accelerations at the ‘‘inputs’’ to soil layers arms are shown (Fig. 2a),as well as amplification of seismic waves by soil layers for acceleration Fa (Fig. 2b),and Vs-30 (Fig. 2c). Below, there are plots showing the obtained estimates of rootmean-square accelerations and velocities arms and vrms (Fig. 2d) and amplification factors
for acceleration and velocity, Fa and Fv (Fig. 2e), as functions of the distance from thefault; their approximations by power and linear functions are also shown. In the lower
row, we can see the dependencies of the obtained amplification factors on the level of‘‘input’’ motion to soil layers (i.e., on arms and vrms, respectively) (Fig. 2f) and on Vs-30(Fig. 2g), as well as the dependency of rms accelerations on the surfaces (arms)S on rms
accelerations at the bottoms of soil layers arms (Fig. 2h). Thus, the obtained results allow
us to analyze the influence of various factors on the values of amplification of seismic
waves by soil layers.

Figure 2Upper raw: distribution around the fault plane of (a) – ‘‘input’’ motion to soil layers (rms accelerations at thebottoms of soil layers) arms, (b) – factors of amplification of seismic waves by soil layers for acceleration Fa,(c) – average S-wave velocities in the upper 30 m VS-30. Lower raw: (d) – ‘‘input’’ motion to soil layers arms,(e) – amplification factors for acceleration and velocity Fa and Fv as functions of the distance from the fault.
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Values of arms and vrms decrease with increasing distance from the fault plane as *r -1(Fig. 2d), which corresponds to theoretical decrease of amplitudes due to geometricalspreading. Amplification factors Fa and Fv are greater than 1 and smaller than 4 forvirtually all the sites (Fig. 2b, e-g; Table 1). As seen from the figures, amplification
increases with distance (Fig. 2d), i.e., with decreasing amplitudes of ‘‘inputs’’ to soil
layers, arms, which is clearer for acceleration than for velocity. Linear functions can beused as approximating ones, however, scattering of the obtained estimates around linear
regression lines is rather large, and it can be due to different factors.
As known, three main mechanisms of seismic wave transformation in subsurface soils
are: (1) Transition of seismic waves to upper soil layers with (usually) smaller values of
Vs-30 and density, q, leading to amplification of seismic oscillations according to energy
conservation law, (2) resonant phenomena the upper softer soil layers also leading to
amplification, (3) nonlinearity of soil response, often leading to de-amplification ofseismic oscillations.
To evaluate the influence of different mechanisms on amplification of seismic waves
in soil layers during the Chi-Chi earthquake, let us consider separately sites with‘‘softer’’ and ‘‘harder’’ subsurface soils (in Figs. 2e–g they are shown by points andcircles, respectively). As seen from the figure, amplification factors for acceleration, Fa,at ‘‘softer’’ and ‘‘harder’’ soil sites are close to each other, and can be approximated by
the same function of the distance from the fault (or of the level of ‘‘input’’ motion),whereas, amplification factors for velocity, Fv, are substantially smaller at ‘‘harder’’subsurface soils than at ‘‘softer’’ soils. This is clearly seen from Figure 2f and agrees
with seismological observations that ‘‘peak ground velocity and displacement show
higher amplifications for soil sites than for rock sites (in our case, softer soil sites andharder soil sites), while peak ground acceleration is roughly independent of the siteclassification’’ (AKI and IRIKURA, 1991) (that is, does not show higher amplification at
soft soil sites).
The obtained results are in a good agreement with the dependencies of amplification
factors on the intensity of ground motion and on average S-wave velocities in upper 30 mof soil described in the paper by STEWART et al. (2001). The authors discuss generalregularities of reduction of amplification factors with increasing Vs-30 or reference motion
amplitude, obtained by various researchers for various strong earthquakes. Preliminary
data on the 1999 Chi-Chi earthquake, obtained by STEWART et al., are also in agreementwith the results of this work (Fig. 2g).
The observed dependencies of amplification factors on the level of ‘‘input’’ motion tosoil layers is evidently due to the influence of nonlinearity of soil response, which is higher
closest to the fault sites. At rather long distances from the fault (*40–50 km),amplification factors Fa and Fv are close to each other (Fig. 2e), whereas at short distances,nonlinearity of soil response substantially decreases amplification for acceleration and, toa lesser extent, for velocity. This can be due to nonlinear transformations of seismic waves
propagating in soil layers: Their spectra tend to take the form E(f) * f –n, when the highand medium-frequency spectral components are decreased and the low-frequency
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components remain virtually at the same level. Obviously, the effect is stronger for
accelerations than for velocities and displacements.
In the paper by PAVLENKO and WEN (2008), it was concluded that at the majority ofsoil sites, soil behavior during the Chi-Chi earthquake was defined by resonant
oscillations induced in soil layers (in the upper 40–60 m) during strong motion and by
nonlinearity of soil response.
At near-fault sites, subsurface water-saturated sandy soils possess hard-type
nonlinearity, where de-amplification of seismic oscillations due to nonlinear damping
can be rather small, because: (1) Stresses in soil layers rapidly increase at large strains(especially, in near-fault zones) due to pore-pressure build-up (and therefore, accelerations also increase); (2) nonlinear damping (which is proportional to areas within
hysteretic curves) can be rather small, as at TCU065 site, for example (PAVLENKO and
WEN, 2008). As a consequence, in near-fault zones in sandy water-saturated soils
possessing hard-type nonlinearity, de-amplification of seismic oscillations due tononlinearity often cannot compensate their amplification stipulated by the other two(linear) mechanisms; as a whole, we observe amplification of oscillations on the surface.
This is clearly seen, for example, in vertical array records of the 1995 Kobe earthquake at
SGK site: in the upper *11 m of sandy soils possessing hard-type nonlinearity seismic
oscillations were noticeably amplified, peak accelerations increased from 0.2–0.3 g at
depths of *25 m and 100 m up to *0.7 g on the surface. At the same time at the Port
Island site, liquefied surface soils possessing soft-type nonlinearity substantially deamplified seismic oscillations, especially their high-frequency components; peakaccelerations at 83 m, 32 m, 16 m, and on the surface were almost similar, *0.4–
0.5 g (PAVLENKO and IRIKURA, 2003).
Thus, amplification factors can be rather large even in cases of strong nonlinearity (athigh levels of ‘‘input’’ motion, in near-fault zones) at sites possessing hard-type
nonlinearity of subsurface soils, which is clearly seen in Figure 2b: at TCU065 andTCU072 sites located very close to the fault plane, amplification factors are rather high,Fa * 2.5–2.7.
Figure 2h shows the obtained estimates of rms accelerations on the surfaces of soil,(arms)S, versus estimates of rms accelerations at the bottoms of soil layers, arms. This
figure can be compared to the well-known findings of Idriss (1990), such as, plots peakground acceleration (PHA) on rock versus PHA on soft soil (accounting for the fact thatpeak accelerations correlate well with rms accelerations, at least, in the case of the ChiChi earthquake). As a whole, the dependence shown in Figure 2h agrees well withIdriss’s data, but two points with increased (arms)S values attract attention, whichcorrespond to TCU065 and TCU072 sites, where subsurface soils possess strong hardtype nonlinear behavior. Our previous experience in studying soil behavior during strong
earthquakes shows that we can mostly find areas in the closest vicinities of the fault
plane, where soils possess such behavior.
Amplification of oscillations on the surface resulting from resonant phenomena insubsurface soils and hard-type soil nonlinearity are also observed at other near-fault sites,
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such as, CHY101 (Fa * 1.5), CHY036 (Fa * 2.4), TCU102 (Fa * 1.4), CHY104(Fa * 2.2), TCU115 (Fa * 1.4), CHY074 (Fa * 1.6), CHY002 (Fa * 1.9), etc.
‘‘Hard’’ character of soil response nonlinearity virtually disappears at distances ofmore than *12–15 km from the fault plane (PAVLENKO and WEN, 2008), because of thedecrease of ‘‘input’’ motion intensity. At rather long distances from the fault,
amplification of seismic oscillations results from the two above described linear
mechanisms; whereas nonlinear effects decrease with distance and can no longer
effectively de-amplify seismic oscillations.
3.2. Stresses and Strains Induced in Soil Layers in Near-Fault Zones During
the Chi-Chi Earthquake
Analyzing stresses and strains induced in soil layers by the Chi-Chi earthquake, it
is also reasonable to distinguish sites with ‘‘softer’’ (Vs-30 B 300 m/s) and ‘‘harder’’(Vs-30 C 450 m/s) subsurface soils. Figure 3 represents estimated average (upper rows)
and maximum (lower rows) stresses and strains induced in soil layers at the studied sites
during the Chi-Chi earthquake. Names of sites possessing ‘‘harder’’ subsurface soils areunderlined. We can see from the figures that closest to the fault plane sites (within*20 km from the fault), resonant phenomena are observed in the upper soft soil layers(down to *40–60 m), i.e., trapping of seismic waves due to the impedance contrast
between softer and neighboring denser layers. Stresses in soil layers increased with depth,
whereas maximum strains usually occurred in the upper 15–40 m of soil (Fig. 3).
At sites where soft surface layers with Vs-30 B 300 m/s were underlayed by denser
layers, and impedance contrast was higher, resonant phenomena were more pronounced.
Maximum strains were achieved closest to the fault plane sites, such as, TCU065,
TCU110, TCU115, CHY101 (*0.6–0.8%), CHY025, and CHY036 (*0.4–0.6%). At
other sites maximum strains in soil layers did not exceed *0.1–0.4%. In the paper by
PAVLENKO and WEN (2008), it is concluded that liquefaction phenomena occurred at
TCU065, TCU110, TCU115, CHY101, CHY036, and CHY039 sites.
The obtained estimates of average stresses and strains induced in the upper 30 m ofsoil during the strong motion, s30 and c30, are given in Table 1, and the distributions ofthese parameters around the fault plane are shown in Figure 4a and 4b. As seen from thefigures, areas of softer subsurface soils with Vs-30 B 300 m/s in Bajada, to the west of thefault, correspond to zones of decreased stresses and increased strains.
Average stresses and strains in the upper 30 m of soil, s30 and c30, are shown asfunctions of the distance from the fault (Fig. 4d) and as functions of the level of ‘‘input’’
motion to soil layers, rms accelerations arms (Fig. 4f). At sites with ‘‘softer’’ subsurface
soils (shown by points in the figures), average stresses and strains decrease with distance(in Fig. 4d, the corresponding approximations by functions *r -1 are shown), and they
increase with the level of ‘‘input’’ motion, however scattering of estimates aroundapproximating linear functions is rather large. At sites possessing ‘‘harder’’ subsurface
soils, average stresses and strains (shown by circles) deviate from power functions andJournal : 24

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Figure 3
Estimated average (upper rows) and maximum (lower rows) stresses (dash lines) and strains (solid lines),
induced in soil layers during the Chi-Chi earthquake. Stations possessing ‘‘harder’’ subsurface soils areunderlined.

Figure 4Upper raw: distribution around the fault plane of (a) – average stresses in the upper 30 m of soil s30, (b) –average strains in the upper 30 m of soil c30, (c) – estimates of shear moduli reduction in the upper 30 m of soil
DG/Gmax-30 (dotted lines indicate areas showing signs of soil liquefaction). Lower raw: (d) – average stressess30, (e) – average strains c30, (f) – estimates of shear moduli reduction DG/Gmax-30 as functions of the distancefrom the fault.

appreciably increase scattering. At these sites, average stresses are higher and averagestrains are lower than at sites with ‘‘softer’’ subsurface soils.
Evidently, average stresses and strains in the upper soil layers depend on the
distance from the fault plane (or the level of ‘‘input’’ motion), as well as on themechanical parameters of a soil (initially, S-wave velocities and densities). Stresses andstrains naturally decrease with increasing distance from the fault, and, at the same time,
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stresses s30 increase, and strains c30 decrease with increasing Vs-30. Decreased stressvalues at some sites in the vicinity of the fault (for example, at CHY092 and CHY002)
are obviously related to decreased Vs-30 values in the upper layers at these sites,
whereas decreased strain values at some other sites (for example, at TCU116, TUC138,
TCU082, and TCU054) are due to relatively high Vs-30 in the upper soil layers at thesesites.
Thus, according to the obtained estimates, at sites possessing ‘‘softer’’ soils, averagestrains decrease with distance from the fault more quickly than average stresses, probably
because stresses in soil layers are defined to a larger extent by radiation from theearthquake source (level of ‘‘input’’ motion to soil layers) than by mechanical properties
of soils, whereas strains depend more on soil properties, i.e., on resonant phenomena inupper soil layers.
3.3. Shear Moduli Reduction in Soil Layers in Near-Fault Zones during the Chi-Chi
Earthquake
As concluded in PAVLENKO and WEN (2008), closest to the fault plane sites soil
behavior during the Chi-Chi earthquake was substantially nonlinear. Nonlinearity of soil
response can be characterized by reduction of shear moduli in soil layers (PAVLENKO andIRIKURA, 2005). Thus, the constructed models of soil behavior were used to estimate shear
moduli reduction in the upper 30 m of soil, DG/Gmax-30. The obtained estimates arepresented in Table 1; Figure 4c, e, g show the distribution of DG/Gmax-30 estimatesaround the fault plane, and the dependencies of the estimates on the distance from thefault and on the level of ‘‘input’’ motion to soil layers, respectively.
The evaluated values of DG/Gmax-30 testify to high nonlinearity of soil response
during the Chi-Chi earthquake: In the closest vicinity of the fault plane, at TCU110,
CHY025, TCU065, TCU102, and CHY074 sites, shear moduli reduction in the upper
30 m achieved *40–50% (Figs. 4c, e; Table 1). The highest DG/Gmax-30 values wereobtained at CHY101, CHY036, and CHY039 sites, where the constructed models of soil
behavior show substantial differences in the shapes of stress-strain curves at the
beginning and end of the strong motion, indicating softening (probably, liquefaction) of
surface layers. This area is marked by a dotted line in Figures 1 and 4c.
High values of shear moduli reduction DG/Gmax-30 *30–50% were obtained in theclosest vicinity of the fault (within *25 km from the surface rupture) at ‘‘soft’’ soil sites:
TCU102, TCU110, TCU115, TCU072, CHY074, TCU116, CHY025, and CHY092(Fig. 4c). At sites TCU138, TCU082, TCU054, and TCU033, possessing ‘‘harder’’subsurface soils (Vs-30 * 450–605 m/s), lower values of shear moduli reduction wereobtained: DG/Gmax-30 * 10–20%. At sites CHY104, CHY002, CHY026, CHY094, andCHY032, shear moduli reduction can be underestimated because of the presence of basininduced surface waves in records (Fig. 1), which noticeably increases amplitudes ofoscillations on the surface and cannot be simulated in our one-dimensional problem(PAVLENKO and WEN, 2008).
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With increasing distance from the fault, shear moduli reduction values decrease to*10% at 35–50 km and to *5% at 50–70 km from the fault (Figs. 4c, e), where soil
response becomes virtually linear.
In Figures 4e, g shear moduli reduction values for ‘‘softer’’ and ‘‘harder’’ sites areshown by points and by circles, respectively. It is seen from the plots that shear moduli
reduction estimates at ‘‘softer’’ sites decrease with distance approximately as *r -1 andthey grow in proportion to the level of ‘‘input’’ motion to soil layers. Points, noticeably
deviating from the approximating functions, correspond to CHY039 and CHY036 sites
with increased DG/Gmax-30, where the constructed models of soil behavior showliquefaction phenomena, and to CHY074 site with decreased DG/Gmax-30, possessing
dense soils (Class C). As seen from the plots, DG/Gmax-30 estimates at ‘‘harder’’ sites
substantially increase scattering of points around the approximating relationships(Figs. 4e,g).
Thus, reduction of shear moduli in the upper 30 m of soil at ‘‘softer’’ sites can berather accurately described as a function inversely proportional to the distance from thefault, *r -1 and as a linear function of the level of ‘‘input’’ motion, arms. As mentioned
above, strong ground motion during the Chi-Chi earthquake induced resonant amplification of seismic oscillations in the upper soft layers at many sites, and since soil
conditions were similar at soil sites located mostly to the south and south-west of the fault(Fig. 1), average strains in the upper 30 m are proportional to the level of ‘‘input’’ motion
to soil layers, and their decrease with distance from the fault can be approximately
described as *r -1. Accordingly, shear moduli reduction values depend on distance andon the level of ‘‘input’’ motion in the same manner.
At the same time, at sites with ‘‘harder’’ subsurface soils, resonant phenomena were
not observed in the upper 30 m of soil (according to our estimates, maximum strains atthese sites correspond to depths of *40 m and more (Fig. 3)), and estimates of shear
moduli reduction depend not only on the distance from the fault (or on the level of‘‘input’’ motion), but, to a greater extent than for ‘‘softer’’ soils, on the profiling data,
which are very diverse at these sites, dispersed over a large area around the fault.
Consequently, shear moduli reduction values can be quite different, even at sites locatedequidistant from the fault.
3.4. Nonlinear Components of Soil Response in Near-Fault Zones during the Chi-Chi
Earthquake
To estimate nonlinear components of soil response, models of soil behavior
constructed in PAVLENKO and WEN (2008) were tested by the Gaussian white noise. Linear
and nonlinear components of soil response were distinguished, and their intensities were
estimated in percent of the entire intensity of the response.
The obtained estimates are presented in Table 1, and in Figure 5. Figures 5a–c
represent the distributions of the estimates of the whole nonlinear component, Nl,nonlinear quadratic, nl-2, and cubic, nl-3, components of soil response, respectively, in the
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Figure 5Upper raw: distribution around the fault plane of (a) – whole nonlinear components of soil response Nl, (b) –nonlinear quadratic components nl-2, (c) – nonlinear cubic components nl-3. Lower raw: (d) – whole nonlinear
components of soil response Nl, (e) – nonlinear quadratic components nl-2, (f) – nonlinear cubic components nl-3,(g) – quasi-static deformations of the surface h0 as functions of the distance from the fault.

vicinity of the fault plane. Below in Figures 5d–k, estimates of Nl, nl-2, and nl-3, and theconstant component of soil response, h0, are shown as functions of the distance from thefault r and of the level of ‘‘input’’ motion to soil layers arms. Values obtained for sites with‘‘softer’’ and ‘‘harder’’ subsurface soils are shown by points and circles, respectively.
Soft soils in the closest vicinity of the fault possess the highest nonlinearity of the
response: According to our estimates, the whole nonlinear components of soil response
achieve Nl * 60–80%, and nonlinear quadratic and cubic components are up to*12–16% of the intensity of the response. At the same time, nonlinear residualcomponents of soil response related to higher-order nonlinearities (the 4th order andhigher) are also high, up to *30–40% of the intensity of the response. Evidently, thisindicates very high nonlinearity of soil response in near-fault zones during the Chi-Chi
earthquake.
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Note that nonlinear quadratic and nonlinear cubic components (their ratio indicatesthe ratio of even-order and odd-order nonlinear components in soil response) are almost
equal closest to the fault (i.e., in conditions of high nonlinearity), however, withincreasing distance from the fault (that is, decreasing nonlinearity), nonlinear cubic
components become predominant (Figs. 5e, f).
With increasing distance from the fault plane, nonlinear components of soil response
decrease, and their dependence on distance can be described in the same manner as forother parameters, such as, approximately *r-1. Accounting for sites possessing ‘‘harder’’subsurface soils substantially increases scattering of points around the approximating
functions. For sites with ‘‘softer’’ subsurface soils, the dependencies of the obtained
estimates of nonlinear components on the level of ‘‘input’’ motion can be approximately
described by linear functions (Figs. 5h–k). This is in agreement with our representationsof soil nonlinearity: at soft soils, manifestations of nonlinearity increase with the level of‘‘input’’ motion, i.e., with approach to the fault.
At two closest to the fault plane sites possessing ‘‘harder’’ subsurface soils, such as,
TCU072 and TCU102, nonlinearity of soil response was also high, evidently because of
expressed resonant phenomena in the upper soft soil layers. At TCU072 site, resonant
amplification of seismic oscillations occurred in the upper *11 m of colluvium(VS & 250 m/s), and at TCU102 site, resonant phenomena were related to the upper*4–6 m of soft silty soils, which were softened during the strong motion. The behaviorof these upper soft layers was substantially nonlinear and described by very sloping
stress-strain relations (PAVLENKO and WEN, 2008). Since surface soft layers were
underlayed by hard breccia (at TCU072) and gravel (at TCU102), average S-wave
velocities in the upper 30 m were higher than *300 m/s at both sites, and the sites wereassigned as possessing ‘‘harder’’ subsurface soils, however, nonlinear components atthese sites satisfy regularities obtained for sites possessing ‘‘softer’’ subsurface soils(Figs. 5d–k).
Quasi-static shift deformations on the surface, h0, related to nonlinearity of soil
response, achieve 20–35 cm closest to the fault plane sites, according to our estimates(Fig. 5g). They decrease approximately as *r-1 with increasing distance fromthe fault; in this case, estimates for ‘‘softer’’ and ‘‘harder’’ soil sites possess similar
regularity.
With increasing distance from the fault, nonlinearity of soil response decreases and at
distances of *40–50 km (*1/2 of the length of the fault plane), nonlinear components insoil response do not exceed 10–15%, according to our estimates (Fig. 5d).
A good illustration of changes in the ratios of linear and nonlinear components insoil response with increasing distance from the fault is provided by impulse
characteristics of soil layers. They are shown in Figure. 6 and arranged according totheir distance from the fault. They are calculated based on acceleration time histories
on the surfaces and at the bottoms of soil layers simulated in PAVLENKO and WEN(2008). Impulse characteristics represent estimates of the first-order Wiener kernels,that is, they describe linear parts of soil response. At sites located at lengthy distances
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Figure 6
Impulse characteristics of soil response during the Chi-Chi earthquake at the studied soil sites.

from the fault plane, they possess oscillating character, indicating an essential role ofresonant phenomena in soil response. With approach to the fault, nonlinear damping
increases and the oscillations decrease; impulse characteristics become smoothed andlow-frequency, which indicates substantial changes in spectral contents of seismic
waves propagating in soil layers, noticeable decrease of linear components and increaseof nonlinear components in soil response.
Nonlinearity of soil response during the Chi-Chi earthquake has been studied by
ROUMELIOTI and BERESNEV (2003) and by K.-L. Wen (pers. communic.). They investigatedspectra of acceleration time histories at soil sites and interpreted lower amplification ofseismic waves in some frequency bands during strong ground motions compared to
weaker ones (aftershocks) as an indicator of nonlinearity of soil response. ROUMELIOTI and
BERESNEV (2003) simulated soil site records using the linear-response assumption
whereby the simulated soil site input motions are amplified by weak-motion amplification
functions, estimated by the spectral ratio technique from the aftershock records. Their
comparison with the observations revealed an average reduction in strong-motion
amplification to about 0.5–0.6 of that in weak motions, with an acceleration ‘‘threshold’’for detectable nonlinearity near 200–300 cm/s2. However, the authors emphasize a large
interstation response variability, which did not allow them to derive a statistically
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Pure appl. geophys.,significant difference in weak and strong-motion amplifications, based on the responses
available at the studied sixteen stations.

4. Discussion and Conclusions
To date, the behavior of subsurface soils down to *100 m during a strong earthquake
was thoroughly studied, based on vertical array records of the 1995 Kobe earthquake(Mw = 6.8) at three sites (PAVLENKO and IRIKURA, 2002, 2003, 2005) and of the 2000
Tottori earthquake (Mw = 6.7) at five sites (PAVLENKO and IRIKURA, 2006).
Only a limited number of vertical array records of strong ground motion areavailable worldwide, though the database is growing quickly: For example, records ofDigital Strong-Motion Seismograph Network Kik-Net (Japan) have been collected since
October, 1997 and are accessible through the internet. The majority of strong motion
records are made only on the surface, such as in the case of the Chi-Chi earthquake.
For the Chi-Chi earthquake, we could simulate rather accurately acceleration time
histories at the bottoms of soil layers, at depths of *70–80 m, and study soil behavior
at many sites using methods developed for vertical array records. Thus, the 1999 ChiChi earthquake became the third strong earthquake for which models of soil behavior
in near-fault zones down to *70–80 m were constructed PAVLENKO and WEN (2008). At
the same time, it is the first strong earthquake for which soil behavior was extensively
studied in detail at many sites over a large area within *100 km around the fault
plane.
The results presented in this paper, such as estimates of amplification of seismic
waves in soil layers, average stresses and strains induced in soil layers by the strong
motion, shear moduli reduction and characteristics of nonlinearity of soil response
describe soil behavior in near-fault zones during the Chi-Chi earthquake. In spiteof the approximate character of the obtained estimates, they allow us to draw
conclusions.
As shown above, factors of amplification of seismic waves in subsurface soils
estimated for accelerations and velocities increase approximately in proportion to the
distance from the fault, *r. Other estimated parameters decrease with distance (or with adecrease in the level of ‘‘input’’ motion to soil layers). Since the obtained estimates
possess a rather large scattering, their behavior was approximated by simple functions.
The dependencies of soil response parameters on the level of ‘‘input’’ motion wereapproximated by linear functions, and their decrease by increasing the distance from thefault – by functions inversely proportional to distance, *r -1.
Note a slower (than other parameters) decrease of average stresses in soil layers(the upper 30 m) with distance and a large scattering around the approximating curvesof the obtained estimates of amplification factors, average stresses and strains, andnonlinear components in soil response (whereas, scattering of DG/Gmax-30 estimates issmaller).
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As concluded in PAVLENKO and WEN (2008), the main site effects in near-fault zonesof the Chi-Chi earthquake were resonant phenomena in subsurface soils and nonlinearityof soil response. Resonant patterns involved rather thick soil layers, down to *40–60 m,
and noticeably increased strains in upper layers, but only slightly influenced stresses(Fig. 3). Thus, average strains and shear moduli reduction values were influenced byresonant effects, whereas average stresses can be considered as parameters, which wereless influenced by these effects, and this evidently was the cause of another character of
their decrease with distance.
A large scattering in the obtained estimates of parameters of soil response in the nearfault zones testifies to the variety of manifestations of soil response, which depends on the
profiling data and on the proximity of a site to an earthquake source. In soft subsurface
horizontally layered soils, resonant amplification of seismic waves occurs, andparameters of soil response show certain dependencies on the distance from the fault(or on the level of ‘‘input’’ motion), whereas parameters of the response of ‘‘harder’’ soils
are more diverse and cannot be easily approximated by functions of the distance and thelevel of ‘‘input’’ motion. At the same time, scattering of parameters describing the
response of soft soils is strongly related to the level of ‘‘input’’ motion. Closest to
the fault plane sites, in water-saturated sandy soils, a noticeable amplification of seismic
oscillations occurs at rather large strains (exceeding a certain level of ‘‘input’’ motion)
due to pore pressure build-up and transition from ‘‘soft-type’’ nonlinear soil behavior tothe ‘‘hard-type’’, as described in PAVLENKO and WEN (2008).
Estimates of nonlinear components of soil response characterize the wholesoil thickness down to *70–80 m. According to the theory of nonlinear interactions,amplitudes of combinational-frequency harmonics generated on the system’s nonlinearity
are proportional to products of amplitudes of the corresponding interacting normal
oscillations (ZAREMBO and KRASIL’NIKOV, 1966). Thus, estimates of quadratic and cubic
nonlinear components should be proportional to the second and third powers of the levelof ‘‘input’’ motion, respectively. The whole nonlinear component, which includes, among
quadratic and cubic, higher-order nonlinearities, should also be proportional to somepower of the level of ‘‘input’’ motion (the power is evidently higher than 2 and depends
on the contents of nonlinear components of various orders in the system’s response). In
this case, ‘‘input’’ motion means testing Gaussian white noise signals, which were used
for estimating nonlinear components in soil response during the Chi-Chi earthquake. The
intensities of the testing signals (influencing the estimates of nonlinear components) wereselected so that average stresses and strains induced in soil layers by seismic waves fromthe earthquake and by testing noise-like signals were as close to each other as possible.
The dependencies of the obtained evaluations of nonlinear components in soil responseon the levels of testing signals, which were used for the estimations, agree with thetheoretical predictions. However, plots in Figure. 5 show other dependencies, such as, thedependencies of the estimated nonlinear components in soil response on the level of
preliminary calculated ‘‘input’’ motion from the Chi-Chi earthquake to soil layers, andthese dependencies can be roughly approximated by linear functions (a large scattering of
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points around the approximating lines can be partially due to inaccuracies of theestimation methods).
Thus, the estimated values of nonlinear components in soil response show the same
regularities as shear moduli reduction values, which also characterize nonlinearity of soil
response during a strong earthquake. In papers by PAVLENKO and IRIKURA (2005, 2006),
records of the 1995 Kobe and the 2000 Tottori earthquakes were analyzed, and it was
shown that shear moduli reduction values expressed in percent approximately coincidewith the estimated nonlinear components of soil response. In this work, records of thestronger Chi-Chi earthquake at 31 soil sites are analyzed, and this conclusion is confirmed
for the closest to the fault plane sites, where both estimates achieve *60–80% (Table 1).
However, shear moduli reduction values decrease with distance more quickly thanestimates of nonlinear components in soil response: At *35–50 km from the fault (*1/2of the length of the fault) shear moduli reduction values and nonlinear components of soil
response were *2–7% and *10–15%, respectively. Probably, this is partially due to thefact that shear moduli reduction values were estimated for the upper 30 m of soil, whereas
estimates of nonlinear components relate to the whole soil thickness (*70–80 m).
Based on the estimates of shear moduli reduction and the contents of nonlinear
components in soil response, we can distinguish the area of strong nonlinearity within*20–25 km from the fault (*1/4 of its length). In this area, shear moduli in the upper
30 m of soil reduced by *40–50% of their initial values during strong motion, and thecontents of nonlinear components in soil response were also high, *40–50% of thewhole intensity of the response. This area includes, in particular, the following sites
possessing soft subsurface soils: CHY101, TCU110, TCU116, CHY025, TCU065,
CHY036, CHY092, CHY104, and TCU115. According to our estimates, at these sites
strong ground motion induced changes in rheological properties of the upper layers, andspectra of oscillations on the surface were close to the form E(f) * f -n.
If we compare soil behavior during the Chi-Chi earthquake (Mw = 7.6), the 1995
Kobe earthquake (Mw = 6.8), and the 2000 Tottori earthquake (Mw = 6.7), we notice that
virtually at all studied sites (excluding Port Island) in near-fault zones, hard type of
nonlinear soil behavior prevails. Bright examples are SGK site (Kobe earthquake),
TTRH02 site (Tottori earthquake); TCU065, TCU102, and TCU110 sites (Chi-Chi
earthquake). Strong ground motion led to resonant phenomena in surface soil layers, tolarge strains and pore-pressure build-up; as a consequence, soil behavior assumed a‘‘hard-type’’ character, which was particularly expressed nearest the fault planes. In thesecases, strong ‘‘hard-type’’ nonlinearity of soil response did not lead to noticeable deamplification of oscillations on the surface.
Resonant amplification of seismic oscillations in the upper soil layers occurred atmany sites during the three earthquakes, however, during the Chi-Chi earthquake,resonant phenomena involved thicker soil layers, down to *40–60 m (instead of *10–
15 m during the Kobe and Tottori earthquakes), because of the larger magnitude of the
Chi-Chi earthquake and the rather homogeneous structure of the upper soil layers down
to *70–80 m at the majority of soil sites.
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On the whole, along with a diversity of manifestations and patterns of soil response
depending on many different factors such as the structure of soil layers, their mechanicalproperties and saturation with water, spectral composition and intensity of the radiationfrom the earthquake source, we note a similarity in the behavior of similar soils during
different strong earthquakes, indicating a fundamental possibility of forecasting soil
behavior in future strong earthquakes.

Acknowledgements
This research was a continuation of the research performed together with Prof. K.-L.
Wen and supported by the National Science Council (Taiwan) under Grant No. NSC 952811-M-492-001. The profiling data at soil stations provided by NCREE are greatly
appreciated. The author thanks Prof. K.-L. Wen for his collaboration.

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(Received February 27, 2008, accepted July 7, 2008)

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Journal : 24

Dispatch : 17-10-2008

Article No. : 0401

h LE

Pages : 24
h TYPESETMS Code : 0401

4 CP
h

4 DISKh