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Bulletin of the Seismological Society of America, Vol. 96, No. 6, pp. 1–, December 2006, doi: 10.1785/0120060069

Nonlinear Behavior of Soils Revealed from the Records of the 2000 Tottori,
Japan, Earthquake at Stations of the Digital Strong-Motion Network
Kik-Netby Olga V. Pavlenko and Kojiro Irikura

Abstract Acceleration records of the Tottori earthquake (6 October 2000), provided by stations of the Digital Strong-Motion Network Kik-Net, show clear evidenceof the nonlinearity of soil response at sites located in near-fault zones. In this study,
records of the mainshock of the Tottori earthquake are analyzed, and stresses andstrains, induced by the strong motion in the upper 100 or 200 m of soil, are reconstructed at sites located within 80 km from the fault plane. For reconstructing stresses
and strains, the method is applied, which we developed and used previously forstudying the response of soils during the 1995 Kobe earthquake. Nonlinear timedependent stress–strain relations in the soil layers are estimated based on verticalarray records. A good agreement between the observed and simulated accelerogramsof the Tottori earthquake testifies to the validity of the obtained vertical distributionsof stresses and strains in the soil layers. We also evaluated variations of the shear
moduli of the soil layers, caused by the strong motion, at stations located at different
distances from the fault plane. Changes in the rheological properties of the upper
soil layers were found closest to the fault-plane stations. A similarity in stress–strain
relations, describing the behavior of similar soils during the 1995 Kobe earthquake
and the 2000 Tottori earthquake, was obtained, indicating the possibility of precastingsoil behavior in future earthquakes at sites where profiling data are available.
Introduction
earthquake at depths of the recording-device locations has
shown that (1) at least within ⬃8–10 km from the fault
plane, the nonlinearity in the soil response was substantiallyhigher than that stipulated by conventional computer programs of the nonlinear ground-response analysis, and (2)stress–strain relations of different types, depending on thecomposition of soil layers, their saturation with water, anddepth, describe the behavior of the layers. In particular, thebehavior of sandy, water-saturated or wet subsurface soils is
described by stress–strain relations of “hard” type, declining
to the stress axis at large strains. In such soils, amplificationof large-amplitude oscillations occurs, which is related to
the “hard-type” nonlinearity of the soil response, as at SGKsite during the 1995 Kobe earthquake (Pavlenko and Irikura,2003).
Acceleration records of the Kobe earthquake gave agood illustration of the fact that in strong ground motion,
maxima of energy of oscillations at soil sites shift to a lowerfrequency domain. This fact was explained by the nonlinearity of the soil response: mutual interactions of spectral
components of seismic waves propagating in soil layers leadto redistribution of the energy of oscillations over the spec-

Experimental data provided by recent large earthquakes,
such as the 1994 Northridge earthquake (MW ⬃6.7), the1995 Kobe (MW ⬃6.8) and the 2000 Tottori (MW ⬃6.7)
Japanese earthquakes, the 1999 Chi-Chi (MW ⬃7.7) Taiwanese earthquake and others, have shown clear evidenceof the nonlinear behavior of subsurface soils in near-fault
zones. During the Kobe earthquake, nonlinear soil behavior
was identified at sites located within ⬃16 km from the fault
plane, and the content of nonlinear components in the soil
response was estimated. It turned out to be rather high, up
to ⬃60% of the whole intensity of the response, at ⬃2 km
from the fault plane and about 10–15% of the intensity of
the response at ⬃16 km from the fault plane (Pavlenko and
Irikura, 2005).
This type of analysis and estimations became possible
because of the availability of vertical-array records of theKobe earthquake. Seismic vertical arrays usually containtwo, three, or four three-component accelerometers, installedon the surface and at depths down to ⬃100 or ⬃200 m, oneof the primary motivations for observations with borehole
arrays is to understand nonlinear soil response.
Numerical simulation of accelerograms of the Kobe
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tral band, and the spectra of signals on the surface tend to
take the form E(f) ⬃ f ⳮk (Pavlenko, 2001).
Numerous surface records obtained during the 1999
Chi-Chi (Taiwan) earthquake possess similar features, indicating nonlinearity of the soil response in many places near
the fault plane. Although these records can not be analyzed
in the same manner as records of the Kobe earthquake, because of the absence of borehole data, we can suppose thatcertain typical nonlinear distortions occur in seismic waves
of similar intensities in subsurface soils.
The Tottori earthquake occurred in the Tottori Prefecture of Japan at approximately 1:30 p.m. on 6 October 2000.
The earthquake mechanism was a strike-slip fault, and thefault-rupture plane surface was about 30 km wide by 10 km
deep, nearly vertical (86 degrees). This earthquake was recorded by stations of the Kiban-Kyoshin Digital StrongMotion Seismograph Network (Kik-Net) at 220 sites locatedat epicentral distances of 7 to 626 km. It resembled the 1995
Kobe earthquake in its magnitude and focal depth and therefore represented a good opportunity to check the conclusions
made based on records of the Kobe earthquake.
Acceleration records of the 2000 Tottori earthquake,provided by the Kik-Net stations, show clear evidence of thenonlinearity of soil response at sites located in near-fault
zones, such as evident differences in shapes and spectra ofrecords on the surface and at depth, emphasizing lowfrequency oscillations on the surface. In this study, we analyze accelerograms of the 2000 Tottori earthquake and reconstruct stresses and strains, induced in soil layers at sites
where the nonlinear soil behavior was identified. We estimate reduction of the shear moduli of the soil layers, causedby the strong motion, and discuss transformations of spectraof seismic waves in the soil layers.

Data and Methodology
Figure 1 (derived from the Kik-Net web site) shows thelocations of the mainshock of the Tottori earthquake and the
Kik-Net stations in the vicinity of the epicenter. The stations
contain two accelerometers, installed on the surface and at
a depth of ⬃100 or ⬃200 m. Simultaneous records of thetwo devices allow us to simulate the behavior of soil layers
from the surface down to the location of the deep device.
For data processing, we chose stations located within⬃80 km from the epicenter, where maximum recorded accelerations exceeded 100 Gal, assuming that at larger distances or at smaller accelerations the soil response is linear.
The list of the studied Kik-Net stations with their epicentral
distances, maximum recorded accelerations, and soil conditions is given in Table 1.
Nonlinear soil behavior was identified at five Kik-Net
stations, namely the TTRH02, SMNH01, HRSH06,
SMNH03, and HRSH05 stations, located at 7 km, 8 km, 57
km, 57 km, and 80 km from the epicenter, respectively. At
other stations, listed in Table 1, either the profiling data wereabsent, or the thickness of soft subsurface soil layers wasless than ⬃10 m and they were underlaid by dense rock, sothat resonant phenomena predominated over nonlinear ones.
We used the Tottori earthquake records, provided by
the Kik-Net stations, for the estimation of nonlinear stress–
strain relations in soil layers at different depths, from thesurface down to ⬃100 or ⬃200 m. The method for the estimation of nonlinear stress–strain relations in soil layers,
based on vertical array records, is described in detail in Pavlenko and Irikura (2003).
The profiling data, such as the composition of the soil
layers, P- and S-wave velocities, were provided by the KikNet web site. At TTRH02, the upper 10.5 m represent sandand gravel (VS ⬃210 m/sec); at SMNH01, the upper 12 m
are fill soil with sand, gravel, silt, and cobble stone (VS ⬃290
m/sec). At both stations, below these layers down to⬃100 m, granites, andesites, and basalts are identified withVS values gradually increasing from 340 m/sec (at 10.5–20 m) to 790 m/sec (at 42–100 m) at TTRH02 and from
550 m/sec (at 12–22 m) to 2800 m/sec (at 54–100 m) at
SMNH01. At HRSH06, the upper 6 m represent weatheredmudstone (VS ⬃170 m/sec), below which mudstones, conglomerates, and granites are found with VS values increasingfrom 270 m/sec (at 6–19 m) to 1650 m/sec (at 51–100 m).
At SMNH03, the soil profile consists of fill soil, concrete,sand, and gravel with cobble stone (VS ⬃240 m/sec) in theupper 7 m and mudstones, sandstones, and porphyrites below with VS values increasing from 390 m/sec (at 7–14 m)
to 1300 m/sec (at 51–100 m). At HRSH05, the upper 7.5 mof surface soil, clay, sand, and gravel (VS ⬃280 m/sec) are
underplayed by more dense layers of sand and gravel withcobble stone, sandy clays, slates, and diabases with VS values
increasing from 420 m/sec (at 7.5–32.5 m) to 2390 m/sec(at 80–100 m).
For calculations, the soil profiles were divided into twogroups of layers, according to the profiling data. At all stations the groups of upper soft layers were distinguished (10.5m at TTRH02, 12 m at SMNH01, 6 m at HRSH06, 7 m at
SMNH03, and 7.5 m at HRSH05), and “hard-type” stress–
strain relations were selected to describe the behavior ofthese layers. To describe the behavior of deeper layers at all
the stations, we used stress–strain relations obtained in laboratory experiments by Hardin and Drnevich (1972). We
calculated propagation of vertically incident “input” waves(records of the borehole devices) up to the surface; we developed the calculation program was based on the algorithm
by Joyner and Chen (1975). In this program, hard-type
stress–strain relations and stress–strain relations obtained inlaboratory experiments by Hardin and Drnevich (1972) wereused to describe the behavior of the upper and lower layers,respectively. Sets of parametric hard-type stress–strain
curves (250 curves) were generated, and an item-by-item
examination was applied to identify curves showing the bestfit approximation to observed accelerograms on the surface
and at depth. To account for temporal changes in the soil
behavior, successive 1.5-sec intervals were analyzed; calculations were performed successively, interval by interval.

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Figure 1. Locations of the mainshock of the 2000 Tottori earthquake and Kik-Net
stations in the vicinity of the epicenter (derived from the Kik-Net web site).

Table 1
Maximum Recorded Accelerations, Epicentral Distances, andSoil Conditions at the Kik-Net Stations Located in Near-Fault
Zones of the 2000 Tottori Earthquake (Data Derived from the
Kik-Net Web Site)

Site CodeSite Name

Maximum
Acceleration(Gal)

TTRH02
SMNH01
SMNH02
OKYH07
SMNH10
OKYH09TTRH04
OKYH08
OKYH14
SMNH12
SMNH11
OKYH10
HRSH06
SMNH03
OKYH05
OKYH03
OKYH11
SMNH05
HRSH05

Hino
HakutaNita
Shingou
Mihonoseki
YubaraAkasaki
Tetsuta
Hokubou
YoshidaHirataKamisaibara
Kuchiwa
Sada
TakebeOkayamaSyououHasumiKannabe

927.2
720.4
564.0
179.7
226.4
283.8
218.1
238.5
443.0
258.6
58.2
280.7
240.3
154.8
149.0
129.5
139.1
121.5
131.0

Epicentral
Distance(km)

Thickness of theUpper Soft
Soil Layer withVs ⬍300 m/sec
(m)

7
8
24
26
31
32
33
41
45
46
52
53
57
57
65
69
74
79
80

11
10
0
0
no profiling data0
no profiling data0
no profiling datano profiling datano profiling data
8
18
7
4
7
9
4
7

We selected stress–strain relations of the hard type (declining to the stress axis at large strains) to describe the behavior of the upper layers, because at all the stations, except
HRSH06, the upper layers represent sandy soils, and P-wave
velocities indicate the presence of underground water inthe upper layers (VP ⬃860–900 m/sec at TTRH02 and
SMNH01; VP ⬃1300–1480 m/sec at SMNH03 and
HRSH05, and VP ⬃600 m/sec at HRSH06). Evidently, characteristics of oscillations on the surface are defined by thestress–strain relations in the soil layers. Real stress–strain
relations of soils obtained in experiments are diverse anddepend on the granulometric composition of a soil, its humidity, and so on. In the stress–strain curves of watersaturated soils, the initial convex-up part is followed by adeviation to the stress axis (concave-up part). In such soils(water-saturated sands and clays) possessing hard type of
behavior, we can expect shock waves beyond the limit ofelasticity (Zvolinskii, 1982), whereas soft soils like loessloams and sands possess stress–strain relations represented
by only the convex-up parts, which are often called “soft”
diagrams (Zvolinskii, 1982). Thus, hard-type stress–strain
relations are typical for water-saturated sandy soils; we usedthem to describe the behavior of upper soil layers at SGK
and TKS sites during the 1995 Kobe earthquake.
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cause they account for all the features of the soil behavior:in the domain of small strains, these curves are close to linear
ones; with increasing strain, they decline to the strain axis,
describing “soft” behavior, and, if strains increase more, thecurves decline to the stress axis. Therefore, application of
our method (and hard-type stress–strain curves) is also possible in cases of quasi-linear soil behavior and in cases ofsoft soil behavior, if strains are not too large (as at the
HRSH06 station). In these cases, the stress–strain relations
will be selected that adequately describe the soil behavior inthese particular situations.
Because the profiling data provided by the Kik-Net website contain only the composition of the soil and P- and Swave velocities in the layers, we estimated other parameters
used in calculations, such as shear stress in failure, smax,
density, and damping in the soil layers. We also defined
more exactly S-wave velocity profiles at the closest to thefault-plane stations TTRH02 and SMNH01. Density anddamping were estimated based on the soil composition. To
estimate other profiling parameters, we performed inversion
by using the genetic algorithm. For the inversion, we used
20 aftershocks of the Tottori earthquake recorded by the twostations during one month after the mainshock. Intervals defining allowed values of S-wave velocities VS in the soil
layers (input data in the inversion problem) included VS values provided by the Kik-Net web site; limiting estimates ofsmax were based on empirical relationships, accounting forthe composition of a soil layer, S-wave velocity, and preexisting stress in the layer. For each model (combining VS
and smax profiling values), we calculated the propagation of
the aftershock waves in the soil layers; the behavior of thelayers was described by the stress–strain relation obtainedby Hardin and Drnevich (1972). All the models were evaluated by the summary deviations of the simulated accelerograms from the recorded ones. The deviations were calculated as sums of the mean square “point-by-point”
deviations and the differences of the mean intensities of thesimulated and recorded accelerograms. The “best” model
was produced after crossing of 50 initial models during
about 500 generations.
For the TTRH02 station, the four-layer (as given at the
Kik-Net web site) and seven-layer (as proposed by someseismologists) models were considered. Figure 2a shows the
VS profile given on the Kik-Net web site, the best obtained
VS and smax profiles, and the plots illustrating the decreaseof the deviation between the simulated and recorded accelerograms with increasing the generation number for the
four-layer and seven-layer models at TTRH02. As seen from
Figure 2, the profiling values for both models are similar,
and the seven-layer model does not provide any advantages
over the four-layer model in simulating the aftershock wave
fields. Finally, the best four-layer model, shown in Figure
2a, was selected for further calculations. Figure 2b shows
similar results for the SMNH01 station, that is, the VS profile
given at the Kik-Net web site, and the best obtained VS andsmax profiles.

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For the HRSH06, SMNH03, and HRSH05 stations, theprofiling data were estimated based on the empirical relationships, accounting for the composition of the soil layers,
S-wave velocities, and pre-existing stresses in the layers.
Based on the profiling data obtained, stresses and strains
induced in the soil layers at the five stations during the mainshock of the earthquake were estimated. The obtained
stresses and strains were used to trace changes in the shear
moduli in the soil layers.

Results
Stresses and strains at depths of 0–100 m or 0–200 m,changing with time during the strong motion, were estimatedfor TTRH02, SMNH01, HRSH06, SMNH03, and HRSH05(Figs. 3, 4, 5, 6, 7). As seen from these figures, a good
agreement was obtained between the simulated and observed
accelerograms for all the stations, though the agreement isworse than that achieved for SGK and TKS sites in simulating accelerograms of the 1995 Kobe earthquake (Pavlenko and Irikura, 2003). Evidently, the accuracy of simulation sufficiently depends on the available information on
the parameters of the soil profiles. At SGK and TKS sites,
these parameters were measured before and after the Kobe
earthquake; 28 and 40 soil layers, respectively, were distinguished at these sites, for which P- and S-wave velocities
and densities were determined and laboratory testing of soil
samples was performed, which allowed rather accurate estimations of shear stress in failure, smax, in the soil layers.
At Kik-Net stations, such information is not available, andinversions based on genetic algorithm have not substantially
improved our knowledge of the soil parameters. Apparently,
the results of simulation shown in Figures 3–7 cannot be
improved without additional information on the parametersof the soil profiles.
However, the applied method of simulation allows somecorrection of the soil parameters. Stress–strain relations usedin calculations are defined in their normalized form in themanner proposed by Hardin and Drnevich (1972): stress isnormalized by multiplying by 1/smax, and strain is normalized by multiplying by Gmax /smax. During the calculations,stress–strain relations are selected that satisfy the prescribed(probably, with some error) values of Gmax and smax to simulate oscillations on the surface close to the observed ones.
At the same time, the result, that is, vertical distributions ofstresses and strains in the soil layers, is expressed in absolutestress and strain units (Figs. 3–7); this decreases its dependence on the selected Gmax and smax and allows us to makeconclusions about the soil behavior.
At the closest to the fault-plane stations TTRH02 and
SMNH01, the soil response was substantially nonlinear, as
seen from Figures 3 and 4. At these stations, the behaviorof the upper soil layers during the earthquake can not be
described by a single stress–strain relation; an agreement
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Figure 2. (a) VS profile, given at the Kik-Net web site (marked by filled circles on
the left-hand figure), the best obtained VS and smax profiles, and the plots, illustrating
the decrease of the deviation between the simulated and recorded accelerograms withincreasing the generation number for the four-layer and seven-layer models at the
TTRH02 station. (b) VS profile, given at the Kik-Net web site (marked by filled circles)
and the best obtained VS and smax profiles at the SMNH01 station.

different stress–strain relations at different intervals. Thus,
strong ground motion changes rheological properties of theupper soil layers in near-fault zones.
As seen from Figures 3 and 4, strains induced by thestrong motion achieve 0.6% in the upper 10.5 m at TTRH02
and 0.3% in the upper 12 m at SMNH01. At both stations
resonant oscillations in the upper soil layers are observed;
maximum stresses are as high as ⬃0.6 bars in the upper 10–
12 m and increase with depth up to ⬃5 bars at 50–100 m,
whereas strains decrease with depth. The shapes of thestress–strain curves in the upper soil layers reveal pore pressure development during the strong motion (Figs. 3 and 4).
At stations HRSH06, SMNH03, and HRSH05, locatedat epicentral distances of 57 km and more, the behavior of
the upper soil layers is described by the same stress–strain
relation at all intervals (Figs. 5–7); rheological properties ofthe soil are not changed. During the 1995 Kobe earthquake,changes of the rheological properties of the upper soil layers
were detected at Port Island and SGK sites, located within⬃6 km from the fault plane. Thus, records of two earthquakes with magnitudes Mw ⬃6.7–6.8 and focal depths lessthan ⬃30 km allow a rough estimation of the area where therheological properties of the upper soil layers change, as⬃7–8 km, or ⬃1/4 of the length of the fault. Stresses andstrains in the soil layers at these stations are substantiallylower than at TTRH02 and SMNH01: up to 0.12 bars and

0.05% in the upper 5–8 m; stresses increase up to ⬃0.5 bars
at 50–100 m (Figs. 5–7).
Also we analyzed records of other stations listed in Table 1. For SMNH02, we could not obtain an agreement between the simulated and observed accelerograms with the
VS profile provided at the Kik-Net web site. The agreement
can be obtained if we assume that the VS in the layers is⬃30–80% higher than indicated on the web site. Higher Swave velocities would better correspond to P-wave velocities in the layers, and the profiling data would resemble thedata at the neighboring station SMNH01. That would bereasonable, because the stations are close to each other, andthe earthquake recordings look similar at the two stations.
The ground response at stations OKYH07, OKYH08,
OKYH09, and OKYH10, where the upper layers represent
dense soil with high VS values, can be simulated, and an
agreement between the simulations and observations can beobtained if we describe the behavior of all the soil layerswith the stress–strain relation obtained in laboratory experiments by Hardin and Drnevich (1972). At stations
OKYH05, OKYH03, OKYH11, and SMNH05, the thickness of the soft soil layer is less than 10 m, whereas theepicentral distances are rather large, and the ground response
is virtually linear. Quasi-monochromatic oscillations predominate in records on the surface at these stations, indicating the predominance of resonance effects over nonlinear

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Figure 3.

The acceleration time histories of the mainshock of the Tottori earthquake,observed and simulated, and estimated stress–strain relations in the soil layers, changing with time during the strong motion, at the TTRH02 station (stresses are given in
Pa; strains, in strains, the same scales for depths 0–10 m and 11–100 m).

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Figure 4. Same as Figure 3 for the SMNH01 station (stresses are given in Pa;
strains, in strains, the same scales for depths 0–12 m and 13–100 m).

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Figure 5.

Same as Figure 3 for the HRSH06 station (stresses are given in Pa; strains,in strains, the same scales for depths 0–5 m and 6–100 m).

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Figure 6. Same as Figure 3 for the SMNH03 station (stresses are given in Pa;
strains, in strains, the same scales for depths 0–7 m and 8–100 m).

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Figure 7.

Same as Figure 3 for the HRSH05 station (stresses are given in Pa; strains,in strains, the same scales for depths 0–7 m and 8–100 m).

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ones. At these stations, the soil behavior can also be simulated with the stress–strain relation obtained by Hardin andDrnevich (1972).
The estimated stresses and strains, changing with time
during the strong motion, were used to trace changes in theshear moduli of the soil layers. As seen from Figures 3–7,
these changes are observed in the upper 9–12 m of the soil
profiles at the closest to the fault-plane stations. The behavior of the deeper layers at these stations and the behavior of
all the layers at remote stations HRSH06, SMNH03, andHRSH05 were stable. Figure 8 represents changes in theshear moduli at the studied Kik-Net stations during thestrong motion estimated for both east–west and north–south
components. Shear moduli were calculated as slopes ofstress–strain curves averaged over the groups of upper layers
and over oscillations within each interval during the strong
motion. At the TTRH02 and SMNH01 stations, the reduction of the shear moduli in the upper layers achieved ⬃60%of their initial values, at the HRSH06 station the reductionof the shear moduli did not exceed 15% of the initial value,
though scattering does not allow accurate estimation, and at
the SMNH03 and HRSH05 stations it was negligible(Fig. 8).
Though scattering of the obtained estimates of shear
moduli reduction indicate some inaccuracy in our simulations (which is due to insufficiency of information on thesoil parameters, as shown previously), we can see from Figure 8a total recovery of the shear modulus at the TTRH02
station and its almost total recovery at the SMNH01 station.
Also, we can see that the recovery starts immediately following the decrease of the intensity of the strong motion(Figs. 3, 4, and 8), which testifies to a high permeability of
the upper soil layers as composed of noncohesive soils:
sands, gravels, silts with cobble stones. Similar shear modulus behavior was observed at SGK and TKS sites during
the 1995 Kobe earthquake (Pavlenko and Irikura, 2002).
Note a significant amplification of low-frequency oscillations on the surface at TTRH02, which is due to the hardtype nonlinearity of the soil response, as seen in Figure 3.
A similar tendency is seen in records of the SMNH01 station. At other stations, the thickness of the soft soil layer israther small, and resonance effects predominate in oscillations on the surface. As a result, transformations of spectra
caused by the nonlinearity of the soil response are almost
insignificant.
Figure 9 represents acceleration spectra of the Tottori
earthquake at some Kik-Net stations. As known, nonlinearity of the soil response induces changes in spectra of seismic
waves propagating in the soil layers: the energy of the waves
is redistributed over the spectral bands, because of mutualinteractions of spectral components of the propagatingwaves. Low-frequency components are amplified, spectral
peaks and spectral gaps are smooth, and spectra of oscillations on the surface tend to take the form E(f) ⬃ f ⳮk. This
spectral shape can be achieved in cases of strong nonlinearity

11(intense seismic waves and/or thick soft soil layers), whereas
in cases of weak nonlinearity, we only see the tendencies ofthese spectral transformations. These tendencies are clearlyseen in spectra of the TTRH02 station (Fig. 9). At otherstations, however, resonance phenomena prevail, and spectral changes, induced by the soil nonlinearity, are inconspicuous.

Discussion and Conclusions
Thus, we constructed models of the soil behavior innear-fault zones of the 2000 Tottori earthquake. We estimated the stresses and strains induced in the soil layers by
the strong motion (Figs. 3–7). Noticeable changes in theshear moduli occurred in the upper layers (9–12 m) at theclosest to the fault-plane stations TTRH02 and SMNH01.
At these stations, strong ground motion induced changes in
the rheological properties of the upper layers. At stations
located at epicentral distances of 57 km and more, shear
moduli of the soil layers were almost not changed during
the earthquake.
A similarity was found in the soil behavior in near-fault
zones during the 1995 Kobe earthquake and the 2000 Tottori
earthquake, that is, the behavior of soils of similar composition, bedded in similar geotechnical conditions at different
sites, is described by similar stress–strain relations. Soils
possessing stress–strain relations of the hard type predominate in areas where the level of the underground water isclose to the surface. In this case, acceleration amplitudes
increase in the upper layers at rather large strains.
As known, there are three basic mechanisms of seismicwave transformations in soil layers: (1) amplification of oscillations in subsurface layers possessing lower values ofseismic velocities and densities; (2) resonance phenomena,
also leading to amplification of oscillations on the surface;and (3) nonlinearity of the soil response, usually leading todeamplification of oscillations.
The first two “linear” mechanisms have been studied
extensively during past decades, and now they are adequately accounted for in engineering practice. Regarding thethird “nonlinear” mechanism, the results obtained in thiswork allow us to formulate the following conclusions:First, nonlinearity of ground response leads to changes
in spectra and amplification of seismic waves propagatingin the soil layers.
Spectral transformations reveal themselves in shifting
the resonance frequencies of the soil layers to the lowfrequency domain and in tendencies to take the smoothed
form E(f) ⬃ f ⳮk. This spectral shape is due to the action of
nonlinear damping mechanisms: they weaken spectral components at high and medium frequencies and do not influence low-frequency components. Nonlinear damping mechanisms not depending on the dissipative properties of themedium are due to wasting energy of the propagating waves
on generating their higher-frequency harmonics, which are

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Figure 8. Shear moduli changes of the upper soil layers at the studied stations during
the 2000 Tottori earthquake.

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Nonlinear Behavior of Soils Revealed from the Records of the 2000 Tottori, Japan, Earthquake

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Figure 9. Acceleration spectra of the 2000 Tottori earthquake (north–south andeast–west components) at the Kik-Net stations.

damped more quickly than the main-frequency waves, because damping usually increases with frequency (Zarembo
and Krasil’nikov, 1966; Rudenko, 1986). In seismology,
nonlinear damping is related to the area within hysteretic
stress–strain curves; as known, it increases with increasing
the intensity of seismic oscillations (Hardin and Drnevich,1972).
If low-frequency components were reduced or absent at
the input of the soil profile, they appear at the output, resulting from nonlinear interactions and generating combination frequencies of “difference type,” f1 ⳮ f2; therefore,
they can be amplified. At the same time, nonlinear damping
does not decrease amplitudes of low-frequency components,
and they remain high even in cases of strong nonlinearity ofthe soil response, as at Kik-Net stations TTRH02 and
SMNH01 during the Tottori earthquake and at SGK and
TKS sites during the Kobe earthquake (Pavlenko and Irikura, 2003).
Concerning the influence of the soil nonlinearity on amplification of seismic waves in subsurface soil layers, weshould distinguish two cases, namely “soft” and “hard” typesof nonlinearity (stress–strain relations), which were described previously.
Sometimes nonlinearity of the soil behavior is unambiguously connected to deamplification of oscillations on thesurface; decrease of amplification of intense seismic waves

compared with weak ones in soil sites is treated as an indicator of soil nonlinearity (Beresnev et al., 1995; Field et al.,1997). However, our results show that this is true only incases of soft-type nonlinearity, when the behavior of theupper layers is described by soft-type stress–strain relations,declining to the strain axis at large strains; usually, this corresponds to cases when the level of the underground water
is below ⬃10 m. An example is the Port Island site (Pavlenko and Irikura, 2003). If the behavior of the upper soil
layers is described by hard-type stress–strain relations (usually, in cases when the level of the underground water isabove ⬃10 m), amplification of oscillations on the surface
occurs at rather high strains. TTRH02 and SMNH01 possess
this type of nonlinearity, as well as the SGK and TKS sites
during the Kobe earthquake (Pavlenko and Irikura, 2003).
The mechanism of amplification is illustrated by Figures 3
and 4: at large strains, stress–strain relations in the upper
layers decline to the stress axis, and amplitudes of lowfrequency oscillations increase.
In articles by Dimitriu et al. (2000) and Dimitriu (2002),
statistical analysis of weak- and strong-motion records has
shown that at resonant sediment sites, deamplification wasrestricted to a limited frequency band, below which the nonlinear (strong-motion) response exceeded the linear (weakmotion) one. At the same time, Yu et al. (1992) showed bynumerical simulation of strong-motion accelerograms at soil

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sites that nonlinearity does not affect spectral amplitudes in
the lowest frequency range, decreases amplitudes in the central band, and slightly increases spectral amplitudes in thehigh-frequency range.
Dimitriu et al. (2000) and Dimitriu (2002) do not describe soil conditions at the observation sites, and according
to our conclusions, we can suppose the “hard” type of soil
behavior at these sites. Only, in this case, the nonlinear soil
response can exceed linear one.
Note that the problem of seismic-wave amplificationand transformation of their spectra in the soil layers is rather
complicated, and we are preparing a separate article dealing
with this problem and referring to the results of the statisticalnonlinear acoustics. In this article, we wanted to emphasizethat changes in spectra and amplification of seismic waves
in subsurface soils at Kik-Net stations TTRH02 and
SMNH01 during the Tottori earthquake, as well as at stations
SGK and TKS during the Kobe earthquake (Pavlenko and
Irikura, 2003), represent good illustrations of the earlier
stated regularities.
Second, in cases when the thickness of subsurface soft
soil layers is less than ⬃20 m, resonance phenomena usually
predominate over nonlinear ones. Nonlinearity of soil response stipulates the dependence of resonance frequencies
on the intensity of seismic oscillations. Therefore, any presumable estimates of frequency-dependent amplification
factors are not correct; a correct approach is calculation of
the ground response in concrete situations.
Third, maximum strains are usually induced at the bottom of subsurface soft layers; they correspond to lowfrequency oscillations, caused by the soil nonlinearity. Thisshould be considered in constructing underground structures.
Based on processing records of the 1995 Kobe and 2000
Tottori earthquakes, we can formulate the limitations of conventional computer programs of ground-response analysis(i.e., widely used programs in which the behavior of all soil
layers is described in a similar manner: SHAKE, FDEL,CHARSOIL, NONLI3, EERA, NERA, etc.): (1) disregardof the differences in the behavior of separate soil layers during strong ground motion and (2) ignoring of changes inrheological properties of the upper soil layers, induced by
the strong motion.
According to our estimations, based on records of theKobe (1995) and Tottori (2000) earthquakes, during crustal
earthquakes with magnitudes Mw ⬃6.7–6.8, strong nonlinearity of the soil response (changes in rheological propertiesof the upper soil layers and shear modulus reduction of⬃50–60% and more) are observed within an area up to⬃7–8 km from the fault plane (⬃one-fourth of the length of
the fault). Within this area, noticeable manifestations of soil
nonlinearity are observed in the upper 15–25 m of the soil
profiles. At distances of ⬃15 km from the fault plane(⬃ one-half of the length of the fault), nonlinearity is much
weaker, even in soft subsurface soils. Stress–strain relations,pg 14 # 14

O. V. Pavlenko and K. Irikurasuggested by Hardin and Drnevich (1972), adequately describe the behavior of soils at all depths in conditions ofmoderate dynamic loadings. In conditions of large loadings,
in cases of strong nonlinearity, these stress–strain relations
can be used to describe the behavior of dense soils at depths
below some level (15–25 m for Kobe and Tottori earthquakes), depending on the composition of the soil layers andtheir saturation with water, as well as on the magnitude andlocation of the earthquake; whereas the behavior of soft subsurface soils should be described by other, more “nonlinear”
stress–strain relations. Such relations are found in this work.
Ignoring the features of soil behavior in strong groundmotion leads to underestimation of maximum accelerationin near-fault zones and mistaken estimates of spectra of oscillations on the surface at soil sites.

Acknowledgments
We thank L. F. Bonilla and an anonymous reviewer for their valuablecomments and suggestions. We also thank the web site of the Kik-Net
Digital Strong-Motion Seismograph Network, www.kik.bosai.go.jp, for records of the 2000 Tottori earthquake and profiling data.

References
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Nonlinear Behavior of Soils Revealed from the Records of the 2000 Tottori, Japan, Earthquake
Institute of Physics of the Earth
Russian Academy of Sciences
B. Gruzinskaya 10
Moscow 123995, Russia
olga@ifz.ru(O.V.P.)
Earthquake Motion Research Institute4-3-2 Itachibori, Nishi-ku
Osaka, 550-0012, Japan
irikura@geor.or.jp(K.I.)
Manuscript received 25 March 2006.

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