-To improve our understanding of nonlinear elastic properties of soils, a method is proposed of estimation of stress-strain relations of soils in situ in strong ground motion based on vertical array data. Strong motion records provided by seismic vertical arrays allow estimation of nonlinear stressstrain relations in soil layers at different depths, from the surface down to the location of the deepest device. As an example, records obtained during the main shock of the 1995 Kobe earthquake at PortIsland, SGK, and TKS sites were used to estimate the stress-strain relations in the soil profiles. For different layers, different types of nonlinear stress-strain relations were selected, according to the profiling data. To account for temporal changes in the soil behavior, consecutive parts of records were examined, and for successive time intervals, the relations were found showing the best-fit approximation to the observed data. At Port Island and SGK sites, where the strongest accelerations were recorded, the obtained stress-strain relations showed systematic changes in the upper layers (0-14 m), such as, a progressive reduction of the slopes of the stress-strain curves due to liquefaction at Port Island and reduction and recovery of the slopes at SGK and TKS sites. At the three sites, the stress-strain relations remained stable in layers below 11-14 m. Thus, the proposed approach gives us a representation of the soil behavior in layers at different depths in strong ground motion; it allows calculation of the propagation of arbitrary seismic signals in the studied profiles and estimation of nonlinear components in the ground response by the nonlinear system identification technique. The method can also be applied to evaluate the ground response at sites where profiling data are available and an imposed motion can be estimated.

The 1999 Chi-Chi, Taiwan, earthquake (M w = 7.6) was one of the strongest earthquakes in recent years recorded by a large number of strong-motion devices. Though only surface records are available, the obtained strong-motion database indicates the variety of ground responses in the near-fault zones. In this study, accelerograms of the Chi-Chi earthquake were simulated at rock and soil sites, and models of soil behavior were constructed at seven soil sites (TCU065, TCU072, TCU138, CHY026, CHY104, CHY074, and CHY015), for which parameters of the soil profiles are known down to depths of at least *70 m and at 24 other soil sites, for which parameters of the soil profiles are known down to 30-40 m; all the sites were located within *50 km from the fault. For reconstructing stresses and strains in the soil layers, we used a method similar to that developed for the estimation of soil behavior based on vertical array records. As input for the soil layers, acceleration time histories simulated by stochastic finite-fault modelling with a prescribed slip distribution over the fault plane were taken. In spite of the largeness of the earthquake's magnitude and the proximity of the studied soil sites to the fault plane, the soil behavior at these sites was relatively simple, i.e., a fairly good agreement between the spectra of the observed and simulated accelerograms and between their waveforms was obtained even in cases where a single stress-strain relation was used to describe the behavior of whole soil thickness down to *70-80 m during strong motion. Obviously, this is due to homogeneity in the characteristics of soil layers in depth. At all the studied sites, resonant phenomena in soil layers (down to *40-60 m) and nonlinearity of soil response were the main factors defining soil behavior. At TCU065, TCU110, TCU115, CHY101, CHY036, and CHY039 liquefaction phenomena occurred in the upper soil layers, estimated strains achieved *0.6-0.8%; at other stations, maximum strains in the soil layers were as high as 0.1-0.4%, according to our estimates. Thus, valuable data on the in situ soil behavior during the Chi-Chi earthquake was obtained. Similarity in the behavior of similar soils during the 1995 Kobe, 2000 Tottori (Japan), and Chi-Chi (Taiwan) earthquakes was found, indicating the possibility of forecasting soil behavior in future earthquakes. In the near-fault zones of the three earthquakes, ''hard-type'' soil behavior and resonant phenomena in the upper surface layers prevail, both leading to high acceleration amplitudes on the surface.

To study the effects of nonlinearity in the seismic response of soils, a numerical simulation of the propagation of vertically incident seismic waves in horizontal soil layers were performed. Shear noiselike and monochromatic seismic waves of various intensities were used as input signals. The behavior of soils was described by a nonlinear hysteretic model. To extract and study nonlinear components in the ground response, the nonlinear system identification method and analysis of higher-order spectra of oscillations on the surface were applied. Even for weak input signals, the response of the simulated soils contained a noticeable nonlinear component. An increase in the intensity of input signals led to increasing distortions of propagating signals, due to the generation and growth of combination-frequency harmonics. The results show that odd types of nonlinearity are most typical for soils, such as cubic and fifth-order nonlinearities, causing generation of the third and fifth higher harmonics of main frequencies of input signals. Nonlinearities of even types, such as quadratic, fourth-order, and sixth-order, concerned with asymmetry, or skewness, of oscillations (i.e., quasi-static deformations of the surface) are usually weak, except some special cases, in which a stress-strain relationship of a soil can be represented by functions with noticeable even components. A weak nonlinearity results in an increase in high-frequency components, due to the generation of higher harmonics. In cases of strong nonlinearity, in which a decrease in amplification and in shear moduli become noticeable, changes in spectra of propagating signals achieve their maximum. As a result, input signals with arbitrary spectra are transformed into output signals with spectra of the type of E(f) ϳ f k , where k depends on the properties of the medium.

Acceleration records of the 1995 Kobe earthquake and its first aftershocks, provided by vertical arrays at Port Island (PI), SGK, and TKS sites, were used to estimate changes in the shear moduli of subsurface soils caused by strong ground motion. Shear-moduli estimates are based on stress-strain relations determined for consecutive time intervals during the mainshock and aftershocks. We found that in the upper 0-13 m at PI (reclaimed fill above the groundwater level), the shear modulus decreased by ϳ80%-90% of its initial value owing to liquefaction. Signs of its recovery appeared 3-5 min after the decrease in the intensity of strong motion. At depths of 13-18 m (reclaimed fill below the water level) and 27-32.5 m (water-saturated sand) at PI, 0-11 m at SGK, and 0-14 m at TKS (water-saturated alluvium), the shear modulus decrease was estimated at about ϳ80%, 50%-60%, 60%-70%, and ϳ50%, respectively. Recovery began immediately after the decrease in the intensity of strong motion and was completed within a few minutes. The results show that the behavior of the upper layers at sites PI and SGK, where the highest accelerations were recorded, was dynamically unstable. So far as the method can be applied to any site where vertical-array records and profiling data are available, accumulation of representative data on nonlinear soil behavior during strong motion for various soil conditions is desirable. Summarizing and generalizing these data, we may be able to predict soil behavior in future earthquakes.

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