NONLINEARITY IN SITE AMPLIFICATION AND SOIL PROPERTIES DURING THE 1995 HYOGOKEN-NAMBU EARTHQUAKE

SPECIAL ISSUE OF SOILS AND FOUNDATIONS 1-9, Sept. 1998 Japanese Geotechnical Society NONLINEARITY IN SITE AMPLIFICATION AND SOIL PROPERTIES DURING THE 1995 HYOGOKEN-NAMBU EARTHQUAKE TiAICAJ KOKUSHOi) and MASAKI MATSUMOTOii) ABSTRACT Nonlinear seismic amplifications and associated nonlinear soil properties are investigated based on the vertical array records obtained during the 1995 Hyogoken-Nambu earthquake at four sites at very different distances from the earthquake fault zone. These accelerograms were recorded in surface soil layering systems of about 100 m thick consisting of fill, Holocene and Pleistocene or rock base layers. In this research, amplifications in acceleration and velocity between the base and the surface for the main shock and aftershocks are first examined in terms of S-wave velocity ratio between the two levels. A correlation can be found between the amplification and the velocity ratio for linear site responses in the aftershocks, while the amplification is evidently lower for nonlinear response in strong seismic motions for the mainshock. The amplification in acceleration or velocity obviously decreases with increasing input at the base level, indicating remarkable nonlinear amplification characteristics. The acceleration amplification becomes less than unity for base acceleration larger than 0.4 G `0.9 G while velocity amplification stays above unity even for a very large base velocity. Based on the mainshock records, variations in the shear modulus and the damping ratio in the surface soil layers are then evaluated by means of an inversion analysis assuming 1-D vertical SH-wave propagation. A clear strain-dependency can be found in the back-calculated modulus and damping, which are consistent with previous laboratory test results for each kind of soils. Key words: alluvial deposit, damping, diluvial deposit, earthquake, wave propagation (IGC: D7/ E8 / C7) INTRODUCTION Local site amplification is one of the most important factors in seismic zonation study. The site amplification is correlated with properties of soil layers such as soil densities, wave velocities and material dampings. At the same time it is expected to be highly dependent on the nonlinearity of soil properties, particularly in soft soil sites in. The nonlinear seismic response of soft ground due to nonlinear soil properties has been numerically evaluated either by equivalent linear analyses (e.g., Schnabel et al., 1972) or by step-by-step nonlinear analyses (e.g., Constantopoulos et al., 1973) for the past two decades. In model tests, Kokusho et al. (1979) performed shaking table tests of a model ground consisting of fine sand in a laminar shear box about one meter in depth, and demonstrated a very clear reduction in dynamic amplification due to the increasing input acceleration level. The first author (1982) also compared the test results with the equivalent linear analysis and the step-by-step nonlinear analysis based on the soil properties of the model ground under a very low confining pressure to find a fair agreement between them. More recently centrifuge shaking table tests (e.g., Idriss et al., 1993) have been conducted for sand layers in laminar shear boxes to find clear amplification reduction with increasing acceleration again. Thus, the nonlinearity of site amplification due to strong input motions is obviously shown in numerical analyses and model tests. However, due to the absence of vertical array records during strong earthquakes, few people seem to have believed that the nonlinear seismic response would actually occur in local site amplification before the Hyogoken-Nambu earthquake. SITE CONDITIONS AND SEISMIC RECORDS Vertical arrays which could record the main-shock of the 1995 Hyogoken-Nambu earthquake (M3=7.2) were located in four sites in the coastal zone around the Osaka-Bay area, as shown in Fig. 1. The same figure also indicates the fault zone including the epicenters of the main-shock as well as aftershocks. The arrow marks in the figure indicate the principal axes which were deter- Professor, Faculty of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-0003. Kansai Electric Power Company, Osaka. Manuscript was received for review on September 10, 1997. Written discussions on this paper should be submitted before April 1, 1999 to the Japanese Geotechnical Society, Sugayama Bldg., 4F, Kanda Awaji-cho, 2-23, Chiyoda-ku, Tokyo 101-0063, Japan. Upon request the closing date may be extended one month. 1

2 KOKUSHO AND MATSUMOTO mined from NS and EW components to give maximum horizontal accelerations for the four sites. The principal Fig. 1. Location of vertical array sites around Osaka Bay (Sato et al., 1996) and epicenters of main-shock and aftershocks axis for the SGK site shown here differs from the previous results (Sato et al., 1996) reflecting a recent information on the polarization error (Personal communication, 1997) for the surface instrument in the NS direction. The four sites were by chance very properly distributed in terms of distances from the fault zone, as can be estimated from the aftershock epicenters plotted in Fig. 1. PI (the Port Island) array belonging to the Kobe Municipal Office was located just next to the fault zone, while the other three arrays SGK, TKS and KNK belonging to the Kansai Electric Power Company were approximately 15 km, 35 km and 65 km from the fault zone, respectively. The soil profiles and the depths of three dimensional down-hole seismographs are shown for the four sites in Fig. 2, together with P and S-wave velocities measured by the down-hole logging method and SPT N-values along the depth. The deepest seismographs at the base layers were located at GL-83m in PI, GL-97m in SGK, and GL- 100m in TKS and KNK respectively, and the geological condition there were Pleistocene dense gravelly soils, except for KNK (a hard rock). Upper soil conditions at the four sites are rather similar, as shown in Fig. 2, consisting of sandy fill at the surface in most sites, underlain by Holocene clay and/ or sand and farther underlain by Pleistocene soils. The S-wave velocity, Vs, at the base layer of the Pleistocene gravelly soil in PI, SGK and TKS is 380-480 m/ s while V. at the base rock in KNK is as high Fig. 2. Soil profiles, wave logging test results and SPT N-values at four vertical array sites

NONLINEARITY IN AMPLIFICATION AND PROPERTIES 3 as 1630 m/s. The mainshock records obtained in the vertical arrays in the four sites were first examined to discover directional offsets of the buried seismographs in the horizontal plane (Sato et al., 1995). This examination revealed the following directional offsets; a) 15 degrees clockwise rotation at GL-83.4m in PI, b) reverse in the NS-component at GLOm and 34 degrees anti-clockwise rotation at GL- 97m in SGK, c) 30 degrees anti-clockwise rotation at GL- 25m in TKS and d) reverse in the EW-component and 60 degrees anti-clockwise rotation at the ground surface in KNK. All data were accordingly corrected for the later analyses, except for the PI record in which 15 degrees of rotation was judged to have negligible effects on subsequent analyses. These directional offsets were evaluated by drawing the orbits in the horizontal plane for particle motions the periods of which were longer than 5 seconds. More details of the measured time histories and some related discussions are available in other literature (Sato et al., 1996). In order to examine the reliability of these offset values, the maximum coherence method (Yamazaki et al., 1991) has also been applied to the same data set in this research, yielding the offset values as listed in Table 1. Comparison of the two methods reveals that the offset values employed by Sato et al. (1996) are essentially consistent with those by the coherence method despite some quantitative differences. The offset values shown in this table indicates that the original data should be rotated by that angle (anti-clockwise for the plus and clockwise for the minus respectively) to be corrected. A recent information given by a personal communication with researchers taking care of the instrumentation system (Personal communication, 1997) has additionally indicated that, in the SGK site, the polarization in the NS direction was right for the surface level instrument while it was reverse for the two down-hole instruments unlike the previous informations on the installation errors. Considering this fact, the positive and negative signs in values Table 1. Directional offsets of vertical array accelerometers compared by other evaluation methods for the SGK site listed in the table should be totally altered for the correction. The original records all taken by accelerometers were integrated to obtain velocity time histories. Long period drifts unfavorably introduced during the numerical integration were corrected to give reliable time histories with residual drifts as small as possible. AMPLIFICATION ACCELERATION OF MAXIMUM AND VELOCITY Acceleration amplifications along the ground depth are normalized and compared in Fig. 3 between the main shock and the aftershocks for the four vertical array sites. In Fig. 4 normalized velocity amplifications along the ground depth are compared between the main shock and the aftershocks for the four vertical array sites. Amplifications in aftershocks are highly variable, probably due to different dominant frequencies, different incident angles, etc. Amplifications in the main shock are relatively small compared to aftershocks, with some exceptions for KNK where an almost linear response took place and for the EW-direction at PI. It is also noteworthy that each site has its own features in the amplification mode; even the main shock, despite the difference in amplification, still shares the same feature, except for the PI site where liquefaction considerably changed surface layer amplification. In Fig. 5 the ratios of maximum horizontal accelerations between surface and base are plotted against the ratio of S-wave velocities between the two layers. In the figure, open marks represent the mostly linear response for the aftershocks (AS). It should also be noted that the response for the main-shock in KNK was almost linear (Kokusho et al., 1996). The dashed line in the same figure indicates the relationship proposed by Shima (1978) between the peak amplification values of transfer functions between surface and base and the S-wave velocity ratio. Although the open marks are widely scattered, the linear seismic response approximated by the solid line is about 0.4 times of the Shima's line on average. Thus it is clearly indicated that the acceleration amplification for linear response is primarily dependent on the Vs-ratio between the base and the top and is about two fifths of the amplification under the sinusoidal motion on average. On the other hand, the solid marks representing the nonlinear response for the main-shock (MS) in PI, SGK and TKS are located obviously lower than the line approximating the linear response. In Fig. 6 the ratios of maximum horizontal velocities between surface and base are plotted against the ratio of S-wave velocities between the two layers. Almost the same correlation can obviously be found between the velocity amplification approximated by the solid line and the Vs-ratio. In some previous research V, averaged in the upper 30 m of a surface layer is taken instead of V. in the top surface layer (e.g., Midorikawa, 1987). In Fig. 7 the acceleration amplification is plotted against the Vs-ratio, which is taken as the average in the upper 30 m and the base.

4 KOKUSHO AND MATSUMOTO Fig. 3. Normalized acceleration amplification along depth for four vertical array sites Fig. 4. Normalized velocity amplification along depth for four vertical array sites

NONLINEARITY IN AMPLIFICATION AND PROPERTIES 5 Fig. 5. Maximum horizontal acceleration ratio plotted against Vs-ratio between surface and base for four vertical array sites Fig. 7. Maximum horizontal acceleration ratio plotted against Vs-ratio between upper 30 m average and base for four vertical array sites Fig. 6. Maximum horizontal velocity ratio plotted against Vs-ratio between surface and base for four vertical array sites Fig. 8. Maximum horizontal velocity ratio plotted against Vs-ratio between upper 30 m average and base for four vertical array sites Although the data concentrates around 2 in the Vs-ratio, the linear response may be approximated by the solid line in Fig. 7, while nonlinear acceleration ratios are located mostly below this. Figure 8 shows a similar relationship for the velocity amplification to give almost the same trend. In Fig. 9 the maximum horizontal acceleration ratio between the surface and the base is plotted against the maximum acceleration at the base. The solid marks are for the hard rock base in KNK with a Vs-ratio of 7, the amplification of which are obviously located higher than other sites, indicating a significant influence of Vs-ratio on the amplification. The open marks in the same figure corresponding to the other three sites of the Pleistocene soil base with a Vs-ratio of 2 to 4 appear to show nonlinear effects with increasing base accelerations as indicated by a pair of dashed thin curves. On the basis that the data for the three sites are mixed together, despite rather large Fig. 9. Maximum horizontal acceleration ratio plotted against maximum base acceleration for four vertical array sites

6 KOKUSHO AND MATSUMOTO Fig. 10. Maximum horizontal velocity ratio plotted against maximum base velocity for four vertical array sites scatters, they may be approximated as a single group a straight line on the chart (the regression coefficient = 0.57) and by the following empirical formula; where Acc.face and A CCbase stand for the maximum accelerations at the ground surface and at the base respectively and are in cm/s'. By extrapolating this line, the amplification lowers to the 1.0 line at A ccbase 900 cm/ s2. If special attention is given to the open circle at the extreme right of the chart corresponding to the PI NS-direction, which reflects soil nonlinearity in deeper layers and the extensive liquefaction in the fill layer, the nonlinear curve in the same chart may be drawn. In this case that critical value is A ccbase 400 cm / s2. These critical accelerations at the Pleistocene base layer may be comparable to the cross-over acceleration of 0.4 G at out cropping rocks proposed by Idriss (1990) based on surface earthquake records for North American earthquakes and numerical The velocity amplification shown in Fig. 10 also indicates an evident decrease with increasing base velocity, which may be approximated by the straight line (the regression coefficient = 0.51) and by the following formula; in which Velsur face and Velbase a are maximum velocities at the surface and base respectively and in cm/s. Unlike the acceleration, the velocity amplification takes larger values as a whole and does not seem to go lower than unity even for a base velocity as large as 100 cm/ s, indicating that the velocity is unlikely to deamplify even at a very soft soil site during a strong shaking like the Hyogoken-Nambu earthquake. BACK-CALCULATED STRAIN-DEPENDENT SOIL PROPERTIES The above discussed nonlinearity in amplifications of (1) (2) acceleration and velocity may possibly reflect nonlinearity in soil properties due to seismically induced strain amplitude. In order to back-calculate the degree of soil nonlinearity exerted during the main-shock earthquake, inversion analyses were carried out for the vertical array records at the four site. The details of the analysis are available in other literature (Sato et al., 1996). Based on the back-calculation for dynamic soil properties best reproducing site responses in the four vertical array sites, it becomes possible to synthesize strain-dependent curves of modulus degradation and damping ratio. The shear modulus ratio, G/ Go, where G and Go are shear modulus for a certain strain level and the initial modulus for infinitely small strain, respectively, can be readily calculated as the square of the Vs-ratio between the back-calculated V; and Vs for the wave logging test. Effective shear strain, yeff, corresponding to a modulus degradation may be assumed at 2/3 of maximum strain, ymax, in a similar manner to that employed in design practice and calculable from the max. strain distributions as shown in Fig. 11. The maximum strain distributions in this figure are computed by linear multi-reflection analysis employing the back-calculated moduli and damping ratios. The shear modulus ratios thus calculated in NS and EW directions for all individual soil layers in the soil profiles in the four sites are plotted against the logarithm of the corresponding effective strain in Fig. 12. The plots with the arrow marks correspond to soil layers where it was evidenced by the inversion analysis (Kokusho et al., 1996) or actually witnessed that liquefaction fully or partially took place during the earthquake. By excluding these plots and also several other plots exceeding G/ Go= 1.0, the modulus degradation can be obviously represented by the chain-dotted curves in the chart. Those points which exceed G/ Go= 1.0 all belong to KNK site, implying that some review in the optimized properties or in the site investigation results might be needed. The damping ratios back-calculated in NS and EW directions for all individual soil layers in the soil profiles in the four sites are plotted against the logarithm of the corresponding effective strain in Fig. 13. Although some damping ratios as high as 50% corresponding to the liquefied layer in PI should better be excluded in discussing strain-dependent damping ratio for design purposes, there is an evident trend of increased damping with the increase of effective strain in all other data. Numerous laboratory tests have been conducted to date to measure the strain-dependent changes of modulus and damping on many types of soil. Based on these data, modulus degradation curves for clay and sand may be represented for example by Fig. 14 (Kokusho et al., 1982; Kokusho, 1980). It is clearly seen that the curve for sand is positioned more to the left than that for clay on the chart, and for sand the curves tend to shift to the right with the increase of confining stress. For clay the curve, which is insensitive to the difference in confining stress, tends to shift from an original position for nonplastic soil (sand) to the right with the increase of the plasticity index, Ip. For gravels, as shown in Fig. 15(a), the

NONLINEARITY IN AMPLIFICATION AND PROPERTIES 7 Fig. 11. Maximum shear strain versus depth relationships at four sites evaluated by multi-reflection analysis based on back-calculated soil properties (Sato et al., 1996) Fig. 12. Shear modulus ratio versus effective strain charts obtained from back-calculation at four sites Fig. 13. Damping ratio versus effective strain charts obtained from back-calculation at four sites curves are positioned more left than sand and clay, and also shift with varying confining pressure (Kokusho and Tanaka, 1994). For damping ratio, laboratory test data for gravel are shown compared with other soil types in Fig. 15(b), indicating that a similar trend to the modulus degradation curve seems to exist for the damping curves for different soil types and confining stress. In order to know the field performance in strain-dependent variations of modulus and damping ratio for different soil types, the data in Figs. 12 and 13 are further classified into four soil types; clay, silt, sand and gravel, based on original descriptions in boring logging data sheets as indicated in Fig. 2. Figure 16 shows the same plots of modulus degradation as in Fig. 17 but with different symbols representing the four types of soil. Despite rather large data scatter, it may be judged from this

8 KOKUSHO AND MATSUMOTO Fig. 16. Shear modulus ratio versus effective strain charts classified for four soil types Fig. 14. Laboratory test results on shear modulus degradation for clay and sand (a) (b) Fig. 17. Damping ratio versus effective strain charts classified for four soil types Fig. 15. Laboratory test results on strain-dependency of modulus and damping for gravel figure that modulus degradation curves can obviously be separated into different groups according to different soil types; the degradation curve for clays is positioned at the extreme right and that for gravels of the extreme left, while silts and sands are located between the two. In the same manner, damping ratios are shown only for the damping values less than 20% and classified into the four soil types in Fig. 17. This figure also indicates a clear trend of strain-dependent damping variation which is unique to each type of soil: clay is the most rightward, gravel the most left and the others are in between. The solid marks in Figs. 16 and 17, indicating the results similarly back-calculated by other researchers (Yamaguchi et al., 1996) for the vertical array data in the off-shore Kansai Airport during the same earthquake are also consistent with this research. In Figs. 16 and 17, modulus degradation curves and strain-dependent damping variation curves by laboratory tests discussed before are drawn for gravel, sand and clay to compare with the back-calculation results. In comparing the laboratory properties with the back-calculated insitu properties, the following should be borne in mind; The plasticity indices Ip of clays around the Osaka bay area cover a wide range between 100 and 20, with their majority falling in between 80 and 40 while the laboratory test data are for /p= 40 to 83. The interval of in-situ confining stress for sands may be approximated as 20 to

NONLINEARITY IN AMPLIFICATION AND PROPERTIES 9 300 kpa, which coincides with the lab test data. Because of the great depth of gravel layers in the PI, TKS and KNK sites, the interval of in-situ confining stress for gravels is likely to slightly exceed the higher stress limit of 400 kpa for the lab test data. Though there is a certain amount of scatter in back-calculated properties, relatively good agreement can be recognized between the back-calculated field performance and laboratory tests, demonstrating that laboratory dynamic soil properties can basically be applied to the evaluation of nonlinear site response during strong earthquakes. CONCLUSIONS Strong motion records obtained during the Hyogoken- Nambu earthquake in four vertical array sites have been utilized to evaluate nonlinear site amplifications and nonlinear soil properties during the main-shock and aftershocks, yielding the following principal findings. 1) Acceleration and velocity amplifications between the surface level and the base level are correlated to the 5- wave velocity ratio between the same two levels. A correlation between the linear amplification for weak motions and the wave velocity ratio can be seen, while nonlinear amplification for strong motions is evidently lower than that. 2) The amplification tends to monotonically decrease with increasing acceleration or velocity at the base level, and eventually becomes lower than unity for acceleration, while for velocity it stays higher than unity. 3) Strain-dependent changes in the shear modulus and the damping ratio are clearly back-calculated from the vertical array records, in which different strain-dependency curves can be identified for clay, silt, sand and gravel. 4) The strain-dependency curves thus back-calculated for different soil types are found to agree well with those by laboratory tests, demonstrating that nonlinear dynamic soil properties measured in the laboratory can be basically applicable to numerical analyses for nonlinear site response during strong earthquakes. Further study is obviously needed, however, to examine quantitative applicability of the amplification which has been site-specifically found in this research and to modify it for better estimation for nonlinear response during strong earthquakes. ACKNOWLEDGMENTS The earthquake records used in this research have been provided by the Kansai Electric Power Company and the Committee of Earthquake Observation and Research in Kansai Area. The authors gratefully appreciate their activities and kindness. Four students of the Chuo University, T. Aoyagi, M. Honma, R. Motoyama and Y. Takahashi, implemented the coherence analysis for the directional offsets of the vertical array accelerometers and two students of the same University, T. Endo and M. Sakano, performed the integration of the acceleration records. Drs. N. Yoshida and I. Suetomi of Sato Kogyo Company Ltd. who widely helped their analyses are also gratefully REFERENCES acknowledged. 1) Constantopoulos, I. V., Roesset, J. 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