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In this paper,the non-linearity of the gravelly and clayey soils in Japan is investigated based on KiK-net down-hole array seismic observations.Shear modulus reduction ratios at 18 sites under 165 strong motions are calculated by comparing the response amplification spectra(surface response normalized by bedrock response)subjected to strong motions with those subjected to weak motions and are plotted versus the corresponding seismically induced shear strains.The back-calculated shear modulus reduction ratios are categorized into several groups under different effective confining pressures and a best-fit line is proposed for each group as the corresponding empirical shear modulus degradation curve.The obtained results are compared with the existing studies based on both in-situ and laboratory tests,highlighting the influence of different testing techniques on non-linear soil behavior.Furthermore,a modified cyclic non-linear model is employed to formulate the proposed empirical curves to account for the shear modulus degradation under a wide range of effective confining pressure.This modified model can then be employed to specify material constitutive relations for the future numerical analysis of geotechnical structures under seismic loads.