Theoretical Solution To Liquefaction-Induced Change of Site Predominant Period

Abstract eng:
Not only the ground failure but also the change of natural frequency of the site is induced by the liquefied layer, while from the vibration point of view the structure seismic response from the vibration point of view would be effected by the change of the site natural frequency due to the liquefaction. In this paper, the analytical solution to the site predominant period with a liquefied interlayer is presented by simplifying the actual horizontal site into the three-mass system with a liquefiable mass. The natural frequency decreasing ratio of the site (NFDRS) due to the liquefaction is derived and the influence of the main factors on NFDRS is demonstrated. The effects of the liquefied layer on NFDRS is ranked to four degree. The results in the paper indicate that the natural frequency of the site would be decreased by the liquefied interlayer and the NFDRS depends on three factors: the two thickness ratio of the liquefied layer to the non-liquefied upper layer , the non-liquefied sub layer to the liquefied layer, and shear modular ratio of the liquefiable soil before and after liquefaction. The effect of liquefied layer on NFDRS is heavy in most cases, medium in some cases, very heavy in a few cases and slight in few cases. NFDRS is mainly depends on the thickness ratio of the liquefied layer to the non-liquefied upper layer , and the relation between NFDRS and λ 1 can be describe in three modes. The thickness ratio of the non-liquefied sub layer to the liquefied layer play the second prominent part in NFDRS and the curve of NFDRS with λ 2 could be divided into two stages, i.e., rapid growth and smooth growth. Although NFDRS increases with the increasing of the shear modular ratio of liquefiable soil before and after liquefaction, the maximum increasing amplitude of NFDRS is less than 0.15. For the thin hard site, the liquefied layer shows the significant effect on NFDRS. While the liquefied layer exists the lower part of the site the effect is very significant. For the medium site, NFDRS due to the liquefaction varies gradually from the slight level to the medium degree and to the significant degree with increasing of the thickness and depth of the liquefiable layer. For the deep soft site, NFDRS due to the liquefaction varies gradually from the slight degree to the medium degree with increasing of the thickness of the liquefiable layer.

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