The limit state for liquefaction triggering\u00a0is obtained using a neural network-based searching technique developed\u00a0by Juang et al. \u00012000b\u0002. The technique involves the training\u00a0of supervised feed-forward neural networks with the \u201cfull\u201d\u00a0database of case histories and its subsets or samples. The successfully\u00a0trained neural network that generates the most accurate\u00a0input\u2013output relationship is adopted in the subsequent step for\u00a0searching \u201cdata points\u201d on the unknown boundary surface.\u00a0Regression analyses of the searched data points, with some engineering\u00a0judgment, yields the following empirical equation for\u00a0liquefaction resistance:<\/p>\n
CRR = exp\u0003(-2.8781 + 0.000309\u0001(qc1N,m\u0002)1.8\u0004 \u00011<\/sup>\u0002) \u00a0 \u00a0(1)<\/strong><\/p>\n where:<\/p>\n qc1N,m=stress-normalized cone tip resistance qc1N adjusted\u00a0for the effect of \u201cfines\u201d on liquefaction \u0001thus, qc1N,m=K\u00b7qc1N\u0002.<\/p>\n The \u00a0stress-normalized cone tip resistance qc1N used herein follows the\u00a0definition by Idriss and Boulanger \u00012004\u0002, although the difference\u00a0between this definition and that by Robertson and Wride \u00011998\u0002 is\u00a0rather small for the cases examined.<\/p>\n K is part of the regression model and expressed as:<\/p>\n K = 1 for Ic <\u0005 1.64\u0002 (2)<\/strong> Both Ic and qc1N in Eqs. \u00012\u0002 are dimensionless. The term Ic in\u00a0Eqs. \u00012\u0002 is a variant of the soil behavior type index defined by\u00a0Lunne et al. \u00011997\u0002 and Robertson and Wride \u00011998\u0002, and updated\u00a0in Zhang et al. \u00012002\u0002. Although Ic was initially developed for soil\u00a0classification, use of Ic to \u201cgage\u201d the effect of \u201cfines\u201d on liquefaction\u00a0resistance is well accepted \u0001Robertson and Wride 1998;\u00a0Youd et al. 2001;<\/p>\n As with any simplified methods that follow the general framework \u00a0by Seed and Idriss \u00011971\u0002, CRR is defined as the critical\u00a0CSR that causes liquefaction for a given soil. Thus, it is essential
\n=1 + 80.06\u0001(Ic \u2212 1.64\u0002)(\u0001qc1N\u0002)\u22121.2194<\/sup> for 1.64\u0001 <Ic< \u0001 2.38\u0002
\n=1 + 59.24\u0001(qc1N\u0002)\u22121.2194<\/sup> for Ic>\u0002 2.38 \u0002<\/p>\n
\nthat the CRR equation has to be used along with the reference\u00a0CSR equation. To use Eq. \u00011\u0002 for determination of CRR, the\u00a0following cyclic stress ratio model must be used:<\/p>\n