## Limit State of Liquefaction C. Hsein Juang 2006

The limit state for liquefaction triggering is obtained using a neural network-based searching technique developed by Juang et al. 2000b. The technique involves the training of supervised feed-forward neural networks with the “full” database of case histories and its subsets or samples. The successfully trained neural network that generates the most accurate input–output relationship is adopted in the subsequent step for searching “data points” on the unknown boundary surface. Regression analyses of the searched data points, with some engineering judgment, yields the following empirical equation for liquefaction resistance:

CRR = exp(-2.8781 + 0.000309(qc1N,m)1.8 1)    (1)

where:

qc1N,m=stress-normalized cone tip resistance qc1N adjusted for the effect of “fines” on liquefaction thus, qc1N,m=K·qc1N.

The  stress-normalized cone tip resistance qc1N used herein follows the definition by Idriss and Boulanger 2004, although the difference between this definition and that by Robertson and Wride 1998 is rather small for the cases examined.

K is part of the regression model and expressed as:

K = 1 for Ic < 1.64 (2)
=1 + 80.06(Ic − 1.64)(qc1N)−1.2194 for 1.64 <Ic<  2.38
=1 + 59.24(qc1N)−1.2194 for Ic> 2.38 

Both Ic and qc1N in Eqs. 2 are dimensionless. The term Ic in Eqs. 2 is a variant of the soil behavior type index defined by Lunne et al. 1997 and Robertson and Wride 1998, and updated in Zhang et al. 2002. Although Ic was initially developed for soil classification, use of Ic to “gage” the effect of “fines” on liquefaction resistance is well accepted Robertson and Wride 1998; Youd et al. 2001;

As with any simplified methods that follow the general framework  by Seed and Idriss 1971, CRR is defined as the critical CSR that causes liquefaction for a given soil. Thus, it is essential
that the CRR equation has to be used along with the reference CSR equation. To use Eq. 1 for determination of CRR, the following cyclic stress ratio model must be used:

CSR7.5σ = 0.65·(σv/σ’v)·(amax/g)·rd·(1/MSF)·(1/Kσ) (3)

where:

g=acceleration of gravity, which is the unit for amax;
rd=depth-dependent shear stress reduction factor dimensionless;
MSF=magnitude scaling factor dimensionless;
Kσ=overburden correction factor dimensionless for CSR.

In Eq. 3, CSR7.5, is the CSR defined by Seed and Idriss 1971 adjusted to the conditions of Mw moment magnitude=7.5 and σ=100 kPa. Such adjustment makes it easier to process case histories from different earthquakes and with soils of concern at different overburden pressures Juang et al. 2003. It should be noted that in this paper, the terms rd, MSF, and Kσ are calculated with the formulae recommended by Idriss and  Boulanger 2004;

The method C. Hsein Juang was implemented in software LIQUITER

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