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Although, different approaches and methodologies have been used to develop predictive models for evaluation of liquefaction potential over the years by various researchers any attempt to improve the existing methods for assessing liquefaction potential is considered as a contribution to the field of geotechnical engineering in mitigating the liquefaction hazards. In recent years, soft computing techniques such as ANN, SVM and RVM have been successfully implemented for evaluation liquefaction potential. However, the ANN has poor generalization, attributed to attainment of local minima during training and needs iterative learning steps to obtain better learning performances. The SVM has better generalization compared to ANN, but the parameters ‘C’ and insensitive loss function (ε) needs to be fine- tuned by the user. Moreover, these techniques will not produce a comprehensive relationship between the inputs and output, and are called as ‘black box’ systems.
In the recent past, evolutionary soft computing technique, genetic programming (GP) based on Darwinian theory of natural selection is being used as an alternate soft computing technique. The GP is defined as the next generation soft computing technique and also called as a ‘grey box’ model (Giustolisi et al. 2007) in which the mathematical structure of the model can be derived, allowing further information of the system behaviour. The GP models have been applied to some difficult geotechnical engineering problems (Yang et al. 2004; Javadi et al. 2006; Rezania and Javadi 2007; Alavi et al. 2011; Gandomi and Alavi 2012b; Muduli et al. 2013) with success. However, its use in liquefaction susceptibility assessment is very limited (Gandomi and Alavi 2012b). The main advantage of GP and its variant, MGGP over traditional statistical methods and other artificial soft computing techniques is its ability to develop a compact and explicit prediction equation in terms of different model variables.
Out of different analysis frameworks, which are in use deterministic method is preferred by the geotechnical engineering professional because of its simple mathematical approach with minimum requirement of data, time and effort though, probabilistic methods are also in use for taking risk-based (i.e., PL-based) design decisions. Thus, in the present study first,
MGGP has been used as an analysis tool to develop deterministic models using available high quality post liquefaction SPT and CPT-based case history databases. Here, the
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liquefaction potential is evaluated and expressed in terms of liquefaction field performance indicator, referred as liquefaction index (LI) and factor of safety against occurrence of liquefaction (Fs). The predicted value of LI in a future seismic event can be obtained by
using developed SPT and CPT-based LIp model equations with the help of a spread sheet,
which will indicate the occurrence or non-occurrence of liquefaction. The efficacy of the developed LIp models in terms of rate of successful prediction of liquefaction and non-
liquefaction cases have been compared with available soft computing technique (ANN, SVM)-based models using independent data and are found to be comparable. Further, the developed LIp models have been used to develop both SPT and CPT-based CRR models.
These developed CRR models in conjunction with the widely used CSR7.5 model, form the
proposed MGGP-based deterministic methods. These developed SPT and CPT-based deterministic models can be used to evaluate liquefaction potential in terms of Fs. The
efficiency of both the developed SPT and CPT-based deterministic models have been compared with that of available statistical and ANN-based models on the basis of independent database and it has been found that the results are quite good. Using the obtained Fs, further design decision can be taken by the geotechnical professionals regarding
extent of ground improvement techniques to be followed for a liquefaction susceptible site. Two examples have been solved to show the use of developed deterministic methods to find out the extent of ground improvement works needs to be done in terms of N1,60 and qc1N
using the adopted factor of safety.
However, because of uncertainties associated with the parameters and developed deterministic models, Fs greater than 1.0does not necessarily guarantee zero chance of being
liquefied and similarly, Fs less or equal to 1 does not always correspond to liquefaction. In
order to overcome the mentioned difficulties in the proposed SPT and CPT-based deterministic methods, probabilistic evaluation of liquefaction potential has been performed where liquefaction potential is expressed in terms of probability of liquefaction(PL) and the
degree of conservatism associated with developed deterministic models are quantified in terms of PL. By calibrating the calculated Fs of each of the case of the database with field
manifestations (liquefaction or non-liquefaction) as recorded in the database and using Bayesian theory of conditional probability the Fs is related with the PL through the
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developed mapping functions. The developed SPT and CPT-based probabilistic models have been compared in terms of rate of successful prediction within different limits of PL, with
that of the available statistical and ANN-based probabilistic models. The results are found to be better than that of the available methods. Two examples, one from SPT-based and the other from CPT-based post liquefaction data, have been illustrated to show the use of developed probabilistic methods to take risk-based (i.e., on the basis of PL) design decision
for carrying out ground improvement work for a site susceptible to liquefaction.
Several probabilistic models including the present SPT and CPT-based probabilistic models as presented in the Chapter-V, have been developed for evaluation of liquefaction potential in terms of PL. These models are all data-driven as they are based on statistical analyses of
the databases of post liquefaction case histories. Calculation of PL using these semi-
empirical models requires only the mean values of the input variables, whereas the uncertainties in both the parameters and the model are excluded from the analysis. Thus, resulting PL might be subjected to error if the effect of parameter and model uncertainties
are significant. To overcome these disadvantages reliability analysis following FORM has been carried out using high quality SPT and CPT database, which considers both model and parameter uncertainties. In the framework of reliability analysis, the boundary curve separating liquefaction and non-liquefaction is a limit state. The multi-gene GP (MGGP) has been used to develop CRR model of soil using new SPT and CPT database as per Cetin (2000) and Moss (2003), respectively. Each of the developed CRR model along with most recent CSR model (Idriss and Boulanger 2006) forms the limit state model of liquefaction for reliability analysis. The uncertainties of input parameters were obtained from the database. But, a rigorous reliability analysis associated with the Bayesian mapping function approach was followed to estimate model uncertainty of the limit state, which is represented by a lognormal random variable, and is characterized in terms of its two statistics, namely, the mean and the coefficient of variation. Four examples, two from SPT data (one liquefied and the other non-liquefied case) and the other two from CPT data (one liquefied and the other non-liquefied case), have been illustrated to show the procedure of reliability-based liquefaction potential evaluation in terms of notional probability of liquefaction (PL)
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limit state models in the analysis. The PL of a site in a future seismic event using the
proposed reliability-based analysis can be evaluated if the uncertainties of soil and seismic parameters of the site are known and without any more back analysis of post liquefaction SPT/CPT database.
7.2 CONCLUSIONS
The major conclusions of the present study are given as below:
7.2.1 Based on Deterministic method
i. A compact MGGP-based LIp model equation is presented to predict the soil
liquefaction in a future seismic event using SPT data. The liquefaction classification accuracy (94.19%) of the above developed model is found to be better than that of available ANN-based model (88.37%) and at par with the available SVM-based model (94.19%) on the basis of the testing data.
ii. A MGGP-based model equation is also presented for CRR of soil using SPT data which in conjunction with CSR7.5 (Youd et al. 2001) can be used to predict the factor
of safety against occurrence of liquefaction. The overall success rate of prediction of liquefaction and non-liquefaction cases by the proposed method for all 288 cases in the present database is found to be 93.40%.
iii. Using an independent database (Idriss and Boulanger 2010) the proposed MGGP- based deterministic method (87%) is found to more accurate in predicting liquefied and non-liquefied cases than the existing ANN based method (86%) and statistical method (84%) on the basis of calculated Fs. The proposed method is also found to
be efficient in isolating non-liquefied cases without considering the effect of fines content.
iv. CPT-based post liquefaction database (Juang et al. 2003) is analyzed using multi- gene genetic programming approach to predict the liquefaction potential of soil in terms of liquefaction field performance indicator, LI.
v. The efficacy of the developed MGGP based models (Mode-I and Model-II) are compared with that of the available ANN and SVM-based models, respectively. It is