4.5.8 Thickness of sand layer -- 4.6 Methods for assessing liquefaction potential -- 4.7 Machine learning methods -- 4.7.1 Back propagation neural network -- 4.7.2 Support vector machine -- 4.7.3 Radial basis function neural network -- 4.8 Methodology -- 4.9 Conclusion -- References -- 3 Machine learning in numerical modelling of geotechnical problems -- 5 Introduction to system reliability analysis for geotechnical infrastructures -- 5.1 Introduction -- 5.2 Basic statistical concepts -- 5.2.1 Random variable -- 5.2.2 Mean of a random variable -- 5.2.3 Standard deviation of a random variable -- 5.2.4 Variance of a random variable -- 5.2.5 Independent random variables -- 5.2.6 Covariance -- 5.2.7 Correlation coefficient -- 5.2.8 Probability density function and cumulative distribution function -- 5.2.9 Probability distribution functions -- 5.2.9.1 Normal distribution function -- 5.2.9.2 Lognormal distribution function -- 5.2.9.3 Probability distribution function -- 5.2.9.4 Exponential distribution function -- 5.2.9.5 Beta distribution function -- 5.3 Reliability assessment methods -- 5.3.1 Fundamental reliability concepts -- 5.3.1.1 Central safety factor, reliability index, and probability of failure (Pf) -- 5.3.2 Monte Carlo simulation -- 5.3.3 First order reliability method -- 5.3.3.1 Illustrative example 1 -- 5.4 Series, parallel, and combined systems -- 5.4.1 Reliability of series systems -- 5.4.2 Reliability of parallel systems -- 5.4.3 Cornell bound method -- 5.4.4 Reliability of combined systems -- 5.4.5 Equivalent linear safety margin for parallel systems -- 5.4.5.1 Illustrative example 2 -- 5.5 Sequential |