Reliability analysis of soil liquefaction using truncated distributions

Abstract

Soil liquefaction is a phenomenon caused by seismic activity in the ground which may result in surface settlement, the formation of sand boils, lateral spreading that ultimately damages the super-structure and loss of lives. This kind of natural disasters has been reported vastly from last few decades in different regions of the world. Soil Liquefaction triggering occurs in silty and sandy soils. The huge damage due to liquefaction at Niigata, Japan, and Alaska due to the earthquake that occurred in 1964, extensively grabbed the attention of many geotechnical researchers. SPT based empirical relationship is usually used to evaluate soil liquefaction. However, a few parameters involved in the analysis are associated with a great extent of uncertainties. A reliability-based analysis provides an approach to consider various uncertainties and provides the probability for the failure of the structure. Due to site conditions and other reasons, it is difficult to obtain complete information about a random variable. Therefore, very often we come across censored samples. It is important that we design an reliable engineering structure based on censored samples. The primary objective of the research is to perform a reliability analysis based on censored samples. The research focuses on developing the deterministic, probabilistic and reliability-based models to calculate soil liquefaction resistance using historical liquefaction database based on the SPT. The principle of maximum entropy is incorporated to develop probability density function that includes various uncertainties associated with soil and site parameters. With the development of computing techniques like artificial intelligence, it is possible to frame the empirical relationship between the seismic load and resistance offered by the soil. Standard penetration test based database of soil liquefaction is used in the artificial neural network to predict the liquefaction index. Further, the developed liquefaction index model is utilized for modeling the empirical relationship between clean sand equivalence corrected standard penetration test-N count and cyclic resistance ratio. The deterministic model is developed, and the relationship for estimating the resistance offered by soil to liquefaction is established by identifying the best fit curve. Bayesian mapping theory is used for determining the function for liquefaction probability. With the knowledge about the expected values from the database, maximum entropy distributions are plotted for seismic, site and soil parameters. The developed probability density function of the random variables are utilized for performing the first order reliability analysis. Using sensitivity analysis, the degree of conservatism is identified and eliminated from performance function. Finally, the calibrated performance function is framed which can be used for performing reliability analysis on truncated samples. The truncated normal and log-normal probability density function are developed using the information available on censored samples. The parameters of the truncated normal distribution are estimated using maximum likelihood method and Newton-Raphson’s iterative procedure. When dealing with censored samples, the flow of iteration points has a limitation in reliability analysis. For this reason, a new algorithm is proposed to identify the reliability index for liquefaction potential based on global search.