Evaluation of prior probability distribution of undrained cohesion for soil in Nasiriyah
The objective of the study is to evaluate the prior probability distribution (PPD) of undrained cohesion (Cu) parameter for soil in Nasiriyah, southern Iraq, based on prior knowledge and observations. Estimated PPD of Cu can be used in Bayesian approach to update the observed value in any project in this region using the posterior probability distribution, because it is considered as a measure of the initial belief about a random variable before considering any data. The research used five methods to express the PPD of Cu. Two of them are for non-informative data, i.e. uniform distribution and Jeffreys prior, and three of them – for informative data, which include maximum entropy, regression analysis and subjective probability. They were applied to data collected from different sources in Nasiriyah, based on site investigation reports. The ranges of mean, standard deviation and vertical scale of Cu fluctuation were found to be 12–62 kPa, 0.5–27.6 kPa and 6–8 m, respectively. It was concluded that Jeffreys method is used well with individual models at the mean value of cohesion of 28.66 kPa and the standard deviation of 1.19 kPa. The maximum entropy can be used for the least informative data, while respecting the given constraints. The mean value of cohesion was 28.7 kPa, and the standard deviation was 1.2 kPa. Finally, for a finite number of 152 cohesion values, the subjective probability assessment approach, which takes into account expert knowledge and judgment, is the most appropriate method with the mean value of cohesion of 37 kPa and the standard deviation of 8.8 kPa.