Statistical Model of Boulder Size and Fraction

Abstract

The presence of boulders in a soil stratum could pose problems during construction and affect satisfactory performance of a geotechnical system. Statistical description of boulders can be useful in assessing the reliability of satisfactory geotechnical performance and in decision making. Statistics of boulder size and volume fraction may be inferred from boring logs. However, the dimension of each boulder recorded in a boring log does not necessarily represent its diameter (assume spherical boulder); moreover, larger boulders are more likely to be encountered. Bayesian method is applied to treat this censored sampling problem, with the objective of determining the distribution of the in situ boulder population from the observed chord length of boulders intercepted by borings. The spatial variation characteristic of the fraction of boulder volume across a given site can also be inferred from the boring logs at scattered locations. A method for updating these statistics established for a macro region with additional local data in a specific construction site is developed. The technique is applied to a site in Singapore where a large number of borings through a boulderous stratum has been reported.