Optimal multi-parameter sampling for geostructural design

The common use of a minimal number of samples to determine geotechnical material parameters is a frequent source of difficulty for structural design engineers. One-parameter decision analysis has suggested that numbers of samples greater than that commonly used in current practice would be more risk-optimal. Building on this result, a multi-parameter theory is developed for the risk-optimal number of samples to be measured when characterising individual material parameters. The theory also considers the effect of coupled (measured in a single test) and correlated parameter pairs. As in the single-parameter case, the number of samples appropriate to a particular problem is dictated by the level of reliability used in the design, the cost of testing, and the damages for which the owner would be liable in the event of failure. By implementing the framework for a square footing and a slope embankment, it is shown that optimal sample sizes of 5-20 measurements per parameter are optimal, with the upper end of the spectrum commensurate with more severe failure consequences. It is suggested that the single-parameter end-case provides a conservative guideline to the risk-optimal number of sample measurements, appropriate for use in standards of practice.