Effect of sampling plan and trend removal on residual uncertainty

The ground is one of the most highly variable of all engineering materials. As a result, geotechnical designs depend upon a site investigation to estimate the ability of the ground to perform acceptably. For example, when a shallow foundation is being proportioned to avoid a bearing capacity failure under a certain applied load, the frictional and cohesive properties of the ground under the foundation must first be estimated through a site investigation. Questions which arise are: How does the quality and intensity of the site investigation affect the design? Is more investigation cost effective? If the site is sampled at one location and the foundation placed at a different location, how does this mismatch affect the target design and the reliability of the final foundation? By modelling the ground as a spatially variable material, questions such as the above can be investigated through Monte Carlo simulation and sometimes theoretical probabilistic models. Using such tools, this paper looks specifically at how the intensity (frequency and spatial distribution) of a site sampling plan, and how the samples are used, affects the understanding of the ground properties under a foundation. Interestingly, it is found that removing the sample mean outperforms removing the best linear unbiased estimate (BLUE) when the actual field correlation length is small but the BLUE correlation length is assumed equal to the field size. Recommendations are made regarding number of samples and the type of trend to best characterise the field. Abbreviations: BLUE: best linear unbiased estimate; MCS: Monte Carlo simulation; LAS: local average subdivision