Robustness of Fitted Behavioural Relationships from Limited Geotechnical Datasets: Application to Sand Castle Test Data

Abstract

Engineering decisions are often based on fitted relationships derived from limited datasets, where individual observations may exert disproportionate influence on interpretation. This paper presents a practical framework for assessing the robustness of such relationships using a simple leave-one-out influence analysis. The approach is demonstrated using Sand Castle Test (SCT) data, in which relative compaction (RC) is related to collapse time ( T ) through a logarithmic relationship governing collapsibility and crack-stopping behaviour. The fitted slope is treated as a sensitivity descriptor, while the compaction window ΔRC (15 → 60) provides a physically meaningful measure of behavioural transition. Two case studies illustrate both robust and point-sensitive datasets. A normalised slope influence index is introduced to quantify dependence on individual observations and to identify data points controlling interpretation. Results show that apparently well-defined relationships may be sensitive to single observations, and that uncertainty in slope propagates directly into uncertainty in the inferred transition between collapsible and crack-holding behaviour. The proposed framework links statistical robustness to engineering interpretation by enabling identification of critical data points and supporting more defensible assessment of behaviour. Although demonstrated for SCT data, the approach is broadly applicable to geotechnical problems where fitted relationships are used to define project-specific criteria from limited datasets.