Quantitative characterisation of Quaternary glaciofluvial aquifer heterogeneity using cluster analysis

Hydrogeological modelling requires the characterisation of hydrofacies and the representation of their spatial distribution. In this work, a workflow was developed to characterise heterogeneous unconsolidated glaciofluvial sediments in Northwest Cumbria (UK), which involved: (1) field sampling; (2) lithofacies classification; (3) in situ porosity measurements using the sand-replacement method; (4) determination of the particle size distribution (PSD); (5) hydrofacies definition via K-means cluster analysis using PSD data; (6) evaluation of empirical equations for predicting porosity using field measurements and regression analysis; and (7) estimation of hydraulic conductivity (K) using the Kozeny–Carman equation. Nine lithofacies were identified, including glaciofluvial silts, sands and gravels, and local till deposits. Three clusters were defined on the basis of PSD: fine-dominated (cluster-1), sand-dominated (cluster-2) and gravel-dominated (cluster-3). Cluster-1 exhibited the highest porosities (average 44%); cluster-2 showed intermediate to high porosities, with an average porosity of 40%; and cluster-3 had the lowest porosities (average 27%). The logarithm of d50 was the parameter with the highest correlation with measured porosities (R2 of 0.789). K values estimated using the Kozeny–Carman equation ranged between 0.06 and 0.2 m/d for cluster-1, 0.2–11 m/d for cluster 2, and 0.1–62 m/d for cluster 3. Measured porosities were higher than previously reported, while estimated K values were consistent with those from hydraulic tests. Comparison between lithofacies and clustering classification suggests that, for hydrofacies classification, the unsupervised cluster analysis approach is able to generate a classification that captures the hydrogeologically important details without creating an excessive number of categories.