Statistical Assessment of the Representative Elementary Area for Areal Fracture Intensity (P21) in Digital Outcrop Models

Abstract. The definition of a representative elementary volume (REV) or area (REA) for a target parameter is a fundamental step toward the upscaling of fracture network properties generated by discrete fracture network models (DFN) to an equivalent continuous medium for in situ applications in engineering geology, hydrogeology, and structural geology. The target parameter of this work is the areal fracture intensity (P₂₁), a key metric often used as a stopping criterion in stochastic DFN simulations, that is derived directly from surface data collected at natural outcrops. We propose a novel approach to define the REA as a range bounded by a lower and an upper limit. The upper limit, often overlooked but nonetheless theorized, identifies the largest representative domain, which is crucial for optimizing computational efficiency. We evaluate the REA range based on three statistical parameters, namely: the shape, mean, and variance of the P₂₁ distributions obtained with progressively increasing scan area sizes. Each statistical parameter is assessed by combining formal statistical tests and diagnostic plots. Within a multi-parametric framework, the method enables a detailed analysis of the statistical behaviour of the dataset, supporting informed decisions in defining the REA range. The methodology is tested on two fractured limestone outcrops with markedly different characteristics: (i) an abandoned quarry in the Murge Plateau (Puglia, Italy) and (ii) the Lilstock Benches in the southern Bristol Channel basin.