Probabilistic modelling of Copenhagen limestone mechanical behaviour with the Hoek–Brown failure criterion

Accurately predicting the mechanical behaviour of geological materials is crucial for ensuring the safety of geotechnical structures. However, calibrating advanced models for heterogeneous rocks, such as Copenhagen limestone, which exhibits diverse properties due to silicification, cementation, and glaciotectonic fractures, poses significant challenges. Deterministic approaches often encounter limitations due to data variability and scarcity. Upon embracing a probabilistic approach, recent research emphasises the importance of considering correlations among geotechnical properties to reduce structural variability. This study focuses on the Hoek–Brown (H-B) constitutive model, addressing the challenges of determining parameters, especially with scattered data. The objective is to establish a comprehensive multivariate distribution function encompassing seven pivotal intact rock properties, which are crucial for calibrating the H-B model in the compression zone. Notably, three distinct distribution functions were developed based on the bulk density of intact samples, informed by observed behaviours under triaxial loading (σ₁-σ₃ plane). Rigorous validation using an independent database, including unconfined compressive strength (UCS) and tensile tests, demonstrates the effectiveness of the constructed distributions. The analyses reveal the fundamental role of bulk density through correlations with other parameters. The validated model was employed to back analyse large-scale triaxial tests of layered rock mass samples. The results indicated that under compressive loading, the weakest layer determines the strength and stiffness of the samples when variability within the representative volume is significant. The proposed equivalent rock mass stiffness showed excellent agreement with the observed response. This study establishes a set of probabilistically calibrated H-B multivariate models and provides a practical tool for reliability-based design of underground constructions within Copenhagen limestone.