A comprehensive regression-based framework for integrating petrographic indices, index properties, and mechanical characteristics of geologically diverse Himalayan Sandstones: Insights from the Lesser, Siwalik, and Purvanchal Ranges

Abstract

Rock Engineering (RE) projects in the Indian Himalayas often encounter sandstone formations within the Lesser, Siwalik, and Purvanchal ranges. Understanding Himalayan sandstone's petrographic, index, and mechanical properties, particularly in the Lesser, Siwalik, and Purvanchal ranges, is crucial for effectively planning and designing RE projects. This study establishes relationships between petrographic, index, and mechanical properties to identify key predictors of the mechanical behaviour of Himalayan sandstones. The present study analyses a large set of databases, including twenty-two-petrographic indices, nine-index and five-mechanical properties, creating 353 possible combinations. The analysis employed t-statistics and F-statistics tests and results to identify 120 bivariate most significant regression equations supported by performance indicators such as R², RMSE, and MAPE. The study presents the first comprehensive correlations and regression-based framework for predicting unconfined compressive strength and Compaction-Dilatancy (CD) transition stress in Himalayan sandstones, enabling the identification of favourable and unfavourable stress conditions. Key predictors such as grain area ratio (GAR), void percentage (Void), packing density (P_d), consolidation factor (P_c), porosity (n), Schmidt hammer rebound number (Rh), water content (w), and sonic wave velocities (V_p and V_s) exhibited strong correlations with R² values of at least 0.86, demonstrating high predictive reliability. These findings offer an approach to estimate studied sandstone strength and CD transition stress. Identification of the CD transition threshold provides insight into the onset of dilatancy, which marks the transition from stable to unstable damage conditions. As a result, CD transition stress emerges as a critical mechanical parameter for the safe and stable design of RE structures and for mitigating stress-induced failures, especially in the complex and geologically diverse Himalayan terrain.