Investigation of the Quantitative Impact of the Negative Correlation between Strength Parameters on Tunnel Support Designs in Weak Rock Masses

Abstract The cohesion and friction angle within rock mass exhibit a negative correlation, and traditional deterministic tunnel support design cannot account for it. Tunnel reliability analysis findings suggest that this negative correlation can be ignored due to conservative results, thereby underestimating its significance. This manuscript re-examines this issue from a design perspective, aiming to quantify the quantitative impact of this negative correlation and to reveal the underlying laws and associated influence ranges. A quantitative analysis model with concise indicators is established by developing a deterministic design framework for tunnel supports, pioneered by Hoek, and by introducing direct reliability-based design methods. Results reveal that the required support pressure can decrease by approximately 10% and 18% in the common scenario when considering negative correlation coefficients of −0.5 and −0.99, respectively. These results are further confirmed by numerical simulations, underscoring the significance of the negative correlation in tunnel support design. Furthermore, an investigation into the laws and influence ranges of this impact reveals that this impact weakens as the deformation requirement increases and diminishes with a rise in in situ stress. For tunnel support design in a weak rock mass, this negative correlation can theoretically be neglected when the limiting strain reaches 1%, and similarly, it can be overlooked when the in situ stress increases to 4.05 MPa.