Kinematic Limit Analysis of Roof Stability for Elliptical Tunnels in Rock Masses

Abstract

Noncircular cross-sections are commonly encountered in engineering practice; however, primary attempts to analyze roof stability have focused on circular and rectangular configurations. This study investigates the roof stability of elliptical tunnels with varying aspect ratios, employing two semi-analytical approaches: piecewise linear and continuous analytical failure mechanisms. The former directly incorporates the generalized Hoek–Brown criterion, whereas the latter requires approximating its shear strength envelope through regression analysis. Notably, when the regression analysis achieved sufficient accuracy, the two approaches produced computationally consistent results (<1% difference), including closely aligned failure surface geometries. The findings demonstrate that the roof stability of elliptical tunnels—evaluated in terms of stability number, factor of safety, and support pressure—varies significantly from that of standard cross-sections. Considering the self-weight of a detached rock block as the primary cause of roof collapse, elliptical tunnels with a small horizontal-to-vertical axis ratio (i.e., a vertically elongated major axis) exhibit enhanced stability compared to circular tunnels. This improved stability is attributed to increased confining stress in the roof region and a reduced collapse block size. Furthermore, a comparative analysis encompassing various practical tunnel cross-sections, including horseshoe and mining configurations, provides a comprehensive understanding of roof stability across diverse geometric profiles.