Spatial distribution and targeted support of key blocks in jointed rock mass tunnels

The variability in the scale and spatial configuration of structural planes introduces uncertainty, which poses significant challenges to the prevention and control of key block collapses and the optimization of targeted support design for tunnels. In this study, we developed a three-dimensional extension algorithm for structural planes based on two-dimensional trace features extracted from sequential tunnel face images. This algorithm was integrated with multi-scale modeling to establish an equivalent rock mass model retaining only the large-scale controlling structural planes. By conducting a comprehensive analysis on the spatial interactions between key blocks and tunnel faces and using a block-search algorithm, the geometric characteristics of surrounding key blocks were identified. Subsequently, probabilistic models describing block height and volume distributions of these blocks were constructed, and their spatial patterns—including size and shape—were illustrated through rose diagrams. Taking the Fanshishan Tunnel on the Dongliang Expressway in Shandong Province as a case study and considering its specific structural plane characteristics, a targeted rock-bolt support scheme considering key block stability was proposed and compared with conventional support. The comparison reveals that the targeted support reduces the maximum surrounding rock displacement to 26.96 mm and lowers the peak axial force of the rock bolts by approximately 34%. These findings demonstrate that targeted support effectively mitigates local deformation and lowers the peak axial force induced by key block instability, thereby enhancing tunnel stability and optimizing support resource allocation. The proposed scheme provides a theoretical foundation and practical engineering reference for stability analysis and support design in structurally controlled jointed rock mass tunnels.