A parametric method for maximum key block on tunnels excavation and its verification

Abstract

During the engineering design stage, it is challenging to precisely identify the number and spatial distribution of joints within rock masses. To address this, joint orientations are assumed to be constant and evaluate all possible combinations of joints and excavation surfaces to identify the most critical scenario. The maximum key block serves as a vital indicator for tunnel alignment optimization. However, existing methods are limited and primarily focus on pyramidal blocks. In practice, wedged blocks (non-pyramidal) are common and often exhibit larger volumes. This study proposes a parametric method to determine the maximum key blocks formed by four joint groups on tunnel excavation surfaces. The method uniformly characterizes both wedged and pyramidal blocks using a parameter t, enabling efficient identification of maximum key blocks. Implemented through a computer program, the method was validated in an engineering case study, revealing that wedged blocks constitute the maximum key block in 62.7% of scenarios. This finding emphasizes the necessity of incorporating both block types in stability analysis.