Stability Design for Spalling Behavior in Deep Hard Rock Tunnel under Uncertainty Using Inverse-Reliability Strategy

The spalling behavior is considered as a representative failure mode involved in the hard rock surrounding the deep tunnel, which has a strong influence on the resulting safety of tunnelling operations. Since the stability design for such a type of the deep hard rock tunnel is a significant aspect of geotechnical community dominated heavily by the inherent uncertainty, it is desirable to employ the reliability methods (via the reliability index or probability of failure) to produce meaningful results in a logical and realistic fashion. With the tremendous development of those reliability methods, the current design standards have an increasing tendency to guarantee stability of geotechnical structures by prescribing a target reliability index. This manifests that the reliability level of a deep hard rock tunnel is pre-defined as a target to be fulfilled. In this scenario, an inverse-reliability strategy is proposed to solve the stability problem of the deep hard rock tunnel. The basic idea behind this strategy is to, when knowing the target reliability index, how to back-calculate the design variable involved in the process of stability analysis to ensure the acceptable level of the pre-set reliability. In conformity with this strategy, an inverse first-order reliability method (IFORM) is developed and its solution procedure is also summarized. By using a typical example of the deep hard rock tunnel, the computational accuracy and efficiency are both verified in identifying the design variable pertinent to the spalling behavior. On this basis, its associated stability design is implemented, considering various levels of the target reliability index in the analysis process. By dint of the presented IFORM, the design variable relevant to the spalling behavior can be adjusted conveniently, thus providing effective guidelines which are found to be in accordance with the practical situations for the stability design of the deep hard rock tunnel.

Keywords: Deep tunnel, Hard rock, Spalling, Stability design, Inverse-reliability, Target reliability index.