Limit Analysis of Tunnel Collapse According to the Hoek–Brown Criterion and Bolt Parameter Research

Based on the plasticity theory of upper bound limit analysis, the expression of a potential collapse profile of a tunnel can be obtained from the \(\sigma \)\(_{n}\) \(-\) \(\tau \)\(_{n}\) form of the Hoek–Brown criterion. However, because the parameters Aand B in the Hoek–Brown expression are difficult to determine, the bolts parameters cannot be determined easily. Therefore, it is necessary to adopt a parameter transformation method to establish the relation between the parameters in the general form (\(\sigma \)\(_{1}\) \(-\) \(\sigma \)\(_{3}\) form) and the \(\sigma \)\(_{n}\) \(-\) \(\tau \)\(_{n}\) form of the Hoek–Brown criterion. The field rock data can be used to determine the critical span of tunnel collapse under different parameters. Then, the impact of the parameters of the rock mass, such as GSI, \(m_{i}\), D, \(\sigma \)\(_{ci}\), and \(\gamma \) are studied. And based on the L and h of the profile (L is the half span of the profile and h is the height), we studied the reasonable bolt parameters. The result shows that if the rock is more intact (GSI is larger), \(m_{i}\) is smaller, the blasting disturbance is smaller (D is smaller), the compressive strength is larger (\(\sigma \)\(_{ci}\) is larger), and the density of the rock is smaller, the range of the potential collapse profile is smaller. Generally, the support effect is more efficient when the length of the bolts is 2h and the spacing between the bolts is 15–20% of L. This research can provide a reliable reference for the accurate judgment of tunnel stability and effective control of roof settlement.