Explicit Solution for Spalling Profile around Circular Tunnels Based on the Empirical Hoek-Brown Spalling Criterion

Spalling is the common mode of failure in deep tunnels excavated in strong rocks which results in notches around the tunnel boundary. Recent developments in the analysis of spalling failure have resulted in the empirical Hoek-Brown spalling criterion which is used for prediction of spalling profile. However, this criterion is commonly applied following elastic numerical analyses and in an implicit way. In this paper, an explicit solution is derived for spalling profile around circular tunnels. The stress distribution around tunnel is obtained using the well known analytical elastic solution, and then the locus of points which satisfy the empirical Hoek-Brown spalling criterion is determined. The derived polar function is used for graphical illustration of the effect of governing parameters on the spalling profile. Finally, the results obtained from the solution are compared with observations made in real tunnels. Showing good agreement with in-situ measurements as well as having explicit and easy-to-use form, the derived solution is expected to be extensively used in the future for prediction of spalling profile around circular tunnels.