Upper bound analysis of progressive failure mechanism of tunnel roofs in partly weathered stratified Hoek–Brown rock masses

• We propose a progressive collapse mechanism of tunnel roofs in partly weathered stratified Hoek–Brown rock masses for limit analysis.
• Upper bound theorem ensures the analytic solutions obtained with the help of variational principle.
• Specific cases of square and circular profiles give numerical results and parametric analysis.
• The results gained show the region of collapsing blocks with two sections due to the presence of interface.

A reliable prediction of roof stability in stratiform or deteriorated rock banks remains a difficult problem in tunnel engineering, while it is still one of the most classical engineering issues needed to be investigated so as to provide relevant reference to practical projects. In previous research, homogeneous geomaterials were adopted to determine the analytic solutions of collapse profile in Hoek–Brown rock masses. However, when rock heterogeneities are considered in different rock layers, the results gained from existing collapse mechanisms would underestimate the dimensions of falling blocks. Thus in this paper, a new curved failure mechanism constructed with two continuous lines intersecting at the interface, namely progressive failure mechanism, is employed to derive the analytic solutions of the shape and region of roof collapse on the basis of upper bound theorem and variational approach. The corresponding results calculated are in well accordance with the existing findings, which shows sound agreement and validity of the proposed mechanism, and from which one can notice that additional detaching blocks would occur apart from the initial collapsing block when there exist various rock layers with different mechanical parameters, due to physical erosion or other factors, such as weathering process. To investigate the influence of different parameters on the range of roof failure, special attention is given to some examples of square and circular tunnels, and the results computed can give some instruction for practical engineering projects.