The support characteristic curve for blocked steel sets in the convergence-confinement method of tunnel support design

Construction of support characteristic curves is an important aspect of the implementation of the convergence-confinement method of tunnel support design. This paper presents a detailed analysis of the equations required to construct the support characteristic curve of a combined support system consisting of closed circular steel sets linked to the periphery of the tunnel by equally spaced prismatic wood blocks. This particular problem has been treated in the classical literature of underground excavation design in rock, although without providing details of the origin or validity of the equations. This paper fills this gap, providing the derivation and validation of all the equations required to construct the support characteristic curve for the combined support system. The paper shows that both the stiffness and maximum load that the combined support system can take increases as the angle between equally spaced wood blocks is decreased (or the number of blocks for the steel section is increased). In the limit, when the angle between wood blocks is assumed to be zero, the paper shows that the classical equations for construction of support characteristic curve for a steel set subjected to uniform radial load are recovered. The paper presents also a practical example illustrating the application of all equations needed to construct the support characteristic curve for the combined support system.