Influence of the depth and shape of a tunnel in the application of the convergence–confinement method

One of the most widely used methods in tunnel support analysis and design is the convergence–confinement method (CCM). For its practical application, it is necessary to study the influence of the depth and cross-section of the tunnel and to confirm the calculations with two- or three-dimensional simulations carried out with finite elements or explicit finite differences programs. These simulations require elevated calculation times. In this paper, a modification of the CCM is proposed that directly introduces the effect of depth and the shape of the tunnel cross-section in the determination of the radial displacement of the tunnel. To do so, a series of functions are determined that approximate the radial displacement at points situated on the perimeter of the cross-section of the tunnel, considering several cross-sections at different distances from the working face. Should the cross-section of the tunnel or its depth be modified, it will not be necessary to perform new numerical simulations in order to apply the CCM. It will only be necessary to use the calculated shape functions. It is thus possible to use the CCM in the analysis and design of the support elements in a quite precise and significantly faster way.