Estimation of shaft radial displacement beyond the excavation bottom before installation of permanent lining in nondilatant weak rocks with a Novel formulation

The convergence-confinement method (CCM) applies to circular tunnels in in situ stress fields in which all three principal stresses are equal and the rock mass exhibits elastic-perfectly plastic shear failure. As radial wall displacement cannot be obtained easily using analytical methods, extensive parametric analysis of bidimensional numerical modelling to investigate the strain of the shaft wall close to the excavation bottom was performed. In all, 81 cases were derived from combinations of geometrical parameters and three weak rock categories. Through processing data relating to values of uR0 (radial displacement of the shaft wall at the excavation bottom) obtained by numerical calculation in the different cases studied, it was possible to calculate the uR0/R ratio as a function of the lithostatic stress p0, the lining thickness s, and the shaft radius R. Novel equations were obtained to quickly estimate the value of uR0 given the thickness of the lining concrete, the shaft depth, and the shaft radius for the qualities of rock considered.