New equations for estimating radial loads on deep shaft linings in weak rocks

Structural support in soft rock can be very difficult in deep mining. Shaft sinking is typically a critical phase of the project. An analytical method called the convergence-confinement method (CCM), often applied in tunnels, can be used to calculate both the radial displacements associated with the construction of the shafts and the equivalent loads that the planned shaft support must guarantee. Also, the CCM can be used to calculate the plastic zone. A relationship between the stress acting on a shaft lining and the most important parameters governing the behavior of the rock (cohesion, friction angle, and elastic modulus) and the geometric parameters of the shaft (depth, radius, and lining thickness) has been obtained. The Mohr-Coulomb model was used to represent shear failure in weak rocks, considering ductile behavior (ideal strength criterion). The equations found in this paper allow for the quick estimation of the stress acting on the lining extrados.