ABSTRACT
Shafts must be engineered for a long, stable design life; they must be safe at all points along the shaft route. Calculation of a safety factor (FS) for an unlined shaft wall is straightforward in principal, but requires attention to geological details. Stress concentration factors are obtained from solutions to problems in the mathematical theory of elasticity and are simply the ratios of peak to reference stresses. An elliptical shape introduces two additional considerations for unlined shaft safety factor calculations: aspect ratio and orientation. An interesting exception to the rule of peak stresses occurring at the semi-axes ends occurs when tension is present at the walls of an inclined ellipse. Strengths entering shaft wall safety factor calculations limit the range of elastic deformation. Concrete may be used with steel liner plate or steel rings which may be embedded in the concrete. Numerous small joints and fractures are considered in estimation of rock mass strength and corresponding safety factor calculations.
