Stability of a rock block in a tunnel roof under constant normal stiffness conditions
The roof of a tunnel in a jointed rock mass will often contain blocks whose stability depends on their geometry, the mechanical properties of the joints, the method and shape of the excavation, fluid pressures, the deformability of the block and of the surrounding rock mass, as well as the in situ stresses (Crawford and Bray 1983; Brady and Brown 2004; Elsworth 1986; Goodman and Boyle 1987; Sofianos et al. 1999; Asadollahi and Tonon 2010; Indraratna et al. 2010). In the past, methods of analysing the stability of a block in the roof of a tunnel were typically based on the limit equilibrium of forces (Goodman and Shi 1985; Brady and Brown 2004; Warburton 1981). The shear displacement characteristic of the joints between an unstable block and the adjacent rock mass was rarely considered, except in a limited number of studies. For example, Yow and Goodman (1987) emphasised that block instability could be better assessed through a function of shear displacement, rather than adopting the limit equilibrium method that is often too conservative.