Sedimentary rocks, with well developed bedding, and schistose metamorphic rocks, exhibit strength anisotropy to some degree when the loading direction varies with respect to their planes of weakness. When constructing underground excavations in rock, it is common to deal with this anisotropy, as the secondary stress field is oriented parallel to the tangent of the excavation boundary. For statistically homogeneous joint direction and spacing there will be regions around the tunnel boundary where the rock strength will attain minimum and maximum values. In particular, for relatively shallow overburdens, intact rock strength is usually not attained, while failure may be exclusively due to joint slip. In such cases the effect and the importance of strength anisotropy depends on the relative size of the problem in point with respect to the size of the rock structural characteristics (Amandie 1996). On account of the rock strength anisotropy, a circular tunnel is subjected to non-uniform deformations around its circumference. The pressure exerted by the rock to a ring support (e.g. a shotcrete or concrete lining) will be non-uniform while bending stresses may be developed. In the present study, such tunnel over stressing is examined numerically.
Goodman (1989) illustrated the effect of joint slip by its well-known geometrical method that can be used to identify the extent of slip along the periphery of an underground opening. In this methodology the essential information needed are the exact cross section of the opening and the friction angle of the joint planes. Then, with the aid of a simple geometrical construction, zones of joint slip with potential sliding and flexure around a tunnel of any shape can easily be identified. In Figure 1 this is shown for a circular tunnel driven in a rock mass with one joint set dipping at an angle 45° from the horizontal. To identify the zones of layer slip, the tunnel and the layers are drawn in their correct orientation and two lines inclined at φj to the normal to the layers are drawn as tangents to the tunnel periphery. In Figure 1 two values are considered for the joint friction angle, φj =50° and φj =20°. Goodman's geometrical method offers a fast and precise estimation of the zones that may slip at the tunnel periphery in the case of excavating in an anisotropic rock. The required support pressure to prevent any joint slip is also provided by goodman closed form solutions for calculating the extent of the joint slip zones through the rock mass around circular tunnels are presented by Daemon (1983). For a Hoek-Brown rock mass the extent of slip zones has been studied by Kama (1997). According to Daemon the distribution of elastic stresses, at first, is calculated. Then, the elastic shear stress is compared to joint shear strength, considering a Coulomb slip criterion for the joint. The joint is considered to slip, when the elastic shear stress exceeds the joint shear strength. Therefore, slip zones identified by Daemon correspond to excess shear stress contours τ/τp>=1.