Constitutive equations for 3-D anisotropy in jointed rocks and its effect on tunnel closure

Joints occurring in regular sets not only make the rock mass more deformable but also induce anisotropy in it. The rock mass has a special anisotropy in which the shear modulus is very low compared to its modulus of deformation. The assessment of the anisotropic deformational behaviour of the jointed rock thus becomes an important aspect in tunnel design. The constitutive equations for elastic-anisotropic-dilatant rock mass have been suggested in order to compute the strains for the following situations: * Plane strain deformations under a uniaxial loading condition, * Plane strain deformations under a biaxial loading condition, * 3-D deformations under a triaxial loading condition. The rock mass may have any number of joint sets with representative values of normal stiffness kn, shear stiffness ks and the joint spacing S. The dilation of the joints is considered through the dilatancy factor λ. An approximate method is proposed to assess the tunnel closure in different directions. The equations derived are applied to estimate the closure of the tail race tunnel of Salal Hydel Project Stage-II (India). The tunnel is aligned through a single litho unit of dolomite rocks and three joint sets with dip and dip directions of 53/340, 25/180 and 75/090° traverse through the rock. The computed horizontal closure of the tunnel wall is compared with the observed closure and the value of the parameter λ is adjusted to match the results. After calibration, the model is used for parametric analysis to observe how the tunnel closure responds to the variation in in situ stresses. It is concluded that the tunnel closure is highly anisotropic (Fig. 1) and all the three principal stress components have a significant effect on the tunnel closure. The proposed method may be used to analyse anisotropy of tunnel closure which can then be monitored by instrumentation carefully, so that one is able to record the maximum closure.