Stability of a Rock Block in a Tunnel Roof Under Constant Normal Stiffness Conditions

List of symbols b Width of rock block c Constant relating to calculate boundary normal stiffness c0; c1; c2 Empirical constants defining joint dilation rate F Support force Er Young’s modulus of rock mass i Dilation angle JRC Joint roughness coefficient JCS Compressive strength of joint surface Kn Normal stiffness at an external boundary K Ratio of horizontal stress to vertical stress kni Initial normal stiffness of joint ks Shear stiffness of joint L Length of rock block M Damage coefficient N0 Initial normal force p Vertical stress component R Radius of tunnel r Radial distance of the point from the centre of opening S0 Initial shear force Vm Maximum joint closure W Weight of rock block z Depth below surface _ v Dilation rate _ vpeak Peak dilation rate a; b; k Components relating to shear stress-shear displacement equation h Polar angle with respect to horizontal axis x w Polar angle with respect to vertical axis y cr Unit weight of rock mass dh Shear displacement dh peak Shear displacement at peak stress ratio r Normal stress rn Normal stress at shear displacement dh rn0 Initial normal stress (at dh 1⁄4 0) rrr Radial stress component rrh Shear stress component rhh Tangential stress component smob Mobilised shear stress s Shear stress s Average shear stress along the vertical joints /b Basic friction angle of joint /mob Mobilised friction angle & Buddhima Indraratna indra@uow.edu.au