Modelling joint response under constant or variable normal stiffness boundary conditions

The response of a rock joint to shear loading in situ depends not only on the joint surface properties but also on the boundary conditions that are applied across the joint surfaces. These boundary conditions can take multiple forms and vary as the rock mass is subject to cycles of loading and unloading. For instance, in rock slope stability, the moving block above a critical joint surface is free to move upward. In this case, the normal stress across the joint remains essentially constant. On the other hand. a block constrained between dilatant joints in the roof or sidewalls of an underground excavation does not move as freely as in the previous case. As the block moves, joint dilation is restricted by the surrounding rock and is controlled by the deformability (or stiffness) of the rock mass. Hence, the normal stress across the joint planes along which sliding takes place, is no longer constant but increases. In general, joint shear strength under increasing normal stress will be different from its shear strength under constant normal stress. The range of joint normal loading conditions in situ and the importance of properly modelling rock joint behaviour have been emphasized by Goodman [1], Heuze [2], Leichnitz [3] and Goodman and Boyle [4] among others. Lam and Johnston [5] also recognized the importance of properly modelling the joint interface between concrete and rock when assessing the side resistance induced in concrete piles in rough rock sockets as the pile is loaded and displaced vertically. The range of joint normal loading conditions can best be represented by assuming that the deformability of the surrounding rock mass is modelled by a spring with normal stiffness K = dan/dr where da, and dv are the changes in joint normal stress and displacement, respectively. The stiffness K varies between zero for a joint under constant normal stress (as in slope stability problems) and infinity if the rock mass is very stiff for which no change in joint normal deformation is allowed. The stiffness is constant if the change in joint normal stress remains proportional to the change in normal displace-