A mathematical model is presented to determine the effect of boundary conditions on the shear behavior of a dilatant rock joint. The model relates the normal load-deformation response of a joint to its shear load-deformation and dilatant behavior.
In two recent papers (Saeb and Amadei, 1989 and 1990), the authors presented a graphical method to predict the shear response of a dilatant rock joint under constant or variable applied stiffness boundary conditions. The method used the joint shear stress-shear displacement curves and corresponding dilatancy curves for different constant normal stress levels and the joint normal stress-normal displacement curve. The proposed method was also verified using the results of constant stiffness tests previously reported in the literature.
In this paper, the graphical method has been shaped into a more general mathematical form that can be included in the numerical modeling of jointed rock masses. The mathematical model presented herein makes use of existing formulationsuch as that of Bandis et al (1983) for joint normal behavior and those of Ladanyi and Archambault (1970), Goodman (1976) and Goodman and St. John (1977) for joint shear behavior and dilatancy. At the outset, these formulations are summarized. Then, they are coupled to relate the normal load-deformation response of a joint to its shear load-deformation and dilatant behavior. This coupling is used to predict the increase in deformability of an initially mated joint as it traverses a range of unmated conditions during shearing. Then the model is presented in an incremental form that can be implemented in non-linear finite element programs. Finally, an example illustrates how the model can predict the shear response of a dilatant joint under boundary conditions other than constant normal stress.
