  In this paper, the Barton-Bandis model for rock joints is extended to cyclic
loading conditions, without any new material parameter. Also developed herein
is an algorithm for implicit numerical solution of the extended Barton-Bandis
model, which can also be used for the original Barton-Bandis model for which an
implicit algorithm has been unavailable. To this end, we first cast the
Barton-Bandis model into an incremental elasto-plastic framework, deriving an
expression for the elastic shear stiffness being consistent with the original
model formulation. We then extend the model formulation to cyclic loading
conditions, incorporating the dependence of shear stress and dilation on the
joint position and the shearing direction. The extension is achieved by
introducing a few state-dependent variables which can be calculated with the
existing material parameters. For robust and accurate utilization of the model,
we also develop an implicit algorithm based on return mapping, which is
unconditionally stable and guarantees satisfaction of the strength criterion.
We verify that the proposed model formulation and algorithm produces the same
results as the original Barton-Bandis model under monotonic shearing
conditions. We then validate the extended Barton-Bandis model against
experimental data on natural rock joints under cycling loading conditions. The
present work thus enables the Barton-Bandis model, which has been exceptionally
popular in research and practice, to be applicable to a wider range of problems
in rock mechanics and rock engineering.
