Extended Barton-Bandis model for rock joints under cyclic loading: Formulation and implicit algorithm

TL;DR

This paper extends the Barton-Bandis model for rock joints to cyclic loading without new parameters, and develops an implicit algorithm for stable numerical solutions, validated against experimental data.

Contribution

The paper introduces a cyclic loading extension of the Barton-Bandis model and provides an implicit solution algorithm, enabling broader application in rock mechanics.

Findings

Model extension accurately captures cyclic loading behavior.

Implicit algorithm is unconditionally stable and satisfies strength criteria.

Validation confirms model's effectiveness against experimental data.

Abstract

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.