An Uzawa-type augmented Lagrangian numerical manifold method for frictional discontinuities in rock masses

The problem of frictional discontinuities in rock masses is addressed computationally in the context of the NMM (numerical manifold method). The use of the NMM allows the use of nonmatching meshes to discretize the problem domain. To impose frictional contact conditions, the Uzawa-type ALM (augmented Lagrange method), which inherits the merits of the LMM (Lagrange multiplier method) and the PM (penalty method), is incorporated into the NMM, and a numerical model termed as Uzawa-type augmented Lagrangian numerical manifold method (UALNMM) is proposed. In the UALNMM, two layers of iterations are adopted, which are NewtonRaphson iterations for the inner layer and augmentation iterations for the outer layer. The implementation of the UALNMM is discussed in details. Four benchmark examples of frictional/frictionless contact problems and an example of rock slope with multiple frictional fractures are used to validate the accuracy and robustness of the UALNMM. The proposed UALNMM deserves further investigation for three dimensional rock mechanics problems with frictional contact.

Automated summary

The computational treatment of frictional discontinuities in rock masses within the NMM framework is discussed in this study, proposing a new numerical method UALNMM. This method combines the advantages of Lagrange multiplier method and penalty method, adopts multi-layer iterations, and discusses the detailed implementation. The accuracy and robustness of the method are validated through the use of benchmark examples.