An Uzawa-type augmented Lagrangian numerical manifold method for frictional discontinuities in rock masses. (December 2021)

• Record Type: Journal Article
• Authors: Yang, Yongtao; Wu, Wenan; Zheng, Hong
• Is Part Of: International journal of rock mechanics and mining sciences. Volume 148(2021)
• Publication Date: 2021-12
• Subjects: Numerical manifold method -- Rock masses -- Augmented Lagrange method -- Stick-slip condition -- Frictional discontinuities; Rock mechanics -- Periodicals; Soil mechanics -- Periodicals; Mining engineering -- Periodicals; Roches, Mécanique des -- Périodiques; Sols, Mécanique des -- Périodiques; Technique minière -- Périodiques; 624.151305
• DOI: 10.1016/j.ijrmms.2021.104970
• Languages: English
• ISSNs: 1365-1609

Abstract

Abstract: 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 Newton-Raphson 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.