An optimized augmented Lagrangian method and its implementation in discontinuous deformation analysis (DDA)

One of the key factors regarding the validity of the results of discontinuous deformation analysis (DDA) is the computational accuracy of the contact force. The classic DDA employs a penalty function to enforce the contact constraints between blocks, which is easy to implement but challenging to choose the penalty value in the actual computation. To overcome the limitation, a three-dimensional (3-D) DDA based on an optimized augmented Lagrangian method (ALM), abbreviated as DDA-3a, is established to modify the treatment of the contact constraints. This study provides necessary knowledge to fully implement and further optimize the ALM in the 3-D DDA by integrating it with the open-close iteration, and an adaptive penalty update scheme. Numerical examples are designed to exhibit the capability of DDA-3a in the computational accuracy, efficiency, and robustness. This study reveals that the DDA-3a can be used to analyze the discontinuous mechanical behavior of polyhedral block systems, such as the stability analysis of jointed rock-masses.