Recent insights into analytical precision and modelling of DDA and NMM for practical problems

Abstract

This paper discussed the analytical precision on equations of motion in some practical studies that use 2-D DDA, 2D-Coupled analysis of NMM & DDA, and 3D-DDA. We point out the main reason for numerical instability in DDA is loss of the effective digits when superposing the global stiffness matrix under the variable conditions of large and the small blocks. Categories of analyses are distributed in 2D-DDA static masonry structures such as the Great Pyramid and the Pont du Gard, 2D-DDA dynamic rock fall problems and the sensitivity of its analysis on the velocity ratio and the penalty, earthquake response analysis of rock slopes, 2D-NMM, 2D-coupled analysis of DDA and NMM and 3D-DDA rock fall problem. The selected examples on the Great Pyramid, Pont du Gard and Bayon Temple at Angkor Thom are located in Egypt, France and Cambodia respectively as UNESCO world heritages sites. The authors evaluated the applicability of the methods and the reliability of the results by comparing different methods and site observations from the practical problems.

Keywords:

• analytical precision
• 2D DDA
• NMM
• DDA and NMM coupled analysis
• rock fall problem
• 3D-DDA

Acknowledgement

The authors would like to thank Dr. G.H. Shi for many valuable discussions.