Procedure to detect the of contact of three-dimensional blocks using penetration edges method

Practical geotechnical problems generally are three-dimensional in nature. The geometry of the solution or the construction works, the properties of the various rock materials and the discontinuities all possess strong three-dimensional characteristics. At present, Discrete element method (DEM) and Discontinuous deformation analysis (DDA) are mainly limited to two-dimensional analysis and there are not many three-dimensional studies. Three-dimensional analysis is however important in many real engineering problems and should be considered. In DDA and DEM analyses, the system is composed of discrete blocks. Detecting and representing contacts between blocks becomes one of the key problems of these two methods. First of all, the numerical analysis depends heavily on the contacts between blocks. Wrong detection or description of contacts may lead to wrong analysis, and breakdown of the computation may even happen. Secondly, because both DDA and DEM analyses adopt an iterative scheme to account for the large displacement and deformation, the coordinates of the blocks and contacts between blocks can change at each iterative step. The efficiency of the algorithm for detecting and representing the contacts will directly and strongly influence the efficiency of the numerical analysis of the blocks system. In fact, there are great differences in the computational time required between the use of different methods to detect and represent contacts. Detection of contacts under two-dimensional condition is a simple problem and many famous algorithms and codes are available which will not be discussed here. Detection of contacts between general 3D blocks is however much more complicated. Currently, direct determination and common plane (c-p) method are the two most popular approaches for contacts detection and representation. Direct computation is the simplest but most time-consuming approach. Compared with direct test, c-p method can greatly reduce the amount of calculation for contact detection and representation and is adopted in most of the 3D DEM and DDA programs. The computer time consumed for contact detection using c-p method is however a significant portion of the entire time for analysis. In general, there are many possible forms of 3-D blocks that make the contact detection and representation a very difficult and time-consuming task. It is however the key problem in the development of 3-D DEM and DDA programs. In this paper, a new approach for detecting and representing contacts between 3-D blocks is developed and the advantages of the new method are discussed.