Identifying rock blocks based on exact arithmetic

• A robust block identification method is presented based on exact arithmetic.
• Block structures are constructed accurately without introducing rounding errors.
• The robustness of the algorithm is guaranteed even if the fractures are densely packed.
• Degenerated geometries can be handled without special measures.
• There is no limit to the quantity and complexity of the identified blocks.

This paper presents a block identification method for jointed rock masses that is based on exact arithmetic. Block structures are constructed accurately without introducing rounding errors, and therefore the robustness of the block identification algorithm is guaranteed. A rational number type is defined and the basic arithmetic operations of the rational numbers are implemented exactly. Thus, the degenerated geometries can be handled without special measures and accurate modeling results can be obtained even if the fractures are densely packed. In order to ensure the efficiency of the proposed method, floating-point filters and lazy evaluation strategy are used in this study to avoid unnecessary exact computations. The fractures can be either planer or curved and the only limitation to the shape and size of the resulting blocks is the available memory of the host system. Several examples are given to demonstrate the capability and performance of this method.