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This paper describes research being conducted under a cooperative agreement between the Colorado School of Mines and the U.S. Bureau of Mines, Denver Research Center to develop a public domain discrete element software package for modeling ground control failures in coal mines. An updated Lagrangian approach is used to extend the usual rigid block discrete element method model by incorporating large displacement elasto-plastic block deformability using four noded isoparametric finite elements. One point integration with hourglass control is used to preserve accuracy and reduce computational expense. This formulation is implemented in an object oriented C++ program integrated with a graphical user interface to simplify model construction and provide for rapid engineering analysis of results. A two-entry gateroad design analysis has been performed to validate the computational algorithms.
The U.S. Bureau of Mines under a contract with the Colorado School of Mines is developing a hybrid discrete element-finite element code to model floor heave and pillar failure in underground coal mines. Discrete element methods (DEMs) were first proposed by Peter Cundall (Cundall, 1971; Cundall and Strack, 1979) in the 1970s. Other researchers have built upon their work and have added mechanisms for cracking (Hocking et al., 1987) and block deformability (Barbosa and Ghaboussi, 1992). In a series of papers describing the so-called [discrete finite element method], Barbosa and Ghaboussi use a modified Total Lagrangian formulation to model each discrete block element as a finite element. External contact forces acting on the surface of each block are added to internal forces computed from standard finite element analysis. In this paper, a velocity-based updated Lagrangian approach for treating finite displacement elasto-plastic block deformability in quadrilateral elements has been implemented in an object-oriented program. The program has been developed as a C++ class library, and may be used as either a deformable discrete element program or a large strain explicit finite element program. The object-oriented frame- work has enhanced the development of effective data structures in the program by allowing logical parts of the problem domain to be modeled as separate objects. Access to these objects is accomplished either through classes or through methods attached to the objects themselves. The program is actually a collection of classes that implement the data structures and algorithms associated with the motions of individual DEM blocks and the several types of finite elements. The primary advantage of using finite elements for block deformability instead of the more usual finite difference approximation is that it allows the analyst to draw upon the considerable body of knowledge gained in nonlinear finite element analysis over the last three decades. The main disadvantage is increased computation time, but this limitation has been reduced considerably in the program by using one point quadrature to integrate the element stresses and then applying anti-hourglassing to control the element zero-energy modes.
In discrete element computations, central difference schemes are used to integrate the equations of motion and have the advantages of decreased storage costs and relatively simple implementation.
