Discontinuous deformation analysis: A new numerical model for the statics and dynamics of block systems

In this thesis a forward and a backward numerical model of deformable block structures is presented. The forward model can analyze the mechanical response of rock block systems under general loading and boundary conditions. Large displacements and deformations are considered under both static and dynamic loadings. Output data give the movements, deformations, stresses and strains of each block, and the contact force, sliding, and detaching or rejoining between blocks. The forces acting on each block, from external loading or contact with other blocks, satisfy the equilibrium equations. Equilibrium is also achieved between external forces and the block stresses. Furthermore, the analysis fulfills constraints of no tension between blocks and no penetration of one block into another. Also, Coloumb's Law is fulfilled at all contact positions for both static and dynamic computations. To achieve equilibrium and satisfy these constraints, simultaneous equations are solved repeatedly with partial changes of the coefficients each time the contact constraints are chosen.; As the measurement of displacement tends now to be automatic and refined, rock engineering related displacements and strain measurements are becoming more abundant. The backward model works directly with time dependent displacement or strain measurements of individual points to compute the movements and deformations of whole block systems. The output data are the best least square fitted block displacements and block strains and the relative sliding and opening of interfaces between blocks which can determine the state of global stability for an entire block system. The backward analysis performs an honest interpretation of measured displacements and offers material constants, initial stresses or possible boundary conditions for further forward analysis; the forward analysis then can predict future states of stabilities for the rock structure. The combination of the forward and backward analyses will allow a complete practical numerical analysis procedure for problems in blocky rock.