Validation and error analysis of a strata modelling technique

Summary Sources of error are investigated for a two-dimensional finite difference computer program designed to model strata deformation. The program calculates the displacements of a mesh of mass points, by the iterative solution of equations of equilibrium for the stresses acting on each mass point. The effect of errors on both displacement estimates and stress estimates is considered.Round-off errors are discussed analytically, while the effect of choosing too coarse a mesh density is demonstrated by comparison of two runs of the program with identical material properties, but different mesh densities. The influence of boundary conditions and the result of incomplete relaxation of the finite difference equations is estimated by comparison with Kirsch's analytical solution for a thin plate of finite width with a circular hole under unidimensional load.As a result of the analysis, estimators for stresses and displacements are derived, which make allowance for some of the sources of error; suitable boundary conditions for first and subsequent runs of the program are proposed; and a convergence criterion for the iterative process is suggested. These results are then applied to simulations of mining situations, together with various refinements of the basic model, such as separation and slip between adjacent strata, and an allowance for failure of material.