A displacement-discontinuity program incorporating a frictionless, laminated overburden with "homogeneous stratifications" has recently been developed. This program, LAMODEL, simulates the overburden as a stack of homogeneous isotropic layers with frictionless interfaces, and with each layer having the identical elastic modulus, Poisson's Ratio, and thickness. This formulation does not require specific material properties for each individual layer, and yet it still provides a realistic suppleness to the overburden that is not possible with the classic, homogeneous isotropic elastic overburden. The program calculates stresses and displacements at the seam level and at requested locations in the overburden or at the surface. Both linear elastic and non-linear seam materials can be used; and free surface effects, uneven topography effects, multiple seams, and multiple mining steps can be simulated. As part of the initial investigation and validation of this new laminated formulation, the program is used to model the underground stresses and displacements, the topographic stresses and the inter-seam interactions from two field studies. The results from the model are compared with the field measurements and with previous results from an elastic homogeneous isotropic analysis. Ultimately, it is shown that the many features of the new program coupled with the laminated overburden model help provide realistic stress and displacement calculations for various mining situations.
The initial mathematical models relating the mechanical behavior of the overburden to mining in seam type deposits were first presented in the early sixties (Berry, 1960; Berry and Sales, 1961, 1962; and Salamon, 1964a, 1964b, 1965a, and 1965b). In the initial publication by Berry (1960), the closed-form equations for the displacements and stresses surrounding a single thin opening or slit in both an infinite two-dimensional homogeneous isotropic elastic plane and a similar half-plane were derived. In this initial work, Berry was primarily interested in solving for the vertical displacements at the surface for the purpose of subsidence prediction. However, he found that his initial numerical results for an elastic medium did not match the observed subsidence. In the next papers by Berry and Sales (1961, 1962), the assumption of an isotropic medium was replaced with the assumption of a transversely isotropic medium, and the math was extended to the three- dimensional solution around a thin rectangular opening. Using this new, non-isotropic, formulation and optimized values for the necessary elastic constants, Berry and Sales were able to show very good correlation between calculated and measured subsidence. In the paper by Salamon (1964a), Berry and Sales's work is extended in several directions. Salamon introduces the idea of a "face element" which is essentially used to discretize the seam into "small" two-dimensional, horizontal areas for implementation of a numerical three-dimensional formulation. (This face element is essentially the same as the presently known displacement-discontinuity (DD) variation of the boundary-element method.) Salamon then goes on to provide the essential mathematical formulas for applying the face element method to both an infinite space and an infinite half- space using four kinds of elastic media; homogeneous isotropic, homogeneous transversely isotropic, frictionless laminated, and multi-membrane.