Computer assisted finite element model analysis, originally developed to study stress distributions in aircraft, has been modified into a versatile mining program, that can be used to assist the engineer with predictions of mine subsidence. International Exploration, Inc. has developed an in-house finite element model program which incorporates a multitude of factors influencing mine subsidence such as mine design, physical rock properties, structure, faults, joints and topography. Finite element analysis of a mine model can mathematically determine the magnitude and direction of the principal stresses within each of the elements forming the model. By comparing the calculated in-situ stresses to the actual rock strengths, high risk regions within a mine can be identified. These potentially unstable regions of the mine can be allowed to fail within the model and the resultant stress redistribution and element movement calculated. Thus, the effects of the mine collapse at the surface can be predicted for the purpose of determining the potential damage, if any, that could occur to surface structures from deep mine failure. Stabilization materials can also be mathematically inserted into the model to design and analyze the effectiveness of subsidence prevention programs. Two examples are presented of the finite element program being used' to predict mine subsidence at substantially different geologic and mining provinces in Pennsylvania.
Abandoned subsurface coal mines in Pennsylvania have posed a substantial problem to hundreds of property owners situated above them. The mines may collapse, with time, from various causes such as weathering, pillar robbery or mine flooding. The resulting subsurface collapse may cause significant surface movement of a magnitude and direction capable of damaging surface structures. As a result, mine stabilization projects are faced with determining which areas within hundreds of square miles warrant special consideration. Through the use of computer assisted finite element modeling, specific high risk areas can be delineated and recommendations suggested for developing strategies to prevent future damage to surface structures. Using finite element modeling, the mining and geologic conditions of a specific study site are mathematically recreated to calculate the stresses present within mine pillars and rooms. Over stressed areas within the model can then be caused to fail and the resulting magnitude and direction of surface movement and stress then determined. The mathematical model can be modified to consider the effects of pillar decay and robbery as well as introduce faults, secondary mining and stabilization materials. The ability of the program to calculate the stress conditions within a mine under the complex situations commonly found in Pennsylvania greatly exceeds the capabilities of empirical approaches.
FINITE ELEMENT MODELING
The finite element method is a general mathematical technique of structural analysis in which the body to be studied is subdivided into individual structural elements, in this case, triangles (Zienkiewicz, 1977) (Figure 1). The triangles are interconnected at .their corners or nodes. When forces are applied to the body, the nodes displace, and the triangles experience strain. The amount of displacement of each triangle depends on the level of the forces applied to the triangles and the material properties of each triangle.