Prediction of surface subsidence due to underground mining based on the zenith angle

There have been numerous methods developed for predicting the subsidence caused by underground coal mining. For discussion purposes, these can be classified into six categories: theoretical, profile function, influence function, graphical, physical, and numerical modeling [1]. The theoretical methods, including elastic, plastic, viscoelastic and elastoplastic, employ mainly continuum mechanics theories and attempt to explain the mechanisms that lead to surface subsidence. The profile function method is essentially a method of curve-fitting against the observed subsidence profiles in a particular mine or region. Since it was first proposed, the influence function has been further developed over various stages, and its application gradually widened. It has been employed worldwide with various degrees of success, and includes the "Subsidence Engineer's Handbook" (SHE) model established on observations of approximately 200 sites in the UK coal fields, and influence function based computer models [2]. The physical models include sand and gelatin and are used mainly to study the parameters that control subsidence behavior. Numerical methods are based on numerical approximations of the governing equations, i.e. the differential equations of equilibrium, the displacement-strain relation, the strain-stress relation and stress-strength relation. They can simulate nearly every conceivable material behavior, inhomogeneity, bedding planes, anisotropy, and various boundary conditions and can predict the induced displacements and stresses in the analyzed area. This versatility is absolutely necessary considering the varied geological and mining conditions encountered [1-3]. However, some disadvantages of these methods exist in practice. Theoretical methods must be simplified in order to solve for complex conditions. The profile function method is only suitable for prediction in cases of rectangular work face mining and flat or gently inclined seams. Although the influence function method can forecast the subsidence caused by irregular-shaped polygonal work face, its application is restricted by large dip angles. The accuracy of numerical methods depends on the properties of the rock mass, measurement of the natural stress field, scale effects and other parameters. It is also controlled by the exactness of the governing equations. Internationally, the profile function and influence function methods are now widely employed, given their practicality and ease of use [4].