Mining subsidence of overlying strata is a three-dimensional problem which has a large calculation scope. The present numerical methods have given answers to rock mechanics aspect, however, the answers are inadequate, especially on conditions of greater inclination and thick overlying alluvium. The author proposed a method of semi-analytical numerical analysis which could solve three-dimensional analysis problem of overlying bed rock subsidence caused by mining. This method uses the standard analytic solution of a number of stratiform units and columnar units, combining with discretization analysis of the finite element. It not only overcomes difficulties in mathematics and limitations on application of purely analytical theoretical analysis, but also significantly reduces the amount of calculating work based on purely numerical method of the fully discrete principle. The developed computer program has a wide range applicability for displacement and stress calculation of overlying bed rock subsidence caused by mining.


The reason why semi-analytical numerical method is effective to solve rock mechanics problems is that analytical solution or analytic functions has been introduced to the solution functions of basic control equation[1–2], rather than using a unified discrete and interpolating model as purely numerical methods.

1. Analytic and interpolation function

The main sections of semi-analytical solution function are analytic function groups from some directions and piece wise interpolation function on some other directions.

2. Analysis model of overlying bed rock

The coupled computation model of limited layer and finite prism are shown in Fig.1. The upper soil overburden which is a horizontal bar unit is horizontal surface A, which can be regarded as transversely isotropic material [3]; the lower sloping block B is like a triangular, which is discreted to triangular prism unit; C is the total sloping rock stratum which includes excavation, and they are sloping strip units discrete. A and C are computed with stratiform unit of two-dimensional analysis, and A's local coordinate coincides with the global coordinate; C's local coordinate has an inclination a with the global coordinate. If the seams are excavated, we only need to remove its(their) effect during the integral calculation. A typical stratiform unit is shown in Fig.2. For the triangular-shaped block B, when the automatic segmentation method is adopted, it will be discreted to many one-dimensional analytic triangular prism units shown in Fig.3. In the calculation, the left, right, front, back and bottom borders should be all clamped boundary, and the upper part is free boundary.

4. Dealing with the triangular block

Because the triangular block is automatically discreted to a lot of triangular prism units, it can increase the whole degree of freedom. In order not to make prismatic generalized displacement appear in the whole degree of freedom, it is necessary to deal with the triangular block as follows. (1) Coagulation of internal freedom By means of making rows and columns, the pitch lines on left and right boundary can meet the boundary conditions of consistency with the layer unit = 0,w = 0.

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