This paper features a numerical study that is carried out by using discontinuous deformation method (DDA) and fractal geometry. The configurations of rock strata calculated by DDA were imported into a code that is written by using VC++ called “Fractal” to calculate the fractal dimension of the rock strata. As illustrated, a long wall mining case in China was presented. The relationship of the fractal dimension, excavation length, stress, and movement of strata were discussed. The evolution of fractal dimension can be considered as an index of instability or failure. The method proposed in this paper can be employed to predict the period weighting in long wall mining engineering.
Numerical methods which are rapidly developing and have been widely employed in various engineering fields like geotechnical engineering, mining engineering, civil engineering, and so forth from the past decades [
The important information obtained from a numerical analysis is displacements, stresses, and failure area. Besides, the evolution of fracture network can also be simulated by using discontinuous method, such as UDEC [
Study of fracture network is of great significance to underground engineering, such as deep mining, since stability of surrounding rock, the movement of strata, gas, and water flow are all associated with it. Wang et al. [
The fractal theory was widely used to study the geomaterials, especially rocks, after the pioneer work of Xie and Chen [
Two tools are used in this study; one is the numerical method—DDA—and the other is the fractal theory and fractal dimension.
The DDA is a discrete element method following the definition by Cundall and Hart [
The displacement function of DDA can be written as
In DDA, the large deformation and displacement are calculated by accumulating the small deformation and displacement with a time matching scheme. Based on the definition of Cauchy strain, (
Here, the deformation of the
We thus have the displacement as the following form:
Minimization of the potential energy of the system of blocks, following the FEM convention, results in the following equation:
The fractal is a word from Lingua, which means fracture. Fractal geometry, developed by Mandelbrot et al. [
Koch curve.
In this paper we employed the software called “Fractal” to calculate the fractal dimension of fracture network and to study the configurations and evolution of fracture network of overburden rocks during the mining excavation. The flow chart is shown in Figure
Flow chart of the present study.
A long wall mining case of Jining number 2 mine (China) is selected for study. The length and height of the model as shown in Figure
Mechanical properties of rocks.
Rock | Property | |||
---|---|---|---|---|
|
|
Thickness/m | Note | |
Sand and soil | 15 | 0.29 | 50 | 5 m of each layer |
Siltstone | 36 | 0.2 | 10 | key stratum |
Mudstone | 16 | 0.22 | 12 | 2 m of each layer |
Fine sandstone | 19 | 0.17 | 5/7 | Inferior key stratum and floor |
Coal | 8.8 | 0.23 | 3 | Excavation objects |
Coarse sandstone | 16 | 0.20 | 13 | Roof, 3.25 m of each layer |
Numerical model.
As the excavation may result in the change of fracture network, the configurations of rock blocks after every excavation step were recorded as shown in Figure
Configurations after excavation.
After 30 m excavation, the direct roof collapses (Figure
Figure
Plot of first principal stress and displacement of key stratum with excavation length.
As mentioned above and illustrated in Figure
In general, the first time fracture of the key stratum increased the displacement and the stress; the second time fracture of the key stratum caused stress release. To understand the reason of this phenomenon, we carried out the study on the stress around the work face, which is the key factor during the excavation.
Based on Figure
Plot of maximum stress around work face and fractal dimension with excavation length.
In the previous section, the stress and displacement were analyzed. In this section, the fractal dimension of the fracture network was calculated and the relationship between the stress and fractal dimension was studied. To calculate the fracture dimension, the configurations of the fracture network (Figure
Obviously, the fracture network of the overburden rock changes with the configuration of the rock stratum. The displacement and fractal dimension were thus firstly studied. Figure
For the stress in key stratum, before 150 m of excavation, the stress of key stratum increased with the excavation length. When the fractal dimension decreased, the stress reached its maximum value.
From Figure
In this paper, the numerical method, discontinuous deformation analysis, was employed to calculate a long wall mining case of Jining number 2 coal mine, and for further study, the code “Fractal” was used to calculate the fractal dimension of the fracture network. The evolution of the movement and stress of the overburden rock as well as the fractal dimension were studied. The release of stress in key stratum can be due to the stress release in the work face. The fractal dimension changes with the subsidence of rock strata and decreases with the compaction degree. The fracture of key stratum can also cause an increase of fractal dimension. The decrease of fractal dimension indicates that the stress might have reached the maximum value. The decrease of fractal dimension may serve as a forewarning of periodic weighting.
The method in this paper extends the results of numerical study and provides a new way to predict the strata movement and ground pressure in mining engineering.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This project is supported by the Fundamental Research Funds for the Central Universities (no. 2013QNB19) and the National Basic Research Program of China (no. 2011CB201205).