For deep mining engineering, heat transfer of coal mass is a vital factor in the thermal environment of coal mines. In order to study the thermal conduction mechanism, we obtained gray images of coal mass microstructu...For deep mining engineering, heat transfer of coal mass is a vital factor in the thermal environment of coal mines. In order to study the thermal conduction mechanism, we obtained gray images of coal mass microstructure by scanning samples with a digital microscope. With the use of Matlab, these gray images were transformed into binary images, which were then transformed into a corresponding matrix consisting only of the values 0 and 1. According to the calculation method of box-counting dimension, we calculated the fractal dimension of the loose coal to be approximately 1.86. The thermal conductivity expressions of loose coal were derived based on the simulation method of thermal resistance. We calculated the thermal conductivity of loose coal by using a fractal model and compared the calculated values with our experimental data. The results show that the test data show an encourag-ing agreement with the calculated values. Hence fractal theory is a feasible method for studying thermal conductivity of loose coal.展开更多
One dimensional non-steady, non-Darcy flow of water in a rock stratum was reduced into a system described by six ordinary differential equations involving five controlling parameters. Through response computations and...One dimensional non-steady, non-Darcy flow of water in a rock stratum was reduced into a system described by six ordinary differential equations involving five controlling parameters. Through response computations and time series analysis, chaotic behavior in the reduced system was discussed in details. Firstly, the dynamical response of the reduced system under a set of parameters was calculated, and the power spectrum of the attractor was obtained through fast Lagrangian transformation; then the phase space was reconstructed by fixing embedding dimension to be 6 and delay time to range from 1 to 20, and the correlation dimension of the attractor was calculated based on the curves under the coordinates of logarithm of correlation integral vs. logarithm of covering radius; and lastly, the Lyapunov indices of the attractor were calculated by using Gram-Schmit's orthogonalization method. The results show that the power spectrum of the attractor is continuous; the correlation dimension of the attractor is equal to 2.36; among the Lyapunov indices, LE1, LE2, LE3 are positive, LE5, LE6 are negative, and LE4 fluctuates near zero. All the analysis indicates that there may exist chaos in the system of non-steady, non-Darcy flow.展开更多
In order to quantify the characteristics of the surface of jointed rock mass,new equipment,the three-dimensional laser surface topography instrument,was used to accurately measure surface morphology of joints.Scan pic...In order to quantify the characteristics of the surface of jointed rock mass,new equipment,the three-dimensional laser surface topography instrument,was used to accurately measure surface morphology of joints.Scan pictures and parameters were obtained to describe the rock joint surface characteristics,for example,the height frequency of surface,and mean square roughness.Using the method of fractal dimension,the values of joint roughness coefficient(JRC) were calculated based on the above parameters.It could access to the joint surface rock sample morphology of the main parameters of characteristic.The maximum peak height is 2.692 mm in the test joint plane.The maximum profile height is 4.408 mm.JRC value is 6.38 by fractal dimension computing.It belongs to the smooth joint surface.The results show that it is a kind of the effective method to quantitatively evaluate the surface topography by the three-dimensional laser surface topography instrument and the fractal dimension method.According to the results,during the process of underground large-scale mining,safe measures to prevent slip failure of the joint plane by controlling surface tension and shear mechanical response were proposed.展开更多
The characterization of pore structure in rocks is relevant in determining their various mechanical behaviors. Digital image processing methods integrated with fractal theory were applied to analyze images of rock sli...The characterization of pore structure in rocks is relevant in determining their various mechanical behaviors. Digital image processing methods integrated with fractal theory were applied to analyze images of rock slices obtained from industry CT, elucidating the characteristics of rock pore structure and the relationship between porosity and fractal dimensions. The gray values of pixels in CT images of rocks provide comprehensive results with respect to the attenuation coefficients of various materials in corresponding rock elements, and these values also reflect the effect of rock porosity at various scales. A segmentation threshold can be determined by inverse analysis based on the pore ratios that are measured experimentally, and subsequently binary images of rock pores can be obtained to study their topological structures. The fractal dimension of rock pore structure increases with an increase in rock pore ratio, and fractal dimensions might differ even if pore ratios are the same. The more complex the structure of a rock, the larger the fractal dimension becomes. The experimental studies have validated that fractal dimension calculated directly from gray CT images of rocks can give an effective complementary parameter to use alongside pore ratios and they can suitably represent the fractal characteristics of rock pores.展开更多
基金support for this study, provided by the National Natural Science Foundation of China (Nos50534040 and 50974117)the Research Fund of the State Key Laboratory of Coal Resources & Mine Safety, CUMT (No07KF10)
文摘For deep mining engineering, heat transfer of coal mass is a vital factor in the thermal environment of coal mines. In order to study the thermal conduction mechanism, we obtained gray images of coal mass microstructure by scanning samples with a digital microscope. With the use of Matlab, these gray images were transformed into binary images, which were then transformed into a corresponding matrix consisting only of the values 0 and 1. According to the calculation method of box-counting dimension, we calculated the fractal dimension of the loose coal to be approximately 1.86. The thermal conductivity expressions of loose coal were derived based on the simulation method of thermal resistance. We calculated the thermal conductivity of loose coal by using a fractal model and compared the calculated values with our experimental data. The results show that the test data show an encourag-ing agreement with the calculated values. Hence fractal theory is a feasible method for studying thermal conductivity of loose coal.
基金supported by the National Natural Science Foundation of China (No.50874104)
文摘One dimensional non-steady, non-Darcy flow of water in a rock stratum was reduced into a system described by six ordinary differential equations involving five controlling parameters. Through response computations and time series analysis, chaotic behavior in the reduced system was discussed in details. Firstly, the dynamical response of the reduced system under a set of parameters was calculated, and the power spectrum of the attractor was obtained through fast Lagrangian transformation; then the phase space was reconstructed by fixing embedding dimension to be 6 and delay time to range from 1 to 20, and the correlation dimension of the attractor was calculated based on the curves under the coordinates of logarithm of correlation integral vs. logarithm of covering radius; and lastly, the Lyapunov indices of the attractor were calculated by using Gram-Schmit's orthogonalization method. The results show that the power spectrum of the attractor is continuous; the correlation dimension of the attractor is equal to 2.36; among the Lyapunov indices, LE1, LE2, LE3 are positive, LE5, LE6 are negative, and LE4 fluctuates near zero. All the analysis indicates that there may exist chaos in the system of non-steady, non-Darcy flow.
基金Project(2011QNZT087) supported by the Freedom Explore Program of Central South University of ChinaProject(51074178) supported by the National Natural Science Foundation of China+1 种基金Project(09JJ4025) supported by Hunan Provincial Natural Science Foundation of ChinaProject(2010QZZD001) supported by the Fundamental Research Funds for the Central Universities of China
文摘In order to quantify the characteristics of the surface of jointed rock mass,new equipment,the three-dimensional laser surface topography instrument,was used to accurately measure surface morphology of joints.Scan pictures and parameters were obtained to describe the rock joint surface characteristics,for example,the height frequency of surface,and mean square roughness.Using the method of fractal dimension,the values of joint roughness coefficient(JRC) were calculated based on the above parameters.It could access to the joint surface rock sample morphology of the main parameters of characteristic.The maximum peak height is 2.692 mm in the test joint plane.The maximum profile height is 4.408 mm.JRC value is 6.38 by fractal dimension computing.It belongs to the smooth joint surface.The results show that it is a kind of the effective method to quantitatively evaluate the surface topography by the three-dimensional laser surface topography instrument and the fractal dimension method.According to the results,during the process of underground large-scale mining,safe measures to prevent slip failure of the joint plane by controlling surface tension and shear mechanical response were proposed.
基金supported by the National Natural Science Foundation of China (10802092, 50974125)the National Basic Research Program of China (2009CB724602, 2010CB226804)+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education (20070290011)the Fundamental Research Funds for the Central Universities (2009QM03)
文摘The characterization of pore structure in rocks is relevant in determining their various mechanical behaviors. Digital image processing methods integrated with fractal theory were applied to analyze images of rock slices obtained from industry CT, elucidating the characteristics of rock pore structure and the relationship between porosity and fractal dimensions. The gray values of pixels in CT images of rocks provide comprehensive results with respect to the attenuation coefficients of various materials in corresponding rock elements, and these values also reflect the effect of rock porosity at various scales. A segmentation threshold can be determined by inverse analysis based on the pore ratios that are measured experimentally, and subsequently binary images of rock pores can be obtained to study their topological structures. The fractal dimension of rock pore structure increases with an increase in rock pore ratio, and fractal dimensions might differ even if pore ratios are the same. The more complex the structure of a rock, the larger the fractal dimension becomes. The experimental studies have validated that fractal dimension calculated directly from gray CT images of rocks can give an effective complementary parameter to use alongside pore ratios and they can suitably represent the fractal characteristics of rock pores.