The square root relationship of gas release in the early stage of desorption is widely used to provide a simple and fast estimation of the lost gas in coal mines. However, questions arise as to how the relationship wa...The square root relationship of gas release in the early stage of desorption is widely used to provide a simple and fast estimation of the lost gas in coal mines. However, questions arise as to how the relationship was theoretically derived, what are the assumptions and applicable conditions and how large the error will be. In this paper, the analytical solutions of gas concentration and fractional gas loss for the diffusion of gas in a spherical coal sample were given with detailed mathematical derivations based on the diffusion equation. The analytical solutions were approximated in case of small values of time and the error analyses associated with the approximation were also undertaken. The results indicate that the square root relationship of gas release is the first term of the approximation, and care must be taken in using the square root relationship as a significant error might be introduced with increase in the lost time and decrease in effective diameter of a spherical coal sample.展开更多
The characters of limestone in weak interlayer of a high rocky slope in Xuzhou, China, are studied by shear static test and shear creep test. The results show that limestone specimens have attenuation creep properties...The characters of limestone in weak interlayer of a high rocky slope in Xuzhou, China, are studied by shear static test and shear creep test. The results show that limestone specimens have attenuation creep properties and constant rate creep properties, almost have no accelerated creep properties. The exponential type empirical formula is selected to fit creep grading curves by polynomial regression analysis method, and the square sums of the fitting results residual are in the order of 10^(-7). Then grade creep curves at every shear loads are set up. Combining creep rate-time curve, the creep properties of limestone are analyzed. As the physical meaning of component model is clearer, the Poytin–Thomson model is set up. Through the least square method, the optimal parameters of Poytin–Thomson model are obtained,and the sums of squared residuals belong to 10^(-3)order of magnitude, which can meet the accuracy requirements of engineering calculation. So the Poytin–Thomson model can reflect the shear creep characteristics of limestone very well.展开更多
文摘The square root relationship of gas release in the early stage of desorption is widely used to provide a simple and fast estimation of the lost gas in coal mines. However, questions arise as to how the relationship was theoretically derived, what are the assumptions and applicable conditions and how large the error will be. In this paper, the analytical solutions of gas concentration and fractional gas loss for the diffusion of gas in a spherical coal sample were given with detailed mathematical derivations based on the diffusion equation. The analytical solutions were approximated in case of small values of time and the error analyses associated with the approximation were also undertaken. The results indicate that the square root relationship of gas release is the first term of the approximation, and care must be taken in using the square root relationship as a significant error might be introduced with increase in the lost time and decrease in effective diameter of a spherical coal sample.
基金funded by the State Key Development Program for Basic Research of China(No.2013CB227900)the Joint Funds of the National Natural Science Foundation of China(NoU1261201)Prof.Mao Xianbiao for his valuable assistance in the preparation of manuscript
文摘The characters of limestone in weak interlayer of a high rocky slope in Xuzhou, China, are studied by shear static test and shear creep test. The results show that limestone specimens have attenuation creep properties and constant rate creep properties, almost have no accelerated creep properties. The exponential type empirical formula is selected to fit creep grading curves by polynomial regression analysis method, and the square sums of the fitting results residual are in the order of 10^(-7). Then grade creep curves at every shear loads are set up. Combining creep rate-time curve, the creep properties of limestone are analyzed. As the physical meaning of component model is clearer, the Poytin–Thomson model is set up. Through the least square method, the optimal parameters of Poytin–Thomson model are obtained,and the sums of squared residuals belong to 10^(-3)order of magnitude, which can meet the accuracy requirements of engineering calculation. So the Poytin–Thomson model can reflect the shear creep characteristics of limestone very well.
