During the excavation of deep coal and rock mass, the radial stress of the free face changes from three-dimensional compression state to two-dimensional stress, bearing the combined action of dynamic disturbance and static load at the same time. With that, many mines suffer from dynamic disasters, such as coal and gas outburst, rock burst and rock caving during deep mining excavation, which is often accompanied by plate crack, spalling and other disasters, seriously affecting the stability of stope and roadway. Taking thin rectangular coal and rock mass as the research object, the dual equation of the free vibration was derived and the exact solution model of the free vibration was established with the use of Hamilton dual system. Based on the action characteristics of the uniform impact load, the effective mode of the forced vibration was obtained by using the Duhamel integral principle and the orthogonality of the mode function. Based on the third strength theory and the numerical simulation results, the dynamic damage process and development trend of coal and rock mass were analyzed under uniform impact load. It was concluded that the starting position of dynamic damage can be judged by the first order main mode, and the development direction and trend of the damage can be judged by the fifth and sixth order main modes. It was concluded that the vibration mode functions of coal and rock mass with four side fixed

A variety of gaseous products are formed when mine fires and coal and gas outbursts occur in mines. On the one hand, these gas products affect the normal production of mines and the occupational health of miners; on the other hand, the gaseous products can also provide much important information to prevent mine disasters. Thus, the rapid and accurate determination of the component content of multicomponent mixed gases is of great significance. However, the distortion of gas chromatography measurement results, which deviate from the true values, has a serious impact on gas composition determination in mines. To reduce the influence of distortion, an Agilent 490 portable gas chromatograph is used to measure the component content of 11 groups of standard multicomponent mixed gases. It is found that the error rate of the measured result is highly related to the concentration of the selected reference component and the component to be measured. Besides, the key point of each gas concentration is determined according to the scatter diagram of the error rate. Each gas is divided into a high and a low concentration group by the key points, and each gas is selected as the reference component to measure the corresponding component concentration in other gases with multiple-point external standards. Researchers have used the least-squares method to fit univariate linear regression analysis between the measured values and true values of mixed gases. Then, the optimal analysis function and the optimal reference component concentration of each gas can be determined by comparing the regression analysis parameters. Finally, it is found that the error rate of measured values corrected by the optimal analysis function is significantly reduced. It is proved that this method can effectively alleviate the measurement results’ distortion, which solves the problem of gas composition determination in underground areas.