Taking into account the inadequacy of the Knothe time function model to predict the dynamic surface subsidence caused by underground mining, a new hypothesis is proposed, and the improved Knothe time function model is established. Theoretical analysis shows the improved model agrees well with surface subsidence dynamic change, velocity change, and acceleration change rules. Combined with field measured data, the probability integral method, dual-medium method, and least square method are adopted to determine the time influence parameter C and the model order n. Based on monitoring data from four monitoring stations in the Guotun coal mine subsidence basin strike main profile from Heze city, Shandong Province, China, the accuracies of the Knothe time function and improved model are compared and analyzed. Results show the improved model can accurately describe the dynamic surface subsidence process and subsidence velocity with mining time. The average relative standard error between the predicted and measured values is only 4.8%—far lower than the Knothe time function model is 23%, verifying the improved model’s accuracy and reliability.

To study the energy evolution law and damage constitutive behavior of high-strength concrete based on the conventional triaxial compression tests of C60 and C70 high-strength concrete subjected to five different confining pressures, the failure characteristics of high-strength concrete are analyzed at different confining pressures, and the evolution of the input energy density, elastic strain energy density, and dissipation energy density with axial strain and confining pressure are quantified. Combined with a continuous damage theory and non-equilibrium statistical method, the ratio of dissipation energy density of concrete to dissipation energy density corresponding to peak stress is used as the mechanical parameter. Assuming that the mechanical parameter obeys the Weibull distribution laws, the statistical damage variable describing the damage characteristics of concrete were derived. According to the Lemaitre strain equivalent principle, the damage variable is introduced to the generalized Hooke law to establish the statistical damage constitutive model for high-strength concrete. The results show that: (1) the input energy density and dissipation energy density increases with the increase of axial strain, while the elastic strain energy density increases first and then decreases as a function of the axial strain and reaches the maximum value at the peak stress; (2) the input, elastic strain, and dissipated energy densities corresponding to the peak stress of the two high-strength concretes all increase as a function of confining pressure, and the elastic strain energy density corresponding to the peak stress increases linearly as a function of the confining pressure; (3) the statistical damage constitutive model results of C60 and C70 high-strength concrete are in good agreement with the test results, and the average relative standard deviations are only 3.64% and 3.99%. These outcomes verify the rationality and accuracy of the model.