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.

In this work, we aimed to solve the problems that exist in the brittleness evaluation method of high-strength concrete through a triaxial compression test of C60 and C70 high-strength concrete. Then, the relationship between the energy evolution of its elastic energy, dissipative energy, pre-peak total energy and additional energy and its axial strain, confining pressure, and concrete strength grade was analyzed. Taking the accumulation rate of pre-peak elastic strain energy and the dissipation rate of dissipative energy, and the release rate of post-peak elastic energy, as the evaluation indicators to characterize the brittleness of high-strength concrete. A brittleness evaluation method that reflects the whole failure process of high-strength concrete is proposed and verified by experiments. The results show that with the increase of the confining pressure, the proportion of elastic energy in the whole process of high-strength concrete failure gradually decreases. The storage rate of pre-peak elastic energy and the release rate of post-peak elastic energy are gradually reducing, the brittleness index gradually decreases, and the confining pressure inhibits the brittleness of high-strength concrete. Under the same confining pressure, the brittleness index of C70 concrete is greater than that of C60 concrete, which indicates that, with the increase of the strength grade, the brittleness level of concrete gradually increases and the ductility decreases. These findings have a certain theoretical significance for the scientific design of high-strength concrete structures and the improvement of their safety in the future.

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.

To determine the nonlinear creep characteristics of rocks under cyclic loading and unloading conditions, a nonlinear Kelvin model and damage viscoplastic model are proposed. The models are connected in series with a linear elastic body to establish a nonlinear damage creep model. The differential damage constitutive equations of the proposed creep model under one‐dimensional and three‐dimensional stress states are derived based on the creep mechanics and elasticity theory. The damage and unloading creep equations are then obtained based on the superposition principle, and a simple and feasible method for determining the model parameters is determined. Finally, the step cyclic loading and unloading creep test data for lherzolite and limestone are used to verify the rationality and feasibility of the nonlinear damage creep model. The results show that the theoretical creep curves of the nonlinear damage creep model are consistent with the experimental curves which indicates that the proposed model can not only determine the creep properties of lherzolite and limestone under cyclic loading and unloading but also determine the nonlinear characteristics of rocks in the transient and steady‐state creep stages and particularly within the accelerating creep stage.

In engineering, loose sandy (gravelly) strata are often filled with cement-based grout to form a mixed material with a certain strength and impermeability, so as to improve the mechanical properties of sandy (gravelly) strata. The tortuosity effect of sandy (gravelly) strata and the time-varying viscosity of slurry play a key role in penetration grouting projects. In order to better understand the influence of the above factors on the penetration and diffusion mechanism of power-law slurry, based on the capillary laminar flow model, this research obtained the seepage motion equation of power-law slurry, the time-varying constitutive equations of tortuosity and power-law fluid viscosity were introduced, and the spherical diffusion equation of penetration grouting considering both the tortuosity of porous media and time-varying slurry viscosity was established, which had already been verified by existing experiments. In addition, the time-varying factors of grouting pressure, the physical parameters of the injected soil layer, and slurry viscosity on penetration grouting diffusion law and the influencing factors were analyzed. The results show that considering the tortuosity of sandy (gravelly) strata and the time-varying of slurry viscosity at the same time, the error is smaller than the existing theoretical error, only 13~19%. The diffusion range of penetration grouting in the sandy (gravelly) strata is controlled by the tortuosity of sandy (gravelly) strata, the water–cement ratio of slurry, and grouting pressure. The tortuosity of sandy (gravelly) strata is inversely proportional to the diffusion radius of the slurry, and the water–cement ratio of slurry and grouting pressure are positively correlated with the diffusion radius. In sandy (gravelly) strata with a smaller particle size, the tortuosity effect of porous media dominates the slurry pressure attenuation. When the particle size is larger, the primary controlling factor of slurry pressure attenuation is the tortuosity effect of porous media in the initial stage and the time-varying viscosity of slurry in the later stage. The research results are of great significance to guide the penetration grouting of sandy (gravelly) strata.

In this study, an improved Knothe time function model is established via analogical reasoning from a phenomenological perspective, based on an inverse “Hohai creep model” function, in accordance with the antisymmetric relationship between the unstable creep curve and surface dynamic subsidence curve. An empirical method and fitting method are proposed to determine the parameters of the improved model based on the availability of measured field data. The accuracies of the two models are compared with monitored data from eight monitoring points in the main strike profile of the Guotun coal mine subsidence basin. The results show that the improved model can more accurately reflect the dynamic process of surface subsidence. The average relative standard deviation of the improved model is only 4.9%, which is far lower than the 23.1% associated with the Knothe model. This verifies the improved model’s accuracy and reliability. The model parameters for different monitoring stations obtained using the fitting method are similar, which shows that the model parameters are regular and can be easily applied.