Abstract
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.
Highlights
Ese research results have been well applied to the prediction of surface subsidence in coal mining
An improved Knothe time function model based on an inverse “Hohai creep model” function is established by analogical reasoning
It can be seen from a comparison of the results shown in Figure 5 that there is a big difference between the fitted values of the Knothe time function model and the monitored data
Summary
According to the rock creep theory, rock will undergo unstable creep under high stress levels as shown in the blue curve in Figure 2 (the curve does not include the instantaneous strain generated during stress loading). It can be seen that the shape of the unstable creep curve is similar to a reverse “S” curve, which is the inverse of the surface subsidence curve. Erefore, as long as the unstable creep function is determined and its inverse function is calculated, the time function describing the dynamic surface subsidence can be established. Where σ is stress; σS is long-term strength; η is the viscosity coefficient of the “Hohai creep model”; n is model order; ε is strain; and t is time. E inverse function of equation (3) can be solved to obtain the new relationship between the independent and dependent variables. At this time, the independent variable a (t) (mm·d –2). It can be seen that the surface subsidence curve is approximately S-shaped, and the surface subsidence velocity curve approximates a normal distribution curve. e surface subsidence characteristics that are reflected are consistent with the real-world process and can be used to describe the dynamic process of surface subsidence
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