Application of the Time Function Model for Dynamic Deformation Prediction in Mining Areas under Characteristic Constraints

Abstract

The fundamental model for dynamically predicting surface subsidence is the time influence function. However, current research and the application of time functions often neglect the comprehensive characteristics of the entire surface deformation process, leading to a less systematic representation of the actual deformation law. To rectify this, we explore ground point deformation along the strike line from two perspectives: dynamic subsidence and dynamic horizontal movement. Moreover, we develop prediction models for dynamic subsidence and dynamic horizontal movement at any point along the strike line, utilizing the probability integral method (PIM) and considering the surface deformation features. We then use characteristic constraints based on the prediction models to constrain the time influence function. For this purpose, we employ the Richards time function which has strong universality to establish the time functions for dynamic subsidence and horizontal movement under these constraints. We provide an illustrative example of its application in the 12,401 working face. Additionally, we explore the suitability of interferometric synthetic aperture radar (InSAR) technology for acquiring dynamic subsidence data on the surface. The experimental findings reveal the following key observations: the Richards model, when applied for dynamic subsidence prediction under constraints, exhibits high accuracy with an R-squared (R2) value of 0.997 and a root mean squared error (RMSE) of 94.6 mm, along with a relative mean square error of 1.9%. Meanwhile, the dynamic horizontal movement prediction model exhibits an accuracy in fully mined areas with an R2 of 0.986, an RMSE of 46.2 mm, and a relative mean square error of 2.6%.

Application of a Variable Weight Time Function Combined Model in Surface Subsidence Prediction in Goaf Area: A Case Study in China

“…Based on a substantial amount of measured data [21,[41][42][43][44][45], it was evident that during a complete subsidence process, a ground point typically undergoes three phases as depicted in Figure 1.…”

“…However, this time function falls short in effectively describing the sinking speed and acceleration of surface points, leading to disparities with actual surface subsidence processes. Consequently, many scholars have continuously refined the Knothe time function model and proposed new time function models, including Usher [11,12], Weibull [13][14][15][16][17], Richards [18][19][20][21], and MMF [22][23][24], among others. While these models partially reflect the dynamic process of surface movement and deformation to some extent, they also have their own limitations.…”

Surface Deformation Calculation Method Based on Displacement Monitoring Data

“…After initial testing of several commonly used interpolation methods for discrete points (such as inverse distance weighting, natural neighbor interpolation, ordinary Kriging, radial basis function interpolation, etc. ), it is known from existing research that ordinary Kriging and radial basis function interpolation are relatively convenient and effective methods [23][24][25][26][27][28][29][30]. The specific usage of these two methods in this problem is described as follows.…”

“…Furthermore, there is little systematic description regarding the monitoring interpolation method at present. Overall, as a calculation method for surface deformation, the main advantage of the monitoring interpolation method is that it can quickly obtain the entire surface deformation field based on monitoring data, bypassing the need for complex constitutive relationships and rock mechanics parameters, and it often achieves good results [26,27]. However, its main disadvantage is that it cannot predict surface deformation [28,29]; thus, it can only be used for calculating assessment of surface deformation in mining areas or studying the historical patterns of surface deformation [30].…”