Calculation Model for Progressive Residual Surface Subsidence above Mined-Out Areas Based on Logistic Time Function
Abstract
:1. Introduction
- (1)
- Variation of surface subsidence should reflect the fundamental evolution of surface subsidence. This would consider the subsidence from 0 to its maximum value Wmax, the subsidence rate from 0 to the maximum rate Vmax then back to 0, and the subsidence acceleration from 0 to the maximum positive acceleration +amax, then to the maximum negative acceleration −amax, and eventually to 0, as caused by longwall coal mining.
- (2)
- Evolution of the curve of surface subsidence rate should embody the features consistent with observed in situ subsidence rate.
2. Materials and Methods
2.1. Construction of the Logistic Time Function
2.2. Model for Calculating the Surface Dynamic Residual Subsidence
2.3. Parameter Inversion
2.4. Two Studied Areas
2.4.1. Geological Setting and Mining Conditions over Subcritical Mining
2.4.2. Geo-Mining Settings and Field Measurement over Supercritical Mining
3. Results
3.1. Prediction of Surface Dynamic Residual Subsidence over Subcritical Mining
3.1.1. The Features of Surface Subsidence Based on In Situ Investigation
3.1.2. Predictive Result of Dynamic Residual Subsidence
3.2. Calculation for Residual Subsidence over Supercritical Mining
3.2.1. Parameter Inversion
3.2.2. Validation of the Mathematical Model
4. Discussion
4.1. Spatiotemporal Integrity Analysis over Logistic Time Function
4.2. Evolution of Residual Subsidence Coefficient
5. Conclusions
- (1)
- The logistic time function is essentially an ideal mathematical model. It can render the general evolution of surface subsidence from downward surface movement, subsidence rate, and sinking acceleration; the function can be utilized to predict time-dependent surface subsidence induced by an underground mining operation.
- (2)
- Considering the surface subsidence rate over MSP within subsidence basin, the timeline of the entire surface subsidence process from the outset to termination is divided into three periods: the duration period, residual subsidence period, and a long-term subsidence period. Based on this classification and the logistic time function, this study proposes a novel mathematical model for calculating surface progressive residual subsidence. The surface duration period and residual subsidence period are theoretically separated following the threshold of surface subsidence rate. The surface residual subsidence coefficient varies inversely with time and directly with the model parameters involved in the proposed model.
- (3)
- The validation of the mathematical model proposed is verified through field investigations. Back-calculating the parameters with the mathematical model, we found that the greater the volume of in situ data, the more accurate the predictive results of residual surface subsidence becomes. Suppose observation of surface subsidence induced by longwall coal mining is stopped within an active period. In that case, the precision of parameter inversion becomes much lower than that deduced with all of the data. Therefore, it is strongly recommended that subsidence measurement implemented above mined-out voids not be terminated until the surface subsidence rate extends beyond the active period. Only then can back-calculated parameters with field-based data be reliable in predicting forthcoming surface residual subsidence.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Time-Section | Time, d | Period | Max. Subsidence Value, mm | Derived Model Parameters | R-Square | Maximum Deviation, mm | RMSE, mm | ||
---|---|---|---|---|---|---|---|---|---|
q | x0 | p | R2 | ||||||
7 February 2015–28 May 2015 | 110 | Active | 2479 | 0.992 | 93.77 | 12.91 | 0.993 | 272 | ±249 |
7 February 2015–7 June 2015 | 120 | Active | 2563 | 0.923 | 92.36 | 14.56 | 0.994 | 82 | ±48 |
7 February 2015–28 June 2015 | 141 | Weakening | 2605 | 0.905 | 92.02 | 15.21 | 0.996 | 34 | ±11 |
7 February 2015–14 August 2015 | 188 | Residual | 2618 | 0.901 | 91.93 | 15.41 | 0.997 | 35 | ±9 |
7 February 2015–7 December 2016 | 669 | Long-term | 2649 | 0.906 | 92.04 | 15.16 | 0.998 | - | - |
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Li, C.; Ding, L.; Cui, X.; Zhao, Y.; He, Y.; Zhang, W.; Bai, Z. Calculation Model for Progressive Residual Surface Subsidence above Mined-Out Areas Based on Logistic Time Function. Energies 2022, 15, 5024. https://doi.org/10.3390/en15145024
Li C, Ding L, Cui X, Zhao Y, He Y, Zhang W, Bai Z. Calculation Model for Progressive Residual Surface Subsidence above Mined-Out Areas Based on Logistic Time Function. Energies. 2022; 15(14):5024. https://doi.org/10.3390/en15145024
Chicago/Turabian StyleLi, Chunyi, Laizhong Ding, Ximin Cui, Yuling Zhao, Yihang He, Wenzhi Zhang, and Zhihui Bai. 2022. "Calculation Model for Progressive Residual Surface Subsidence above Mined-Out Areas Based on Logistic Time Function" Energies 15, no. 14: 5024. https://doi.org/10.3390/en15145024