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Prediction of Longwall Progressive Subsidence Basin Using the Gompertz Time Function

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Abstract

It is imperative for the mining area to timely and accurately predict the longwall progressive subsidence basin. However, the mainstream method that uses time function still has limitations, which impede extensive application. In this study, we analyzed the flaws of the optimized segmented Knothe time function in detail, and expounded the possible improvement directions. Subsequently, we proposed the Gompertz time function for predicting longwall progressive subsidence basin, based on the modeling idea that three origins are consistent. Afterward, we analyzed the variation law between parameters of the Gompertz time function and the geological mining conditions, and elaborated the parameter calculation method and the prediction algorithm for the longwall progressive subsidence basin. Finally, we demonstrated the practical application effect of this method with experiments. The average RMSE and average relative RMSE of predicted progressive subsidence using the Gompertz time function are 58.4 mm and 6.9%, respectively, and compared with the same statistics using the optimized segmented Knothe time function, the accuracy is increased by 27.9% on average. The results show that the accuracy of this article proposed method can achieve centimeter-level, meet the requirements of practical engineering application, and this method is expected to enable the mining proceeding in a safe, effective and environmentally sustainable way.

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Data availability

All data generated or analyzed during this study are included in this published article.

Abbreviations

OSK:

Optimized segmented Knothe

TOC:

Three origins are consistent

RMSE:

Root mean square error

RRMSE:

Relative RMSE

c :

Time coefficient

τ :

The moment of maximum subsidence velocity of the surface point

\(T_{{\text{t}}}\) :

Total subsidence time of the surface point

t :

Time

\(W_{0}\) :

Final subsidence of the surface point

ω :

Advance influence angle

\(l_{{\text{A}}}\) :

Advance influence distance

\(W(t)\) :

Subsidence of surface point at the moment t

\(v(t)\) :

Velocity of surface point at the moment t

\(a(t)\) :

Acceleration of surface point at the moment t

v :

Mean mining velocity

L :

Panel length in critical mining condition

\(W_{{\text{f}}}\) :

Subsidence of surface point since the underground extraction had just advanced to the point

i :

Surface point in strike line of the working panel

\(k_{i}\) :

Velocity coefficient of the point i to reach stabilized status

\(b_{i}\) :

The moment of maximum subsidence velocity of the point i since the underground extraction had just advanced to the point

\(x_{i}\) :

Strike critical factor of point i

\(l_{i}\) :

Distance from point i to the setup entry of the working panel

\(r_{0}\) :

Main influence radius of the working panel

\(\beta\) :

Main influence angle of the working panel

\(H_{0}\) :

Mean depth of the working panel

T s :

The time of subsidence reaching basic stabilized status

P :

Lithology

\(H_{{\text{a}}}\) :

Thickness of the alluvium

f :

Hardness coefficient of the bedrock

\(f_{{\text{m}}}\) :

Hardness coefficient of medium–hard bedrock

\(f_{{\text{a}}}\) :

Hardness coefficient of the bedrock under actual geological mining conditions

\(h_{\eta }\) :

Normal thickness of the ηth overlying stratum

\(R_{\eta }\) :

Uniaxial compressive strength of the ηth overlying stratum

\(b_{\min }\) :

Minimum value of \(b_{i}\)

\(b_{{\text{C}}}\) :

Constant of \(b_{i}\)

B :

Linear slope of \(b_{i}\) concerning \(x_{i}\)

\(l_{{\text{s}}}\) :

Delay distance of maximum subsidence velocity of the surface point under critical mining

y :

Dip critical factor of the working panel

m :

Mining thickness of the working panel

\(k_{\max }\) :

Maximum value of \(k_{i}\)

\(k_{{\text{C}}}\) :

Constant of \(k_{i}\)

M :

Linear slope of \(k_{i}\) concerning \(x_{i}\)

\(q_{T}\) :

Subsidence coefficient in predicted time T

T :

Predicted time

\(n_{x}\) :

Mining degree coefficient in the strike of the working panel

q :

Subsidence coefficient in final state

\(x_{T}\) :

Strike critical factor corresponding to the advancing length \(l_{T}\)

\(l_{T}\) :

Advancing length of the working panel at the predicted time T

b D :

Displacement factor

θ 0 :

Influence transference angle

S 1 :

Offset distance of the inflection point in downslope

S 2 :

Offset distance of the inflection point in upslope

S 3 :

Offset distance of the inflection point in left strike

S 4 :

Offset distance of the inflection point in right strike

\(l_{{\text{U}}}\) :

Unit division length

j :

Mining unit

\(x_{j}\) :

Strike critical factor of mining unit j

\(T_{j}^{{\text{W}}}\) :

Extracted time of mining unit j

\(T_{j}^{{\text{J}}}\) :

Elapsed time from underground extraction had just advanced to the center of mining unit j to the predicted time

\(b_{j}\) :

The parameter b of the mining unit j

\(k_{j}\) :

The parameter k of the mining unit j

\(\Phi_{j} (t)\) :

Gompertz time function value of each mining unit j

\(\overline{R}^{2}\) :

Adjusted \(R^{2}\)

\(\phi\) :

Leveling point

\(W_{{{\text{P}}_{\phi } }}\) :

Predicted subsidence at leveling point \(\phi\)

\(W_{{{\text{M}}_{\phi } }}\) :

Leveling subsidence at leveling point \(\phi\)

\(W_{\max }\) :

Maximum value of the leveling subsidence

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 41971401), and the Fundamental Research Funds for the Central Universities (No. 2021YJSDC17); this support is greatly appreciated. The authors are grateful to the Huaibei Mining Co., Ltd. and the Chexplor Resource Exploration Technology Co., Ltd. for their support. The thanks also go to editors and anonymous reviewers for their in-depth reading and valuable comments and suggestions.

Funding

This work was supported by the National Natural Science Foundation of China (No. 41971401), and the Fundamental Research Funds for the Central Universities (No. 2021YJSDC17).

Author information

Authors and Affiliations

  1. School of Geodesy and Geomatics, Wuhan University, Wuhan, 430079, China

    Jian Wang

  2. College of Geoscience and Surveying Engineering, China University of Mining and Technology-Beijing, Beijing, 100083, China

    Jian Wang, Keming Yang, Xiaoyu Shi & Shuyi Yao

  3. General Defense Geological Survey Department, Huaibei Mining Co., Ltd., Huaibei, 235000, China

    Xiangping Wei

Authors
  1. Jian Wang
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  2. Keming Yang
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  3. Xiangping Wei
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  4. Xiaoyu Shi
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Contributions

JW implemented the computer program and wrote the first draft of this paper. KY conceived the research work and provided the research funds and contributed to paper revision. XW contributed to experiment implementation and provided relevant data. XS and SY performed the analysis work and gave suggestions.

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Correspondence to Keming Yang.

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Wang, J., Yang, K., Wei, X. et al. Prediction of Longwall Progressive Subsidence Basin Using the Gompertz Time Function. Rock Mech Rock Eng 55, 379–398 (2022). https://doi.org/10.1007/s00603-021-02664-z

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