
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

39223282
71434
10.1038/s41598-024-71434-y
Article
Research on prediction method of coal mining surface subsidence based on MMF optimization model
Piao Chunde piaocd@cumt.edu.cn

1
Zhu Bin 12
Jiang Jianxin 13
Dong Qinghong 1
1 https://ror.org/01xt2dr21 grid.411510.0 0000 0000 9030 231X School of Resources and Geosciences, China University of Mining and Technology, Xuzhou, China
2 Qingdao West Coast New District Comprehensive Administrative Law Enforcement Bureau, Qingdao, China
3 Sichuan Zhongding Blasting Engineering Co, Ltd., Ya’an, China
2 9 2024
2 9 2024
2024
14 203166 7 2024
28 8 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
Coal seam mining causes fracture and movement of overlying strata in goaf, and endangers the safety of surface structures and underground pipelines. Based on the engineering geological conditions of 22,122 working face in Cuncaota No.2 Coal Mine of China Shenhua Shendong Coal Group Co., Ltd. a similar material model test of mining overburden rock was carried out. The subsidence of overburden rock was obtained through the full-section strain data of distributed optical fiber technology, and the characteristics of mining surface subsidence were studied. The Weibull model was used to adjust the mathematical form of the first half of the surface subsidence curve via the MMF function. On this basis, the prediction model of coal seam mining surface subsidence was established, and the parameters of the prediction model of surface subsidence were determined. The test results show that with the advancement of coal seam mining, the fit goodness of the surface subsidence prediction curve based on the MMF optimization model reaches 0.987. Compared with the measured values, the relative error of the surface subsidence prediction model is reduced to less than 10%. The model displays good prediction accuracy. The time required for settlement stability in the prediction model is positively correlated with parameter a and negatively correlated with parameter b. The research results can be further extended to the prediction of overburden “three zones” subsidence, and provide a scientific basis for the evaluation of surface subsidence compression potential in coal mine goaf.

Keywords

Surface subsidence prediction
Distributed monitoring
MMF optimization model
Coal seam mining
Sensing optical fiber
Subject terms

Natural hazards
Environmental impact
http://dx.doi.org/10.13039/501100001809 National Natural Science Foundation of China 42277159 issue-copyright-statement© Springer Nature Limited 2024
==== Body
pmcIntroduction

The underground mining of coal mine is accompanied by the initiation, expansion and penetration of the internal cracks in the overlying rock and soil mass, which leads to the movement, deformation and destruction of the rock strata to the goaf, causes the surface subsidence, and endangers the safety of the surface structures and underground pipelines1. The surface subsidence of coal mining is the result of deformation and failure of overlying strata from bottom to top. Through the monitoring of subsidence in the deformation evolution stage of overlying strata in coal seam mining, the prediction method of mining surface subsidence can be established, and effective prevention and control measures can be taken in advance to avoid and reduce the safety problems caused by surface subsidence2.

The settlement of overlying strata in goaf caused by underground coal mining is nonlinear and uncertain. It has become a new research direction to characterize the deformation and dynamic settlement of rock and soil mass through mathematical model. Combined with the field measured data to determine the time influence parameter C and the model order n, Zhang et al.3,4 established an improved Knothe time function model by using the probability integral method, the two-medium method and the least square method. Based on actual geological conditions of a mine in East China, Ma et al.5,6 t substituted he mechanical parameters into the Weibull composite subsidence prediction model (WCSPM) and the probability integral composite subsidence prediction model (PICSPM). Accordingly, they obtained the predictions of surface subsidence movement parameters. Chi et al.7 introduced the multi-population genetic algorithm into the Boltzmann function and established a calculation model of mining subsidence parameters. Based on the dynamic model of improved probability integral method, Jiang et al.8 established the observation condition equation of differential interferometric synthetic aperture radar (D-InSAR) monitoring mining subsidence, and proposed a three-dimensional deformation prediction method of mining subsidence. Sui et al.9 established a mining subsidence prediction method combining D-InSAR technology and support vector machine regression algorithm. Oh HJ et al.10 used logit boost meta-integrated machine learning model to predict land subsidence. Pal et al.11 proposed a correction method for surface subsidence by using FNSE model and combining with the excavation parameters of long-arm mining face. The MMF (Morgan-Mercer-Flodin) model in the time function prediction model can well describe the development process of ground subsidence, and the model has a high consistency with the ground subsidence rate12–14. Surface subsidence is a dynamic problem caused by the voids in the goaf entering the surface along the overlying strata. The MMF model suffers reduced prediction accuracy when the geological conditions of rock strata are complex.

The advantage of distributed optical fiber sensing technology lies in using the optical fiber path to obtain the continuous distribution information of the measured field in time and space at the same time. It has been applied to the deformation monitoring of mining overburden15. Cuncaota No.2 Coal Mine of China Shenhua Shendong Coal Group Co., Ltd. is located in Yijinhuoluo Banner, Ordos City, Inner Mongolia Autonomous Region. Photovoltaic panels are installed on the surface above the 22,122 working face for power generation. Coal mining leads to the hidden danger of deformation and fracture of photovoltaic panels. This study set the 22,122 working face of Cuncaota No.2 Mine as the research object. Through the indoor similar material model test of mining overburden rock, the distributed optical fiber sensing technology was used to obtain the strain distribution of overburden rock in the process of coal seam mining, and the surface subsidence caused by mining was calculated. Aiming to solve the problem of insufficient accuracy in the prediction of surface subsidence caused by coal mining based on MMF model, Weibull model was introduced into the prediction method of surface subsidence based on MMF model, and MMF optimization model based on measured surface subsidence was established to determine the relevant parameters of the prediction model of surface subsidence. This study provides a theoretical basis for real-time control and treatment of surface subsidence above coal mine goaf.

Prediction model of surface subsidence induced by coal seam mining

Settlement prediction method based on MMF model

The MMF model is a growth curve model with a 'S' type characteristic curve, and its model function form conforms to the evolution characteristics of surface subsidence caused by coal seam mining. The prediction expression of overburden subsidence related to MMF model is:1 St=W0tba+tb

where St denotes the surface settlement at time t; W0 is the maximum settlement of the surface; a and b are parameters related to the geological conditions of overlying strata; and t represents the time of settlement.

The first and second derivatives of the MMF model of Eq. (1) are solved, and the expressions of surface subsidence velocity and acceleration are obtained.

Let W0= 1000mm, a = 1, b = 5, the relationship between surface subsidence value, settlement velocity and settlement acceleration based on MMF model is obtained, as shown in Fig. 1.Fig. 1 Curves of surface subsidence, subsidence velocity and subsidence acceleration changing with mining time.

As can be seen from Fig. 1, the surface subsidence curve of the MMF model exhibits obvious segmentation, and the settlement value of the initial stage and the stable stage of the settlement is small. Under the coal seam mining conditions in the underground coal mine, the strata in the caving zone first moves to the goaf and the subsidence develops rapidly, which is not consistent with the evolution characteristics of the initial stage of the MMF model.

Surface subsidence prediction method of MMF optimization model

In view of the difference between the predicted curve of MMF time function model and the actual subsidence curve in the early stage of coal seam mining, Weibull model is used to optimize and adjust the mathematical form of the first half of MMF function curve, so as to solve the problem that the overall prediction accuracy is reduced due to the small settlement value in the initial stage of settlement. The phased function form of the improved MMF model is established by using the time when the subsidence velocity of the surface monitoring point reaches the maximum τ as the demarcation point, as shown in Eq. (2).2 W(t)=u1∗ω01-e-ctk+u2∗W0tba+tb,0≤t≤τW0tba+tb,τ≤t≤T

where u1 and u2 denote combined weights, which are non-negative numbers, and u1 + u2 = 1, which are determined according to Eq. (3); τ refers to the maximum surface subsidence velocity moment; and t is the total time of surface subsidence deformation.3 ui=1/ei2∑1n(1/ei2)

where ei is the settlement prediction error, and ei = predicted settlement value-actual settlement value.

Two methods are used to determine the maximum surface subsidence velocity time τ.Through the real-time monitoring of the whole section of the mining overburden, the second derivative of the fitting equation of the monitoring data is equal to zero, and the maximum settlement velocity moment τ is obtained.

For the actual observation data missing conditions, according to the “Specification on Building, Water, Railway and Main Roadway Coal Pillar Setting and Coal Mining”, the total time of surface movement and deformation is calculated by Eq. (4):4 T=2.5H0

where H0 denotes the average mining depth of coal seam.

The time experienced by the active stage of ground surface subsidence deformation is 0.56 times of the total time T of the moving deformation, as shown in Eq. (5).5 τ=0.56T

Similar material model test of mining overburden rock

Model monitoring and excavation scheme

The 22,122 working face of Cuncaota No.2 Coal Mine of China Shenhua Shendong Coal Group Co., Ltd. is mined along the long arm of the coal seam. The length and width of the working face are 800 m and 340 m, respectively. According to the engineering geological conditions of the 22,122 working face of Cuncaota No.2 Coal Mine and the histogram of BK26 borehole, the average burial depth of the 2–2 coal seam to be mined is 255 m, and the average mining thickness is 3 m. Given the mining conditions, the physical and mechanical properties of the overlying rock and the size of the model test, the geometric similarity ratio was determined to be 200, and the stress similarity ratio was 333.33. River sand, lime, gypsum and other materials were selected to configure similar materials according to the ratio number; and the test model of similar materials in mining area was made. In the model test, the uppermost Quaternary clay layer is replaced by weights of the same weight. The physical and mechanical parameters and ratio numbers of the prototype and model of Cuncaota No.2 Mine are shown in Table 116.Table 1 Physical and mechanical parameters and ratio numbers of prototype and model of Cuncaota No.2 Mine.

Ordinal Number of Stratum	Lithologic Characters	Thickness of Stratum (m)	Density (kg/m3)	Bulk modulus (GPa)	Tensile strength (MPa)	Thickness of Model (cm)	Total Thickness (cm)	Proportion Number	
(11)	Medium sandstone	42	2579	3.31	1.2	21	21	773	
(10)	Sandy mudstone	12	2511	2.55	0.75	6	27	837	
(9)	Sandstone	23	2978	2.89	3.7	11.5	38.5	373	
(8)	Sandy mudstone	26	2511	2.56	0.75	13	51.5	837	
(7)	Sandstone	20	2978	2.89	3.7	10	61.5	373	
(6)	Sandy mudstone	23	2511	2.56	0.75	11.5	73	837	
(5)	Siltstone	29	2631	5.02	2.51	14.5	87.5	637	
(4)	Sandy mudstone	13	2511	2.56	0.75	6.5	94	837	
(3)	Siltstone	19	2631	5.02	2.51	9.5	103.5	637	
(2)	2–2 Coal seam	3	1400	0.85	0.5	1.5	105	927	
(1)	Sandy mudstone	26	2509	2.56	0.75	13	118	837	

In order to grasp the deformation and failure characteristics of overlying strata in the process of coal seam mining, four vertical tight sheath strain optical fibers were laid in the similar material test model, and BOTDR ( Brillouin optical-time-domain reflectometer ) was used to monitor the strain distribution of overlying strata. The laying of the sensing fiber in the model test is shown in Fig. 2.Fig. 2 Sensor optical fiber layout and coal seam mining area diagram in the model.

As can be seen, the coal seam mining face is advanced from the left side of the 50 cm open-off cut. The excavation distance of the coal seam is 5cm each time. A total of 30 steps are mined. After each excavation, data acquisition and next mining are performed 30 min later when the rock layer is stable.

Analysis of strain distribution characteristics of overburden rock

Due to space limitation, this paper only analyzes the deformation characteristics of mining overburden according to the overburden strain distribution curve measured by A2 vertical sensing optical fiber during the mining process of 2–2 coal seam. The strain distribution and deformation and failure characteristics of overlying strata during coal seam mining are shown in Fig. 3.Fig. 3 Strain distribution and deformation failure diagram of mining overburden rock. (a) Overburden rock strain distribution curve and (b) Deformation and failure characteristics of overburden rock.

From the strain distribution curve of overburden rock in Fig. 3, it can be seen that before the coal seam working face passes through the A2 monitoring hole, the compressive strain measured by the sensing optical fiber increases continuously with the advancement of the working face. When the coal seam working face advances from the open-off cut position to 60 cm, the optical fiber compressive strain reaches the extreme value, and the roof collapses for the first time. At this time, the roof failure height is 6 cm. When the coal seam is mined to 70 cm, the working face of the coal seam passes through the A2 sensing fiber monitoring hole. The strain measured by the A2 sensing fiber is gradually converted from compressive strain to tensile strain. The roof collapses for the second time, and the tensile strain concentration occurs at 12 cm from the roof of the coal seam. As the mining of the working face continues, the continuous collapse of the roof strata causes the stress release; the lower strain of the section measured by the optical fiber gradually decreases; and the strain value gradually shifts to the upper part of the monitoring hole. When the working face of the coal seam reaches the stop line, the tensile stress concentration occurs at 38 cm from the roof of the coal seam, and the tensile strain value of the A2 sensing fiber is 2200 με. Based on the measured strain, the mining fracture discrimination method17reveals that the development height of the caving zone is 12 cm, and that of the water-conducting fracture zone is 38 cm. It can be seen from Fig. 3 that there exists a good correspondence between the strain change measured by the sensing fiber and the deformation and failure characteristics of the overburden rock.

Prediction method of mining surface subsidence model

Calculation of subsidence of mining overburden rock

There is a good coupling between the sensing fiber and the rock and soil mass around the monitoring hole. The settlement deformation of the mining rock and soil mass is calculated by the strain integral method18. The calculation formula of mining overburden subsidence is shown in Eq. (6).6 S=∫h12ε¯dh

where S denotes the settlement of overlying strata within the range of h1 and h2 from the roof of the coal seam, and the minimum spacing of BOTDR instrument is 0.05 m; and ε¯ refers to the average strain in the calculation area.

Mining surface subsidence prediction

According to the measured strain distribution and Eq. (6) displacement calculation formula, the surface subsidence during coal seam mining is obtained. Based on the MMF model and the Weibull model, the surface subsidence measured by the A2 fiber is fitted to obtain the surface subsidence prediction curve. The surface subsidence curve based on A2 optical fiber monitoring data and theoretical prediction model is shown in Fig. 4.Fig. 4 Surface subsidence curve based on A2 optical fiber monitoring data and theoretical prediction model.

From the surface subsidence curve shown in Fig. 4, it can be seen that the surface subsidence speed is accelerated after 14 times of coal seam mining, and the surface subsidence speed is reduced after 24 times of coal seam mining. The surface deformation is mainly affected by the compaction of the caving zone and the subsidence of the fracture zone and the bending subsidence zone. The subsidence deformation of the mining surface is 'S' type. When the MMF model is used to predict the mining surface subsidence, the error between the measured values is large when the surface subsidence velocity does not reach the maximum velocity. After the local surface subsidence reaches the maximum subsidence velocity, there is a high consistency between the prediction model and the measured values. The goodness of fit reaches 0.992, verifying a good calculation and prediction result. When the Weibull model is used to predict the surface settlement, the relative error between the measured value and the measured value is less than 5% before the settlement development reaches the maximum settlement speed. Compared with the MMF model, it boasts of higher accuracy. However, in the later stage of settlement development, the overall prediction accuracy and goodness of fit of the Weibull model display a downward trend, and the relative error is large.

According to the fitting curves of Eqs. (1), (2) and Fig. 4, the parameters W0, a, b of MMF model and the parameters W0, c, k of Weibull model are determined respectively, and the theoretical calculation formula of surface subsidence is obtained, as shown in Eqs. (7) and (8).7 Wt=16.87t4.9110382+t4.91

8 St=15.591-e-1.59∗10-5∗t3.81

According to Eqs. (7) and (8), the time when the surface subsidence reaches the maximum subsidence speed τ of MMF model and Weibull model in the 14th mining of coal seam is obtained. According to Eq. (3), the error weights u1 and u2 in the MMF optimization model are 0.78 and 0.22, respectively.

The settlement prediction formula of the MMF optimization model is shown in Eq. (9):9 W(t)=0.78∗15.591-e-1.59∗10-5∗t3.81+0.22∗16.87t4.9110382+t4.91,0≤t≤1416.87t4.9110382+t4.91,14≤t≤T

The surface prediction curve of Eq. (9) is analyzed with the settlement based on the measured data of A2 fiber, and the comparison results are shown in Fig. 5.Fig. 5 Settlement prediction curve and error analysis of MMF optimization model.

It can be seen from Fig. 5 that the overall accuracy of the prediction curve is high when the MMF optimization model is used to predict the surface subsidence. When the coal seam is mined for the fourth time, the relative error is less than 20%. With the advancement of mining, the prediction error is reduced to less than 10%, and the goodness of fit reaches 0.987, indicating that the overall prediction accuracy of the MMF optimization model meets the requirements.

The parameter evolution characteristics of the prediction model

It can be seen from Eq. (1) and Fig. 1 that the parameters a and b have a great influence on the function form and prediction accuracy of the MMF model. Figure 6 shows the function curves when W0 is 100mm with varying a and b. To be specific, when b is 2.5, a is 50, 100, 5000, 1000, 5000, 8000; when a is 500, b is 2, 2.5, 3, 5, 7, 10, respectively.Fig. 6 The influence of MMF model parameters on the predicted value. (a) The influence of the change of parameter a on the model and (b) The influence of the change of parameter b on the model.

It can be seen from Fig. 6 that the effects of MMF model parameters a and b on the predicted values are opposite. With the increase of parameter a, the settling velocity decreases obviously, and the time to reach the stable stage of settlement increases. With the increase of parameter b, the settling velocity increases obviously, and the time to reach the stable stage of settlement decreases. Therefore, according to the rock and soil properties of mining overburden and the mining conditions of coal seam, the surface subsidence velocity and stability time are analyzed. Combined with the field monitoring data, the parameters a and b in the MMF prediction model are determined to improve the prediction accuracy of surface subsidence.

Conclusion

The study has achieved the following research results.According to the evolution characteristics of mining-induced surface subsidence in coal mines, the Weibull model is used to adjust the mathematical form of the first half of the MMF function curve, and the MMF optimization model for mining-induced surface subsidence prediction is established. The goodness of fit of the prediction curve based on the MMF optimization model is 0.987, the average residual sum is 0.25, and the prediction error is less than 10% with the coal seam mining. The model displays good prediction accuracy, indicating that the model is suitable for mining surface subsidence prediction.

In the MMF prediction model, the time required for the settlement stability stage increases with the increase of parameter a, and decreases with the increase of parameter b. The values of parameters a and b in the MMF prediction model should be determined according to the rock and soil properties of mining overburden, coal seam mining conditions and on-site monitoring data.

There is a close relationship between the subsidence evolution stage of overlying strata in coal mine goaf and the engineering properties of 'three zones', namely, overburden caving zone, fracture zone and bending subsidence zone. Based on the full-section strain distribution data of distributed optical fiber technology, the settlement of the three zones is calculated. In the next stage, the MMF optimization model is used to predict the subsidence evolution process of the 'three zones' of the overburden rock, which can provide a basis for the evaluation of the compression potential of the surface subsidence evolution stage of the coal mine goaf.

Author contributions

Piao. CD: Conceptualization, Methodology, Writing manuscript. Zhu. B: Data Curation, Revisions manuscript. Jiang. JX: Assistance for data acquisition and data analysis. Dong. QH: Provided theoretical insights, Funding acquisition.

Funding

This article was funded by National Natural Science Foundation of China, under Grant No. 42277159.

Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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