# Mining Subsidence Prediction Model and Parameters Inversion in Mountainous Areas

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Probability Integral Method

_{e}(x) is shown in Equation (1):

_{e}(x) is shown is shown in Equation (3):

_{x}is the linear strain along the x direction, ε

_{z}is the linear strain along the z direction. Minus “−” represents the w-axis is opposite to the Z-axis. B = b·r, b is the horizontal movement coefficient, r is the major influence radius(m), i(x) is the inclination.

_{0}is the mining influence propagation angle (°); H is the average mining depth (m).

_{0}= mqcosγ is the maximum surface subsidence value under the critical extraction, m is the thickness of coal seam (m), q is the subsidence coefficient, and γ is the average dip angle of coal seam (°), R represents the mining region.

_{1}and D

_{3}are the inclination and strike lengths of the working panel; s

_{1}, s

_{2}, s

_{3}, and s

_{4}are the inflection point offsets of downhill, uphill, left, and right borders; tanβ is the main influence tangent.

#### 2.2. Fruit Fly Optimization Algorithm

**Step 1: Initialize parameters.**First, the initial fruit fly swarm location (X

_{-axis}, Y

_{-axis}), the maximum iteration number (maxgen), the population size (sizepop), the random direction rand( ) and step length k should be considered.

**Step 2: Evolution starting.**The generation = 0, the random flight path and the route for food finding of a single fruit fly are considered.

**Step 3: Preliminary computations.**The specific direction of the food is determined by calculating the distance Dist

_{i}of the individual fruit fly from the initial position. Subsequently, smell concentration judgment value S

_{i}is determined. Then, the fitness function value (also called the smell concentration Smell

_{i}) is calculated.

**Step 4**

**: Record the optimal individual and the location**. Compare the smell concentration values of fruit flies in the current population and mark the fruit fly individual with the highest (or lowest) smell concentration as the optimal fruit fly individual. Record and keep the best smell concentration value bestSmell and the coordinates position (X, Y) of the optimal fruit fly individual. The fruit fly swarm will use vision to fly towards that position:

**Step 5: Iteration stops.**Consider generation = generation + 1, the fitness function value is determined again. Judge if the smell concentration is superior to the previous iterative smell concentration. When the generation attains the maximum iteration number, and the optimized parameter value of the specific model can be reached. Otherwise, the optimization process should go back to Step 2.

#### 2.3. Dynamic Step Fruit Fly Optimization Algorithm

_{g}be the search step length of the gth iteration, S′

_{g}be the optimal smell concentration value of the gth iteration, Δ = |S′

_{g}—S′

_{g−}

_{1}|;

_{1}, S′

_{1}is calculated;

_{g}< S′

_{g−}

_{1}, it indicates that the current optimal smell concentration value is better than the previous generation optimal smell concentration value, the step should be shorted to improve the optimization accuracy, then

_{g}≥ S′

_{g−1}, it indicates that the optimal smell concentration value of the previous generation is better than or equal to the current optimal smell concentration value. The step should be enlarged to increase the search range and improve the global search ability.

_{0}, s

_{i}(i = 1, 2, 3, 4) related to the subsidence values were inversed first, and the horizontal movement coefficient b related to the horizontal movement U was obtained separately.

_{0}s

_{1}s

_{2}s

_{3}s

_{4}], P is the search space of vector p (the value range of the prediction parameters), and the optimization principle which is used as the fitness function(f

_{p}) is the minimum mean square error (MSE) between fitting values of the probability integral method whose parameters are obtained by DSFOA and the measured data of the corresponding n points. f

_{p}is shown in Equation (23):

_{i}is the measured subsidence values, w

_{i}is the fitting subsidence values, and n is the number of observation points.

- (1)
- Set the parameters such as the initial populations number and the maximum iteration number, and generate the initial population according to the range of the probability integral method parameter vector p. The position of initialization population is the initial solution of the N-dimensional vector, and N is the number of parameters optimized (N = 7).
- (2)
- Calculate the fitness function value, combine the information of the working panel to the mining subsidence of the probability integral method and update the step.
- (3)
- In each iteration process, judge and select the population with the optimal fitness value, and loop until the optimal solution is found.

_{p}) as in Equation (24):

_{i}is the measured horizontal movement values, u

_{i}is the fitting horizontal movement values, and n is the number of observation points.

#### 2.4. Prediction Model of Mining Subsidence in Mountainous Areas Considering Slopes Slip

#### 2.4.1. Expression of Movement Vector and Slopes Slip Vector

_{i}(x,y) at a point P

_{i}on the mountainous surfaces under the influence of coal mining can be regarded as the sum of the movement vector R

_{i}(x,y) produced by mining in the plain areas and slopes slip vector ΔR

_{i}(x,y) on the mountainous surface. It can be expressed as the superposition principle shown in Equation (25):

#### 2.4.2. Establishment of the Mining Subsidence Prediction Model

_{α}(x,y) along the inclination direction of the surface slope determines the magnitude of the slip vector ΔR(x,y) (Figure 5a).

^{−1}(W(x,y)/U(x,y)), α is the slope angle of the surface.

_{x}, ∂U/∂x = ε(x,y)

_{x}, φ = 0°.

_{l}= ∂ΔR/∂l, it is the deformation of the slip vector along the l direction.

#### 2.4.3. Calculation of the Values of the Parameters in the Mining Subsidence Model

_{s}should be determined, as they are strongly associated with the geological and mining conditions and the nature of the topsoil. Parameters δ and K

_{s}are important in the proposed mining subsidence model in mountainous areas, and they are discussed in this section.

**Values about δ**

**:**

^{−1}(W(x,y)/U(x,y)); when the slope is shown in Figure 6b,d, δ = 180° + tan

^{−1}(W(x,y)/U(x,y)).

**Values about surface characteristic coefficient K**

_{s}:_{S}reveals the influence degree of the topography on the amount of slip, which is mainly related to the topography and the nature of the soil.

_{i}, Suppose that ith block undergoes resistance from the (i − 1)th block below itself when it slips and the resistance is proportional to the amount of ith block slips, which refers KS

_{i}, and it also bears the force generated by the slip of the upper (i + 1)th block, namely Ks

_{i}

_{+1}. The block tends to balance after it slips:

_{i+1}− S

_{i}:

_{x}in Equation (43) is the critical horizontal deformation value when the slope starts slipping, shown in Equation (44) [42].

_{xm}or the horizontal deformation is always compression deformation, the maximum of the horizontal deformation is selected, as shown in Figure 7b.

_{1}, when the coal unit 1 and the coal unit 2 are mined, the curve of horizontal deformation is shown in ε

_{2}, and the other coal units are similar. When the horizontal deformation of a point on the surface exceeds ε

_{xm}for the first time during the process of coal mining, the slip subsidence ΔW(x, y) and the slip horizontal movement ΔU(x,y) are calculated. When ε(x,y)

_{x}is determined, i(x,y)

_{x}is also determined.

## 3. Case Study

#### 3.1. Study Area

_{3}= 440 m, and a length along the inclination D

_{1}= 140 m, the mining height m = 3.18 m, the dip angle γ = 1~3°, and the average mining depth H = 220 m. Two observation lines were laid along the strike of the main section and the inclination of the main section, respectively. Forty-five monitoring points were laid along the two observation lines shown in Figure 9, the image of a point is shown in Figure 10. Each monitoring point was filled with concrete and buried with prefabricated piles in the soil pit. The kind of data at these 45 points includes the plane position of each point (x,y) and the elevation of each point (h), traverse measurement was carried out according to the accuracy requirement of 5, “and triangulation elevation traverse was measured at the same time. The Leica T402 total station instrument was used for the measurement of the 45 points. The nominal accuracy of angle measurement is 2“, and the distance measurement accuracy is 3 mm + 2 ppm.

#### 3.2. Information of Topsoil

_{xm}is 3.2 mm/m.

#### 3.3. Analysis of the Results

#### 3.3.1. Inversion Results of Prediction Parameters Based on DSFOA

_{0}is 80∼90°, the inflection point offsets s1, s2, s3, s4 are −30~30 m.

_{0}is 5, 8, and the inflection point offset s is 10, 20, 30. The value range of the horizontal movement coefficient b is given from 0.1 to 0.5, the population size sizepop is 5, 10, and 20, and the number of iterations is 50, 100, and 500. The step length is 0.1 and 0.2.

_{0}= 90°-k

_{0}γ (k

_{0}is the constant), the inflection point offsets s

_{1}= s

_{2}= 0.05 H, s

_{3}= s

_{4}= 0.1 H, b = 0.35.

_{1}≤ (0.05~0.1) W

_{max}is satisfied, the mean square error of horizontal movement MSE

_{2}≤ (0.1~0.3) U

_{max}is satisfied, and it means that the distribution law of the movement and deformation revealed by the method is reliable and feasible [41]. According to the measured data, the maximum subsidence value is 1898 mm at No. 18 point, and the maximum horizontal movement value is 1324 mm at No. 40 point, (0.05~0.1). W

_{max}ranges from 94.9 mm to 189.8 mm. (0.1~0.3) U

_{max}ranges from 132.4 mm to 397.2 mm, and it indicates that the prediction parameters of the probability integral method inversed by DSFOA are reliable and effective.

#### 3.3.2. Prediction Results of the Proposed Model

## 4. Discussion

#### 4.1. Prediction Results of the Existing Model in Mountainous Areas

_{x}

_{,y}is a coefficient reflecting the surface feature, the value of which can be obtained from Table 3. φ is the prediction direction for surface displacement, it is the angle that the positive x-axis counterclockwise to the specified direction shown in Figure 1, α

_{x,y}is the slope angle, ψ is the angle between the slope direction of the ground surface and the main section, P[x] and P[y] are the mining landslide influence functions, as expressed in Equations (47) and (48).

_{m}is the max value of surface subsidence. A, P and t are the coefficients of landslide effect, with reference values of 2π, 2 and π, respectively. The other parameters are the same as the parameters in the probability integral method.

#### 4.2. Comparison of the Proposed Model and the Existing Model

_{xm}, then the slip subsidence ΔW and the slip horizontal movement ΔU can be calculated accurately. At the border of the pillar, the predictive effect of subsidence is good for both models, while the predictive effect of horizontal movement is relatively poor for both models; this is because the prediction accuracy of the horizontal movement for the probability integral method is imperfect at the boundary of the coal pillar due to the deficiency in principle. We can make a further improvement for the probability integral method.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Yuan, L. Scientific conception of precision coal mining. J. China Coal Soc.
**2017**, 42, 1–7. [Google Scholar] [CrossRef] - Zhang, C.; Zhao, Y.; Han, P.; Bai, Q. Coal pillar failure analysis and instability evaluation methods: A short review and prospect. Eng. Fail. Anal.
**2022**, 138, 106344. [Google Scholar] [CrossRef] - Zhang, J.; Zhang, Q.; Sun, Q.; Gao, R.; Germain, D.; Abro, S. Surface subsidence control theory and application to backfill coal mining technology. Environ. Earth Sci.
**2015**, 74, 1439–1448. [Google Scholar] [CrossRef] - Yang, Y.; Erskine, P.D.; Zhang, S.; Wang, Y.; Bian, Z.; Lei, S. Effects of underground mining on vegetation and environmental patterns in a semi-arid watershed with implications for resilience management. Environ. Earth Sci.
**2018**, 77, 605. [Google Scholar] [CrossRef] - Yang, Z.; Li, W.; Pei, Y.; Qiao, W.; Wu, Y. Classification of the type of eco-geological environment of a coal mine district: A case study of an ecologically fragile region in Western China. J. Clean Prod.
**2018**, 174, 1513–1526. [Google Scholar] [CrossRef] - Bai, E.; Guo, W.; Tan, Y. Negative externalities of high-intensity mining and disaster prevention technology in China. Bull. Eng. Geol. Environ.
**2019**, 78, 5219–5235. [Google Scholar] [CrossRef] - Yang, X.; Wen, G.; Dai, L. Ground Subsidence and Surface Cracks Evolution from Shallow-Buried Close-Distance Multi-seam Mining: A Case Study in Bulianta Coal Mine. Rock Mech. Rock Eng.
**2019**, 52, 2835–2852. [Google Scholar] [CrossRef] - Zhou, D.; Wu, K.; Bai, Z. Formation and development mechanism of ground crack caused by coal mining: Effects of overlying key strata. Bull. Eng. Geol. Environ.
**2019**, 78, 1025–1044. [Google Scholar] [CrossRef] - He, X.; Zhao, Y.; Yang, K. Development and formation of ground fissures induced by an ultra large mining height longwall panel in Shendong mining area. Bull. Eng. Geol. Environ.
**2021**, 80, 7879–7898. [Google Scholar] [CrossRef] - Lian, X.; Zhang, Y.; Yuan, H. Law of Movement of Discontinuous Deformation of Strata and Ground with a Thick Loess Layer and Thin Bedrock in Long Wall Mining. Appl. Sci.
**2020**, 10, 2874. [Google Scholar] [CrossRef] [Green Version] - Yan, W.; Chen, J.; Yang, W. On-Site Measurement on Surface Disturbance Law of Repeated Mining with High Relief Terrain. Sustainability
**2022**, 14, 3166. [Google Scholar] [CrossRef] - Liu, B.; Dai, H. Research Development and Origin of Probability integral method. Coal Min. Technol.
**2016**, 21, 1–3. [Google Scholar] [CrossRef] - Cui, X.; Deng, K. Research review of predicting theory and method for coal mining subsidence. Coal Sci. Tech.
**2017**, 45, 160–169. [Google Scholar] [CrossRef] - Jianjun, Z.; Xun, W.; Yanbing, S.; Jiangbo, W.; Lee, M.L.; Xue, Y. Deformation Behavior of Mining beneath Flat and Sloping Terrains in Mountainous Areas. Geofluids
**2021**, 2021, 6689966. [Google Scholar] [CrossRef] - Zhang, C.; Mitra, R.; Hebblewhite, B. Evaluation of valley closure subsidence effects under irregular topographic conditions. Min. Technol.
**2013**, 122, 172–183. [Google Scholar] [CrossRef] - He, W. Mountains surface movement under the influence of the mining. Coal Sci. Tech.
**1981**, 9, 23–29+62. [Google Scholar] [CrossRef] - He, W. Mountain surface movement and deformation prediction caused by mining. Coal Sci. Tech.
**1983**, 11, 46–52+60. [Google Scholar] [CrossRef] - He, W.; Kong, Z.; Kang, J. Mechanism and vector analysis of surface mining slip in mountainous areas. Min. Surv.
**1991**, 21–25. [Google Scholar] - Wanlong, H.; Jianrong, K. Research on the laws of mountain surface movement and deformation. J. China Coal Soc.
**1992**, 9, 79–89. [Google Scholar] - Zha, J.; Feng, W.; Zhu, X. Research on Parameters Inversion in Probability integral method by Genetic Algorithm. J. Min. Saf. Eng.
**2011**, 28, 655–659. [Google Scholar] [CrossRef] - Li, P.; Peng, D.; Tan, Z.; Deng, K. Study of probability integration method parameter inversion by the genetic algorithm. Int. J. Min. Sci. Technol.
**2017**, 27, 1073–1079. [Google Scholar] [CrossRef] - Xu, M.; Zha, J.; Li, H. Parameters Inversion in Probability integral method by Particle Swarm Optimization. Coal Eng.
**2015**, 47, 117–119, 123. [Google Scholar] [CrossRef] - Wang, L.; Li, N.; Zhang, X.; Wei, T.; Chen, Y.; Zha, J. Full parameters inversion model for mining subsidence prediction using simulated annealing based on single line of sight D-InSAR. Environ. Earth Sci.
**2018**, 77, 161. [Google Scholar] [CrossRef] - Wei, T.; Guo, G.; Li, H. Fusing Minimal Unit Probability Integration Method and Optimized Quantum Annealing for Spatial Location of Coal Goafs. KSCE J. Civ. Eng.
**2022**, 26, 2381–2391. [Google Scholar] [CrossRef] - Wei, T.; Wang, L.; Jiang, K.; Wang, Y.; Yang, X. One spatial geometric characteristic identification method of a coal mine working face based on ground movement and deformation monitoring data. Energy Sources Part A Recovery Util. Environ. Eff.
**2021**, 26, 1–15. [Google Scholar] [CrossRef] - Wang, L.; Jiang, K.; Wei, T.; Jiang, C.; Zha, J.; Chi, S. Estimation of parameters of probability integral method model based on improved fireworks algorithm. Surv. Rev.
**2020**, 53, 366–382. [Google Scholar] [CrossRef] - Wang, L.; Jiang, K.; Wei, T. Development of a new inversion method for detecting spatiotemporal characteristics of coal mines based on earth observation technology. Int. J. Appl. Earth Obs. Geoinf.
**2021**, 26, 102346. [Google Scholar] [CrossRef] - Yang, J.; Liu, C.; Chen, T.; Zhang, Y. The invasive weed optimization–based inversion of parameters in probability integral model. Arab. J. Geosci.
**2019**, 12, 424. [Google Scholar] [CrossRef] - Pan, W.-T. A new Fruit Fly Optimization Algorithm: Taking the financial distress model as an example. Knowl. Based Syst.
**2012**, 26, 69–74. [Google Scholar] [CrossRef] - Pan, W.-T.; Zhu, W.-Z.; Ma, F.-X.; Zhong, Z.-C.; Yuan, X.-F. Modified fruit fly optimization algorithm of logistics storage selection. Int. J. Adv. Manuf. Technol.
**2017**, 93, 547–558. [Google Scholar] [CrossRef] - Zhang, Y.; Cui, G.; Wu, J.; Pan, W.-T.; He, Q. A novel multi-scale cooperative mutation Fruit Fly Optimization Algorithm. Knowl. Based Syst.
**2016**, 114, 24–35. [Google Scholar] [CrossRef] - Fu, Y.; Zhou, M.; Guo, X.; Qi, L. Stochastic multi-objective integrated disassembly-reprocessing-reassembly scheduling via fruit fly optimization algorithm. J. Clean Prod.
**2021**, 278, 123364. [Google Scholar] [CrossRef] - Hesami, M.; Alizadeh, M.; Naderi, R.; Tohidfar, M. Forecasting and optimizing Agrobacterium-mediated genetic transformation via ensemble model- fruit fly optimization algorithm: A data mining approach using chrysanthemum databases. PLoS ONE
**2020**, 15, e0239901. [Google Scholar] [CrossRef] - Luo, R.; Zheng, H.; Guo, J. Solving the Multi-Functional Heterogeneous UAV Cooperative Mission Planning Problem Using Multi-Swarm Fruit Fly Optimization Algorithm. Sensors
**2020**, 20, 5026. [Google Scholar] [CrossRef] [PubMed] - Yan, H.; Zhang, T.; Qi, Y.; Yu, D.-J. Short-term traffic flow prediction based on a hybrid optimization algorithm. Appl. Math. Modell.
**2022**, 102, 385–404. [Google Scholar] [CrossRef] - Li, Y.; Xu, F. Acoustic emission sources localization of laser cladding metallic panels using improved fruit fly optimization algorithm-based independent variational mode decomposition. Mech. Syst. Signal Process.
**2022**, 166, 108514. [Google Scholar] [CrossRef] - Qisong, Q.; Gening, X.; Xiaoning, F.; Jun, W. A new type bionic global optimization: Construction and application of modified fruit fly optimization algorithm. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf.
**2014**, 229, 1614–1621. [Google Scholar] [CrossRef] - Sang, H.-Y.; Pan, Q.-K.; Duan, P.-Y. Self-adaptive fruit fly optimizer for global optimization. Nat. Comput.
**2017**, 18, 785–813. [Google Scholar] [CrossRef] - Pan, Q.-K.; Sang, H.-Y.; Duan, J.-H.; Gao, L. An improved fruit fly optimization algorithm for continuous function optimization problems. Knowl. Based Syst.
**2014**, 62, 69–83. [Google Scholar] [CrossRef] - Hou, Y.; Li, J.; Yu, H.; Li, Z. BIFFOA: A Novel Binary Improved Fruit Fly Algorithm for Feature Selection. IEEE Access
**2019**, 7, 81177–81194. [Google Scholar] [CrossRef] - He, G.Q.; Yang, L. Mining Subsidence; China University of Mining and Technology Press: Xuzhou, China, 1991; pp. 188–195. [Google Scholar]
- Gao, C.; Xu, N. Research on surface crack depth and crack width caused by coal mining. Coal Eng.
**2016**, 48, 81–83+87. [Google Scholar] [CrossRef]

**Figure 3.**(

**a**) Unit mining subsidence and unit horizontal movement; (

**b**) Three-dimensional coordinate system.

**Figure 5.**(

**a**) Slopes slip vector analysis; (

**b**) Deformation of the slip vector along the l direction.

**Figure 11.**Ground surface section planes of two observation lines: (

**a**) The strike line, (

**b**) The inclination line.

**Figure 15.**Comparison of the horizontal movements fitting values and measured values considering slopes slip.

**Figure 16.**Comparison of the horizontal movements fitting values and measured values considering slopes slip.

**Figure 17.**Comparison of the horizontal movements fitting values and measured values considering slopes slip.

Name | Natural Density(Kg/m ^{3}) | Cohesion (KPa) | Poisson’s Ratio | Elasticity Modulus (MPa) | Compression Modulus (MPa) | Internal Friction Angle (°) |
---|---|---|---|---|---|---|

Loess of Malan | 1420 | 43 | 0.4 | 17.5 | 7 | 24 |

Algorithm | q | tanβ | θ_{0} | s_{1} | s_{2} | s_{3} | s_{4} | MSE/mm |
---|---|---|---|---|---|---|---|---|

traditional method | 0.79 | 2.4 | 88 | −12 | −12 | −22 | −22 | 248.40 |

DSFOA | 0.59 | 2.19 | 83.19 | −2.43 | −2.43 | 7.57 | 7.57 | 122.27 |

Features of the Topsoil and Ground Vegetation | Feature Coefficient D_{x}_{,}_{y} | |
---|---|---|

Concave Landforms | Convex Landforms | |

Sandy clay slope of <2 m thickness, with dense bushes or trees | −0.1~−0.2 | +0.2~+0.3 |

Sandy clay slope of 2–5 m thickness, with bushes and open forest | −0.2~−0.3 | +0.3~+0.6 |

Loess slope with >5 m thickness, with the plough and orchard | −0.3~−0.4 | +0.6~+1.0 |

Collapsible loess slope with vertical joints and >5 m thickness, and growing of the plough | −0.4~−0.5 | +1.0~+1.5 |

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## Share and Cite

**MDPI and ACS Style**

Zhou, B.; Yan, Y.; Dai, H.; Kang, J.; Xie, X.; Pei, Z.
Mining Subsidence Prediction Model and Parameters Inversion in Mountainous Areas. *Sustainability* **2022**, *14*, 9445.
https://doi.org/10.3390/su14159445

**AMA Style**

Zhou B, Yan Y, Dai H, Kang J, Xie X, Pei Z.
Mining Subsidence Prediction Model and Parameters Inversion in Mountainous Areas. *Sustainability*. 2022; 14(15):9445.
https://doi.org/10.3390/su14159445

**Chicago/Turabian Style**

Zhou, Bang, Yueguan Yan, Huayang Dai, Jianrong Kang, Xinyu Xie, and Zhimiao Pei.
2022. "Mining Subsidence Prediction Model and Parameters Inversion in Mountainous Areas" *Sustainability* 14, no. 15: 9445.
https://doi.org/10.3390/su14159445