# An FDM-Based Dynamic Zoning Method for Disturbed Rock Masses above a Longwall Mining Panel

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## Abstract

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## 1. Introduction

^{3D}software. FLAC

^{3D}is inherently capable of solving nonlinear and large-strain problems; in particular, it can be well applied to modeling the distribution patterns of the stress, strain, and displacement of surrounding rock masses in underground mining [22].

## 2. The Dynamic Zoning Method

#### 2.1. Overview of Our Method

#### 2.2. Establishing the Simplified Complete Stress-Strain Curve

#### 2.3. Determining the Zoning Criteria

#### 2.4. Adaptive Adjustment of Mechanical Parameters of Disturbed Rock Masses

#### 2.5. Numerical Modeling of Longwall Mining Based on the FDM

^{3D}by means of step-by-step excavation. More details of the simulation process are introduced as follows (Figure 7):

^{−5}), then it should further conduct mining with distance L and repeat Step 2; otherwise, it needs to repeat Step 2 directly until the computation is balanced.

^{−5}), the calculation model is saved, and the next mining step according to the above method is then simulated until the coal-seam excavation of the working face is completed.

## 3. Case Study

#### 3.1. Background of the Study Site

#### 3.1.1. Geological Setting

_{p}) stratum is mainly composed of yellow clay loam intercalated with multilayer sand. The stratum has an average thickness of approximately 215.55 m and is in unconformable contact with the Neogene.

_{2m}) stratum is mainly composed of red, yellow-brown mudstone and fine–coarse sandstone. The stratum has an average thickness of approximately 152.85 m and is in unconformable contact with the Permian.

_{1+2s}) is mainly composed of grey, purple, and other variegated mudstones and sandstones, and the bottom is carbonaceous mudstone. The stratum is in continuous deposition with the underlying Shanxi formation, with an average thickness of approximately 167.8 m.

_{1x}) is composed of black mudstone and greyish white sandstone. The average thickness of the Shanxi formation is approximately 52.94 m. The #3 coal seam is located in the lower part of the Shanxi formation, with an average thickness of approximately 3.5 m.

_{2t}) stratum is mainly composed of green-grey siltstone, mudstone, grey-white medium sandstone, fine sandstone, and limestone. The average thickness of this formation is approximately 174.69 m.

#### 3.1.2. Mine Layout

#### 3.2. Computational Model

#### 3.2.1. Model Domain

#### 3.2.2. Generalization of Strata

#### 3.2.3. Geological Model

#### 3.2.4. The Constitutive Model and Yield Criterion

#### 3.2.5. Boundary Conditions

#### 3.2.6. Calculation Parameters

_{1x}) as an example, the determination process of ${\epsilon}_{residual}^{p}$ is briefly described. The Shanxi formation (P

_{1x}) is mainly composed of sandstone and mudstone. First, the complete stress-strain curves of sandstone and mudstone are obtained by triaxial tests (see Figure 3), which are simplified as ideal curves, as shown in Figure 11, and ${\epsilon}_{residual}^{p}$ of sandstone and mudstone under various confining pressures are obtained. Second, based on the thicknesses of sandstone and mudstone in the formation, the weighted average value ${\epsilon}_{residual}^{p}$ of the Shanxi formation under each confining pressure is calculated. Finally, the ${\epsilon}_{residual}^{p}-{\sigma}_{3}$ relation curve (Figure 12) can be drawn, and the ${\epsilon}_{residual}^{p}$ corresponding to arbitrary confining pressure σ

_{3}can be obtained on the basis of the curve.

#### 3.3. The Simulation Procedure

^{3D}software to simulate the longwall mining process and implement the proposed dynamic zoning method. The step-by-step excavation simulation is carried out, and in each step, 10 m of the coal seam is planned to be explored. In each step of the mining process, the simulation is conducted as Figure 7 shows, and temporary stability is expected in each step. After achieving the stability of the calculation model, the calculation results are recorded, including the displacement of all nodes and the state of all elements, and then simulation of the next step of the mining process begins.

#### 3.4. Numerical Simulation Results

#### 3.4.1. Progressive Caving Caused by Longwall Mining

_{0}, the first caving occurs due to the impact of gravity. With the advancement of mining, the coal-seam roof begins to bend down like cantilever beams. With a critical length of Lp, the cantilever beams break and fall. Periodic caving occurs with each advance of Lp until mining is completed.

_{0}= 30 m). When further mining reaches the 40 m position (Phase 3), the coal-seam roof bends again, and when mining reaches the 50 m position (Phase 4), the coal-seam roof collapses for the second time (Lp = 20 m). Before the completion of longwall mining, with the advancement of Lp (Lp 10~30 m), repeated roof falls occur.

_{0}or Lp), the roof of the coal seam begins to crack and collapse.

#### 3.4.2. Dynamic Development Characteristics of the Four Zones in Longwall Mining

#### 3.4.3. Ground Surface Movement

#### 3.4.4. Risk Assessment

## 4. Discussion

_{p}(L

_{p}= 10~30 m), the coal-seam roof caves periodically until the end of mining. The periodic caving characteristics of the coal-seam roof conform to the caving phenomenon in actual mining [2] and other research work [3]. More specifically, Gao et al. [3] used UDEC to reveal the progressive caving of strata above a longwall panel. Their numerical results indicated that the immediate roof acts like beams and collapses periodically. The features of progressive caving fit reasonably well with the field observations in the Ruhr coalfield. Wang et al. [11] conducted a physical modeling experiment to simulate the overlying strata destruction induced by mining and revealed the different roof failure zones. Their results showed that the overburden failure evolution was accompanied by periodic collapse in the layer group and that the developing height of fractures discontinuously jumps.

_{cm}is the maximum value of subsidence, M is the mining thickness, q is the surface subsidence coefficient, and $\alpha $ is the dip angle of the coal seam.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Algorithm A1. Algorithm Code of Dynamic Rock Parameter Adjustment. |

loop while p_z # null id=zone.id(p_z) w=zone.extra(p_z,11) if zone.model(p_z)# 'null' then if zone.group(p_z)#'50' then if zone.group(p_z)#'2' then if zone.group(p_z)#'1' then if zone.group(p_z)#'0' then ai1=zone.strain.inc.xx(p_z) ai2=zone.strain.inc.yy(p_z) ai3=zone.strain.inc.zz(p_z) ai4=zone.strain.inc.xy(p_z) ai5=zone.strain.inc.yz(p_z) ai6=zone.strain.inc.xz(p_z) dum2= zone.stress.prin.dir(p_z,as,ad) l=ad(1)/math.sqrt(ad(1)*ad(1)+ad(2)*ad(2)+ad(3)*ad(3)) m=ad(2)/math.sqrt(ad(1)*ad(1)+ad(2)*ad(2)+ad(3)*ad(3)) n=ad(3)/math.sqrt(ad(1)*ad(1)+ad(2)*ad(2)+ad(3)*ad(3)) e1 = -(l*l*ai1+m*m*ai2+n*n*ai3+2*l*m*ai4+2*m*n*ai5+2*l*n*ai6) if e1 > e1_max(id) then e1_max(id) = e1 endif if zone.state(p_z,1)=0 then ee(id) = e1_max(id) endif if zone.state(p_z,1)>0 then zone.extra(p_z,1) =-as(1)/1e6;;;;sigma1 zone.extra(p_z,2) =-as(2)/1e6;;;;sigma2 zone.extra(p_z,3) =-as(3)/1e6;;;;sigma3 sigma_1=zone.extra(p_z,1) sigma_3=zone.extra(p_z,3);;;;sigma_1>sigma_3 sig_1=as(1)/1e6 sig_3=as(3)/1e6;;;;sig_1<sig_3 sig_t=zone.prop(p_z,'tension')/1e6 nfri=(1+math.sin(zone.prop(p_z,'friction')*math.degrad))/(1-math.sin(zone.prop(p_z,'friction')*math.degrad)) ap=math.sqrt(1+nfri*nfri)+nfri sig_p=sig_t*nfri-2*zone.prop(p_z,'cohesion')*math.sqrt(nfri)/1e6 h=sig_3-sig_t+ap*(sig_1-sig_p) if zone.group(p_z)# 'fracture_zone_sr' then if zone.group(p_z)# 'fracture_zone_tr' then if h<0 then if ep(id)>0 then if ep(id)<epr(id) then zone.group(p_z)='fracture_zone_ss' mm1=-mp(w,1)*mp(w,3)*ep(id)/epr(id)+mp(w,1) nn1=-mp(w,2)*mp(w,4)*ep(id)/epr(id)+mp(w,2) zone.prop(p_z,'cohesion')=mm1 zone.prop(p_z,'friction')=nn1 else zone.group(p_z) = 'fracture_zone_sr' msr=-mp(w,1)*mp(w,3)+mp(w,1) nsr=-mp(w,2)*mp(w,4)+mp(w,2) zone.prop(p_z,'cohesion')=msr zone.prop(p_z,'friction')=nsr endif endif endif if h>0 then zone.group(p_z)='fracture_zone_tr' mtr=-mp(w,1)*mp(w,3)+mp(w,1) ntr=-mp(w,2)*mp(w,4)+mp(w,2) zone.prop(p_z,'cohesion')=mtr zone.prop(p_z,'friction')=ntr endif endif endif if zone.group(p_z)='8' then if h<0 then zone.group(p_z) = 'failure-shear' zone.prop(p_z,'cohesion')=0.006e6 endif if h>0 then zone.group(p_z) = 'failure-tension' zone.prop(p_z,'cohesion')=0.006e6 endif endif if w>0 then if zone.group(p_z) # 'caving_zone' then if zone.group(p_z) # 'failure_shear' then if zone.group(p_z) # 'failure_tension' then if sigma_3<5 then epr(id)=sigma_3*mp(w,5)+mp(w,9) else if sigma_3<10 then epr(id)=sigma_3*mp(w,6)+mp(w,10) else if sigma_3<15 then epr(id)=sigma_3*mp(w,7)+mp(w,11) else if sigma_3<20 then epr(id)=sigma_3*mp(w,8)+mp(w,12) endif endif endif endif endif endif endif endif if zone.group(p_z)='fracture_zone_sr' then if ep(id)>10 then zone.prop(p_z,'cohesion')=0 zone.group(p_z)='fracture_zone_sr-0' if zone.pos.z(p_z)<-0.034012*(zone.pos.y(p_z)-81500)-486.424 zone.group(p_z)='caving_zone' endif endif endif if zone.group(p_z)='fracture_zone_tr' then if ep(id)>1 then zone.prop(p_z,'cohesion')=0 zone.group(p_z)='fracture_zone_tr-0' if zone.pos.z(p_z)<-0.034012*(zone.pos.y(p_z)-81500)-486.424 zone.group(p_z)='caving_zone' endif endif endif zone.prop(p_z,'tension')=0.1*2*zone.prop(p_z,'cohesion')*math.cos(zone.prop(p_z,'friction')*math.degrad)/(1-math.sin(zone.prop(p_z,'friction')*math.degrad)) ;1/10*sigma_c zone.prop(p_z,'poisson')=(1-math.sin(zone.prop(p_z,'friction')*math.degrad))/2+0.01 endif endif endif endif endif endif p_z=zone.next(p_z) endloop end |

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**Figure 6.**Softening model of strength parameters: (

**a**) softening model of cohesion; (

**b**) softening model of friction angle.

**Figure 12.**Schematic diagram of the relationship between the residual critical plastic strain and confining pressure.

**Figure 15.**Evolution laws of the four zones due to excavation (200 m, 400 m, 600 m, 800 m, and 1000 m).

Strata | Rock Formation | Elastic Modulus (GPa) | Poisson’s Ratio | Density (kg/m^{3}) | Initial | Residual | ||||
---|---|---|---|---|---|---|---|---|---|---|

Cohesion (MPa) | Friction Angle (°) | Tensile Strength (MPa) | Cohesion (MPa) | Friction Angle (°) | Tensile Strength (MPa) | |||||

Q | 0.05 | 0.32 | 1980 | 0.06 | 23 | 0.02 | 0.01 | 23 | 0.002 | |

N | 3.27 | 0.30 | 2340 | 0.21 | 25 | 0.07 | 0.12 | 19.8 | 0.033 | |

P | P_{1+2s} | 10.20 | 0.23 | 2517 | 0.97 | 34 | 0.37 | 0.09 | 19.3 | 0.025 |

P | P_{1x} | 10.90 | 0.21 | 2650 | 0.97 | 37 | 0.39 | 0.10 | 18.5 | 0.027 |

P | Coal seam | 0.35 | 0.34 | 2350 | 0.17 | 20 | 0.05 | - | - | - |

C | C_{2t} | 14.80 | 0.28 | 2700 | 0.87 | 27 | 0.28 | - | - | - |

Mining Area | Thickness (m) | Dip Angle (◦) | Mining Method | ${\mathit{\sigma}}_{\mathit{c-}\mathit{a}\mathit{v}\mathit{e}\mathit{r}\mathit{a}\mathit{g}\mathit{e}}$ * (MPa) | Subsidence Coefficient |
---|---|---|---|---|---|

Fengfeng | 0.8 | 19 | Longwall | 47.7 | 0.78 |

2.4 | 11 | 57.9 | 0.84 | ||

Zaozhuang | 1.5 | 24 | Longwall | - | 0.88 |

1.9 | 4 | - | 0.78 | ||

Yanzhou | 7.8 | 4 | Fully mechanized caving | 23.1 | 0.81 |

8.2 | 4.3 | 13 | 0.84 | ||

0.9 | 6.5 | Longwall | 24.5 | 0.80 | |

8.5 | 4 | 22 | 0.83 |

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**MDPI and ACS Style**

Zhao, K.; Jia, S. An FDM-Based Dynamic Zoning Method for Disturbed Rock Masses above a Longwall Mining Panel. *Appl. Sci.* **2023**, *13*, 4336.
https://doi.org/10.3390/app13074336

**AMA Style**

Zhao K, Jia S. An FDM-Based Dynamic Zoning Method for Disturbed Rock Masses above a Longwall Mining Panel. *Applied Sciences*. 2023; 13(7):4336.
https://doi.org/10.3390/app13074336

**Chicago/Turabian Style**

Zhao, Kunyang, and Suizi Jia. 2023. "An FDM-Based Dynamic Zoning Method for Disturbed Rock Masses above a Longwall Mining Panel" *Applied Sciences* 13, no. 7: 4336.
https://doi.org/10.3390/app13074336