# Numerical Analysis of Groundwater Effects on the Stability of an Abandoned Shallow Underground Coal Mine

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Stratigraphy and Soil Properties

_{sat}) unit weight, Young’s modulus (E) and Poisson ratio (ν), the effective soil shear strength parameters: friction angle (φ’) and cohesion (c’), the dilation angle (ψ), and the permeability coefficient (k

_{s}) are included for all layers. The tensile strength (σ

_{t}) is additionally provided for rock materials. The initial groundwater table was 2 m above the coal seam and 6 m below the ground surface. The coal and shale layers were considered non-porous for the analysis; thus, porewater pressures were not calculated in these layers. The groundwater table was within the water-bearing sandstone stratum.

#### 2.2. Numerical Methodology

_{o}for all layers (k

_{o}equals horizontal over vertical effective stress). Based on the simplified form of Jaky’s equation k

_{o}= 1 − sinφ [39], with φ the friction angle, and the stratigraphy of Figure 1 and properties of Table 1, an average friction angle of around 30° results in an average k

_{o}= 0.5 for all layers. A staged-construction approach was then followed to simulate the underground voids as the material within the voids was removed to represent the opening of the rooms in discrete calculation stages. Each stage corresponds to the excavation of a single opening followed by the equilibrium of the stresses based on an elasto-plastic drained calculation. The final formation of the underground openings’ configuration was obtained after three consecutive calculation stages. The outer boundaries were set at an adequate distance from the openings so that the numerical results were not affected. The simple elastic-perfectly plastic Mohr-Coulomb constitutive model was used for all materials [40]. The yield surface defining the limit to plasticity is identical to the failure surface defined by φ’, c’, and the dilatancy angle ψ is the crucial parameter for the plastic potential functions and plastic deformations herein defined by a non-associative flow rule. Both shear and tensile strength were considered for the roof, pillar, and floor rock materials.

_{s}) (k

_{s}= 5 ∙ 10

^{−6}cm/s) was equal to 20, implying a great amount of ponding and surface runoff water; merely a small percentage of the total rainfall height would infiltrate into the soil, and so, the remaining part would remain outside the upper soil layer boundary, acting as a ponding water external surcharge. In the case of greater rainfall intensity, greater amounts of surface runoff water were anticipated, which were not expected to affect the infiltration process crucially, e.g., see [44]. The two days rainfall duration is a noticeable time; in principle, low and moderate-intensity rainfall incidents are often long-lasting [45]. The rainfall event was modeled by imposing an external constant flux boundary condition (q) on the model’s upper horizontal boundary simulating the ground surface. This modeling approach aimed to investigate whether the stability of the underground space was affected by a noticeable individual rainfall incident.

_{w}) above the groundwater table, in the unsaturated zone, is expressed as a function of the negative porewater pressure u

_{w}(soil suction) as:

_{r}indicates the soil’s residual saturation, S

_{s}is the soil’s saturation at the fully saturated state, g

_{a}is a fitting parameter of the SWCC related to the air entry value of the soil, g

_{n}is a fitting parameter of the SWCC governing mainly its slope, and γ

_{w}is the unit weight of water equal to 9.81 kN/m

^{3}. Moreover, the unsaturated soil permeability coefficient (k

_{w}), a key soil parameter in the analysis of the rainfall infiltration, is evaluated according to the relative permeability coefficient function:

_{l}is a fitting parameter typically equal to 0.5 [36], regardless of the soil type, and S

_{e}is the effective saturation of the soil, expressing the normalized moisture content of the unsaturated soil at a given value of soil suction:

_{w}) increases with the increase of saturation degree (S

_{w}) and the decrease of soil suction, obtaining its maximum value (equal to the saturated permeability coefficient (k

_{s})) when the soil is fully saturated (S

_{w}= S

_{s}= S

_{e}= 1).

#### 2.3. Safety Definition

_{t}) to the maximum tensile stress applied to the roof (σ

_{3,max}):

## 3. Results and Discussion

#### 3.1. Individual Rainfall Event

_{w}= 6 m). The analysis focused on the evolution of the minor principal stress (σ

_{3}) at the middle of the span of the roof of the openings, as it was crucial for the defined safety factor (see Equation (4)).

_{3}in the immediate roof of the underground openings (positive values define tension). These stresses represent the effective tensile stresses concentrated in the middle of the sandstone roof’s span due to bending development in this area. Tensile stresses developed in the form of an arch within the sandstone roof surrounding the openings, providing the confinement needed to support the overburden loading. Thus, the development of this stress distribution was beneficial for the safety of the formed underground openings, providing that their maximum values did not exceed the tensile strength of the roof material (σ

_{3,max}< σ

_{t}, SF > 1).

^{−6}cm/s), leading to forming the perched water above this aquitard. That layer notably inhibited the infiltration of rainwater into the ground. Therefore, due to the difficulty of the stormwater to considerably infiltrate within the ground after the individual rainfall incident, the initial phreatic line (located 6 m below the ground surface) remained unchanged. Thus, the individual rainfall event did not alter the stress field around the opening, so the stability of the underground voids was unchangeable due to the rainfall event. Overall, the underground stability was not influenced by this individual rainfall event.

#### 3.2. Groundwater Recharge

_{3}), which is the horizontal tensile stress responsible for the safety of the opening, increased. As a result, the SF decreased, as was expected, due to the groundwater recharge. There was a difference in the initial state at the stress σ’

_{3}and the SF for the two boundary conditions (phreatic line and steady-state) due to the differences in the pore pressure calculation; more details on the porewater pressures are discussed in the following. However, in both cases, the initial and final SFs are close to 1, denoting possible instability. The groundwater recharge had a more dramatic influence on the phreatic line case (SF from 1.18 to 1); for the steady-state, there was a smaller change from 1.28 to 1.23. The phreatic line was a conservative approach that denotes that such a groundwater recharge could lead to instability and sinkhole potential.

_{3}—denoting tension—increased. In simplified terms, the increase can be seen as the effect of the total weight on top of the roof of the opening that increased with the rise of the groundwater table. As a result, a higher load was applied to the roof that bent, and the horizontal stress σ’

_{xx}(equal to σ’

_{3}) increased (see Figure 4). In practice, the porewater pressures in the soil and rock layers were critical for the evolution of the horizontal (σ’

_{xx}= σ’

_{3}) and vertical (σ’

_{yy}= σ’

_{1}) effective stresses at that point. Thus, as the groundwater level rose and the porewater pressures evolved, the soil unit weight changed from unsaturated (γ) to saturated (γ

_{sat}), and the horizontal and vertical effective stresses at the roof also rose.

_{w}= 2 m), the SF became 1. Figure 7a illustrates the distribution of minor principal effective stresses around the underground openings at this state; these were all tensile stresses (positive values denote tension). The σ’

_{3}coincided with the cartesian normal stress σ’

_{xx}at the mid-bottom of the roof span because of the absent shear stress at the same point (see Figure 3 and Figure 4). Figure 7b presents the distribution of the effective tensile stresses around the underground rooms for the steady-state flow boundary condition. The stress distributions for the two cases were very similar. A significant stress concentration is presented in the middle of the immediate roof. However, the magnitude of the effective tensile stresses was remarkably different due to the consideration of the critical effect of the groundwater.

_{w}= 59.4 kPa). Meanwhile, almost zero porewater pressures were presented for the steady-state flow analysis (see Figure 8b, u

_{w}= 1.3 kPa). Figure 8b presents the porewater pressure distribution on the vertical boundaries very close to the openings; note that the total model was much wider (see Figure 2), and no boundary conditions arose. For the steady-state flow conditions, the openings defined conditions with zero porewater pressure and thus edges and roofs with very small porewater pressures. On the other side, an important hydrostatic pressure developed on the roof for the phreatic line. Both of these conditions represent limit conditions and are practically the limits of this analysis.

_{w}) during the groundwater recharge for the two approaches. The porewater pressures computed by the phreatic line approach increased notably with the groundwater rising; practically, hydrostatic conditions denote a significant pressure due to a higher water depth. Instead, for steady-state groundwater flow, only a slight rise in the porewater pressures was noticed as the opening was defined as dry and the roof had practically zero water pressure. The seepage flow that develops above and towards the voids notably inhibited the build-up of porewater pressures in the area of the immediate roof. Consequently, the zero pore pressures in the middle lower part of the immediate roof remained practically unchanged.

## 4. Conclusions

- (1)
- The short-term safety remained unaffected by an individual rainfall event as a lowpermeability upper soil layer (silty clay) limited rainfall’s infiltration into the materials surrounding the underground openings to form perched water above an aquitard.
- (2)
- The long-term safety deteriorated when considering the gradual recharge of groundwater, representing the accumulation of infiltrated stormwater from several rainfall events. This decrease in the safety factor was due to the increase of the tensile stresses in the roof of the underground openings with the rise of the groundwater table for both examined approaches for porewater pressure calculation limits (phreatic line versus steady-state flow).
- (3)
- The phreatic line approach is the most conservative, resulting in lower safety factors than the steady-state flow analysis due to the build-up of higher hydrostatic pressure on the roof of the opening.
- (4)
- The steady-state analysis provided smaller tensile stresses on the opening’s roof due to groundwater flow conditions. In this case, the porewater pressure inside the openings was, by definition, zero and very small at the openings’ edges and roofs.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

c’ | effective cohesion |

E | Young’s modulus |

g_{a} | fitting parameter of the SWCC related to the air entry value |

g_{l} | fitting parameter of the SWCC equal to 0.5 |

g_{n} | fitting parameter of the SWCC governing its shape that is a function of the rate of water extraction from the soil once the air entry value has been exceeded |

GWT | groundwater table |

H_{p} | height of the coal layer |

H_{w} | groundwater depth |

k_{s} | permeability coefficient |

k_{w} | unsaturated soil permeability coefficient |

q | rainfall intensity |

SF | Safety Factor |

S_{e} | effective soil saturation |

S_{r} | residual soil saturation |

S_{s} | soil saturation at the fully saturated state |

S_{w} | saturation degree |

u_{w} | porewater pressure |

γ | moist soil unit weight |

γ_{sat} | saturated soil unit weight |

γ_{w} | unit weight of water equal to 9.81 kN/m^{3} |

ν | Poisson ratio |

σ’_{yy} | vertical effective stress |

σ_{t} | tensile strength |

σ’_{xx} | horizontal effective stress |

φ’ | effective friction angle |

ψ | dilation angle |

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**Figure 2.**Finite element discretization based on the initial stratigraphy (H

_{w}groundwater depth, H

_{p}height of the coal layer).

**Figure 6.**Effect of groundwater recharge on (

**a**) the minor principal effective stress in the middle of the roof span and (

**b**) the safety factor.

**Figure 7.**Minor principal effective stresses after groundwater recharge: (

**a**) phreatic line, and (

**b**) steady-state flow.

**Figure 8.**Porewater pressures after groundwater recharge (

**a**) phreatic line and (

**b**) steady-state flow.

**Figure 9.**Pore pressures during groundwater recharge for the phreatic line and steady-state groundwater flow approaches.

**Figure 10.**Large ground settlements due to the bending of the roof of the underground openings (phreatic line analysis).

Material Parameters | γ (kN/m^{3}) | γ_{sat} (kN/m^{3}) | Ε (MPa) | ν (-) | c’ (kPa) | φ’ (deg) | ψ (deg) | σ_{t}(kPa) | k_{s}(cm/s) |
---|---|---|---|---|---|---|---|---|---|

Silty clay | 15.4 | 17.4 | 5.2 | 0.30 | 11 | 38.5 | 0 | 0 | 5 × 10^{−6} |

Silty sand | 15.4 | 17.4 | 52 | 0.30 | 2 | 30.5 | 0 | 0 | 4 × 10^{−3} |

Sand, gravel, and clay | 16.2 | 18.2 | 52 | 0.30 | 3 | 35.5 | 0 | 0 | 3 × 10^{−4} |

Silty gravel | 16.2 | 18.2 | 21.84 | 0.30 | 3 | 29.5 | 0 | 0 | 8 × 10^{−3} |

Glacial till | 16.2 | 18.2 | 52 | 0.30 | 10 | 29.5 | 0 | 0 | 3 × 10^{−4} |

Sandstone (roof) | 25.0 | 26.0 | 4300 | 0.34 | 360 | 35.0 | 0 | 170 | 4 × 10^{−3} |

Coal (pillar) | 15.0 | 15.0 | 4630 | 0.33 | 460 | 36.0 | 0 | 230 | non-porous |

Shale (floor) | 27.0 | 27.0 | 11,550 | 0.30 | 1300 | 43.0 | 0 | 750 | non-porous |

Material Parameters | S_{r} (-) | S_{s} (-) | g_{a} (1/m) | g_{n} (-) |
---|---|---|---|---|

Silty clay | 0.20 | 1.00 | 0.05 | 1.09 |

Silty sand | 0.15 | 1.00 | 1.24 | 2.28 |

Sand, gravel, and clay | 0.25 | 1.00 | 0.59 | 1.48 |

Silty gravel | 0.10 | 1.00 | 1.45 | 2.68 |

Glacial till | 0.25 | 1.00 | 0.27 | 1.23 |

Sandstone (roof) | 0.15 | 1.00 | 3.30 | 3.56 |

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**MDPI and ACS Style**

Zevgolis, I.E.; Theocharis, A.I.; Deliveris, A.V.; Koukouzas, N.C. Numerical Analysis of Groundwater Effects on the Stability of an Abandoned Shallow Underground Coal Mine. *Sustainability* **2023**, *15*, 529.
https://doi.org/10.3390/su15010529

**AMA Style**

Zevgolis IE, Theocharis AI, Deliveris AV, Koukouzas NC. Numerical Analysis of Groundwater Effects on the Stability of an Abandoned Shallow Underground Coal Mine. *Sustainability*. 2023; 15(1):529.
https://doi.org/10.3390/su15010529

**Chicago/Turabian Style**

Zevgolis, Ioannis E., Alexandros I. Theocharis, Alexandros V. Deliveris, and Nikolaos C. Koukouzas. 2023. "Numerical Analysis of Groundwater Effects on the Stability of an Abandoned Shallow Underground Coal Mine" *Sustainability* 15, no. 1: 529.
https://doi.org/10.3390/su15010529