# From Climate Conditions to the Numerical Slope Stability Analysis of Surface Coal Mines

^{1}

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## Abstract

**:**

## Featured Application

**This work has application in coal and lignite mining excavations and areas, especially during decarbonization and towards a post-coal and post-lignite era. Areas that hosted coal and lignite mines are now being reclaimed—often by installing renewable energy systems—and targets are being set to fulfill new energy principles in relation to energy production, harvesting, and storage. The appropriate and sustainable exploitation of these areas is directly related to their safety and stability.**

## Abstract

## 1. Introduction

## 2. The Methodology and the Case Example of Greek Lignite Mines

_{a}is a parameter of the soil–water characteristic curve; φ’ and c’ are the effective friction angle and cohesion; k

_{s}is the saturated permeability; H is the height of the slope; q is rainfall intensity; H

_{w}defines the groundwater table’s depth. The upper part of Figure 1 describes the present work’s approach to evaluating precipitation, while for the other aspects, the most critical parameters are included in a parametric analysis. Unlike previous works where precipitation was estimated based on global data [2,3,5,9,16,17,18,19,20,21,22,23,24,25] or was derived for a specific period as a particular time series [3,14,26,27,28,29,30], the way to assess the precipitation range is through past events and climate projections of the investigated area. This approach provides a clear advantage in terms of how the rainfall range is calculated. Greek mining areas are utilized to quantify the precipitation range because it is area-specific, and the methodology followed needs specific to the areas to be implemented.

## 3. Baseline Climate Description—Past Events

## 4. Climate Projections—Future Events

## 5. Numerical Analysis of Slope Stability of Lignite Mines under Extreme Rainfall Events

#### 5.1. Numerical Model Overview

_{w}, in the unsaturated zone, is described as a function of the matric suction, u

_{w}(negative pore-water pressure), according to:

_{r}denotes the soil’s residual saturation; S

_{s}the soil saturation at the saturated state; g

_{a}and g

_{n}are material parameters governing the shape of the SWCC; and γ

_{w}is the water’s unit weight (9.81 kN/m

^{3}).

_{r}and the material parameter g

_{a}are critical factors for the unsaturated soil’s state [52]. In this work, the residual degree of saturation, S

_{r}, was assumed to equal 0.2, a typical value for fine-grained soils, and the reference g

_{a}to equal 0.01 m

^{−1}. However, the range of this parameter for fine-grained soil materials of 0.001–0.1 m

^{−1}was considered through a parametric analysis [16,27,30,53,54]. This range slightly differs from the literature, referring more to surface mines with fine-grained soils; thus, it has not been thoroughly examined, especially concerning the precipitation range investigated herein. Finally, the parameter g

_{n}is assumed to equal 1.3, representing fine-grained soils [55]. Figure 6 presents the SWCC for three different values of g

_{a}. As g

_{a}decreases, the suction needed to initiate soil’s desaturation (95% of the saturation degree) increases. The soil parameter g

_{n}is constant, leading to the same gradient of the linear part of the three SWCCs. Finally, the residual saturation S

_{r}= 0.2 is constant, and all three curves will eventually reach that value for large suction.

_{l}is a fitting parameter equal to 0.5, regardless of the soil type. The effective degree of saturation, S

_{e}, expresses a normalized water content between the saturated and the residual state of the soil and equals:

_{w}, decreases with the decrease of the soil water content, S

_{w}, and suction increases.

_{w}|, and the effective friction angle) represents the effect of suction in the unsaturated soil shear strength.

#### 5.2. Effect of Rainfall on Slope Stability

_{a}, as analyzed in the previous section. Finally, the soil’s permeability, the main soil property related to infiltration, was parametrically investigated. The chosen saturated permeability lies in the range of the dominant overburden material of Greek open-pit lignite mines [31].

_{w}at the left border and the bottom of the excavation.

_{w}, was 20 m, and a medium rainfall intensity was chosen of 3.6 mm/h (86.4 mm/day). All the physical and hydro-mechanical parameters of the reference model’s soil material are provided in Table 2. The fundamental parameters employed in the numerical model, including the geometry (height and angle) and the soil shear strength, have been validated to represent actual cases of Greek lignite mines. The parameters that have not been extensively validated are considered in the parametric analysis that follows to obtain the range of the results. The possible spatial and temporal variability of the basic parameters was not considered in this work to retain the practical and general nature of the framework. Nevertheless, if the soil variability is known, this could be involved in the methodology by applying the appropriate changes in the numerical models.

_{w}, the soil’s saturated permeability, and the SWCC parameter, g

_{a}. Table 3 shows the examined values; all other parameters are kept constant. Typical parameters affecting slope stability, such as the soil’s strength, are not investigated. They are well-known to affect slope stability but do not relate to the influence of rainfall infiltration.

^{2}at the slope’s crest. As the rainfall infiltrates the slopes, the suction decreases at the slope’s edges, where the rainfall infiltrates. Figure 9b illustrates the final matric suction distribution in the slope at the end of the one-day rainfall. As time passes, rainfall infiltrates deeper into the soil, and thus a new distribution emerges with zero suction at the slopes’ edges and the groundwater table. For fine-grained materials, such as those investigated herein, the suction reduction is the primary mechanism of rainfall affecting slope stability.

_{a}, on the pit slope’s safety factor for a 3.6 mm/h intensity rainfall event that lasts 24 h (total rainfall height equal to 86.4 mm). The selected values of the SWCC material parameter, g

_{a}, cover the range of a fine-grained over-consolidated clayey soil. The safety factor reduction rate increases significantly with the decrease of parameter g

_{a}. In particular, for g

_{a}values equal to 0.001 m

^{−1}, 0.005 m

^{−1}, and 0.01 m

^{−1}, SF reduces with a rate of 16.5%, 10.0%, and 4.7%, respectively. As g

_{a}increases further (0.05 m

^{−1}and 0.1 m

^{−1}), the slope safety factor is practically constant during rainfall. This difference between the five examined cases is attributed to the shape of the SWCC and the permeability function. Higher g

_{a}values correspond to lower suction (lower effective saturation degree) and lower soil permeability values within the unsaturated zone. Thus, as the parameter g

_{a}increases, the unsaturated soil permeability, k

_{w}, decreases, and rainwater’s infiltration into the unsaturated zone becomes more difficult than before. Indicatively, for the extremes g

_{a}= 0.001 m

^{−1}and g

_{a}= 0.1 m

^{−1}, the values of soil’s unsaturated permeability, in the area of the slope’s crest, are equal to 10

^{−5}cm/s and 10

^{−7}cm/s, respectively, i.e., they differ by two orders of magnitude.

_{w}ranges from a medium shallow (10 m) to a deep (40 m) groundwater table. Before the rainfall, the initial SF increases with the groundwater’s head rise—an expected result, since a high groundwater table corresponds to lower SF, whereas a deep groundwater table corresponds to higher SF. During the rainfall event, the safety factor reduction rate decreases with the increase of the groundwater head. The SF’s reduction rate for the groundwater head of H

_{w}= 10 m is 9.5%, for H

_{w}= 15 m is 7.0%, and for H

_{w}= 20 m is 4.7%. For the cases of deep groundwater tables corresponding to the high groundwater heads of H

_{w}= 30 m and H

_{w}= 40 m, the slope safety factor is practically constant. Again, high suction stresses and low effective saturation degrees develop in the extended unsaturated zones, leading to lower unsaturated permeability, impeding the infiltration procedure. It is noted that the groundwater head of H

_{w}= 0 m, corresponding to a groundwater table that starts from the ground surface, was also examined. Since this value corresponds to a high groundwater table, the unsaturated zone’s extent is quite limited for large suction stresses to develop.

_{s}= 10

^{−3}cm/s, 5 × 10

^{−4}cm/s, and 10

^{−4}cm/s, the SF reduction rates are equal to 5.3%, 5.1%, and 4.7%, respectively. The slope’s SF is practically constant for lower saturated permeability values, k

_{s}= 5 × 10

^{−5}cm/s and 10

^{−5}cm/s. Obviously, as the saturated permeability decreases, soil permeability in the unsaturated zone decreases, and hence water infiltration during rainfall becomes more difficult. The observed minor effect is because of the low values of k

_{s}.

## 6. Discussion

_{a}. The considered range of g

_{a}was rather broad, including the whole range of fine-grained materials, and thus its effect, although important, is not critical. Notice, however, that, in practice, having an accurate estimation of the SWCC is rare, and a broad range should generally be examined. The soil saturation complements the SWCC for the infiltration analysis, which has a similar effect, important but not critical.

## 7. Conclusions

_{a}, the initial groundwater head, H

_{w}, the saturated permeability, k

_{s}, and the rainfall intensity, q—were investigated through parametric finite element analyses. Rain infiltration primarily produces dissipation of suction stresses in the unsaturated zone, which induces a decrease in unsaturated soil shear strength, with the subsequent deterioration of pit slope stability. However, it is demonstrated that the impact magnitude of the examined parameters varies significantly. According to the numerical results, the effect of the SWCC material parameter, g

_{a}, in SF’s decrease rate during rainfall is more important among the other parameters. As g

_{a}decreases, the reduction rate of the pit slope’s safety factor during rainfall dramatically increases.

_{w}, and the rainfall intensity, q, showed a modest effect in reducing the pit slope’s SF. As H

_{w}decreases (higher initial groundwater table location) or as the rainfall intensity, q, increases, SF’s reduction rate during rainfall moderately increases. Finally, as the parameter k

_{s}increases, the SF reduction rate during rainfall increases slightly. Further work could include a more in-depth sensitivity analysis of the parameters affecting slope stability and various geometries. The particular geometry, stratigraphy, geotechnical, and groundwater conditions should be evaluated for any specific case study.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Geographical distribution of lignite mining areas and Koppen–Geiger classification for Greece [35].

**Figure 4.**Measurements for the last ten years of (

**a**) maximum mean monthly and (

**b**) maximum daily precipitation.

**Figure 5.**Mean and maximum monthly precipitation projections for the 2020–2099 period for the (

**a**,

**b**) RCP 4.5 and (

**c**,

**d**) the RCP 8.5 scenario.

**Figure 9.**Distribution of matric suction for the reference slope (

**a**) at the initial stage and (

**b**) at the final stage.

**Figure 10.**Slope safety factor variation with rainfall time duration, for various values of (

**a**) g

_{a}and (

**b**) H

_{w.}

**Figure 11.**Slope safety factor variation with rainfall time duration, for various values of (

**a**) k

_{s}and (

**b**) q.

References | g_{a}(m ^{−1}) | φ’ (°) | c’ (kPa) | k_{s} (cm/s) | H (m) | q (mm/h) | H_{w}(m) | Comments |
---|---|---|---|---|---|---|---|---|

Cai and Ugai [2] | 1.06–7.09 | 25 | 8 | 10^{−4}–6 × 10^{−3} | 10 | 5–50 | * 0 | Cut |

Zhang, Fredlund, Zhang, and Tang [20] | 0.05–10 | - | - | 10^{−3} | 20 | 0.036–18 | ** 20 | Cut |

Griffiths and Lu [6] | 0.05–0.5 | 20–30 | 5–10 | 10^{−11}–10^{−3} | 10 | 4 × 10^{−8}–10^{−3} | * 2.5 | Cut |

Rahardjo, Ong, Rezaur, and Leong [5] | 0.1–10 | 26 | 10 | 10^{−4}–10^{−2} | 5–40 | 9–900 | * 2.5–15 | Natural |

Rahimi, Rahardjo, and Leong [9] | 0.01–10.0 | 26 | 10 | 10^{−5}–10^{−2} | 15 | 0.036–360 | * 2 | Natural |

Tommasi, Boldini, Caldarini, and Coli [27] | 0.02 | 21 | 18 | 1 × 10^{−4} | 100 | 0.02–4.2 | - | Natural—Case study |

Leshchinsky, Vahedifard, Koo, and Kim [28] | 0.20 | 20 | 15 | 5 × 10^{−3} | 58 | 0.04–10.4 | - | Natural—Case study |

Qi and Vanapalli [24] | 0.03–1.00 | 17.5 | 5 | 4 × 10^{−9}–6 × 10^{−7} | 20 | 0.02 | * 8–23 | Cut |

Robinson, Vahedifard, and AghaKouchak [4] | 1.60 | 30 | 10 | 4 × 10^{−4} | 10 | 2.1–4.2 | * 2 | Cut |

Yeh and Tsai [25] | 0.1–1.0 | 26 | 10 | 10^{−4}–10^{−2} | 10 | 0.8–30 | * 10 | Cut |

Rouainia, Helm, Davies, and Glendinning [16] | 0.08 | 20 | 7 | 10^{−7} | 8 | 21–43 | * 1 | Cut |

Chen, Zhang, Zhang, Zhou, Ye, and Guo [3] | 1.00 | 26 | 30 | 5 10^{−3} | 125 | 0.1–2.5 | ** 0 | Natural—Case study |

Current Study | 0.001–0.1 | 25 | 50 | 10^{−5}–10^{−3} | 50 | 0.8–17.0 | ** 10–40 | Cut |

_{w}, is measured from the toe of the slope, downward to the intercept with the line of the GWL. ** Groundwater head value, H

_{w}, is measured from the GWL’s intercept with the vertical left boundary of the model, upward to the ground surface.

Parameter | Symbol | Value |
---|---|---|

Young’s modulus | E’ (MPa) | 50 |

Poisson’s ratio | ν’ (-) | 0.25 |

Effective cohesion | c’ (kPa) | 50 |

Effective friction angle | φ’ (^{ο}) | 25 |

Dilation angle | ψ (^{ο}) | 0 |

SWCC parameter | g_{a} (m^{−1}) | 0.01 |

SWCC parameter | g_{n} (-) | 1.3 |

SWCC parameter | g_{l} (-) | 0.5 |

Bulk water unit weight | γ_{w} (kN/m^{3}) | 9.81 |

Unsaturated soil unit weight | γ’ (kN/m^{3}) | 16 |

Saturated soil unit weight | γ_{s} (kN/m^{3}) | 18 |

Void ratio | e_{o} (-) | 0.8181 |

Residual saturation degree | S_{r} (-) | 0.2 |

Saturated saturation degree | S_{s} (-) | 1.0 |

Saturated permeability | k_{s} (cm/s) | 10^{−4} |

Geostatic stress coefficient | K_{o} (-) | 0.3333 |

SWCC material parameter g_{a} (m^{−1}) | 0.001 | 0.005 | 0.01 | 0.05 | 0.1 |

Saturated permeability k_{s} (cm/s) | 10^{−5} | 5 × 10^{−5} | 10^{−4} | 5 × 10^{−4} | 10^{−3} |

Initial groundwater head H_{w} (m) | 10 | 15 | 20 | 30 | 40 |

Rainfall intensity q (mm/h) | 1.2 | 2.4 | 3.6 | 4.8 | 6 |

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Theocharis, A.I.; Zevgolis, I.E.; Deliveris, A.V.; Karametou, R.; Koukouzas, N.C. From Climate Conditions to the Numerical Slope Stability Analysis of Surface Coal Mines. *Appl. Sci.* **2022**, *12*, 1538.
https://doi.org/10.3390/app12031538

**AMA Style**

Theocharis AI, Zevgolis IE, Deliveris AV, Karametou R, Koukouzas NC. From Climate Conditions to the Numerical Slope Stability Analysis of Surface Coal Mines. *Applied Sciences*. 2022; 12(3):1538.
https://doi.org/10.3390/app12031538

**Chicago/Turabian Style**

Theocharis, Alexandros I., Ioannis E. Zevgolis, Alexandros V. Deliveris, Rania Karametou, and Nikolaos C. Koukouzas. 2022. "From Climate Conditions to the Numerical Slope Stability Analysis of Surface Coal Mines" *Applied Sciences* 12, no. 3: 1538.
https://doi.org/10.3390/app12031538