# Failure Prediction of Open-Pit Mine Landslides Containing Complex Geological Structures Using the Inverse Velocity Method

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{f}) of landslides, published examples (from the investigation of some large open-pit slope failures) of successful implementation are proposed to predict impending failure based on the results of the conventional application of INV methods [25,26,27,28].

^{3}) in Northeastern Nevada, Rose and Hungr [24] demonstrated the accuracy and efficacy of this method. The result of the largest event was even forecasted 3 months before the impending failure. Dick et al. [19] further discussed the application of the INV method in open-pit mines by using new systematic multi-pixel and machine-learning models to complement the scarcity of conventional geodetic monitoring programs for near-real-time deformation measurements. Carlà et al. [9] took an anonymous copper open-pit mine into account and defined the appropriate strategy for the setup of alarms, which were deduced from the presented nine cases of slope instability and the relationship between the reciprocal displacement rate and duration time in the accelerating stage before the slope failure. To address the reliability of the prediction method and simultaneously provide guidelines for the proficient usage of this method, Zhou et al. [32] developed the modified INV method when analyzing the five landslides of Fushun West Pit slope failure. Similarly, Chen and Jiang [33] supposed that the selection of thresholds is usually over-conservative, considering the low-risk tolerance, and therefore introduced a dimensionless inverse velocity method (DINV) to provide a general solution framework that was used to assess the slope failure risk and avoid false alarms. The main characteristic of the inverse velocity method is its simplicity of use which has provided a useful tool for the interpretation of instrument data to anticipate eventual slope failure. These developments notwithstanding, the practical usefulness of the INV method for early warning in open-pit mines may be fairly constrained because of the following major drawbacks. In general, the INV method was formulated from fixed and human-controlled laboratory conditions, which are extremely unlikely to suffice in engineering slopes and field conditions. Furthermore, limitations connected to previous point-wise monitoring analysis of the INV method in open-pit mines are significant, often resulting in undersampled or poorly collected data. Additionally, the surface mining environment produces manifold noise patterns (e.g., mining extraction action, transportation equipment destabilization, human activities, measurement errors, etc.), which are considered to be a defect for early-warning purposes. Finally, the prediction performance of the INV method under different displacement scales does not appear to have been analyzed to date. All these mentioned gaps can decisively hinder the interpretation of the inverse velocity plot and affect the precision and dependability of t

_{f}prediction.

## 2. Materials and Methods

#### 2.1. Study Area

^{2}. The mining depth reaches 400 m. However, the Fushun West open-pit mine faces serious landslide hazards due to factors including open-pit mining, underground excavation, faults, and weak layers. Specifically, the mine has experienced over 900 collapse events attributable to landslides. More than 50% of these incidents occurred from June to September when rainfall is relatively concentrated. These landslide events have resulted in a total damaged area of 635,000 m

^{2}and have given rise to a series of safety and geological environmental issues concerning open-pit mining.

^{2}. The landslide caused the burial of the bottom sections 12 and 14 of the mainline, with the sliding tongue extending. This resulted in the complete interruption of the internal electrical railway lines in the eastern section of the mine, as well as the disruption of the western slope’s transportation roads, including the Xingping Road and the car transport highway. These disruptions had a significant impact on the internal drainage of the eastern open pit and the upper soil removal in the western area of the mine, severely impeding normal production in the mining area.

#### 2.2. Geological Setting

#### 2.3. Data Description

_{0}is (x

_{0}, y

_{0}, z

_{0}), the 3D coordinate value corresponding to any moment t

_{n}is (x

_{n}, y

_{n}, z

_{n}), and the cumulative displacement (Δx, Δy, Δz) component of the monitoring point within the moment from t

_{0}to t

_{t}is:

#### 2.4. The Basal INV Method

^{−1}→ 0) as the velocity asymptotically increases.

_{f}is the time of failure. This method consists in depicting a tangent line to the curve at an arbitrary point Ʌ

_{1}that tallies to moment t

_{1}. The tangent passes across the horizontal axis at moment t

_{c}

_{1}(t

_{c}

_{1},0). Afterward, the point P

_{1}is plotted vertically above Ʌ

_{1}, on a line that passes through Ʌ

_{1}and parallel to the Y axis. The segments of t

_{1}Ʌ

_{1}and t

_{1}t

_{c}

_{1}have an equal displacement from the perspective of geometric shapes. The abovementioned procedure is repeated for another random point Ʌ

_{2}. Then, the time of failure t

_{f}can be obtained as the abscissa of the intercept of a straight line that passes through P

_{1}and P

_{2}(Figure 6c).

_{f}is presumably provided for the point of abscissa of the extrapolated linear inverse velocity trend with the time axis.

#### 2.5. The Moving Average Filtering INV Method Architecture

_{1}, v

_{2}, …, v

_{t}. The mean over the latest k velocity data points is represented as SSBF

_{k}(${\overline{v}}_{t}$) and calculated as follows:

_{k, next}, ${\overline{v}}_{t}^{\prime}$) is collected with the invariable sampling width m, the scope from t – k + 2 to t + 1 is considered. A new value v

_{t+}

_{1}comes into the sum and the earliest value v

_{t+}

_{1}drops out. This simplifies the computations by proceeding with the antecedent mean SSB

_{Fk, antecedent}: (${\overline{v}}_{t}$)

_{i}(1/Ω

_{i}is the reciprocal of displacement rate at t

_{i}) and t equal to t

_{i}(t

_{0}is the most recent instant).

## 3. Results

#### 3.1. Slope Displacement Velocity, Acceleration, and Cumulative Displacement Analysis

^{2}, was measured by the monitoring point GN11 on 13 July. The maximum acceleration, which was 4.30 cm/d

^{2}, was measured by the monitoring point GN5 on 14 August. The acceleration value span of GN10 is the smallest, ranging from −0.2 to 0.65 cm/d

^{2}. The acceleration value of GN5 at the monitoring point has the largest span, ranging from −0.2 to 4.30 cm/d

^{2}.

#### 3.2. Analysis of Slope Displacement Inverse Velocity and Cumulative Displacement

#### 3.3. Source Velocity Data Model Analysis

#### 3.4. SMA Model Analysis

#### 3.5. LMA Model Analysis

#### 3.6. ESF Model Analysis

## 4. Discussion

## 5. Conclusions

- (1)
- A landslide event comprises a rather complicated process. The results show that the sliding process of a landslide can be divided into three stages based on the INV: the initial attenuation stage (regressive stage), the second attenuation stage (progressive stage), and the linear reduction stage (autoregressive stage).
- (2)
- Compared with the raw data and the exponential smoothing filter (ESF) models, the fitting effect of short-term smoothing filter (SSF) and long-term smoothing filter (LSF) in the linear autoregressive stage is better.
- (3)
- In terms of fitting accuracy, among the four models proposed in this study, the fitting accuracy of the multiplicative inverse model is the lowest, followed by the ESF model; the SMA model is better, and the LMA model is the best. In terms of prediction accuracy, ESF is the lowest among the four models, followed by the SMA model; the multiplicative inverse model is better, and the LMA model is the best.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Location of the study area and geomorphology of the open-pit mine: (

**a**) Location map of the Fushun West open-pit mine; (

**b**) aerial view of landslide form.

**Figure 5.**Landform and diagram of the open-pit mine landslide: (

**a**) current situation of the open-pit mine; (

**b**) layout scheme of displacement measurement points in the landslide area.

**Figure 6.**Conventional three-stage interpretation of creep behavior. (

**a**) Three-stage deformation process of the progressive landslide (modified after Saito, [20]); (

**b**) kinematic evolution of a landslide (modified after Intrieri et al. [16]); (

**c**) graphical approach for determining the time of failure in the tertiary creep stage (Intrieri et al. [16]); and (

**d**) schematic diagram of INV (modified after Fukuzono, [21]).

**Figure 7.**Different orders of moving average applied to displacement rates in an anonymous open-pit mine of the instability before the failure. n, m, p, and q represent the four order values of successive increments (i.e., n < m < p < q). (

**a**) Displacement rate at successive incremental order values of n; (

**b**) Displacement rate at successive incremental order values of m; (

**c**) Displacement rate at successive incremental order values of p; (

**d**) Displacement rate at successive incremental order values of q.

Monitoring Point | The Initial Stage | The Second Stage | The Third Stage | |||
---|---|---|---|---|---|---|

Start | End | Start | End | Start | End | |

GN1-E200-200 | 28 June | 15 July | 16 July | 11 August | 12 August | 31 August |

GN2-E300-184 | 12 July | 13 July | 10 August | 11 August | ||

GN3-E400-200 | 22 July | 23 July | 10 August | 11 August | ||

GN4-E400-188 | 21 July | 22 July | 10 August | 11 August | ||

GN5-E500-280 | 22 July | 23 July | 10 August | 11 August | ||

GN6-E500-200 | 24 July | 25 July | 10 August | 11 August | ||

GN7-E600-200 | 22 July | 23 July | 10 August | 11 August | ||

GN8-E700-200 | 18 July | 19 July | 10 August | 11 August | ||

GN9-E800-232 | 22 July | 23 July | 9 August | 10 August | ||

GN10-E900-220 | 22 July | 23 July | 12 August | 13 August | ||

GN11-E1000-200 | 16 July | 17 July | 11 August | 12 August | ||

GN12-E1200-200 | 14 July | 15 July | 11 August | 12 August |

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**MDPI and ACS Style**

Tao, Y.; Zhang, R.; Du, H.
Failure Prediction of Open-Pit Mine Landslides Containing Complex Geological Structures Using the Inverse Velocity Method. *Water* **2024**, *16*, 430.
https://doi.org/10.3390/w16030430

**AMA Style**

Tao Y, Zhang R, Du H.
Failure Prediction of Open-Pit Mine Landslides Containing Complex Geological Structures Using the Inverse Velocity Method. *Water*. 2024; 16(3):430.
https://doi.org/10.3390/w16030430

**Chicago/Turabian Style**

Tao, Yabin, Ruixin Zhang, and Han Du.
2024. "Failure Prediction of Open-Pit Mine Landslides Containing Complex Geological Structures Using the Inverse Velocity Method" *Water* 16, no. 3: 430.
https://doi.org/10.3390/w16030430