Preventive Model for Slope Failure Forecasting at the Quellaveco Mine Early Detection Approach Using MLP–PyTorch, Random Forest, and Logistic Regression with SMOTE

2.1 Hydrometeorological characterization of the study area

Daily records from four SENAMHI stations in the Moquegua region (Figure 1) were processed and weighted with IDW to obtain representative values for the Quellaveco area. This hydrometeorological calibration is the baseline on which the environmental variables of the predictive model were subsequently built; its correct characterization was therefore indispensable before addressing the machine learning methodology itself.

Figure 2 shows the monthly climatology of the four stations and the resulting IDW precipitation. The seasonal pattern of the southern Andean altiplano is observed: a wet period from December to March (maximum IDW PP: 4.70 mm/day in February) and a dry period from May to October (minimum: 1.76 mm/day in October). Calacoa registers the highest values (8.49 mm/day in February) due to its higher altitude and exposure to Amazonian air masses. The weighted mean annual precipitation resulted in 32.8 mm, consistent with the semi-arid character of Moquegua [17]. This pattern has direct implications for the pore pressure of the rock mass, a variable among those with the highest predictive importance in the trained model. It is worth noting that, although the weighted mean annual precipitation is relatively low in absolute terms, its seasonal concentration during the austral summer months generates infiltration peaks that can suddenly raise pore pressure, punctually increasing the probability of instability even in slopes with favorable geomechanical conditions during the rest of the year.

image003.png

image004.png

Amplitude Figures 3–5 show the monthly Tmax, Tmin, and the resulting IDW thermal amplitude ΔT. The IDW Tmax oscillates between 23.85 ℃ (July) and 26.63 ℃ (October), with an annual mean of 25.1 ℃. The mean amplitude is 16.1 ℃, with maximums in September–October (17.4 ℃). These thermomechanical cycles favor the propagation of structural discontinuities, affecting the GSI and the discontinuity index, two of the variables with the highest importance. The daily thermal amplitude, by inducing repeated cycles of expansion and contraction within the rock matrix, acts as a mechanical fatigue mechanism that, sustained over several years of operation, contributes to the progressive weakening of preexisting discontinuities and, therefore, to the gradual reduction of the shear strength of the rock mass.

image005.png

image006.png

image007.png

Figure 6 synthesizes the three climatic components analyzed in this section — precipitation, maximum temperature, and minimum temperature — showing the semi-arid regime with marked seasonality that characterizes the study area: the months with the highest precipitation (December–March) coincide with relatively stable temperatures, whereas the dry period (May–August) exhibits the greatest daily thermal amplitude, a condition that, as noted, favors the mechanical fatigue of the rock mass.

image008.png

2.2 Study design, area, and variables

This study followed a quantitative approach, because it analyzes numerical data on the geotechnical behavior of open-pit slopes. Geotechnical, environmental, and operational variables — such as cohesion, internal friction angle, precipitation, pore pressure, and blasting vibration — were statistically processed to implement predictive models for classifying stability and instability conditions [21]. Cumulative ground displacement was measured throughout the monitoring campaign, but it was not used as a predictor: it intervenes exclusively in the definition of the target variable (alert-threshold criterion, Section 2.1) and was therefore deliberately excluded from the 21 input variables listed in Table 1, in order to avoid any circularity between the label and the predictors. Consequently, no displacement variable appears in Table 1, and the description of the processed variables in this section is now consistent with that table.

Table 1. Variables employed in the predictive models

Note: * Calibrated with SENAMHI (IDW, four stations).

A predictive, comparative, and evaluative design was adopted, since the research implemented, trained, and compared the performance of the Logistic Regression, Random Forest, and MLP algorithms in order to identify the model with the highest capacity for the early detection of slope failures at the Quellaveco mine. Accuracy, precision, recall, and F1-score were used to analyze model performance objectively [22].

The database comprises 1,500 historical records (January 2022–December 2024) obtained from geotechnical sensors, vibrating-wire piezometers, triaxial blasting accelerometers, and the SENAMHI stations described in Section 2.1. The class distribution is markedly imbalanced: 1,370 stable records (91.33%) and 130 potential-failure records (8.67%), a situation characteristic of geotechnical monitoring in real operations, where failure events are statistically infrequent but of high impact. Figure 7 shows this distribution. Imbalance of this kind, common in the detection of rare but critical events such as structural failures, financial fraud, or low-prevalence medical diagnoses, requires specific methodological tdreatment during training, because a classifier trained without adjustment tends to favor the majority class and to miss the failure cases that are precisely of greatest operational interest.

image009.png

Each record was labeled according to the stability condition observed in the corresponding monitoring window, using measurable, auditable field criteria rather than a subjective assessment. A record was assigned to the potential-failure class (1) when the monitored sector met at least one of the following criteria, defined by the mine's geotechnical protocol and by the applicable Peruvian regulation (MEM-Peru, RCD N°023-2016-EM): (i) a back-calculated factor of safety below the admissible regulatory threshold (FS < 1.3) during the window, and/or (ii) cumulative measured displacement exceeding the alert threshold established for the monitored bench (based on the displacement-rate / inverse-velocity criterion derived from prism and slope-stability-radar monitoring). Records that met none of these criteria throughout the window were labeled as stable (0). This operational definition links the target variable directly to quantitative field conditions and makes the labeling reproducible.

Limitation of the labelling scheme. The factor of safety participates in the definition of Class 1 (FS < 1.3) and is, at the same time, one of the 21 predictors listed in Table 1. For the subset of positive records generated by that criterion, the classifiers can therefore recover part of the labelling rule instead of learning an independent relationship, and any importance measure obtained for FS is partly determined by construction. Cumulative displacement, the second labelling criterion, was excluded from the predictor set precisely for this reason. The factor of safety was retained because it is a continuous quantity that is back-calculated in real time in the operation and carries geomechanical information beyond the 1.3 threshold, and because removing it would have made the input set inconsistent with the variables actually available to the geotechnical team. Nevertheless, no claim of discovery is attached to its importance: Sections 3.2 and 5 state explicitly that the high Gini value of FS reflects the labelling rule and that an ablation experiment in which FS is removed from the input set is required before that ranking can be read as independent evidence. This ablation is identified as immediate future work.

Twenty-one predictor variables grouped into three categories (Table 1) and one binary target variable were selected. The geotechnical variables capture the intrinsic strength of the rock mass; the environmental variables integrate the climatic and hydrogeological effects calibrated with the SENAMHI stations; and the operational variables record the impact of extractive activities on slope stability. This tripartite grouping also allows the relative contribution of each dimension — intrinsic, environmental, and anthropic — to be evaluated independently, which facilitates the physical interpretation of the variable-importance analysis.

Before training, collinearity among the 21 predictor variables and the target variable was assessed with a Pearson correlation matrix (Figure 8). This exploratory analysis identifies strong linear relationships between variable pairs that could introduce redundancy in tree-based models or instability in the Logistic Regression coefficients. As expected, a high correlation appears between the factor of safety and cohesion (r = 0.83) and between the principal stresses σ₁ and σ₃ (r = 0.92), consistent with their intrinsic geomechanical relationship. In contrast, the linear correlation of each individual variable with the stability condition is comparatively low (maximum |r| = 0.27 for slope angle), which confirms that geotechnical failure responds to non-linear interactions among multiple factors rather than to a single dominant predictor and justifies the use of machine learning models able to capture such interactions.

image010.png

2.3 Preprocessing and SMOTE

Before the predictive models were implemented, the database underwent a preprocessing stage to guarantee the quality, consistency, and reliability of the information used for training, reducing errors associated with incomplete records, outliers, and scale differences among variables [23]. Because the geotechnical, environmental, and operational variables have different ranges and units, they were standardized with StandardScaler to mitigate the influence of heterogeneous scales, optimize convergence, and improve the stability of the predictions [24]. All processing was carried out with Python-based data-analysis and machine learning tools.

To avoid optimistic bias, SMOTE was never applied to the complete dataset before partitioning. A stratified 80% / 20% split first isolated a held-out test set (n = 300) that preserved the original class proportions. Within the remaining 80% used for training, SMOTE (k = 5 nearest neighbors) was applied independently inside the training portion of each of the ten cross-validation folds, so that the synthetic minority samples generated for a given fold never informed the fold reserved for validation.

The final models were then fitted on the fully balanced training set (2,192 samples, 50% / 50%) and evaluated once on the untouched test set. Because the test set contained no synthetic data and never participated in the resampling, no information leaked between subsets, and the reported test metrics reflect the expected performance on realistic operational data. Figure 9 illustrates the class distribution of the training partition before and after applying SMOTE.

image011.png

For illustrative purposes, Figure 10 presents a representative schematic cross-section of a typical slope at the Quellaveco mine, showing the physical elements that the variables in Table 1 characterize numerically: the geometry of the benches, the potential failure surface, the position of the monitoring piezometers, and the water table. The range of the factor of safety shown (1.25–2.48) illustrates the real geomechanical variability that the predictive model must capture from the 21 input variables.

image013.png

2.4 Predictive models: Multi-Layer Perceptron, Random Forest, and Logistic Regression

The implemented neural network (Figure 11) follows a 21–20–10–5–1 architecture with double regularization in each hidden layer: batch normalization to stabilize the activation distribution between layers, and dropout (20%) to reduce overfitting by randomly deactivating neurons during training. The binary cross-entropy (BCE) loss function (Eq. (1)) is the standard choice for binary classification:

$\zeta_{B C E}=-\frac{1}{N} \sum_{i=1}^N\left[y_i \ln \hat{y}_{i_i}+\left(1-y_i\right) \ln \left(1-\hat{y}_i\right)\right]$   (1)

where, yᵢ ∈ {0, 1} is the true label and ŷᵢ = σ(f(xᵢ)) ∈ (0, 1) is the probability predicted by the network.

image014.png

Training used 300 epochs, the Adam optimizer (η = 10⁻³, weight decay = 10⁻⁴), and a CosineAnnealingLR scheduler for the progressive reduction of the learning rate, which favors smooth convergence toward the minimum of the loss function. The classification threshold was set at 0.5 on the sigmoid output. The combination of batch normalization and dropout responds to a complementary regularization strategy: the former accelerates and stabilizes convergence by normalizing intermediate activations, while the latter reduces the network's dependence on individual neurons, lowering the risk of overfitting given a training set of moderate size.

Logistic Regression was used as a baseline binary classifier because it estimates the probability of a geotechnical event and allows the individual influence of the predictor variables to be interpreted, which facilitates the statistical reading of the results [25]. Random Forest was implemented because it handles non-linear relationships and highly variable geotechnical data. Built from multiple decision trees trained on random subsets of samples and variables, it reduces overfitting and improves robustness; it also manages heterogeneous variables, identifies complex patterns, and estimates the relative importance of each predictor, which strengthens the interpretation of slope behavior and the early detection of instability in open-pit mining [26].

Random Forest was configured with B = 200 decision trees, a maximum depth of 15, min_samples_split = 4, and class-weight adjustment (class_weight = "balanced"). The model averages the predictions of the individual trees, reducing variance through ensemble diversity:

$\hat{\mathrm{y}} R F(x)=\frac{1}{B} \sum_{h=1}^B T_b(x)$   (2)

Logistic Regression, with L2 regularization, max_iter = 1,000, and balanced weights, estimates the probability of failure through the sigmoid function:

$P(Y=1|(x)|)=\frac{1}{1+e^{-\left(\beta_0+\beta^T x\right)}}$   (3)

The simplicity of this post-normalization linear model allows the contribution of each variable to be interpreted directly through the β coefficients. Such interpretability is a practical advantage in mining, where geotechnical teams often need not only a prediction but also a physical justification of the variables driving it, so that the alerts generated by the model can be validated in the field by specialized personnel.

2.5 Evaluation and validation

The performance of the models was evaluated with supervised-classification metrics oriented toward accuracy and predictive capacity, which allowed the behavior of Logistic Regression, Random Forest, and the MLP in identifying stability and instability conditions to be compared. The models were evaluated with the standard binary-classification metrics of (Eqs. (4)-(6)).

Accuray $=\frac{T P+T N}{T P+T N+F P+F N}$   (4)

Precision $=\frac{T P}{T P+F P}, \quad$ Recall $=\frac{T P}{T P+F N}$   (5)

$F 1=\frac{2 \cdot \text { Precision } \text { ⋅ } \text { Recall }}{\text { Precision }+ \text { Recall }}$   (6)

where TP, TN, FP, and FN are the true positives, true negatives, false positives, and false negatives, respectively. In addition, the area under the ROC curve (AUC-ROC) was computed as a threshold-independent measure of discriminability.

2.6 Tools and study population

Data processing and model implementation were carried out with Python, given its wide use in machine learning and predictive-analysis research [27]. Figure 12 summarizes the overall workflow followed in this study, from data acquisition to the early-detection system.

image020.png

The study population consisted of the geotechnical, environmental, and operational records associated with the behavior of the open-pit slopes at the Quellaveco mine, obtained through monitoring systems, operational reports, and geotechnical controls. The sample consisted of the records selected for training and validating the predictive models, integrating geotechnical, environmental, and operational variables corresponding to stable and unstable conditions. Given the predictive focus of the research, all available records that met the quality and consistency criteria established during data cleaning were used, which improved the learning capacity of the algorithms and adequately.

The results show that machine learning is a viable alternative for the early prediction of geotechnical failures in mining slopes. Although the MLP achieved the highest overall accuracy (0.870) and the Random Forest a comparable value (0.867), the Logistic Regression provided the best performance for early detection, with a recall of 0.731 and an AUC-ROC of 0.785, correctly identifying 19 of the 26 failures in the test set. This is consistent with evidence that machine learning algorithms can model complex relationships between geotechnical and environmental variables and overcome several limitations of traditional slope-stability approaches [6]. The results also confirm that integrating geomechanical, hydrogeological, and climatic variables improve the identification of patterns associated with potentially unstable conditions.

The superiority of the Logistic Regression in sensitivity partially contrasts with results that identified Random Forest as the best performer for factor-of-safety estimation, with coefficients of determination above 0.96 [7]. That difference is attributable to the nature of the present problem: whereas that work addressed the continuous prediction of the factor of safety under controlled conditions, this study addressed a binary classification with strong class imbalance, where failures represent only 8.67% of the records. In this setting, the Logistic Regression identified critical events more effectively, while the Random Forest tended to favor the majority class, raising overall accuracy but reducing the detection of real failures.

The findings also differ from those reporting coefficients of determination above 0.92 with an optimized hybrid support vector regression model [8]. Although such advanced algorithms are effective for estimating the factor of safety, the present results show that statistically simpler models can offer operational advantages when the primary objective is the early detection of risk conditions.

In real mining, where the cost of a false negative can imply significant economic losses, equipment damage, or harm to personnel, the ability to identify potentially unstable events in time is more relevant than maximizing overall accuracy alone.

This is precisely why the low precision of the Logistic Regression, analyzed in Section 3.7, must be managed through the proposed screen-and-triage architecture rather than by shifting to a higher-accuracy but lower-recall model.

The results are also consistent with work reporting accuracies above 92% with Random Forest for natural-hazard vulnerability estimation, whose authors frame predictive models as decision-support tools rather than substitutes for professional judgment [10]. In agreement with that stance, the model developed for Quellaveco does not aim to replace specialized geotechnical evaluation but to complement existing monitoring with early warnings based on historical data and real SENAMHI environmental variables, which increases the representativeness of the operational conditions and strengthens preventive capacity.

Finally, the predictive importance of the factor of safety, the GSI, and the internal friction angle confirms the relevance of parameters traditionally used in the geomechanical evaluation of slopes. The leading position of the factor of safety is conditioned by its role in the labelling rule and is not read as evidence of predictive value; the informative part of the ranking is the weight of the GSI, the RQD, and the internal friction angle, none of which intervenes in the definition of the target variable. Their predominance within the Random Forest model shows that slope stability remains strongly conditioned by the shear-strength properties of the rock mass; at the same time, the simultaneous incorporation of climatic and hydrogeological variables captured operational conditions that conventional approaches rarely integrate jointly. The results therefore support the use of machine learning models as complementary tools for strengthening the preventive management of geotechnical risk in large-scale operations such as the Quellaveco mine.