Data-driven risk assessment of hydrothermally altered goafs in deep metal mines via unsupervised typing and nonlinear evolution

Abstract

As the “Resource Lifeline” strategy of the China National Gold Group (CNGG) extends to greater depths, its subsidiary mines encounter severe challenges, primarily characterized by tectonic fracturing, intense hydrothermal alteration, and data scarcity. Crucially, traditional empirical stability classifications function as mere “static snapshots” that fail to capture the nonlinear accumulation of hidden hazards, rendering them ineffective for early warning in complex deep environments. To bridge this gap, this study proposes a data-driven stability assessment framework that seamlessly integrates unsupervised structural typing with nonlinear phenomenological evolution. Diverging from reliance on subjective experience, this study first extracts the intrinsic geometric features of 40 typical goafs using K-means clustering to establish an objective structural typology. Subsequently, an Analytic Hierarchy Process (AHP)-Entropy combined weighting model reveals that hydro-environmental factors account for over 50% of the total risk contribution, highlighting the overwhelming statistical significance of water-rock coupling in driving instability. To quantify the continuous progression from a metastable to a high-risk state, a non-linear dynamic evolution model based on the logistic map is introduced. By incorporating the comprehensive static risk index, this model effectively characterizes the nonlinear damage amplification process. The derived critical threshold (Rc = 0.57) accurately delineates high-risk zones, providing a transparent, quantitative paradigm for prioritizing the remediation of concealed hazards in data-scarce deep mining operations.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-50767-w.

Introduction

With the gradual depletion of high-quality, easily accessible shallow resources, the core production bases of the CNGG (hereinafter referred to as “the Group”)-including the Qinling (Henan), Wushan (Inner Mongolia), and Tibet mines-have comprehensively transitioned into the deep mining stage^1–3.

Compared with other metal mines globally, the geological environment and engineering conditions of the Group’s mines exhibit distinct complexities, primarily manifested in three aspects. First, the occurrence of the ore vein is complex. Most ore bodies manifest as steeply dipping thin or fragile veins, resulting in goafs (mined-out areas) with long, narrow, and irregular morphologies, characterized by large exposed roof areas that are difficult to support. Second, wall rock alteration and tectonic structures are well-developed. Ore bodies typically occur within fault fracture zones where wall rocks have universally undergone intense hydrothermal alterations, such as sericitization and chloritization.

These rock masses are highly susceptible to softening and argillization upon contact with water, exhibiting significant rheological characteristics. Third, historical legacy challenges remain acute. During the Group’s promotion of regional resource integration, numerous undocumented goafs-remnants of early artisanal mining-were incorporated into the official mining boundaries. These voids exhibit chaotic spatial configurations and completely lack historical data, culminating in a vast cluster of “hidden hazard bodies.”

Addressing the practical challenges of “adverse geological conditions and widespread hidden hazards,” existing stability assessment methods face severe limitations in their practical application⁴. Traditional empirical classification methods (e.g., the Mathews Stability Graph), while computationally simple, are essentially “static snapshots” based on the assumption of homogeneous rock masses⁵. They often fail to quantitatively account for the chemical weakening effects of groundwater on the intensely altered rock masses specific to the Group’s mines, leading to assessment results that deviate significantly from reality. Numerical simulation methods (e.g., FEM/DEM), although capable of revealing local failure mechanisms, are prohibitively expensive and difficult to implement for mine-wide rapid screening when dealing with legacy goafs characterized by highly irregular morphologies and uncertain geological parameters⁶.

Facing the dual dilemma of “small samples” and “missing physical and mechanical parameters” prevalent in deep engineering, the international academic community has begun to reflect on the limitations of purely data-driven models and high-fidelity numerical simulations in complex, concealed environments, gradually shifting towards a hybrid assessment paradigm based on the intrinsic structure of engineering data and phenomenological laws. Regarding rock mass structural characterization, researchers have started utilizing dimensionality reduction and unsupervised clustering techniques to mine the statistical distribution patterns of goaf geometric parameters, providing objective mathematical descriptors for the structural typing of undocumented goafs. However, relying solely on static geometric typing still cannot reflect the cumulative process of hazards deteriorating over time or environmental changes. The instability of goafs often exhibits nonlinear acceleration characteristics; however, constrained by the complexity of the micro-constitutive relations of deep, intensely altered rock masses, establishing rigorous physical-mechanical evolution equations directly from first principles is often difficult to implement at engineering sites.

To overcome this, this study proposes a novel goaf risk assessment framework that fuses unsupervised structural cognition with non-linear dynamic evolution modeling. Rather than pursuing generic “big data” mining, this study addresses the status quo of data scarcity in the Group’s mines. Utilizing 40 typical goaf samples, the study employs the K-means clustering algorithm to mine their intrinsic geometric structures characteristic of steeply dipping thin veins. Simultaneously, recognizing that goaf risk accumulation possesses significant nonlinear acceleration features, this study abandons the forced fitting of complex microscopic physical constitutive models and introduces a Logistic nonlinear iterative phenomenological model. This model aims to reveal the evolutionary law of goafs from static risk accumulation to accelerated deterioration in intensely altered, water-rich environments through mathematical mapping. This study aims to provide a closed-loop analysis paradigm integrating unsupervised cognition and risk evolution assessment, solving the Group’s challenge of supervising deep concealed hazard bodies that are currently “invisible, unclear, and unpreventable.”

Methods

This study constructs a data-driven stability evaluation framework tailored for hydrothermally altered, water-rich goafs. It primarily comprises four core modules: Data Preprocessing and Indicator System Construction, Unsupervised Structural Typing, Combined Weighting and Static Risk Evaluation, and a Nonlinear Risk Evolution Model based on the Logistic Map. These modules are organically coupled through unified indicators and state variables: First, a fuzzy comprehensive evaluation based on multi-criteria decision-making provides a static risk index R, serving as a comprehensive statistical indicator to measure the relative vulnerability of the system. Subsequently, by introducing a nonlinear iterative phenomenological model, the mathematical amplification behavior of this risk index under the progression of time or environmental degradation is characterized, thereby identifying the empirical risk threshold for the accelerated deterioration of goafs in this mining area. This establishes a closed-loop evaluation system from static hazard grading to long-term risk evolution assessment (Fig. 1).

Fig. 1.

The overall framework of the data-driven stability assessment: bridging unsupervised structural typing with nonlinear risk evolution.

Dataset and evaluation indicators

This study relies on the extensive mine geological database of the CNGG. As a leading enterprise in China’s gold industry, the Group’s mines span diverse typical geological environments, ranging from tectonic fracture zones, altered rock types, and skarn types to porphyry types⁷. The accumulation of massive goaf detection and monitoring data provides a solid foundation for stability analysis under multiple working conditions (Table 1).

Table 1.

Summary of geological and alteration backgrounds for the 40 typical goaf samples.

Typical tectonic and alteration classification	Representative lithology and alteration features	Typical hydro-mechanical response	Sample quantity (proportion)
Tectonic fracture zone, intense alteration type	Cataclastic rock mass; intense sericitization and silicification	Highly fragmented structure, extremely low mechanical strength; strong water conductivity	18(45.0%)
Medium alteration softening type	Porphyry/skarn; significant chloritization and kaolinization	Significant hydrophilic swelling upon water contact, highly susceptible to mudding and rheology	12 (30.0%)
Relatively intact weak alteration type	Relatively intact massive/layered rock mass; weak alteration	High inherent strength, relatively less affected by hydro-weakening	10 (25.0%)

Given the limited dataset size, the research focus is placed on constructing a physically interpretable evaluation framework and identifying dominant control mechanisms, rather than pursuing cross-mine statistical generalization. Integrating engineering experience with data availability, an evaluation system comprising eight indicators was established for subsequent structural typing and risk quantification. The definitions and significance of each indicator are as follows:.

Based on a systematic compilation of geological exploration reports, goaf detection results, and in-situ monitoring records, 40 representative goaf samples were selected. To clarify the representativeness of the samples and the geological variability among different mining areas, these 40 samples were scientifically categorized into three core tectonic and alteration background types typical of the Group’s deep mines:

1. Tectonic fracture zone with intense alteration type (characterized by intense sericitization and silicification, with highly fragmented rock masses);

2. Medium alteration softening type (characterized by chloritization and kaolinization, highly susceptible to mudding and rheology upon water contact);

3. Relatively intact weak alteration type.

Formation time (years)

This indicator reflects the duration of goaf exposure and the cumulative degree of time-dependent damage, seepage, and softening effects. A longer formation time implies a higher probability of creep, argillization, and structural degradation under identical geological conditions.

Goaf scale

This composite indicator integrates parameters such as length, width, height, and volume to characterize spatial scale and exposed volume. The span directly governs the roof stress state and secondary stress redistribution, serving as a key geometric factor controlling roof stability, while the volume reflects the magnitude of the potential hazard space.

Signs of surface deformation (0/1)

A binary variable, where 1 indicates that the goaf has induced or contributed to surface deformation, and 0 indicates no observable deformation. This indicator characterizes the intensity of the surface response to goaf instability and is crucial for assessing external disaster impacts.

Roof caving degree

Quantified into three levels (0-No caving, 1-Partial caving, 2-Full caving), this indicator reflects the integrity and bearing status of the roof strata. The engineering significance of each level is detailed in Table 2.

Table 2.

Engineering significance of roof caving degrees.

Code	Engineering significance
2	Full caving: bearing structure has vanished. indicates high short-term risk, though the system may tend towards stability in the long term due to void filling.
1	Partial caving: most dangerous state. characterized by significant stress concentration and structural incompleteness (e.g., hanging blocks).
0	No caving: roof is weak but maintains overall integrity. The strata are intact despite potential minor fracturing.

Water accumulation status

A binary indicator, where 1 denotes significant water accumulation or direct recharge by groundwater, and 0 indicates a basically dry state or minor seepage. This is the most critical environmental indicator for altered rock mines. Water accumulation significantly weakens wall rock strength through mechanisms such as effective stress reduction, induced pore water pressure, and chemical weakening, making it a primary disaster-inducing factor in strongly altered, water-rich mining areas.

Residual pillars

A binary indicator, where 1 indicates the presence of effective residual pillars or artificial support structures, and 0 indicates a lack of significant pillar support. Pillars serve as key structural units bearing the overburden load; their integrity directly influences stress transmission paths and global stability^8,9.

Stability level (1–4)

Based on long-term field experience and safety inspection records, goaf stability is qualitatively evaluated. Levels 1–4 correspond to “Stable, Basically Stable, Unstable, and Extremely Unstable,” respectively. Note that this indicator is excluded from the clustering operation and serves solely as a reference for validating and calibrating model results (Figure2).

Treatment measures (0–4)

Quantified into five levels (ranging from 0-No measures to 4-Backfilling), this indicator reflects the mitigation effect of human intervention on risk. Backfill bodies, for instance, can significantly constrain wall rock deformation. The engineering effects of different measures are presented in Table 3.

Table 3.

Classification of treatment measures and engineering significance.

Code	Treatment measure	Control mechanism	Applicable scenario
0	No measures	Relies on the surrounding rock’s natural arch effect.	Small, dry goafs with intact roofs.
1	Sealing/isolation	Physically isolated without changing the void’s stress or deformation.	Remote from main haulage drifts and surface structures.
2	Caving	Induces roof caving to fill voids with waste rock.	Permissible subsidence areas with no major aquifers.
3	Support/reinforcement	Anchor cables and shotcrete improve the rock’s shear strength and limit expansion.	Key access nodes or locally unstable areas.
4	Backfilling	Backfill supports the roof, limits rock deformation, and eliminates free surfaces.	High-risk, large-scale goafs affecting critical facilities or water-rich zones.

Fig. 2.

(a) Typical surface subsidence induced by underground goaf instability; (b) Severe roof caving observed within the high-risk goaf; (c) Mudding and water accumulation in hydrothermally altered rock mass; (d) Typical isolation barrier and drainage control measures.

Data preprocessing

To enhance the stability and reliability of the subsequent clustering and evaluation models, systematic preprocessing was performed on the raw data before modeling. This process included missing value imputation, outlier identification and correction, standardization, and the encoding of discrete variables.

Missing value handling

A hierarchical strategy was adopted based on the missing data ratio. For ratios < 5%, mean imputation (for continuous variables) or mode imputation (for categorical variables) was applied; for ratios between 5% and 20%, K-Nearest Neighbors (KNN) imputation (k = 5) was utilized; for ratios > 20%, the variable or sample would be discarded to avoid systematic bias. In this dataset, the missing rate was < 3%, necessitating no deletion operations.

Outlier identification and correction

Outliers were identified using box plots and the 3 principle. Logical verification based on mine spatial relationships (e.g., Volume≈Length×Width×Height) was conducted to correct or exclude values violating physical logic.

Data standardization

To eliminate dimensional discrepancies among indicators, Z-score standardization was applied to all continuous variables:

1

Where x is the raw value, µ is the mean, and σ is the standard deviation. This ensures that all variables participate in clustering and weight calculation on a unified scale.

Numerical encoding of discrete indicators

Discrete indicators such as surface deformation signs, roof caving degree, water accumulation, residual pillars, and treatment measures were encoded using ordinal values with engineering physical significance. This ensures that the encoded values maintain a consistent trend with risk levels or structural states. In the K-means clustering process, only continuous variables highlighting the intrinsic geometric-structural characteristics of the goafs were selected for computation to prevent human interventions (e.g., treatment measures) from directly biasing the structural typing results; discrete variables were subsequently incorporated into the risk evaluation and mechanism analysis¹⁰.

Unsupervised structural typing

In deep mining engineering, “data sparsity” is an unavoidable challenge. For the high-quality, small-sample dataset in this study, high-complexity deep models face extreme overfitting risks. Therefore, this study adopts the K-means algorithm, known for its low bias and strong geometric interpretability, to identify structural heterogeneity¹¹.

(1) Feature construction: Based on goaf geometric attributes and spatial morphological features, a subset of continuous indicators covering core parameters like span and volume was selected to construct feature vectors These standardized features form an n-dimensional feature space used to characterize the intrinsic structural differences among goafs. To avoid the “curse of dimensionality,” the number of features was controlled within a moderate range relative to the sample size.

It is important to clarify the rationale behind the selection of clustering variables. Engineering interventions (e.g., treatment measures and backfilling) were deliberately excluded from the geometric feature space. This decision was made to isolate the inherent spatial vulnerability of the goafs prior to human modification, ensuring that the structural typing reflects the natural hazard potential rather than post-mining support states. Furthermore, while fine morphological indicators such as roof curvature are theoretically valuable for stability analysis, they were not included in this study. This is due to the extreme technical limitations of conducting high-resolution 3D laser scanning in deep, water-filled, and completely concealed legacy goafs. Therefore, macroscopic indicators like span and volume were selected as the most reliable and accessible geometric descriptors under current deep-mining conditions. From a pragmatic engineering perspective, these fundamental scale parameters are entirely sufficient to support the initial risk triage of massive hidden hazard bodies, effectively fulfilling the primary objective of macroscopic structural typing.

(2) Algorithm parameter setting and initialization basis: Addressing the typical “small sample” characteristics of deep engineering data, to avoid clustering results falling into local optima and to enhance global stability, strict settings were applied to the algorithm parameter selection: First, the Euclidean distance was chosen as the similarity metric within the standardized feature space to ensure the isotropy of continuous geometric variables (span, volume) weights in multi-dimensional space. Second, the traditional random initialization method was discarded in favor of the K-means + + algorithm for selecting initial cluster centers. This mechanism ensures, through probability distribution, that the initial centroids are as far apart as possible in the feature space, significantly enhancing the convergence speed and the robustness of the clustering boundaries under small-sample datasets.

(3) Algorithm principle: The objective is to minimize the sum of squared distances between samples and their respective cluster centroids:

2

Where K is the number of clusters, is the centroid of the k-th cluster, and is the set of samples in the k-th cluster.

(4) Determination of cluster number (K): As an unsupervised learning method, the core of K-means lies in discovering the low-dimensional manifold structure within the data rather than fitting high-dimensional decision boundaries. To validate the clustering results, this study introduces the Silhouette Coefficient.

(5) Stability validation: To test the stability of the clustering results, sensitivity analyses were conducted using different random initializations and sample subsets. Results indicated that the majority of samples maintained identical or similar class assignments across different runs, demonstrating stable cluster boundaries. Furthermore, combined with dimensionality reduction visualization techniques like t-SNE, the distribution differences of different classes in low-dimensional space were intuitively observed, verifying the distinctiveness of the three structural types in geometric-spatial features and providing a basis for the subsequent structure-based risk evolution analysis.

Combined weight determination

To avoid biases resulting from purely subjective or objective weighting, this study employs a combined weighting approach integrating the AHP and the Entropy Weight Method¹².

(1) AHP subjective weighting: A judgment matrix is constructed based on expert scoring (using the 1–9 scale). The weights are derived using the eigenvector method, followed by a consistency check:

3

This ensures the reliability of the subjective judgments.

(2) Entropy objective weighting: Objective weights are calculated based on the information entropy Ej of each factor:

4

This quantifies the information contribution of each indicator.

(3) Combined weighting: The comprehensive weights omega are calculated to unify subjective and objective perspectives:

5

where is the fusion coefficient, determined comprehensively by considering consistency checks and the degree of information entropy dispersion.

Non-linear dynamic evolution model

The static risk index R(0 ≤ R ≤ 1) derived from the AHP-Entropy combined model and fuzzy comprehensive evaluation is essentially a dimensionless composite indicator that integrates heterogeneous variables (e.g., discrete caving grade encodings, binary hydrological status, and standardized geometric dimensions). It reflects the relative vulnerability of the goaf under multi-factor coupling, rather than a true physical damage variable derived from continuum thermodynamics¹³. To address any potential conceptual ambiguities, the static risk index R derived from the AHP-Entropy combined model is strictly defined as a macroscopic statistical indicator for engineering triage, rather than a physical state variable or thermodynamic order parameter. The weighting scheme does not aim to replace rigorous mechanical constitutive equations¹⁴ but serves as a practical, data-driven tool to fuse site-specific engineering heuristics with objective data variance under small-sample conditions.

Considering that the instability of deep goafs often exhibits a nonlinear characteristic of slow initial accumulation followed by accelerated deterioration^4,15, and because obtaining microscopic constitutive parameters for hydrothermally altered goafs is exceedingly difficult, deriving a strict physical-mechanical evolution equation from first principles is practically unfeasible in engineering. Therefore, this study employs the Logistic map to construct a purely nonlinear iterative phenomenological model to explore the evolutionary trend of high-risk hazards^16,17:

6

This governing equation explicitly encapsulates two competing physical mechanisms driving goaf instability in water-rich environments:

1. Nonlinear Risk Amplification Term (): Represents the positive feedback trend of risk evolution within the system. Over time or with increased disturbance, existing hazards (e.g., fracture propagation, hydro-softening) promote further risk amplification.

2. Mathematical Saturation Term (): Acts as a geometric boundary constraint, ensuring that the risk index remains bounded within the rational domain of [0,1] during iteration, preventing mathematically unbounded divergence.

It must be explicitly stated here that this equation is an artificial mathematical fitting of the evolutionary trend of multi-criteria statistical indicators; initially used to describe population dynamics in ecology, its interior does not contain the true mechanical evolution mechanism of rock mass failure or the principle of free energy dissipation. The parameter λ serves as a phenomenological evolution coefficient, characterizing the relative rate at which the risk indicator approaches the limit state under a specific engineering geological environment. By analyzing the iterative convergence characteristics of this map equation, we can identify the empirical critical threshold for the system’s transition from a low-risk metastable state to a high-risk state, thereby providing a quantitative reference basis for long-term risk management.

Results and analysis

Structural classification results

The K-means clustering analysis was performed on the 40 goaf samples within the standardized geometric-spatial feature space. Figure 3a illustrates the variations in the Sum of Squared Errors (SSE) and the Silhouette Coefficient across different cluster numbers (K). It can be observed that as K increases from 2 to 3, the SSE exhibits a sharp decline; however, beyond K = 3, the rate of decline plateaus, presenting a distinct “elbow” characteristic. Correspondingly, the average Silhouette Coefficient peaks at approximately 0.453 when K = 3, indicating that this cluster number achieves an optimal balance between intra-cluster compactness and inter-cluster separation (Table 4).

Fig. 3.

Validation of K-means clustering results. (a) The Elbow method curve for determining the optimal number of clusters (K). The X-axis represents the Number of Clusters (K), and the Y-axis represents the Sum of Squared Errors (SSE). The “elbow” point at K = 3 indicates the optimal balance. (b) Leave-One-Out Cluster Stability. The X-axis represents the Adjusted Rand Index (ARI), and the Y-axis represents the Frequency. (c) Bootstrap Stability Analyses of Cluster Centroids (N = 1000). The X/Y-axes represent the Standardized Span and Volume (Z-Score). (d) t-SNE Visualization of Goaf Structural Clusters. The X/Y-axes represent the t-SNE Dimensions 1 and 2.

Table 4.

Evaluation metrics for K-means clustering results.

Number of clusters (K)	SSE (sum of squared errors)	Average silhouette coefficient
2	94.63	0.467
3	64.33	0.453
4	41.17	0.448
5	26.73	0.473
6	21.07	0.439

Based on the determination of K = 3, a visualization analysis of the clustering results was conducted. Figure 3(d) presents the sample distribution obtained after dimensionality reduction using t-Distributed Stochastic Neighbor Embedding (t-SNE). The three classes of samples exhibit clear separation in the low-dimensional space with only a few samples located near the cluster boundaries, confirming that the typing possesses significant discriminative power in terms of geometric-spatial features.

Based on the cluster centroids and the mean values of the original indicators, the goafs were categorized into three typical structural types:

1. Class I (Small-Scale Stable Type): Comprising 21 samples (52.5%), this class is characterized by “small span and small volume” geometry, with an average span of approximately 9 m and an average volume of 3,235 m³. Most samples possess intact roofs with no significant signs of surface deformation or large-scale caving. These are primarily goafs formed by standardized mining practices promoted by the Group in recent years, maintaining a self-stable state.

2. Class II (Medium-Scale Transition Type): Comprising 8 samples (20.0%), this class exhibits significantly increased geometric dimensions, with an average span of roughly 60 m and an average volume of 31,366 m³. Some goafs show signs of local roof caving and fracture development. They represent an intermediate state transitioning from self-stability to potential instability, mostly corresponding to transitional goafs from the resource integration period, and possess a lower structural safety margin.

3. Class III (Large-Scale High-Risk Type): These samples exhibit extreme geometric features, with an average span reaching 113 m and an average volume of 115,147 m³, far exceeding the other two classes. This category primarily corresponds to legacy clusters of ultra-large goafs characterized by large spans and long exposure times. The massive exposed space induces drastic redistribution of wall rock stress, making it a potential source of large-scale disasters in the mining area.

Although the aforementioned typing results possess clear physical significance in terms of geometric features, the sample size (N = 40) is relatively limited due to the difficulty of data acquisition in deep concealed engineering. To eliminate random interference and ensure that the structural typing is not an accidental product dominated by individual samples, this study introduced Bootstrap resampling and Leave-One-Out Cross-Validation (LOOCV) for rigorous statistical robustness testing.

First, the Bootstrap method was employed to perform 1,000 iterations of resampling with replacement and K-means clustering on the original dataset. Figure 3(c) displays the distribution of the three structural centroids in the feature space (Span-Volume). The results show that the three centroids form three distinct, internally compact clusters. The 95% confidence ellipses do not overlap, and the separation is particularly high between Class I (Stable, Green) and Class III (High-Risk, Red). This indicates that even with significant data perturbation, the three identified structural patterns remain highly stable.

Second, to quantify the influence of individual samples on the overall typing structure, the ARI was calculated using the Leave-One-Out method. By sequentially removing one sample and comparing the clustering result of the remaining (N-1) samples with the baseline result, an average ARI of 0.86 (standard deviation 0.25) was obtained. This value is far above the statistically recognized threshold for “excellent stability” (ARI > 0.80), with the majority of iterations yielding ARI values close to 1.0. This further confirms that the identified structural types are global robust features of the dataset rather than being determined by outliers or specific subsets.

Identification of dominant control factors

The AHP-Entropy combined model reveals the core driving factors controlling stability in this mining area (Fig. 4). The results indicate that the cumulative weight contribution of Water Accumulation (weight 0.293) and Signs of Surface Deformation (weight 0.231) reaches 52.6%. This weight distribution profoundly reflects the specific disaster mechanism of the mine:

Fig. 4.

Comparison of entropy and combination weights.

1. Dominance of Hydro-Physical Action: The high weight of water accumulation confirms that the softening, argillization, and pore water pressure effects of groundwater on the wall rock are the primary causes of system stability reduction, surpassing the influence of purely geometric parameters.

2. Correlation with Surface Response: The high weight of surface deformation signs suggests that goaf instability has generated significant surface responses, making it an intuitive indicator for judging the severity of hidden hazards.

3. Other Factors: Stability Level (0.160) and Roof Caving (0.091) follow in importance, while traditional geometric indicators such as Volume (0.065) carry relatively lower weights under multi-factor coupling. This demonstrates that under water-rich complex geological conditions, environmental and hydrological factors have ascended to become decisive control variables.

Static risk assessment and validation

Based on the fuzzy comprehensive evaluation model, the static risk index for all samples was calculated, as shown in Fig. 5. The risk value R ranges from 0 to 1, with larger values indicating greater instability. Based on the model output, goaf stability can be classified into four levels, as detailed in Table 5.

Fig. 5.

Sorted static risk values of 40 goaf samples. The X-axis represents the Sample Rank, and the Y-axis represents the Comprehensive Risk Value (R).

Table 5.

Risk classification criteria based on static risk index.

Risk level	Risk index range R	Stability description
Ⅰ	R ≤ 0.30	Overall stable. low risk; the structure is self-supporting.
Ⅱ	0.30 < R ≤ 0.57	Generally stable. metastable state; routine monitoring is required.
Ⅲ	0.57 < R ≤ 0.70	Significant risk. signs of instability are present; treatment is necessary.
Ⅳ	R > 0.70	Critical risk. high probability of instability; immediate remediation/remediation is required.

The risk level distribution for the 40 goafs is as follows: Level I: 13 (32.5%); Level II: 24 (60%); Level III: 2 (5.0%); Level IV: 1 (2.5%).

Model Validation: The high-risk samples identified by the model (Level III + IV, totaling 3) were compared with the mine’s actual hidden hazard ledger. Goafs #25, #4, and #3 are all located in water-rich areas with complex geological conditions. The model’s identification of high-risk hidden hazards aligns highly with the actual field situation. In particular, the determination of extreme risk for sample #25 accurately pinpointed a “disaster zone” requiring urgent priority remediation. It should be pointed out that this comparison is primarily to verify the logical self-consistency of the multi-criteria weighting model within the current sample set, rather than an independent prospective prediction for unknown goafs.

Dynamic evolution and critical thresholds

Empirical Threshold Determination and Parameter Calibration: To reveal the evolutionary path of goafs from “static characteristics” to “accelerated deterioration,” the aforementioned static risk value R was taken as the initial state R₀ and substituted into the iterative equation. This study conducted a rigorous quantitative iterative calibration for the control parameter λ. The specific calculation process was: the initial search interval for λ was set to [1.5,3.0] with an iteration step of 0.01. The objective function was to minimize the Root Mean Square Error (RMSE) between the final convergent/divergent state of the model’s evolution curve and the actual instability performance of the samples in the mine’s hazard ledger. The fitting results showed that when the evolution coefficient is λ = 2.30, the model achieved the optimal goodness-of-fit, with a coefficient of determination reaching R² = 0.88 and a RMSE = 0.062. Therefore, the representative evolution coefficient for the goaf system in this mining area was determined to be λ = 2.30. According to the bifurcation characteristics analysis of the logistic map, the median empirical critical risk threshold for this mining area system was derived as 0.57 (Figure 6).

Fig. 6.

Sensitivity analysis of the critical risk threshold (Rc) with respect to the evolution coefficient (λ). The X-axis represents the Evolution Coefficient (λ), and the Y-axis represents the Critical Risk Threshold (Rc). The blue shaded region represents the 95% confidence interval of the critical point for the system’s nonlinear divergence when λ fluctuates by ± 10%.

Parameter Sensitivity and Confidence Interval Analysis: To further verify the statistical robustness of this empirical threshold, a parameter sensitivity test was conducted on the evolution coefficient λ. λ was set to fluctuate by ± 10% around the optimal fitting baseline value (i.e., λ ∈ [2.07,2.53]) to simulate the potential random uncertainties during deep geological environmental changes and the multi-criteria evaluation process. The calculation results showed that as λ fluctuated, the critical threshold Rc for the system’s nonlinear divergence varied accordingly, with its 95% Confidence Interval falling within the range of [0.52,0.61], presenting a narrow uncertainty band. This demonstrates that despite certain data fluctuations, the evolutionary boundary point distinguishing high-risk from low-risk states remains stable around 0.57. Therefore, selecting c = 0.57 as the representative threshold criterion for determining whether the system enters a nonlinear amplification state possesses a strong statistical basis (Figure 7).

Fig. 7.

Final risk state distribution heatmap after nonlinear iteration. The X-axis represents the Sample Rank (sorted by initial risk R₀), and the color scale represents the Final Risk State (R_∞), where 0 indicates stable and 1 indicates unstable.

Stable Converging Type (Corresponding to Class I Structure): The initial risk value is low (R < 0.30). It gradually trends towards a low value with scale iteration, converging rapidly. This characterizes a stable-to-stable evolution, indicating low risk.

Progressive Instability Type (Corresponding to Class II Structure): The initial risk is moderate (0.30–0.57). A slight increase occurs during evolution, eventually tending towards the stable or critical zone. This belongs to a metastable-critical boundary structure.

Rapid Instability Type (Corresponding to Class III Structure): The initial risk is relatively high (R > 0.57). It exhibits exponential growth with iteration, rapidly approaching the limit state of instability. This presents typical critical instability behavior and marks the object for priority remediation.

Through statistical analysis of the 40 evolution curves, the critical risk threshold for the goaf system in this mining area was established as : when , the system tends towards ultimate stability; when , the system enters an irreversible state of instability.

Physical interpretability and mechanisms

(1) Intrinsic coupling between Although the structural typing (derived from unsupervised K-means clustering) and the risk classification (derived from multi-indicator comprehensive evaluation) are based on distinct mathematical logics, they exhibit significant physical consistency (Figure 8).

Fig. 8.

Coupling mechanism between unsupervised structural types and risk levels.

Class I (Small-Scale) overlaps with the low-risk level (Level I) by over 90%. This confirms that within limited exposure spaces, the “arching effect” of the wall rock can function effectively, and the geometric stiffness of the structure itself dominates the system’s self-stabilizing capacity¹⁸. Class III (Large-Scale) encompasses all extreme risk (Level IV) samples. This indicates that when the goaf span breaks through a specific boundary, the intensity of wall rock stress redistribution undergoes a qualitative change, causing the system to enter a highly unstable, high-risk state¹⁹. This strong “geometry-risk” coupling proves that the K-means typing accurately captures the macroscopic engineering attributes of the goafs.

(2) Statistical dominance of hydro-physical action under multi-factor coupling and empirical evidence.

The combined weighting model identified “Empty Area Water Accumulation” as the highest individual weight factor (0.293), which, together with signs of surface deformation, accounts for 52.6% of the weight. In the mathematical framework of multi-criteria decision-making, this indicates that this variable plays a decisive role statistically in distinguishing between stable and unstable goafs.

To further provide empirical support for the microscopic mechanical mechanism and respond to the high weight allocation given by the model, this study integrated and referenced laboratory mechanical immersion test results of typical hydrothermally altered wall rocks (rich in secondary minerals such as sericite and chlorite) from the study area²⁰. To explicitly quantify this micro-mechanical degradation, experimental testing was conducted on typical hydrothermally altered rock specimens (rich in sericite and chlorite) from the study area. As illustrated in Fig. 9, the transition of rock samples from a dry to a fully saturated state triggers a significant nonlinear exponential decay in macroscopic bearing capacity^21,22. Figure 9(a) reveals that the average Uniaxial Compressive Strength (UCS) of the dry specimens reaches 103.72 MPa, whereas under saturated conditions, the strength plummets to approximately 33.90 MPa - a drastic reduction exceeding 67%. Concurrently, the shear resistance is severely compromised; Fig. 9(b) demonstrates that the internal cohesion drops sharply from 17.51 MPa to a mere 5.74 MPa. This pronounced non-linear attenuation directly visualizes the severe mechanical deterioration induced by hydro-softening²³.

Fig. 9.

Experimental curves illustrating the hydro-chemical weakening effect on altered rock specimens: (a) Nonlinear degradation of UCS from dry to saturated state; (b) Exponential attenuation of shear cohesion under varying moisture degrees.

This microscopic experimental data confirms that the hydration swelling and dissolution of cementing materials, triggered by water molecules wedging into the crystal lattices of hydrophilic phyllosilicate minerals, indeed cause a dual physical-chemical weakening of the rock strength^23,24. This empirical regularity achieves a logical closed-loop with the macro-conclusion derived via the AHP-Entropy method that “the water accumulation factor has the highest statistical weight.” However, since the remaining ~ 50% of the weight is distributed among factors like geometric scale and pillar support, it indicates that the ultimate instability of the goaf remains the comprehensive result of complex interactions among multiple factors, including the hydrological environment, geometric exposure, and engineering interventions. By introducing the nonlinear iterative model, this study further quantified the evolutionary trend of such hydro-physically dominated risk indices as the environment deteriorates, and its calibrated goodness-of-fit reached R² = 0.88, providing strong support for the above analysis.

(3) Internal consistency and statistical limitations of the empirical threshold.

This study derived an empirical critical threshold of Rc ≈ 0.57 both when determining the static risk grading boundary and when inverting the phenomenological evolution model parameters. It must be explicitly pointed out here that these two analysis processes are not mutually independent. Because the exact same hidden hazard ledger records and goaf classification standards were used when calibrating the evolution coefficient λ as were used to determine the static threshold, the numerical convergence of these two thresholds is essentially the inevitable result of fitting the static classification rules and the nonlinear mathematical model to the same dataset. This phenomenon demonstrates that the constructed ‘static grading-risk evolution’ evaluation framework exhibits rigorous internal consistency and mathematical self-consistency. However, since the exact same hidden hazard ledger records were utilized for both the static threshold determination and the parameter calibration, the numerical convergence of the thresholds primarily reflects the framework’s optimal fit to the specific geological conditions of the current dataset. Therefore, treating this convergence as an independent validation of universal predictive capacity requires caution. To firmly establish the generalized predictive validity of the critical threshold Rc = 0.57, future research must employ more rigorous methodologies, specifically temporal sequence forecasting and spatiotemporal cross-validation across distinct mining regions.

Furthermore, constrained by the extreme difficulty of acquiring deep concealed engineering data, the sample size in this study is relatively small (N = 40), among which high-risk samples (Levels III and IV combined) account for only 3. Although the previous Bootstrap analysis confirmed the statistical robustness of the cluster centers, the current statistical testing power remains limited for identifying a significant threshold with universal predictive value.

Addressing these limitations, in future research, more rigorous validation methods must be employed to establish the actual predictive value of this threshold: one is to conduct temporal sequence forecasting validation, i.e., using data from one period to predict goaf instability in a subsequent period; the second is to introduce spatial cross-validation, training the model on data from certain mining areas and conducting independent blind tests on other mining areas with differing geographical and geological conditions²⁵.

(4) Spatial correlation characterization of deep and shallow disasters.

The high weight of “Signs of Surface Deformation” (0.231) reveals the spatial correlation between deep and shallow disasters. In the mining of steeply dipping thin veins, roof caving is not confined to the deep underground but propagates upward along high-angle joints or weak tectonic zones. Tensile cracks appearing on the surface are not isolated phenomena but are macroscopic responses to the accumulation of damage and the breakthrough of wall rock fractures from underground deep goaf groups to the surface²⁶. This finding confirms that, in the absence of precise underground monitoring data, surface response serves as the most reliable external indicator for identifying the transition of a deep system from a metastable state to an accelerated deterioration state.

Conclusion

Targeting the critical engineering challenge of governing hidden goaf hazards in deep metal mining, this study proposes a novel static classification and long-term risk assessment paradigm that integrates “unsupervised structural typing,” “combined weighting fuzzy evaluation,” and “nonlinear phenomenological evolution.” The main innovations and conclusions are as follows:

1. Constructed an objective structural typing method based on macroscopic geometric features: Based on the K-means algorithm, utilizing continuous-dimension spatial geometric parameters such as span and volume, the complex goaf cluster was classified into three objective patterns: “Small-Scale Relatively Stable (Class I),” “Medium-Scale Transition (Class II),” and “Large-Scale Potential High-Risk (Class III).” Bootstrap and LOOCV indicated that this typing possesses excellent statistical robustness, providing an objective mathematical description for the preliminary screening of mine hazards.

2. Revealed the high statistical correlation of hydro-environmental factors in multi-criteria risk differentiation: The AHP-Entropy combined model showed that the individual weight of empty area water accumulation reached 0.293, and together with signs of surface deformation, it exceeded 50%. Supplementary laboratory water content-mechanical strength degradation tests further confirmed the microscopic softening mechanism, wherein the UCS of typical hydrothermally altered rocks drops sharply by 40%−60% upon water contact. The mutual corroboration of macroscopic statistics and microscopic experiments highlights the potential risks of hydro-physical effects under complex multi-factor interactions, providing a quantitative reference for optimizing deep drainage designs.

3. Constructed a nonlinear risk evolution model: To overcome the limitations of traditional static evaluations in quantifying risk evolution trends, the logistic map was introduced to characterize the mathematical amplification trajectory of the static composite risk index. Through high-precision parameter iterative optimization (R²=0.88 and RMSE = 0.062), the empirical critical risk threshold for the accelerated deterioration of the system in this mining area was identified as approximately 0.57. Using this threshold as a criterion, the model verified the internal consistency of the evaluation system, providing a quantitative basis for the long-term risk grading and remediation priority sorting of deep high-risk goafs.

4. Formed a “triage” remediation strategy: This strategy guides the mine to prioritize backfilling for Class III high-risk goafs to eliminate hazards at the root, while implementing sealing and monitoring for Class I stable goafs, thereby optimizing safety investment efficiency while ensuring operational safety.

5. Future outlook and improvements: Currently, the unsupervised typing has not incorporated mechanical morphological parameters; future work needs to introduce dimensionless variables such as the span-to-height ratio. Furthermore, limited by the relatively small sample scale, future research will be dedicated to constructing cross-mine databases to establish the external scientific validity of this empirical threshold through rigorous time-series retrospective prediction and spatial cross-validation mechanisms.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Shuai Li: Conceptualization, Methodology, Formal analysis, Investigation, Writing - original draft. Designed the overall research framework, conducted data preprocessing, K-means clustering, and RG-inspired model calibration, and drafted the initial manuscript.Jingliang Xue: Resources, Validation, Investigation. Provided critical mine geological data and field monitoring records, verified the structural typing results through engineering practice, and participated in field investigation of goaf stability.Zhenyu Dan*: Supervision, Conceptualization, Funding acquisition, Writing - review & editing. Proposed the core research idea, supervised the study design and data analysis, secured financial support, and revised the manuscript for intellectual content.Tubing Yin*: Supervision, Methodology, Writing - review & editing. Guided the development of the AHP-Entropy combined weighting model and dynamic evolution mechanism analysis, supervised the validation of critical thresholds, and polished the manuscript.Jun Hou: Resources, Validation. Contributed legacy goaf data from the Changchun Gold Research Institute, assisted in cross-validating high-risk goaf identification results, and provided engineering insights for remediation strategy optimization.*Corresponding authors (Zhenyu Dan and Tubing Yin) share equal supervisory responsibilities, including final approval of the published version, handling of reviewer comments, and correspondence with the editorial office. All authors have read and approved the final manuscript.

Funding

Major National Science and Technology Project for Deep Earth of China (Grant No. 2024ZD1003808). Science and Technology Innovation Program of Hunan Province (Grant No. 2023RC3035).

Data availability

Data will be made available on request.

Declarations

Competing interests

The authors declare no competing interests.