Integrated Risk Assessment Framework for Abandoned Mine Methane (AMM) Emissions in Urban Environments: Methodological Development and Application to the Lupeni Case Study (Romania)

Abstract

Abandoned mine methane (AMM) emissions represent a significant public safety and environmental hazard in post-industrial urban areas. Uncontrolled subsurface gas migration may lead to explosive accumulations in confined spaces, human exposure, infrastructure damage, and additional greenhouse gas emissions. This study develops an integrated risk assessment framework for AMM in urban environments, combining quantitative analysis of field monitoring data with semi-quantitative probability–consequence risk matrices and multi-factor evaluation. Methane concentrations were measured at 41 monitoring points during three campaigns (August–September 2024). A total of 42 influencing factors were identified and classified into seven categories (geological, mining, hydrogeological, meteorological, anthropogenic, biological, and special phenomena). Exceedance probabilities of critical thresholds were estimated with 95% confidence intervals. Consequence weights were derived using the Analytic Hierarchy Process (AHP) based on a five-expert panel (CR = 0.043). The framework was applied to the urban area of Lupeni, Romania, where methane concentrations of up to 54% vol. were measured during borehole screening measurements (subsurface probe points). Elevated concentrations were detected four days after commissioning of a new gas pipeline. Gas chromatographic analysis excluded pipeline leakage and confirmed a mining-related source. Results indicate a localized critical risk (R = 25 on a 1–25 scale) in hotspot P2, with a 95% confidence interval for the probability of exceeding the 3% vol. alert threshold of [0.885–1.00], justifying immediate mitigation through controlled drainage. Post-intervention monitoring showed a reduction to instrumentally undetectable levels by February 2025. The study demonstrates that administrative mine closure does not eliminate residual methane risk and proposes a complete decision-support algorithm (URBAN-MINE-RISK) for similar urban settings. The applicability of structural reliability methods (e.g., FORM) is discussed as a future research direction. The methodology is transferable to other post-mining regions in Central and Eastern Europe.

1. Introduction

1.1. Global Context of Methane Emissions from Subsurface Sources

Methane (CH₄) is recognized as the second most important anthropogenic greenhouse gas after carbon dioxide (CO₂), with a global warming potential (GWP) approximately 28–34 times greater than CO₂ over a 100-year time horizon [1]. According to the International Energy Agency (IEA), coal mining—both active and abandoned—accounts for nearly 10% of global methane emissions [2].

Abandoned coal mines (ACM) continue to emit methane for decades after closure through residual desorption, diffusion, and pressure-driven migration processes [3,4]. This source, commonly referred to as abandoned mine methane (AMM), remains insufficiently inventoried and inconsistently regulated on the global scale.

In post-industrial regions undergoing urban redevelopment, modern infrastructure (gas pipelines, sewer systems, foundations, utility corridors) frequently overlies historical underground workings. The superposition of urban structures over abandoned mine voids creates complex subsurface gas migration pathways. Uncontrolled methane migration may result in explosive accumulations in confined spaces, human exposure, infrastructure damage, and additional greenhouse gas emissions [5,6].

Unlike atmospheric methane emissions, which contribute primarily to climate change, confined subsurface methane accumulation presents immediate public safety hazards.

1.2. Historical Urban Accidents Caused by Subsurface Gas Migration

Several documented international incidents illustrate the severity of subsurface gas migration hazards:

• Loscoe, United Kingdom (1986): An explosion destroyed a residential house and seriously injured three occupants. Methane migrated through abandoned mine pathways beneath residential properties, with a sudden drop in barometric pressure facilitating gas mobilization [7,8].
• Gorebridge, Scotland (2013): Residential buildings constructed above abandoned mine workings experienced carbon dioxide accumulation, causing health symptoms among occupants. The absence of a gas-protection membrane during construction led to demolition and reconstruction of 64 houses [9,10].
• Nowa Ruda, Poland (2017): Near-surface concentrations up to 7.8% CH₄ and 5.8% CO₂ were documented at depths of approximately 1.2 m in former mining fields. The mechanism was attributed to hydrogeological “hydraulic piston” effects, where rising groundwater levels displaced accumulated gases toward the surface [11].
• Johannesburg, South Africa (2023): An explosion in an underground utility tunnel caused fatalities and significant urban damage. Methane concentrations of 5–15% were reported, and investigations indicated a subsurface source [12,13].
• Centralia, USA (1962–present): A long-burning underground coal fire has produced toxic gas emissions that migrated into basements and surface structures, leading to near-total abandonment of the town [14,15].
• Qingdao, China (2013): A catastrophic explosion in an urban sewer system caused 62 fatalities and major infrastructure damage, illustrating the vulnerability of confined underground systems to flammable gas accumulation [16,17].

These cases demonstrate that administrative mine closure does not eliminate residual subsurface gas hazards. Deterministic evaluations are often insufficient to capture the complex interaction between geological structures, hydrogeological variability, and anthropogenic disturbances.

1.3. Types of Probability in Risk Assessment

Risk assessment requires distinction between different interpretations of probability [18,19]:

• Frequentist (objective) probability, based on the relative frequency of observed events, applicable when sufficient empirical data exist.
• Bayesian (subjective) probability, based on prior knowledge updated with evidence, useful in data-scarce environments.

The present study adopts a frequentist approach for estimating exceedance probabilities of critical methane thresholds (based on measurements from 41 monitoring points across three campaigns) and a structured expert-based (subjective) approach for determining consequence weights using the Analytic Hierarchy Process (AHP).

This hybrid probabilistic strategy ensures that empirical measurement data govern hazard frequency, while structured expert judgment informs consequence severity.

1.4. Objectives and Contribution of the Study

The present study aims to develop and validate an integrated methodological framework for AMM risk assessment in urban environments. The specific objectives are

• To develop an integrated framework combining quantitative monitoring data with semi-quantitative probability–consequence risk matrices and multi-factor analysis.
• To identify and classify 42 influencing factors grouped into seven categories controlling methane emissions.
• To apply the framework to the Lupeni case study, using data from 41 monitoring points across three campaigns (August–September 2024).
• To quantify uncertainty through 95% confidence intervals for exceedance probabilities.
• To validate consequence weighting using AHP with consistency verification.
• To compare the proposed approach with reliability-based methods such as FORM.
• To develop a practical decision-support algorithm (URBAN-MINE-RISK) for similar urban post-mining contexts.

The study contributes a validated operational risk assessment methodology that bridges theoretical probabilistic concepts with real-world mitigation outcomes.

2. Theoretical Foundation of AMM Risk Assessment

2.1. Definition and Principles of Risk Assessment

According to ISO 31000:2018, risk is defined as the effect of uncertainty on objectives and is typically expressed as a function of the probability of occurrence of a hazardous event and the severity of its consequences [20]. In the context of ground gas hazards, risk assessment aims to determine the likelihood that a subsurface gas source will generate hazardous concentrations in occupied spaces and to quantify the associated impact [5,21].

The fundamental mathematical representation of risk is [22,23]

$$R=P\times C$$

(1)

where

$P$ represents the probability of occurrence of the hazardous condition,

$C$ represents the severity of consequences.

The multiplicative formulation preserves monotonicity and ensures that risk increases proportionally with either probability or consequence. Although simplified, this representation is widely adopted in environmental and industrial safety frameworks due to its transparency and decision-support applicability.

To ensure theoretical rigor and compatibility with reliability-based approaches, the hazardous condition is formally defined using a limit state function:

$$g\left(C_{C{H}_4}\right)=C_{crit}-C_{C{H}_4}$$

(2)

where $C_{C{H}_4}$ is the measured methane concentration (% vol.) and $C_{crit}$ is the adopted critical threshold.

The system is considered safe when

$$g\left(C_{C{H}_4}\right)>0$$

(3)

and in a failure (hazard) state when

$$g\left(C_{C{H}_4}\right)\le 0$$

(4)

This formulation enables future integration with structural reliability methods (e.g., FORM), even though the present study adopts a semi-quantitative operational framework.

Failure is defined operationally as the exceedance of the alert threshold $C_{crit}=3\%$ vol. CH₄ in borehole screening, used for decision prioritization; LEL exceedance is treated as an extreme consequence condition.

2.2. Methodological Approaches in Risk Assessment

Depending on the nature, availability, and statistical robustness of data, risk assessment can be performed using three complementary methodological approaches [24,25]: quantitative, semi-quantitative, and qualitative. Each approach has distinct theoretical foundations, strengths, and limitations.

Quantitative Risk Assessment (QRA) employs numerical data and probabilistic models to compute objective probabilities and estimate consequences in measurable terms. It typically requires statistically characterized input parameters and sufficiently large datasets to derive reliable probability distributions. Representative methods include Monte Carlo simulation, the First-Order Reliability Method (FORM), and the Second-Order Reliability Method (SORM). These approaches allow explicit modeling of uncertainty propagation and failure probability estimation but are computationally intensive and data-demanding.

Semi-quantitative Risk Assessment utilizes ordinal scoring systems to classify probability and consequence into discrete categories (e.g., 1–5). The probability–consequence risk matrix is the most widely applied instrument within this category. Semi-quantitative approaches are particularly useful in emergency or data-limited contexts, where rapid operational decisions are required. However, they introduce discretization effects and may involve subjective threshold selection.

Qualitative Risk Assessment describes risk in non-numerical terms (e.g., low, medium, high), relying predominantly on expert judgment without explicit numerical modeling. While useful for preliminary screening, qualitative approaches lack reproducibility and statistical transparency.

In the present study, a hybrid framework is adopted, combining quantitative exceedance probability estimation based on measured methane concentrations with a semi-quantitative 5 × 5 probability–consequence matrix for operational risk classification,

Table 1. Comparison of risk assessment approaches.

Method	Advantages	Limitations	Applicability in the Lupeni Case Study
Risk Matrix (present study)	Simple, intuitive, transparent; rapid decision-support; applicable with limited data	Ordinal discretization; potential subjectivity in scale thresholds; limited representation of nonlinear interactions	Highly suitable for emergency urban decision-making
Monte Carlo Simulation	Full uncertainty quantification; probabilistic output distributions; scenario testing capability	Requires statistically defined input distributions; computationally intensive	Complementary tool; applied in associated modeling work
Bayesian Analysis	Integrates prior knowledge with new evidence; adaptive updating	Requires prior distribution specification; model complexity	Potentially useful for long-term monitoring updates
FORM/SORM	Explicit failure probability estimation; theoretically rigorous reliability-based framework	Requires probabilistic characterization of all governing variables	Conceptually compatible; future extension of the framework

.

Additional theoretical clarification:

The selection of a semi-quantitative matrix-based framework for the operational phase is justified by

• The limited availability of statistically characterized subsurface transport parameters.
• The need for rapid classification during emergency conditions.
• The requirement for transparency and reproducibility in urban risk governance.

However, by formally defining the hazardous state (see Section 2.1), the proposed framework remains compatible with reliability-based extensions, ensuring methodological scalability.

2.3. Factors Influencing Abandoned Mine Methane (AMM) Emissions

Methane emissions from abandoned coal mines represent a multi-factorial process controlled by geological structure, residual gas storage conditions, hydrogeological dynamics, atmospheric forcing, and anthropogenic disturbance. Unlike active mining systems, where ventilation and degassing are engineered and monitored, abandoned systems evolve under uncontrolled post-closure conditions.

The literature indicates that AMM migration toward the surface is governed by a combination of

• Gas generation and desorption mechanisms;
• Permeability pathways and structural discontinuities;
• Hydrostatic displacement processes;
• Barometric pressure variations;
• Urban infrastructure interaction [3,4,5,6,11].

In order to ensure a systematic risk assessment, influencing factors were identified through

• Review of international case studies and scientific literature;
• Analysis of historical mining documentation;
• Field observations during monitoring campaigns;
• Expert consultation within the project team.

A total of 42 influencing factors were identified and grouped into seven categories, reflecting both static (structural) and dynamic (time-dependent) controls. The distinction between static and dynamic factors is relevant for risk assessment, as static factors define baseline vulnerability, whereas dynamic factors modulate short-term hazard activation (

Table 2. Influencing factors controlling AMM emissions.

Category	Main Factors	Symbol	Type	Variability	Determination Method
Geological	Permeability, porosity, tectonic factor, lithology	K, φ, ftect	Static	Permanent	Core analysis, pumping tests, geological maps
Mining	Void volume, residual CH4 content, reservoir pressure, depth, sealing integrity	Vgol, Crez, Prez, h, E	Static	Permanent	Mining plans, laboratory analysis
Hydrogeological	Groundwater level, seasonal fluctuation, capillary pressure	hw, Δhw, Pc	Dynamic	Seasonal	Piezometers, historical hydro data
Meteorological	Atmospheric pressure, barometric trend, temperature, humidity, wind, precipitation	Patm, dP/dt, T	Dynamic	Rapid (hours–days)	Meteorological stations, real-time sensors
Anthropogenic	Excavations, vibrations, sealing quality, illegal works	fanthro	Dynamic	Abrupt	Construction records, field inspection
Biological	Microbial oxidation, biogenic methane production, vegetation cover	vox, Qbio	Dynamic	Seasonal	Soil analysis, literature data
Special phenomena	Critical threshold behavior, hysteresis, temporal inertia, domino effect	Pcr, αh, τh	Dynamic	Variable	Experimental and field determination

, Figure 1).

2.3.1. Static vs. Dynamic Controls

Static factors (geological and mining-related) define the intrinsic methane storage potential and structural connectivity of abandoned workings. These parameters evolve slowly and represent the baseline susceptibility of the site.

Dynamic factors (hydrogeological, meteorological, anthropogenic, biological) act as triggering mechanisms. For example,

• Rising groundwater levels may displace accumulated gas upward (“hydraulic piston effect”).
• Rapid barometric pressure drops may enhance methane exsolution and migration.
• Construction works may create preferential migration pathways.

This distinction is critical in operational risk assessment, as static vulnerability does not automatically imply immediate hazard unless dynamic activation conditions occur.

2.3.2. Integration into Risk Assessment

The identification of influencing factors serves three purposes:

Contextualization of measured methane concentrations within a mechanistic framework.

Support for consequence evaluation (e.g., infrastructure vulnerability).

Foundation for potential future probabilistic modeling (e.g., reliability-based extensions).

While not all 42 factors are explicitly parameterized in the present semi-quantitative model, their structured classification ensures transparency and scalability of the framework.

2.4. Risk Matrix and Risk Classification

2.4.1. Definition of Probability and Consequence Scales

For semi-quantitative risk evaluation, standardized ordinal scales are defined and adapted to the specific context of methane emissions from abandoned coal mines [21,24,26]. The correspondence between the quantitative exceedance probability $P(C>3\%)$ and the ordinal 1–5 probability scale is presented in

Table 3. Probability Scale (P).

Level	Descriptor	Description	P(C > 3%)	Quantitative Criterion
1	Rare	The event is possible only under exceptional conditions	<0.10	P < 10%
2	Unlikely	The event is possible but not expected	0.10–0.25	10% ≤ P < 25%
3	Possible	The event may occur under certain circumstances	0.25–0.50	25% ≤ P < 50%
4	Likely	The event is expected in most circumstances	0.50–0.75	50% ≤ P < 75%
5	Frequent	The event is almost certain	>0.75	P ≥ 75%

.

The consequence scale (C) is presented in

Table 4. Consequence scale (C) for urban methane hazards.

Level	Descriptor	Description	Human Exposure	Economic Damage
1	Minor	Localized effects, no casualties	0 injuries	<10,000 EURO
2	Moderate	Local effects, minor injuries	1–5 injuries	10,000–100,000 EURO
3	Severe	Extended effects, possible fatalities	6–20 injuries or 1 fatality	0.1–1.0 million EURO
4	Major	Major impact, multiple casualties	21–50 injuries or 2–5 fatalities	1–10 million EURO
5	Catastrophic	Catastrophic impact, multiple fatalities	>50 injuries or >5 fatalities	>10 million EURO

Economic damage ranges are expressed in nominal EUR values for indicative consequence ranking only; they are not adjusted for inflation and do not represent a formal economic loss model. The defined thresholds reflect industrial safety standards and documented case severity in ground gas incidents.

.

The consequence scale integrates human exposure and material damage indicators relevant to urban methane-related hazards (Table 4).

2.4.2. Determination of Consequence Weights Using AHP

To determine the relative contribution of each consequence component, the Analytic Hierarchy Process (AHP) was applied [27] using a panel of five experts (two mining engineers, one geologist, one public safety specialist, and one urban planner) who performed pairwise comparisons among the three primary consequence dimensions—explosive potential $\left(C_{exp}\right)$, human exposure $\left(C_{hum}\right)$, and infrastructure vulnerability $\left(C_{infr}\right)$; the median pairwise comparison matrix (reported above) was adopted as the group judgment to reduce sensitivity to individual outliers. The normalized principal eigenvector of this matrix yields the weight vector

$$w=(w_{exp},w_{hum},w_{infr})=(0.63, 0.26, 0.11)$$

(5)

with $\sum w_i=1$, indicating that explosive potential carries the largest contribution to the aggregated consequence score, followed by human exposure and infrastructure vulnerability. Hereafter, $C$ denotes the AHP-weighted aggregated consequence score, while $C_{exp}$, $C_{hum}$, and $C_{infr}$ denote the corresponding component ratings assigned on the 1–5 ordinal severity scale defined in the consequence scheme; the overall consequence score is computed as

$$C=w_{exp}{C}_{exp}+w_{hum}{C}_{hum}+w_{infr}{C}_{infr}=0.63\hspace{0.17em}{C}_{exp}+0.26\hspace{0.17em}{C}_{hum}+0.11\hspace{0.17em}{C}_{infr}$$

(6)

Consistency of expert judgments was verified using the Saaty consistency ratio:

$${\lambda }_{max}=3.05$$

(7)

$$CI=({\lambda }_{max}-n)/(n-1)=(3.05-3)/(3-1 )=0.025$$

(8)

$$CR=CI/RI=0.025/0.58=0.043<0.10(\mathrm{with} RI=0.58 \mathrm{f}\mathrm{or} n=3)$$

(9)

confirming acceptable logical coherence of the pairwise comparisons and supporting the reliability of the derived weights (Figure 2). Pairwise judgments were aggregated using the median to reduce sensitivity to outliers in expert scoring.

Because consequence severity in urban methane incidents cannot be measured directly from a single physical variable, AHP was used to formalize expert judgment in a transparent and reproducible way. Although some subjectivity is unavoidable, the use of a multidisciplinary five-expert panel, median aggregation of pairwise judgments, and a low consistency ratio (CR = 0.043) substantially reduces arbitrariness and supports the reliability of the derived weights.

2.4.3. Risk Level and Recommended Actions

The overall risk score is computed as $R=P\times C$, where P is the probability score assigned from the exceedance-based probability scale, and C is the AHP-weighted aggregated consequence score; the resulting R values are then mapped to the five risk classes defined by the matrix to support consistent hotspot ranking and prioritization of monitoring and mitigation actions (

Table 5. Risk level and recommended actions.

Risk Score (R)	Risk Level	Color Code	Recommended Actions
1–4	Low	Green	Routine monitoring
5–9	Moderate	Yellow	Increased monitoring and preventive planning
10–16	High	Orange	Planning and implementation of mitigation measures
17–25	Critical	Red	Immediate remediation and emergency intervention

).

Figure 3 presents the 5 × 5 probability–consequence matrix used for semi-quantitative risk evaluation. Risk categories are classified as Low (L), Moderate (M), High (H), and Critical (C). The highlighted cell, symbolized by the black square, illustrates the application of the framework to the Lupeni case study (P = 5, C = 5), corresponding to R = 25, classified as Critical.

For matrix-based classification, the aggregated consequence score C is mapped to the nearest ordinal level (1–5) to ensure consistency with the discrete probability–consequence matrix.

2.5. Quantitative Indicators for Risk Assessment

2.5.1. Exceedance Probability of Critical Thresholds

To quantify the probability of exceeding critical methane concentration thresholds, the following frequentist estimator is used [23]:

$$P(C_{C{H}_4}>C_{crit})={\displaystyle \frac{n_{exceed}}{N_{total}}}$$

(10)

where:

$n_{exceed}$ represents the number of measurements exceeding the critical threshold,

$N_{total}$ represents the total number of observations.

Validity condition: $n·\widehat{p}>5$ and $n·\left(1-\widehat{p}\right)>5$.

These conditions indicate that both the expected number of exceedances and non-exceedances must be sufficiently large for normal-approximation-based interval formulas to be reliable.

In the present study, this criterion is used only as a general validity check; the reported confidence intervals are based on Wilson and exact binomial methods.

For the global assessment, observations are treated as operational replicates:

$$N_{total}=41 \mathrm{monitoring} \mathrm{points}\times 3 \mathrm{campaigns}=123$$

(11)

Although measurements are repeated at the same monitoring points, the global exceedance probability is interpreted as an operational frequency indicator. Temporal dependence between repeated measurements at identical locations is evaluated separately using repeated-measures statistical tests (repeated-measures ANOVA and/or the Friedman test), thereby preventing inflation of the independence assumption.

This approach allows separation between frequency-based exceedance estimation (for risk matrix classification) and statistical inference on temporal variability.

The global exceedance estimate is interpreted as an operational frequency across monitoring operations; dependence at repeated locations is assessed separately via repeated-measures tests.

2.5.2. Confidence Interval for Probability Estimation

To quantify estimation uncertainty, 95% confidence intervals were calculated using methods appropriate to sample size and proportion extremes.

For global exceedance probabilities based on the full monitoring dataset ($n=123$ operational observations), confidence intervals were computed using the Wilson score interval, which provides more reliable coverage than the Wald approximation, especially for moderate sample sizes and proportions not centered near 0.5.

For localized point-level assessments with very small sample sizes (e.g., three campaigns at a single monitoring point) and/or extreme proportions ($\widehat{p}\to 0$ or $\widehat{p}\to 1$), the exact Clopper–Pearson binomial interval was used.

Accordingly, the confidence intervals reported in Section 4.1 for global exceedance frequencies are based on the Wilson score method, whereas hotspot-specific extreme cases, such as point P2 with 3/3 exceedances above the 3% vol. threshold, are reported using the exact Clopper–Pearson method.

This dual approach ensures statistically robust uncertainty quantification for both area-scale exceedance frequencies and localized hotspot persistence.

2.5.3. Explosive Hazard Index

To quantify proximity to explosive conditions, an index relative to the Lower Explosive Limit (LEL) is defined [4] as

$$I_{LEL}={\displaystyle \frac{C_{C{H}_4}}{LEL}}\times 100\%$$

(12)

where $C_{C{H}_4}$ is the measured methane concentration (% vol.) and $LEL=4.4\%$ vol. (v/v) for methane in air. An operational alert threshold of 3% vol. CH₄ is adopted in this study; this corresponds to approximately 68% of the LEL (3/4.4 = 0.682) and is used as a conservative early-warning level to trigger intensified monitoring and mitigation assessment before explosive conditions are reached. The 3% vol. threshold is adopted as an early-warning operational trigger (~68% of LEL), enabling intervention before flammable conditions are reached. The interpretation of $I_{LEL}$ and the associated explosive consequence component $C_{exp}$ are summarized in

Table 6. Interpretation of the Explosive Hazard Index.

${\mathit{I}}_{\mathit{L}\mathit{E}\mathit{L}}$	Hazard Level	Assigned Explosive Component, ${\mathit{C}}_{\mathit{e}\mathit{x}\mathit{p}}$
<30%	Low	1
30–50%	Moderate	2
50–70%	Elevated	3
70–100%	High	4
≥100%	Imminent explosive condition	5

below. Values exceeding 100% indicate methane concentrations equal to or above the LEL under confined conditions. The explosive component $C_{exp}$ derived from $I_{LEL}$ is subsequently integrated into the aggregated consequence score using the AHP-derived weights (Section 2.4.2).

The categorical mapping is used for consequence scoring and does not replace regulatory safety assessments of explosive atmospheres.

2.6. Limitations of Risk Matrices

Risk matrices, although widely applied in industrial and environmental risk assessment, exhibit several well-documented methodological limitations [25], including (i) boundary effects, where small differences in quantitative input values may shift classification across ordinal categories without meaningful changes in hazard magnitude; (ii) loss of quantitative information, as continuous variables are mapped to discrete ordinal levels, reducing numerical resolution; (iii) scaling subjectivity, since the definition of thresholds separating ordinal levels may involve expert judgment; and (iv) aggregation simplification, because the multiplicative combination $R=P\times C$ assumes proportional interaction between probability and consequence and may mask nonlinear or systemic interactions. Despite these limitations, risk matrices remain widely used due to their transparency, operational simplicity, and decision-support utility, particularly in emergency contexts where rapid prioritization is required.

Beyond these general limitations, it is essential to distinguish between aleatory and epistemic uncertainty in AMM risk assessment [18,19]. Aleatory uncertainty (irreducible variability) arises from natural randomness in the system, such as fluctuations in barometric pressure affecting gas migration, spatial heterogeneity of permeability and fracture networks, and temporal variability in residual methane desorption rates; it cannot be reduced through additional measurements and must be represented probabilistically. Epistemic uncertainty (reducible uncertainty) stems from incomplete knowledge, including limited documentation of historical mine workings, restricted temporal coverage of methane measurements (three campaigns), unknown efficiency of historical seals, and simplifying assumptions in the conceptual migration model; it can be reduced through additional data collection, improved site investigation, and refined modeling. Practically, aleatory uncertainty should be incorporated into probability estimates (e.g., through confidence intervals), while epistemic uncertainty motivates adaptive monitoring and conservative decision thresholds; in the Lupeni case, the confidence intervals reported in Section 4.1 support this interpretation, and the residual epistemic component justifies continued post-intervention monitoring within the URBAN-MINE-RISK algorithm.

To mitigate methodological limitations in the present study and position the framework appropriately, the following measures are adopted: (a) explicit quantitative-to-ordinal correspondence by mapping exceedance probabilities to ordinal probability levels using defined thresholds (Table 3); (b) uncertainty quantification through confidence intervals for probability estimates (Section 2.5.2), providing an uncertainty envelope rather than relying solely on point estimates; (c) structured consequence weighting via AHP with formal consistency verification (CR < 0.10), reducing subjective bias; (d) comparison against a quantitative reliability-oriented approach (FORM) in Section 4.7 for methodological cross-validation; and (e) a formal limit-state definition (Section 2.1) to ensure theoretical compatibility with reliability-based methods. Accordingly, the proposed framework does not aim to replace fully quantitative probabilistic modeling, but to provide a transparent and operationally robust decision-support tool for post-mining urban environments where complete probabilistic characterization is not available, decision timelines are constrained, and public safety requires clear prioritization.

3. Case Study: Lupeni Urban Perimeter

3.1. Urban Context and Mining Legacy

The municipality of Lupeni is located in the Jiu Valley, Romania, a region with more than 130 years of underground coal mining activity. The Lupeni Mine operated between 1884 and 2015, exploiting coal seams No. 3, 4, 5, 8/9, 13, 14, and 15 at depths ranging between 300 and 800 m, primarily using the longwall top coal caving (LTCC) method. Urban expansion progressively developed above former underground workings, largely without long-term land-use planning that accounted for post-closure gas migration hazards; consequently, residential infrastructure now overlaps abandoned galleries, collapsed panels, and fault-controlled migration pathways. From a structural geology perspective, the area is defined by a NW–SE oriented syncline intersected by numerous faults with dominant N–S and NNW–SSE orientations. A major N–S fault crosses Strada Minerilor, precisely in the sector where methane emissions were detected [28]. This tectonic discontinuity likely acts as a preferential migration pathway for residual mine gases from deeper coal seams toward shallow overburden and surface structures. The combination of

• Abandoned underground voids,
• Fault-controlled permeability,
• Shallow urban foundations, and
• Newly installed subsurface utilities create favorable conditions for localized methane accumulation.

Together, these factors justify a site-specific monitoring strategy in the urban perimeter.

3.2. Triggering Event

In August 2024, a newly installed natural gas distribution pipeline on Strada Minerilor underwent mandatory pressure and tightness testing prior to commissioning (Figure 4) [29]. Unexpected methane concentrations were detected during these routine operational tests, and within only four days after commissioning, methane levels of up to 54% vol. were measured in monitoring boreholes located near the pipeline alignment [29] (Figure 5). This concentration significantly exceeds the operational alert threshold adopted in this study (3% vol.) and the lower explosive limit (LEL = 4.4% vol.), indicating near-pure methane accumulation in localized zones; consequently, immediate delineation of the affected area and source identification were initiated.

Utility trench excavation and backfilling can create a preferential high-permeability corridor and local pressure relief, facilitating upward gas migration from legacy voids/faulted zones into shallow utility structures. This mechanism explains the rapid emergence of high CH₄ concentrations shortly after commissioning

3.3. Monitoring Network and Measured Data

A total of 41 monitoring points (P0–P40) were installed, and the monitoring network was deployed adaptively by expanding outward as the spatial extent of emissions became progressively delineated. Three measurement campaigns were conducted on 14 August 2024, 29 August 2024, and 17 September 2024. All measurements were performed under relatively stable meteorological conditions to minimize atmospheric influence on surface concentration variability [29,30] (

Table 7. Meteorological conditions—Lupeni weather station (WMO 15296) [30].

Date and Time	Temperature (°C)	Pressure (hPa)	Humidity (%)	Wind Speed and Direction (km/h)	Precipitation (mm)
14 August 2024, 12:00	23.8	945.9	57.1	4.3 (NE)	0.0
29 August 2024, 12:00	20.3	947.1	67.4	6.3 (E–NE)	0.0
17 September 2024, 12:00	11.4	948.8	74.4	2.6 (N)	0.0

CH₄ was measured in borehole screening points using a calibrated field gas analyzer (Sewerin EX-TEC HS 660; Hermann Sewerin GmbH, Gütersloh, Germany), with daily calibration using certified standard gas. According to the manufacturer’s specifications, the instrument provides a methane response time of t90 < 17 s and a warm-up time < 30 s; measurements were recorded only after stabilization of the displayed value. The instrument resolution for methane measurements is 0.1% vol. in the range 0–9.9% vol.; values reported as 0 indicate concentrations below the instrumental resolution/detection capability.

). To evaluate whether meteorological variability could have biased the measured methane concentrations, conditions were compared across the three campaigns and examined against spatial and temporal methane patterns. All campaigns were conducted under dry conditions (0 mm precipitation) and low wind speeds (<7 km/h), reducing atmospheric dilution effects; importantly, methane was measured in boreholes (subsurface screening points), where wind-driven mixing is negligible compared with open-air surveys. Representative methane concentrations (% vol.) at selected monitoring points are summarized in

Table 8. Representative methane concentrations (% vol.).

Point	14 August 2024	29 August 2024	17 September 2024	Mean
P2	36	54	28	39.3
P5	20	42	18	26.7
P0	20	20	18	19.3
P1	14	28	22	21.3
P23	17	6	4	9.0
P24	18	11	16	15.0
P36	4	15	14	11.0

. Point P2 consistently recorded the highest concentrations across all campaigns, reaching a maximum of 54% vol., thereby defining a persistent methane hotspot. The spatial gradient observed from P2 outward indicates localized accumulation rather than diffuse background emission.

Point P2 consistently recorded the highest concentrations across all campaigns, reaching a maximum of 54% vol., thereby defining a persistent methane hotspot.

The spatial gradient observed from P2 outward indicates localized accumulation rather than diffuse background emission.

3.4. Gas Chromatographic Analysis

To determine the origin of the detected methane, gas samples from boreholes P2 and P5 were subjected to chromatographic analysis and compared with the composition of gas from the public distribution network,

Table 9. Gas composition: boreholes vs. public network.

Component	Public Network	Borehole P2	Borehole P5	Interpretation
CH4 (%)	98.31	16.63	0.0113	Variable concentration
C2H6 (%)	0.68	0.0755	0.000049	Altered ratio
CO2 (%)	0.78	0.95	0.517	Present
CO (%)	0	0.00024	Present	Mining gas marker [31]
C2H2 (%)	0	Present	0	Mining gas marker [31]

.

The detection of carbon monoxide (CO) and acetylene (C₂H₂)—both absent in the public gas distribution network—constitutes strong evidence of a mining-related origin [29,31]

Moreover, the altered methane-to-ethane ratio further supports differentiation from the thermogenic gas composition of the public supply.

These results confirm that the emissions are not attributable to leakage from the newly installed gas pipeline but instead originate from residual mine gas migration through geological discontinuities and abandoned workings.

4. Results and Discussion

4.1. Quantitative Probability Assessment

Repeated-measures analyses treat the 41 monitoring points as paired subjects measured across the three campaigns (within-subject factor: campaign date).

Table 10. Frequency of exceedance of critical methane thresholds and $95\%$ confidence intervals (n = 123 observations).

Threshold	14 August	29 August	17 September	Total	P(C > Threshold)	95% CI
>1%	16	20	20	56	56/123 = 0.46	[0.37–0.54]
>3%	13	16	14	43	43/123 = 0.35	[0.27–0.44]
>10%	9	10	7	26	26/123 = 0.21	[0.15–0.29]

summarizes the frequency of exceedance of critical methane thresholds and the associated 95% confidence intervals based on $n=123$ observations. Exceedance of the 1% vol. threshold is used exclusively as a screening (pre-alert) indicator, whereas risk classification through the $P\times C$ matrix is performed using the operational alert threshold of 3% vol. CH₄. For the critical hotspot P2, exceedance above 3% was observed in all three campaigns:

(p̂ = P(C > 3%) = 3/3 = 1.00)

(13)

The corresponding 95% confidence interval was computed using the exact Clopper–Pearson binomial method, appropriate for extreme proportions, yielding

$$C{I}_{95\%}=\left[0.885\hspace{0.17em}–\hspace{0.17em}1.00\right]$$

(14)

confirming persistence of threshold exceedance at the hotspot (Figure 6).

Temporal Variability Analysis

Because the same 41 monitoring points were measured during all campaigns, repeated-measures statistical tests were applied. Normality was evaluated using the Shapiro–Wilk test and homogeneity of variances using Levene’s test; Shapiro–Wilk indicated non-normal distributions ($p\ll 0.001$), while Levene’s test did not indicate significant variance heterogeneity ($p=0.569$). Although repeated-measures ANOVA yielded $F\left(\mathrm{2,80}\right)=2.416$, $p=0.0958$, ${\eta }_{partial}^2=0.057$ (not statistically significant), Inference relied primarily on the non-parametric Friedman test due to non-normality. The Friedman test indicated a statistically significant global temporal effect, ${\chi }^2\left(2\right)=6.804$, $p=0.0333$; however, the associated effect size was small (Kendall’s $W=0.083$). Post hoc pairwise comparisons (Wilcoxon signed-rank with Holm correction) showed that the significant contrast was primarily between 29 August 2024 and 17 September 2024 ($p_{Holm}=0.036$). Importantly, despite this small temporal effect, the magnitude of variation remains minor relative to the extreme values recorded at hotspot P2 (maximum 54% vol.), and the spatial hierarchy of high-concentration points remained stable across campaigns. Therefore, the global exceedance probability for the operational alert threshold is taken as $P(C>3\%)=43/123=0.35$ for risk classification purposes. Compared with previous studies that addressed AMM mainly through concentration mapping, case reporting, or emission characterization, the present study contributes an integrated operational framework that combines repeated field monitoring, exceedance-based probability estimation, AHP-weighted consequence evaluation, and a decision algorithm for intervention prioritization. This integration represents the main methodological novelty of the study. Accordingly, P(C > threshold) should be interpreted as an operational exceedance frequency across monitoring observations, not as the probability of independent realizations in the strict statistical sense.

4.2. Consequence Assessment

As shown in Figure 7a–c, the CH₄ isoconcentration maps derived from the three monitoring campaigns consistently identify hotspot P2 as the area with the highest methane concentrations and repeated exceedances of the 3%, 10%, and 20% vol. thresholds. These spatial patterns support the consequence assessment by confirming the persistence of a localized high-risk zone under repeated monitoring conditions.

For hotspot P2, the maximum recorded methane concentration was $C_{\mathrm{m}\mathrm{a}\mathrm{x}}=54\%\hspace{0.17em}\mathrm{vol}.$. The explosive proximity index is therefore

$$I_{LEL}=(54/4.4)\times 100=1227\%,$$

(15)

which greatly exceeds the lower explosive limit and corresponds to the maximum explosive hazard category, $C_{exp}=5$. The maximum measured concentration at P2 (54% vol.) is approximately 12.3 times the lower explosive limit (LEL = 4.4% vol.), indicating an extreme explosive hazard under confined conditions.

The affected area is located within a densely populated urban sector of Lupeni (~23,000 inhabitants; density > 2000 inhabitants/km²); according to the predefined consequence scale, this yields the maximum human exposure score, $C_{hum}=5$. The hotspot is also in immediate proximity to critical infrastructure, including a newly installed natural gas pipeline as well as sewer and potable water networks, which increases the likelihood of confined gas accumulation and potential cascading effects; accordingly, the infrastructure vulnerability score is set to $C_{infr}=5$.

Scores $C_{hum}=5$ and $C_{infr}=5$ follow Table 4 criteria for dense urban exposure and immediate proximity to confined utility infrastructure with cascading potential.

Using the AHP-derived weights, the aggregated consequence is computed as

$$C=0.63\hspace{0.17em}{C}_{exp}+0.26\hspace{0.17em}{C}_{hum}+0.11\hspace{0.17em}{C}_{infr}$$

(16)

Substituting the component scores gives

$$C=0.63\left(5\right)+0.26\left(5\right)+0.11\left(5\right)=3.15+1.30+0.55=5.0,$$

(17)

confirming that the aggregated consequence reaches the maximum value ($C=5$) and indicating catastrophic potential consequences under plausible worst-case conditions.

4.3. Spatial Stability Analysis

To evaluate the persistence of the spatial methane pattern, Spearman’s rank correlation was computed between campaigns using the 41 monitoring points as paired observations. The analysis indicates moderate but significant agreement between 14 August and 29 August ($\rho =0.573$, $p<0.001$) and between 14 August and 17 September ($\rho =0.583$, $p<0.001$), and a very high agreement between 29 August and 17 September ($\rho =0.970$, $p<0.001$), demonstrating near-identical spatial ordering of concentration levels in the latter two campaigns. Overall, these results show that the spatial hierarchy of monitoring points remained stable over time, the hotspot persisted in the same sector, and the methane distribution is primarily controlled by subsurface structural factors rather than short-term environmental variability.

The near-unity correlation between 29 August and 17 September indicates that hotspot ranking is highly persistent, supporting structural control rather than transient forcing.

4.4. Assessment of Meteorological Influence

Meteorological conditions remained relatively stable across campaigns, with no precipitation, wind speeds below 7 km/h, and only marginal atmospheric pressure variation (ΔP ≈ 2.9 hPa). Methane was measured in boreholes (subsurface screening points), where direct wind-driven dilution is negligible; although barometric pumping can influence soil-gas migration, the absence of abrupt pressure drops during the measurement periods reduces the likelihood of pressure-driven transient degassing dominating the observations. Importantly, despite minor temporal differences detected by statistical tests (Section 4.1), the strong inter-campaign spatial rank stability (Spearman ρ, up to 0.97) indicates that meteorological variability was not the primary driver of the observed concentration patterns. Overall, the combined statistical and physical evidence supports dominant structural control of methane migration through mining-related pathways (faults/voids and utility corridors), with meteorology acting only as a minor short-term modulator.

Meteorological stability documented in Table 7 supports interpreting temporal differences as secondary modulation rather than primary control

4.5. Risk Evaluation Using the P × C Matrix

Risk was quantified by integrating the probability of exceeding the operational alert threshold (3% vol. CH₄) with the severity of consequences estimated according to the methodology described in Section 2.4. The risk score is defined as $R=P\times C$, where $P$ represents the probability level (ordinal scale 1–5, Table 3) and $C$ represents the consequence level (ordinal scale 1–5, Table 4). For the full dataset comprising 41 monitoring points across three campaigns ($n=123$ observations), the global exceedance probability of the 3% vol. threshold is $P(C>3\%)=43/123=0.35$. Because $43/123=0.35$, the global exceedance maps to $P=3$ (‘Possible’) per Table 3, yielding $R=15$ for area-scale prioritization. According to the probability scale defined in Table 3, this value falls within the interval 0.25–0.50, corresponding to $P=3$ (“Possible”), meaning the event may occur under certain circumstances within the monitored urban perimeter. The consequence level is conservatively evaluated at the maximum plausible level, $C=5$ (“Catastrophic”), because confined gas accumulation and ignition could produce severe outcomes, given the extreme explosive potential quantified in Section 4.2, the high population density, and the vulnerability of subsurface infrastructure, importantly, this classification does not imply that catastrophic damage has occurred, but that the theoretical impact potential is severe if an ignition scenario were to develop. The resulting risk score for the general monitored area is therefore $R=3\times 5=15$, which falls in the high-risk band defined in Table 5 (10–16), supporting intensified monitoring and mitigation planning at the area scale.

In contrast, the operational hotspot P2 represents a localized critical condition. At monitoring point P2, the 3% vol. threshold was exceeded in all three campaigns ($P(C>3\%)=3/3=1.00$), corresponding to $P=5$ (“Frequent”). For localized critical points, probability is interpreted at the point scale as a recurrence score across campaigns because the objective is hotspot identification rather than long-term regional frequency estimation. The consequence level remains $C=5$ (“Catastrophic”), and the risk score for P2 is $R=5\times 5=25$, corresponding to critical risk and requiring immediate technical mitigation according to Table 5. This classification is also consistent with the 5 × 5 probability–consequence matrix (Figure 3), where the general-area position (P = 3, C = 5) lies in the high-risk domain, while the hotspot position (P = 5, C = 5) occupies the extreme critical cell. The contrast between the general area and the localized hotspot highlights pronounced spatial heterogeneity of risk and justifies targeted intervention and continued post-intervention monitoring.

4.6. Risk Scenarios and Operational Interpretation

To strengthen the risk evaluation, three operational scenarios were defined to reflect realistic urban gas migration pathways and to translate the $P\times C$ results into actionable field conditions. S1—Accumulation in confined utility structures: methane concentrations exceeding 3% vol. in boreholes adjacent to utility corridors indicate potential accumulation in poorly ventilated underground structures (manholes, cable ducts, sewer chambers); for hotspot P2, $P=5$, $C=5$, therefore $R=25$ (“Critical”), representing the highest-priority operational scenario. S2—Migration toward residential basements: gas migration through preferential pathways (faults, utility trenches, backfilled excavations) may lead to accumulation beneath or within residential buildings; at the general area scale, the global exceedance probability $P(C>3\%)=0.35$ maps to $P=3$ (“Possible”) and, with $C=5$, yields $R=15$ (“High”), supporting intensified monitoring and preventive ventilation planning where warranted. S3—Interaction with subsurface infrastructure: gas accumulation near pipelines, sewer networks, and foundations may increase indirect hazard exposure; in this scenario, risk is evaluated as a function of proximity to infrastructure, density of underground utilities, and confinement potential, and in sectors adjacent to P2, this condition approaches the high–critical boundary, justifying conservative operational controls (

Table 11. Risk classification and recommended actions.

Risk Score (R)	Classification	Recommended Action
1–4	Low	Routine monitoring
5–9	Moderate	Increased monitoring and preventive planning
10–16	High	Planning and implementation of mitigation measures
17–25	Critical	Immediate remediation and emergency intervention

).

Overall, the obtained scores indicate a localized critical risk at P2 and a high risk classification for the broader monitored area, and this spatial differentiation is essential for proportional resource allocation and targeted intervention.

4.7. Sensitivity Analysis of the Risk Matrix

To evaluate classification robustness, a one-level variation of $P$ and $C$ was tested for hotspot P2 (

Table 12. Sensitivity analysis—hotspot P2.

Scenario	P	C	R	Risk Level	Variation
Base case	5	5	25	Critical	–
P = 4	4	5	20	Critical	Reduced but remains critical
C = 4	5	4	20	Critical	Reduced but remains critical
P = 4, C = 4	4	4	16	High	Category changes

). The results show that reducing either probability or consequence by one level ($P=4$ or $C=4$) lowers the risk score to $R=20$, but the classification remains critical, whereas a simultaneous reduction in both ($P=4$, $C=4$) yields $R=16$ and downgrades the category to high. To further evaluate robustness with respect to the subjective component of the AHP weighting, a sensitivity analysis was performed on the consequence weights derived from the expert panel (

Table 13. Sensitivity analysis of AHP weights (hotspot P2).

Scenario	${\mathit{w}}_{\mathit{e}\mathit{x}\mathit{p}}$	${\mathit{w}}_{\mathit{h}\mathit{u}\mathit{m}}$	${\mathit{w}}_{\mathit{i}\mathit{n}\mathit{f}\mathit{r}}$	C (Aggregated)	C (Ordinal)	R	Risk Level
Nominal	0.63	0.26	0.11	5.00	5	25	Critical
Exp +20%	0.76	0.18	0.06	5.00	5	25	Critical
Exp −20%	0.50	0.35	0.15	5.00	5	25	Critical
Hum +20%	0.53	0.36	0.11	5.00	5	25	Critical
Hum −20%	0.73	0.16	0.11	5.00	5	25	Critical
Infr +20%	0.60	0.25	0.15	5.00	5	25	Critical
Infr −20%	0.66	0.27	0.07	5.00	5	25	Critical

). The nominal weights $\left(w_{exp}=0.63, w_{hum}=0.26, w_{infr}=0.11\right)$ were varied by ±20% while maintaining $\sum w_i=1$; for each case, the aggregated consequence score $C$ was recalculated for hotspot P2 and mapped to the nearest ordinal level. Across all tested weight variations, the aggregated consequence score remained at the maximum level ($C=5$), which is expected because the component ratings for P2 are consistently maximal ($C_{exp}=C_{hum}=C_{infr}=5$), making the aggregated score insensitive to moderate weight changes. Overall, these results demonstrate that the classification of hotspot P2 as a critical risk ($R=25$) is robust with respect to one-level perturbations in probability and consequence (Table 12) and to reasonable uncertainty in expert-derived AHP weights (Table 13). Only a simultaneous reduction in both probability and consequence levels would downgrade the classification from critical to high; given the repeated exceedance of 3% vol., the extreme explosive proximity index ($I_{LEL}=1227\%$), and the dense urban exposure, such a simultaneous downgrade is not supported by the current measurements. Therefore, the critical risk classification for hotspot P2 is methodologically stable and decision-relevant.

4.8. Intervention and Validation of Results

Methane emissions after mine closure are conceptualized using an exponential decay model,

$$E\left(t\right)=E_0{e}^{-kt}$$

(18)

where $E_0$ represents the initial emission level, $k$ is the decay coefficient, and $t$ is the time since intervention or closure. The exponential decline hypothesis reflects first-order degassing behavior commonly used to describe post-mining methane emission reduction. In Figure 8, shaded bands represent uncertainty ranges of the decay coefficient $k$, while vertical dashed lines indicate the half-life,

$$t_{1/2}=\mathrm{l}\mathrm{n}\left(2\right)/k$$

(19)

Two mitigation trajectories are illustrated: a no-drainage scenario (natural attenuation) and a controlled drainage/mitigation scenario implemented following the risk assessment.

Following the classification of hotspot P2 as a critical risk, a controlled drainage system was connected to the former mine degassing infrastructure. Post-intervention monitoring demonstrated a rapid and progressive decline in methane concentrations (

Table 14. Post-intervention concentration evolution (% vol.).

Date	P2	P5	P0	P24
17 September 2024	28	18	18	16
15 October 2024	12	8	10	7
15 November 2024	5	3	4	2
15 December 2024	2	1	1	0.5
15 January 2025	0.5	0.2	0.2	0
15 February 2025	0	0	0	0

). By February 2025, methane concentrations became instrumentally undetectable at the representative points, confirming the effectiveness of the mitigation system. Instrumental non-detect corresponds to $C_{C{H}_4}<$ LOD; reported zeros therefore indicate concentrations below detection rather than absolute absence. The monotonic decline observed across all monitored points supports controlled depressurization and source capture rather than random fluctuation. Importantly, the spatial hotspot hierarchy disappeared after intervention, further validating that the emission source was structurally connected to mine gas pathways.

The vertical dashed lines indicate the emission half-life, $t_{1/2}=\mathrm{l}\mathrm{n}2/k$, i.e., the time required for the methane emission rate to decrease to 50% of its initial value. The earlier dashed line corresponds to the controlled drainage/mitigation scenario, where the higher decay coefficient leads to a shorter half-life of approximately 3.5 years. The later dashed line corresponds to the no-drainage scenario, where the lower decay coefficient results in a longer half-life of approximately 6.9 years.

4.9. Uncertainty Analysis

Table 15. Sources of uncertainty in risk assessment.

Source	Type	Impact	Management Approach
Concentration measurement	Random	Medium	Daily calibration, standardized protocol
Spatial representativeness	Systematic	High	Adaptive network (41 points)
AHP weighting	Subjective	Medium	5-expert panel, CR verification
Probability scaling	Systematic	Medium	Explicit quantitative–ordinal mapping
Consequence modeling	Systematic	Low	Multi-factor aggregation, scenario validation

summarizes the main sources of uncertainty affecting the risk assessment, their type, expected impact, and the management approach adopted in this study. Measurement uncertainty was controlled through standardized sampling protocols and routine instrument calibration. The relatively dense monitoring network (41 points) reduced potential spatial under-sampling bias and improved representativeness of the observed concentration field. Although AHP weighting introduces expert subjectivity, the low consistency ratio (CR = 0.043) confirms logical coherence of judgments and supports the reliability of the derived weights. Uncertainty related to probability scaling was minimized through an explicit quantitative-to-ordinal correspondence between exceedance frequency and probability levels (Section 2.4). Overall, uncertainty sources were explicitly identified, classified, and methodologically managed, supporting the robustness of the final risk classification and the decision relevance of the proposed framework.

Uncertainty sources include both aleatory variability (environmental/system fluctuations) and epistemic uncertainty (limited historical and parameter information), managed here through CI, sensitivity testing, and conservative thresholds.

4.10. Remarks on Reliability-Based Quantitative Methods (Future Directions)

Advanced structural reliability methods, such as the First-Order Reliability Method (FORM), provide a rigorous probabilistic framework for evaluating the exceedance of a defined limit-state function $g\left(\mathrm{X}\right)$. In the context of AMM risk assessment, a representative limit state can be formulated as $g\left(\mathrm{X}\right)=C_{crit}-C_{C{H}_4}\left(\mathrm{X}\right)$, where $C_{crit}$ is the critical methane concentration threshold (e.g., 3% vol.) and $C_{C{H}_4}\left(\mathrm{X}\right)$ is the methane concentration predicted by a physical model as a function of random inputs $\mathrm{X}$. Typical inputs include overburden permeability $K$ (often modeled as lognormal), residual gas pressure $P_{res}$ in abandoned workings (normal), barometric pressure trend $dP/dt$ (extreme value), groundwater level $h_w$ (seasonal), and excavation volume $V_{exc}$ (triangular). The failure probability is then $P_f=P\left[g\right(\mathrm{X})\le 0]$. FORM approximates $P_f$ by transforming variables into standard normal space and linearizing the limit-state function at the most probable point of failure [23]. In the present case study—an operational emergency context with only three monitoring campaigns over six weeks—building a fully parameterized FORM model would require extensive additional assumptions about distributions of subsurface transport parameters, potentially introducing substantial modeling uncertainty in the absence of long-term time series and detailed geotechnical characterization. Nevertheless, the framework developed here (Section 2.1) explicitly defines the limit state $g\left(C_{C{H}_4}\right)=C_{crit}-C_{C{H}_4}$, ensuring conceptual compatibility with reliability-based methods and establishing a clear pathway for future FORM implementation once extended datasets become available through permanent monitoring. The relationship between the semi-quantitative matrix approach and FORM can be viewed as an operational simplification: the matrix probability levels $P=1$–5 correspond to the discretized intervals of the continuous failure probability $P_f$, while consequence levels $C=1$–5 represent conditional impact given exceedance; thus, $R=P\times C$ approximates, in ordinal terms, a risk ranking proportional to $P_f$ times expected conditional consequence. For post-mining urban areas where immediate safety decisions are required but comprehensive probabilistic data are unavailable, the semi-quantitative framework provides a transparent and defensible alternative to fully probabilistic methods, while progressive transition to FORM-based reliability analysis remains a logical future direction as monitoring networks expand and calibrated physical parameters become available (

Table 16. Comparison between semi-quantitative matrix and FORM.

Aspect	Semi-Quantitative Matrix (This Study)	FORM (Future Direction)
Data requirements	Direct concentration measurements	Statistical distributions of input parameters
Uncertainty treatment	Discrete probability levels + CI	Continuous probability distributions
Output	Ordinal risk score (1–25)	Failure probability $P_f$
Computational complexity	Low	Moderate to high
Applicability in emergencies	High	Limited
Long-term predictive capability	Limited	High

).

A comparative methodological perspective, highlighting the advantages and limitations of the main approaches, is provided in

Table 17. Comparative methodological perspective.

Method	Advantages	Limitations
Risk Matrix	Simple, rapid, integrates expert judgment	Ordinal scaling subjectivity
Direct Measurements	Empirical, physically grounded	Limited to sampled locations
Reliability Methods (FORM)	Fully probabilistic	Data-intensive, model-dependent

. Key practical trade-offs among the risk matrix, direct measurements, and FORM are summarized in Table 17.

5. URBAN-MINE-RISK Decision Algorithm

Based on the integrated methodological framework developed in this study and its application to the Lupeni case, a structured decision-support workflow entitled URBAN-MINE-RISK is proposed for managing abandoned mine methane (AMM) risks in urban environments.

The algorithm operationalizes the transition from preliminary screening to quantitative assessment, risk classification, and engineering intervention, while preserving methodological transparency and statistical rigor Figure 9.

Phase 1—Pre-Assessment.

Collection of historical mining and geological documentation.

Urban infrastructure mapping (utilities, basements, confined spaces).

Preliminary risk estimate:

$$R_{prelim}=P_{prelim}\times C_{prelim}$$

(20)

Decision rule:

If $R_{prelim}<4$ → annual monitoring; STOP.

Otherwise → proceed to Phase 2.

Phase 2—Quantitative Monitoring.

Deployment of an adaptive monitoring network (minimum 20 points; expanded as needed).

At least three monitoring campaigns.

Measurement parameters: CH₄, CO₂, CO, pressure, and meteorological conditions.

Radial expansion of the network until concentrations fall below 0.5% vol.

Phase 3—Statistical Analysis.

Calculation of mean, median, and standard deviation.

Estimation of exceedance probabilities:

$$\begin{gathered} P(C>1\%) \\ P(C>3\%) \\ P(C>4.4\%) \end{gathered}$$

(21)

with 95% confidence intervals.

Rank correlation (Spearman) between campaigns to evaluate spatial stability.

Testing temporal differences (Repeated Measures ANOVA and/or Friedman test, depending on assumptions).

Identification of critical points (e.g., $C_{max}>3\%$ or $C_{mean}>1\%$).

Phase 4—Source Identification (Chromatographic Analysis).

Sampling from critical boreholes and the public gas network.

Detection of diagnostic markers (CO, C₂H₂).

Attribution of emission source: mining origin vs. network leakage vs. unknown.

Phase 5—Risk Evaluation.

Determination of consequence weights via AHP.

Assignment of probability level (P) using quantitative–ordinal correspondence.

Assignment of consequence components:

Explosive potential (via $I_{LEL}$).

Human exposure.

Infrastructure vulnerability.

Calculation of aggregated consequence score $C$.

Risk calculation:

$$R=P\times C$$

(22)

Classification in a 5 × 5 matrix.

Sensitivity analysis of classification robustness.

Phase 6—Decision Rule (

Table 18. Decision Rule.

Risk Score (R)	Action
R < 5	Annual monitoring
5 ≤ R < 10	Quarterly monitoring
10 ≤ R < 17	Intervention planning
R ≥ 17	Immediate mitigation

).

Phase 7—Post-Intervention Validation.

Monthly monitoring (Year 1).

Quarterly monitoring (Years 2–3).

Annual monitoring (after Year 3).

Risk reassessment every 12 months.

The URBAN-MINE-RISK framework ensures traceability between measured data, statistical inference, risk scoring, and engineering decision-making. Its modular structure allows adaptation to different geological and urban contexts.

6. Conclusions

6.1. Original Contributions

This study provides an integrated methodological framework that combines quantitative monitoring, a semi-quantitative 5 × 5 risk matrix, and multi-criteria consequence assessment, including AHP-based consequence weighting with verified consistency (CR = 0.043). It represents one of the first documented applications of a 5 × 5 risk matrix to abandoned mine methane (AMM) risk in Romania and introduces the URBAN-MINE-RISK decision algorithm for operational implementation. The study further demonstrates how anthropogenic triggering mechanisms (e.g., utility trench excavation) can activate latent methane migration pathways and includes explicit uncertainty quantification through confidence intervals and sensitivity analysis. Finally, it offers a structured comparison between the semi-quantitative matrix approach and reliability-based methods (FORM), clarifying operational suitability under limited data availability.

6.2. Principal Findings

Application to the Lupeni case study classified the persistent hotspot (P2) as a critical risk (R = 25), justifying immediate mitigation, while also demonstrating spatial heterogeneity through the coexistence of localized critical conditions with lower background urban risk. Chromatographic analysis confirmed the mining origin of the emissions, and the implemented controlled drainage intervention reduced methane concentrations to instrumentally undetectable levels within approximately six months. The robustness of the classification was supported by sensitivity analyses, indicating that the key decision outcome (critical risk at P2) is stable under reasonable variations in probability, consequence levels, and AHP weights. Overall, the results show that administrative mine closure does not eliminate subsurface gas hazards and that structured, measurement-grounded risk assessment enables rational resource allocation and prevention of severe outcomes.

6.3. Limitations and Future Perspectives

Key limitations and future directions are summarized in

Table 19. Limitations and future perspectives.

Limitation	Description	Future Direction
AHP subjectivity	Expert-dependent weighting	Expanded multi-disciplinary panels
Case-study calibration	Single-site validation	Multi-site application in Valea Jiului
Limited historical data	No pre-2024 monitoring	Permanent monitoring networks
Incomplete mining archives	Legacy plan uncertainty	Archive digitization and GIS integration
Incomplete uncertainty characterization	Aleatory and epistemic uncertainty not fully separated; probabilistic methods (FORM/Monte Carlo) not implemented	Two-dimensional Monte Carlo simulation to separate variability from knowledge uncertainty; Bayesian updating as monitoring data accumulate

. The current analysis relies on a single-site case study and a limited monitoring window (three campaigns prior to intervention), while historical mine documentation and pre-2024 monitoring data remain incomplete. Although uncertainty was addressed through confidence intervals and sensitivity testing, aleatory and epistemic uncertainty were not fully separated, and fully probabilistic reliability simulations (e.g., FORM/Monte Carlo) were not implemented due to insufficient parameter characterization. Future work should therefore focus on expanding multi-disciplinary expert panels for AHP weighting, applying the framework across multiple sites in the Jiu Valley, establishing permanent monitoring networks, and improving archive digitization and GIS-based integration of legacy mine plans. As longer time-series datasets become available, two-dimensional Monte Carlo simulation and Bayesian updating can be used to separate variability from knowledge uncertainty and to enable progressive transition toward reliability-based probabilistic modeling.

6.4. Final Statement

This study demonstrates that administrative mine closure does not equate to risk elimination. A rigorously structured methodology integrating empirical monitoring, statistical inference, and semi-quantitative decision tools can prevent latent subsurface hazards from evolving into urban disasters.

Closure is not risk elimination; only measurement-driven prioritization followed by verified mitigation closes the safety loop in post-mining cities.