Risk assessment methods for third-party damage to natural gas pipelines are primarily divided into qualitative and quantitative categories. Qualitative risk assessment mainly relies on expert experience, analyzing accident causes and consequences and classifying risk levels based on their understanding of incident patterns. While straightforward, this approach is relatively subjective. Quantitative risk assessment, in contrast, uses mathematical models to analyze statistical data based on failure databases and pipeline material mechanical parameters, yielding more objective results but requiring higher data completeness [5]. Currently, China’s in-service natural gas pipeline network is extensive, with complex laying environments, and samples of third-party damage incidents are relatively sparse, making a fully quantitative analysis challenging. Therefore, semi-quantitative methods—such as safety checklists, preliminary hazard analysis, fault tree analysis (FTA), and event tree analysis—are commonly adopted in practice to balance evaluation efficiency with economic costs. Accordingly, based on the current state of China’s natural gas pipeline infrastructure, specific national conditions, and data availability, this study employs the FTA method to systematically identify the root causes of third-party damage and clarify key safety monitoring points, thereby providing targeted support for risk prevention and control.

2.2.1. FTA Procedure

Fault Tree Analysis (FTA), first proposed by H. A. Watson at Bell Telephone Laboratories in 1961, is a logical diagramming method that works deductively from system failure to underlying causes [6]. This method starts with the “top event”—the most undesirable system accident—and traces all direct and indirect factors that may lead to it, using standard logic gates (such as AND and OR gates) to describe causal relationships, until reaching “basic events” that require no further decomposition. The entire analysis follows a progressive sequence of “preparation → investigation → core identification → analysis → calculation,” with each step providing the foundation for subsequent stages. The basic procedure is illustrated in Figure 1.

2.2.2. Fault Tree Construction

Using “Third-party damage to natural gas pipelines” as the top event, the immediate consequence chain of “pipeline strength failure → natural gas leakage → fire and explosion” is set as the secondary top event. A layered analysis is then conducted across three dimensions: pipeline integrity, personnel behavior, and management mechanisms. The constructed fault tree for third-party damage to natural gas pipelines is shown in Figure 2. The top event in this fault tree analysis—“third-party damage to natural gas pipelines”—is defined as the full accident chain wherein external human activities (excluding the operator’s own maintenance) directly or indirectly cause physical damage to the pipeline, leading to gas leakage and potentially culminating in fire or explosion.

The fault tree comprises 22 basic events, as detailed in Table 1. To ensure comprehensiveness and scientific validity, the selection of these events was determined based on the following four criteria: 1) Statistical analysis of historical accident cases to extract high-frequency causative factors—for instance, events X1, X5, and X11 were identified as direct causes in multiple typical vases including the Qingdao “11·22” oil pipeline leakage and explosion accident and the San Bruno pipeline explosion in the United States; 2) Regulatory and standard requirements from documents such as the Petroleum and Natural Gas Pipeline Protection Law, Safety Management Regulations for Hazardous Chemical Pipeline Transportation, GB 50251 Code for Design of Gas Transmission Pipeline Engineering, and SY/T 6620 Specifications for Inspection and Maintenance of Oil and Gas Pipelines—events X6, X7, and X15 directly correspond to mandatory management requirements in these regulations; 3) Field investigations at multiple pipeline operating enterprises, where events including X4, X14, and X20 emerged from expert assessments of current technological equipment shortcomings and management blind spots; 4) Reference to similar fault tree studies in the literature, where events X2, X3, and X13 have been repeatedly validated as significant basic events in risk analysis models published in core journals, demonstrating high universality and representativeness.

Figure 1. FTA development procedure.

Figure 2. Fault tree for third-party damage to natural gas pipelines.

Table 1. List of basic events corresponding to the fault tree.

Based on the structural characteristics of the fault tree shown in Figure 2, the following analytical consensus is summarized:

1) Structural importance decreases as the path length increases. The shorter the path from the top event to a basic event, the higher the weight of that event in the structural importance ranking. Such events do not depend on complex preconditions; once they occur, they can directly propagate risk to higher system levels and should therefore be prioritized for monitoring. For instance, events X1 and X5 are located directly at the bottom of the M1 branch with shorter paths, exerting a more direct impact on the top event.

2) Logic gates control or amplify risk propagation. Input events connected by an AND gate are mutually necessary conditions, forming redundant barriers that reduce top event probability. For instance, M2 employs an AND gate requiring X9, X10, X11, and X21 to occur simultaneously for the intermediate event to hold, reflecting multi-factor coupling control. Conversely, input events connected by an OR gate are mutually sufficient conditions—any single path can trigger the output, producing a risk amplification effect. For example, M6 connects X1, X2, X3, X5, X7, and X22 via an OR gate—the occurrence of any single event can lead to construction damage. Consequently, branches with higher OR gate density typically correspond to lower-order minimal cut sets, making the top event probability more sensitive to changes in basic events.

3) The probability of intermediate events is determined by combinations of basic events, and they themselves possess no independent physical meaning. Intermediate events such as M1 through M8 are merely products of logical abstraction, not actual risk factors. All control measures must be implemented at the level of the 22 basic events, reducing system failure frequency by cutting off minimal cut sets.

4) It should be noted that the fault tree analysis conducted in this section focuses on qualitative structural analysis, aiming to reveal the logical relationships among basic events and their contribution paths to the top event, rather than performing probability-based quantitative calculations.

A cut set refers to a collection of basic events whose occurrence can lead to the top event T. If no proper subset of a cut set can itself constitute a cut set, the set is defined as a Minimal Cut Set (MCS). The quantity and order (i.e., the number of basic events contained) of MCSs jointly determine the risk level of the system. A greater number of MCSs indicates more potential failure paths, while higher-order cut sets exhibit exponentially decreasing sensitivity to changes in the probability of basic events. Consequently, lower-order cut sets—particularly first-order and second-order ones—constitute critical points for risk prevention and control.

Common methods for solving MCSs include Boolean algebra, the determinant method, and matrix approaches. Any fault tree can be described by a Boolean function, whose disjunctive normal form is expressed as [7]:

The conjunctive normal form is:

where A_i and B_i represent the cut sets and path sets of the fault tree, respectively. If there is no inclusion relationship among the terms within A_i, then the disjunctive normal form is the simplest, and A_i constitutes the minimal cut sets of the structural function f.

Based on the method described above, Boolean simplification was applied to the fault tree for third-party damage to natural gas pipelines shown in Figure 1. A total of 19 minimal cut sets were derived, as summarized in Table 2. The analysis reveals that the system possesses 19 distinct failure modes capable of leading to the top event. Among these, the minimal cut sets {X5} (Reckless Construction) and {X18} (Long-term Storage of Overweight Materials Above Pipeline) represent single-point failure events with the highest structural importance and should be prioritized as key targets within the risk prevention and control framework.

Table 2. Minimal cut sets for third-party damage incidents in natural gas pipelines.

In a fault tree, a set of basic events whose non-occurrence guarantees the prevention of the top event is termed a path set. If the set cannot be further reduced, it is defined as a minimal path set (MPS). Each MPS represents an independent pathway for preventing the top event. A larger number of MPSs indicates greater flexibility in selecting strategies to block accidents. This study employs the dual tree method to obtain MPSs. First, the fault tree is transformed into its dual success tree by interchanging all logic gates (OR gates become AND gates, AND gates become OR gates) and complementing all events. The minimal cut sets of the success tree then correspond to the MPSs of the original fault tree. Each MPS identifies a combination of basic events that must all be prevented to avoid the top event, representing the minimal necessary configuration for accident prevention.

The analysis shows that the fault tree for third-party damage to natural gas pipelines contains two MPSs, as presented in Table 3. Both sets are of high order, indicating low system redundancy and underscoring the need for simultaneous control across multiple elements to effectively prevent accidents.

Table 3. Minimal path sets for third-party damage incidents in natural gas pipelines.

In the absence of occurrence probability data for basic events, the structural importance coefficient I_S (i) can be used to quantitatively evaluate the influence of each basic event on the top event based on the system’s topological structure [8]. This provides a logical-structure-based ranking for risk classification, resource allocation, and prevention strategy development. By mapping the 22 basic events to their corresponding cut sets and calculating the structural importance, the ranking of the basic events for third-party damage to natural gas pipelines is obtained as follows:

X1 = X4 = X5 = X6 = X8 = X18 = X22 > X12 = X13 = X14 = X15 = X16 = X17 > X9 = X10 = X11 = X21 > X2, X3, X7, X19, X20

1) X1, X2, X3, X4, X5, X6, X7, X8, X18, X19, X20, and X22 are first-order minimal cut sets—any single event can independently trigger the top event, constituting “single-point failure” risks. With the highest structural importance, these events require “zero tolerance” control. Priority deployment of mandatory protective measures is recommended, including intelligent excavation alarm systems, construction permit linkage mechanisms, removal of illegal encroachments, enhanced warning signage, and meteorological early warning systems.

2) X12, X13, X14, X15, X16, and X17 are second-order minimal cut sets. These events cannot independently trigger accidents, but as components of second-order cut sets, their structural importance is secondary to first-order events. It is recommended to establish a closed-loop “inspection-rectification” management mechanism to ensure these two types of events do not fail simultaneously, thereby effectively mitigating risks.

3) X9, X10, X11, and X21 are fourth-order minimal cut sets—requiring all four factors to pose a threat. Structurally, these events contribute to the top event only through multi-factor coupling; individually they pose no threat, thus their importance is relatively lowest. Combined engineering measures such as “protective casing installation during road reconstruction + load limit management + densified marker posts” are recommended to achieve one-time risk elimination.