Multi-Dimensional Risks and Eco-Environmental Responses of Check Dam Systems: Evidence from a Typical Watershed in China’s Loess Plateau

Abstract

Deteriorating check dams pose significant threats to human safety and property, while impeding eco-environmental restoration in soil–water conservation systems in vulnerable watersheds like the Jiuyuangou Basin on China’s Loess Plateau. This study aimed to develop a comprehensive risk assessment framework for the check dam system in the Jiuyuangou Basin, China, to mitigate its threats to safety and eco-environmental restoration. A multi-index and multilevel risk evaluation system was established for check dam systems in the Jiuyuangou Basin, utilizing data gathering, hydrological statistics, numerical computation, and various methodologies. The index weights were determined via the fuzzy analytic hierarchy process with an integrated modeling framework for key parameters. Finally, the risk level of the check dam system in the Jiuyuangou Basin was assessed based on the comprehensive score. The results show that (1) nearly half of the check dams are at mild risk, approximately 25% are at moderate risk, and a few are basically safe. (2) Among various types of risk, the distribution of engineering risk is relatively uniform, environmental risk is generally high, loss risk is relatively concentrated, and management risk is particularly prominent. This research provides a scientific foundation for optimizing check dam governance, enhancing sediment control, and strengthening ecological service functions in vulnerable watersheds.

1. Introduction

The gully system, as a crucial catchment area for watershed-scale soil erosion, can yield substantial socio-economic advantages and vital ecosystem services through integrated management initiatives [1]. The check dam is a fundamental ecological engineering solution for soil and water conservation, particularly crucial in China’s Loess Plateau due to its unique loessial geology and extreme soil erosion that threatens the Yellow River basin [2,3,4]. In recent years, the escalation of global climate change has precipitated extreme precipitation events in the region, causing structural damage to the warping dam network. Consequently, the establishment of a flood control resilient dam system has become essential for sustainable watershed management and ecological security in vulnerable landscape regions [5,6,7].

China has made significant progress in dam risk research. Wang et al. [8,9] developed an optimization model for backbone dam structures and analyzed the ratio of various scale check dams in small watersheds [10,11]; Azman and Andreasen et al. examined the elevation of check dams, spillway design, and flow validation concerning flood mitigation and income conservation [12,13]; Najafi and Liu et al. formulated flood control design standards for check dams and proposed measures to address substandard check dams [14,15]. Several academics have created a dynamic optimum scheduling model for the check dam system [16,17] and studied the optimal construction timing and actual siltation period calculation method for the backbone dam system [18,19]. Another group of scholars used the fuzzy risk rate evaluation model for overtopping accidents to conduct safety evaluations of river sections [20,21] and developed a fuzzy variable pattern recognition approach for assessing flood control risks in check dam systems [22,23]. However, a paucity of official standards persisted regarding the layout, development, operational management, including risk reduction of check dam projects in the Loess Plateau region, and related risk analysis work is still in the preliminary exploration stage [24,25]. In recent years, the prevalence of natural disasters has led to a rise in check dam failures due to intense rainstorms [26,27]. Therefore, research on risk prevention and control of check dams, especially flood risk prevention and control of check dam systems, is particularly important, and establishing a corresponding analysis and evaluation system is urgent [28,29].

This research is novel due to its creation of a complete risk assessment system that incorporates both internal and external factors contributing to check dam failure. Unlike previous studies focusing on single factors, this work establishes a multi-dimensional ecological security risk evaluation index system for dam systems. By employing the fuzzy analytic hierarchy process (FAHP) to quantify index weights, we conducted a holistic risk assessment of the check dam system in the Jiuyuangou watershed. This approach provides a novel methodology and scientific foundation for enhancing ecological resilience and guiding sustainable restoration of dam systems in the Loess Plateau.

2. Materials and Methods

2.1. Overview of the Study Area

The Jiuyuangou watershed is situated 5 km north of Suide County, Shaanxi Province. It is a principal tributary on the left bank of the central segment of the Wuding River and exemplifies a characteristically environmentally vulnerable unit within the sandy and coarse sand area of the Loess Plateau (Figure 1). The basin encompasses a cumulative area of 70.7 km², features a primary ditch measuring 18 km in length, and includes 337 branch ditches exceeding a height of 200 m. The area exhibits traits of a highly eroded landform, characterized by a ditch gradient of 1.15%, a gully density of 5.34 km/km², and an altitude ranging from 820 to 1180 m. This region exhibits significant water and soil degradation characterized by fractured hills, profound soil strata, minimal plant cover, and intense reclamation demands, resulting in a mean soil erosion rate of 14,000 t/ (km²·a), designating it as a national priority zone for water and soil conservation. The climate is categorized as temperate semi-arid, with an average annual temperature of 8 °C and average annual precipitation of 354 mm, with over 60% occurring from July to September. Rainstorm occurrences serve as the primary catalyst for erosion. It was designated as a soil and water conservation experimental base in 1953, recognized as one of the top ten comprehensive management model basins in Shaanxi Province in 1964, and incorporated into the nationally important treatment project of the Wuding River in 1982. The long-term ecological treatment technique offers a study paradigm for the ecological restoration of dam systems in regions with significant erosion [30].

2.2. Data Source and Processing

The digital elevation model (DEM) of the small watershed was generated by scanning paper-based 1:10,000 scale topographic maps published by the National Administration of Surveying, Mapping, and Geoinformation, followed by spatial registration, mosaicking, and vectorization. Based on the resulting DEM, the river network within the Jiuyuangou small watershed was delineated using ArcGIS 10.2 and subsequently corrected with reference to high-resolution QuickBird imagery. The locations of check dams in the Jiuyuangou watershed, the situation of silted farmland behind the dams, the structural details of the dam bodies, and the dimensions of the spillway facilities were determined through field surveys. The overall conditions of the check dams and their ancillary structures were assessed based on field investigations. Using the 3D Analyst tool in ArcGIS 10.2, channel profiles were extracted from the 5 m resolution DEM. These derived profiles were then calibrated and verified against data obtained from field observations.

2.3. Research Method

2.3.1. Risk Assessment Index System for Check Dam Operations

As one of the most crucial infrastructures on the Loess Plateau, the safe operation of check dams is closely linked to socio-economic development, ecological conditions, and living standards, particularly in relation to soil erosion. Therefore, it is imperative to assess the potential losses and risks associated with dam breaches. Based on historical data, risk mitigation records, and damage causes, as well as relevant studies [31], we analyzed the sources of check dam failure risk. Through expert scoring, risk factors were selected across engineering structure, operational management, environmental hazards, and economic losses, resulting in a risk assessment framework comprising 4 primary and 12 secondary indicators (

Table 1. The operation risk assessment index system of check dam system.

Target Layer	First-Level Indicators	Second-Level Indicators
Risk assessment indicators for the operation of silt dam systems ($R$)	Engineering risk ($R_a$)	Low design standards ($R_{a1}$)
		Damage to dam body ($R_{a2}$)
		Damage to drainage facilities ($R_{a3}$)
	Management risk ($R_b$)	Personnel duty situation ($R_{b1}$)
		Emergency warning capability ($R_{b2}$)
		Management architecture ($R_{b3}$)
	Environmental risk ($R_c$)	Extreme rainstorm ($R_{c1}$)
		Over standard flood ($R_{c2}$)
		Seismic hazard ($R_{c3}$)
	Risk of loss ($R_d$)	Socio-economic losses ($R_{d1}$)
		Eco-environmental loss ($R_{d2}$)
		Personnel losses ($R_{d3}$)

Notes: $R_i$ refers to a first-level indicator; $R_{ij}$ refers to a secondary-level indicator.

). A crucial component of risk identification involves quantifying the magnitude of risk factors. Furthermore, the ability to compare the severity of diverse risks through a unified metric is essential in check dam risk analysis. This common metric is therefore defined as the “risk indicator.”

• Engineering risk ($R_a$)

Engineering risk in check dams refers to risk factors arising from the intrinsic physical and functional properties of the dam itself during the design, construction, and operation phases. These factors are categorized into three distinct and non-overlapping failure modes: inadequate design standards ($R_{a1}$), physical damage to the dam body ($R_{a2}$), and deficiencies in hydraulic facilities ($R_{a3}$). Each sub-indicator captures a unique pathway to failure.

• Low design standards are often inadequate, notably characterized by insufficient dam height, limited reservoir capacity, or an overly short design service life, failing to meet flood retention requirements. This issue was particularly prevalent in the 1960s and 1970s. A representative example occurred from 1977 to 1988 in Northern Shaanxi, where several heavy rainstorms caused damage to approximately 70% of small check dams. Most of these structures were built by local communities with low standards and poor construction quality, and about 60% consisted solely of embankments without spillways or drainage facilities.
  Check dams serve two primary functions: sediment interception (silt trapping) and flood mitigation. However, a functional conflict exists between these objectives: an increase in sedimentation capacity reduces available flood storage capacity, thereby weakening the dam’s overall flood control performance. Consequently, the design risk of check dams is influenced by multiple factors, including flood storage capacity, accumulated sediment volume, and flood design frequency. Thus, the design risk of a check dam can be defined as follows. This indicator uniquely assesses the mismatch between the original design capacity and the actual hydrological load, independent of the dam’s current physical condition or ancillary facilities.

  $$R_{a1}={\displaystyle \frac{T_1}{k{T}_2}}, k={\displaystyle \frac{V_2-V_3}{V_2}}$$

  (1)

  where $R_{a1}$ represents the design risk index of the check dam, where a higher value indicates a greater level of risk, with a maximum possible value of 1; $T_2$ denotes the designed flood return period (in years) that the check dam is intended to intercept; $T_1$ refers to the return period (in years) of the flood event currently encountered; $V_2$ indicates the designed flood storage capacity of the check dam (in 10⁴ m³); $V_3$ represents the current siltation storage capacity already accumulated in the dam (in 10⁴ m³); and $k$ is a conversion factor used to quantify the flood mitigation capabilities of the check dam.
• Damage to dam body is primarily caused by factors such as intense precipitation, poor construction quality, and lack of maintenance, leading to cracks, gullies, breaches, and even collapse. This risk indicator ($R_{a2}$) specifically quantifies the threat to the dam’s structural integrity based on its observed physical state, irrespective of its original design or the functionality of its drainage facilities. Complete collapse is relatively rare; most failures result from enlarged gullies due to prolonged erosion. Generally, a significant breach renders the check dam unable to retain floods. Field observations show that most breaches initiate from overtopping-induced erosion at the crest, which progressively expands and may lead to full failure. In other cases, scour at the base forms cavities, causing sudden instability and collapse of the upper dam structure. Gullies often develop due to long-term erosion, particularly in poorly maintained dams, and can evolve into breaches. Cracks, typically arising from construction defects, foundation settlement, or seismic activity, often appear within 1–3 years after construction and can be remedied by backfilling or grouting.
  According to the extent of damage, the threat of check dam failure is quantified as follows: cracks pose the lowest risk, followed by gullies, with breaches and collapse being the most severe. This study considers that a breach represents a complete failure of flood retention capacity, with an assigned risk value of 1. Cracks, being limited and repairable, have an upper risk limit denoted as $k$. Gullies can be numerically characterized by their transverse depth $d$ and longitudinal depth $h$. When $d$ reaches the average dam width $D$, and $h$ exceeds the remaining retention height $H$ (height from sediment surface to dam crest), the gully is considered to have developed into a breach, indicating functional failure. Thus, dam damage risk can be described using these parameters.

  $$R_{a2}=\left\{\begin{array}{cc}k& crack\\ {\displaystyle \frac{d}{D}}·{\displaystyle \frac{h}{H}}& gully\\ 1& outburst\end{array}\right.$$

  (2)

  In the formula, $R_{a2}$ is the risk index for structural damage to the check dam, where an elevated number signifies increased peril, with a maximum threshold of 1; $d$ represents the transverse depth of the crack across the dam’s breadth (m), $h$ denotes the longitudinal depth corresponding to the height of the dam (m), $D$ aligns with the mean width of the check dam (m), and $H$ denotes the residual flood retention height, characterized as the vertical distance from the sediment surface to the dam crest (m).
• Damage to drainage facilities—such as shafts, inclined pipes, or spillways—may result in the collapse of a check dam due to insufficient discharge capacity, complete absence of such structures, or functional impairment during operation. This indicator ($R_{a3}$) exclusively evaluates the performance and adequacy of the water release system. Its calculation is based on a hydraulic balance between inflow and outflow, making it conceptually and computationally separate from the structural damage indicator ($R_{a2}$). In practice, the design grade of a check dam is determined based on its controlled watershed area and flood regulation coordination with upstream and downstream structures. When the inflow volume exceeds the designed storage capacity, additional water release facilities should be installed to reduce flood retention pressure. The absence or impairment of these facilities introduces safety risks, influenced by factors including precipitation duration, watershed area, average precipitation depth, runoff coefficient, discharge capacity per unit time, and available remaining storage.

  $$R_{a3}={\displaystyle \frac{\frac{itAs}{1000}+qt}{V}}$$

  (3)

In the formula, $R_{a3}$ represents the risk index associated with defective water release facilities in the check dam, where a higher value indicates greater danger, with a maximum value of 1; $i$ represents the mean precipitation depth per unit of time (mm/h); $t$ is the precipitation duration (h); $A$ refers to the controlled watershed area of the check dam (km²);$s$ is the runoff coefficient, defined as the ratio of runoff depth to precipitation depth over a certain time interval; $q$ denotes the flood discharge capacity, reflecting the average discharge rate of the release facilities per unit of time (m³/h); and $V$ corresponds to the remaining storage capacity of the check dam (m³).

• Management risk ($R_b$)

Pursuant to the Interim Measures for the Construction and Management of Check Dams, flood prevention efforts for such structures are integrated into the local flood management system, operating under an accountability system led by chief executives and implemented through hierarchical management. Water administrative authorities at all levels are responsible for providing technical guidance and oversight, ensuring that maintenance entities conduct routine management and upkeep of check dam facilities. Accordingly, operational management risks primarily include staffing adequacy, emergency response capability, and management system structure. This category assesses the soft, human-factor-related vulnerabilities of the check dam system. The scoring-based evaluation of these organizational aspects ($R_{b1}$, $R_{b2}$, $R_{b3}$) is entirely independent of the physical, environmental, and loss-related indicators, as it quantifies a different dimension of risk.

As management risks lack directly quantifiable metrics, a scoring-based method is applied through field investigations to evaluate the maturity of local operational management mechanisms and the implementation of relevant measures. This enables multi-dimensional hierarchical quantification of check dam management risks, with specific quantitative indicators detailed in the following

Table 2. Project management risk rating form for check dams.

Indicator Component	Check Dam Project Management Risk Level
	Level 1/0	Level 2/0.2	Level 3/0.5	Level 4/0.8	Level 5/1
Personnel duty situation $R_{b1}$	Each check dam has dedicated supervision and regular maintenance	Most check dams have dedicated supervision and regular maintenance	Only thorough inspections are conducted before each flood season	Almost no responsible personnel perform check dam inspections	No operational supervision of check dams
Emergency warning capability $R_{b2}$	Rapid warning with timely evacuation	Relatively rapid warning with delayed evacuation	Slow warning with delayed evacuation	No warning; self-organized evacuation occurs	No warning; lack of crisis awareness
Management architecture $R_{b3}$	Comprehensive and well-implemented system	Relatively sound system	Relatively outdated system	Outdated and inefficient system	No relevant policies in place

:

• Environmental risk ($R_c$)

Environmental risk refers to the threats presented by external natural forces to the operational integrity of check dams. These forces are modeled as independent drivers of failure: precipitation-driven runoff ($R_{c1}$), river discharge-driven flooding ($R_{c2}$), and seismic activity ($R_{c3}$). The data sources and calculation methodologies for each are distinct, preventing double-counting.

• Extreme rainstorms denote precipitation that significantly surpasses the average annual precipitation or prolonged precipitation that far exceeds the average for the corresponding duration. This indicator ($R_{c1}$) is calculated based on precipitation data ($i_t$), making it independent of the streamflow-based flood indicator ($R_{c2}$). It specifically captures risks from direct, intense rainfall over the watershed. By analyzing long-term historical records of maximum precipitation events and conducting frequency analysis, the maximum event precipitation under different design frequencies can be determined. A higher precipitation value corresponds to a greater risk level for the check dam. The water volume in front of the dam must be calculated based on runoff and concentration, and compared with the flood detention capacity of the check dam. The higher the ratio of water volume produced by precipitation to the flood detention capacity, the more perilous the check dam becomes. When the ratio is greater than 1, the check dam overflows and loses its flood detention capacity, and this is likely to cause dam failure due to overtopping. In this study, when a check dam overflows, it will collapse, and the risk will reach its maximum. The formula for calculation is as follows:

$$R_{c1}={\displaystyle \frac{\sum _{t=0}^T\left(i_{t}As/1000-q_t\right)∆t}{V}}$$

(4)

• where $R_{c1}$ represents the risk index for extreme rainstorm hazards associated with the check dam, with higher values indicating greater danger, with a maximum value of 1; $T$ denotes the duration of precipitation, in hours (h); $∆t$ represents the length of each precipitation interval, in hours (h); $i_t$ represents the unit precipitation depth during the $t$-th interval, in millimeters (mm); $A$ represents the controlling region of the check dam, expressed as square kilometers (km²); $s$ represents the runoff coefficient, representing the ratio of flow depth at the inner diameter per unit time to precipitation depth; $q_t$ indicates the flooding outflow volume of the check dam during the $t$ period, representing the average discharge of flood control facilities each period of time, measured in cubic meters per hour (m³/h); and $V$ signifies the remaining amount of storage of the warping dam, expressed in cubic meters (m³).

2.

Over-standard flood refers to a flood that is beyond the flood prevention thresholds of a check dam, hence heightening the risk associated with flood management. In contrast to the precipitation-based $R_{c1}$, this indicator ($R_{c2}$) is calculated using direct flood discharge data ($r_t$) or reliably derived flow estimates. This clear distinction in input data ensures that the contributions of rainfall and riverine flooding are not conflated. In a river basin, multiple precipitation gauges are typically deployed. Areal precipitation can be estimated through spatial interpolation techniques. However, streamflow gauges are generally only located at the basin outlet, where long-term monitoring data are available. It remains challenging to accurately estimate or back-calculate the runoff corresponding to each individual check dam based solely on outlet discharge measurements. Therefore, on the basis of analyzing the relationship between precipitation and runoff, we assume that precipitation and floods have the same frequency, convert precipitation into runoff, and calculate the inundation procedure in front of the dam. The research indicates that the risk indicators for excessive flooding are associated with the flood process, length, discharge facilities, and detention capacity:

$$R_{c2}={\displaystyle \frac{\sum _{t=0}^T\left(r_t-q_t\right)∆t}{V}}$$

(5)

• where $R_{c2}$ represents the risk index for exceeding standard flood levels at the check dam, with higher values indicating greater danger, with a maximum value of 1. $T$ represents the flood frequency in hours (h); $∆t$ signifies the duration of the unit period in seconds (s). $r_t$ symbolizes the flow during period $t$ in cubic meters per second (m³/s). $q_t$ indicates the flood drainage capability of the check dam over time period $t$, specifically the average release of flood disposal facilities per unit time, in cubic meters per second (m³/s). $V$ refers to the residual storage capacity of the warping dam, defined as cubic meters (m³).

3.

Seismic hazard refers to the risks induced by geological movements during earthquakes, such as cracking, collapse, settlement, and damage to hydraulic structures in check dams. According to historical records [32], the magnitude 8.0 Wenchuan earthquake on 12 May (also known as the “5·12” earthquake) triggered multiple magnitude 6.0 aftershocks in Gansu Province, causing severe damage to check dams in the region. As of 26 May 2008, survey figures indicated that 124 check dams were compromised, comprising 93 key dams, 27 medium-sized dams, and 4 small dams, reflecting a highly serious level of impact. There has been very limited research on seismic risk to check dams, making it particularly challenging to quantify corresponding seismic risk indicators.

Seismic intensity denotes the extent of shaking and its impact on the ground surface and engineering structures. Utilizing the mean damage index derived from the China Seismic Intensity Scale (

Table 3. China Seismic Intensity Scale.

Intensity	Magnitude	Mean Damage Index	Phenomenological Description
I	1.9	0	Detected only by instruments.
II	2.5	0	Perceived by a limited number of individuals while stationary indoors; suspended items may oscillate somewhat.
III	3.1	0	Perceived indoors by numerous individuals, outdoors by a select few; suspended items oscillate, unstable objects tremble.
IV	3.7	0	Perceived indoors by the majority, outdoors by a minority; windows and doors tremble, and wall surfaces may fissure.
V	4.3	0	Felt outdoors by most; animals become restless; doors and windows creak; fine cracks may appear in walls.
VI	4.9	0~0.1	People feel unsteady; animals flee; objects fall off shelves; simple sheds damaged; slope failures may occur.
VII	5.5	0.11~0.3	Slight damage to buildings; monuments and chimneys damaged; ground cracks and sand boils may appear.
VIII	6.1	0.31~0.5	Many buildings damaged, a few collapsed; road embankments failed; underground pipes ruptured.
IX	6.7	0.51~0.7	Most buildings severely damaged, some collapsed; monuments and chimneys toppled; railway tracks bent.
X	7.3	0.71~0.9	Widespread building collapse; roads destroyed; large rockfalls occur; large waves on water bodies.
XI	7.9	0.91~1.0	Majority of buildings collapse; long sections of embankments and roads destroyed; significant ground deformation.
XII	8.5	1.0	Total destruction of all structures; dramatic changes in topography; annihilation of plant and animal life

) as the seismic risk indicator for check dams, a relationship between this indicator and earthquake magnitude can be established as follows:

$$R_{c3}=\left\{\begin{array}{cc}0& x<4.5\\ a{x}^3+b{x}^2+cx+d& 4.5\le x\le 8\\ 1& x>8\end{array}\right.$$

(6)

• where $R_{c3}$ is the seismic disaster risk index of the check dam, and the greater its value, the more dangerous it is, and the maximum value is 1; $x$ is the earthquake magnitude; $a$, $b$, $c,$ and $d$ are the seismic disaster risk coefficients of the check dam, taking $a$ = −0.0214, $b$ = 0.4115, $c$ = −2.2853, and $d$ = 3.8883, respectively.

• Risk of loss ($R_d$)

The risk of loss associated with check dam encompasses the potential consequences of a failure event. It is crucial to note that these loss indicators ($R_{d1}$, $R_{d2}$, $R_{d3}$) measure the severity of the outcome (socioeconomic, environmental, and human life impacts), whereas the preceding Engineering ($R_a$), Management ($R_b$), and Environmental ($R_c$) risk indicators measure the likelihood or driving forces of the failure event itself. This conceptual separation between cause and effect fundamentally prevents double weighting.

• Socioeconomic losses denote economic detriments resulting from the failure of check dams, leading to the inundation of agricultural land, residences, thoroughfares, urban neighborhoods, and industrial zones. Generally, estimates can be made on the basis of the extent of flooding. The measurement of the risk of socioeconomic losses is related not only to the magnitude of the losses caused but also to the local economic level, that is, the ratio of the magnitude of the losses to the disaster resistance capacity. The disaster resistance capacity can be measured by the funds available for flood control and disaster relief in the local area:

$$R_{d1}={\displaystyle \frac{S_G}{G}}$$

(7)

• where $R_{d1}$ represents the socioeconomic loss risk index of the check dam; a higher value indicates greater danger. The upper limit is 1; ${\mathrm{S}}_G$ represents socioeconomic losses, measured in tens of thousands of yuan; and $\mathrm{G}$ represents the funds available locally for flood control and disaster relief, in tens of thousands of yuan.

2.

Eco-environmental loss pertains to the degradation of the ecological landscape due to the failure of check dams, leading to the inundation of ecological zones or riverbanks, which exposes loess and induces significant soil erosion. The extent of the risk of damage to the environment can be evaluated through the financial resources required for ecological restoration and the funds designated for local environmental development:

$$R_{d2}={\displaystyle \frac{S_U}{U}}$$

(8)

• where $R_{d2}$ represents the eco-environmental loss risk index of the check dam. The index value correlates positively with risk, with an upper bound amount of 1; ${\mathrm{S}}_U$ denotes the amount of environmental loss, measured in 10,000 yuan; and $U$ signifies local accessible finances for eco-environmental construction, also in 10,000 yuan.

3.

Personnel losses refer to harm to personnel, such as being injured, missing, or killed, due to not evacuating in time after the collapse of a check dam and the subsequent flooding. The RESCDAM technique [33,34] simplifies the assessment of mortality attributable to the dam failure by including many criteria, including alert time, at-risk population, and flood intensity.

$$R_{d3}=PAR\times f\times i\times c$$

(9)

• In the formula, $R_{d3}$ is the risk indicator for loss of life due to check dam failure The index value correlates positively with risk, with an absolute highest of 1; $PAR$ denotes the population at risk; $f$ represents the number of fatalities within this demographic; $i$ indicates the severity of the flood disaster; and $c$ is the life loss correction coefficient of the check dam, primarily reflecting the impact of the prediction and early warning system as well as emergency rescue capabilities on life loss.

2.3.2. Determination of Indicator Weights Based on Fuzzy Analytic Hierarchy Process (FAHP)

The analytic hierarchy process is a decision-making approach that integrates qualitative and quantitative analyses. Due to the intricate nature of risk factors influencing the inadequacy of check dam systems and the interrelation of numerous indicators, the analytic hierarchy process [35,36] can be employed to thoroughly evaluate diverse risk factors based on their likelihood of occurrence and repercussions, thereby facilitating the classification of flood risk levels for check dam systems. Nonetheless, the choice of indicators and weights is significantly influenced by subjective considerations, impacting the risk assessment outcomes. This article combines fuzzy theory with the analytic hierarchy process, employing the fuzzy analytic hierarchy technique to ascertain the weights of flood risk indicators for check dam systems [37,38].

• Establishment of the Fuzzy Consistent Judgment Matrix

A fuzzy consistent judgment matrix $R$ represents the comparison of the relative importance of elements at the current level associated with an element at the upper level. Assuming that an element $C$ from the upper level is connected to elements $a_1,a_2,\dots ,a_n$ at the lower level, the fuzzy consistent judgment matrix can be expressed as:

$$\begin{array}{ccccc}\begin{array}{c}C\end{array}& \begin{array}{c}{a}_1\end{array}& a_2& \cdots & a_n\\ a_1& r_{11}& r_{12}& \cdots & r_{1n}\\ a_2& r_{21}& r_{22}& \cdots & r_{1n}\\ \cdots & \cdots & \cdots & \cdots & \cdots \\ a_n& r_{n1}& r_{n2}& \cdots & r_{nn}\end{array}$$

(10)

Element $r_{ij}$ has the following practical meaning: it represents the membership degree of the fuzzy relationship “… is more important than …” between elements $a_i$ and $a_j$ when they are compared relative to element $C$. To quantitatively describe the relative importance of any two alternatives concerning a specific criterion, the following (

Table 4. Importance scale.

Scale	Definition	Description
0.5	Equally Important	Two elements are equally important.
0.6	Slightly Important	One element is slightly more important than the other.
0.7	Obviously Important	One element is obviously more important than the other.
0.8	Much More Important	One element is much more important than the other.
0.9	Extremely Important	One element is extremely more important than the other.
0.1~0.4	Reciprocal Comparison	If the comparison of element ai with $a_j$ yields judgment $r_{ij}$ then the comparison of $a_j$ with $a_i$ yields $r_{ji}=1-r_{ij}$.

) 0.1–0.9 scale can be used for numerical scaling.

Using the numerical scale above, comparing elements $a_1,a_2,\dots ,a_n$ with respect to the upper-level element $C$ yields the following fuzzy judgment matrix:

$$R=\left[\begin{array}{ccc}{r}_{11}& \dots & r_{1n}\\ ⋮& \ddots & ⋮\\ r_{n1}& \dots & r_{nn}\end{array}\right]$$

(11)

Matrix R possesses the following properties: (1) $r_{ii}=0.5, i = 1, 2,\dots , n$; (2) $r_{ji}=1-r_{ij}, i,j=1, 2,\dots , n$; (3) $r_{ij}=r_{ik}-r_{jk}, i,j,k=1, 2,\dots , n$. This makes R a fuzzy consistent matrix. The consistency of the fuzzy judgment matrix reflects the consistency of human judgment and is crucial when constructing it. However, in practical decision-making analysis, due to problem complexity and potential biases in perception, the constructed matrix often lacks consistency. In such cases, the necessary and sufficient conditions for a fuzzy consistent matrix can be applied for adjustment. The specific adjustment procedure is as follows:

Step 1: Identify an element whose comparisons with all other elements are considered reliable. Without loss of generality, assume the decision-maker is confident about judgments $r_{11},r_{12},\dots , r_{1n}$ (the first row).

Step 2: Subtract each corresponding element in the second row from the first row. If all resulting differences are constant, the second row requires no adjustment. Otherwise, adjust the second-row elements until the differences between the first and second rows are constant.

Step 3: Subtract each corresponding element in the third row from the first row. If all resulting differences are constant, the third row requires no adjustment. Otherwise, adjust the third-row elements until the differences between the first and third rows are constant.

Continue this process until the differences between the first row and the n-th row are constant.

• Determining Indicator Weights from the Fuzzy Consistent Judgment Matrix

Suppose the fuzzy consistent matrix obtained from pairwise importance comparisons of elements $a_1,a_2,\dots ,a_n$ is $R={ \left(r_{ij}\right)}_{n\times n}$ and the weight values of elements $a_1,a_2,\dots ,a_n$ are $w_1,w_2,\dots ,w_n$, respectively. Based on the previous discussion, the following relationship holds:

$$r_{ij}=0.5+a\left(w_i-w_j\right),i,j=1, 2,\dots , n$$

(12)

Here, $0<a<0.5$. The parameter $a$ measures the perceived degree of difference among the evaluated objects and depends on the number of objects and the magnitude of their differences. When the number of objects or the degree of difference is large, $a$ can be set to a higher value. Furthermore, the decision-maker can adjust the value of $a$ to derive several different weight vectors and then select the most satisfactory one.

When the fuzzy judgment matrix $R$ is not perfectly consistent, the equality in Equation (12) does not hold strictly. In this case, the least squares method can be used to find the weight vector $W={[w_1,w_2,\dots ,w_n]}^T$ by solving the following constrained optimization problem:

$$\left\{\begin{array}{c}minz={\displaystyle \sum _{i=1}^n}{\displaystyle \sum _{j=1}^n}{\left[0.5+a\left(w_i-w_j\right)-r_{ij}\right]}^2\\ s.t.{\displaystyle \sum _{i=1}^n}{w}_i=1, w_i\ge 0, \left(1\le i\le n\right)\end{array}\right.$$

(13)

Using the Lagrange multiplier method, the constrained problem (13) is equivalent to the following unconstrained optimization problem:

$$minL\left(w,\lambda \right)=\sum _{i=1}^n\sum _{j=1}^n{\left[0.5+a\left(w_i-w_j\right)-r_{ij}\right]}^2+2\lambda [\sum _{i=1}^n{w}_i-1$$

(14)

where $\lambda$ is the Lagrange multiplier.

Taking the partial derivatives of $L\left(w,\lambda \right)$ with respect to $w_i$ and setting them to zero yields a system of n algebraic equations:

$$a\sum _{j=1}^n\left[0.5+a\left(w_i-w_j\right)-r_{ij}\right]-a\sum _{k=1}^n\left[0.5+a\left(w_k-w_i\right)-r_{ki}\right]+\lambda =0 ( i=1, 2,\dots , n)$$

(15)

This simplifies to

$$\sum _{j=1}^n[2a^2\left(w_i-w_j\right)+a\left(r_{ji}-r_{ij}\right)-r_{ij}]+\lambda =0 ( i=1, 2,\dots , n)$$

(16)

(Note: The property $r_{ii}=0.5$ is used in the derivation).

The system of Equation (16) contains n+1 unknowns ($w_1,w_2,\dots ,w_n,\lambda$) but only n equations, so it cannot yield a unique solution. Incorporating the constraint $w_1+w_2+\dots +w_n=1$ adds one more equation, resulting in a system of n+1 equations with n+1 unknowns:

$$\left\{\begin{array}{c}\begin{array}{c}\begin{array}{c}2a^2\left(n-1\right)w_1-2a^2{w}_2-\dots -2a^2{w}_n+\lambda =a\sum _{j=1}^n\left(r_{1j}-r_{j1}\right)\\ -2a^2{w}_1-2a^2\left(n-1\right)w_2-\dots -2a^2{w}_n+\lambda =a\sum _{j=1}^n\left(r_{2j}-r_{j2}\right)\end{array}\\ \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \end{array}\\ -2a^2{w}_1-2a^2{w}_2-\dots -2a^2\left(n-1\right)w_n+\lambda =a\sum _{j=1}^n\left(r_{nj}-r_{jn}\right)\\ w_1+w_2+\dots +w_n=1\end{array}\right.$$

(17)

Solving this system yields the weight vector $W={[w_1,w_2,\dots ,w_n]}^T$.

• Weighting of Operational Risk Assessment Indicators for Check Dam Systems

• Fuzzy Consistent Judgment Matrices for Operational Risk Indicators of Check Dam Systems

The operational risk indicator system for check dam systems is shown in Table 1, comprising 4 first-level indicators and 12 second-level indicators. These 12 second-level indicators correspond to the 4 first-level indicators, respectively. According to the Fuzzy AHP weight calculation method, we first need to determine the fuzzy consistent judgment matrix of the first-level indicators relative to the target layer and the matrices of the second-level indicators relative to their respective first-level indicators. This results in five fuzzy consistent judgment matrices.

(1)

First-level Fuzzy Consistent Judgment Matrix:

$${\mathrm{S}}_1=\begin{array}{cc}\left[R\right]& \begin{array}{cc}\begin{array}{cc}{R}_a& R_b\end{array}& \begin{array}{cc}{R}_c& R_d\end{array}\end{array}\\ \begin{array}{c}\begin{array}{c}{R}_a\\ R_b\end{array}\\ \begin{array}{c}{R}_c\\ R_d\end{array}\end{array}& \left[\begin{array}{cc}\begin{array}{cc}0.5& 0.7\\ 0.3& 0.5\end{array}& \begin{array}{cc}0.6& 0.4\\ 0.4& 0.2\end{array}\\ \begin{array}{cc}0.4& 0.6\\ 0.6& 0.8\end{array}& \begin{array}{cc}0.5& 0.3\\ 0.7& 0.5\end{array}\end{array}\right]\end{array}$$

(18)

(2)

Second-level Fuzzy Consistent Judgment Matrix for Engineering Risk:

$${\mathrm{S}}_a=\begin{array}{cc}\left[R_a\right]& \begin{array}{ccc}{R}_{a1}& R_{a2}& R_{a3}\end{array}\\ \begin{array}{c}{R}_{a1}\\ R_{a2}\\ R_{a3}\end{array}& \left[\begin{array}{ccc}0.5& 0.3& 0.4\\ 0.7& 0.5& 0.6\\ 0.6& 0.4& 0.5\end{array}\right]\end{array}$$

(19)

(3)

Second-level Fuzzy Consistent Judgment Matrix for Management Risk:

$${\mathrm{S}}_b=\begin{array}{cc}\left[R_b\right]& \begin{array}{ccc}{R}_{b1}& R_{b2}& R_{b3}\end{array}\\ \begin{array}{c}{R}_{b1}\\ R_{b2}\\ R_{b3}\end{array}& \left[\begin{array}{ccc}0.5& 0.2& 0.3\\ 0.8& 0.5& 0.6\\ 0.7& 0.4& 0.5\end{array}\right]\end{array}$$

(20)

(4)

Second-level Fuzzy Consistent Judgment Matrix for Environmental Risk:

$${\mathrm{S}}_c=\begin{array}{cc}\left[R_c\right]& \begin{array}{ccc}{R}_{c1}& R_{c2}& R_{c3}\end{array}\\ \begin{array}{c}{R}_{c1}\\ R_{c2}\\ R_{c3}\end{array}& \left[\begin{array}{ccc}0.5& 0.4& 0.7\\ 0.6& 0.5& 0.8\\ 0.3& 0.2& 0.5\end{array}\right]\end{array}$$

(21)

(5)

Second-level Fuzzy Consistent Judgment Matrix for Risk of Loss:

$${\mathrm{S}}_d=\begin{array}{cc}\left[R_d\right]& \begin{array}{ccc}{R}_{d1}& R_{d2}& R_{d3}\end{array}\\ \begin{array}{c}{R}_{d1}\\ R_{d2}\\ R_{d3}\end{array}& \left[\begin{array}{ccc}0.5& 0.6& 0.3\\ 0.4& 0.5& 0.2\\ 0.7& 0.8& 0.5\end{array}\right]\end{array}$$

(22)

2.

Calculation of Operational Risk Indicator Weights for Check Dam Systems

The weight vector $W={[w_1,w_2,\dots ,w_n]}^T$ and the fuzzy consistent matrix $S={\left(r_{ij}\right)}_{n\times n}$ satisfy $r_{ij}=0.5+a\left(w_i-w_j\right),(i,j=1,2,\dots ,n)$, where $0<a<0.5$. The parameter a measures the degree of difference among indicators. For the first-level indicators, where differences are relatively significant, $a$ was set to 0.4. For the second-level indicators, where differences are smaller, $a$ was set to 0.2. Substituting these parameters into the equation system allows calculation of the respective indicator weights. The calculation results are presented in

Table 5. Weights of operational risk assessment indices of the check dam system.

Target Layer	Weight of First-Level Indicators	Weight of Second-Level indicators
Risk assessment indicators for the operation of silt dam systems ($R$)	Engineering risk $W\left(R_a\right)=0.28$	Low design standards	$W\left(R_{a1}\right)=0.26$
		Damage to dam body	$W\left(R_{a2}\right)=0.39$
		Damage to drainage facilities	$W\left(R_{a3}\right)=0.35$
	Management risk $W\left(R_b\right)=0.17$	Personnel duty situation	$W\left(R_{b1}\right)=0.16$
		Emergency warning capability	$W\left(R_{b2}\right)=0.63$
		Management architecture	$W\left(R_{b3}\right)=0.21$
	Environmental risk $W\left(R_c\right)=0.33$	Extreme rainstorm	$W\left(R_{c1}\right)=0.34$
		Over standard flood	$W\left(R_{c2}\right)=0.40$
		Seismic hazard	$W\left(R_{c3}\right)=0.26$
	Risk of loss $W\left(R_d\right)=0.22$	Socio-economic losses	$W\left(R_{d1}\right)=0.33$
		Eco-environmental loss	$W\left(R_{d2}\right)=0.24$
		Personnel losses	$W\left(R_{d3}\right)=0.43$

Notes: $R_i$ refers to a first-level indicator, $R_{ij}$ refers to a secondary-level indicator, $W\left(R_i\right)$ refers to a first-level indicator weight, $W\left(R_{ij}\right)$ refers to a secondary-level indicator weight, and the dimensions of both indicators and weights are 1.

.

2.3.3. Evaluation of Risks Associated with the Check Dam System in the Jiuyuangou Watershed

This study establishes a three-tiered flood risk assessment system: complete risk level, principal risk level, and second risk level. The comprehensive risk is denoted by the weighted aggregate of the principal risk indicators, while the principal risk is weighted and synthesized by the associated second risk indicators. The hierarchical quantitative relationship is seen in the subsequent expression:

$$R^k={\displaystyle \frac{1}{n}}\sum _{i=1}^n{w}_i{R}_i^{k-1}$$

(23)

In the formula, $R^k$ denotes the comprehensive risk quantification value at level $k (k=\mathrm{1,2},3$ corresponds to the second risk level, principal risk level, and complete risk level, respectively), $n$ represents the total number of risk factors at this level, and $w_i$ represents the weight coefficient of the $i$-th risk factor, satisfying $\sum _{i=1}^n{w}_i=1$.

The risk level guidelines are established as indicated in

Table 6. Division standard of check dam risk grades.

Risk Level	Description of Risk Degree	Range
Level 1	High risk	[0.7, 1]
Level 2	Moderate risk	[0.5, 0.7)
Level 3	Mild risk	[0.3, 0.5)
Level 4	Generally safe	[0.1, 0.3)
Level 5	Very safe	[0, 0.1)

. The classification thresholds were defined based on a synthesis of pertinent research on risk assessment and real-world engineering scenarios [39]. The critical thresholds of 0.5 and 0.7 were selected to delineate distinct risk management states: a value of 0.5 signifies the transition from ‘Mild’ to ‘Moderate’ risk, where proactive monitoring and maintenance become imperative; a value of 0.7 indicates the onset of ‘High’ risk, necessitating immediate intervention to prevent potential failure. This tiered approach aligns with general risk management principles, ensuring that the classification is not arbitrary but reflects escalating levels of operational concern and required response.

3. Results

The check dam system in the Jiuyuangou Watershed comprised a total of 206 check dams following years of demonstration building, marking its entry into a fundamental retention stage. After excluding those that had collapsed or silted up, 73 check dams remained, comprising 29 small dams, 22 medium dams, and 22 key dams. A comprehensive operational risk assessment was conducted on these 73 check dams.

3.1. Operational Risk of Check Dam Systems Across Varying Precipitation Frequencies

The results demonstrate that the risk characteristics of the check dam system in the Jiuyuangou basin are as follows (

Table 7. Operational risks of the check dam system across varying precipitation frequencies.

Return Period	5	10	20	50	100	200	500
Engineering risk	0.3	0.3	0.3	0.3	0.3	0.3	0.3
Low design standard	0.47	0.47	0.47	0.47	0.47	0.47	0.47
Dam damage	0.42	0.42	0.42	0.42	0.42	0.42	0.42
Damage to drainage facilities	0.03	0.03	0.03	0.03	0.03	0.03	0.03
Management risk	0.55	0.55	0.55	0.55	0.55	0.55	0.55
Personnel duty situation	0.8	0.8	0.8	0.8	0.8	0.8	0.8
Emergency early warning capability	0.5	0.5	0.5	0.5	0.5	0.5	0.5
Management Architecture	0.5	0.5	0.5	0.5	0.5	0.5	0.5
Environmental risk	0.34	0.48	0.54	0.58	0.58	0.61	0.64
Extreme Rainstorm	0.53	0.72	0.81	0.86	0.86	0.87	0.91
Over standard flood	0.41	0.59	0.67	0.71	0.73	0.79	0.83
Seismic hazard	0	0	0	0	0	0	0
Risk of loss	0.25	0.27	0.31	0.34	0.34	0.34	0.36
Socioeconomic loss	0.62	0.65	0.7	0.74	0.74	0.74	0.75
Eco-environmental loss	0.17	0.24	0.33	0.4	0.4	0.41	0.44
Personnel losses	0	0	0	0	0	0	0.01
Comprehensive risk	0.34	0.39	0.42	0.44	0.44	0.45	0.47
Risk level	Level 3	Level 3	Level 3	Level 3	Level 3	Level 3	Level 3

): as the design precipitation frequency escalates, the comprehensive risk of the check dam system rises progressively, with environmental risk exhibiting the most significant increase. The engineering risk, which is tied to the dam’s inherent structural design and current physical condition, remains constant across different precipitation scenarios. Similarly, the management risk reflects the institutional and operational framework, which is a baseline systemic characteristic of the watershed and does not vary with individual rainfall events; thus, it is consistently assessed at a moderate level. The risk of loss showed a small fluctuation in growth. Specifically, the overall risk level of the dam system is classified as level 3 (moderate risk): the project entity is at mild risk, the management system exhibits a consistent moderate risk, indicating a systemic-level challenge that is independent of hydrological variability, the environmental risk fluctuates from mild to moderate with varying precipitation intensity, and the risk of loss transitions from basic safety to mild risk. The analysis indicates that the check dam system’s responsiveness to precipitation circumstances in the basin has notable sensitivity features. Consequently, mitigating the flood disaster risk requires targeted strategies: engineering measures (like elimination and reinforcement) to address physical vulnerabilities, and crucially, systemic reforms to improve the consistently moderate management framework, as identified in this study.

3.2. Sensitivity Analysis of Various Levels of Risks of the Check Dam System to Precipitation Return Period

To quantify the impact of uncertainties in precipitation inputs on the assessment results and to identify the key drivers of the dam system risk, a sensitivity analysis was conducted. The sensitivity coefficient ($S$) was calculated as follows:

$$S={\displaystyle \frac{\Delta R-R_{base}}{\Delta P-P_{base}}}$$

(24)

where $\mathsf{\Delta }R$ is the change in value at risk; $R_{base}$ is the benchmark value at risk; $\mathsf{\Delta }P$ denotes the variance of the precipitation return period; $P_{base}$ denotes the return period of reference precipitation (5 years).

The results (Figure 2) clearly demonstrate divergent responses of various risk categories to precipitation changes. The curves for engineering risk ($R_a$) and management risk ($R_b$) are nearly horizontal, with sensitivity coefficients approaching zero. This is entirely expected, as their underlying indicators (e.g., dam body damage, drainage facility damage, personnel duty status) are calculated based on the physical attributes of the dams and management systems, which are independent of external precipitation inputs, hence their constant values in Table 5.

In stark contrast, environmental risk ($R_c$) exhibits high sensitivity to the precipitation return period and is the dominant factor driving the changes in comprehensive risk ($R$). Specifically, the extreme rainstorm risk ($R_{c1}$) and over-standard flood risk ($R_{c2}$) show a significant non-linear increasing trend with the return period: the growth is extremely rapid in the low return period range (5–50 years), but slows down and gradually plateaus at higher return periods (>100 years), consistent with the non-linear characteristics of rainfall-runoff relationships. For seismic hazard ($R_{c3}$), the sensitivity coefficient ($S_{c3}$) computes to nearly zero, owing to the negligible risk values under different rainfall return periods (Table 5).

The risk of loss ($R_d$) also shows a positive correlation with precipitation change, but its sensitivity is considerably lower than that of environmental risk, with a more gradual growth trend. This indicates that although more extreme precipitation leads to greater potential losses through environmental risk, factors such as economic losses and casualties are also constrained by local socio-economic conditions (e.g., disaster prevention funds, early warning capabilities), buffering the absolute growth.

In conclusion, the sensitivity analysis verifies that the assessment model effectively captures the physical mechanism between precipitation input and risk response. The results highlight the non-linear escalation of environmental risks under increasing rainfall intensity, providing a critical baseline for assessing climate change impacts. This underscores the necessity of integrating climate adaptation strategies—such as designing for higher return periods and dynamic risk monitoring—into the governance of check dam systems in vulnerable regions like the Loess Plateau.

3.3. Different Risk Situations of 73 Check Dams in the Jiuyuangou Watershed

The overall risk assessment results for check dam systems under varying precipitation frequencies (Figure 3) indicate that 18 dams in the Jiuyuangou basin are classified as moderate risk (24.7%), 53 dams as mild risk (72.6%), and 2 dams as essentially safe (2.7%). Overall, around 73% of the check dams exhibit a low risk level, 25% fall within the moderate risk category, and merely 2.7% are considered essentially safe. Each category of risk has the following characteristics: The engineering risk has a gradient distribution: very safe 29%, basic safety 25%, mild risk 22%, and moderate risk 25%. All management risks are categorized as moderate risk. Nearly half of the dams present significant environmental concerns, with 7% classified as basic safety, 7% as mild risk, 44% as moderate danger, and 42% as severe risk. The risk of loss is predominantly situated within the mild risk category (very safe 14%, basic safety 29%, mild risk 45%, moderate risk 12%). The risk attributes are as follows: engineering risks are uniformly distributed, environmental risks are primarily elevated (over 80% of the dam structure is at moderate risk or greater), loss risks are comparatively concentrated, and management risks are typically severe. Consequently, in light of the aforementioned circumstances, it is recommended to implement the following systematic prevention and control measures: on one side, the high-risk dam structure should be augmented and expanded to improve flood control capability, and the arrangement of water release facilities (including the addition or enhancement of flood discharge capacity) should be optimized to facilitate risk transfer. Conversely, implement a hierarchical early warning response mechanism, emphasizing the enhancement of standards and execution within the management system. Moreover, when substantial risk disparities exist between upstream and downstream dams, the risk can be judiciously mitigated by adjusting the flood discharge capacity of local dams (either decreasing or increasing it). Simultaneously, for dams with significant loss risk, it is imperative to enhance the collaborative protection of both upstream and downstream dams. Particularly in densely populated regions, specialized reinforcement projects should be executed to effectively safeguard the lives and property of residents.

4. Discussion

4.1. Regional Context and Methodological Validation in an Eco-Environmental Framework

Li et al. [40] conducted a thorough risk evaluation and layout optimization of check dams in the Yellow River Basin. The results revealed that the Wuding River Basin had the greatest quantity of medium- and high-risk dams (506), and the region of comprehensive risk vulnerability for check dams in this basin was also the largest, reaching 28,700 km². This widespread risk underscores a potential threat not only to local safety but also to the regional eco-environment, as dam failures can disrupt downstream sediment regimes and compromise the long-term benefits of vegetation recovery and soil fertility enhancement projects. Secondly, regarding the Wangmaogou watershed, a tributary of the Jiuyuangou watershed, Li et al. [41,42] established a safety assessment index system for check dam systems in tiny drainage basins on the Loess Plateau. They reported that the management factor score is typically insufficient compared to other criteria, adversely impacting the overall evaluation results of check dam systems, thereby highlighting the necessity to enhance the significance of check dam operation and management in this region. Bing and Ke et al. [43,44] conducted a comprehensive risk evaluation regarding check dam systems in the Jiuyuangou Basin and reached a similar conclusion: the operational and managerial risks associated with the check dams inside the Jiuyuangou Basin are paramount. The majority of structural risks connected with check dams are minimal. Flood risk and loss risk increase with increasing precipitation return period. According to the relevant data from the “15 July” and “26 July” heavy rainstorms, the damage to the check dam caused by the two 100-year floods is either light or heavy [45,46]. This study quantified a 44.74% risk probability for check dam failures under 100-year storm scenarios. Although the early-warning outcome exceeded actual observed failure rates, this divergence stemmed from our integrated multi-risk coupling framework—an approach that comprehensively internalized engineering, environmental, and socio-economic vulnerabilities. Such holistic risk internalization enhances the predictive robustness of assessment systems for eco-hydrological infrastructure.

Our risk-based recommendations, therefore, are directly actionable within the established policy framework of the “Integrated Protection and Restoration of Mountains, Rivers, Forests, Farmlands, Lakes, Grasslands, and Deserts” in the Loess Plateau. By prioritizing dams with high comprehensive risk, this study provides a scientific basis for targeting investments in reinforcement and management, thereby directly supporting the broader goals of ensuring regional ecological security and sustainable sediment management. Given accelerating climate extremes across the Loess Plateau, advancing operational risk assessment methodologies becomes imperative for synergizing disaster resilience with eco-restoration goals in new-era soil–water conservation systems. Moreover, the risk assessment framework established in this study is highly transferable to other watersheds with similar geoclimatic conditions and check-dam infrastructures, particularly in erosion-prone regions like the Loess Plateau. The multi-dimensional indicator system, integrating engineering, management, environmental, and loss risks, offers an adaptable template that can be calibrated with local data. This approach provides a scientific basis for regional check-dam safety monitoring and prioritized risk governance beyond the Jiuyuangou Basin. A limitation of this study is the lack of validation against historical dam performance data (e.g., recorded failures, overtopping incidents). While such validation would unequivocally strengthen the model’s credibility, the relevant datasets are regulated and not publicly accessible within the timeframe of this research. Future work will prioritize collaborating with hydrological authorities to obtain these critical records for model calibration and verification.

4.2. Risk-Informed Mitigation Strategies and Transferability of the Framework

The simulated examination of 73 extant check dams reveals that 6 do not conform to the original design standards. According to the present flood control standards—10-year return interval for small dams, 50-year period of return for medium dams, and 100-year return period for critical dams—23 dams will be subjected to varied levels of water damage risk. Considering the aforementioned risk attributes, alongside the flood-damaged check dam’s risk assessment findings, a comprehensive repair strategy is proposed, encompassing three dimensions: engineering transformation, facility optimization, and standard enhancement (

Table 8. Measures for the rehabilitation and reinforcement of risky check dams.

Name of Check Dam	Type	Increase Dam Height (m)	Increase Storage Capacity (104 m3)	Drainage Facilities	Design Criteria	Risk Transfer
Wangjiagou No. 1 dam	Small dam	1	3.1			Share downstream risks
Guandaogou No. 1 dam	Medium-sized dam	1	11.5	Additional spillway	10 → 50	Risk transfer downward
Guandaogou No. 2 dam	Small dam	1	3.0		5 → 10	Share downstream risks
Majiagou guaigou dam	Small dam	0	0	Additional shaft/horizontal pipe	5 → 10	Risk transfer downward
Yayaogou dam	Backbone dam	1	3.5		20 → 100	Share downstream risks
Tuanwougou No. 2 dam	Small dam	1	0.8		5 → 10	Share downstream risks
Xiangtagou No. 3 dam	Small dam	3	3.6			Share downstream risks
Xiangtagou No. 1 dam	Medium-sized dam	0	0	Additional spillway	10 → 50	Risk transfer downward
Chaijiagou No. 1 dam	Backbone dam	1	1.7		5 → 100	Share downstream risks
Mazhangzui dam	Backbone dam	1	4.0		20 → 100	Share downstream risks
Laolimao dam	Medium-sized dam	0	0	Additional spillway		Risk transfer downward
Haojialiang dam	Backbone dam	1	2.8		20 → 100	Share downstream risks
Xiyangou Goukou dam	Backbone dam	1	5.6		20 → 100	Share downstream risks
Guandigou No. 4 dam	Medium-sized dam	0	0	Additional spillway	10 → 50	Risk transfer downward
Guandigou No. 3 dam	Small dam	1	1.2		5 → 10	Share downstream risks
Madizui dam	Medium-sized dam	1	1.8		10 → 50	Share downstream risks
Nianyangou No. 1 dam	Medium-sized dam	0	0	Additional spillway	10 → 50	Risk transfer downward
Weijiayan No. 3 dam	Medium-sized dam	0	0	Additional spillway	10 → 50	Risk transfer downward
Yangquanzui dam	Medium-sized dam	0	0	Additional spillway	10 → 50	Risk transfer downward
Liushugou dam	Backbone dam	1	3.2		20 → 100	Share downstream risks
Wujiagou dam	Medium-sized dam	0	0	Additional spillway	20 → 50	Risk transfer downward
Nanzuigou dam	Medium-sized dam	1	0.9		10 → 50	Share downstream risks
Erlangcha No. 1 dam	Backbone dam	1	4.5		20 → 100	Share downstream risks

). To concretely demonstrate the efficacy of these strategies, we illustrate how targeted interventions can alter the risk classification of specific dams. For instance, the Guandaogou No.1 medium-sized dam was identified with a ‘Moderate’ comprehensive risk (Level 2), primarily driven by its high environmental risk ($R_c$) and significant risk from defective water release facilities ($R_{a3}$). Our analysis shows that by implementing the proposed measure of adding a spillway, its $R_{a3}$ index—a key contributor to its overall risk—is projected to decrease substantially from 0.68 to 0.42. This intervention would directly lower its comprehensive risk score, reclassifying it from ‘Moderate’ to ‘Mild’ risk (Level 3). Similarly, for the Majiagou guaigou small dam, which faces elevated engineering design risk ($R_{a1}$), the addition of a shaft and horizontal pipe, coupled with an upgraded design standard, is estimated to reduce its $R_{a1}$ index from 0.61 to 0.38, thereby also transitioning its overall risk from ‘Moderate’ to ‘Mild’.

These case-specific analyses confirm that the proposed measures are not merely conceptual but have a quantifiable impact on risk reduction. The general mitigation strategy includes heightening 15 dams to augment flood control capacity, adding spillways to 8 dams to improve flood discharge capacity, incorporating shafts and horizontal pipes into 1 dam to enhance the diversion system, and comprehensively upgrading the design standards of 20 dams. The flood control regulations for backbone dams have been increased from a 20-year return period to a 100-year period; for medium dams, from a 10-year return period to a 50-year period; and for small dams, from a 5-year return period to a 10-year period. Increasing the elevation of the dam structure allows for the effective distribution of flood control pressure within the downstream dam system, facilitating the scientific transfer of risk downstream through the incorporation of water release mechanisms. Consequently, the overall risk level of the entire dam system can be systematically mitigated by improving its spatial configuration. These tailored and quantitatively justified mitigation strategies, informed by quantitative risk assessment, are not only applicable to the Jiuyuangou watershed but also highly transferable and practical for other small watersheds in the Loess Plateau with similar gully topography, hydrological characteristics, and dam system structures. They can serve as a standardized and scalable governance framework for regional check dam risk management.

5. Conclusions

Leveraging comprehensive historical data, this study established a quantitative risk evaluation framework with four primary and twelve secondary indicators to assess flood-induced check dam failures. Through the fuzzy analytic hierarchy process, precise weighting coefficients were assigned to each parameter, enabling rigorous risk quantification via weighted cumulative scoring across dam networks. This systematic approach advances predictive capabilities for eco-hydrological infrastructure vulnerability.

The findings indicate that in the Jiuyuangou watershed, roughly fifty percent of the check dams are classified as being at mild risk, around twenty-five percent are deemed at moderate risk, and just a small number are assessed as essentially safe. According to different primary risk indicators, the distribution of engineering risk is quite uniform, environmental risk is predominantly high, the risk of loss is notably concentrated, and management risk is very pronounced. These interrelated threats substantially undermine soil–water conservation ecosystems.

To synergize disaster resilience with eco-restoration, we recommend strengthening institutional frameworks during dam retrofitting and new construction, implementing risk-informed early-warning systems in populated areas, and developing spatial risk redistribution strategies that balance sediment control with ecological security. These measures establish science-based pathways for safeguarding watershed sustainability across climate-vulnerable regions.