A comprehensive DEMATEL-ISM model-based safety analysis of the Lianghekou earth-rock dam

Abstract

Earth-rock dam failures account for the largest proportion of all dam failure accidents. There are many factors inducing accidents in hydroelectric projects, and the relationships between them are intricate and complex. Therefore, it is crucial to explore the relationship between the influencing factors and identify the key factors leading to accidents. Through an analysis of the factors influencing earth rock dam failures, an index system for failure influence factors was constructed in this paper. Considering complexity and integration in influence factors analysis, a DEMATEL-ISM model (Decision Making Trial and Evaluation Laboratory; Interpretive Structural Model) analysis method was employed to examine the internal relationship among various factors based on the influence degree between them, and a MICMAC model (Matrix Impacts Cross-reference Multiplication Applied to a Classification methodology) was introduced to analyze the hierarchical relationship between various factors. The results showed that The results show that the seismic capacity and flood discharge capacity of the dam body are the key influencing factors of dam safety during the operation of the earth-rock dams. The comprehensive method employed in this paper overcame the complexity of evaluation results and was capable of more directly presenting relationships of factors. As suggested by these results, the analysis model employed in this paper has great significance for preparing a flexible-efficient management scheme for earth-rock dams.

1. Introduction

Earth-rock dams are widely used and developed rapidly in hydraulic and hydropower engineering construction, which have played an important role in flood control and power generation [1,2]. However, dam failure disasters typically result in significant loss of life, property damage, and environmental destruction [3]. According to a statistical analysis by the International Commission on Large Dams (ICOLD) involving 534 dam failures in 43 countries, earth-rock dams accounted for the largest proportion of all dam failures, at 70 percent [4]. According to a survey of Chinese data, it was found that more than 3600 dam failures occurred in various provinces of China between 1954 and 2023 (Fig. 1). Among them, there were 3356 earth-rock dam failures, accounting for 85 percent of the total failures [5].

Fig. 1.

Number of dam failures per year in China from 1954 to 2023.

In recent years, with the development and application of earth and rock dams, their safety evaluation has received more and more attention. The analysis of factors affecting the safety of dams has gradually led to a series of quantitative analyses and numerical methods from the initial qualitative analysis. The safety management of earth and rock dams has gradually become systematic, dynamic, informative, and intelligent.

However, traditional safety evaluation methods tend to list the safety-influencing factors and calculate their influence weights on the project, while ignoring the influence relationships between the factors. In particular, as a complex system of a large-scale earth-rock dam project, its safety status implicates many factors, and there are various types of hierarchical relationships among these factors [6]. The Lianghekou Hydropower Station, with the highest earth-rock dam in China and the second highest in the world, is a world-class mega hydropower station constructed in the earthquake-prone region of the Tibetan Plateau in China. The hybrid pumped storage method, which enables the generation of electricity up to 19 times from a single drop of water, is a rare occurrence among energy projects globally. This exemplary project has far-reaching significance in terms of global energy and environmental protection. The Lianghekou earth-rock dam, as a representative of the world's large-scale earth-rock dams, is subject to a multitude of factors that may impact its safe operation. There is a paucity of research that systematically analyses and summarises the intrinsic relationship between these influencing factors.

This paper presents an exhaustive analysis of the causal relationships and hierarchical divisions between the various factors influencing the safety of the Lianghekou earth-rock dam. This analysis allows for the adjustment of one factor according to the logical relationship between the factors, thus indirectly controlling and managing the other factors affected by this factor. The findings of this model assist field workers in developing flexible and efficient management programs for earth and rock dams. It is conducive to more effective management of engineering safety, ensuring that the safety risks are always under control and in control. This is significant in managing engineering risks and preventing earth and rock dam failures. In addition, this paper focuses on the internal influence mechanism of high earth-rock dam safety, which provides a new entry point for the safety evaluation research of large-scale projects similar to the Lianghekou earth-rock dam. This is of great significance to the construction and scientific management of water conservancy and hydropower projects.

Our research findings have used the DEMATEL-ISM model to determine the key factors that affect the safety of the Lianghekou earth-rock dam project and know how these factors interact to affect dam safety. The structure arrangement of this research is delineated as follows.

• •Through literature analysis and the Delphi method, to identify the important factors affecting the safety of the earth-rock dam of Lianghekou Hydropower Station;
• •Use the DEMATEL method to determine the causal relationship between the influencing factors and the relative importance of each factor in maintaining the safety of earth-rock dams;
• •Couple the ISM method with the DEMATEL calculations to explore the interrelationships between the influencing factors and establish a clear hierarchical structure;
• •Apply the MICMAC analysis method to determine the classification of every factor to validate and analyze the hierarchical relationship between various factors obtained by the ISM method;
• •In light of the findings of the study and the specifics of the engineering, provide recommendations that can serve as a reference for similar large-scale earth-rock dam projects.

2. Literature review

To explore the academic literature on the safety evaluation of earth and rock dams, this research reviews academic journals related to "earth and rock dam failure", "dam safety evaluation" and from 2010 to 2023.

With the construction of numerous dams and the occurrence of dam failures, the focus of research in the field of water conservancy and hydropower engineering has gradually turned to the operational management and safety evaluation of dams. Since 2010, numerical computational methods, such as artificial neural networks [7], have begun to be applied to dam safety evaluation. The HTT model, MLR model [8], TOPSIS method [9] are successively proposed for dam safety assessment.

Considering the ambiguity and randomness of the evaluation process, the information entropy [10], the fuzzy best-worst method (FBWM), the grey clustering method [11], the toughness theory, the DEMATEL method, game theory [12] have also been combined with dam safety evaluation. Furthermore, it has been confirmed that with the growing concept of uncertainty, a shift from reactive to proactive "fine-grained + adaptive" resilience concepts applies to the safety management of complex systems [13].

Mathematical models such as cloud models, and attribute identification models are also gradually used in safety evaluation [14,15]. By numerical simulation [16], building information modeling (BIM) and other technologies [17,18], dam safety information can be effectively integrated, which is conducive to improving the risk management efficiency of water conservancy and hydropower projects.

In recent years, a considerable number of high earth-rock dam projects have been completed and put into operation in China. For large earth-rock dams with a large reservoir capacity, the consequences of dam failure are more serious, which has led to a great deal of research being carried out on the safety evaluation of large hydropower projects. A study was conducted by L. Dianqing et al. to investigate the stability design of high dam slopes utilizing the data from 30 typical high earth-rock dams in China, including the Lianghekou project [19]. It demonstrates that the Lianghekou earth-rock dam is representative of the high earth-rock dams in China, thereby reflecting its research value. C. Shuisheng selected high earth-rock dams as the research subject, employing numerical simulation techniques to elucidate the underlying mechanisms and laws governing the deformation of such dams [20]. The findings of this study indicate that reservoirs equipped with high earth-rock dams present more complex construction conditions and operating environments, and thus face heightened challenges in terms of safety assurance. N. Xiangtian et al. employed the DEMATEL-ISM method to construct a risk transfer model for the operational safety of long-distance water diversion projects, with the South-to-North Water Diversion Project in China serving as the research object [21]. This study demonstrates the high engineering reliability and adaptability of the DEMATEL-ISM method in the field of safety evaluation of hydraulic engineering.

The preceding studies illustrate the significance of a comprehensive examination of the risk factors associated with the operational safety of large earth-rock dams. Additionally, they highlight the lack of existing studies about the correlations and transfer patterns between the influencing factors of earth-rock dam safety. Consequently, this paper employs the DEMATEL-ISM method to comprehensively analyze the causal relationship and hierarchical division between various influencing factors affecting the safety of the Lianghekou earth-rock dam, and to study their internal influencing mechanisms. This approach is conducive to more effective management of project safety and provides a new idea for the safety evaluation study of large-scale projects similar to the Lianghekou earth-rock dam.

3. Research methodology

In this study, the research methodology consists of three stages, as depicted in Fig. 2. Initially, the literature review and Delphi method were utilized to identify influencing factors that affect the safety of the Lianghekou earth-rock dam project, constructing a framework for the follow-up study. Subsequently, the ISM method was used to determine the interdependence of the variables, while DEMATEL was used to discover the causal links between them [22]. The results of both methods were combined to construct the hierarchical model. Finally, the MICMAC was applied to validate the model, categorize influencing factors by determining their driving and dependence power, and analyze the correlation paths between these factors.

Fig. 2.

Research methodology flowchart.

3.1. Application of the DEMATEL-ISM methodology

The Decision Making Trial and Evaluation Laboratory (DEMATEL) method can effectively analyze the degree of direct influence and causal relationship between different factors, and present the degree of direct influence between various factors in the form of a matrix. It can also be used to identify key factors and determine the weight of indicators [23]. Until now, it has been widely used in many fields such as urban planning, security and decision-making [24,25].

Interpretive Structural Modelling (ISM) could make a complex system refined, and get a hierarchical structure that can be easily understood at a glance, making it easy to grasp the key factors. Therefore, ISM models are widely used in the analysis of complex systems [26,27].

The DEMATEL-ISM coupled model combines the advantages of the above two approaches. Thus it is widely used in the fields of management science and operations research such as cost analysis, risk management and the Internet of Things [28,29].

Based on a comprehensive review, the following hypothesis has been formed.

Hypothesis 1

There exist key factors that significantly influence the safety of earth-rock dams.

Hypothesis 2

There is a significant interaction among the identified factors in influencing the safety of earth-rock dams.

Hypothesis 3

The DEMATEL-ISM model enables to analysis of the interrelationships and hierarchy of factors affecting the safety of earth-rock dams.

3.2. DEMATEL-ISM modeling

Step 1

Suppose a system consists of N factors and the degree of influence between factor f_i and f_j can be expressed as x_ij $\in$ 0,1,2,3,4; i, j = 1,⋯,n. The initial direct relationship matrix (IDR matrix) that describes the direct influence degrees between all pairs of factors in the system is defined as X = [x_ij]_n×n, where x_ij represents the matrix of the direct effects of factor x_i on factor x_j [30].

In Step 1, the degree of influence between two factors is ‘0–4’(Table 1).

Step 2

Normalize the IDR matrix X separately to obtain the normalized impact matrix M (M = [m_ij]_n×n). The normalized IDR matrix of X is.

$$M=X·\frac{1}{\underset{1\le i\le n}{\mathit{max}}{\sum }_{j=1}^n{x}_{ij}}$$ (1)

From Equation (1), we know that 0 ≤ m_ij ≤ 1 and we have $\underset{1\le i\le n}{\mathit{max}}{\sum }_{j=1}^n{m}_{ij}$ = 1.

Step 3

Suppose the normalized IDR matrix is M = [m_ij]_n×n, the n × n identity matrix is I, and the combined influence matrix T is.

$$T=\underset{K\to \infty }{\mathit{lim}}\left(M+M^2+\cdots +M^K\right)=M{\left(I-M\right)}^{-1}$$ (2)

Step 4

Suppose r and d represent the sum of rows and the sum of columns of the combined influence matrix T, respectively. According to T = [t_ij]_n×n, r_i is the total influence given by the factor f_i to other factors, calculated as:

$$r_i={\sum }_{j=1}^n{t}_{ij},\left(i=1,2,\cdots n\right)$$ (3)

d_i is the total influence received by the factor f_i from other factors, calculated as:

$$d_i={\sum }_{j=1}^n{t}_{ji},\left(i=1,2,\cdots n\right)$$ (4)

r_i + d_i is defined as prominence, showing the degree of the important role that the factor f_i plays in the complex system; r_i −d_i shows the net influence that the factor f_i contributes to the complex system.

Categorize factors into cause-and-effect groups. If r_i −d_i is positive, the factor f_i is a cause, and if r_i −d_i is negative, the factor f_i is an effect.

Step 5

In combination with the ISM method, Calculate the overall system impact matrix H = ([ℎ_ij]_n×n):

$$H=I+T$$ (5)

Step 6

The interactions of factors are reflected by the reachable matrix K (K = [k_ij]_n×n). The elements in K take values in the range K $\in$ [0,1]. If K = 0, (i = 1,2, $\cdots$,n; j = 1,2, $\cdots$,n), it means that there is no interaction between factor f_i and factor f_j; otherwise, it means that there is an interaction between factor f_i and factor f_j.

Given the thresholdλ, the solution of the reachable matrix K by Equation (5) is discussed in two cases as follows:

$$K_{ij}=1,if{h}_{ij}\ge \lambda ,\left(i,j=1,2,\cdots ,n\right)$$ (6)

$$K_{ij}=0,if{h}_{ij}<\lambda ,\left(i,j=1,2,\cdots ,n\right)$$ (7)

where k_ij is an element of the reachable matrix K, the value of λ directly affects the composition of the reachability matrix and the subsequent hierarchy division. The specific value can be analyzed by taking several values based on experience to obtain satisfactory results. In this paper, the value of λ is the sum of the average and standard deviation of h_ij to improve the accuracy of the results of calculating the reachability matrix.

Step 7

Determine the reachable set and the set of antecedents for each factor. The equations for the reachability set R_i and the antecedent set S_i of factor c_j are as follows:

$$R_i=\left\{c_j|c_j\in C,k_{ij}\ne 0\right\},\left(i=1,2,\cdots ,n\right)$$ (8)

$$S_i=\left\{c_j|c_j\in C,k_{ji}\ne 0\right\},\left(i=1,2,\cdots ,n\right)$$ (9)

Step 8

Verify that $R_i=R_i\cap S_i$ holds. If it holds, then its corresponding factor c_i is the underlying factor and row i and column i are removed from the matrix K, and repeat this step until all factors have been crossed out. Finally, draw a multi-level recursive directed graph (ISM structured graph).

Table 1.

Safety influence degree between factors of Lianghekou earth-rock dam project.

Level	Level 1	Level 2	Level 3	Level 4	Level 5
Semantics	No influence	Low influence	General influence	Medium influence	High influence
Assignment	0	1	2	3	4

3.3. MICMAC assessment

The study employed the Matrix impacts Cross-reference Multiplication Applied to a Classification (MICMAC) strategy to classify digitalization dimensions by their level of influence and dependence. We supposed E_i and F_i represent the dependence power and the driving power of the factors, calculated as:

$$E_i=\sum _{i=1}^n{k}_{ij},\left(i=1,2,\cdots ,n\right)$$ (10)

$$E_i=\sum _{i=1}^n{k}_{ij},\left(i=1,2,\cdots ,n\right)$$ (11)

The variables “identified through the MICMAC framework were classified into four clusters”, as described by Gupta [31].

• •Cluster I (Autonomous factors): Consists of autonomous variables with a low dependence power.
• •Cluster II (Dependent factors): Contains dependent variables that possess a high driving power, but a low dependence power.
• •Cluster III (Linkage factors): Comprises linkage variables with strong driving force and dependability. These factors can be effectively employed to manipulate other factors to support managers in formulating a blueprint to successfully maintain the safety of the dam.
• •Cluster IV (Driver factors): Includes variables that have a strong affection for the safety of the Lianghekou earth-rock dam but aren't strongly influenced by other variables themselves.

4. Application of the DEMATEL-ISM model in the Lianghekou earth-rock dam

In this paper, 17 factors affecting the dam safety of the Yalong River Lianghekou earth-rock dam project in Sichuan were selected to assess the risk to its operational safety. A DEMATEL-ISM model was used to assess the influencing factors affecting the safety of the operation.

4.1. Constructing the indicators system for the factors

Lianghekou Hydropower Station is located on the mainstream of the Yalong River in Yajiang County, Ganzi Prefecture, Sichuan Province, in China. It is the controlling reservoir power station project of a large hydropower energy base in China. The hub building of Lianghekou Hydropower Station consists of an earth heart wall rockfill dam, spillway, release hole, powerhouse, water diversion, and tailwater building.

It has led to a major improvement in the regulation performance of the hydropower station complex in Sichuan Province. In addition, the Lianghekou hydropower station can increase the multi-year average annual power generation of the Three Gorges and Gezhouba hydropower stations.

By collecting information and statistically analyzing the types of failures in earth-rock dam failures [[32], [33], [34]], it was analyzed that earth-rock dam failures are mainly due to internal erosion, seepage and piping, overtopping and structural causes(Fig. 3). From the above, it is clear that many influencing factors induce earth-rock dam failures.

Fig. 3.

Percentage of factors contributing to earth-rock dam failures in China.

In this investigation on the safety impacts of Lianghekou earth-rock dams, 17 influencing factors were selected due to relevant codes and literature, expert consultation, and engineering information [35,36]. Eighteen experts were invited to participate in scoring to evaluate the DEMATEL and ISM methods through the Delphi method, aligning with Ou Yang et al.’s recommendation for DEMATEL analysis [37].

Our study employed three well-established multi-criteria decision-making approaches: ISM, DEMATEL, and MICMAC. We employed DEMATEL to discover causal links among factors. Subsequently, the ISM was applied to develop an ISM-based framework that identified significant factors, followed by the MICMAC analysis to facilitate the classification of variables based on their driving power and dependence and interpret key factors.

4.2. DEMATEL-ISM model application

Based on Step 1 and Table 2, the initial direct relationship matrix X (IDR matrix) based on the degree of the interactions between the factors was derived (Fig. 4), showing the average expert responses.

Table 2.

The factors that influence the safety of the dam of the Lianghekou earth-rock dam project.

Variable	Factor	Definition	Literature Source
f1	Quality of treatment for dam foundations and slopes	Excavation and clearing of dam foundations and bank slopes.	[5,14,33,35,36,38]
f2	Dam impermeable material	- Compaction, shear strength, and permeability of impermeable soil materials. - Quality of concrete seepage control wall and seepage control curtain. - Integrity of the dam's anti-filtration layer, and durability of the anti-filtration material.	[3,5,11,20,22,33,35,36,38]
f3	Dam-slope integrity	The quality of dry masonry revetment and the integrity of upstream and downstream dam slopes.	[3,11,14,33,35,36,38,39]
f4	Biological hazard	Termite infestation in the dam and its treatment.	[3,23]
f5	Filling and compaction quality of dams	- Selection of material yard. - Thickness of paving, rolling equipment, number of rolls. - Quality of core wall, filter back material, transition material and rockfill material.	[5,14,19,22,33,35,36,39]
f6	Flood protection elevation	The difference between the current flood defence elevation and the safety dam crest elevation.	[3,14,20,33,35,36]
f7	Capacity of the dam to release floodwater	- Quality of design and construction of inlet and outlet channels and buckets. - Section size of cave spillways. - Elevation of WES curve profile weir.	[[3], [4], [5],14,20,22,33,35,36,39]
f8	Water-retaining capacity of the dam	- Elevation of concrete wave walls - The quality of the gravel core wall, and the ability to resist scouring of upstream and downstream weirs. - Whether longitudinal cracks occur in the dam body during continuous rainfall	[3,20,33,35,39]
f9	Quality of metal structures	- Mechanical equipment integrity of accidental maintenance gates and working gates of inlet and control gates - Flexibility of opening and closing machinery	[3,4,14,20,33,35,36]
f10	Drainage capacity of the dam	Completeness of drainage facilities such as drainage ditches and holes as well as their drainage effect	[3,11,20,22,35,36]
f11	Seepage control stability of the dam	- Effectiveness of concrete footings against concentrated infiltration. - Quality of construction of drapery grouting, consolidation grouting, and back filtering layers. - Infiltration slopes, cracks and other seepage channels.	[3,5,11,14,20,22,24,33,35,38]
f12	Capacity of the dam to resist sliding	- Stability of downstream dam slopes at normal, design and check levels. - Stability of upstream slopes during sudden water level reductions. - Quality of construction of rockfill area and frame girders on slopes.	[14,19,20,32,33,35,36,39]
f13	Seismic capacity of the dam	- Minimum value of safety factor for sliding stability of dam slopes under seismic conditions. - Comparison of the magnitude of the project defence with the magnitude of the earthquake in the project area.	[3,14,20,35,36,39]
f14	Capacity of the dam to resist shear	- Quality of the transition layer between the core wall and the dam shell. - Vertical displacement rate and relative longitudinal tensile strain at the dam surface.	[8,11,14,20,20,35,38]
f15	Hydrographic dispatch management	Degree of implementation of hydrological dispatch protocols as well as the completeness of hydrological measurement and communication facilities	[4,24,35]
f16	Conservation and Maintenance	Degree of implementation of the< Code of maintenance and repair for earth rockfill dam>	[4,5,12,14,24,35]
f17	Monitoring and inspection of works sites	- Completeness of monitoring facilities and standard deviation of monitoring work - Monitoring and inspection of dam deformation, seepage and stability	[4,5,11,12,14,35]

Fig. 4.

The Initial direct relationship (IDR) matrix.

Based on this, the normalized IDR matrix M and the combined impact matrix T are derived, respectively. The latter is presented in Table 3.

Table 3.

Combined influence matrix T.

	f1	f2	f3	f4	f5	f6	f7	f8	f9	f10	f11	f12	f13	f14	f15	f16	f17
f1	0.040	0.128	0.079	0.019	0.068	0.013	0.015	0.086	0.115	0.167	0.139	0.043	0.095	0.124	0.229	0.075	0.121
f2	0.114	0.128	0.183	0.064	0.146	0.047	0.028	0.137	0.190	0.265	0.217	0.070	0.219	0.194	0.286	0.183	0.267
f3	0.032	0.101	0.090	0.104	0.066	0.007	0.015	0.029	0.144	0.176	0.144	0.042	0.193	0.157	0.210	0.112	0.129
f4	0.021	0.079	0.137	0.022	0.054	0.007	0.038	0.048	0.051	0.071	0.053	0.025	0.125	0.081	0.108	0.079	0.093
f5	0.059	0.144	0.096	0.046	0.035	0.008	0.013	0.031	0.102	0.152	0.130	0.032	0.087	0.088	0.161	0.068	0.136
f6	0.014	0.051	0.026	0.008	0.014	0.008	0.008	0.044	0.027	0.069	0.026	0.074	0.060	0.023	0.066	0.026	0.032
f7	0.034	0.105	0.148	0.110	0.040	0.010	0.019	0.040	0.093	0.184	0.118	0.129	0.176	0.138	0.240	0.144	0.160
f8	0.135	0.225	0.168	0.095	0.116	0.105	0.082	0.065	0.143	0.198	0.121	0.145	0.176	0.138	0.263	0.168	0.225
f9	0.029	0.082	0.093	0.014	0.032	0.007	0.014	0.027	0.076	0.208	0.129	0.063	0.115	0.056	0.185	0.127	0.136
f10	0.063	0.077	0.140	0.023	0.067	0.009	0.045	0.037	0.203	0.142	0.178	0.127	0.170	0.078	0.247	0.173	0.162
f11	0.053	0.051	0.115	0.016	0.055	0.005	0.011	0.022	0.096	0.173	0.067	0.058	0.132	0.055	0.176	0.089	0.098
f12	0.021	0.036	0.040	0.015	0.021	0.040	0.043	0.101	0.042	0.163	0.039	0.035	0.074	0.029	0.066	0.044	0.048
f13	0.023	0.081	0.114	0.016	0.028	0.005	0.011	0.023	0.067	0.139	0.092	0.030	0.081	0.109	0.147	0.116	0.129
f14	0.045	0.176	0.192	0.028	0.051	0.013	0.021	0.048	0.200	0.249	0.174	0.137	0.254	0.098	0.276	0.142	0.213
f15	0.099	0.155	0.195	0.028	0.080	0.010	0.019	0.043	0.234	0.279	0.209	0.062	0.230	0.206	0.186	0.170	0.195
f16	0.028	0.094	0.065	0.015	0.058	0.009	0.015	0.056	0.096	0.146	0.096	0.033	0.142	0.084	0.155	0.070	0.191
f17	0.040	0.190	0.114	0.027	0.046	0.015	0.045	0.095	0.114	0.151	0.117	0.043	0.220	0.110	0.189	0.173	0.115

The total influence received or given from other factors(r_i, d_i), the degree of the important role that the factor f_i plays (r_i + d_i), and the net influence that the factor f_i contributes to the complex system (r_i-d_i) were then obtained.

The weight in Table 4 is normalized r_i + d_i, and rank it from largest to smallest value, sa shown in Fig. 6 we obtain the results shown in Table 4 and the corresponding causal-effect relation diagram is shown in Fig. 5.

Table 4.

Prominence and other information conducive to decision-making.

Factor	ri	di	ri + di	ri - di	Identify	Weight	Rank
f1	1.209	0.614	1.823	0.595	Cause	0.0386	15
f2	2.191	1.693	3.885	0.498	Cause	0.0823	3
f3	1.288	1.682	2.970	−0.393	Effect	0.0629	8
f4	0.892	0.585	1.477	0.308	Cause	0.0313	16
f5	1.114	0.803	1.917	0.311	Cause	0.0406	13
f6	1.241	1.596	2.837	−0.356	Effect	0.0601	9
f7	1.771	2.461	4.232	−0.690	Effect	0.0896	2
f8	1.122	1.672	2.794	−0.550	Effect	0.0592	10
f9	0.856	1.149	2.006	−0.293	Effect	0.0425	12
f10	1.357	1.978	3.336	−0.621	Effect	0.0707	5
f11	1.340	2.183	3.523	−0.843	Effect	0.0746	4
f12	0.890	2.235	3.125	−1.345	Effect	0.0662	7
f13	2.159	2.994	5.153	−0.834	Effect	0.1091	1
f14	1.750	0.298	2.048	1.452	Cause	0.0434	11
f15	0.518	0.403	0.921	0.115	Cause	0.0195	17
f16	1.500	0.403	1.902	1.097	Cause	0.0403	14
f17	2.409	0.860	3.268	1.549	Cause	0.0692	6

Fig. 6.

Normalized weights of the influencing factors.

Fig. 5.

Cause-effect relation diagram.

The DEMATEL analysis revealed cause-and-effect relationships among the identified factors. Factors in the cause group, including the quality of treatment for dam foundations and slopes, dam impermeable materials, a biological hazard, the filling and compaction quality of dams, the capacity of the dam to resist shear, hydrographic dispatch management, conservation and monitoring of works sites, were found to significantly impact the safety of earth-rock dam.

Notably, dam impermeable material, capacity of the dam to release floodwater and seismic capacity of the dam emerged as the factors with the highest r_i + d_i values, suggesting that they are key factors in maintaining the safety of earth-rock dams.

The reachability matrix K is found in Equation (5)–(7), which is shown in Fig. 7. The value of λ is the sum of the average and standard deviation of h_ij.

Fig. 7.

The reachability matrix; Threshold (λ) Value: 0.145.

Based on the reachability matrix K and Equations (8), (9), the risk factors influencing the operational safety of the Lianghekou earth-rock dam project are divided as shown in Table 5. Based on the reachability matrix K and Equation (10), (11), the dependence power and the driving power of each factor are also calculated as shown in Table 5. According to Table 5, the correlation between the multi-level progressive structure model of the factors influencing the safety of the Lianghekou earth-rock dam project is shown in Fig. 8.

Table 5.

Division to find levels of factors.

Factor	Reachability Set	Antecedent Set	Intersection	Dependence power	Driving power
f1	1,13	1	1	1	2
f2	2,3,6,7,8,10,11,12,13	2,11,13,17	2,11,13	4	9
f3	3,12,13	2,3,13,14,17	3,13	5	3
f4	4	4	4	1	1
f5	5,13	5	5	1	2
f6	6,7,13	2,6,7,13,14	6,7,13	5	3
f7	6,7,8,10,11,12,13	2,6,7,8,9,13,14,16,17	6,7,8,13	9	7
f8	7,8,13	2,7,8,13,14	7,8,13	5	3
f9	7,9	9,17	9	2	2
f10	10,11,13	2,7,10,13,14,17	10,13	6	3
f11	2,11,12,13	2,7,10,11,13,14,17	2,11,13	7	4
f12	12	2,3,7,11,12,13,14,16,17	12	9	1
f13	2,3,6,7,8,10,11,12,13	1,2,3,5,6,7,8,10,11,13,16,17	2,3,6,7,8,10,11,13	12	9
f14	3,6,7,8,10,11,12,14	14	14	1	8
f15	15	15	15	1	1
f16	7,12,13,16	16	16	1	4
f17	2,3,7,9,10,11,12,13,17	17	17	1	9

Fig. 8.

The multi-level recursive directed graph (ISM structured graph) of the factor.

4.3. MICMAC results

The driving and dependent power of factors affecting the safety of the Lianghekou dam project were obtained by calculating the number of influencing factors in a row and column of the reachability matrix with matrix element '1′, as shown in Table 5. These values were then used as coordinates to fill in the MICMAC analysis quadrant diagram, which was categorized as autonomous variables, dependent variables, linkage variables, and driver variables, as illustrated in Fig. 9.

Fig. 9.

Categories of factors by MICMAC assessment.

5. Discussion of findings

5.1. Discussion of the results obtained by DEMATEL-ISM modle

The DEMATEL analysis revealed cause-and-effect relationships among the identified factors. Factors in the cause group as shown in Fig. 5, including the quality of treatment for dam foundations and slopes, dam impermeable materials, a biological hazard, the filling and compaction quality of dams, the capacity of the dam to resist shear, hydrographic dispatch management, conservation and monitoring of works sites, were found to significantly impact the safety of earth and rock dam. Notably, dam impermeable material, the capacity of the dam to release floodwater and the seismic capacity of the dam emerged as the factors with the highest r_i + d_i values as shown in Fig. 6, suggesting that they are key factors in maintaining the safety of earth and rock dams [6,40].

As shown in Fig. 8, biological hazard, flood protection elevation, water-retaining capacity of the dam and hydrographic dispatch management are isolated factors. As can be seen from the multi-level recursive directed graph, no directional segments are pointing from other factors to them, and no directional segments are emanating from them pointing to other factors. From the point of view of the combined influence matrix T, the rows and columns corresponding to them have values less than λ. From the above, it can be seen that biological hazard, flood protection elevation, water-retaining capacity of the dam and hydrographic dispatch management are the four factors that have the weakest interactions with other factors of the system and the least influential role [21].

Except for isolated factors, the capacity of the dam to resist sliding is located in Layer 1, also known as the surface factor, which is the result of the various risks involved in the operation of an earth-rock dam [40].

Capacity of the dam to release floodwater in Layer 4 of Fig. 8 directly affects the stability of the dam's drainage and acts as a bridge, also known as a connecting factor.

Monitoring and inspection of works sites in Layer 6 of Fig. 8 is at the bottom, which is the most fundamental element of the hierarchy, playing an important role in maintaining the operational safety of earth-rock dams.

5.2. MICMAC analysis

The MICMAC methodology groups factors into four groups due to their “dependencies and driving forces,” which are vital for assessing their significance. Fig. 9 presents the findings, and Table 5 provides a “driving and reliance power” analysis, with dependent, autonomous, linkage, and driver” groups.

Autonomous factors. As shown in Fig. 9, there are 6 independent factors to consider in Quadrant I, including quality of treatment for dam foundations and slopes (f₁), biological hazard (f₄), filling and compaction quality of dams (f₅), quality of metal structures (f₉), hydrographic dispatch management (f₁₅) and the conservation and Maintenance (f₁₆). The autonomous variables (in addition to the isolated factors f₄ and f₁₅) are less dependent and less driven and are mostly located in the middle of a multi-level recursive directed graph (Fig. 8). They are set during the construction period of Lianghekou earth-rock dams and hardly change much during operation, which almost does not affect the process. These factors are rarely influenced by and have less impact on other factors, acting as a bridge between them.

Dependent factors. The factors in Quadrant II include dam-slope integrity (f₃), flood protection elevation (f₆), water-retaining capacity of the dam (f₈), drainage capacity of the dam (f₁₀), seepage control stability of the dam (f₁₁) and the capacity of the dam to resist sliding (f₁₂). Factors in this quadrant are more dependent but less driven and are generally located in the middle and upper levels of the multi-level recursive directed graph(Fig. 8), with a lower degree of influence on other factors, but are more vulnerable to the influence of other factors and often rely on them to address issues [41].

Linkage factors. There are capacity of the dam to release floodwater (f₇) and seismic capacity of the dam (f₁₃) in Linkage Variables in Quadrant III. Such factors have a powerful driving force and high dependency strength, easily influenced by and affecting other factors [42]. Capacity of the dam to release floodwater (f₇) has seven driving powers and nine dependent powers. Earth-rock dams have the engineering characteristics of flood water overtopping which is dam failure, so its flood discharge capacity is closely related to the safety of the project. As shown in the multi-level recursive directed graph (Fig. 8), the metal structure, seepage control safety as well as the deformation and displacement of the dam should be inspected and maintained in time to ensure the normal operation of the spillway building and protect the safety of the dam. The tectonic stability of the Lianghekou project area is relatively poor. Moreover, within the project area, the maximum intensity of seismic effects ever experienced at the Lianghekou project site reaches VI to VII degrees. This shows that it is necessary to pay attention to the seismic safety of the project. In particular, after an earthquake, the upstream and downstream dam slopes should be thoroughly checked for landslides.

Driver Factors. Quadrant IV includes dam impermeable material (f₂), capacity of the dam to resist shear (f₁₄) and monitoring and inspection of works sites (f₁₇). Driver variables possess high driving strength and low dependent strength. Other factors have less influence on them and are generally at the bottom of the multi-level recursive directed graph (Fig. 8). They are fundamental factors in the influencing process and will influence the system continuously and deeply. Personnel managing the Lianghekou project should seriously summarize and analyze the problems found in the daily monitoring and conservation management work. Through strict enforcement of the monitoring system and implementation of maintenance responsibilities, the level of dam management will be improved to ensure the safe operation of the dam.

6. Conclusion

In this paper, we took the Lianghekou earth-rock dam project as the research object and constructed an explanatory structural model of the influencing factors by using the DEMATEL-ISM method. Furthermore, we analyzed the hierarchical relationships between the factors using the MICMAC method and elucidated the mechanism of accident generation. This information helps managers plan specific adjustment measures to successfully achieve the goals of safety management in earth-rock dam projects.

It was shown that.

• (1)Dam impermeable material (f₂), capacity of the dam to release floodwater (f₇) and seismic capacity of the dam seismic capacity of the dam (f₁₃) are the factors with the largest values of ri + di values, indicating that they are the key factors in maintaining the safety of earth-rock dams. Among them, the capacity of the dam to release floodwater (f₇) and seismic capacity of the dam seismic capacity of the dam (f₁₃) have both strong driving force and high dependence strength, which are easily influenced by other factors. It is noteworthy and important that the capacity of the dam to release floodwater (f₇) is also considered a linking factor, which directly affects the stability of the dam drainage and the stability of the slip resistance, and plays an important bridging role in the whole path of safety impacts of earth-rock dams. It can be seen that those responsible for monitoring the safety of earth-rock dams should focus on the routine maintenance of flood-release-related hydraulic structures (such as spillways and gates) to ensure the effective flood-release capacity of the dam. In addition, it is recommended that early warning measures for earthquakes should be strengthened, especially in project areas with poor geological conditions where earthquakes are more likely to occur.
• (2)Regarding the isolated factors in the multi-level recursive directed graph, it has been analyzed that this may be due to the use of the result-first method in building the hierarchy based on the reachability set Ri and the antecedent set Si. If the cause-first method or the result-cause rotation method is used to build the hierarchy, it should be possible to improve the position of the isolated factors in the multi-level recursive directed graph.
• (3)Monitoring and inspection of works sites (f17) is at the bottom of the ISM structured graph, which is the most fundamental element of the hierarchy, playing an important role in maintaining the operational safety of earth-rock dams. This indicates that the high earth-rock dam project should pay attention to the monitoring and management of the project site. In particular, attention is paid to the implementation of real-time monitoring of the dam and gate maintenance and other tasks to ensure that the integrity of the gate and other equipment is qualified to avoid flood release accidents and to ensure that the safety status of the dam can be controlled.

Although this research only analyzed the earth-rock dam safety influence factors in Lianghekou hydropower station engineering, the demonstrated approach and research findings will benefit the other large-scale earth-rock dam projects' construction and management industry. Firstly, the study combines quantitative and qualitative analyses, which fills the gap of exploring the interrelationships of influencing factors in the current research on earth-rock dam safety evaluation. The use of multi-level recursive directed graph enables the regularity of the safety impacts of earth-rock dams to be revealed in a more intuitive manner, thereby assisting field staff in the formulation of a flexible and efficient management program for earth-rock dams. This is conducive to ensuring that the safety risk is always in a controllable and in-control state, which is of great significance for the management of engineering risks and the prevention of earth-rock dam failures. Secondly, this study validates the applicability of the DEMATEL-ISM method for the safety evaluation of hydropower high earth-rock dams. High earth-rock dams operate in complex and diverse environments, with different factors contributing to risk and different failure paths leading to dam failure under different circumstances (dam type, reservoir capacity or elevation, etc.). In this context, the methodology adopted in this study may serve as a valuable reference for other large earth-rock dam projects where the interrelationships between risk factors need to be investigated.

7. Recommendations and future works

Based on this study's findings and the background of the Lianghekou earth-rock dam project, the following suggestions are proposed: |(1) Improve the management of the earth and stone dams at the Lianghekou Project by clarifying the division of responsibilities and management process and ensuring the implementation of maintenance work. To ensure the long-term stability and safe operation of earth-rock dams during flood control through regular inspection and testing, timely detection and problem-solving. (2) The intelligent monitoring system should be fully utilized to strengthen the observation and rescue of buried pipes under the dam after an earthquake. Buried pipes underground are prone to breakage, cracking, and leakage, and are highly likely to form large seepage channels during intense earthquakes. If rescue efforts are not prompt, the dam may collapse in a very short period. (3) To predict heavy rainfall, it is recommended to use a radar weather forecasting system. During the rainy season, it is important to strengthen water level monitoring in reservoirs due to the limited pressure-resistant capacity of each dam. After the design water level is reached, flood discharge should be carried out promptly to prevent the water level from continuing to rise and causing excessive lateral pressure on the dam, which could lead to dam failure. Mobile meteorological stations are installed in the dam site area to predict heavy rainfall based on a comparative summary of rainfall time, wind speed, and other recorded information. This allows for advance preparation for flood discharge.

However, this study is subject to certain limitations, which need to be improved in future work.

• (1)Constructing the initial direct relationship matrix using the expert survey method may not be entirely objective. Although two rounds of questionnaires and statistical summaries were carried out using the Delphi method, subjective factors were inevitably mixed in. In future research, the risk of earth-rock dam projects under different circumstances can be further investigated from the perspective of fuzzy mathematics by introducing uncertainty theory.
• (2)The indicators were selected and the indicator system was established based on cases and literature. To apply this system to other engineering cases, it should be analyzed in specific cases. Furthermore, the refinement of indicator selection and classification needs further research to ensure the results of earth-rock dam safety analysis are more reasonable.
• (3)The determination of the threshold λ has a significant impact on establishing the reachability matrix in the study. As is common with other studies using the DEMATEL-ISM methodology, the value of λ is the sum of the average and standard deviation of the overall system impact matrix in our research. Mathematical-statistical techniques can improve the determination of thresholds.

Ethical statement

Not applicable.

Funding

This study received funding from the Natural Science Foundation of Sichuan Province (Grant No. 2022NSFSC1009).

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

CRediT authorship contribution statement

Ankui Hu: Writing – original draft, Validation, Software, Methodology, Funding acquisition, Data curation, Conceptualization. Yajing Li: Software, Methodology, Conceptualization. Haizhen Li: Writing – review & editing. Baoda Wang: Validation, Data curation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.