1. Introduction

2. Leakage Evaluation Model for Tunnels near Reservoirs

1.2. Classical Domain Matter Elements, Sectional Domain Matter Elements, and Target Matter Elements

Based on the matter-element theory and tunnel leakage evaluation indicators, the classical domain matter-element Rab, the node domain matter-element RP, and the target matter element R are determined as follows,

(1)

(2)

(3)

Where μ represents the value taken by the evaluation indicator C, which usually needs to be evaluated according to relevant norms, standards, or by professional technicians. The matter-element analysis method typically uses three elements: "object P," "characteristic C," and "value μ" to describe and form a triplet matter-element R = (P, C, μ).

1.3. Selection of Status Values for Indicators and Consistency Check

To compare the importance of various evaluation indicators, the Saaty scale method is applied[21], as shown in Table 1, and the judgment matrix is as follow in Table 2.

Based on Table 2, the weight set of tunnel leakage evaluation indicators can be obtained, and the square root method is applied to calculate the weight values:

(4)

Where a_ij is the ith row and jth column element in the judgment matrix.

After normalization, the weight vectors of each indicator in the target model are obtained:

(5)

The maximum eigenvalue of the judgment matrix is calculated as follows:

(6)

Where R is the judgment matrix; A is the normalized vector of A_i (α₁α₂…α_i…α_n); and n is the order of the judgment matrix.

Finally, a consistency check is conducted, with the ratio expressed as follows:

(7)

Where CI is the consistency index; CR is the consistency ratio; and RI is the random consistency index.

1.4. Correlation Calculation

The correlation degree of tunnel leakage levels is calculated based on the matter-element correlation matrix, as follows:

(8)

(9)

(10)

Where k_ji represents the correlation degree of evaluation indicator i concerning evaluation level j; μ_ji is the value range of the classical domain, and μ_pi is the value range of the specific domain.

After determining the weight of each matter-element indicator in the evaluation model, the correlation degree of the evaluation indicators concerning the severity level of structural leakage is using the above formula. Consequently, the comprehensive correlation degree of each evaluation indicator concerning the evaluation level of the tunnel to be assessed is derived, as follows:

(11)

Where α_i is the weight of each evaluation indicator in the matter-element model, and k_ji represents the correlation degree of evaluation indicator i concerning tunnel leakage level j.

1.5. Determination of Water Seepage Levels

When all of the above parameters have been determined, the water leakage level of the target tunnel can be assessed:

(12)

2. Effects of Water Level Changes on the Stability of Near-Reservoir Tunnels

3. Determination of Status Values for Water Leakage Evaluation Indicators

3.1. Surrounding Rock Classification

The comprehensive indicators of the surrounding rock are usually determined by its classification, considering factors such as strength, structural influence, and weathering condition. Based on the Rock Mass Rating (RMR) classification standards for rock geomechanics, a scheme for classifying the impact of tunnel leakage water is determined, as shown in Table 4.

Table 4. Parameters of numerical calculation.

Table 4. Parameters of numerical calculation.

Scale	Description of the technical situation
1	Score of RMR classification >80
2	Score of RMR classification is between 60 and 80
3	Score of RMR classification is between 40 and 60
4	Score of RMR classification <40

3.2. Surrounding Rock Fracture

Indicators for rock mass joints and fractures are typically evaluated using the volume of joint number in the rock mass. The development degree of rock mass joints and fractures is used to classify the water leakage levels of tunnels, as shown in Table 5.

Table 5. Evaluation criteria for surrounding rock fracture.

Table 5. Evaluation criteria for surrounding rock fracture.

Scale	Description of the technical situation
1	Volumetric joint count of the rock mass(jv) <10 lines/m3
2	10<Jv <20 lines/m3
3	20< Jv <30 lines/m3
4	Jv >30 lines/m3

3.3. Overlying Relative Water Aquicludes

The indicator for the overlying relative aquiclude is evaluated by the thickness of the aquiclude. Aquicludes refer to impermeable layers, which are rock layers and soil layers with poor permeability, making it difficult for groundwater to pass through. The classification table for tunnel water leakage levels is determined, as shown in Table 6.

Table 6. Evaluation criteria for relative water aquicludes.

Table 6. Evaluation criteria for relative water aquicludes.

Scale	Relatively impermeable layer thickness
1	>6m
2	3~6m
3	0.5~3m
4	<0.5m

3.4. Aquifer Permeability

The seepage performance of rock mass aquifers is an important indicator for evaluating tunnel seepage water, reflecting the permeability of the rock mass. The greater the permeability, the higher the likelihood of tunnel seepage water occurrence. The permeability index of the rock mass can be represented by the permeability coefficient of the rock mass. The classification table for tunnel water leakage levels is determined, as shown in Table 7.

Table 7. Evaluation criteria for the aquifer permeability.

Table 7. Evaluation criteria for the aquifer permeability.

Scale	Description of the technical situation
1	Permeability coefficient(K) <10-4 (cm/s)
2	Permeability coefficient (K) is between 10-4 and 0.5×10-3 (cm/s)
3	Permeability coefficient (K) is between 0.5×10-3 and 10-2 (cm/s)
4	Permeability coefficient(K) >10-2 (cm/s)

3.5. Water Levels of Reservoirs

The groundwater level is closely related to the overlying water pressure and the burial depth of tunnels, and this relationship is not linear. Based on the analysis of the effects of different groundwater levels on tunnel structural displacement, stress, and plastic zones, the relative depth of tunnel burial to groundwater level is used to measure the impact of reservoir water levels on tunnel water leakage. The classification table is determined, as shown in Table 8.

Table 8. Evaluation criteria for water level of reservoirs.

Table 8. Evaluation criteria for water level of reservoirs.

Scale	Description of the technical situation
1	Relative height greater than design pavement elevation 0~5 (m)
2	Relative height greater than design pavement elevation 5~15 (m)
3	Relative height greater than design pavement elevation 15~25 (m)
4	Relative height greater than design pavement elevation >25 (m)

3.6. Water Erosion

Water erosion significantly impacts the durability of concrete structures. The erosion indicators are affected by the external environment and different mineral compositions of the water. The classification table for the impact of tunnel water leakage is determined, as shown in Table 9.

Table 9. Evaluation criteria for water erosion.

Table 9. Evaluation criteria for water erosion.

Scale	Ph	Erosive CO2(mg/L)	Water Cl-(mg/L)
1	>6.5	<15	<100
2	5.0-6.5	15-30	100-500
3	4.0-5.0	30-60	500-5000
4	<4.0	>60	>5000

3.7. Buried Depth of Tunnels

The greater the tunnel depth, the larger the catchment area, and the more groundwater groundwater supplied. Therefore, the average depth of the tunnel affects tunnel water leakage. For a specific tunnel, there is a minimum inflow depth that influences tunnel water leakage. The relative height of the minimum inflow depth can be used for evaluation. The classification table for the impact of tunnel water leakage is determined , as shown in Table 10.

Table 10. Evaluation criteria for the buried depth of tunnels.

Table 10. Evaluation criteria for the buried depth of tunnels.

Scale	Description of the technical situation
1	The tunnel depth is near the buried depth of the theoretical minimum water inflow.
2	The tunnel depth is less than the theoretical minimum water inflow.
3	The tunnel depth is greater than the theoretical minimum water inflow.
4	The tunnel depth is far greater than the theoretical minimum water inflow.

3.8. Area of Tunnel Cross-Section

After tunnel excavation, the water pressure in the surrounding area decreases, acting like a drainage channel. Therefore, the larger the cross-sectional area of the tunnel, the more serious the water leakage. The classification table for the impact of tunnel water leakage is determined, as shown in Table 11.

Table 11. Evaluation criteria for the cross section of tunnel.

Table 11. Evaluation criteria for the cross section of tunnel.

Scale	Description of the technical situation
1	Cross-sectional area <10 (m2)
2	10<Cross-sectional area<30 (m2)
3	30<Cross-sectional area<50 (m2)
4	Cross-sectional area >50 (m2)

3.9. Tunnel Drainage Facilities for Water Leakage

Tunnel drainage systems span the design, construction, and operational service stages. The effectiveness of drainage facilities depends on whether the design is reasonable, construction quality meets standards, and regular inspections are conducted during the operational service stage. It also depends on whether issues are promptly identified and addressed. The classification table for the impact of tunnel drainage facilities on water leakage is determined as shown in Table 12.

Table 12. Evaluation criteria for the drainage facilities.

Table 12. Evaluation criteria for the drainage facilities.

Scale	Description of the technical situation
1	Well-designed anti-drainage, standardized construction, regular maintenance
2	Well-designed anti-drainage, poor construction quality, regular maintenance
3	Well-designed anti-drainage, poor construction quality, irregular maintenance
4	Poor drainage protection design, poor construction quality, irregular maintenance

4. Leakage Evaluation of Tiebeishan Tunnel

4.1. Surrounding Rock Classification Project overview

Tiebeishan tunnel, located within the Gaoliyingzi region on the Heida line in Fushun City, Liaoning Province, China, was built in 1989. The tunnel has a total length of 178 meters, a clear width of 7 meters, and a vertical clearance height of 5 meters. The geological conditions at the tunnel site are complex, with a maximum tunnel depth of 48 meters. The surrounding rock is composed of relatively stable granite gneiss. There is a fault zone trending from northwest to southeast passing 1 kilometer to the southeast. The joint fractures in the surrounding rock are well developed, causing varying degrees of surface water infiltration at the tunnel's entrance and exit sections, leading to the emergence of a certain amount of groundwater. Over the years, regular inspections have found serious water leakage problems in the tunnel, as shown in Figure 7. Consequently, major repairs have been undertaken on the drainage system to address these issues.

Figure 7. Leakage diseases of tunnel: (a) water seepage; (b) water stain.

Figure 7. Leakage diseases of tunnel: (a) water seepage; (b) water stain.

The spatial relationship between the tunnel and the reservoir is illustrated in Figure 8. The average distance between the tunnel and the reservoir is 128 meters, with the closest point being 8 meters from the water source. The Dahuofang Reservoir, which holds water year-round, has a controlled catchment area of 5,437 square kilometers and a total storage capacity of 21.81 billion cubic meters. The proximity of the tunnel to the reservoir, combined with the well-developed fractures in the surrounding rock, creates a water seepage pathway on the side of the tunnel nearest to the reservoir. Changes in the reservoir water level can affect the stress on the tunnel lining structure. Inspections have confirmed severe leakage problems in the tunnel, which, at their worst, can compromise the structural stability of the tunnel and traffic safety.

Figure 7. Location of tunnel.

Figure 7. Location of tunnel.

4.2. Determination of the Matter-Element Model

The classification of tunnel water leakage damage is divided into four categories: P1 for intact condition, P2 for minor leakage, P3 for moderate leakage, and P4 for severe leakage. After determining the classical domain and section domain of the matter-element model, the matter-element to be evaluated is determined based on the actual engineering situation of the Tiebeishan Tunnel.

(12)

4.3. Determination of Evaluation Indicator Weights and Consistency Tests

Based on the criterion of relative importance, a judgment matrix for the nine evaluation indicators in the matter-element evaluation model is formed, as shown in Table 13.

After establishing the judgment matrix, the weight for each indicator and the maximum eigenvalue of the judgment matrix are calculated by Equation (4), based on the square root method.

After calculation, the values for A1, A2, A3, A4, A5, A6, A7, A8 and A9 are 2.579, 2.579, 0.416, 0.717, 1.730, 0.728, 0.364, 0.373 and 2.819, respectively. The normalized weight vector for each evaluation indicator is:

A=(0.210,0.210,0.034,0.058,0.141,0.059,0.030,0.030,0.229)T

The maximum eigenvalue λ is 9.81. Therefore, the value of the consistency indicator can be derived from the following equation.

(13)

By calculating the stochastic consistency index RI as 1.46, followed by the following equation, the consistency ratio can be found.

(14)

The result proves that the weight set meets the consistency test requirement. A is the calculated weight set of each matter-element, representing the weight accounted for by each evaluation indicator.

4.4. Correlation Calculation and Determination of Disease Levels

Based on the four levels of the tunnel disease degree classified in Section 4.2, combined with Equations (8) to (10), the correlation of each index is calculated. The specific process is as follows:

(15)

(16)

(17)

(18)

Where, k_ji represents the relevance of evaluation indicator i to evaluation level j. μ_ji​ denotes the value range of the classical domain, and μ_pi denotes the value range of the section domain. ρ(μ_i​,μ_ji​) is the distance from point μ_i ​to the interval (μ_jimin,μ_jimax), and ρ(μ_i​,μ_pi​) is the distance from point μ_i​ to the interval (μ_pimin,μ_pimax). The relevance matrix, which summarizes the relevance of each evaluation indicator to the different evaluation levels, is presented in Table 14.

After calculating the correlation of each evaluation indicator regarding the four classes, based on Equation (11), the combined correlation of the disease classes of the evaluation model can be calculated as follows:

(19)

Calculation yields k1, k2, k3, k4 as -0.439, -0.191, -0.032, -0.228, according to the rating rules, the tunnel disease level is:

(20)

The evaluation grade of water leakage in the tunnel is Grade 3, indicating moderate water leakage.

4. Conclusion

(1)

Based on the existing methods for evaluating tunnel water leakage, the impact of external environmental changes on tunnels near reservoirs was considered. It is proposed that the leakage evaluation index should be divided into geological conditions, hydrological conditions and tunnel engineering aspects. Various factors influencing tunnel water leakage were analyzed, and a hierarchical evaluation index system for tunnel water leakage was proposed.

(2)

The changes in reservoir water level significantly affect the stability of tunnels. With increasing water levels, the displacements and stresses of the tunnel structure gradually increase, with the inner side of the water level experiencing significantly greater than the outer side. The plastic zone undergoes notable changes, and structural damage progresses from the inner side to the entire cross-section. Tunnels near reservoirs should focus on water level changes and implement targeted reinforcement measures to improve the stress state of tunnels.

(3)

Combining the qualitative and quantitative descriptions of leakage conditions, the evaluation indicators and value standards for water leakage were specified, based on Analytic Hierarchy Process (AHP) and the theory of extension. A hierarchical evaluation model for the leakage of tunnels near reservoirs was constructed.

(4)

The proposed leakage evaluation model was applied to the Tiebeishan Tunnel project. A judgment matrix was constructed, and the comprehensive relevance degree of the leakage grade was determined. The leakage level of the Tiebeishan tunnel is Grade 3, indicating moderate leakage. This application verified the rationality and applicability of the evaluation model.

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