## Abstract

Pumped-storage power stations (PSPSs) have higher requirements for anti-seepage compared with regular power stations. As a result, investigating the seepage distributions of PSPSs is particularly important. However, existing researches remain limited in assessing engineering needs such as ensuring the efficiency of a power station. Taking the Qingyuan PSPS as a typical case, this study aims to investigate the large-scale seepage field distribution while exploring the efficiency of the anti-seepage system. Considering the geological characteristics and structural location, a 3D finite element model is established. Based on the continuous medium model while combined with seepage control measures, the change in leakage while the anti-seepage system failed is further assessed. It is concluded that the operation status of anti-seepage measures will have a certain impact on the leakage volumes of each part. Using a comprehensive assessment, anti-seepage measures can effectively prevent seepage. When failure occurs on anti-seepage curtains, the leakage volume at the corresponding position will show an obvious growth. In summary, the findings of this study highlight the significance of avoiding excessive leakage caused by anti-seepage structure failure, the effective operation of anti-seepage measures must be ensured. The abovementioned results can provide scientific support for the seepage optimization design of PSPSs.

## HIGHLIGHTS

The refined finite element model is established.

Based on the continuous medium model.

The distribution of the large-scale seepage field is analysed.

The leakage volume and external water pressure under different deployment schemes of seepage control measures are assessed.

A parameter sensitivity analysis of the curtain failure rate is carried out.

## INTRODUCTION

*et al.*2019). Notably, pumped-storage power stations (PSPSs) have the advantages of flexibly deployed hydropower resources, high efficiency and low carbon outputs, which presents a growing development trend. By the end of 2021 in China, the installed capacity of PSPSs reached 36.39 million kW and the power generation capacity has reached 39 billion kW·h (Zhao

*et al.*2022). The distribution of some typical PSPSs China's coastal areas is shown in Figure 1. Compared with ordinary hydropower stations, PSPSs equipment is mostly located underground. Due to the complex geological conditions and numerous underground structures, the anti-seepage requirements of PSPSs are high. Therefore, it is of great significance to reasonably evaluate the anti-seepage effects of various seepage control measures to guarantee the safety of PSPSs and reduce construction costs.

Generally speaking, the seepage phenomenon in nature exists in two different media: porous media and fractured media (Du *et al.* 2000). In practical research, researchers usually adopt different research methods for different rock types located in the project area. Since large-scale projects are generally constructed on hard rock masses, typically contain small cracks that can be considered as fractured media. Therefore, various methods for determining the permeability of fractured rock masses have also been developed (Sun *et al.* 2006). Under this premise, the equivalent continuum theory provides an alternative method for equating fractured rock masses to continuum, which has lower computational costs and can describe the seepage characteristics of bedrock (Kottwitz *et al.* 2021). It should be noted that the percolation theory of equivalent continuous media has been developed maturely. Also, it is in good agreement with the actual situation (Du *et al.* 2000). In other words, the equivalent continuum model enjoys some conveniences in effortless meshing and acceptable computational cost (Azizmohammadi & Sedaghat 2020; Wang *et al.* 2022), and also it has a strong descriptive ability for the macroscopic seepage characteristics of fractured rock masses. Therefore, it has been widely used in large-scale engineering seepage analysis (Che *et al.* 2014).

In recent years, as one of the typical projects often deployed in hard rock masses, seepage problems in PSPSs have gradually attracted the attention of relevant researchers. Yang *et al.* (2021) proposed a simplified analysis method for calculating the leakage of a reservoir basin for a PSPS and deduced a calculation formula for the reservoir leakage volume applicable to different groundwater levels. In recent decades, similar to the calculation of reservoir basin leakage volume, many researchers have proposed seepage analysis methods that are generally applicable to tunnels or rivers (Li *et al.* 2017; Wang & Li 2018; Ying *et al.* 2019), which can quickly calculate river leakage volume without complex modelling work. In terms of theoretical research, Zhu (1996) proposed using the improved drainage substructure method to finely simulate the calculation boundaries of drainage holes (DH), drainage corridors (DC) and powerhouses. This solved the numerical treatment problem of many DH crossing the free seepage surface in a project. Tian *et al.* (2022) summarized the current commonly used drainage hole simulation methods and the finite element method for locating the free surface accurately to provide theoretical support for similar work.

Meanwhile, optimizing an anti-seepage system is also a key issue in engineering. For example, Zhang *et al.* (2021) proposed an anti-seepage optimization scheme for a group anti-seepage curtain at a reservoir dam site. Their research results provide support and reference for anti-seepage optimization designs of reservoir dams constructed in karst areas. Wang *et al.* (2015) examined the Huilong PSPS, and a numerical simulation calculation was carried out by using a 3D seepage model of a double-crack system. By comparing the corresponding effects of four anti-seepage schemes, the leakage volume of the fractured rock mass under each scheme was obtained. At the same time, an optimal anti-seepage scheme was selected from multiple factors such as the anti-seepage effect, engineering difficulty and engineering cost, to provide reference value for similar projects with similar geological conditions. Furthermore, Zhang *et al.* (2020) based on Mopanshan Reservoir, proposed an optimized reservoir seepage control system to ensure the normal operation of the dam under this optimized scheme while ensuring that the leakage volume met the seepage control requirements. For seepage control measures, Miao *et al.* (2022) proposed a new control inversion method suitable for the structural plane of a fractured rock mass and simulated the seepage field in the study area using the corrected model. The change in leakage volume in each part of a project area under partial and total damage of the anti-seepage system of the Jurong PSPS was also assessed to explore the effect of the anti-seepage system and put forward optimization suggestions. Based on the Hongping PSPS, an analysis method combining drainage hole secondary dissection technology and the modified node virtual flow method was adopted by Zhou *et al.* (2015), which could easily solve a seepage field problem containing complex seepage control measures. They also made a corresponding evaluation on the seepage control measures of the Hongping PSPS, which has guiding significance for the seepage control optimization of similar projects. Lin & Xu (2022) studied the seepage characteristics of a water conveyance and power generation system of a PSPS under normal conditions. Meanwhile, they assessed the role of seepage control measures such as multilayer drainage galleries and drainage hole curtains in the actual project. The results showed that the seepage control measures of the project had a good effect on water diversion and drainage. Zhang *et al.* (2018) established a large-scale 3D seepage model and analysed the characteristics of the seepage field and rationality of seepage control measures in a PSPS under normal operation. Meanwhile, a reinforcement scheme of the dam abutment position by grouting was proposed, and the original seepage control scheme was optimized. Xu *et al.* (2019), examining the Qingyuan PSPS, proposed a new drainage hole array simulation method using an existing theory. Additionally, a 3D equivalent continuous seepage finite element simulation model was established to simulate the seepage field in an underground powerhouse (UP). Shen *et al.* (2015) compared the effects of overall and local seepage control of the upper reservoir of the Zhenan PSPS. As a result, the local seepage control scheme considering both safety and economic benefits was obtained, which provided reference value for similar projects. In addition, based on an existing theory for water conveyance and power generation system, underground powerhouses, etc. Wu (2007), Zhou *et al.* (2009) and Yao & Gao (2017) estimated the seepage prevention effects of various seepage control measures in actual project operations. The seepage field in the local area was also analysed and calculated. It should be noted that seepage in fractured rock masses, which is difficult to avoid in actual engineering construction, has interested many researchers. Wen *et al.* (2020) focused on seepage control in underground chamber engineering. Based on the Wunonglong Hydropower Station Project, the long-term seepage control effect of a complex seepage control system on the fracture surrounding rock of the Wunonglong UP was studied by using a finite element numerical model. The rationality of the seepage control system for the fractured rock of the Wunonglong UP and the potential for further optimization were assessed by combining a global equivalent model with a refined submodel. The inversion method and basic theory of the permeability coefficient of fractured rock masses are also being continuously developed (Chen *et al.* 2015a, 2015b; Gan *et al.* 2020). In conclusion, few studies have focused on the large-scale seepage field distribution characteristics of a PSPS project area. In particular, this cannot be duplicated between different projects. Due to the high anti-seepage requirements and special geological conditions of a PSPS, investigating the distribution characteristics of large-scale seepage fields is one of the challenges brought by current engineering design. More importantly, under the different layout schemes of seepage control measures, the seepage characteristics and leakage volume will be changed. In other words, whether the abovementioned schemes will affect the normal operation of a power station is still a scientific problem to be solved urgently in PSPSs.

## CALCULATION METHOD AND THEORY

### Calculation model of continuous medium seepage

In practice, an intact rock mass can be regarded as a continuous porous medium, but rock often shows anisotropic seepage characteristics under the influence of structural planes such as fractures, joints and faults. However, since the sizes of rock fractures are much smaller than those of structures and buildings, the effect of the fractures can be averaged into the surrounding rock of the structures. In other words, the surrounding rock is still assumed to be a continuous porous medium that is in accordance with Darcy's law, and the groundwater within the rock is regarded as a steady flow. The analysis method based on steady flow theory usually obeys the following assumptions: (1) the surrounding rock is an isotropic continuous porous medium; (2) the seepage meets Darcy's law; and (3) the stress field of the surrounding rock and coupling effect between the seepage field and the stress field are not considered (Fang *et al.* 2007).

*v*is the seepage velocity vector;

*K*is the permeability, which is related to the structural characteristics of the porous medium itself; is the dynamic viscosity coefficient of the fluid;

*p*is the dynamic water pressure at a given point, , and

*P*is the total pressure; is the density of the fluid;

*g*is the acceleration of gravity; and is the relative height between the given point and the reference surface. Generally, water pressure is represented by water head , that is, Darcy's law can be expressed as follows:where

*k*is the permeability coefficient. The continuity equation is a mathematical expression for the conservation of fluid mass. Take any control volume in the flow field of porous media with porosity , and the outer surface surrounding the control volume is . Taking any panel on the outer surface, its outer normal direction is

*n*, and the seepage velocity through panel is

*v*. The total mass of the fluid flowing through the entire outer surface is:

### Leakage calculation method

*et al.*2022). A typical section is shown in Figure 3. For any eight-node hexahedral isotropic element, the middle section (

*abcd*) is chosen as the overflow cross-section. Meanwhile,

*S*is projected on the

*yoz*,

*zox*and

*xoy*planes, denoted as

*Sx*,

*Sy*and

*Sz*, respectively. The equation for obtaining the seepage flow through the middle of the element is as follows:

### Validation of the numerical method

*et al.*2017), meanwhile, the problem of mixing the two can also be solved through this software (Li & Xu 2015). In the use of ABAQUS, the seepage law can adopt not only Darcy's law but more extensive nonlinear law (Zhang & Dai 2010). It also has a specialized pore pressure element, which has one more degree of freedom of pore water pressure compared to conventional stress displacement elements, making it convenient for seepage stress coupling analysis (Lv

*et al.*2017). In summary, ABAQUS has significant advantages in seepage calculation, so it is appropriate to use it for numerical simulation calculations in this research. The feasibility of the numerical simulation method is verified based on the on-site seepage monitoring data of a typical tunnel engineering project in the Water Diversion Project in central Yunnan. Figure 4 presents the schematic diagram of a grid division of the typical section of the tunnel. Taking the left branch line as an example, the change in the marked tunnel leakage volume was monitored on site. At the same time, the seepage field and leakage volume are calculated by a numerical simulation method that aims to compare with the on-site measured results, to verify the rationality of the calculation method. The underground water level of the tunnel engineering changes obviously with the seasons. The water level boundary conditions are set according to the water level fluctuation. The comparison between the simulation results and measured results in the marked tunnel is revealed in Table 1. It can be observed that the simulation results are in good agreement with the measured results in different periods, and the error remains around 7%, which verifies the acceptability of the numerical simulation method in this study.

Time . | Average Water level (m) . | Monitor value . | Calculated value . | Error (%) . |
---|---|---|---|---|

2,020.8 | 2,041.85 | 2.520 | 2.333 | 7.4 |

2,020.9 | 2,030.00 | 2.043 | 2.168 | 6.2 |

2,020.10 | 2,034.22 | 2.122 | 2.225 | 4.6 |

2,020.11 | 2,034.41 | 2.104 | 2.228 | 6.0 |

2,020.12 | 2,027.86 | 1.621 | 1.684 | 3.6 |

2,021.1 | 2,028.07 | 1.222 | 1.379 | 12.9 |

2,021.2 | 2,023.56 | 1.205 | 1.300 | 7.88 |

2,021.3 | 2,018.07 | 1.199 | 1.254 | 4.25 |

Time . | Average Water level (m) . | Monitor value . | Calculated value . | Error (%) . |
---|---|---|---|---|

2,020.8 | 2,041.85 | 2.520 | 2.333 | 7.4 |

2,020.9 | 2,030.00 | 2.043 | 2.168 | 6.2 |

2,020.10 | 2,034.22 | 2.122 | 2.225 | 4.6 |

2,020.11 | 2,034.41 | 2.104 | 2.228 | 6.0 |

2,020.12 | 2,027.86 | 1.621 | 1.684 | 3.6 |

2,021.1 | 2,028.07 | 1.222 | 1.379 | 12.9 |

2,021.2 | 2,023.56 | 1.205 | 1.300 | 7.88 |

2,021.3 | 2,018.07 | 1.199 | 1.254 | 4.25 |

## CASE STUDY

### Project introduction

#### Project overview

^{2}and a total storage capacity of 12.07 million m

^{3}. The normal storage level is 1,185.00 m, and the dead water level is 1,164.00 m. The dam is a reinforced concrete face rock-fill dam, with a maximum dam height of 55.8 m and a dam crest width of 10 m. The reservoir bank and dam foundation are impervious with vertical curtain grouting, with a 3.0 Lu anti-seepage standard. The channel system is located in the mountains between the upper and lower reservoirs, with a total length of approximately 2,470 m. It includes two parts: the water diversion system and the tailwater system. The diversion system adopts a straight line form in plane and two inclined shaft arrangements in elevation. The tailwater system is arranged in two folds while the elevation takes the layout type of a flat slope and vertical shaft. The main buildings of the UP system include the main and auxiliary powerhouse, main transformer cavern, tailgate chamber. The three main chambers are in parallel, with three-layer DC around them, which are connected by DH. Similar to the upper reservoir area, the watershed area of the lower reservoir is 7.08 km

^{2}. For the lower reservoir, the normal and dead water levels are 681.00 and 639.00 m, respectively, with a total storage capacity of 10.8 million m

^{3}. The dam is a reinforced concrete face rock-fill dam, with a maximum dam height of 102 m and a crest width of 10 m. The aerial view and typical section of the hub (along unit #1) are presented in Figures 5 and 6, respectively.

#### Geological overview

*et al.*2020). The lithology is mostly rhyolitic tuff with hard texture (Xing

*et al.*2017). According to the on-site exploration results, the rock mass at the location of the project area is intact, and the exposed faults are relatively small in scale, without large structural planes developed. The project area is dominated by fault structures, with undeveloped folds. The Grade II structural plane is mainly represented by f2 and f3, the width is generally 2–4 m; and other faults are on a small scale. The details can be seen in Figure 7.

### Three-dimensional calculation model

Project area . | Weathering degree . | Permeability coefficient (×10^{−7}m/s)
. | Permeability classification . |
---|---|---|---|

The upper reservoir | Weak | 4.5 | Slightly ∼ weakly permeable |

Slight | 1.5 | Slightly ∼ weakly permeable | |

Water transmission and power generation system | Intense | 300 | Slightly ∼ weakly permeable |

Weak | 4.0 | Slightly ∼ weakly permeable | |

Slight | 1.0 | Slightly ∼ weakly permeable | |

The lower reservoir | Weak | 4.5 | Slightly ∼ weakly permeable |

Slight | 1.5 | Slightly ∼ weakly permeable | |

Faults | 300 |

Project area . | Weathering degree . | Permeability coefficient (×10^{−7}m/s)
. | Permeability classification . |
---|---|---|---|

The upper reservoir | Weak | 4.5 | Slightly ∼ weakly permeable |

Slight | 1.5 | Slightly ∼ weakly permeable | |

Water transmission and power generation system | Intense | 300 | Slightly ∼ weakly permeable |

Weak | 4.0 | Slightly ∼ weakly permeable | |

Slight | 1.0 | Slightly ∼ weakly permeable | |

The lower reservoir | Weak | 4.5 | Slightly ∼ weakly permeable |

Slight | 1.5 | Slightly ∼ weakly permeable | |

Faults | 300 |

### Calculation parameters

In the project area of the Qingyuan PSPS, the lithology is intact tuff, which mainly shows the characteristics of slight weathering and low permeability. The overall calculation area consists of three parts: the upper reservoir area, the water transmission and power generation system and the lower reservoir area. According to the results of the field water pressure test, the material parameters are given in Table 2. In addition, the permeability coefficient of anti-seepage curtains is 1 × 10^{−8} m/s, the permeability coefficient of the concrete structure is 1 × 10^{−9} m/s and the permeability coefficient of the steel plate lining structure is 1 × 10^{−13} m/s.

### Layout scheme of seepage control measures

The storage capacity of the upper and lower reservoirs of Qingyuan PSPS is 12.07 million m^{3} and 10.8 million m^{3}, respectively. The main surface runoff in the project area comes from atmospheric precipitation and surface water. In addition, groundwater is often used to maintain runoff during the dry season. In fact, the reservoir storage capacity of the Qingyuan PSPS is small and the recharge from surface runoff is relatively limited. This is a very practical demonstration that a reasonable seepage control scheme needs to be laid out in both the upper and lower reservoir areas to reduce the leakage of water stored in the reservoir basin. In addition, since the electromechanical facilities are all arranged underground, it is necessary to ensure that the seepage control measures around the UP can undertake the anti-seepage task to ensure the safety of the power station.

To investigate the changes in groundwater level during the operation of the Qingyuan PSPS and the effect of seepage control measures on inducing and discharging seepage water, the overall seepage field of the project area is simulated and analysed by a numerical simulation method. Firstly, the initial seepage field is calculated for the unconstructed state of the power station. On this basis, the distribution form of the seepage field is considered under the normal operation state after completion. Additionally, extreme conditions such as the failure of the seepage control measures during the operation process are considered, and a simulation analysis of different seepage control measure layout schemes is carried out. The specific scheme settings are demonstrated in Table 3 (‘√’ represents that the seepage control measures operate normally, ‘ × ’ represents that the seepage control measure is in the failure state). The storage level of the upper reservoir is set as the normal water level (1,185.00 m), while the lower reservoir storage level is set as the dead water level (639.00 m). The upper and lower reservoir anti-seepage curtain is laid at the bottom of the dam base, and the anti-seepage curtain of the UP is located at the tail of the powerhouse. Notably, the drainage measures of the UP include three-layer DC and DH.

Schemes . | Brief description of working conditions . | Anti-seepage curtain of the upper reservoir . | Anti-seepage curtain of underground powerhouse . | Drainage measures of underground powerhouse . | Anti-seepage curtain of the lower reservoir . |
---|---|---|---|---|---|

S01 | Normal operation | √ | √ | √ | √ |

S02 | Anti-seepage failure of the upper storage reservoir | × | √ | √ | √ |

S03 | Anti-seepage failure of underground powerhouse | √ | × | √ | √ |

S04 | Drainage measures failure of underground powerhouse | √ | √ | × | √ |

S05 | Anti-seepage failure of the lower storage reservoir | √ | √ | √ | × |

S06 | Anti-seepage failure at all parts | × | × | √ | × |

Schemes . | Brief description of working conditions . | Anti-seepage curtain of the upper reservoir . | Anti-seepage curtain of underground powerhouse . | Drainage measures of underground powerhouse . | Anti-seepage curtain of the lower reservoir . |
---|---|---|---|---|---|

S01 | Normal operation | √ | √ | √ | √ |

S02 | Anti-seepage failure of the upper storage reservoir | × | √ | √ | √ |

S03 | Anti-seepage failure of underground powerhouse | √ | × | √ | √ |

S04 | Drainage measures failure of underground powerhouse | √ | √ | × | √ |

S05 | Anti-seepage failure of the lower storage reservoir | √ | √ | √ | × |

S06 | Anti-seepage failure at all parts | × | × | √ | × |

## RESEARCH RESULTS AND ANALYSIS

### Analysis of seepage results

#### Seepage field

In the case of normal operation, the groundwater level equipotential line bends upstream at the starting position near both the middle and lower flat sections of the diversion pipelines (DP). The reason is the fact that the middle and lower flat sections of the DP are equipped with DC. In other words, due to the effect of DC on draining water, the distribution of the surrounding groundwater level changes, which is reflected as a bent equipotential line.

By comparing the groundwater level equipotential distribution under the two schemes, it can be seen that the groundwater level around the UP in the initial state is 600–650 m, approximately 170 m higher than that under normal operation. The calculation results of S01 reveal that the groundwater diving surface shows a rapid downwards trend on the upstream side due to drainage measures near the powerhouse. At this juncture, the groundwater level at the bottom of the powerhouse is similar to the bottom elevation, indicating that the area of the powerhouse is basically dried out and that there is no seepage. One also should note that the drainage system of the UP can quickly drain the seepage water, ensuring the normal operation of the electromechanical equipment in the powerhouse.

Note: When the impermeability standard is 3Lu, the allowable infiltration slope drop of the impermeable curtain is 10 (Sun 2004).

#### Leakage volume

^{3}/day, respectively. The leakage volumes of the upper and lower reservoir basins were 0.0091 and 0.0073% of the total storage capacity, respectively, which were less than 0.2‰ of the total storage capacity and in accordance with the seepage control requirements (DL/T 5016-2011). Assuming that the anti-seepage curtain of the upper reservoir failed (S02), which means the permeability coefficient of the anti-seepage curtain is the same as that of the surrounding rock mass. Under this circumstance, the leakage volume of the URB increased to 2,540.10 m

^{3}/day, which is approximately 2.3 times that of the normal operation condition, while the leakage volume of the LRB is the same as the value of S01. Similarly, in the case of the ASCLR failure, the leakage volume of the LRB increased to 2,716.04 m

^{3}/day, which is approximately 3.4 times that of the normal operation condition, while the leakage volume of the URB was not affected. It is indicated that the anti-seepage curtains of both the upper and lower reservoirs can effectively reduce the leakage volume of the reservoir basin. One should be noted that the interaction of structures far away from each other is very limited. In fact, the effectiveness of the anti-seepage curtain of the upper and lower reservoir will also have a certain impact on the leakage of the UP. For the failure of the upper reservoir curtain, the leakage volume of the UP increased to 101.1% of the normal operation condition. However, this value increased to 128.45% when the lower reservoir curtain failed. This indicates that the failure of the anti-seepage curtain at the lower reservoir has a greater impact on the leakage of the UP than the upper reservoir. The reason might be that the lower reservoir area is closer to the UP.

For the UP, when all the seepage control measures are in normal operation, the total leakage volume of the powerhouses is 447.85 m^{3}/day. When the UP anti-seepage curtain fails, its total leakage volume increases to 1,337.18 m^{3}/day, which is about three times that of the normal operating condition. Correspondingly, when the drainage measures around the UP fail, its total leakage volume increases to 3,472.41 m^{3}/day, which is about 7.7 times that of the normal operating condition. This result indicates that the seepage control measures around the UP can have a positive effect in blocking and discharging seepage water. Meanwhile, they also reduce the possible seepage water of the UP effectively. In contrast, drainage measures have a greater impact and play a vital role in the normal operation of the electrical facilities of the powerhouse. At this juncture, the leakage volume of the upper and lower reservoir basins will also change with the state of the seepage control measures around the powerhouse. When the ASCUP fails, the leakage volume of the upper and lower reservoir basins increases to 101.5 and 112% of the normal operation condition, respectively. Correspondingly, in the case of the drainage measures of the powerhouse failure, the above values increase to 102 and 114.9%, respectively. In conclusion, the total leakage volume of the UP is mainly related to the seepage control measures around the powerhouse. The impact caused by the failure of drainage measures is greater than that of the anti-seepage curtain. Notably, the working state of the seepage control measures around the UP can also be reflected in the variation in the leakage volume in the upper and lower reservoir basins. Due to the influence of distance, the impact on the leakage volume of the lower basin is greater than that of the upper basin.

As can be seen from Figure 12, the DC and the DH around the powerhouse both undertake important drainage tasks under different operating conditions. This means that they can effectively drain water around and inside the powerhouse. It is noteworthy that the leakage volume of the channel system is relatively stable under different cases, while the leakage of TT is greater than that of DP. The maximum leakage volume of the channel system occurs under scheme S03. Compared with the normal operation condition, the leakage volume of the DP and the TT increase by 10 and 13%, respectively.

^{3}/day, about 71.4% of the normal water level. However, the change in the storage level of the upper reservoir has a feeble influence on the leakage volume of the UP and LRB. When the storage level of the lower reservoir is 681.00 m, the leakage volume of the LRB increases to 1,244.37 m

^{3}/day, which is about 151% of that under dead water level conditions. Similarly, the change in the storage level of the lower reservoir mainly affects the leakage of the LRB and does not cause a significant increase in the leakage of the URB and UP.

In summary, the leakage volume of the UP is mainly affected by the seepage control measures around the powerhouse. Simultaneously, the state of the upper and lower reservoir areas will cause corresponding changes in the UP. Among them, the effect caused by the upper reservoir such as the change in water level and the failure of the anti-seepage curtain is the weakest. In contrast, the operation status of the drainage measures around the powerhouse has the most obvious impact.

#### External water pressure

### Parameter sensitivity analysis

*et al.*2022).where is the curtain failure rate, is the initial permeability coefficient of the anti-seepage curtain and is the permeability coefficient of the surrounding wall rock. The calculation results reveal that although the curtain failure rate gradually increases, the distribution characteristics of the seepage field are almost equal to those under normal operating conditions. Its underlying reason is that the DH and DC around the UP carry a very important drainage role. In other words, these measures will weaken a considerable part of the waterhead and play a dominant role in controlling the seepage field behind the curtain of the powerhouse. As a consequence, the change in the anti-seepage curtain will not cause a drastic change in the groundwater equipotential distribution. However, with the gradual failure of the powerhouse curtain, the leakage volume in DH and DC is also increasing. When the curtain of the UP failed by 30%, the leakage volume of DH increases by 75.1% compared with the normal operating condition, and the leakage volume of DC increases by 47.6%. When the curtain of the UP failed by 50%, the leakage volume of DH increases by 151.6%, and the leakage volume of DC increases by 161.7%. However, when the curtain of the UP failed by 80%, these two values increased to 372.0 and 316.1%, respectively. Meanwhile, the failure of the powerhouse curtain is also accompanied by a continuous increase in the leakage volume inside the powerhouse. In summary, the findings of this study highlight the significance of blocking water with a powerhouse curtain. In addition, the curtain is closely related to reducing the leakage volume of the DH and DC around the UP.

Notably, it can also be demonstrated that when the anti-seepage curtains of the upper and lower reservoirs fail, the influence on the leakage volume of the UP, DC and DH is very limited. Additionally, the effect caused by the lower reservoir anti-seepage curtain on the above positions is slightly greater than that of the upper reservoir area. To summarize, in terms of this engineering condition, different areas at far distances have less interaction with each other. Meanwhile, the anti-seepage curtains at different locations play an obvious role in reducing the leakage volume at the corresponding sites. As a result, during the construction and operation of PSPSs, it is recommended to strengthen the patrol inspection of the project area to ensure that the failure of the anti-seepage curtains is found and reinforced in time, so as to reduce leakage in the project area and improve the operational efficiency of the power station.

## CONCLUSION

By establishing a 3D finite element seepage calculation model of the Qingyuan PSPS, a 3D numerical simulation of the large-scale seepage field was conducted, and the effects of various seepage control measures in the project area were assessed. Simultaneously, the distribution of the seepage field, leakage volume and external water pressure under different deployment schemes of seepage control measures are analysed. More importantly, we evaluated the seepage characteristics of the Qingyuan PSPS and obtained the following conclusions:

- (1)
For normal operating conditions, the underground water level of the powerhouse is in accordance with the bottom elevation, which proves that the drainage measures are conducive to rapidly draining the seepage water from the powerhouse. In terms of different calculation conditions, the hydraulic gradient at anti-seepage curtains is less than the allowable hydraulic gradient, which can ensure the seepage stability of the structure.

- (2)
In the case of damage to seepage control measures in the study area, the leakage volume at the damage locations will increase significantly, but the interactions among them are very limited. For example, when the ASCUR fails, the leakage volume of the URB will increase to 2.3 times that of the normal operation, while the leakage volume of other typical locations will not be affected. One should also note that the leakage volume of the UP is mainly affected by the seepage control measures nearby. Especially the influence brought by the availability of drainage measures.

- (3)
Most of the channel system is located below the free face of the groundwater. That means the tunnels need to undertake the external water pressure to a certain degree. From the results of longitudinal profiles at different locations, it can be highlighted that the external water pressure at the lining location is significantly reduced under the protection of the grouting ring, which can ensure the normal function of the lining.

- (4)
Considering the partial failure of anti-seepage curtains, the percentage of curtain failure is set as 0, 30, 50, 80 and 100%. When the failure rate of the anti-seepage curtain at each part is increasing, the corresponding leakage volume of the URB will add up to 22.1, 49.01, 89 and 130%, respectively; the leakage volume of the LRB will increase to 3.53, 92.07, 148.71 and 242.99%. On the other hand, the failure of the powerhouse curtain will cause a significant increase in the leakage of DH, DC and caverns. In summary, the findings of this study highlight the significance of anti-seepage curtains to prevent water seepage, which means that the failure of curtains should be found and handled in a timely manner to guarantee the safety of the power station.

## ACKNOWLEDGEMENTS

The authors gratefully acknowledge the support of the Natural Science Foundation of Tianjin (21JCYBJC00410).

## DATA AVAILABILITY STATEMENT

All relevant data are included in the paper or its Supplementary Information.

## CONFLICT OF INTEREST

The authors declare there is no conflict.