A new controlled drainage system for submarine tunnels using double-adhesive waterproof membrane

Abstract

Traditional submarine tunnels with drainage systems are highly susceptible to water leakage, which is challenging to locate and manage, leading to high maintenance costs. To address this problem, a new controlled drainage system for submarine tunnels was proposed in this study. The system utilizes a double-adhesive waterproof membrane instead of traditional waterproof sheets, which not only reduces the likelihood of leakage but also makes subsequent leak detection and repair easier. In addition, replacing blind pipes with drainage sheets significantly improves the clogging resistance of the drainage system. The influence of grouting circles and drainage sheets on the water inflow and the external water pressure on the lining was then analyzed using numerical calculation methods. Finally, the design process of the new controlled drainage system was proposed. The research suggests that the new system allows for a multi-stage control method using grouting circles and drainage sheets, providing greater design flexibility. In the primary control stage, grouting circles effectively reduce the tunnel water inflow and the external water pressure on the lining, with the permeability coefficient playing a crucial role. In the secondary control stage, the spacing and width of the drainage sheets can regulate the water inflow and pressure. Unlike grouting circles, drainage sheets decrease water pressure while inevitably increasing water inflow, and vice versa. These findings can serve as a valuable reference for the design of waterproof and drainage systems in submarine tunnels.

Graphical abstract

Keywords

submarine tunnel / spray-applied waterproofing membrane / drainage system / numerical simulation / design process

1 Introduction

Compared to other modes of transportation across straits, submarine tunnels offer significant advantages, including minimal impact on the marine environment, 24/7 operability, and no disruption to navigation channels. In recent years, several submarine tunnels have been constructed worldwide [1,2], such as the Eurasian Highway Tunnel completed in 2016 in Turkey [3], the Ryfast Tunnel opened to traffic in 2020 in Norway [4], and the Dalian Bay Submarine Highway Tunnel opened in 2023 in China [5]. Furthermore, many more submarine tunnels are either under construction or in the planning phase, including the Second Jiaozhou Bay Submarine Tunnel in China [6] and the future Qiongzhou Strait-Crossing Tunnel [7]. Submarine tunnels, due to their deep-seated location beneath the seabed with high water pressure and no natural outlets, face significantly more severe water leakage issues during construction and operation compared to mountain tunnels. The water leakage not only impacts the normal operation of tunnels but also accelerates the aging of lining structures and leads to problems such as corrosion of steel reinforcement, posing a serious threat to the structural safety of tunnels [8,9]. For submarine tunnels, the waterproofing-drainage system is a critical aspect to consider due to its close relationship with later operational costs [10].

Currently, there are two main waterproof-drainage systems for submarine tunnels: the full sealing method and the controlled drainage method. Due to the full sealing method’s lining bearing the entire groundwater pressure, it must be designed with sufficient thickness when the water pressure is high. This increases the construction effort and costs, which is why the controlled drainage system is generally used in such cases. For example, the Seikan Submarine Tunnel in Japan, with a total water head height of 240 m, employs a controlled drainage system [11]. Regarding the controlled drainage system, numerous scholars have conducted relevant research using theoretical calculations [12], numerical simulations [13,14], and model experiments [15,16]. These studies have progressed systematically, initially focusing on the patterns of changes in lining water pressure and water inflow [17]. Subsequently, the research expanded to methods for determining the parameters of grouting reinforcement circles [18] and, finally, updated design concepts and methods [19]. Furthermore, Lu et al. proposed a new drainage segment by employing a numerical analysis based on the fluid–structure coupling theory, which can be helpful from the standpoint of developing a simulation method for submarine tunnels [20]. At the same time, construction technologies related to submarine tunnels [21–23] have been gradually advancing. For instance, in the field of grouting, there has been a transition from single-material grouting to the use of multiple materials and processes for composite grouting, maximizing the stability and compactness of grouting circles [24,25]. In terms of waterproofing techniques, the approach of partitioned waterproofing with reserved grout holes for plugging has, to some extent, reduced the cost of later-stage leak remediation and maintenance [26].

While the development of the above-mentioned research and technologies has contributed to some improvements in submarine tunnel drainage control, the issue of water leakage in submarine tunnels has not been fundamentally resolved. The reason for this is that the waterproof sheets used in traditional drainage systems have no bonding ability, allowing groundwater to flow freely between the waterproof sheets and the lining. Once the waterproof sheets are damaged, groundwater flows along the sheets to the weak points of the secondary lining, causing tunnel leaks and rendering the entire waterproofing system ineffective. It turns out that the redundancy of the waterproofing in traditional drainage schemes is very low. In addition, with traditional drainage systems, it is difficult to accurately locate the source of water leakage, and the resulting indiscriminate grouting leads to a significant increase in remediation costs. Relevant studies indicate that once a tunnel is in operation, maintenance costs maybe 20–30 times higher than performing the same work during construction [27], with even higher costs for submarine tunnels. Therefore, the submarine tunnel drainage systems not only need to reduce the probability of water leakage but also facilitate the localization and remediation of post-leakage issues. In response to this demand, double-adhesive sprayed waterproof materials developed in recent years offer significant advantages [28–30]. On the one hand, membrane materials can prevent water from flowing between lining layers, and water leakage only occurs when the primary support, waterproofing layer, and secondary lining are damaged at the same location, significantly reducing the probability of leakage [31]. On the other hand, the location of water leakage coincides with the area that needs grouting for sealing, eliminating the need for blind grouting, which greatly reduces the cost of leakage remediation [32].

In summary, in recent years, spray-applied waterproofing membranes have demonstrated outstanding waterproofing performance and have been widely used in tunnels worldwide [33–35]. They hold significant potential for application in submarine tunnels. However, to date, no researchers have developed a new submarine tunnel drainage control system based on double-sided bonded membrane materials, and related seepage characteristics and design methods remain unexplored. In response to this, a novel controlled drainage system using a double-adhesive waterproof materials was proposed. Furthermore, the influence of grouting circles and drainage sheets on the water inflow and the external water pressure on the secondary lining in the new system was investigated. Finally, the design process for the new controlled drainage system using sprayed waterproofing membrane was proposed.

2 The double-adhesive waterproof materials and the new controlled drainage system

2.1 The double-adhesive waterproof materials

Various types of double-adhesive spray-applied waterproof materials are available, such as MasterSeal 345 produced by Modern Building Contracting Company Group Company and Tamseal 800 produced by Normet Company [36]. These materials exhibit similar construction characteristics, most of which can be applied via spray for enhanced efficiency, and brush application is also feasible for small-area applications.

2.1.1 Material composition and membrane formation mechanism

The double-adhesive waterproof material used in this study is a two-component material primarily composed of liquid-phase polymers, solid-phase special cement, and functional additives, manufactured by Oriental Yuhong Company. During application, the solid and liquid components are uniformly mixed in a 1:1 mass ratio and then applied onto the substrate. This material exhibits characteristics of both volatilization curing and reaction curing. The membrane formation mechanism [37–39] involves the polymer emulsion encapsulating cement particles after uniform mixing, during which part of the moisture in the polymer emulsion is lost through evaporation, while the rest participates in the hydration reaction of the cement particles. As the moisture gradually dissipates from the polymer emulsion, the polymer particles aggregate and form a waterproof membrane together with the hydrated cement gel and unhydrated cement particles. The resulting waterproof membrane possesses both the flexibility grid of polymer materials and the inorganic gel grid structure. As a result, the membrane exhibits the strong aging resistance, high strength, hardness, and bonding strength of inorganic silicate materials, along with good deformability, strong structural integrity, and ease of application characteristic of polymer materials.

2.1.2 Basic parameters

According to the test method for waterproof materials (GB/T 16777) [40], the cured spray-applied waterproofing membrane is prepared into dumbbell-shaped specimens and then subjected to tensile testing. The stress–strain curves of the waterproof materials under different humidity curing conditions are shown in Fig.1. It can be observed that under various curing conditions, the tensile strength of the material exceeds 3.0 MPa, and the elongation at break exceeds 140%, indicating high strength and deformation resistance capabilities.

The performance of the spray-applied waterproofing membrane in preventing water flow between lining layers is closely related to the bonding strength between the material and the concrete. Therefore, according to the test methods for waterproof materials GB/T 16777 [40], bond strength tests were conducted as shown in Fig.2(a). Specimens with various membrane thicknesses, as shown in Fig.2(b), were tested to evaluate their influence on the bond strength. The failure modes of the effective specimens, presented in Fig.3, can be categorized into three types: Type A, mortar self-failure; Type B, mortar-membrane interface failure; and Type C, membrane self-failure.

As shown in Fig.4, the bond strength ranges from 1.0 to 1.8 MPa when the membrane thickness is between 1.5 and 5.0 mm, significantly exceeding the specified value of 0.5 MPa [41–43]. Additionally, there is a negative correlation between bond strength and cured membrane thickness, gradually decreasing with the increase in membrane thickness. To reduce costs, the thickness of the sprayed waterproofing membrane is generally less than 3 mm, which means the adhesive strength exceeds 1.4 MPa. This indicates that the sprayed waterproof membrane material has sufficient resistance to water migration.

2.2 The new controlled drainage system

Traditional submarine tunnels use inter-lining drainage to reduce water pressure, posing significant challenges for later leakage detection and repair. In response to this issue, this paper introduces a novel controlled drainage system for submarine tunnels as shown in Fig.5, combining double-adhesive waterproof materials. The scheme primarily comprises two systems: the waterproofing system and the drainage system. The waterproofing system aims to minimize water inflow into the tunnel, thereby reducing drainage costs during its operational stage. This system is composed, from outermost to innermost, of grouting circles, initial support concrete, spray-applied waterproofing membrane, and secondary lining concrete. On the other hand, the drainage system primarily serves to decrease water pressure on the lining, preventing overdesign of the lining and reducing construction costs during the tunnel’s construction phase. This system mainly consists of circumferential drainage sheets, longitudinal drainage pipes, transverse guide pipes, and drainage ditches.

The system utilizes double-adhesive waterproof materials for rapid spray application, as depicted in Fig.6. Handling overlapping areas is also convenient, requiring only the application of the material over the previous layer to achieve a specified overlap width (20–30 cm), eliminating the need for welding and significantly enhancing construction efficiency. When applying sprayed waterproofing membrane on areas with rough initial support surfaces, not only increases the consumption of waterproof materials but also raises the risk of membrane cracking. Consequently, before conducting the spray waterproofing process, sprayed mortar is typically employed to smooth the substrate. In the new controlled drainage system, circumferential drainage is facilitated using drainage sheets (Fig.7(a)). This drainage structure not only boasts high water passage capacity but also exhibits exceptional compressive strength, rendering it highly resistant to damage. Details regarding the arrangement of drainage sheets, the sprayed mortar regulating layer, and the spray-applied waterproofing membrane are illustrated in Fig.7(b).

Tab.1 below presents a comparison between the new controlled drainage system and the drainage systems of mountain tunnels and traditional submarine tunnels [44,45]. Unlike mountain tunnels, submarine tunnels aim to minimize drainage and pumping costs during the operational phase, which has led to enhanced water resistance of the initial support concrete and an increased use of grouting circles. In contrast to traditional submarine tunnels, the new controlled drainage system employs double-adhesive waterproof materials instead of traditional waterproofing sheets. With this approach, water leakage only occurs when the initial support, secondary lining, and waterproofing layer are damaged at the same location, significantly reducing the probability of leakage and facilitating later grouting repairs. The use of the new material restricts the free flow of groundwater between the lining layers, partially limiting drainage. Additionally, replacing traditional geotextiles and blind pipes with drainage sheets offers two advantages. First, Wider drainage sheets effectively address the high water pressure caused by the inability of the new material to facilitate inter-lining drainage. Secondly, these sheets offer a high drainage capacity and are less susceptible to clogging, reducing the common blockage problems observed in submarine tunnels [12].

3 The water pressure distribution of the new controlled drainage system

The analytical methods typically assume uniform groundwater flow into the tunnel during the seepage process, which is suitable for traditional non-adhesive waterproofing sheets. However, the double-adhesive characteristics of the new spray-applied membrane restricts groundwater flow between lining layers, leading to non-uniform water pressure distribution. Therefore, numerical methods based on Abaqus software, which can capture the spatial water pressure distribution, are used for analysis in this controlled drainage system.

3.1 Numerical model

3.1.1 Geometric model and mesh

The simulation assumes a submarine tunnel with the following parameters: a center-to-rock surface distance of 60 m, a rock surface-to-sea level distance of 50 m, and a grouting circle thickness of 6 m. The tunnel is a standard single-tube, double-lane highway tunnel [46] with external dimensions of 12.5 m in width and 10 m in height. The thickness of the initial support and secondary lining is 25 and 50 cm, respectively. The overall size of the model is 120 m × 120 m × 60 m (x dimension × y dimension × z dimension) as shown in Fig.8. The drainage sheets, each with a width of 0.8 m, are spaced 6 m apart. To avoid the influence of the longitudinal hydraulic boundary of the tunnel on the results, the distance of the drainage sheets at the end of the tunnel from the edge of the model is half of the spacing of the drainage sheets. The reduced integration element C3D8P [20], which is the pore-pressure element considering the fluid effect in Abaqus, was used for model meshing, and the mesh division is depicted in Fig.9.

3.1.2 Material parameters and boundary conditions

The primary aim of this study is to elucidate the water pressure distribution characteristics of the new limited discharge scheme rather than conducting structural stress analysis. Hence, all displacement degrees of freedom in the model were constrained to achieve pure seepage analysis, thereby omitting the discussion of material mechanical parameters. To simulate water seepage influenced by gravity, the entire model was subjected to a gravitational acceleration of 10 m/s², with water density set at 1000 kg/m³. Isotropic permeability coefficients were utilized in the seepage calculation analysis, and the selection of numerical values was informed by previous studies [47] and the Xiang’an Submarine Tunnel in Xiamen [48], as presented in Tab.2. As can be seen from Fig.5, the sprayed waterproofing membrane is set in the upper part of the tunnel and closely connected with the secondary lining. Therefore, to simplify the calculation, the secondary lining in the upper part of the tunnel can be set as impermeable to simulate the impermeable effect of the waterproofing layer.

The entire model’s upper surface is subjected to a constant water pressure boundary to simulate an infinite supply of seawater. The numerical value of the water pressure on the upper surface is set at 0.5 MPa, representing the hydrostatic pressure from sea level to a depth of 50 m, as shown in Fig.10. The model employs linear water pressure boundaries on both sides and a constant water pressure boundary at the bottom, equal to the static pressure of seawater. According to the results from Ref. [49], the water pressure at locations such as the drainage sheets, pipes, and drainage ditches is significantly lower compared to other positions, almost approaching zero. In addition, the drainage sheets have a high water drainage capacity, being 18–38 times that of traditional blind pipes [50]. Therefore, to simulate the drainage effect of the drainage sheets, the interior areas of the initial support, adjacent to the drainage sheets, are set to have a water pressure of 0, indicating the water is well discharged. The same approach is used for the longitudinal drainage pipes, which cannot bear water pressure, indicating successful drainage. Additionally, the transverse guide pipes, side and central drainage ditches are all located within the invert filling and do not affect the hydraulic boundaries or the surrounding seepage field. Therefore, they are not considered in the modeling.

3.2 Results

After achieving stable drainage in the tunnel with the new controlled drainage system, the distribution of pore water pressure in the surrounding rock is as depicted in Fig.11(a). It can be observed that, due to the ample supply of seawater, there is no significant alteration in the overall pre-existing hydrostatic pressure field of the surrounding rock. Upon closer examination in the zoomed-in section, it becomes apparent that the tunnel’s drainage system has effectively lowered the water pressure in the vicinity of the tunnel, resulting in pore water pressures in the surrounding rock being lower than the static water pressure.

The external water pressure distribution on the secondary lining is illustrated in Fig.11(b). The circumferential and longitudinal drainage systems divide the external surface of the secondary lining into several zones. When viewed along the longitudinal axis of the tunnel, the water pressure exhibits a “wave-like” distribution with a noticeable hydraulic gradient between the circumferential drainage systems. The highest water pressure, reaching 0.658 MPa, is observed between the two drainage sheets. This differs significantly from traditional drainage schemes where groundwater can freely flow between the lining layers, resulting in a relatively uniform and lower water pressure across the entire secondary lining.

To mitigate the effects of boundary conditions, the water pressure distribution in the circumferential direction is selected at the midpoint between the two circumferential drainage systems in the central part of the model, as shown in Fig.12. Due to the segmentation effect of the longitudinal drainage system, the circumferential water pressure distribution in the new limited discharge scheme exhibits a “mushroom-like” shape. Compared to the approximate static water pressure of 1.14 MPa, the maximum water pressure in the proposed drainage system is only around 0.66 MPa, representing a reduction of 42% in water pressure. Therefore, the new controlled drainage system based on double-adhesive waterproof materials can effectively reduce pressure.

4 Parametric analysis

Unlike traditional mountain tunnels, submarine tunnels not only need to reduce the lining water pressure but also need to strictly control the amount of water inflow in order to reduce the operating cost. Therefore, external water pressure on the lining and water inflow are the key control indexes for evaluating the feasibility of the waterproof-drainage system [48,51]. In this section, we aim to elucidate the effects of two key components in the new drainage system, grouting circles and drainage sheets, on water pressure and water inflow. These insights can inform the design of the controlled drainage system.

4.1 Grouting circle

In tunnel construction and design, the parameters related to the grouting circle mainly include thickness and permeability coefficient. Therefore, this study primarily investigates the impact of changes in grouting circle thickness and permeability coefficient on tunnel inflow and external water pressure on the secondary lining. The calculations are conducted using the model and parameters described in Subsection 3.1, with the surrounding rock permeability coefficient (k_r) set at 1 × 10⁻⁶ m/s. Only the grouting circle thickness (t_g) and permeability coefficient (k_g) are varied in the analysis.

4.1.1 Influence of grouting circle on water inflow

The relationship between tunnel water inflow and grouting circle thickness is illustrated in Fig.13 where ‘n’ represents the ratio of the permeability coefficients between the surrounding rock and the grouting circle. Fig.13 demonstrates that as the grouting circle thickness increases, the water inflow decreases. Additionally, for the same grouting circle thickness, a lower permeability coefficient of the grouting circle results in a smaller tunnel water inflow. It can be observed that the grouting circle is an effective measure to control tunnel water inflow, and the degree of control can be adjusted by varying the grouting circle thickness and permeability coefficient. When n ≥ 100 and t_g ≥ 6, reducing the permeability coefficient or increasing the grouting circle thickness has a less significant effect on reducing water inflow. Therefore, there exists a relatively economically reasonable range for grouting circle parameters, and it is not necessarily the case that the lower the permeability coefficient and the greater the thickness be more effective [52].

4.1.2 Influence of grouting circle on water pressure

The relationship between external water pressure on the secondary lining and grouting circle thickness is illustrated in Fig.14. Fig.14 demonstrates that as the grouting circle thickness increases, the external water pressure on the secondary lining decreases. Under the same grouting circle thickness, a smaller permeability coefficient of the grouting circle results in lower external water pressure on the secondary lining. When the permeability coefficient of the grouting circle is very high (n ≤ 10), increasing the grouting circle thickness does not significantly reduce the pressure on the secondary lining. However, when n ≥ 50, changes in grouting circle thickness have a significant impact on the external water pressure on the secondary lining, exhibiting a clear nonlinear relationship characterized by a rapid decrease followed by a slower decrease. When t_g ≥ 8, the effectiveness of pressure reduction becomes weaker. Therefore, during grouting circle construction, it is crucial to prioritize grouting effectiveness before considering grouting thickness. Moreover, considering both the pressure reduction effectiveness and grouting cost, there exists a reasonable range for grouting circle thickness, and thicker is not necessarily better.

The grout circle, acting as a robust waterproof barrier, exhibits an augmented waterproofing efficacy through the mitigation of the permeability coefficient or the augmentation of its thickness. This augmentation leads to a diminution in the water inflow of the tunnel, concomitant with an escalation in the water pressure endured by the grout circles. Therefore, given that the total water pressure from the sea surface to the tunnel’s interior remains invariant, it is inferred that the water pressure borne by the tunnel lining is reduced. In summary, both reducing the permeability coefficient and increasing the thickness of the grouting circle are favorable for controlling tunnel water inflow and reducing external water pressure on the lining. Additionally, to achieve the desired control outcomes, there exists an economically reasonable range of values for the grouting circle.

4.2 Drainage sheets

The parameters related to the drainage sheets in tunnel construction and design primarily include spacing and width. Therefore, this study primarily investigates the impact of changes in spacing (d_s) and width (d_w) of drainage sheets on water inflow and lining water pressure. The permeability coefficient for the grouting circle in the calculations is set to 1 × 10⁻⁸ m/s, as recommended in Subsection 4.1, with the remaining parameters consistent with Subsection 3.1.

4.2.1 Influence of drainage sheets on water inflow

The variation of tunnel water inflow with changes in the spacing between drainage sheets is illustrated in Fig.15. It is evident that the tunnel water inflow decreases as the spacing increases. Under the same drainage spacing, a smaller width of the drainage sheets results in lower tunnel water inflow. Additionally, with an increase in the spacing between drainage sheets, the influence of drainage sheets’ width on water inflow gradually diminishes. For instance, the difference in water inflow between drainage board widths of 1.4 and 0.2 m decreases from 0.15 m³·m⁻¹·d⁻¹ at a spacing of 4 m to 0.10 m³·m⁻¹·d⁻¹ at a spacing of 12 m. The drainage sheets, functioning as the sole drainage system within the lining layers, experience a reduction in their drainage capacity with an increase in the spacing and a decrease in the width. Ultimately, the water inflow of the tunnel is reduced. Therefore, for reducing tunnel water inflow, larger spacing between drainage boards and smaller drainage board widths should be considered.

4.2.2 Influence of drainage sheets on water pressure

As shown in Fig.16, the external water pressure on the secondary lining increases with an increase in the drainage sheets’ spacing. Under the same spacing, a lower drainage sheets’ width results in higher external water pressure on the secondary lining. As the spacing between drainage sheets increases, the influence of drainage sheets’ width on water pressure diminishes. This is because reducing the spacing between drainage sheets and increasing their width will enhance the drainage capacity of the entire system. An increase in drainage capacity allows the groundwater accumulated on the secondary lining to be rapidly discharged, thereby reducing the water pressure on the secondary lining. Therefore, for reducing water pressure, smaller spacing between drainage sheets and larger drainage sheets’ widths should be considered.

In comparison with Subsection 4.1, it is evident that the impact of drainage sheets on water pressure and water inflow is less significant compared to grouting circles. Furthermore, grouting circles exert a positive influence on both water pressure and water inflow, reducing the water inflow while also lowering water pressure. Hence, the selection of grouting circle parameters is often based on economic factors. In contrast, drainage sheets cannot simultaneously address both water pressure and water inflow issues; reducing water inflow inevitably leads to increased water pressure, and vice versa. Therefore, after determining the parameters of grouting circles, suitable drainage board widths and spacing can be selected considering factors such as construction convenience and cost. Typically, for ease of construction, drainage board spacing is often set equal to the length of the secondary lining pouring platform, typically 6 or 9 m. This ensures effective waterproofing at construction joint weak points while meeting overall drainage requirements for the tunnel. The width of drainage sheets should be designed to resist clogging, typically ≥ 0.5 m.

5 Design process

In traditional controlled drainage schemes, tunnel water inflow and external water pressure on the lining are primarily controlled by the grouting circle. However, the new controlled drainage system can control water pressure and water inflow not only through the grouting circle but also via drainage sheets. Therefore, compared to the traditional single-stage adjustment approach involving the grouting circle, the multi-stage adjustment approach in the new controlled drainage system as shown in Fig.17, which combines both the grouting circle and drainage sheets, is more flexible. The overall design process of the controlled drainage system for submarine tunnels is outlined as follows.

Step 1: Information collection. This step involves gathering existing construction information and design expectations. The construction information primarily includes hydrogeological data and structural characteristics of the tunnel, which are essential for subsequent calculations. Design expectations include determining allowable water pressure and water inflow. There is no fixed standard for water inflow, which needs to be determined according to the capacity of drainage equipment, operating costs, and the surrounding environment; The determination of the allowable water pressure on the second lining is different from traditional tunnels. Traditional tunnels use non-adhesive waterproof materials, and groundwater can be freely discharged through geotextiles and drainage pipes, with minimal consideration for external water pressure on the lining. Compared to this, the new system uses double-adhesive waterproof materials, groundwater cannot be freely discharged between the lining, which will lead to increased water pressure between the drainage sheets, so the secondary lining is bound to bear a certain amount of water pressure. Therefore, the lining structure calculation must consider the secondary lining water pressure.

Step 2: Preliminary design of multi-stage controlled drainage system. This includes the design of the first-stage grouting circle and the second-stage drainage sheets. According to the analysis in Section 4, the primary consideration for the grouting circle parameters should be the permeability of the grouting circle, and its permeability coefficient should be chosen to achieve the minimum value that is economically reasonable. Based on this, the thickness of the grouting circle is determined. Additionally, considering the stability requirements of the lining structure and the grouting circle, the thickness should not be too small. Subsequently, reasonable parameters for the drainage sheets are determined based on considerations of construction convenience and cost.

Step 3: Model verification and calculation. A model test [49] is designed based on the hydrogeological data obtained from Step 1 to verify the reliability of the numerical calculation method presented in Section 3. If significant discrepancies arise between the calculated results and the experimental data, a fluid-solid coupling numerical model [20] should be considered to enhance the accuracy of the numerical calculations. When field testing conditions are available, an in situ test section can also be set up to verify the rationality of the numerical model. Subsequently, the validated numerical method, confirmed through laboratory experiments, is applied to compute the lining water pressure and flow rate for the drainage control scheme proposed in Step 2.

Step 4: Verification. The calculated results of the controlled drainage scheme obtained in Step 3 are compared with the design expectation in Step 1. If they meet the criteria, the specific design parameters for the new limited drainage scheme are obtained and can be used for on-site construction. If they do not meet the criteria, new scheme parameters are proposed based on the parameter analysis patterns from Section 4, and additional seepage calculations are performed until the results meet the control standards.

6 Conclusions and outlook

1) The new controlled drainage system for the submarine tunnel consists of three main components: a grouting circle, a double-adhesive waterproof membrane, and drainage sheets. Compared to traditional methods, using a double-adhesive waterproof membrane instead of waterproof sheets not only reduces the probability of leakage but also facilitates subsequent leakage detection and treatment. However, the waterproof membrane restricts groundwater flow between the lining layers, thereby limiting the water inflow into the tunnel while increasing the water pressure on the secondary lining. Among them, the water pressure issue can be addressed by setting appropriate parameters for grouting circles and drainage sheets. Additionally, replacing blind pipes with drainage sheets significantly enhances the clogging resistence of the drainage system.

2) In the new controlled drainage scheme, both grouting circles and drainage sheets serve to regulate tunnel inflow and lining water pressure, with grouting circles playing a predominant role. The grouting circle contributes significantly to reducing tunnel inflow and external water pressure on the lining, with the permeability coefficient being a critical parameter. In contrast, drainage sheets cannot address both water pressure and inflow simultaneously, as reducing inflow inevitably leads to increased water pressure and vice versa. Therefore, after determining the parameters of the grouting circle, considerations from construction and cost perspectives are essential for determining suitable drainage sheets’ parameters.

3) For the new controlled drainage system, a multi-stage control design process has been proposed. The first-stage control focuses on the grouting circle. In the specific design, the permeability coefficient should be determined first, considering the surrounding rock conditions and construction techniques, before setting the grouting circle’s thickness, aiming for the most economical and achievable minimum value; The second-stage control focuses on the drainage sheets, specifically involving the selection of spacing and width for the drainage sheets. Unlike traditional submarine tunnel approaches that primarily rely on grouting circles to regulate seepage and lining water pressure, the new limited drainage scheme can employ a multi-stage control method using grouting circles and drainage sheets, providing greater flexibility in scheme design.

The numerical analysis conducted in our study suggests the potential feasibility of the new controlled drainage system, which incorporates a double-adhesive sprayed waterproofing membrane. However, it is important to acknowledge that our findings lack comprehensive validation through practical testing and real-world applications. These aspects, which necessitate further empirical evidence, will be the primary focus of our future research endeavors.

References

[1] Hong K. Typical underwater tunnels in the mainland of China and related tunneling technologies. Engineering, 2017, 3(6): 871–879

[2] Zhou Z, Gao T, Sun J, Gao C, Bai S, Jin G, Liu Y. An FDM-DEM coupling method based on REV for stability analysis of tunnel surrounding rock. Tunnelling and Underground Space Technology, 2024, 152: 105917

[3] Gokce H B, Arioglu E, Copty N K, Onay T T, Gun B. Exterior air quality monitoring for the Eurasia Tunnel in Istanbul, Turkey. Science of the Total Environment, 2020, 699: 134312

[4] Mikula S, Molnar P. Expected transport accessibility improvement and house prices: Evidence from the construction of an undersea road tunnel system. Journal of Transport Geography, 2023, 111: 103649

[5] Zhou H, Wang L, Jiang B, Wang Y. Improved vertical displacement calculation model for immersed tube tunnel considering tidal load. Marine Georesources and Geotechnology, 2022, 40(9): 1073–1083

[6] Liu Q, Liu Z, Xue Y, Zhang G, Li X, Zhou B, Gong H, Li Z. Deformation features and failure mechanism of subsea shield tunnels with different burial depths crossing fault-zone. Marine Georesources and Geotechnology, 2024, 42(6): 679–693

[7] Xu G, Chen X, Xue S, Townsend J F, Chen X, Tang M. Numerical assessment of non-uniform terrain and inhomogeneous wave–current loading effects on the dynamic response of a submerged floating tunnel. Ocean Engineering, 2023, 288: 115942

[8] Sun Z, Zhang D, Fang Q. Technologies for large cross-section subsea tunnel construction using drilling and blasting method. Tunnelling and Underground Space Technology, 2023, 141: 105161

[9] Sun X, Shi C, Xiao G, Ge Y, Cao C. A novel tunnel waterproof-drainage system based on double-bonded waterproofing materials and its seepage characteristics. Frontiers of Structural and Civil Engineering, 2024, 18(9): 1321–1336

[10] Li G, Wang C, Wang G, Xiao Z, Wu X, Jiang F. Effect of the blocking water and limiting discharge and surrounding rock permeability on the stability of subsea tunnel. Geotechnical and Geological Engineering, 2021, 39(2): 1365–1380

[11] Ikuma M. Maintenance of the undersea section of the Seikan Tunnel. Tunnelling and Underground Space Technology, 2005, 20(2): 143–149

[12] WangXTanZWangM. Study on waterproof and drainage technology of drilling and blast subsea tunnel. Strategic Study of CAE, 2009, 11: 71–75 (in Chinese)

[13] Li P, Feng C, Liu H, Zhao Y, Li Z, Xiong H. Development and assessment of a water pressure reduction system for lining invert of underwater tunnels. Marine Georesources and Geotechnology, 2021, 39(3): 365–371

[14] Zhao J, Tan Z, Ma N. Development and application of a new reduction coefficient of water pressure on sub-sea tunnel lining. Applied Sciences, 2022, 12(5): 2496

[15] LiZ. Study on the evolution of seepage field and the waterproof and drainage of the urban mined tunnel. Dissertation for the Doctoral Degree. Chengdu: Southwest Jiaotong University, 2016

[16] Zhao J, Tan Z, Zhou Z. Discussion on the waterproof and drainage system of the coastal tunnel and analysis of water pressure law outside lining: A case study of the Gongbei tunnel. Advances in Civil Engineering, 2021, 2021(1): 6610601

[17] WangXTanZ. Study on the characteristics of water pressure on the composite lining in underwater tunnels. Modern Tunnelling Technology, 2015, 52: 89–97 (in Chinese)

[18] Yang G, Wang X, Wang X, Cao Y. Analyses of seepage problems in a subsea tunnel considering effects of grouting and lining structure. Marine Georesources and Geotechnology, 2016, 34(1): 65–70

[19] ZhangDSunZ. An active control waterproof and drainage system of subsea tunnels and its design method. Chinese Journal of Rock Mechanics and Engineering, 2019, 38: 1–17 (in Chinese)

[20] Lu Y, Huang M, Chen Z, Zeng Z, Liu Y, Du G. Drainage design combining drain holes and pinholes for tunnel boring machine segments subject to high water pressure. Frontiers of Structural and Civil Engineering, 2024, 17: 1723–1738

[21] Shi C, Cao C, Lei M. Construction technology for a shallow-buried underwater interchange tunnel with a large span. Tunnelling and Underground Space Technology, 2017, 70: 317–329

[22] Zhou Z, Zhao J, Tan Z, Zhou X. Mechanical responses in the construction process of super-large cross-section tunnel: A case study of Gongbei tunnel. Tunnelling and Underground Space Technology, 2021, 115: 104044

[23] Zhou Z, Tan Z, Liu Q, Zhao J, Dong Z. Experimental investigation on mechanical characteristics of waterproof system for near-sea tunnel: A case study of the Gongbei tunnel. Symmetry, 2020, 12(9): 1524

[24] Li S, Zhang J, Li Z, Gao Y, Qi Y, Li H, Zhang Q. Investigation and practical application of a new cementitious anti-washout grouting material. Construction and Building Materials, 2019, 224: 66–77

[25] ZhangDSunZChenT. Composite grouting technology for subsea tunnels and its engineering application. Chinese Journal of Rock Mechanics and Engineering, 2019, 38: 1102–1116 (in Chinese)

[26] RuiYHeS. Model test and engineering application of the partitioning waterproofing for composite linings. Modern Tunnelling Technology, 2005, 42: 30–37 (in Chinese)

[27] Dammyr Ø, Nilsen B, Thuro K, Grøndal J H. Possible concepts for waterproofing of Norwegian TBM railway tunnels. Rock Mechanics and Rock Engineering, 2014, 47(3): 985–1002

[28] Jiang Y, He B, Zhao J, Pei H, Liu J, Wang H. Influence of novel polymer waterproofing membrane on mechanical properties of tunnel lining structure. Construction and Building Materials, 2022, 360: 129579

[29] Sun X, Shi C, Ge Y. Experimental investigation and cohesive zone modeling of the interface mechanical behavior in composite tunnel linings. Tunnelling and Underground Space Technology, 2024, 150: 105837

[30] Su J, Bloodworth A. Determination of the stress–strain demand curve of the sprayed waterproofing membrane interface in composite SCL tunnels. Tunnelling and Underground Space Technology, 2023, 142: 105408

[31] SunXShiCXiaoGGeY. A novel limited drainage scheme and design method for high water pressure tunnel based on double-bonded waterproofing membrane. Tunnel Construction, 2024, 44: 564–575 (in Chinese)

[32] ITA. Design Guidance for Spray Applied Waterproofing Membranes. ITAtech Report #2. 2013

[33] Pelz U, Karlovšek J. Spray-applied waterproofing membranes in tunnelling: A construction perspective. Tunnelling and Underground Space Technology, 2023, 142: 105409

[34] Su J, Bloodworth A. Groundwater pressure induced failure of sprayed waterproof membrane interface in tunnels. Proceedings of the Institution of Civil Engineers: Geotechnical Engineering, 2023, 176(6): 594–604

[35] SuJTrigleC. Crossrail sprayed concrete lining (SCL) station platform tunnel advance rate study. In: Proceedings of the 11th International Symposium on Field Monitoring in Geomechanics (ISFMG2022). London: ISFMG, 2022

[36] Pelz U, Karlovšek J. Spray-applied waterproofing membranes in tunnelling: Application and research directions in Australia. Tunnelling and Underground Space Technology, 2022, 122: 104364

[37] Ohama Y. Polymer-based admixtures. Cement and Concrete Composites, 1998, 20(2–3): 189–212

[38] Han S, Wang Y, Wang Q, Han L, Han G. Film-formation processes of polymer emulsions in polymer-cement waterproof coatings and their effect on coatings’ macroscopic properties. Construction and Building Materials, 2024, 438: 137137

[39] Kong X, Emmerling S, Pakusch J, Rueckel M, Nieberle J. Retardation effect of styrene-acrylate copolymer latexes on cement hydration. Cement and Concrete Research, 2015, 75: 23–41

[40] GB/T16777. Test Methods for Building Waterproofing Coatings. Beijing: Standards Press of China, 2008 (in Chinese)

[41] ASTMC1583-04. Standard Test Method for Tensile Strength of Concrete Surfaces and the Bond Strength or Tensile Strength of Concrete Repair and Overlay Materials by Direct Tension (Pull-off Method). West Conshohocken, PA: ASTM, 2004

[42] BSEN 1062-7. Paints and Varnishes-Coating Materials and Coating Systems for Exterior Masonry and Concrete––Part 7: Determination of Crack Bridging Properties. London: Standards Policy and Strategy Committee, 2004

[43] BSISO 16842. Metallic Materials-Sheet and Strip-Biaxial Tensile Testing Method Using a Cruciform Test Piece. London: BSI Standards Publication, 2014

[44] LiangWGuoX. Waterproofing and drainage design and construction of Xiang’an benthal tunnel. China Building Waterproofing, 2008, 26: 23–27 (in Chinese)

[45] WangXTanZWangMLiangWZhangM. Study on waterproof and drainage principles of Xiamen subsea tunnel. Chinese Journal of Rock Mechanics and Engineering, 2007, 26: 3810–3815 (in Chinese)

[46] JTG3370.1. Specifications for Design of Highway Tunnels Section 1 Civil Engineering. Beijing: Ministry of Transport of the People’s Republic of China, 2018 (in Chinese)

[47] Li P, Liu H, Zhao Y, Li Z. A bottom-to-up drainage and water pressure reduction system for railway tunnels. Tunnelling and Underground Space Technology, 2018, 81: 296–305

[48] LiPZhangDZhaoYZhangC. Study of distribution law of water pressure acting on composite lining and reasonable parameters of grouting circle for subsea tunnel. Chinese Journal of Rock Mechanics and Engineering, 2012, 31: 280–288 (in Chinese)

[49] Zhao D, Fan H, Jia L, Song Y. Research on waterproofing and drainage optimization scheme for karst tunnel lining in water-rich areas. Environmental Earth Sciences, 2021, 80(4): 150

[50] MaCMaWGuoXWangZXuXYuD. Research on water discharge capacity of convex shell type waterproof and drainage board for the railway tunnel. Modern Tunnelling Technology, 2020, 57: 204–208 (in Chinese)

[51] He B G, Li H, Zhang X W, Xie J H. A novel analytical method incorporating valve pressure for the controlled drainage of transport tunnels. Tunnelling and Underground Space Technology, 2020, 106: 103637

[52] ZhangCZhangDWangMXiangY. Study on appropriate parameters of grouting circle for tunnels with limiting discharge lining in high water pressure and water-enriched region. Chinese Journal of Rock Mechanics and Engineering, 2007, 11: 2270–2276 (in Chinese)

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