1 Introduction
Throughout the years, water leakage has consistently been a significant concern within the tunnel engineering. It 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 [
1–
3]. Traditional composite lining structures with waterproofing systems are relatively well-established, with the waterproofing primarily relying on the concrete structure itself and waterproofing sheets. If constructed with proper quality, they can achieve satisfactory waterproofing effectiveness [
4,
5]. However, traditional waterproofing layers lack bonding capability with the primary lining and secondary lining, allowing groundwater to flow between the waterproofing sheets and the lining layers. In the event of localized defects in the waterproofing sheets, groundwater can penetrate weak areas of the secondary lining, resulting in tunnel water leakage and rendering the entire waterproofing system ineffective [
6], as shown in Fig.1(a). Therefore, the reliability of traditional waterproofing and drainage systems is relatively low, which is detrimental to the later operation and maintenance of tunnels. In contrast, a new spray-applied waterproofing membrane material has gained rapid momentum in recent years. This material has a double-bonded capability, which enables the waterproofing material to form a sufficient bond with the primary lining and the secondary lining to stop the water flow between the waterproofing layer and the lining. This improvement in bonding capability enhances the overall reliability of the waterproofing system and reduces the probability of water leakage occurring, as shown in Fig.1(b). Simultaneously, spray membrane waterproofing materials exhibit advantageous qualities, including high-quality overlapping and convenient, rapid installation. These materials have been successfully applied in numerous tunnels across multiple countries worldwide [
7–
10].
With the development of double-bonded spray waterproofing materials and technology, extensive research has been conducted by scholars, primarily focusing on construction techniques [
11,
12] and mechanical properties [
13]. The research findings have confirmed the synergistic load-bearing capacity of primary lining and secondary lining in tunnels under the action of double-bonded spray waterproofing materials [
6,
14]. Building upon this, it has been discovered that the spray membrane lining structure has the potential to reduce the total lining thickness [
15,
16] and carbon emissions [
17]. Despite all the benefits of spray waterproofing membrane, there are significant challenges when it is applied to drainage-type tunnels. This is because in a conventional drainage scheme, since the waterproof sheet is not bonded to the primary lining, water from the primary lining can flow between the waterproof sheet and the primary lining and drain and reduce water pressure through geotextiles and blind drainage pipes. However, the spray waterproofing membrane layer has a double-bonded ability, which prevents the flow of water between the waterproofing layer and the primary lining, and therefore the traditional interlayer drainage scheme cannot be used. As a result, existing designs of spray membrane lining structures primarily focus on fully enclosed waterproofing system, as seen in examples such as the Swiss Giswil Road Escape Tunnel, the UK Croydon Cable Tunnel, and the Guangzhou Metro Line 13 Interval Tunnel in China [
18,
19]. When used in drainage-type tunnels, the typical construction approach involves applying a geotextile layer on the surface of the primary lining before applying the sprayed waterproofing membrane. The addition of the geotextile in this approach separates the primary lining from the secondary lining, thereby preventing the synergistic load-bearing effect of the lining structure and compromising its structural advantages [
18]. Besides, the addition of geotextiles will also make the spray membrane material from the original double-sided bonding with the lining to single-sided bonding, weakening the waterproof performance.
In summary, tunnel linings with spray membrane waterproofing layers have advantages in terms of structural load-bearing and waterproofing. However, due to the double-bonded properties of the sprayed waterproofing material, the flow of groundwater between the layers is prevented, which consequently leads to an increase in lining water pressure. As a result, their application in drainage-type tunnels is limited, and their scope of application is restricted.
To maintain the excellent load-bearing and waterproofing properties of the sprayed membrane lining structure and to solve the high water pressure on the lining, a new waterproof-drainage scheme for sprayed membrane lining tunnels has been proposed, which incorporates the concept of localized drainage and pressure relief. The new approach, unlike the traditional method of drainage between lining layers, addresses the challenge of interlayer drainage and reduces water pressure in sprayed membrane lining by employing externally spaced drainage blind pipes and drainage boards between lining layers. Subsequently, the seepage characteristics of this scheme were analyzed using numerical calculation methods. Furthermore, a comparison with other drainage solutions was conducted to demonstrate the superiority and applicability of the novel drainage system. The aim of this analysis is to provide guidance and reference for the design and application of drainage in spray membrane lining structures for drainage-type tunnels.
2 A tunnel waterproof-drainage system based on double-bonded waterproof membrane
2.1 Design background
In recent years, a tunnel bottom drainage scheme has gradually emerged in high-pressure water-rich tunnels [
20,
21], as shown in Fig.2. The original intention of this scheme is to solve the problem of high water pressure in the inverted arch of the tunnel bottom through the drainage ditches arranged outside the tunnel bottom. As the drainage ditch laid outside the tunnel affects the seepage field around the tunnel due to its large flux and strong drainage capacity, it also has the effect of reducing the water pressure around the tunnel’s primary lining.
The above design concept has inspired the design of drainage schemes for tunnels with sprayed waterproofing membranes, and we can use the bottom drainage method outside the tunnel to reduce the water pressure around the tunnel to the acceptable range of sprayed waterproofing membrane materials. In this way, on one hand, by not introducing geotextile between the primary lining and secondary lining, the integrity of the “primary lining-spray waterproofing membrane-secondary lining” (composite shell lining, CSL) is ensured. This allows for the synergistic load-bearing capacity of the primary lining and secondary lining in the CSL structure. On the other hand, the performance of preventing water seepage in the CSL structure remains unaffected, retaining the advantages of convenient operation and maintenance. In summary, adopting the design concept of bottom drainage effectively addresses both the load-bearing and waterproofing requirements of CSL tunnels.
2.2 New tunnel waterproof-drainage system
Using the design concept of local drainage and pressure reduction mentioned in the previous section, and improving the local structure, a waterproof and drainage scheme of the sprayed membrane lining tunnel is designed as shown in Fig.3. The proposed drainage scheme is mainly divided into the following four parts: 1) waterproof system; 2) upper circumferential drainage system; 3) bottom circumferential drainage system; and 4) longitudinal drainage system.
1) Waterproof system. It consists of a spray waterproof membrane and a secondary lining concrete. The double-bonded spray waterproof membrane is located between the primary lining and secondary lining, positioned along the tunnel except for the arch section.
2) Upper circumferential drainage system. It mainly consists of plastic drainage sheets seen in Fig.4(a) and transversal guide pipes seen in Fig.3. The drainage sheets are positioned between the spray waterproof membrane and the primary lining. Groundwater infiltrating through the primary lining is directed toward the longitudinal drainage pipes through the drainage sheets. It is then further guided by the transversal guide pipes to the central drainage ditch, as shown in Fig.3(c).
3) Bottom circumferential drainage system. It mainly consists of bottom drainage blind pipes and vertical guide pipes. The bottom drainage blind pipes directly collect groundwater from the surrounding rock and guide it through the vertical guide pipes to the central drainage ditch.
4) Longitudinal drainage system. It primarily consists of longitudinal drainage blind pipes, side ditches, and a central drainage ditch. This system serves to connect the transversal drainage system and facilitate the discharge of groundwater from the tunnel to the outside.
In addition, the roughness of the shotcrete in the primary lining does affect the sprayed waterproofing membrane. Excessive roughness not only increases the usage of the sprayed material but may also elevate the risk of cracking in the sprayed membrane. Therefore, to ensure the quality of the sprayed membrane, a sprayed smoothing layer (aggregate particle size < 4 mm) is usually applied to repair the roughness of the primary lining. Additionally, the sprayed smoothing layer can cover the positions of the drainage sheets, addressing both the roughness of the boards themselves and their edges, as illustrated in Fig.4(b).
2.3 Comparison of new and traditional waterproof-drainage systems
The main differences of the new and traditional waterproof-drainage scheme are as shown in Tab.1 and with the reasons for the modifications outlined as follows.
1) Spray waterproofing material is used instead of traditional plastic waterproofing sheets, and geotextile is eliminated. Traditional waterproof sheets do not have bonding strength with the initial lining and secondary lining, allowing groundwater to flow freely between the lining layers. Once the waterproof sheet is damaged, groundwater can enter the tunnel through weak points in the lining, causing leakage. The spray waterproofing membrane can be directly bonded to the initial lining and secondary lining. In addition to its excellent waterproofing properties, it can also prevent groundwater from flowing between the lining layers, greatly reducing the probability of water leakage.
2) The new drainage solution includes the installation of circumferential blind pipes at the bottom of the tunnel, whereas traditional drainage tunnel designs typically do not have bottom drainage facilities, or they only have central drainage channels as shown in Fig.2 for high water pressure and rich water tunnels. Compared to the installation of big drainage channels on the outer sides, this approach offers two advantages. On one hand, it avoids extensive over-excavation at the bottom of the tunnel, resulting in a more reasonable stress distribution within the tunnel. On the other hand, it increases the contact surface area between the blind pipes, surrounding rock, and lining, directly reducing the water pressure on the contact area.
3) Plastic drainage sheets are also used to replace the circular drainage blind pipes in the upper part of the traditional tunnel. The traditional tunnel structure adopts the drainage system of geotextile and circular drainage blind pipe. The system utilizes the drainage function of the geotextile, so that the circumferential drainage pipe can reduce the water pressure in a large area around it. However, geotextiles are not included in the CSL tunnel, and a circumferential drainage structure with a wide range of influence must be adopted. Therefore, plastic drainage sheets, which have a large contact area with the primary lining, were chosen as the circumferential drainage system. Drainage sheets cannot only directly reduce the water pressure in the contact part, but also can be conveniently arranged at the construction joints to provide double protection for the weak links of waterproofing. The detailed working mechanism of the drainage system is shown in Fig.5. Groundwater is partly channeled through the plastic drainage board and partly through the bottom drainage blind pipe.
Moreover, the cost and construction convenience of the new drainage system are crucial factors influencing its future applicability. In terms of cost, although the unit price of the double-bonded waterproofing material is higher than that of ordinary waterproof sheets, it significantly reduces the probability of leakage, leading to reduced operating costs in the long run. On the other hand, the new spray membrane waterproofing material eliminates the need for geotextiles, reducing material costs. Additionally, the spray application method speeds up the construction process, lowering labor costs. In terms of construction, the installation of blind pipes at the bottom of the tunnel and vertical drainage pipes is more complex compared to traditional waterproofing methods. For this issue, a solution would be to pre-connect the vertical drainage pipes with the drainage blind pipes, wrap them with geotextile, and prefabricate the components. During usage, these prefabricated parts can be directly placed in their designated positions and backfilled, thereby expediting the construction process. In summary, the new drainage solution is construction-feasible.
3 Seepage characterization of the novel double-bonded sprayed membrane tunnel waterproof-drainage scheme
Due to the intermittent arrangement of drainage structures and the asymmetry of the upper and lower drainage facilities in the new drainage solution, it is difficult to obtain the seepage calculation results through analytical methods. In contrast, utilizing numerical method for seepage calculations allows simulation of complex conditions, with computed results showing good agreement with both experimental and theoretical calculations. Extensively validated through comparisons by numerous scholars, this calculation method has evolved into a mature computational methodology [
22–
24]. Therefore, to assess the performance of the new waterproof-drainage scheme during tunnel operation, this study employs the numerical simulation method of steady-state seepage analysis for calculation [
25]. This analysis aims to obtain the distribution characteristics of external water pressure on the secondary lining of the tunnel.
3.1 Calculation modeling
3.1.1 Geometrical modeling
To make the calculation results representative, a standard single-bore, two-lane highway tunnel [
26] was selected as the calculation model, and the cross-section dimensions of the tunnel are shown in Fig.6. Circumferential drainage systems (drainage sheets, drainage blind tubes) are laid along the tunnel at longitudinal intervals (
l m), which is a typical three-dimensional seepage problem, and therefore a three-dimensional model is established as shown in Fig.7. The model was taken to be 60 m along the longitudinal direction and contained approximately 10 circular drainage systems. The distance of the tunnel end drainage sheets from the edge of the model was half the spacing of the sheets (
l/2 m) to avoid model boundary effects on the results. Tunnel drainage will make the original seepage field change in a certain range, if the modeling size is smaller than this influence range, the hydraulic boundary set will no longer be reasonable, which will have some influence on the calculation results. Therefore, in order to avoid the calculation error caused by the size effect, the size of this stratum modeling is large enough, 400 m × 400 m × 60 m. The tunnel is located in the center of the model and the top of the outer surface of the secondary lining is 194 m from the top of the model.
According to the results from Ref. [
25], the water pressure at locations such as the drainage sheets, pipes, and drainage ditchs is significantly lower compared to other positions, almost approaching zero. Additionally, traditional drainage tunnel designs assume smooth water drainage without considering hydrostatic pressure loads. Moreover, the drainage sheets have a high water drainage capacity, being 18–38 times that of blind pipes [
27]. Hence, it is assumed that water can be smoothly discharged through the drainage sheets, indicating a water pressure of zero in these areas. Considering the above circumstances, specific geometric models for the drainage boards, blind pipes, and water ditches were not constructed during the modeling process. Instead, hydraulic boundary conditions were applied to simulate their effects [
28]. This approach minimally impacts calculation accuracy while greatly improving computational efficiency. Details of the specific methods used for applying hydraulic boundary conditions are provided in Subsubsection 3.1.2.
3.1.2 Boundary conditions
1) Displacement boundary
Since this study focuses on the drainage performance of the new lining structure rather than its mechanical properties, only seepage calculations are performed on the model. Therefore, all displacement degrees of freedom of the entire model are constrained during numerical modeling. Additionally, to ensure the continuity of seepage, the contact interface between the surrounding rock and the primary lining, as well as between the primary lining and the secondary lining, is defined as a tied contact.
2) Hydraulic boundary
Overall water hydraulic boundary. Linearly distributed water pressure boundaries are set on the two sides (YZ plane) of the model, as illustrated in Fig.8. The location of the free water surface is set to have a water pressure of 0. The water pressure at the bottom of the model is set to γh, where γ is the unit weight of water (taken as 10 N/m3) and h is the distance from the free water surface to the bottom of the model. Impermeable boundaries are used for the remaining hydraulic boundaries of the overall model.
Hydraulic boundary of the drainage system. The hydraulic boundary of the new drainage system in the tunnel is set as depicted in Fig.9. It primarily includes three components: drainage sheets, longitudinal drainage pipes, and bottom drainage blind pipes. The drainage sheets, positioned between the waterproofing membrane and the primary lining, are responsible for redirecting groundwater from the primary lining to the longitudinal drainage pipes. Therefore, the positions on the inner surface of the primary support that is in contact with the drainage sheets is set as the 0 hydraulic pressure boundary. The bottom drainage blind pipe is directly in contact with the surrounding rock, and the groundwater from the surrounding rock is directly drained to the central drainage ditch. Therefore, the surrounding rock surface where the bottom drainage pipe is located is set as the 0 hydraulic pressure boundary. Additionally, since the inner surface of the secondary lining is exposed and lacks any waterproofing measures, it is set as the 0 hydraulic pressure boundary.
Hydraulic Boundary of the Waterproofing System. The waterproofing system mainly refers to the spray waterproofing membrane. Based on indoor waterproofing test results, this particular spray waterproofing material showed no permeability under a water pressure of 2.0 MPa for 120 min and had no leakage under a water pressure of 1.2 MPa for one year. It exhibits excellent waterproofing performance, and thus, the spray waterproofing membrane can be considered as an impermeable material. Since the spray waterproofing membrane is directly bonded to the upper part of the tunnel’s secondary lining, the permeability coefficient of the areas in the secondary lining, except for the inverted arch, can be set to 0 m/d to simulate the impermeable effect of the waterproofing membrane.
Furthermore, the transversal guide pipes, vertical guide pipes, side ditches, and central drainage ditch located within the invert filling only serve the purpose of guiding water. They do not affect the hydraulic boundaries based on the above considerations or the surrounding seepage field. Therefore, these structures can be omitted during modeling.
3.1.3 Meshing
The entire model is structured with hexahedral grids, and the element type used is three-dimensional eight-node pore pressure element (C3D8P). To achieve a smooth transition of the grids, the primary lining thickness direction is divided into 4 layers of grids, while the secondary lining thickness direction is divided into 6 layers of grids. To ensure computational accuracy, the grids are refined at the location of the drainage sheets, and the surrounding rock, primary lining, and secondary lining share common nodes in this region. The entire model is divided into approximately 1.3 million grids, and the grid division details are shown in Fig.10.
3.1.4 Calculation parameters
In the aforementioned computational model, the water head height is set to 160 m (distance from the free water surface to the top surface of the secondary lining). The width of the drainage sheets is 0.5 m, and the diameter of the bottom drainage pipes is 0.16 m. The spacing between the circumferential drainage systems is set at 6m. The model adopts the isotropic permeability coefficient, whose values are shown in Tab.2 and obtained from Refs. [
29,
30]. The lining and surrounding rock are modeled using linear elastic materials. Since the analysis focuses only on seepage, the model is fully constrained in terms of displacement, and therefore, the mechanical parameters are not further elaborated. To simulate natural seepage of water under the influence of gravity, the entire model is subjected to the gravitational acceleration of 10 m/s
2.
3.2 Calculation results and discussion
When the new double-bonded tunnel drainage system is used, the pore water pressure distribution of the surrounding rock is shown in Fig.11. It can be seen that the original hydrostatic pressure field of the surrounding rock has been changed, resulting in an obvious landing funnel, indicating that the new drainage scheme has a better drainage effect. As can be seen from the enlarged figure, the water pressure at the bottom of the tunnel is obviously smaller than that at the top of the tunnel. This shows that the bottom drainage blind tubes in direct contact with the surrounding rock have a significantly better effect on pressure reduction than the drainage board located between the lining layers, which directly reduces the groundwater pressure at the bottom of the tunnel.
The longitudinal and circumferential hydraulic pressure distributions of the secondary lining were arranged as shown in Fig.12, in order to further understand the hydraulic pressure distribution characteristics of the new drainage scheme. As can be seen in Fig.12(a), the entire outer surface of the secondary lining is separated into several zones by the longitudinal and circumferential drainage system, in which the water pressure at the bottom of the tunnel is significantly lower than that at the top of the tunnel.
To avoid the influence of the boundary effect, the largest water pressure cross-section in the middle of the model is selected to do the distribution of the annular water pressure as shown in Fig.12(b). It can be seen that due to the existence of the longitudinal drainage system, the new drainage system has a “mushroom-shaped” distribution of the overall circumferential water pressure. The water pressure value decreases from the top of the arch to the bottom of the tunnel, which is very different from the hydrostatic water pressure distribution pattern. It indicates that some of the groundwater around the tunnel is relieved by flowing to the bottom blind pipe. The closer to the bottom blind pipe, the shorter the flow path and the more water pressure is reduced.
Similarly, in order to avoid the influence of the boundary effect, the water pressure at the top of the arch, the side wall and the bottom of the arch within a length of 30 m in the middle of the model is shown in Fig.12(c). It can be seen that the longitudinal water pressure distribution of the new waterproof-drainage system is “wave-shaped”. The lowest water pressure is found at the location of the circumferential drainage system, and the highest water pressure is found between the two circumferential drainage systems. Between the maximum and minimum water pressure, the longitudinal water pressure changes with distance showing obvious nonlinearity. As the distance from the circumferential drainage system increased, the water pressure values first increased rapidly and then slowed down. The nonlinear variation of water pressure at the top of the tunnel is more obvious than that at the bottom of the tunnel, which indicates that the presence of blind drainage pipes at the bottom of the tunnel enhances the longitudinal flow of groundwater, which is conducive to the realization of drainage and pressure reduction in the tunnel.
4 Comparison of different tunnel waterproof-drainage scheme
4.1 Work condition settings
To verify the effectiveness of the new waterproofing-drainage scheme for tunnels based on double-bonded waterproofing materials, three different waterproofing-drainage schemes were selected for comparison, including the fully enclosed waterproof scheme, the traditional drainage system and the new waterproofing-drainage system proposed in this paper. The setting of drainage construction measures for each condition is shown in Tab.3. The three calculation models are generally similar, with only differences in the hydraulic boundary settings for drainage. The boundary setting of the new waterproofing-drainage system is shown in Subsubsection 3.1.2; The traditional waterproofing-drainage system deletes the 0 hydraulic pressure boundary at the bottom of the tunnel compared with the new drainage system because there is no drainage blind pipes at the bottom; The fully enclosed waterproof scheme sets the permeability coefficient of the entire secondary lining to 0 m/s to simulate the impermeability of the waterproofing layer. The adoption of this modeling approach is motivated by the absence of a drainage system in this particular scheme, as well as the entire circumferential installation of the impermeable waterproofing layer within the tunnel. The rest of the calculation parameters are the same as Subsubsection 3.1.4.
4.2 Comparison of water pressure distribution of surrounding rock and secondary lining
When the seepage calculation reaches the steady-state, the pore water pressure distributions of the surrounding rock for different waterproofing-drainage schemes are shown in Fig.13(a). In the case of the fully enclosed waterproof scheme, since there is no drainage measures, the water pressure at each location of the surrounding rock is equal to the hydrostatic pressure, which is consistent with the theoretical results. In the traditional drainage scheme, drainage sheets were installed in the upper part of the tunnel, and a hydraulic gradient occurred in the whole surrounding rock, which had the effect of drainage and pressure reduction. As can be seen from the enlarged figure, the water pressure around the tunnel is significantly lower than that of the fully enclosed scheme. It can also be seen in which the water pressure at the top of the tunnel is significantly less than that at the bottom. In the new waterproofing-drainage scheme, due to the addition of the bottom drainage blind pipes, the surrounding rock undergoes a more obvious hydraulic gradient. From the enlarged diagram, it can be observed that the water pressure around the tunnel is not only lower than that of the traditional approach but also that the bottom water pressure is significantly lower than the top water pressure. This indicates that the bottom drainage blind pipe plays a great role in drainage and pressure reduction.
When the seepage calculation reaches a steady-state, the distributions of outer water pressure on the secondary lining for different drainage schemes are shown in Fig.13(b). In the fully enclosed waterproof scheme, the longitudinal water pressure distribution remains unchanged. As the water depth increases, the outer water pressure on the secondary lining gradually increases, with the highest water pressure observed at the tunnel bottom. In the traditional drainage scheme, the presence of the upper circumferential drainage system results in a “wave-like” distribution of longitudinal water pressure along the upper tunnel, with higher water pressure between the two drainage sheets forming the wave peaks. However, since no drainage system is implemented at the tunnel bottom, the water pressure at the tunnel bottom is the highest. With the same drainage measures in the upper part of the tunnel, the water pressure in the upper part of the tunnel for the traditional drainage scheme is highest at the sidewalls, while the new drainage scheme has the highest water pressure at the top. This indicates that the bottom drainage blind pipes not only directly reduce the water pressure at the bottom of the tunnel but also lower the water pressure in the upper part of the tunnel. Moreover, the closer the distance to the bottom blind pipes, the lower the water pressure.
The maximum water pressure results for each scheme are summarized in Fig.14. The proposed new drainage system in this study achieves a maximum water pressure of only 0.6 MPa, representing a reduction of approximately 65% compared to the fully enclosed scheme. This system greatly alleviates the water pressure in the sprayed membrane lining tunnel, demonstrating a significant pressure relief effect. In contrast, the maximum water pressure in the traditional drainage system is 0.86 MPa, which is 43% higher than that of the new drainage system. This indicates that the pressure relief effect of the traditional drainage system in the spray membrane lining tunnel is not satisfactory.
Furthermore, to provide a more detailed comparison of the water pressure distribution on the external surface of the secondary lining for each scheme, the locations of maximum water pressure are selected, and the circumferential distribution of water pressure is shown in Fig.15. It can be observed that the two drainage schemes significantly reduce the circumferential water pressure on the external surface of the secondary lining compared to the fully enclosed solution. In particular, the proposed new drainage scheme not only has a smaller maximum water pressure but also significantly reduces the water pressure at the entire bottom of the tunnel. Meanwhile, in the new drainage system, there is a noticeable reduction in water pressure in the upper part of the tunnel compared to the traditional drainage system. This indicates that the addition of bottom drainage blind pipes has altered the surrounding seepage field of the tunnel, thereby reducing the water pressure on the entire secondary lining of the tunnel. These results contribute to a more favorable force condition for the tunnel.
In addition, unlike the traditional scheme, the new drainage system exhibits higher water pressure in the upper part of the tunnel compared to the bottom. Therefore, when designing a spray membrane lining tunnel, special attention should be given to the water pressure in the upper part of the tunnel.
In summary, the proposed new drainage scheme demonstrates a significant pressure relief effect in the spray membrane lining tunnel. It can effectively reduce the water pressure on the external surface of the entire secondary lining. Therefore, it is an effective drainage scheme.
5 Applicability analysis
In this section, the adaptability of this system to different groundwater conditions will be further investigated, and the variations in water pressure under different water head heights and permeability coefficients will be revealed. Furthermore, the effectiveness of each drainage structure (drainage sheets, drainage blind pipes) in different water environments will be studied, and the robustness of the new drainage solution will be evaluated.
5.1 Applicability to groundwater environment
5.1.1 Water head height
With the development of tunnel construction technology, engineers have gradually challenged areas with high water pressure or even ultra-high water pressure, such as 4 MPa [
31] for Yangjiang hydraulic tunnel and 5 MPa for Xinyongchun tunnel [
32]. For this purpose, a total of 21 working conditions with different head heights from 100 to 500 m were designed to investigate the effect of head height on the drainage effect of the drainage system in the environment. The calculation model and parameter settings are the same as in Subsection 3.1.
The calculation results of the water pressure in the secondary lining under different water head heights are shown in Fig.16. It can be observed that the water pressure increases linearly with the increase in water head height. The change in water pressure for every 20 m increase in water head height remains approximately 0.078 MPa, which corresponds to a change of about 40% of the hydrostatic pressure (0.2 MPa). Furthermore, the water pressure values under different water head heights are compared with those of the fully enclosed scheme, as shown in Fig.16. It can be seen that as the water head height increases, the ratio slightly increases, indicating a slight decrease in the depressurization effect with increasing water head height. However, the overall ratio remains below 40% of the hydrostatic pressure, demonstrating that the new drainage system exhibits a strong depressurization effect under different water head heights.
5.1.2 Permeability coefficient
According to relevant data [
33], rock mass can be classified into six categories based on its permeability, ranging from extremely low permeability to extremely high permeability. The permeability coefficients of the majority of rock mass fall between 10
−8 and 10
−2 m/s. In light of this, seven working conditions with different perimeter rock permeability coefficients ranging from 10
−8 to 10
−2 m/s were designed to investigate the influence of the perimeter rock permeability coefficient on the drainage effect in the natural environment. The calculation model and other parameter settings are the same as in Subsection 3.1.
The maximum water pressure of the secondary lining with different permeability coefficients and its ratio to hydrostatic pressure are shown in Fig.17. It can be seen that the water pressure on the secondary lining shows a nonlinear variation with the permeability coefficient of the surrounding rock. When the permeability coefficient of surrounding rock is in the range of 10−2–10−5 m/s, the change of water pressure in the secondary lining is small. When the permeability coefficient of surrounding rock is located in 10−6–10−8 m/s (close to the permeability coefficient of the primary lining), the water pressure of the secondary lining decreases sharply, and the effect of pressure reduction is obviously enhanced. This is because when the permeability coefficient of the surrounding rock is small and close to the permeability coefficient of the tunnel lining, the amount of water seepage from the surrounding rock is small, and the water can be easily channeled out through the lining drainage system. This does not cause water pressure to build up, which in turn reduces the water pressure in the secondary lining.
The maximum ratio of the proposed new drainage system to hydrostatic pressure for different surrounding rock permeability coefficients is 60%, indicating that the new anti-drainage system can play at least 40% of the pressure reduction effect. The effect of pressure reduction varies greatly with permeability coefficient, and when the permeability coefficient of surrounding rock is lower than 10−7 m/s, the effect of drainage pressure reduction can be more than 80%. Therefore, when the water level is small, the new drainage system is capable of handling various permeability coefficients. When the water level is high, the new waterproof-drainage system tends to apply to the stratum with weak permeability.
5.2 Applicability to drainage system
In the new waterproof-drainage scheme, the circumferential drainage system (upper drainage board, bottom drainage blind pipe) plays a major role in pressure reduction. In this section, the adaptability of each drainage structure to different groundwater environments is mainly investigated, aiming at evaluating the robustness of the new waterproof-drainage system. Therefore, three calculation conditions are set up: only the upper drainage sheet, only the bottom blind drainage pipe, and the drainage sheet + blind drainage pipe. According to the analysis results in Subsection 5.1, the rock water head has little effect on the depressurization effect (compared to the full encapsulation scheme), while the permeability coefficient has a significant impact. Therefore, in this section, different permeability coefficients are set to represent different groundwater environments in the case study.
The results of the maximum water pressure calculations outside the secondary lining were extracted for each of the drainage structure calculation conditions at different permeability coefficients and are organized as shown in Fig.18. As can be seen from Fig.18, with the reduction of the permeability coefficient, the maximum water pressure of each drainage structure condition shows a decreasing trend. Among them, the new drainage scheme employs a combination of drainage blind pipes and plastic drainage sheets. Under this measure, the water pressure is minimized, resulting in optimal drainage performance, consistent with real-world conditions. At the same time, it can be seen that in the conditions with higher permeability coefficients of the surrounding rock (10−2–10−5 m/s), using only the bottom blind pipe drainage measures achieves a depressurization effect similar to that of the combined drainage measures. This indicates that in conditions with high permeability coefficients of the surrounding rock, the bottom blind pipe drainage plays a primary role in depressurization within the new drainage system. In conditions with lower permeability coefficients of the surrounding rock (10−7–10−8 m/s), the depressurization effect of using only the plastic drainage board is comparable to that of using the combined drainage measures. This indicates that in scenarios with low permeability surrounding rock, top plastic drainage sheets within the new drainage system play a primary role in depressurization. When the permeability coefficient of the surrounding rock is within the range of 10−5–10−7 m/s, both the upper and lower drainage systems in the new drainage scheme play crucial roles in water drainage.
The above calculation results indicate that when the permeability of the surrounding rock is strong, the surrounding groundwater is more likely to flow around the rock and enter the bottom drainage blind pipes, thereby alleviating the water pressure around the tunnel. On the other hand, when the permeability of the surrounding rock is weak, the groundwater around the tunnel is not likely to flow through the surrounding rock and enter the bottom drainage system. However, in the case of low-permeability surrounding rock, the inflow of groundwater into the tunnel is limited. The drainage sheets between the primary support and secondary lining can effectively drain the limited groundwater into the tunnel, thereby reducing the water pressure on the lining. In summary, the new waterproofing-drainage system shows good adaptability to different permeability coefficients of the surrounding rock and exhibits high robustness.
6 Conclusions and outlook
In response to the challenge of the inability of double-bonded waterproofing materials to be applied in drainage-type tunnels, a novel tunnel waterproof-drainage system was designed based on the theory of localized drainage and pressure reduction. On this basis, the seepage characteristics of the proposed waterproof-drainage system were analyzed, and the calculation results were compared with other tunnel waterproof-drainage systems. Furthermore, the applicability of the scheme was discussed. The main research findings are summarized as follows.
1) In the proposed waterproof-drainage system based on double-bonded waterproofing materials, the water pressure distribution around the tunnel differs from that of traditional drainage-type tunnels. The circumferential water pressure exhibits an overall “mushroom-shaped” distribution, while the longitudinal water pressure exhibits an overall “wave-like” distribution. At the location of the drainage sheet, the longitudinal water pressure exhibits a “valley” pattern, while it forms a “peak” pattern between the two drainage sheets.
2) At the typical scenario with a water head of 160 m and a permeability coefficient of 10−6 m/s, the maximum external water pressure on the secondary lining for the full enclosed waterproofing scheme, traditional drainage scheme, and the new double-bonded drainage system are 1.7, 0.86, and 0.6 MPa, respectively. This indicates that the novel double-bonded waterproof-drainage system demonstrates a significant reduction in water pressure. Notably, the maximum water pressure in the double-bonded drainage system occurs at the arch crown, which differs from the other schemes. Therefore, careful attention should be given to the arch crown water pressure load in spray membrane lining tunnel.
3) In various groundwater environments, the novel tunnel drainage system is capable of reducing at least 40% of the static water pressure. As the permeability coefficient of the surrounding rock decreases, the depressurization effect becomes more pronounced, achieving a reduction of approximately 85% in static water pressure within extremely low permeability strata (permeability coefficient of 10−7 m/s).
4) In the presence of highly permeable surrounding rock, the primary drainage and depressurization function is performed by the bottom drainage blind pipes. Conversely, in the case of weakly permeable surrounding rock, the upper drainage boards play a pivotal role in drainage and depressurization. The novel drainage system, incorporating both drainage blind pipes and drainage boards, demonstrates favorable adaptability to different permeability coefficients of the surrounding rock. Consequently, the entire drainage and protection system exhibits high robustness and stability.
The theoretical analysis of our study suggests the potential feasibility of the new waterproof-drainage system incorporating a double-sided adhesive sprayed waterproofing membrane. However, it is important to note that our findings lack comprehensive validation through practical testing and real-world applications. Additionally, there remains a need for further investigation into the reliability of silt plugging resistance. These aspects, requiring more empirical evidence, will be our key areas of focus for future research endeavors.
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