FEM analysis of a new three-way drainage and pressure reduction system for road tunnels

FEM analysis of a new three-way drainage and pressure reduction system for road tunnels | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article FEM analysis of a new three-way drainage and pressure reduction system for road tunnels Zhaolei Teng, Yuanming Liu, Shilong Mei, Yuhang Zhou, Guohua He, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2790049/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 05 Jul, 2023 Read the published version in Scientific Reports → Version 1 posted 9 You are reading this latest preprint version Abstract For the water-rich area tunnel elevation arch in the high-water pressure often causes elevation arch cracking and leakage, bulging and other disasters. When the drainage system is not designed properly, such disasters occur more frequently, and conventional road tunnel drainage cannot effectively reduce the water pressure at the elevation arch. Therefore, this paper proposes a new concept of "three-way drainage". The three-way drainage system is based on the conventional drainage system with a new drainage inlet at the elevation arch. On this basis, a series of numerical simulation studies are conducted to verify the pressure-reducing performance of the three-way drainage system on the lining. After demonstration and analysis, the three-way drainage concept can not only effectively reduce the water pressure at the elevation arch of the tunnel, but also have a significant effect on the overall drainage effect of the tunnel. The factors affecting the performance of the three-way drainage system are discussed by varying the model parameters. It was found that the hydraulic conduction coefficient of the surrounding rock and initial support, the number of reverse diversion holes in the elevation arch, the change in head height and the change in secondary lining parameters all had a significant effect on the water pressure outside the tunnel. Physical sciences/Engineering/Civil engineering Earth and environmental sciences/Ecology three-way drainage system tunnel depressurization water-rich zone numerical simulation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 1. Introduction A country's economic development is inevitably linked to the construction of roads, railroads and other infrastructure. China has made remarkable achievements in tunnel construction in recent years. For example, by the end of 2020, China's total road mileage reaches 5,198,100 kilometers, an increase of 185,600 kilometers over 2019, and China's road tunnels reach a whopping 21,316 and a total mileage of 21,999,300 linear meters. During the construction of road tunnels, a number of tunnel disasters have occurred one after another. Among these problems, cracking of road tunnel lining caused by high-water pressure has become one of the most serious factors affecting tunnel safety and has also attracted the attention of the industry[ 1 , 2 ]. Among the tunnel lining cracking include, arch wall cracking, high pressure water injection and elevation arch bulging [ 3 – 6 ]. The bulging roadbed of the road tunnel will not only seriously affect the service life of the tunnel, but also is a great safety hazard for traffic safety. For the highway, even if the elevated arch bulge is not very obvious, it may bring a terrible traffic accident for the vehicles driving at high speed [ 7 , 8 ]. As we all know, the tunnel elevation arch bulge is due to the tunnel in the flood season drainage is not timely, high-water pressure concentrated in the elevation arch shine. Therefore, it is crucial to eliminate how to economically and effectively solve diseases such as high-water pressure causing damage to the above tunnel lining structure. At present, there are many ways to reduce the lining disease, among which an effective and efficient anti-drainage system is currently the mainstream way to reduce the pressure of the tunnel [ 9 ]. Currently there are two main types of highway tunnel waterproofing and drainage: a fully enclosed model that does not allow groundwater to flow into the tunnel; and a drainage model that allows groundwater to flow into the tunnel. The fully enclosed mode is often used for special locations such as natural environment protection areas and locations where there are important buildings on the ground that cannot be drained by the tunnel for a long-time causing subsidence. Generally, the strength requirements of the lining structure and the waterproof layer are high. Therefore, for non-natural protected areas, drainage systems are generally used to reduce the external water pressure on the tunnel lining. Scholars at home and abroad are currently studying how high-water pressure affects the structural stress characteristics of tunnel linings through a series of theoretical analyses, model tests, field tests and numerical simulations [ 10 – 15 ]. Theoretically, Studied the spatial distribution of pore water pressure in urban tunnels in water-rich areas based on Harr and derived the water pressure equation for the seepage field[ 16 ]. Used complex variable analysis to analyze the stress distribution in elastic half-plane underwater tunnels[ 17 ]. Proposed a semi-analytical approach on tunnel water inflow[ 18 ]. Proposed a structural form suitable for high water level tunnel and the structural form of controlled drainage scheme, and studied the water pressure distribution in the tunnel lining by theoretical analysis, indoor tests and field measurements[ 19 ]. Developed an assessment framework based on a regionally coupled hydrological model to study the effects of tunnel drainage on surrounding vegetation [ 20 – 23 ]. However, the current research results of tunnel drainage prevention are conventional drainage methods. Although it has a significant effect on water pressure reduction outside the liner compared to full closure, it only has a significant pressure reduction effect on the pressure around the tunnel arch wall. On the material side, conducted in-plane permeability tests of drained geotextile filters to assess their mechanism of hydraulic deterioration in tunnels [ 24 , 25 ]. Introduced an optimal lightweight foam mortar mixture for promoting tunnel drainage using the composite lining method [ 26 ]. Designed waterproof and breathable materials based on electros pun nanofibers[ 27 ]. In terms of structure, proposed a new drainage structure containing convex hull drainage slabs by numerical simulation and indoor testing[ 28 ]. Constructed a tunnel drainage system by 3D printing technology and performed a simulation test of drainage system blockage [ 29 ].Proposed three waterproofing and drainage optimization schemes, where placing the central drain at the bottom of the invert had the greatest impact on reducing water pressure by 96%[ 9 ]. Proposed a bottom-up railroad tunnel drainage method with pressure reduction[ 30 ]. Proposed a new drainage network to solve the drainage problem of mountain tunnels crossing high LWP fracture zones[ 31 ]. Have studied and analyzed the waterproof requirements and construction measures of different special tunnels in China[ 32 – 34 ].The above studies explored the tunnel water pressure problem and used various solutions (including external water pressure calculation, optimization of tunnel waterproofing and drainage system, new technologies and materials, etc.), but did not consider how to effectively mitigate the impact of water pressure on the lining structure at the tunnel elevation arch. At the same time, the causes of the increase in water pressure outside the tunnel were analyzed, etc., but none of them considered how to effectively reduce the impact of water pressure at the tunnel elevation arch on the lining structure. Based on this, this paper proposes a new road tunnel drainage concept of three-way drainage. Compared to conventional road tunnel drainage systems, the characteristics of this system are better than those of conventional road tunnel drainage systems by setting up a water catchment area (such as the pebble sand pool in Fig. 3 ) at the elevation arch. After connecting to the central drain through a pipe (with a one-way drain valve inside), the excess water is discharged using the pressure difference. This not only can effectively reduce the high-water pressure at the elevation arch, but also will not affect the surrounding ecological environment by over-discharging too much water under the action of the one-way valve. The research in this paper is as follows: first, a brief review of the latest advances in highway drainage prevention research currently available. The detailed design of the depressurization system for the tunnel lining structure of the three-way drainage system is then presented. Finally, a series of numerical simulations were conducted to verify the pressure reduction performance of the three-way drainage system. At the same time, some key influencing factors affecting the three-way drainage pressure reduction are discussed by changing the hydraulic conduction coefficients of the surrounding rock and initial support, the head height, the number of reverse water diversion openings in the back arch and the secondary lining hydraulic conduction parameters. 2. Road Tunnels Are Designed To Use Anti-drainage In this section, the research results on drainage prevention in China and abroad are briefly reviewed with the main purpose of highlighting the novelty of the research in this paper. 2.1 Tunnel drainage prevention in the world At present, the most advanced tunnel drainage prevention in China and abroad are Europe, Japan, Sweden, South Korea and other developed regions or countries. In most countries, water-rich mountain tunnels are drained to reduce the external water pressure in the tunnel lining under conditions without special requirements. The structure consists of a flashing between the initial support and the secondary lining, a circular drainage blind pipe, a longitudinal drainage blind pipe, a central drainage trench, and a sinkhole set at 50m (88m). As far as the road tunnel drainage system is concerned, the difference lies in the direction of water discharge at the elevation arch and the different pressure-reducing performance of the already studied about four models, as shown in Figure 1: Circular and longitudinal drainage blind pipes were used to draw out water, and water was introduced into the central drainage trench through transverse diversion pipes. The transverse diversion pipe and the central drainage ditch are installed below the roadbed to form a complete drainage system, Figure 1(a).2. the central drainage trench is installed below the tunnel lining and the circular drainage blind pipe is directly connected to it for drainage work, Figure 1 (b). The central drainage trench is set below the tunnel lining, and the circular drainage blind pipe is directly connected to it for drainage work, Figure 1 (b). On the basis of 1, the circular blind pipe is extended below the elevation arch, before connecting to the central drain through the reverse drain to form a complete drainage path. A protective gravel head is usually laid around the central drain, which also serves as a filter for debris, Figure 1(c). So that the lining is in complete closure and does not allow water to flow into the tunnel, outside the body then the water is led out of the tunnel on the basis of 2 in combination with the lateral diversion pipe in 1, which brings the water together in a central drainage trench below the supine arch, Figure 1(d). 2.2 Anti-drainage systems used in Chinese road tunnels The current drainage system frequently used in Chinese road tunnels is shown in Figure 1. Generally this drainage system is installed between the secondary lining and the initial support with ring and longitudinal drainage blind pipes as well as waterproof layer, and the central drainage trench as well as the lateral diversion pipe is installed below the roadbed. The water around the tunnel is directed through the drainage pipes and collected in the central drainage ditch through the lateral drainage pipes. The distance between the drainage pipes in the project and the surrounding rock grade, the amount of water-rich rock and the height of the head has a certain relationship, the general longitudinal distance between the circular drainage blind pipe in 6m ~ 10m or so. The above is about the drainage of the tunnel anti-drainage buck, no matter which drainage is to protect the tunnel safety and service life, but often have certain defects. For example: Figure 2 Chinese road tunnels commonly used anti-drainage system is not difficult to find, unable to drain the water from the elevation arch position of the tunnel. In the case of non-rainy season can ensure the safety of the tunnel, but in the case of relatively high rainfall or long-term operation of the tunnel pipe crystallization can make the drainage is not timely lead to the tunnel lining force damage, and ultimately affect the life of the tunnel. As shown in Figure 1 (c) (d) the central drainage trench is located below the elevation arch of the tunnel. Although it can effectively solve the problem of high-water pressure at the elevation arch of the tunnel, it cannot control the amount of groundwater discharge. It will lead to the phenomenon of how much discharge, which cannot effectively protect the surrounding ecological environment. It will also have an impact on the construction of the tunnel resulting in a huge amount of earth and rock excavation, which will not only affect the construction period, but also increase the economic investment of the project. In Figure 1(b), although the design adds a reverse drain, no protection is provided for the pipe head. The crystallization or blockage of foreign objects will occur with the increase of operation years, which will lead to the decrease of the drainage volume, thus causing the water pressure at the elevation arch to rise. It is detrimental to the tunnel lining in the long run. In order to solve the above problems, the following discussion and analysis of the core contents of this paper will be carried out. 2.3 Concept and design of a three-way drainage depressurization system for highway tunnels This paper studies the three-way drainage and depressurization system of Chinese highway tunnels, which consists of four main components: ① circular drainage system; ② longitudinal drainage system; ③ reverse drainage pipe of the elevated arch; ④ transverse diversion pipe and central drainage trench. Among them, the ring, longitudinal drainage blind pipe and the newly added supine arch reverse drainage pipe to achieve three directions of drainage purposes this paper is called the three-way drainage pressure reduction system (hereinafter referred to as the three-way drainage system). Details of the structure are shown in the figure. ① Circumferential drainage system: The circumferential drainage system is located between the initial support and the secondary lining of the tunnel, and is responsible for directing the water flow around the tunnel to discharge water, as shown in Figure 3. ② Longitudinal drainage system: The longitudinal drainage system is responsible for collecting the water directed down from the circular drainage system as well as the perimeter water seeping down, and then bringing the water to the central drainage ditch through the horizontal diversion pipe. ③ Reverse drainage pipe for the supine arch: the reverse drainage system for the supine arch consists of a sand pond (coarse sand and cobbles, etc.) outside the tunnel lining, a one-way drainage valve set (Bgha B, Hui L A et al., 2020) and a reverse drainage pipe by connecting to the central drainage ditch, which finally leads the huge water pressure at the supine arch out of the tunnel through the central drainage ditch during the flood season, see Figure 6. ④ Transverse diversion pipe and central drainage ditch: The horizontal diversion pipe and central drainage ditch are mainly responsible for diverting the water collected by the three-way drainage system out of the tunnel to achieve the purpose of reducing the water pressure outside the tunnel lining. By comparing the structural differences between the conventional drainage system for road tunnels in water-rich areas (Figure 2) and the new concept drainage system for three-way drainage (Figure 3). It can be seen that the so-called three-way drainage system is to use the high-water pressure at the elevation arch to divert the high-pressure water out of the tunnel through the collecting sand pond and the reverse drainage pipe to achieve the purpose of pressure reduction in the elevation arch of the tunnel. The high-water pressure at the bottom of the elevated arch in Figure 4 will drain the water under the pressure difference. The one-way valve prevents water from backing up and drains only when sufficient design pressure is reached at the elevation arch, and the sand pond has a protective effect on the water inlet, which increases the service life. During the dry season, the drainage will be blocked by the drainage check valve, so that the groundwater will not be discharged excessively in the water-rich area. In order to meet the principle of "blocking mainly, limited discharge" of tunnel drainage prevention, and at the same time can prevent sediment backflow to block the structure. Similar studies are currently available for this area (Li P, Liu H et al., 2018). Although this study also serves to reduce the high-water pressure at the elevation arch, it mainly serves railroad tunnels and the study structure is relatively complex. 3. Numerical Simulation Analysis Since this paper is proposing a new drainage system, which currently has no case in engineering, numerical simulation is used to study it. In this section, the feasibility of the three-way drainage system concept is investigated by numerical simulation with Midas gtsNX software. The research results prove that the three-way drainage concept can not only reduce the overall water pressure of the tunnel lining structure, but also effectively reduce the water pressure at the elevation arch. A detailed analysis will be presented below. The calculation of water pressure outside the liner is mainly based on the theory of well flow in infinite aquifers and Darcy's law. 3.1 Boundary conditions of the numerical models In order to study the performance of the three-way drainage system on the water pressure drop at the elevation arch of the tunnel, this paper uses finite element software to simulate the three-way drainage system and the conventional drainage system for comparative analysis and verification. The model simulation is based on the Tongzi Tunnel, a mega-section high-speed tunnel under construction in Guizhou, China, as a reference. The groundwater level at the top of the tunnel vault is 70m, and the head is applied at the top. Model size of the length × width × height = 180m × 40m × 100m. The perimeter is taken to be greater than 3 by the hole diameter to eliminate the boundary effect, and the mesh model and structure details are shown in Figure 5. All parts of the model are simulated using solid units. The present model makes the following assumptions: the surrounding rock is simulated using the Mohr-Coulomb principal structure model, and the initial support, secondary lining structure and drainage prevention system are simulated using the elastic model. The model is always fully saturated, and the nodal head pressure is set to 0 in the drainage hole area to simulate drainage. Drainage system in order to facilitate the calculation in the actual project commonly used in the PVC pipe diameter as a reference basis. The modeling is equivalent to a square structure of 89 mm * 89 mm * 89 mm using the equal flow principle. the specific parameters of the material are listed in Table 1 below. Table 1. Parameters of each material Note: Due to the existence of a one-way valve group in the reverse drainage pipe at the elevation arch here to solve the problem by controlling the hydraulic conduction coefficient, taking the value of 0.3. 3.2. Analysis of results To verify the performance of the three-way drainage system, a comparative analysis of the fully enclosed undrained, conventional drainage system and the three-way drainage system was performed and normalized based on the values of the fully enclosed undrained. The drainage cross-section and non-drainage cross-section of the tunnel circular monitoring section (C1 to C10) were extracted for analysis. As shown in Figure 6 (a) water pressure distribution at the drainage section of the secondary lining (b) water pressure distribution at the non-drainage section of the secondary lining. According to Fig. 6 (b) (c), the following conclusions can be drawn. The conventional drainage system effectively reduces the water pressure outside the liner by approximately 58% in the section above the longitudinal drain compared to the fully enclosed undrained system. It can be seen that measurement points C1 to C7, if the drainage system drainage capacity is fully developed, the pressure reduction effect will be more obvious. But the conventional anti-drainage system does not have a drainage outlet at the bottom of the supine arch. C8 to C10 measurement points can be seen that the water pressure around the elevation arch is reduced by less than 20%. Therefore, for the time being, the performance of conventional drainage systems in Chinese road tunnels is still lacking in terms of pressure relief at the elevation arch of the tunnel. Such high-water pressure gathered at the elevation arch, if encountered heavy rain, or continuous rainfall time tunnel elevation arch structure is very vulnerable to the threat of high-water level water pressure, thus reducing the life of the tunnel. However, in the study, it was found that the use of reverse drainage of the elevated arch was effective in reducing the occurrence of such situations. The principle is to use the pressure difference to reverse the water out of the tunnel from underneath the elevated arch. The concept of "three-way drainage" in this paper is mainly derived from the concept that pressure difference can cause water to flow in the opposite direction, which can effectively drain the water under natural pressure. It also prevents excessive water discharge which is beneficial to the surrounding ecological environment. From the results of numerical simulation (b). The three-way drainage system has approximately seven times the pressure-reducing performance of the conventional drainage system at the elevation arch. The water pressure at the elevated arch is significantly reduced. It is not difficult to find from (c) figure that there is also a certain effect on the overall pressure reduction of the tunnel structure. The pressure reduction capacity of the non-drainage section is likewise increased, and the pressure reduction effect at the elevated arch is about 57% higher than the conventional one. In the above numerical simulation, the pressure reduction performance and feasibility of the "three-way drainage system" were verified. From the results, it is obvious that the water pressure is greatly reduced after the reverse drainage holes are set in the elevation arches C8 and C9. The following conclusions can be drawn from Figure 7. Where (c) to (h) are the multiplicative relationships of the number of reverse drainage holes in the supine arch for three-way drainage. From the above cloud diagram, it is not difficult to find that the secondary lining in the fully closed state of Figure (a) is in a state of hydrostatic pressure, and the external water pressure is very high. In Fig. (b) conventional drainage method the external water pressure is reduced by about 30%. However, the elevated arch is still subject to high external water pressure, which is unsafe for long-term operation. For the three-way drainage system, it is obvious that when the number of reverse drainage holes increases from 2 to 32 according to the previous multiplicative relationship, it can be found that the more the number of reverse drainage holes at the elevation arch is more beneficial for the elevation arch pressure reduction. However, for the design of this paper to serve the later project, a reasonable and economical number of reverse drainage holes should be found. It can be found that when the number of reverse drainage holes grows from 8 to 16 about 12% decrease, the pressure reduction rate is the highest at this time. For figure (h) infinite number of reverse drainage holes although the pressure reduction effect is significant. However, it is unsafe for the overall structure of the tunnel, so it is recommended to set up 16 reverse drainage holes for every 40m long interval. In general, the feasibility of the new drainage concept of three-way drainage was proven. In addition, the reverse drainage of the elevated arch can realize the tunnel in the flood season when the high pressure, the use of pressure differences so that the water automatically discharged. Retaining water resources during dry weather does not have a significant impact on the surrounding ecosystem. 4. Analysis Of Factors Affecting The Performance Of Three-way Drainage Systems In this section, the performance of the three-way drainage system will be studied by numerical simulation parameters varying the parameters of the hydraulic conductivity of the surrounding rock, the head height, the initial support and the secondary lining. 4.1. Parameter taking and analysis The following paper presents a numerical simulation study by analyzing the three-way drainage under different parameters. The study of the three-way drainage buck performance was carried out by changing the parameters. The following discussion is carried out under the condition that the drainage is completely usual as well as completely symmetrical. The hydraulic conductivity coefficient and head height of the IV enclosure, secondary lining and initial support are changed under the conditions of Table 1, and the specific parameters are changed as shown in Table 2. For numerical calculation, first a variable is selected as a fixed value. Analytical calculations are performed by changing other physical parameters. For example, the hydraulic conductivity of secondary lining 1.3×10-11 in Table 1 remains unchanged, and the hydraulic conductivity of other parameters IV surrounding rock and initial support increases according to 1 to 10 times. Since there are too many combinations only order changes are considered. The head height increases from 25m at a rate of 5m to a head height of 70m. To see the difference in the result curves. The hydraulic conductivity of secondary lining takes two fixed values of 1.3×10-8 and 1.3×10-11 as high and low hydraulic conductivity respectively for analysis, which are noted as SLH1 and SLH2 in the following. Table 2. Parameter values and variations. Calculation variable Permeability Number of vertical drains Height of water head （ m ） IV surrounding rock Initial support Conventional drainage Three-way drainage SLH1 0.1，0.2，…, 1, 2, …, 10 No vertical diversion pipe 1，2，…, ∞ 25，30，…, 70 SLH2 Note: The elevated arch is regarded as the primary support and the second lining superimposed, so the hydraulic conduction coefficient is not considered separately there. The number of three-way drainage pipes keeps increasing from 1, 2, ..., ∞, that is, the number of reverse drainage pipes of the elevated arch keeps increasing from 1 to form a sink which is ∞. Since it was not possible to model so many, only 10 values were selected for the simulation. This is because such a value is already highly intensive in this computational model. 4.2. Analysis of parameter values and variation results The calculations in this section are all in accordance with Table 2 for the analysis of the magnitude values of water pressure affecting the secondary lining outside. The C8 and C9 measurement points with special representation were taken for the results and compared to the fully closed and conventional drainage systems analyzed above. The following plotted results are normalized to the fully enclosed non-drainage results and after changing one condition, the other conditions are the initial values in Table 1. 4.2.1. Hydraulic conductivity of IV surrounding rock The effect of hydraulic conduction coefficient of IV surrounding rock on the water pressure outside the secondary lining under the condition of not changing the surrounding rock grade is shown in Figure 8. It can be seen from Fig. 8that the hydraulic conductivity of the IV envelope increases slowly from 0.1, 0.2, ..., 1, 2 times to 10 times when the external water pressure of the secondary lining is increasing. The growth trend is from rapid increase to steady. The results show that the hydraulic conductivity of the surrounding rock increases the overall external water pressure of the secondary lining is increasing but for the high permeability of the secondary lining can effectively reduce the water pressure. Compared with conventional drainage three-way drainage elevation arch water pressure in the surrounding rock hydraulic conductivity coefficient in 6 to 10 times the size of the water pressure is maintained at about 0.65 times. So it is said that the three-way drainage mode can effectively reduce the external water pressure at the elevation arch of the tunnel. When the hydraulic conductivity of the secondary lining is increased by 100 times, the difference in the water pressure ratio at C8 and C9 is not too great. 4.2.2. Hydraulic conductivity of the initial support It can be seen from Figure 9 that the initial support hydraulic conduction coefficient grows, and the water pressure outside the secondary lining of the three-way drainage system grows slowly and eventually stabilizes. For conventional drainage systems, the numerical solution of the water pressure outside the secondary lining is slowly decreasing and eventually stabilizing. From the results of both, there exists a most unfavorable value for the initial support hydraulic conductivity coefficient. So the external water pressure of the secondary lining will have a maximum peak. After this maximum value the water pressure in the secondary lining will tend to decrease, but only within a small range of fluctuations. 4.2.3 Increase in the number of reverse drainage holes in the supine arch As in Figure 10, the drainage capacity is improved by changing the number of reverse drainage holes in the elevated arch. The numerical study found that the external water pressure of the secondary lining was decreasing regularly with the increase of the reverse drainage hole of the elevated arch. As the number of drainage holes changes from a point to a line, the rate of water pressure reduction becomes slower and slower, and the curve eventually flattens out. This means that when the number of drainage holes slowly increases to a very dense level, there is no longer a significant increase in the external water pressure of the secondary lining. It shows that there is an optimal number of drainage holes set at the elevation arch for three-way drainage. For example, in this paper, if the lining length is 40m, the number of 16 reverse drainage holes of the elevated arch will be set to reach the optimal value. At the same time, the three-way drainage method can also effectively reduce the overall external water pressure of the elevated arch and secondary lining compared with the conventional drainage. 4.2.4 Water head height variation Other initial conditions remain unchanged, the head height change on the secondary lining outside the water pressure influence law is shown in Figure 11. It is not difficult to find that the increase in head height the external water pressure of the secondary lining is basically unchanged. This indicates that the head increases and the water pressure increases the size of the water flow discharged will also increase year-on-year. Since only the highest head of 70m is analyzed here, it is different from the case of deeply buried tunnels. Therefore, the increase in head height has little effect on the external water pressure of the secondary lining for lots where the burial depth is not large. However, compared with conventional drainage, the water pressure reduction after setting the reverse diversion inlet of the elevated arch for three-way drainage is significant, only 0.43 times of conventional drainage. With different hydraulic conductivity coefficients for the secondary lining, it is not difficult to find that the difference between the two is not large under the 100 times multiplier condition, indicating that this is not a major factor. 5. Conclusion In order to efficiently and economically solve the disease problems caused by high-water pressure in the elevation arch of highway tunnels in China. This paper proposes a new drainage concept of "three-way drainage", which has been found to be effective in reducing the high-water pressure at the elevation arch of the tunnel. The drainage and decompression characteristics of the three-way drainage system on the tunnel lining are analyzed in a numerical simulation. The main findings are as follows: (1) The three-way drainage system adds a reverse drainage structure (with a one-way valve set) to the elevated arch, which is theoretically feasible. It can effectively reduce the external water pressure at the elevation arch of the tunnel as well as the water pressure of the overall structure of the lining. (2) The external water pressure of the tunnel secondary lining has a certain relationship with the hydraulic conductivity of the surrounding rock, which shows a synchronous growth trend. (3) For the numerical results of the three-way drainage in this paper, the increase in the hydraulic conductivity of the initial support has little effect on the change in water pressure in the secondary lining. The change in force transfer coefficient will cause a peak in the external water pressure of the secondary lining, causing the secondary lining water pressure to begin to drop. (4) The increase in head height makes the water pressure ratio outside the secondary liner increase linearly. Therefore, in the environment of high head height, the tunnel drainage prevention system as well as the lining structure will need to improve the design requirements. The three-way drainage system in this paper has proven to be feasible. It is not currently used in practice and is still at the stage of theoretical analysis. The indoor model tests will be conducted to provide a reasonable and economic drainage method for road tunnels, and actual engineering experience will be used to verify the drainage and pressure reduction performance of the three-way drainage system. Declarations Author Contributions: Z.T. （Zhaolei Teng） wrote the main manuscript text and Y.L.（Yuanming Liu） and Y.Z. （Yuhang Zhou） prepared figures 1-11. and Y.L. （Yingxiao Li） and S.M. （Shilong Mei） prepared Tables 1 and 2. B.D.（Bitao Du） and G.H.（Guohua He）prepared numerical software modeling. All authors reviewed the manuscript. Funding: This work was supported by the Science and Technology Planning Project of Guizhou Province (Qiankehe major special project [2018] 3011), and Qiankehe Basic Project ZK [2022] General Project 082, and Qiankehe Basic Project [2019] No.1057), Guiyang Metro Line 3 Phase I Engineering Research Project (Project No.GD3-FW-YJ-05-2020-13-ZB), and Regional first-class discipline construction project in Guizhou Province (QYNYL [2017] 0013). Acknowledgments: The authors gratefully acknowledge Mr. Wenrong Ma of China Railway Eighth Engineering Group Third Engineering Co., Ltd and Mr. Xiaoyong He of China Railway Development Investment Group Co. Ltd. for their valuable comments and support. Competing interests We hereby declare that this contribution is our own work. As far as we know, it does not contain materials previously published or written by others. There is no competing interest between authors. Before the journal makes a decision, it will not be considered to be published elsewhere. Institutional Review Board Statement: Not applicable. Informed Consent Statement: The datasets used and/or analysed during the current study available from the corresponding author on reasonable request. Conflicts of Interest: The authors declare no conflict of interest. References Liu, Y.; Feng, Y.; Xu, M.; Zhang, Y.; Long, H.; Zhu, H. Effect of an incremental change in external water pressure on tunnel lining: a case study from the Tongxi karst tunnel. Nat. Hazards 2019 , 98 , 343-377. Liu, N.; Pei, J.; Cao, C.; Liu, X.; Huang, Y.; Mei, G. 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An analysis of the support loads on composite lining of deep-buried tunnels based on the Hoek-Brown strength criterion. Tunn. Undergr. Space Technol. 2021 , 118 , 104174. Chen, Y.; Gao, Y.; Shi, S.; Xu, F.; Zhao, W. Characteristics of transient pressure in lining cracks induced by high-speed trains. J. Wind Eng. Ind. Aerodyn. 2022 , 228 , 105120. Seki, S.; Kaise, S.; Morisaki, Y.; Azetaka, S.; Jiang, Y. Model experiments for examining heaving phenomenon in tunnels. Tunn. Undergr. Space Technol. 2008 , 23 , 128-138. Li, Z.; He, C.; Chen, Z.; Yang, S.; Ding, J.; Pen, Y. Study of seepage field distribution and its influence on urban tunnels in water-rich regions. Bull. Eng. Geol. Environ. 2019 , 78 , 4035-4045. Fang, Q.; Song, H.; Zhang, D. Complex variable analysis for stress distribution of an underwater tunnel in an elastic half plane. Int. J. Numer. Anal. Methods Geomech. 2015 , 39 , 1821-1835. Hwang, J.; Lu, C. A semi-analytical method for analyzing the tunnel water inflow. Tunn. Undergr. Space Technol. 2007 , 22 , 39-46. Wang, X.; Tan, Z.; Wang, M.; Zhang, M.; Ming, H. Theoretical and experimental study of external water pressure on tunnel lining in controlled drainage under high water level. Tunn. Undergr. Space Technol. 2008 , 23 , 552-560. Xu, H.; Li, X.; Gokdemir, C. Modeling and assessing the impact of tunnel drainage on terrestrial vegetation. Tunn. Undergr. Space Technol. 2021 , 116 , 104097. Gokdemir, C.; Rubin, Y.; Li, X.; Xu, H. A vulnerability assessment method to evaluate the impact of tunnel drainage on terrestrial vegetation under various atmospheric and climatic conditions. Adv. Water Resour. 2021 , 147 , 103796. Li, J.; Hong, A.; Yuan, D.; Jiang, Y.; Deng, S.; Cao, C.; Liu, J. A new distributed karst-tunnel hydrological model and tunnel hydrological effect simulations. J. Hydrol. 2021 , 593 , 125639. Lv, Y.; Jiang, Y.; Hu, W.; Cao, M.; Mao, Y. A review of the effects of tunnel excavation on the hydrology, ecology, and environment in karst areas: Current status, challenges, and perspectives. J. Hydrol. 2020 , 586 , 124891. Kim, K.; Park, N.; Kim, H.; Shin, J. Modelling of hydraulic deterioration of geotextile filter in tunnel drainage system. Geotext. Geomembr. 2020 , 48 , 210-219. Ibrahim, A.; Meguid, M.A. CFD-DEM modeling of geotextile clogging in tunnel drainage systems. Geotext. Geomembr. 2022 , 50 , 932-945. Choi, H.; Ma, S. An optimal lightweight foamed mortar mix suitable for tunnel drainage carried out using the composite lining method. Tunn. Undergr. Space Technol. 2015 , 47 , 93-105. Yoon, B.; Lee, S. Designing waterproof breathable materials based on electrospun nanofibers and assessing the performance characteristics. Fiber. Polym. 2011 , 12 , 57-64. Zhang, C.; Liu, N.; Chen, K.; Ren, F. Study on drainage mode and anti-clogging performance of new waterproofing and drainage system in a tunnel. Sci Rep 2023 , 13 . Linyi, L.E.A. Simulation tests on structural deformation and seepage field of high-speed railway tunnels under drainage clogging. Chinese Journal of Geotechnical Engineering 2020 , 39 , 1369-1384. Li, P.; Liu, H.; Zhao, Y.; Li, Z. A bottom-to-up drainage and water pressure reduction system for railway tunnels. Tunn. Undergr. Space Technol. 2018 , 81 , 296-305. Zhou, W.; Liao, S.; Men, Y. Effect of localized water pressure on mountain tunnels crossing fracture zone. Transp. Geotech. 2021 , 28 , 100530. Yuan, Y.; Jiang, X.; Lee, C.F. Tunnel waterproofing practices in China. Tunn. Undergr. Space Technol. 2000 , 15 , 227-233. Gong, C.; Wang, Y.; Ding, W.; Lei, M.; Shi, C. Waterproof Performance of Sealing Gasket in Shield Tunnel: A Review. Applied Sciences 2022 , 12 , 4556. Luciani, A.; Peila, D. Tunnel Waterproofing: Available Technologies and Evaluation Through Risk Analysis. Int. J. Civ. Eng. 2019 , 17 , 45-59. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 05 Jul, 2023 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Major revision 31 May, 2023 Reviews received at journal 19 May, 2023 Reviewers agreed at journal 14 May, 2023 Reviewers agreed at journal 11 May, 2023 Reviewers invited by journal 11 May, 2023 Editor assigned by journal 11 May, 2023 Editor invited by journal 18 Apr, 2023 Submission checks completed at journal 18 Apr, 2023 First submitted to journal 07 Apr, 2023 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2790049","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":192916888,"identity":"3838bbdd-863d-4d11-8479-be19eb065996","order_by":0,"name":"Zhaolei Teng","email":"","orcid":"","institution":"Guizhou University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Zhaolei","middleName":"","lastName":"Teng","suffix":""},{"id":192916889,"identity":"c2ce54aa-f4ea-4f05-b788-b832155ad078","order_by":1,"name":"Yuanming Liu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzElEQVRIiWNgGAWjYBACPmYwZcPDz8x84MCHH0RoYYNoSZOTbGdLPDizhxgtEOqwscF5HuPDHGzEaGHnMZO6wcCc2HCY58NhBh4GeX6xA4QcxmMmncPAltjYzLvhcIEFg+HM2QlEaeFJbGYGapnBw5BgcJs4LRKJbcw8Dw7zsBGvxcCYh5mHgVgtbMXWOQwJchLMbAbAQJYg7Bd+/sMbb+cw/OexP3/48YcPP2zk+aUJaAECFgnGf3COBEHlIMD8gShlo2AUjIJRMHIBAAs0N3eUhYV/AAAAAElFTkSuQmCC","orcid":"","institution":"Guizhou University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Yuanming","middleName":"","lastName":"Liu","suffix":""},{"id":192916890,"identity":"cc80e9b6-0b8a-495d-b496-70ab06227918","order_by":2,"name":"Shilong Mei","email":"","orcid":"","institution":"Guizhou University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Shilong","middleName":"","lastName":"Mei","suffix":""},{"id":192916892,"identity":"0380d3ee-3461-4a82-b687-dba1cc78ae25","order_by":3,"name":"Yuhang Zhou","email":"","orcid":"","institution":"Guizhou University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Yuhang","middleName":"","lastName":"Zhou","suffix":""},{"id":192916893,"identity":"f1df2a9f-f96c-42ce-a165-157b57b49e59","order_by":4,"name":"Guohua He","email":"","orcid":"","institution":"Guizhou University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Guohua","middleName":"","lastName":"He","suffix":""},{"id":192916895,"identity":"c710a468-3b8c-4786-b570-5ba66bba7b27","order_by":5,"name":"Yingxiao Li","email":"","orcid":"","institution":"Guizhou University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Yingxiao","middleName":"","lastName":"Li","suffix":""},{"id":192916897,"identity":"3f2976d1-e679-4e57-8834-456f4f628569","order_by":6,"name":"Bitao Du","email":"","orcid":"","institution":"Guizhou University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Bitao","middleName":"","lastName":"Du","suffix":""}],"badges":[],"createdAt":"2023-04-07 13:14:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2790049/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2790049/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-023-37417-1","type":"published","date":"2023-07-05T21:32:07+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":36090280,"identity":"8e131c99-c15b-44b4-932d-64711a69e125","added_by":"auto","created_at":"2023-04-20 22:03:56","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":459894,"visible":true,"origin":"","legend":"\u003cp\u003eThere are about four different models that have been studied, they should be listed as: (\u003cstrong\u003ea\u003c/strong\u003e) A drainage system; (\u003cstrong\u003eb\u003c/strong\u003e) B drainage system; (\u003cstrong\u003ec\u003c/strong\u003e) C drainage system (\u003cstrong\u003ed\u003c/strong\u003e) D drainage system.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-2790049/v1/f9f44f130a7496837f25f40c.png"},{"id":36090283,"identity":"6e162f41-ac93-4755-87bf-318fcfa9db1a","added_by":"auto","created_at":"2023-04-20 22:03:56","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":279830,"visible":true,"origin":"","legend":"\u003cp\u003eCommonly used anti-drainage systems in Chinese road tunnels\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-2790049/v1/7d2b3044b11fb9995e80a7ee.png"},{"id":36089503,"identity":"b1485dd4-e95e-4dfb-ba67-902531e9cb53","added_by":"auto","created_at":"2023-04-20 21:55:56","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":321965,"visible":true,"origin":"","legend":"\u003cp\u003eThree-way drainage system structure arrangement\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-2790049/v1/61959a60e9d346772c412415.png"},{"id":36089495,"identity":"ea7ff0fe-a9c5-46bb-978f-eeb1a81d9da7","added_by":"auto","created_at":"2023-04-20 21:55:56","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":294542,"visible":true,"origin":"","legend":"\u003cp\u003eDrainage mechanisms of three-way drainage systems\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-2790049/v1/081916dec874d1f1d447c1c0.png"},{"id":36089500,"identity":"7eb5398f-d129-4563-8205-3d2565b19838","added_by":"auto","created_at":"2023-04-20 21:55:56","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":563175,"visible":true,"origin":"","legend":"\u003cp\u003eGrid model and drainage structure details and the arrangement of monitoring points: \u0026nbsp;（a）Three-dimensional simulation model; （b）Conventional and three-way drainage structure; （c）Monitoring layout points.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-2790049/v1/0ef1638bee8490f1a73624a1.png"},{"id":36091345,"identity":"589af20f-19de-4a87-a112-8ae7a7f9f86a","added_by":"auto","created_at":"2023-04-20 22:19:56","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":330924,"visible":true,"origin":"","legend":"\u003cp\u003eEnvelope Diagram of External Water Pressure, they should be listed as: (a) Monitor. ing section; (b) water pressure at the drainage section; (c) water pressure at the drainage section.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-2790049/v1/b5142fa529cc1fefc31cc075.png"},{"id":36090285,"identity":"e80f257c-f73e-4937-b19f-8e86cea80df5","added_by":"auto","created_at":"2023-04-20 22:03:56","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":1494319,"visible":true,"origin":"","legend":"\u003cp\u003eSecondary lining external water pressure cloud: (a) No drainage;（b）Conventional drainage;（c）2 reverse drains;（d）4 reverse drains;（e）8 reverse drains;（f）16 reverse drains;（g）32 reverse drains;（h）Reverse drain.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-2790049/v1/dc505b13d4f54bca6a011980.png"},{"id":36091158,"identity":"4ce69d7c-64ca-4e45-a9da-7988f3affb9a","added_by":"auto","created_at":"2023-04-20 22:11:56","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":263830,"visible":true,"origin":"","legend":"\u003cp\u003eHydraulic conduction coefficient of IV surrounding rock on the effect of water pressure outside the secondary lining\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-2790049/v1/6bf436ccb12ae131091144ac.png"},{"id":36091157,"identity":"7b7dbf60-27ae-42e4-bf15-ebe170087e54","added_by":"auto","created_at":"2023-04-20 22:11:56","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":271704,"visible":true,"origin":"","legend":"\u003cp\u003eEffect of hydraulic conduction coefficient of initial support on water pressure outside the secondary lining\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-2790049/v1/fe2973b7633f682bc312d1c7.png"},{"id":36089498,"identity":"51c97dfa-40a8-4e1c-83c4-d21df31abc98","added_by":"auto","created_at":"2023-04-20 21:55:56","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":286737,"visible":true,"origin":"","legend":"\u003cp\u003eThe effect of the number of reverse drainage holes at the elevation arch on the water pressure outside the secondary lining\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-2790049/v1/8c77073c2e3a6cf5dedb3b96.png"},{"id":36089504,"identity":"59d52db3-1800-4c9c-8e08-061851d602d6","added_by":"auto","created_at":"2023-04-20 21:55:56","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":257395,"visible":true,"origin":"","legend":"\u003cp\u003edifferent head height on the secondary lining outside the water pressure effect\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-2790049/v1/9ea0c7447f90c4db49743c2e.png"},{"id":44733455,"identity":"86d1d41c-ac56-4009-9ccb-6552df964f2a","added_by":"auto","created_at":"2023-10-16 22:05:23","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4321445,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2790049/v1/22243efe-a63f-4e64-a930-fb7555b88b2b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"FEM analysis of a new three-way drainage and pressure reduction system for road tunnels","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eA country's economic development is inevitably linked to the construction of roads, railroads and other infrastructure. China has made remarkable achievements in tunnel construction in recent years. For example, by the end of 2020, China's total road mileage reaches 5,198,100 kilometers, an increase of 185,600 kilometers over 2019, and China's road tunnels reach a whopping 21,316 and a total mileage of 21,999,300 linear meters. During the construction of road tunnels, a number of tunnel disasters have occurred one after another. Among these problems, cracking of road tunnel lining caused by high-water pressure has become one of the most serious factors affecting tunnel safety and has also attracted the attention of the industry[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Among the tunnel lining cracking include, arch wall cracking, high pressure water injection and elevation arch bulging [\u003cspan additionalcitationids=\"CR4 CR5\" citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. The bulging roadbed of the road tunnel will not only seriously affect the service life of the tunnel, but also is a great safety hazard for traffic safety. For the highway, even if the elevated arch bulge is not very obvious, it may bring a terrible traffic accident for the vehicles driving at high speed [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. As we all know, the tunnel elevation arch bulge is due to the tunnel in the flood season drainage is not timely, high-water pressure concentrated in the elevation arch shine. Therefore, it is crucial to eliminate how to economically and effectively solve diseases such as high-water pressure causing damage to the above tunnel lining structure. At present, there are many ways to reduce the lining disease, among which an effective and efficient anti-drainage system is currently the mainstream way to reduce the pressure of the tunnel [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eCurrently there are two main types of highway tunnel waterproofing and drainage: a fully enclosed model that does not allow groundwater to flow into the tunnel; and a drainage model that allows groundwater to flow into the tunnel. The fully enclosed mode is often used for special locations such as natural environment protection areas and locations where there are important buildings on the ground that cannot be drained by the tunnel for a long-time causing subsidence. Generally, the strength requirements of the lining structure and the waterproof layer are high. Therefore, for non-natural protected areas, drainage systems are generally used to reduce the external water pressure on the tunnel lining. Scholars at home and abroad are currently studying how high-water pressure affects the structural stress characteristics of tunnel linings through a series of theoretical analyses, model tests, field tests and numerical simulations [\u003cspan additionalcitationids=\"CR11 CR12 CR13 CR14\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Theoretically, Studied the spatial distribution of pore water pressure in urban tunnels in water-rich areas based on Harr and derived the water pressure equation for the seepage field[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Used complex variable analysis to analyze the stress distribution in elastic half-plane underwater tunnels[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Proposed a semi-analytical approach on tunnel water inflow[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Proposed a structural form suitable for high water level tunnel and the structural form of controlled drainage scheme, and studied the water pressure distribution in the tunnel lining by theoretical analysis, indoor tests and field measurements[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Developed an assessment framework based on a regionally coupled hydrological model to study the effects of tunnel drainage on surrounding vegetation [\u003cspan additionalcitationids=\"CR21 CR22\" citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. However, the current research results of tunnel drainage prevention are conventional drainage methods. Although it has a significant effect on water pressure reduction outside the liner compared to full closure, it only has a significant pressure reduction effect on the pressure around the tunnel arch wall. On the material side, conducted in-plane permeability tests of drained geotextile filters to assess their mechanism of hydraulic deterioration in tunnels [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Introduced an optimal lightweight foam mortar mixture for promoting tunnel drainage using the composite lining method [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. Designed waterproof and breathable materials based on electros pun nanofibers[\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. In terms of structure, proposed a new drainage structure containing convex hull drainage slabs by numerical simulation and indoor testing[\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. Constructed a tunnel drainage system by 3D printing technology and performed a simulation test of drainage system blockage [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e].Proposed three waterproofing and drainage optimization schemes, where placing the central drain at the bottom of the invert had the greatest impact on reducing water pressure by 96%[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Proposed a bottom-up railroad tunnel drainage method with pressure reduction[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Proposed a new drainage network to solve the drainage problem of mountain tunnels crossing high LWP fracture zones[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. Have studied and analyzed the waterproof requirements and construction measures of different special tunnels in China[\u003cspan additionalcitationids=\"CR33\" citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e].The above studies explored the tunnel water pressure problem and used various solutions (including external water pressure calculation, optimization of tunnel waterproofing and drainage system, new technologies and materials, etc.), but did not consider how to effectively mitigate the impact of water pressure on the lining structure at the tunnel elevation arch. At the same time, the causes of the increase in water pressure outside the tunnel were analyzed, etc., but none of them considered how to effectively reduce the impact of water pressure at the tunnel elevation arch on the lining structure.\u003c/p\u003e \u003cp\u003eBased on this, this paper proposes a new road tunnel drainage concept of three-way drainage. Compared to conventional road tunnel drainage systems, the characteristics of this system are better than those of conventional road tunnel drainage systems by setting up a water catchment area (such as the pebble sand pool in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e) at the elevation arch. After connecting to the central drain through a pipe (with a one-way drain valve inside), the excess water is discharged using the pressure difference. This not only can effectively reduce the high-water pressure at the elevation arch, but also will not affect the surrounding ecological environment by over-discharging too much water under the action of the one-way valve.\u003c/p\u003e \u003cp\u003eThe research in this paper is as follows: first, a brief review of the latest advances in highway drainage prevention research currently available. The detailed design of the depressurization system for the tunnel lining structure of the three-way drainage system is then presented. Finally, a series of numerical simulations were conducted to verify the pressure reduction performance of the three-way drainage system. At the same time, some key influencing factors affecting the three-way drainage pressure reduction are discussed by changing the hydraulic conduction coefficients of the surrounding rock and initial support, the head height, the number of reverse water diversion openings in the back arch and the secondary lining hydraulic conduction parameters.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e"},{"header":"2. Road Tunnels Are Designed To Use Anti-drainage","content":"\u003cp\u003eIn this section, the research results on drainage prevention in China and abroad are briefly reviewed with the main purpose of highlighting the novelty of the research in this paper.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2.1 Tunnel drainage prevention in the world\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAt present, the most advanced tunnel drainage prevention in China and abroad are Europe, Japan, Sweden, South Korea and other developed regions or countries. In most countries, water-rich mountain tunnels are drained to reduce the external water pressure in the tunnel lining under conditions without special requirements. The structure consists of a flashing between the initial support and the secondary lining, a circular drainage blind pipe, a longitudinal drainage blind pipe, a central drainage trench, and a sinkhole set at 50m (88m). As far as the road tunnel drainage system is concerned, the difference lies in the direction of water discharge at the elevation arch and the different pressure-reducing performance of the already studied about four models, as shown in Figure 1:\u003c/p\u003e\n\u003col\u003e\n \u003cli\u003eCircular and longitudinal drainage blind pipes were used to draw out water, and water was introduced into the central drainage trench through transverse diversion pipes. The transverse diversion pipe and the central drainage ditch are installed below the roadbed to form a complete drainage system, Figure 1(a).2.\u0026nbsp;the central drainage trench is installed below the tunnel lining and the circular drainage blind pipe is directly connected to it for drainage work, Figure 1 (b).\u003c/li\u003e\n \u003cli\u003eThe central drainage trench is set below the tunnel lining, and the circular drainage blind pipe is directly connected to it for drainage work, Figure 1 (b).\u003c/li\u003e\n \u003cli\u003eOn the basis of 1, the circular blind pipe is extended below the elevation arch, before connecting to the central drain through the reverse drain to form a complete drainage path. A protective gravel head is usually laid around the central drain, which also serves as a filter for debris, Figure 1(c).\u003c/li\u003e\n \u003cli\u003eSo that the lining is in complete closure and does not allow water to flow into the tunnel, outside the body then the water is led out of the tunnel on the basis of 2 in combination with the lateral diversion pipe in 1, which brings the water together in a central drainage trench below the supine arch, Figure 1(d).\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003e\u003cstrong\u003e2.2 Anti-drainage systems used in Chinese road tunnels\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe current drainage system frequently used in Chinese road tunnels is shown in Figure 1. Generally this drainage system is installed between the secondary lining and the initial support with ring and longitudinal drainage blind pipes as well as waterproof layer, and the central drainage trench as well as the lateral diversion pipe is installed below the roadbed. The water around the tunnel is directed through the drainage pipes and collected in the central drainage ditch through the lateral drainage pipes. The distance between the drainage pipes in the project and the surrounding rock grade, the amount of water-rich rock and the height of the head has a certain relationship, the general longitudinal distance between the circular drainage blind pipe in 6m ~ 10m or so.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe above is about the drainage of the tunnel anti-drainage buck, no matter which drainage is to protect the tunnel safety and service life, but often have certain defects. For example: Figure 2 Chinese road tunnels commonly used anti-drainage system is not difficult to find, unable to drain the water from the elevation arch position of the tunnel. In the case of non-rainy season can ensure the safety of the tunnel, but in the case of relatively high rainfall or long-term operation of the tunnel pipe crystallization can make the drainage is not timely lead to the tunnel lining force damage, and ultimately affect the life of the tunnel. As shown in Figure 1 (c) (d) the central drainage trench is located below the elevation arch of the tunnel. Although it can effectively solve the problem of high-water pressure at the elevation arch of the tunnel, it cannot control the amount of groundwater discharge. It will lead to the phenomenon of how much discharge, which cannot effectively protect the surrounding ecological environment. It will also have an impact on the construction of the tunnel resulting in a huge amount of earth and rock excavation, which will not only affect the construction period, but also increase the economic investment of the project. In Figure 1(b), although the design adds a reverse drain, no protection is provided for the pipe head. The crystallization or blockage of foreign objects will occur with the increase of operation years, which will lead to the decrease of the drainage volume, thus causing the water pressure at the elevation arch to rise. It is detrimental to the tunnel lining in the long run. In order to solve the above problems, the following discussion and analysis of the core contents of this paper will be carried out.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2.3 Concept and design of a three-way drainage depressurization system for highway tunnels\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis paper studies the three-way drainage and depressurization system of Chinese highway tunnels, which consists of four main components: ① circular drainage system; ② longitudinal drainage system; ③ reverse drainage pipe of the elevated arch; ④ transverse diversion pipe and central drainage trench. Among them, the ring, longitudinal drainage blind pipe and the newly added supine arch reverse drainage pipe to achieve three directions of drainage purposes this paper is called the three-way drainage pressure reduction system (hereinafter referred to as the three-way drainage system). Details of the structure are shown in the figure.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e① Circumferential drainage system: The circumferential drainage system is located between the initial support and the secondary lining of the tunnel, and is responsible for directing the water flow around the tunnel to discharge water, as shown in Figure 3.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e② Longitudinal drainage system: The longitudinal drainage system is responsible for collecting the water directed down from the circular drainage system as well as the perimeter water seeping down, and then bringing the water to the central drainage ditch through the horizontal diversion pipe.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e③ Reverse drainage pipe for the supine arch: the reverse drainage system for the supine arch consists of a sand pond (coarse sand and cobbles, etc.) outside the tunnel lining, a one-way drainage valve set (Bgha B, Hui L A et al., 2020) and a reverse drainage pipe by connecting to the central drainage ditch, which finally leads the huge water pressure at the supine arch out of the tunnel through the central drainage ditch during the flood season, see Figure 6.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e④ Transverse diversion pipe and central drainage ditch: The horizontal diversion pipe and central drainage ditch are mainly responsible for diverting the water collected by the three-way drainage system out of the tunnel to achieve the purpose of reducing the water pressure outside the tunnel lining.\u003c/p\u003e\n\u003cp\u003eBy comparing the structural differences between the conventional drainage system for road tunnels in water-rich areas (Figure 2) and the new concept drainage system for three-way drainage (Figure 3). It can be seen that the so-called three-way drainage system is to use the high-water pressure at the elevation arch to divert the high-pressure water out of the tunnel through the collecting sand pond and the reverse drainage pipe to achieve the purpose of pressure reduction in the elevation arch of the tunnel. The high-water pressure at the bottom of the elevated arch in Figure 4 will drain the water under the pressure difference. \u0026nbsp;The one-way valve prevents water from backing up and drains only when sufficient design pressure is reached at the elevation arch, and the sand pond has a protective effect on the water inlet, which increases the service life. During the dry season, the drainage will be blocked by the drainage check valve, so that the groundwater will not be discharged excessively in the water-rich area. In order to meet the principle of \u0026quot;blocking mainly, limited discharge\u0026quot; of tunnel drainage prevention, and at the same time can prevent sediment backflow to block the structure. Similar studies are currently available for this area (Li P, Liu H et al., 2018). Although this study also serves to reduce the high-water pressure at the elevation arch, it mainly serves railroad tunnels and the study structure is relatively complex. \u003c/p\u003e"},{"header":"3. Numerical Simulation Analysis","content":"\u003cp\u003eSince this paper is proposing a new drainage system, which currently has no case in engineering, numerical simulation is used to study it. In this section, the feasibility of the three-way drainage system concept is investigated by numerical simulation with Midas gtsNX software. The research results prove that the three-way drainage concept can not only reduce the overall water pressure of the tunnel lining structure, but also effectively reduce the water pressure at the elevation arch. A detailed analysis will be presented below.\u0026nbsp;The calculation of water pressure outside the liner is mainly based on the theory of well flow in infinite aquifers and Darcy\u0026apos;s law.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e\u003cstrong\u003e3.1 Boundary conditions of the numerical models\u003c/strong\u003e\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eIn order to study the performance of the three-way drainage system on the water pressure drop at the elevation arch of the tunnel, this paper uses finite element software to simulate the three-way drainage system and the conventional drainage system for comparative analysis and verification.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe model simulation is based on the Tongzi Tunnel, a mega-section high-speed tunnel under construction in Guizhou, China, as a reference. The groundwater level at the top of the tunnel vault is 70m, and the head is applied at the top. Model size of the length \u0026times; width \u0026times; height = 180m \u0026times; 40m \u0026times; 100m. The perimeter is taken to be greater than 3 by the hole diameter to eliminate the boundary effect, and the mesh model and structure details are shown in Figure 5. All parts of the model are simulated using solid units. The present model makes the following assumptions: the surrounding rock is simulated using the Mohr-Coulomb principal structure model, and the initial support, secondary lining structure and drainage prevention system are simulated using the elastic model. The model is always fully saturated, and the nodal head pressure is set to 0 in the drainage hole area to simulate drainage. Drainage system in order to facilitate the calculation in the actual project commonly used in the PVC pipe diameter as a reference basis. The modeling is equivalent to a square structure of 89 mm * 89 mm * 89 mm using the equal flow principle. the specific parameters of the material are listed in Table 1 below.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cstrong\u003eTable 1.\u0026nbsp;\u003c/strong\u003eParameters of each material\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" width=\"745\" height=\"316\"\u003e\u003c/p\u003e\n\u003cp\u003eNote: Due to the existence of a one-way valve group in the reverse drainage pipe at the elevation arch here to solve the problem by controlling the hydraulic conduction coefficient, taking the value of 0.3.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.2. Analysis of results\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo verify the performance of the three-way drainage system, a comparative analysis of the fully enclosed undrained, conventional drainage system and the three-way drainage system was performed and normalized based on the values of the fully enclosed undrained. The drainage cross-section and non-drainage cross-section of the tunnel circular monitoring section (C1 to C10) were extracted for analysis. As shown in Figure 6 (a) water pressure distribution at the drainage section of the secondary lining (b) water pressure distribution at the non-drainage section of the secondary lining. According to Fig. 6 (b) (c), the following conclusions can be drawn.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe conventional drainage system effectively reduces the water pressure outside the liner by approximately 58% in the section above the longitudinal drain compared to the fully enclosed undrained system. It can be seen that measurement points C1 to C7, if the drainage system drainage capacity is fully developed, the pressure reduction effect will be more obvious. But the conventional anti-drainage system does not have a drainage outlet at the bottom of the supine arch. C8 to C10 measurement points can be seen that the water pressure around the elevation arch is reduced by less than 20%. Therefore, for the time being, the performance of conventional drainage systems in Chinese road tunnels is still lacking in terms of pressure relief at the elevation arch of the tunnel. Such high-water pressure gathered at the elevation arch, if encountered heavy rain, or continuous rainfall time tunnel elevation arch structure is very vulnerable to the threat of high-water level water pressure, thus reducing the life of the tunnel. However, in the study, it was found that the use of reverse drainage of the elevated arch was effective in reducing the occurrence of such situations. The principle is to use the pressure difference to reverse the water out of the tunnel from underneath the elevated arch. The concept of \u0026quot;three-way drainage\u0026quot; in this paper is mainly derived from the concept that pressure difference can cause water to flow in the opposite direction, which can effectively drain the water under natural pressure. It also prevents excessive water discharge which is beneficial to the surrounding ecological environment.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFrom the results of numerical simulation (b). The three-way drainage system has approximately seven times the pressure-reducing performance of the conventional drainage system at the elevation arch. The water pressure at the elevated arch is significantly reduced. It is not difficult to find from (c) figure that there is also a certain effect on the overall pressure reduction of the tunnel structure. The pressure reduction capacity of the non-drainage section is likewise increased, and the pressure reduction effect at the elevated arch is about 57% higher than the conventional one. In the above numerical simulation, the pressure reduction performance and feasibility of the \u0026quot;three-way drainage system\u0026quot; were verified. From the results, it is obvious that the water pressure is greatly reduced after the reverse drainage holes are set in the elevation arches C8 and C9.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe following conclusions can be drawn from Figure 7. Where (c) to (h) are the multiplicative relationships of the number of reverse drainage holes in the supine arch for three-way drainage. From the above cloud diagram, it is not difficult to find that the secondary lining in the fully closed state of Figure (a) is in a state of hydrostatic pressure, and the external water pressure is very high. In Fig. (b) conventional drainage method the external water pressure is reduced by about 30%. However, the elevated arch is still subject to high external water pressure, which is unsafe for long-term operation. For the three-way drainage system, it is obvious that when the number of reverse drainage holes increases from 2 to 32 according to the previous multiplicative relationship, it can be found that the more the number of reverse drainage holes at the elevation arch is more beneficial for the elevation arch pressure reduction. However, for the design of this paper to serve the later project, a reasonable and economical number of reverse drainage holes should be found. It can be found that when the number of reverse drainage holes grows from 8 to 16 about 12% decrease, the pressure reduction rate is the highest at this time. For figure (h) infinite number of reverse drainage holes although the pressure reduction effect is significant. However, it is unsafe for the overall structure of the tunnel, so it is recommended to set up 16 reverse drainage holes for every 40m long interval.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn general, the feasibility of the new drainage concept of three-way drainage was proven. In addition, the reverse drainage of the elevated arch can realize the tunnel in the flood season when the high pressure, the use of pressure differences so that the water automatically discharged. Retaining water resources during dry weather does not have a significant impact on the surrounding ecosystem.\u0026nbsp;\u003c/p\u003e"},{"header":"4. Analysis Of Factors Affecting The Performance Of Three-way Drainage Systems","content":"\u003cp\u003eIn this section, the performance of the three-way drainage system will be studied by numerical simulation parameters varying the parameters of the hydraulic conductivity of the surrounding rock, the head height, the initial support and the secondary lining.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.1. Parameter taking and analysis\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe following paper presents a numerical simulation study by analyzing the three-way drainage under different parameters. The study of the three-way drainage buck performance was carried out by changing the parameters. The following discussion is carried out under the condition that the drainage is completely usual as well as completely symmetrical. The hydraulic conductivity coefficient and head height of the IV enclosure, secondary lining and initial support are changed under the conditions of Table 1, and the specific parameters are changed as shown in Table 2.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFor numerical calculation, first a variable is selected as a fixed value. Analytical calculations are performed by changing other physical parameters. For example, the hydraulic conductivity of secondary lining 1.3\u0026times;10-11 in Table 1 remains unchanged, and the hydraulic conductivity of other parameters IV surrounding rock and initial support increases according to 1 to 10 times. Since there are too many combinations only order changes are considered. The head height increases from 25m at a rate of 5m to a head height of 70m. To see the difference in the result curves. The hydraulic conductivity of secondary lining takes two fixed values of 1.3\u0026times;10-8 and 1.3\u0026times;10-11 as high and low hydraulic conductivity respectively for analysis, which are noted as SLH1 and SLH2 in the following.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 2.\u003c/strong\u003e Parameter values and variations.\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"567\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"13.051146384479718%\" rowspan=\"2\"\u003e\n \u003cp\u003e\u003cstrong\u003eCalculation variable\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"37.56613756613756%\" colspan=\"2\"\u003e\n \u003cp\u003e\u003cstrong\u003ePermeability\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"33.686067019400355%\" colspan=\"2\"\u003e\n \u003cp\u003e\u003cstrong\u003eNumber of vertical drains\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.696649029982364%\" rowspan=\"2\"\u003e\n \u003cp\u003e\u003cstrong\u003eHeight of water head\u003c/strong\u003e\u003cstrong\u003e（\u003c/strong\u003e\u003cstrong\u003em\u003c/strong\u003e\u003cstrong\u003e）\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"29.95049504950495%\"\u003e\n \u003cp\u003eIV\u0026nbsp;surrounding rock\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"22.77227722772277%\"\u003e\n \u003cp\u003eInitial support\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"27.97029702970297%\"\u003e\n \u003cp\u003eConventional drainage\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.306930693069308%\"\u003e\n \u003cp\u003eThree-way drainage\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"13.051146384479718%\"\u003e\n \u003cp\u003e\u003cstrong\u003eSLH1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"37.56613756613756%\" colspan=\"2\" rowspan=\"2\"\u003e\n \u003cp\u003e0.1，0.2，\u0026hellip;, 1, 2, \u0026hellip;, 10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.929453262786595%\" rowspan=\"2\"\u003e\n \u003cp\u003eNo vertical diversion pipe\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.756613756613756%\" rowspan=\"2\"\u003e\n \u003cp\u003e1，2，\u0026hellip;, \u0026infin;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.696649029982364%\" rowspan=\"2\"\u003e\n \u003cp\u003e25，30，\u0026hellip;, 70\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"100%\"\u003e\n \u003cp\u003e\u003cstrong\u003eSLH2\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u0026nbsp;Note: The elevated arch is regarded as the primary support and the second lining superimposed, so the hydraulic conduction coefficient is not considered separately there.\u003c/p\u003e\n\u003cp\u003eThe number of three-way drainage pipes keeps increasing from 1, 2, ..., \u0026infin;, that is, the number of reverse drainage pipes of the elevated arch keeps increasing from 1 to form a sink which is \u0026infin;. Since it was not possible to model so many, only 10 values were selected for the simulation. This is because such a value is already highly intensive in this computational model.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.2. Analysis of parameter values and variation results\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe calculations in this section are all in accordance with Table 2 for the analysis of the magnitude values of water pressure affecting the secondary lining outside. The C8 and C9 measurement points with special representation were taken for the results and compared to the fully closed and conventional drainage systems analyzed above. The following plotted results are normalized to the fully enclosed non-drainage results and after changing one condition, the other conditions are the initial values in Table 1.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.2.1. Hydraulic conductivity of IV surrounding rock\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe effect of hydraulic conduction coefficient of IV surrounding rock on the water pressure outside the secondary lining under the condition of not changing the surrounding rock grade is shown in Figure 8.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIt can be seen from Fig. 8that the hydraulic conductivity of the IV envelope increases slowly from 0.1, 0.2, ..., 1, 2 times to 10 times when the external water pressure of the secondary lining is increasing. The growth trend is from rapid increase to steady. The results show that the hydraulic conductivity of the surrounding rock increases the overall external water pressure of the secondary lining is increasing but for the high permeability of the secondary lining can effectively reduce the water pressure. Compared with conventional drainage three-way drainage elevation arch water pressure in the surrounding rock hydraulic conductivity coefficient in 6 to 10 times the size of the water pressure is maintained at about 0.65 times. So it is said that the three-way drainage mode can effectively reduce the external water pressure at the elevation arch of the tunnel. When the hydraulic conductivity of the secondary lining is increased by 100 times, the difference in the water pressure ratio at C8 and C9 is not too great.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.2.2. Hydraulic conductivity of the initial support\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIt can be seen from Figure 9 that the initial support hydraulic conduction coefficient grows, and the water pressure outside the secondary lining of the three-way drainage system grows slowly and eventually stabilizes. For conventional drainage systems, the numerical solution of the water pressure outside the secondary lining is slowly decreasing and eventually stabilizing. From the results of both, there exists a most unfavorable value for the initial support hydraulic conductivity coefficient. So the external water pressure of the secondary lining will have a maximum peak. After this maximum value the water pressure in the secondary lining will tend to decrease, but only within a small range of fluctuations.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.2.3 Increase in the number of reverse drainage holes in the supine arch\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAs in Figure 10, the drainage capacity is improved by changing the number of reverse drainage holes in the elevated arch. The numerical study found that the external water pressure of the secondary lining was decreasing regularly with the increase of the reverse drainage hole of the elevated arch. As the number of drainage holes changes from a point to a line, the rate of water pressure reduction becomes slower and slower, and the curve eventually flattens out. This means that when the number of drainage holes slowly increases to a very dense level, there is no longer a significant increase in the external water pressure of the secondary lining. It shows that there is an optimal number of drainage holes set at the elevation arch for three-way drainage. For example, in this paper, if the lining length is 40m, the number of 16 reverse drainage holes of the elevated arch will be set to reach the optimal value. At the same time, the three-way drainage method can also effectively reduce the overall external water pressure of the elevated arch and secondary lining compared with the conventional drainage.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.2.4 Water head height variation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eOther initial conditions remain unchanged, the head height change on the secondary lining outside the water pressure influence law is shown in Figure 11. It is not difficult to find that the increase in head height the external water pressure of the secondary lining is basically unchanged. This indicates that the head increases and the water pressure increases the size of the water flow discharged will also increase year-on-year. Since only the highest head of 70m is analyzed here, it is different from the case of deeply buried tunnels. Therefore, the increase in head height has little effect on the external water pressure of the secondary lining for lots where the burial depth is not large. However, compared with conventional drainage, the water pressure reduction after setting the reverse diversion inlet of the elevated arch for three-way drainage is significant, only 0.43 times of conventional drainage. With different hydraulic conductivity coefficients for the secondary lining, it is not difficult to find that the difference between the two is not large under the 100 times multiplier condition, indicating that this is not a major factor.\u0026nbsp;\u003c/p\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eIn order to efficiently and economically solve the disease problems caused by high-water pressure in the elevation arch of highway tunnels in China. This paper proposes a new drainage concept of \"three-way drainage\", which has been found to be effective in reducing the high-water pressure at the elevation arch of the tunnel. The drainage and decompression characteristics of the three-way drainage system on the tunnel lining are analyzed in a numerical simulation. The main findings are as follows:\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e(1) The three-way drainage system adds a reverse drainage structure (with a one-way valve set) to the elevated arch, which is theoretically feasible. It can effectively reduce the external water pressure at the elevation arch of the tunnel as well as the water pressure of the overall structure of the lining.\u003c/p\u003e \u003cp\u003e(2) The external water pressure of the tunnel secondary lining has a certain relationship with the hydraulic conductivity of the surrounding rock, which shows a synchronous growth trend.\u003c/p\u003e \u003cp\u003e(3) For the numerical results of the three-way drainage in this paper, the increase in the hydraulic conductivity of the initial support has little effect on the change in water pressure in the secondary lining. The change in force transfer coefficient will cause a peak in the external water pressure of the secondary lining, causing the secondary lining water pressure to begin to drop.\u003c/p\u003e \u003cp\u003e(4) The increase in head height makes the water pressure ratio outside the secondary liner increase linearly. Therefore, in the environment of high head height, the tunnel drainage prevention system as well as the lining structure will need to improve the design requirements.\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eThe three-way drainage system in this paper has proven to be feasible. It is not currently used in practice and is still at the stage of theoretical analysis. The indoor model tests will be conducted to provide a reasonable and economic drainage method for road tunnels, and actual engineering experience will be used to verify the drainage and pressure reduction performance of the three-way drainage system.\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthor Contributions:\u003c/strong\u003e Z.T.\u0026nbsp;（Zhaolei Teng）\u0026nbsp;wrote the main manuscript text and Y.L.（Yuanming Liu）\u0026nbsp;and Y.Z.\u0026nbsp;（Yuhang Zhou）\u0026nbsp;prepared figures 1-11. and \u0026nbsp;Y.L.\u0026nbsp;（Yingxiao Li）\u0026nbsp;and S.M.\u0026nbsp;（Shilong Mei）\u0026nbsp;prepared \u0026nbsp;Tables 1 and 2. B.D.（Bitao Du）\u0026nbsp;and G.H.（Guohua He）prepared numerical software modeling. All authors reviewed the manuscript.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding:\u003c/strong\u003e This work was supported by the Science and Technology Planning Project of Guizhou Province (Qiankehe major special project [2018] 3011), and Qiankehe Basic Project ZK [2022] General Project 082, and Qiankehe Basic Project [2019] No.1057), Guiyang Metro Line 3 Phase I Engineering Research Project (Project No.GD3-FW-YJ-05-2020-13-ZB), and Regional first-class discipline construction project in Guizhou Province (QYNYL [2017] 0013).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments:\u003c/strong\u003e The authors gratefully acknowledge Mr. Wenrong Ma of China Railway Eighth Engineering Group Third Engineering Co., Ltd and Mr. Xiaoyong He of China Railway Development Investment Group Co. Ltd. for their valuable comments and support.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe hereby declare that this contribution is our own work. As far as we know, it does not contain materials previously published or written by others. There is no competing interest between authors. Before the journal makes a decision, it will not be considered to be published elsewhere.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eInstitutional Review Board Statement:\u0026nbsp;\u003c/strong\u003eNot applicable.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eInformed Consent Statement:\u003c/strong\u003e The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of Interest:\u003c/strong\u003e The authors declare no conflict of interest.\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli dir=\"LTR\"\u003e Liu, Y.; Feng, Y.; Xu, M.; Zhang, Y.; Long, H.; Zhu, H. Effect of an incremental change in external water pressure on tunnel lining: a case study from the Tongxi karst tunnel. \u003cem\u003eNat. 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Waterproof Performance of Sealing Gasket in Shield Tunnel: A Review. \u003cem\u003eApplied Sciences\u003c/em\u003e \u003cstrong\u003e2022\u003c/strong\u003e, \u003cem\u003e12\u003c/em\u003e, 4556.\u003c/li\u003e\n \u003cli dir=\"LTR\"\u003e Luciani, A.; Peila, D. Tunnel Waterproofing: Available Technologies and Evaluation Through Risk Analysis. \u003cem\u003eInt. J. Civ. Eng.\u003c/em\u003e \u003cstrong\u003e2019\u003c/strong\u003e, \u003cem\u003e17\u003c/em\u003e, 45-59.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"three-way drainage system, tunnel depressurization, water-rich zone, numerical simulation","lastPublishedDoi":"10.21203/rs.3.rs-2790049/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2790049/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eFor the water-rich area tunnel elevation arch in the high-water pressure often causes elevation arch cracking and leakage, bulging and other disasters. When the drainage system is not designed properly, such disasters occur more frequently, and conventional road tunnel drainage cannot effectively reduce the water pressure at the elevation arch. Therefore, this paper proposes a new concept of \"three-way drainage\". The three-way drainage system is based on the conventional drainage system with a new drainage inlet at the elevation arch. On this basis, a series of numerical simulation studies are conducted to verify the pressure-reducing performance of the three-way drainage system on the lining. After demonstration and analysis, the three-way drainage concept can not only effectively reduce the water pressure at the elevation arch of the tunnel, but also have a significant effect on the overall drainage effect of the tunnel. The factors affecting the performance of the three-way drainage system are discussed by varying the model parameters. It was found that the hydraulic conduction coefficient of the surrounding rock and initial support, the number of reverse diversion holes in the elevation arch, the change in head height and the change in secondary lining parameters all had a significant effect on the water pressure outside the tunnel.\u003c/p\u003e","manuscriptTitle":"FEM analysis of a new three-way drainage and pressure reduction system for road tunnels","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-04-20 21:55:51","doi":"10.21203/rs.3.rs-2790049/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major revision","date":"2023-05-31T05:34:17+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2023-05-20T01:46:17+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"9fffb976-d650-4655-87db-d75c1b638053","date":"2023-05-14T23:46:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"4fc23f8c-c945-4b87-8b66-7d898afc9b55","date":"2023-05-11T05:48:44+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2023-05-11T05:20:39+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2023-05-11T05:17:05+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2023-04-18T11:08:58+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2023-04-18T11:04:15+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2023-04-07T13:12:49+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"9380ca4d-7fc8-4b58-9a07-406d80f6bf4c","owner":[],"postedDate":"April 20th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":20801367,"name":"Physical sciences/Engineering/Civil engineering"},{"id":20801368,"name":"Earth and environmental sciences/Ecology"}],"tags":[],"updatedAt":"2023-10-16T21:49:08+00:00","versionOfRecord":{"articleIdentity":"rs-2790049","link":"https://doi.org/10.1038/s41598-023-37417-1","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2023-07-05 21:32:07","publishedOnDateReadable":"July 5th, 2023"},"versionCreatedAt":"2023-04-20 21:55:51","video":"","vorDoi":"10.1038/s41598-023-37417-1","vorDoiUrl":"https://doi.org/10.1038/s41598-023-37417-1","workflowStages":[]},"version":"v1","identity":"rs-2790049","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2790049","identity":"rs-2790049","version":["v1"]},"buildId":"WrCJVZZCHTDjtuVLN7oU0","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}