1 Introduction
With the acceleration of urbanization and the rapid development of underground space development technology, China’s subway has shifted from a construction-based to a construction and operation-based phase. However, with the prolongation of service life, tunnel structural diseases are becoming more and more prominent, of which water leakage is one of the most common diseases. China’s operating subway leakage rate increases each year. However, the evolution laws of the seepage and stress fields during tunnel leakage should be noted [
1–
3]. Tunnel leakage not only destroys the lining structure, reducing its bearing capacity and stability, but also shortens the service life of the structure and exacerbates the damage of weak links [
4–
7].
In recent years, a series of research has been carried out on the distribution of seepage fields and the prediction of leakage conditions in tunnels through modeled experiments [
8–
10], numerical simulation [
11–
14], and theoretical analysis [
15–
19]. Wang et al. [
20] studied the seepage mechanism at the junction of the Beijing subway shaft and shield tunnel. Li et al. [
21] conducted variable head seepage modeling tests for small spaced tunnels in Chongqing, revealing the dynamic coupling law between seepage and stress fields. Feng et al. [
22] analyzed the water pressure distribution and lining deformation of water-rich tunnels crossing fault zones through field experiments and numerical simulations, and proposed that prioritizing the reinforcement of the up-arch, arch foot, and vault areas can reduce the probability of seepage by 40%–60%. Gao et al. [
23] revealed that geologic faults are the dominant factor affecting the distribution of seepage fields in operational tunnels through modeling tests and numerical simulations.
With the service period of the city subway extended, water leakage problems occur frequently due to extreme rainfall and the storage environment. According to statistics, about 86% of the 16 subway lines in Beijing have different degrees of seepage and leakage problems, and structural joints account for 48.2% of the seepage [
24–
26]. As the weak link of leakage, the failure mechanism of structural joints has been widely concerned, and studies have shown that joint deformation and aging of waterproofing materials can significantly weaken the sealing performance [
27–
29]. The Hanshin Expressway Tunnel, where leakage from structural joints is triggered by thermal expansion, revealed the amount of seasonal expansion (6 mm on average) and the influence of the cover layer through on-site measurements and proposed a plan to optimize the spacing of joints and a new waterproofing structure [
30]. Wang et al. [
31] proposed quantitative evaluation indexes of lining cracks and leakage based on the data of 116 road tunnels. The research revealed that temperature contraction stress and groundwater source were the main causative factors. Additionally, a probabilistic model for reliability verification was established Deng et al. [
32] pointed out the deterioration of road tunnel linings in China primarily manifests as longitudinal and transverse cracking. This study analyzes the impact of design and construction factors on lining degradation, proposing three remediation approaches: structural replacement, reinforcement, and crack sealing, along with their respective application conditions and technical considerations. According to numerical analysis and model testing, Kawata et al. [
33] revealed that the construction joint positioning significantly influences the lining mechanical properties. The stress and deformation patterns vary substantially based on joint location, necessitating targeted reinforcement measures for structural optimization. The concealed nature of tunnel lining systems makes it difficult to accurately assess internal damage conditions and seepage paths when leakage occurs. This technical challenge has created significant difficulties in leakage management. Current research primarily focuses on the visual leakage through lining cracks [
34–
36], while largely overlooking the coupled interaction between concrete defect development and internal seepage processes within the lining structure. Therefore, systematically studying the relationship between lining’s internal structural defects and crack seepage characteristics holds significant theoretical value for understanding the fundamental mechanisms behind leakage phenomena.
Recent years have witnessed significant advances in tunnel waterproofing research. Many scholars have investigated leakage mechanisms in shield tunnel joints [
37–
40]. It should be emphasized that the composite support system in mined tunnels demonstrates distinct leakage behaviors [
41,
42]. This system not only modifies groundwater leakage paths when concrete cavity defects occur in tunnel linings, but also increases leakage risks in crack and joint areas.
Seepage is closely related to structural defects in the tunnel lining, especially the coupling of the secondary lining cavity and structural joint failure can significantly intensify the leakage risk. Studies have shown that cavity behind the lining can lead to stress redistribution and bending moment reversal, reducing the structural load carrying capacity [
43–
45]. Zhang et al. [
46] investigated the effects of construction defects (e.g., voids) on lining damage in operational tunnels based on on-site investigation and numerical analysis. The results show that voids significantly change the structural stress state and threaten tunnel stability. The study verified the effectiveness of numerical modeling in assessing the damage effects of defects. Fu et al. [
47] the effects of local construction defects (voids, insufficient lining thickness) on the cracking of existing tunnels are simulated based on the extended finite element method, which reveals the local arching effect triggered by the defects and the preferential damage law on the outside of the structure. It also accelerates the crack expansion and the formation of seepage channels [
48–
50].
Tunnel lining leakage is a core challenge that threatens the safety of underground engineering. Existing studies predominantly analyze defects (e.g., cavity depth or structural joints) in isolation, with a lack of systematic knowledge regarding the seepage-mechanical response mechanism under the coupled effect of defects. Consequently, these leakage risk prevention and control strategies are limited. The presence of cavities induces localized stress concentrations within the lining structure, thereby accelerating structural joint leakage. Concurrently, joint seepage intensifies material erosion in cavity-disturbed zones, forming a vicious cycle of defect (Fig. 1). Based on the Beijing subway project, this study systematically investigates the influence of cavity depth, scope, and spatial distribution on water leakage under failed waterproof conditions at structural joints. The experiment focuses on analyzing variations in lining water pressure, earth pressure, and stress–strain behavior. The research results reveal the distribution law of the seepage field under multi-factor coupling, offering critical data for risk assessment and leakage remediation strategies in subway tunnels.
2 Preparation of the experiment
2.1 Engineering background
Since the Beijing section of the South-to-North Water Diversion Project was launched in 2014, external water sources have gradually replaced some local groundwater sources. By June 2024, the average depth of groundwater in Beijing increased to 14.74 m, a significant rise of 11.01 m compared to the same period in 2015. As the groundwater level has risen, water leakage in subway stations and tunnels has become a growing issue. Based on data from 87 tunnels across 24 subway lines in Beijing, a total of 2616 leakage points were identified. Structural joints (construction joints and concrete cracks) constitute critical structural weaknesses, accounting for 74% of all leakage diseases Fig. 2. Consequently, these structural discontinuities emerge as critical zones requiring prioritized leakage mitigation measures.
Notably, about 65% of structural joint leaks are accompanied by lining cavities, indicating these issues often occur together. Lining cavities are interfacial gaps between the lining and primary support caused by construction imperfections. These defects compromise structural integrity through stress concentration effects and significantly elevate the failure risk of the waterproof layer [
44]. It not only compromises the lining’s load-bearing capacity but also significantly intensifies leakage through structural joints by accelerating both the leakage rate and propagation extent. Figure 3 shows the secondary lining structural cavity defects. It is essential to quantify how cavity characteristics (such as depth, size, location, and number) magnify leakage and pressure magnitudes and analyze the lining’s response under coupled water pressure and rock stress.
2.2 Experimental equipment development
2.2.1 Similar principle
Similarity theory is the foundation of physical model testing [
51]. The key principle is to establish similarity criteria between the prototype and the model. This ensures the test results accurately represent actual engineering conditions. Similar phenomena can be categorized into two primary types: geometric similarity and physical similarity [
10,
21,
40,
52]. Geometric similarity requires a strict scale relationship between model and prototype dimensions. Physical similarity demands proportional material parameters (e.g., strength, permeability) to ensure equivalent physical processes.
This study investigates how tunnel lining cavities affect seepage fields through scaled model tests. Based on actual tunnel dimensions and model box constraints, the following similarity ratios: Cγ = 1 (unit weight), CL = 50 (geometry), and CK = 1 (permeability) are adopted, as detailed in Table 1. Furthermore, the similarity ratios for other variables were derived as follows: CT = 50 (time), CP = 50 (water pressure), CH = 50 (hydraulic head), CE = 50 (elastic modulus), and CQ = 2500 (water inflow). The prototype tunnel support structure has a diameter of 5.5 m and a thickness of 0.5 m. Therefore, a tunnel model with a diameter of D = 0.11 m and a thickness of 1 cm was constructed based on geometric similarity ratios.
2.2.2 Experimental equipment
This study investigates how lining cavities exacerbate water leakage through structural joints within subway tunnels. A water head-adjustable experimental apparatus was designed to simulate tunnel lining leakage defects based on the spatial distribution characteristics of tunnel leakage. In addition, a parameter-adjustable lining cavity leakage structure model was fabricated using 3D printing technology.
The experimental equipment dimensions were 1.25 m (length) × 0.6 m (width) × 0.85 m (height), corresponding to a geometric similarity ratio of CL = 50 relative to prototype tunnel dimensions Fig. 4. In addition, the secondary lining structure was made using 3D printing technology. The primary support was simulated using geotextile materials with a certain permeability coefficient and no bearing function. Eventually, the tunnel support system was formed through primary support superposition onto the lining. The vault lining incorporated pre-installed circumferential structural joints to simulate potential seepage pathways, while artificially created lining cavities were positioned at vault and spandrel locations. By adjusting the size and location of the cavities, the role of exacerbating the seepage of the ring-oriented structural joints was investigated Fig. 5.
2.3 Preparation of experiment materials
2.3.1 Tunnel model structure
The lining structure measured 70 cm in length with an 11 cm outer diameter and 1 cm wall thickness. A 1 mm wide × 9 cm long artificial crack was pre-designed at the vault to simulate structural joint leakage. Furthermore, a series of cavity defects with varying dimensions were incorporated along the vault centerline to systematically investigate size-dependent leakage behavior. The lining structure was divided into two parts: Side A and Side B, based on a zoning approach. Using 3D printing technology, two cavity structural units (Type I and Type II) at the ends of two working faces are prefabricated. These units form a modular lining system with adjustable properties for multiple working conditions. This system enables flexible structural condition combinations for transformation. The detailed geometric parameters are provided in Table 2. Two types of cavity-covering plates (5 and 3 mm thickness variants) were fabricated 3D printing. Both designs featured uniform dimensions of 2.45 cm length and a 20° inclined surface to ensure precise dimensional control during experimental installation in Fig. 6.
2.3.2 Test similar materials
Model tests commonly use barite powder, sand, gravel, and gypsum as surrounding rock materials. This study examines the lining-cavity interaction induced by crack leakage and rock infiltration, with the Beijing subway as the engineering case. The permeability coefficient served as the key material design parameter [
21,
52,
53]. While this approach successfully matches the permeability behavior, the differences in mechanical properties (particularly strength and stiffness) between the model material and prototype formation may not be a major consideration. Coarse sand with permeability matching Beijing subway’s sand-pebble strata was selected as the surrounding rock material. Following the Code of China’s Highway Geotechnical Test Specification (JTG 3430-2020) [
54], the head permeability method is used to calibrate the sand’s permeability coefficient. The results obtained were shown in Table 3.
where k represents sand permeability coefficient (m/s), Q is water volume (m3) collected in t seconds, L is specimen height (m), A is specimen cross-sectional area (m2), H1 and H2 is water level difference (m).
The feasibility and high accuracy of 3D printing technology in civil engineering modeling tests have been fully verified. Tests using 3D printing technology to refine the construction of the tunnel secondary lining cavity size. The lining is used as a bearing structure, which is usually made of C35 reinforced concrete with a modulus of elasticity of (E = 31.5 GPa). It must primarily satisfy the modulus of elasticity similarity criterion (CE = 50). Therefore, ABS polymer (elastic modulus E = 0.65 GPa) was selected as the scale model material, offering an optimal combination of cost efficiency and highly stable material for the experimental lining simulations.
In practical tunneling projects, the primary support typically needs to fulfill both structural support and seepage control functions simultaneously. However, this study primarily focuses on the seepage control function. Therefore, the experiment employs a functional decomposition approach, separating the structural support and seepage control functions of the primary support. Geotextiles with specific permeability (but no structural function) were selected to control water seepage and provide sand insulation. Based on previous studies [
53,
55], an 8-layer stacked woven fabric configuration was adopted to match the actual primary support’s permeability coefficient of 1 × 10
−7 m/s. This approach accurately simulated the seepage control function while maintaining consistency in mechanical properties between the model and prototype, as shown in Fig. 7.
2.4 Experimental conditions
Table 4 presents the experimental design for lined cavity seepage analysis, comprising eight test schemes. In tunnel engineering, cavity geometry is strongly influenced by geological conditions and construction disturbances [
44,
56–
58]. The field measurement data indicate that the typical cavity dimensions behind the lining are distributed as follows: depth 0–30 cm, angle 10°–60°, and length 2–5 m. Based on a geometric similarity ratio of 1:50, the model parameters of Scheme 5 (basic dimensions: 2 cm width × 5 cm length × 5 mm depth) fall within the typical value range mentioned above. This setup effectively simulates the mechanical response characteristics of medium-sized cavities in real engineering scenarios. The design of this scheme is reasonable and demonstrates typical engineering. The study adopted the control variable method to systematically classify the test schemes in three dimensions: 1) cavity depth (Schemes 1, 3, and 5); 2) cavity range (Schemes 2, 5, 6, and 7); 3) number of cavity locations (Schemes 4, 5, and 8). Each test condition underwent hydrostatic pressure tests at five levels (1
D, 1.5
D, 2
D, 2.5
D, and 3
D), resulting in a total of 40 tests to ensure comprehensive and reliable data.
2.5 Test process
A series of controlled leakage tests were performed using an adjustable-head experimental apparatus to systematically investigate seepage behavior through tunnel lining cavities of varying dimensions. Considering the shallow depth of the urban subway tunnel (about 20 m), a geometric similarity ratio (CL = 50) was adopted for the experimental setup. The burial depth from the vault to the soil surface is set as 3.5D (38.5 cm), which corresponds to the actual burial depth of 19.25 m. To achieve the hydraulic head adjustment function, drainage holes are arranged along both sides of the model box at 0.5D spacing, using the tunnel vault as a reference. Flow control plugs are pre-installed in these holes. Water is injected into the box to reach the highest water level (H = 3D). The water level is then gradually reduced to H = 2.5D, 2D, 1.5D, and 1D. Data collection begins once the flow in the drainage holes stabilizes (nearly stops). The model box boundary is set approximately five times the distance from the cavity zone to minimize boundary effects on the seepage field. Modeling equipment was arranged from inside to outside with the lining, primary support, and perimeter rock to simulate the seepage field distribution in the lined cavity under different hydrostatic pressures Fig. 8.
The experimental procedure for investigating cavity defect seepage under varying hydraulic heads consisted of the following key steps in Fig. 9: (a) prepare experimental materials (lining structure, woven fabric, coarse sand), and clean the model device; (b) install the secondary lining structure and set up monitoring instruments (earth pressure gauge, water pressure gauge, strain gauge); (c) wrap 8 layers of woven fabric to simulate the primary support, set up water pressure gauges, and seal waterproof; (d) fill with coarse sand, and bury the earth pressure gauges; (e) fill the top of the model device with water to a maximum head height of 3D (33 cm); (f) connect and debug the monitoring equipment; (g) start the test, and install the seepage water collection device; (h) frain water through the relief holes, and carry out the static head condition test in turn to collect the seepage water, water pressure, soil pressure, and strain data; (i) repeat the same condition three times, and take the average value of the data to minimize the error.
2.6 Monitoring method
As illustrated in Fig. 10, water pressure gauges, earth pressure gauges, and strain gauges are deployed on the inner and outer sides of the tunnel lining structure and in the soil layer. It should be noted that this study focuses on how cavity defects in the vault and shoulder areas affect structural joint leakage. Therefore, the experimental design places more sensors in these critical regions for better observation. By contrast, the arch foot and arch bottom areas are located farther from the cavity-damaged zone, where both stress disturbance and seepage field variations remain relatively minor. Therefore, no monitoring points were installed in these regions. A series of high-precision detectors is used to record the data in the experiment. However, the thin lining of the model might introduce certain errors into the calculation results. To minimize error effects, the three parallel tests are conducted to ensure the accuracy of the test results. For analyzing the lining’s internal force characteristics [
10,
21,
53], classical structural mechanics Eqs. (2) and (3) are used for independent verification. These equations calculated the bending moments and axial forces on the lining, further confirming the reliability of test results.
where M denotes the bending moment, N signifies the axial force, while b, h, and E correspond to the width, thickness, and elastic modulus. In addition, εi and εe indicate the strains on the inner and outer surfaces of the lining, respectively.
Two monitoring sections, X and Y were set up with a focus on the cracks at the tunnel vault. Section X was oriented perpendicular to the tunnel opening, while section Y was arranged along the tunnel axis. The seepage field distribution within the cavity region is monitored in both the horizontal and vertical directions.
3 Seepage field distribution under hydrostatic pressure
3.1 Secondary lining seepage field distribution
Tunnels constructed using the concealed excavation method are often exposed to unfavorable conditions of darkness and high humidity. There are potential deficiencies in construction quality. The waterproofing of structural joints in tunnels is particularly problematic. Long-term leakage can seriously affect the bearing capacity and structural stability of the lining. It accelerates the aging of the tunnel and shortens the overall service life of the tunnel. In addition, during concrete pouring, self-weight and insufficient pumping pressure lead to cavities between the lining and the primary support. After a period of time, leakage and flushing action will gradually carry fine particles or fillers, expanding the cavity area and creating more channels for water flow. Consequently, the structural joints will widen, exacerbating the leakage problem. As a result, a mutually reinforcing vicious cycle is established. The following sections analyze the horizontal and vertical distributions of the seepage field.
Defects in the tunnel vault affect the distribution of the surrounding seepage field. In the test, the vertical arch axis is set as the horizontal monitoring section, where monitoring points are installed at the vault and haunches. The arch axis direction is the vertical monitoring section, and four monitoring points are installed in the center of the cavity area.
To ensure the reliability of the experiment, each set of conditions was tested three times and averaged for analysis Fig. 11. Test results show a continuous ‘M’-shaped distribution of water pressure at both the horizontal and Vertical monitoring sections. The descending curve segment represents the leakage process, where the water head height gradually decreases. In contrast, the ascending segment reflects the primary water pressure buildup during the test.
Therefore, the seepage field distribution in tunnels with lined cavities is more complex than that of a single structural joint leakage. Lining cavity expansion will interact with structural joint leakage. The cavities are classified according to their depth, extent, and spatial location. Figure 12(a) presents Schemes 1, 3, and 5, categorized based on single-cavity depth expansion. Figure 12(b) illustrates Schemes 2, 5, 6, and 7, classified according to cavity range expansion, while Fig. 12(c) groups cases by variations in cavity number and location. As cavity size and hydraulic head height increase, the water pressure exhibits a rising trend with a V-shaped distribution in the horizontal monitoring section. Notably, pressure increments in the vertical monitoring section are spatial dependence: locations farther from the cavity show more pronounced increases, while adjacent areas experience slower pressure growth. To systematically investigate the pressure variation patterns and exclude multi-factor interference, Scheme 5 is selected for analysis.
Figure 13 shows the distribution of water pressure in the horizontal monitoring section and vertical monitoring sections of the lining at different head heights for Scheme 5. To guarantee scientific accuracy, all test data were collected after maintaining a constant water level for 2 min. The results of the tests were as follows.
1) Three monitoring points were set up in the horizontal monitoring section of the tunnel lining, which was located in the left haunch, vault, and right haunch. With the increase in water head height, the water pressure at each monitoring point gradually increases. When the water head height reached 22 cm, the average values of three sets of parallel tests were as follows. The water pressures at the left haunch, the vault, and the right haunch were 1.087, 0.817, and 1.022 kPa, respectively. The water pressure at the vault is the lowest, and the water pressure at the right haunch is lower than that at the left haunch. The data has a V-shaped distribution. This observation indicates that the pressure loss effect reduces the water pressure at the vault region.
2) For the vertical monitoring section, influenced by the leakage effect in the cavity area of the vault, the water pressure decreases gradually from the left side (W6) to the right side (W5, W2), and then increases gradually at W1. At a head height of 2D, the average pressure values showed this spatial distribution: 1.491 (W6), 1.297 (W5), 0.817 (W2), and 1.281 kPa (W1). The cavity in the lining enlarged the cross-sectional area of the leakage pathway at the structural joint. As a result, the pressure within the fluid pathway from W6 to W2 decreased by 41.3%.
3) The hydrostatic pressure at the monitoring point increases gradually with the water head height. Measurement point W2 is situated within the leakage area, and the water pressure exhibits a gradual decline from W6 to W2. As the head height increased from 11 to 33 cm, the decay rate of water pressure increased from 41.4% to 43%, 45.2%, 46.4%, and 48.2%. This phenomenon is mainly attributed to the increase in hydrostatic pressure gradient at higher water pressure. According to Darcy’s Law, higher water velocities result in a more concentrated flow through the cavity. This situation gives rise to a steeper localized pressure gradient, thereby accelerating the pressure decay.
Figure 14 illustrates the relationship between cavity characteristics and water pressure under 3D head height. For the horizontal monitoring section, when the cavity depth increases from 0mm to 5mm, the water pressure in the vault decreases from 1.468 to 1.247 kPa. The average decrease by 15.1%, and the variation pattern of the water pressure at the haunches follows a similar trend. As illustrated in Fig. 14(b), when the angle and length of the cavity are increased, the water pressure at the arch drops from 1.411 to 1.129 kPa, with an average decrease of 20.1%. When cavities occur at the shoulder and their number varies (Fig. 14(c)), the water pressures are 1.297, 1.247, and 1.089 kPa, respectively.
For the vertical monitoring section, with the increase in cavity depth, the water pressure decay rate from point W6 to point W2 increases from 42.6% to 45.8%, and 48.2%. As the cavity extent expands (Fig. 14(b)), the hydraulic pressure attenuation rates for schemes S2, S5, S6, and S7 are 43.8%, 48.2%, 49.8%, and 51.5%, respectively. When the location and number of cavities at the vault vary (Fig. 14(c)), the hydraulic pressure decay rates are 46.9%, 48.2%, and 52.6% respectively. This phenomenon is primarily attributed to the enlargement of the cavity, which causes the leakage channel to expand and consequently forms a low-resistance flow path. The siphon effect directs the water flow to these areas, and the higher speed of water flow further worsens the pressure loss. In addition, the flushing action of the water flow enlarged the cavity area and structural joints, which accelerated the rate of water pressure decay.
As the degree of cavity damage increases, the water pressure in the vault leakage zone will gradually decrease. The integrity of the secondary lining will also be compromised, and the stress distribution will be altered due to the pressure relief at the vault. The decrease of lining water pressure implies an enhancement of the pressure loss capacity at the vault, which exacerbates the damage to the cavity. Ultimately, this will lead to an increase in water leakage and further deterioration of the structure.
3.2 Primary support water pressure
To study the cavity feature’s effect on the water pressure of the primary support, monitoring points W7 and W8 were installed on the primary support corresponding to the secondary lining points W2 and W6. Figure 15 demonstrates that both the primary support external and secondary lining water pressure exhibited linear increases with rising water head. In this study, the Water Pressure Sharing Ratio (η) is proposed to assess the water pressure sharing effect of the Primary support under different head heights and cavity characteristics, as depicted follows:
where Pp is the primary support water pressure, and Ps is the secondary lining water pressure. The range η is from 0 to 1. When it is closer to 1, the primary support shares more water pressure. This means it intercepts more pressure from transmitting to the secondary lining. When the head height is 1D, the hydrostatic pressure of the primary support and secondary lining is at a lower level. At this time, the value is 0.18 at W2–W7 and 0.1 at W6–W8. With a low water head, groundwater supply to the outside of the primary support is limited, and Pp maintains a low water pressure. Additionally, cavity defects in the secondary lining cause minor leakage. This results in low water pressure loss, leading to a small Pp–Ps difference. Therefore, the Water Pressure Sharing Ratio (η) takes a smaller value. When the water head height surpasses 1.5D, the hydrostatic pressure rises remarkably, and simultaneously, the pressure difference between the primary support and the secondary lining escalates rapidly. At a water head height of 3D, the hydrostatic pressure values at W8 and W6 rise to 3.01 and 2.408 kPa, η rising to 0.2. Meanwhile, the hydrostatic pressure values at measurement points W7 and W2 are 1.601 and 1.247 kPa, η rising to 0.31. When cavity defects exist in the secondary lining vault, leakage may induce localized loss of water pressure Pp on its surface. Notably, Pp increases as the water head rises. Under high head, groundwater recharge to the primary support is sufficient. Since the primary support itself allows water to pass through, Pp rises with the head. At this time, Pp and Ps show non-synchronous growth, due to secondary lining leakage, the growth of Ps is significantly lower than Pp. This phenomenon confirms that the pressure-blocking effect of the primary support is weak head, resulting in a low η, whereas the water pressure sharing ratio η increases significantly under high water head.
Figure 16 shows a comparison of water pressure variations between the primary support and the secondary lining for different cavity conditions. At 3D hydraulic head height, the expansion of the lining cavity leads to the expansion of the leakage channels, resulting in an increase in leakage water volume. This phenomenon leads to a decrease in the water pressure difference between the primary support and the secondary lining. When the cavity depth is increased from 0 to 5 mm, the differential pressure at W8–W6 decreases from 0.639 to 0.602 kPa, η reduced from 0.22 to 0.18, a reduction of 18%. In contrast, the differential pressure at W7–W2 decreases even more significantly. It reduces from 0.344 to 0.292 kPa, η reduced from 0.16 to 0.13, a reduction of 18.7%. Leakage in the cavity area spiked, leading to a significant reduction in secondary lining water pressure through rapid loss of water flow. The water-blocking effect of the primary support on water pressure has weakened, and the water pressure difference has diminished as the loss rate of Ps far outpaces the growth rate of Pp. In addition, when the cavity range increases, the water pressure difference in the cavity core (W2–W7) decreases from 0.353 to 0.283, η reduced from 0.16 to 0.11, a reduction of 31%. When the number of cavities changes, the water pressure differential (W2–W7) decreases from 0.324 to 0.256, η reduced from 0.14 to 0.08, a reduction of 42%.
3.3 Leakage analysis
The leakage behavior of tunnel linings is strongly influenced by cavity properties and groundwater level. For each test condition, experiments were repeated three times, and the leakage results were averaged. To better understand the interaction between structural defects and hydraulic conditions and reveal their dynamic coupling mechanism, the cumulative leakage V to leakage rate Q (unit: L/(m·s)) is converted as follows:
where Q is the leakage rate (L/(m·s)), V is the cumulative leakage (L), A is the equivalent area of the crack (m2), and T is the test duration (s).
As shown in Fig. 17, the structural joint leakage rate increases significantly with increasing water head height and cavity characteristics (depth, extent, number, and location). Under the 3D head conditions, the increase in cavity depth from 0 to 5 mm resulted in a 30% increase in leakage rate, from 0.65 to 0.88 L/m·s. The enlargement of the cavity extent led to a 43% increase in the leakage rate, rising from 0.71 to 1.01 L/m·s. Alterations in the location and number of cavities caused an increase in the leakage rate from 0.86 to 1.04 L/m·s, representing a 21% rise.
As illustrated in Fig. 18, the characteristics of leakage variation under different cavity conditions are conducted. The leakage data under different hydraulic heads were linearly fitted. The results show that the linear fitting coefficients increase from 0.013 to 0.014 and 0.0176 as the cavity depth increases. When the cavity range was increased (angle increased from 10° to 30°and length increased to 9 cm), the leakage increment increased from 0.0133 to 0.0186. The formation of multi-positioned cavities formed a complex seepage network when the cavities were varied in terms of location and number. The leakage resistance function was affected and the linear fitting coefficient rose from 0.015 to 0.019. In conclusion, the sensitivity of second lining cavity characteristics to water ingress was ranked as: cavity extent > cavity depth > cavity location and number.
4 Stress field distribution at hydrostatic pressure
4.1 Earth pressure distribution
To research the stress field distribution characteristics of the effect of the lining cavity on the leakage of structural joints, earth pressure gauges were embedded in the cavity area and the vertical area above. Figure 19 shows the relationship between earth pressure and hydraulic head height for Scheme 5 (cavity angle 20°, depth 5 mm, length 5 cm). At the 1D head, the earth pressures at the T2 vault, T3 left haunch, and T4 right haunch around the second lining were 1.94, 2.904, and 2.84 kPa.
As the hydraulic head increases, the pore water pressure of the surrounding rock rises. This leads to the redistribution of the total stress, and consequently, the effective stress decreases. As the hydraulic head height increased from 1D to 3D, the earth pressure at the location of the vault was 1.66, 1.37, 1.08, and 0.79 kPa. A comparable trend was noticed at another location of the vault. This observation implies a consistent pattern in which the stress decreases as the water head increases. At the 1D head, measurement points T7 and T8 are located 11 and 22 cm above the vault. The earth pressures were 4.59 and 3.987 kPa, which were significantly higher than those at the vault (T2). As the depth of burial increases, the self-gravitational stress of the overlying soil increases. This results in higher earth pressures at the vault than at the T7 and T8 gauge points.
The leakage formed a continuous leakage path through the cavity, which led to a significant increase in pore water pressure and a decrease in effective soil stress at the vault. At positions farther away from the cavity, the pressure-reducing effect of the leakage phenomenon was diminished. Consequently, the influence of the pore water pressure on the effective stress was also lessened. As a result, the soil pressure at point T2 is notably lower than that at points T7 and T8.
In the vertical monitoring section (Fig. 20), earth pressure gauges were installed in the vault cavity zone and at positions that were 7.5 and 15 cm away from the cavity. The results indicate that as the water head increases from 1D to 3D, the earth pressure exhibits a decreasing trend. This is attributed to the rise in pore water pressure caused by the elevated water level, which reduces the effective stress of the soil. At lower water levels, the effect of pressure release due to leakage in the T2 cavity area is relatively small. Therefore, the change in soil pressure at each measurement point is relatively smooth.
Figure 21 illustrates the influence of different cavity characteristics on earth pressure. Under 3D head, as the depth of the cavity increases from 0 mm to 5 mm, the earth pressure at the vault decreases from 0.927 to 0.84, and 0.78 kPa, representing a decrease of 15.8%. When the cavity extent was expanded, the vault earth pressure decreased from 0.88 to 0.79, 0.73, and 0.67 kPa, a reduction of 23.8%. When the number and location of cavities were changed, the soil pressure at the vault decreased from 0.82 to 0.78, and 0.66 kPa, a decrease of 19.5%.
The decreasing trend in soil pressure is attributed to the increased connectivity of the leakage paths due to the enlarged cavities. This increases the pore water pressure in the soil at the vault and reduces its effective stress. In contrast, the soil pressure at the vault increases with the expansion of the cavity feature. For example, the soil pressure at the vault on the left side of T3 increased from 1.08 to 1.12, and 1.18 kPa as the depth of the cavity increased. Because of the deepening of the vault cavity, the load originally carried by the vault was redistributed to the haunch, resulting in a slight increase in haunch pressure.
4.2 Lining stress distribution
Secondary lining cavities can aggravate leakage from structural joints as the surrounding rock stress field and seepage field interact with each other. Figure 22 depicts the stress distribution with head height for Scheme 5. The maximum axial force in the left haunch is 1943 N at a head of 1D. The axial force tends to increase with increasing head. When raised to 3D, the axial force reaches 2021, 2103, 2236, and 2364 N. The axial force of the right haunch is slightly lower than that of the left haunch. Meanwhile, as the water head increased from 1D to 3D, the axial force at the vault rose progressively from 1394 to 1503, 1608, 1729, and 1846 N, representing an increase of 32.4%. However, the water pressure differential between these zones progressively decreases with cavity feature expansion. The most significant reduction (20.9%) occurs when cavity number and location are modified. This confirms that the haunch is the main concentration area of axial force. The bending moment analysis reveals that at a water head height of 1D, the maximum bending moment at the vault is −0.85 N·m, and the maximum bending moment at the left haunch is −0.35 N·m. With the increase of water pressure, the bending moment of the vault increased from −0.85 to −0.92, −0.99, −1.04, and −1.12 N·m. The maximum bending moment of the left arch was 0.35 N·m at the left haunch. The bending moment at the haunch increased from −0.35 to −0.31, −0.27, −0.22, and −0.185 N·m. The increase in head caused the transition from internal to external tension at the haunch, while the internal tension at the vault became more noticeable. The increase in water pressure after the lining forms a cavity can seriously affect the safety performance of the support structure.
Figure 23 illustrates the effect of three cavity characteristics on the stress distribution in the secondary lining. The variation of cavity characteristics has a significant effect on the axial force distribution. When the depth of the cavity is increased from 0 to 5 mm, the axial force at the vault increases from 1377 to 1846 N, which is an increase of 25.4%. The axial force at the left haunch increased from 1841 to 2364 N, an increase of 28.4%. When the cavity range is enlarged ( = 10°−30°，L = 9 cm), the axial force at the vault increases from 1511 to 2120 N, representing an increase of 40.3%. The axial force at the left haunch increased from 1974 to 2571 N, an increase of 30.2%. When the number and position of the cavities are changed, the axial force in the vault increases from 1741 to 2236 N, which is an increase of 28.4%. The axial force left haunch increased from 2214.58 to 2731 N, an increase of 23.4%.
Bending moment analyses show that cavity expansion can significantly change the bending moment distribution pattern. In addition, it can exacerbate the risk of stretching and crushing. The bending moment at the vault increases from −0.28 to −1.12 N·m as the depth of the cavity increases, representing an approximately threefold increase. Expansion of the cavity range increases the vault bending moment from −0.564 to −1.12, −1.421, and −1.571 N·m, which is an increase of about 1.8 fold. Changes in the number and location of cavities increase the vault moment from −0.961 to −1.91 N·m, an increase of about 1 fold. At the same time, the vault transitions from inner to outer tension. It indicates a decrease in stiffness and load redistribution due to the cavity. This greatly increases the risk of tensile damage and significantly reduces the safety performance of the supported structure.
5 Discussion
Preliminary test results show that the cavity significantly disrupts the balance of both seepage and stress fields in the lining system. Figure 24 (Scheme 5 example) clearly shows the relationship between the lining water pressure, earth pressure, and structural internal forces evolve together under different head heights (H = 1D–3D). As the water head increases, water pressure at both the vault and arch haunch rises nonlinearly (from 0.479 to 1.247 kPa in the vault hollow area). However, due to the pressure relief effect from the leakage channel expansion in the cavity area, the vault consistently shows lower water pressure than the haunch. Simultaneously, rising pore water pressure reduced effective stress, causing vault soil pressure to drop from 1.94 to 0.79 kPa (a 59.28% decrease). This established a “water pressure increase-earth pressure reduction” linkage mechanism. The hydraulic coupling affects lining mechanical behavior through two pathways. 1) The vault cavity’s pressure relief caused axial force redistribution to the arch waist, increasing its axial force from 1943 to 2364 N (21.7% increase). Simultaneously, the arch roof axial force rose by 32.4% (Fig. 24(a)). 2) The localized concentration of water pressure in the vault will increase the reversal of the vault bending moment. The tendency of the haunch will shift from inner tension (−0.35 N·m) to outer tension (−0.185 N·m). The tensile stress at the inner edge of the vault will also increase (from −0.85 to −1.12 N·m, a rise of 31.8%) (Fig. 24(b)). Cavity expansion will further worsen the positive feedback loop of water–soil–structure interaction. This happens because it both increases permeability and reduces lining stiffness. As a result, the lining at the 3D head will enter an accelerated damage phase.
The impact of liner cavity characteristics on leakage was prioritized as follows: cavity extent > cavity depth > cavity location increase. The three-level control strategy is implemented as follows. In high-risk sections where the hydraulic head exceeds 1.5D, additional wells are installed to conduct regional dewatering. This is combined with hydraulic pressure sensors to dynamically adjust drainage and reduce seepage driving forces. The leakage causes are identified through on-site inspections, and cavities with an angle exceeding 20° are filled and repaired using acrylate grouting. Structural joints are simultaneously reinforced to block water flow. Finally, potential cavity development zones are regularly scanned using Ground Penetrating Radar, and defect evolution trends are continuously monitored with hydraulic pressure data. This stepwise approach helps reduce pressure differences in cavity zones, intercept seepage pathways, and decrease water inflow, thereby providing a practical solution for leakage prevention in operational tunnels and ensuring structural integrity.
6 Conclusions
This study investigated the impact of secondary tunnel lining cavities on structural joint leakage. Using a water head-adjustable experimental apparatus for tunnel lining leakage defect simulation. Seepage tests as well as numerical simulations were conducted on variable water level tunnels with different cavity expansion characteristics. The main conclusions of this study are as follows.
1) The water pressure on the lining generally increases with rising water head, while the vault cavity area consistently maintains the lowest pressure, creating a distinct V-shaped distribution pattern. The water pressure attenuation rate in the cavity extends from 41.4% to 48.2% within a 15 cm distance along the tunnel axis. Notably, cavity expansion compromises the lining’s structural integrity, as the enlarged cavity dimensions widen leakage channels, resulting in water pressure losses up to 20.06%.
2) As the water head rises, primary support water pressure (PP) and secondary lining water pressure (PS) usually increase together. But cavity defects in the secondary lining vaults can cause localized water pressure loss on their surfaces. At high water heads, groundwater fully replenishes the primary support, so PP rises in sync with the water head. However, due to seepage in the secondary lining, PS grows much slower than PP, η increases. This forms a pattern: when the water head is low, the primary support weakly blocks water pressure; when the head is high, its share of water pressure increases significantly. When leakage in cavity areas surges, PS drops sharply due to rapid water loss. The primary support’s water-blocking effect also weakens. In the end, the water pressure difference decreases—because PS loses pressure much faster than PP gains it η decreases.
3) The leakage increases linearly with water pressure. Comparison of the linear fitting laws yields leakage sensitivity for different cavity characteristics: cavity extent > cavity depth > cavity location and number.
4) Different the general water pressure distribution pattern, as the water head increases and cavity defects expand, an unpressurized seepage channel forms continuously in the vault cavity area. This results in a sharp rise in pore water pressure within the vault region. The increased pore water pressure decreases the effective earth stress, leading to a gradual reduction of earth pressure in the cavity area. Notably, this earth pressure change is most significant within the vault cavity area, and the effect intensifies as the cavity area expands.
5) With increasing head height and cavity expansion, the arch bending moment rises substantially, causing higher tensile stresses on the inner surface. Simultaneously, the bending moment at the arch waist transitions from inner tension to outer tension. Both the vault and haunch experience increasing axial forces, with the haunch showing a more pronounced increase. The cavity damage significantly affects structural forces. When the cavity area expands, the vault axial force increases sharply by 40.3% the highest increase among all three cavity types. When the cavity deepens, the vault bending moment triples, showing the most significant bending moment variation.
Limitations and further work: this study systematically examined how rectangular cavities affect leakage behavior in tunnel lining joints. However, it did not investigate other cavity shapes (e.g., circular) and their effects on lining leakage characteristics. Different cavity geometries may significantly alter seepage field distributions and structural stress states due to varying boundary conditions, ultimately affecting seepage rates and development patterns. Therefore, future studies will compare different cavity geometries through experiments to systematically analyze how cavity shapes influence lining leakage behavior. This study primarily examined coarse sand strata with high permeability. However, cavity leakage characteristics may differ significantly in other strata (e.g., clay or silt) commonly encountered in engineering practice. Therefore, future work will focus on systematically optimizing the similarity of physico-mechanical parameters of surrounding rock materials. It will also include a comparative study of leakage behavior in cavities under medium and low permeability stratigraphic conditions to enhance practical engineering applicability.
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