Investigation of Seepage Behavior and Structural Stress Evolution Mechanisms in Karst Tunnels under Water-Rich Conditions during Operation

Investigation of Seepage Behavior and Structural Stress Evolution Mechanisms in Karst Tunnels under Water-Rich Conditions during Operation | 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 Research Article Investigation of Seepage Behavior and Structural Stress Evolution Mechanisms in Karst Tunnels under Water-Rich Conditions during Operation An Pengtao, Zhou Liangdong, Huang zhen, Zhang jiabing, Fu Helin This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7492488/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract Utilizing a self-developed indoor model testing system for karst tunnels, the influence mechanisms of cavity location and water pressure on the water pressure distribution behind the tunnel lining, surrounding rock pressure, and lining stress were investigated. Furthermore, the impact patterns of cavity location and water pressure on the development of plastic zones in the surrounding rock of karst tunnels were determined, and the effect mechanism of the net distance between the cavity and the tunnel on structural stresses was revealed. Key findings indicate that: The presence of a cavity induces a distinctive “maple leaf” pattern in the Mises stress distribution on the tunnel lining section; Under identical water pressure, the Mises stress at a specific monitoring point on the lining is most significantly affected when the cavity is located at the tunnel crown, with minimal impact when it is at the tunnel invert; Under water pressure, the deformation curve of the tunnel support structure exhibits a generally “concave” shape, with the indentation directed towards the cavity center. This phenomenon intensifies with increasing water pressure and higher relative cavity positions; The influence mechanism of water head height on the lining axial force is complex, necessitating particular attention to the bearing capacity of the tunnel invert structure; The effect of water head on surrounding rock pressure follows a distinct pattern, and its analysis must account for the evolution characteristics of the rock mass structure under dynamic pore water pressure conditions. Karst tunnel Tunnel lining High water pressure Model test Response characteristics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Introduction With the ongoing advancement of the Western Development Strategy, numerous expressways and railway tunnels are constructed through complex karst formations (Xiao et al., 2025a ; Zhang et al., 2025 ; Liu et al., 2024a ). Under heavy rainfall conditions, water pressure builds up behind the tunnel lining, potentially causing seepage and leakage incidents, and in severe cases, the high water pressure may breach the tunnel lining, thereby posing a threat to operational safety (Li et al., 2025 ; Zhua et al., 2024 ; Hou et al., 2025 ). The distribution characteristics of water pressure behind the lining of karst tunnels in water-rich environments are a critical factor influencing the cracking and structural failure of the tunnel lining (Sidorov, 2025 ; Xiao et al., 2025b ). He et al. ( 2023 ) utilizing a self-developed mechanical analogue testing apparatus based on the mechanical equivalent principle, investigated the mechanism governing how the distribution of water pressure behind the tunnel lining varies with the stress state of the tunnel structure. Jiang et al. ( 2024 ) employed model tests to study the evolution patterns and failure characteristics of water pressure behind the lining. Teng et al. ( 2024 ) through model experiments, examined the distribution patterns of water pressure behind the tunnel lining along both the axial and radial directions of the tunnel under various drainage conditions, and analyzed the functional mechanism of the tunnel drainage system. Fang et al. ( 2023 ) elucidated the distribution characteristics of water pressure behind the tunnel lining under different rainfall intensities. Wu et al. ( 2021 ) applying the limit upper bound theorem and the Hoek-Brown criterion, derived a formula for calculating the critical thickness of the surrounding rock mass between the tunnel and the cavern. Xu et al. ( 2020 ) grounded in structural stability theory, derived a formula for the critical thickness of the tunnel’s surrounding rock. Xiao et al. ( 2024 ) leveraging the limit equilibrium method and principles of elastic mechanics, investigated the analytical solution for the minimum critical thickness of the surrounding rock. Mahmoudi et al. (2023) explored the influence mechanism of karst cavities on the stress distribution and displacement behavior of the tunnel lining. Xu et al. ( 2022 ) utilizing a self-developed tunnel geomechanical model system, investigated the stress response behavior of both the lining and surrounding rock in operating tunnels. The water pressure behind the tunnel lining is significantly influenced by the operational state of the drainage system (Chen et al., 2025 ; Yu et al., 2025 ). Fang et al. ( 2022 ) based on model tests, uncovered the occurrence mechanism and evolutionary patterns of invert slab distress following heavy rainfall and drainage system blockage. Sun et al. ( 2025 ) proposed a novel underwater tunnel drainage system designed to enhance clogging resistance. Kim et al. ( 2024 ) optimized the design of the tunnel drainage system, thereby reducing the risk of tunnel lining cracking and spalling. Yu et al. ( 2024 ) developed various optimized integrated waterproofing and drainage systems, effectively mitigating high water pressure hazards during the operational phase of tunnels. In summary, scholars have conducted extensive research on the sudden water inrush and gushing disasters in karst tunnels, which has effectively guided the design and construction of karst tunnels under such disasters (Tian et al., 2025 ; Fan et al., 2025 ). Controlling the water pressure in cavities within karst strata is highly challenging. Scholars have primarily relied on theoretical analysis and numerical calculations to study the stress and deformation evolution characteristics of tunnel linings in water-rich environments. However, the accuracy and applicability of these calculations are difficult to guarantee (Dai et al., 2024 ; Liu et al., 2024b ). To address this, this paper, based on an independently constructed indoor model test system, investigates the influence mechanism of cavity location and water pressure on the distribution characteristics of water pressure behind the tunnel lining, clarifies the distribution pattern of surrounding rock pressure, and explores the stress evolution characteristics of the tunnel support structure. On this basis, numerical calculations are employed to analyze the influence of cavity location and water pressure on the Mises stress of the support structure and the distribution of the surrounding rock plastic zone, to study the influence mechanism of cavity scale on the stress of the surrounding strata and structures, and to analyze the evolution law of the surrounding rock plastic zone with respect to the distance between the cavity and the tunnel. The aim is to provide guidance for the design and construction of support structures for karst tunnels in water-rich environments. 1 Model Experiment 1.1 Experimental Setup The primary objective of this study is to reveal the stress evolution mechanisms in karst strata and tunnel structures under water-rich conditions. The model box, constructed entirely of high-strength tempered glass on all sides and the base, maximizes experimental visibility. To prevent leakage at joints, sealing strips are attached using high-strength adhesive and subsequently sealed and fixed with transparent silicone sealant. Based on experimental requirements and prior research, the model box dimensions are 80 cm (length) × 60 cm (width) × 80 cm (height). A circular hole (diameter 20 cm) is drilled on one long side. Adjacent to the model box, a support platform holds a 100-liter plastic bucket. A valve installed at the bucket’s base connects via tubing to a pre-embedded concealed cavity within the model box. Water pressure is controlled by adjusting the water level height in the bucket. To simulate the cavity, most of a PVC pipe wall is removed using a cutting machine, leaving a small structural frame. Additionally, a layer of stainless steel mesh is wrapped around the PVC frame to prevent surrounding soil ingress and blockage during testing. The experimental setup is illustrated in Fig. 1 . 1.2 Model test materials and structural fabrication The material for the model lining is mainly composed of gypsum, borax, and glass fibers. 2.5% glass fibers are incorporated into the gypsum to improve the crack resistance of the lining material, and the borax content is added at 1% of the gypsum, referencing previous studies (Qian et al., 2025 ). The elastic modulus and strength of gypsum specimens under different similar material mix ratios are determined through unconfined compressive strength tests. Based on the experimental results, the mix ratio of the materials for the tunnel support structure is determined. Based on the uniaxial compression test results, the final lining structure model for this model test was prepared using gypsum, water, glass fibers, and borax in a ratio of 1.2:1:0.025:0.012. The basic dimensions of the lining structure are: outer diameter 19.5 cm, inner diameter 16.5 cm, thickness 1.5 cm, and the lining structure length is 60 cm. Clay and fine sand were mixed in a specific ratio to create a composite soil simulating the surrounding rock. For the tests, the simulant material ratio was clay: fine sand = 1.4:1. The lining fabrication process is shown in Fig. 2 . 1.3 Monitoring point layout and acquisition system Variations in structural forces within the lining and surrounding rock-soil-water pressure constituted the key focus of this experimental investigation. Lining strain was measured using BMB120-30AA bondable strain gauges suitable for materials including stone, limestone, and concrete. Pore water pressure during model testing was monitored with custom-designed BWK miniature resistive pore water pressure sensors, featuring a range of 50 kPa and an error margin below 0.5%. The data acquisition system employed was the DH3816N Static Stress-Strain Test and Analysis System manufactured by Jiangsu Donghua Testing Technology Co., Ltd. The acquisition unit was connected to a computer via crossover Ethernet cables, enabling real-time data measurement through the system’s proprietary software. The sensor configuration and data acquisition system are illustrated in Fig. 3 . Eight measuring points were uniformly arranged in a circumferential direction along the tunnel lining cross-section, with strain gauges symmetrically placed inside and outside each measuring point. Considering the position of the hidden karst cavity in this paper, water pressure measuring points were arranged at the four vertices (top, bottom, left, right) of the tunnel. To investigate the distribution law of water pressure along the cross-sections of the tunnel under the influence of the hidden karst cavity, five water pressure monitoring points were arranged along the longitudinal direction of the tunnel. At the same time, to verify the water pressure transmission path, three water pressure monitoring points were arranged at equal intervals between the tunnel and the cavity. To determine the stress of the surrounding soil between the cavity and the tunnel lining, six earth pressure measuring points were arranged around the hidden karst cavity and the tunnel. 1.4 Scheme design and experimental procedure Considering the two influencing factors of the relationship between the cavity and the tunnel position and the cavity water pressure, research on the hidden karst cavity’s effect on the structural stress of the operational tunnel and the stability of the surrounding rock was carried out. The influence mechanism of the tunnel lining and stratum stress under different water pressures when the cavity is located at the top, right side, and bottom of the tunnel was simulated, and the experimental process is shown in Fig. 4 . 2 Evolution of water pressure and earth pressure around tunnels in karst formations under water-rich conditions 2.1 Characteristics of water pressure distribution behind the tunnel lining in karst formations Affected by recharge and discharge conditions, the water pressure in karst strata cavities is in a state of fluctuation. Due to the limitations of the construction technology conditions at the time of construction, the lining structure of the karst strata operational tunnel often suffers from water leakage and seepage diseases, and even the lining structure is hit by local high water pressure, resulting in water inrush, quicksand, or collapse, which threatens the safety of the tunnel structure (Bayat et al., 2024 ). Investigating the characteristics of water pressure distribution behind the lining of karst tunnels is a prerequisite for revealing the stress and deformation of the tunnel lining. The distribution law of water pressure around the tunnel under different water heads is shown in Fig. 5 . Figure 5 shows that when the cavity is located at the top of the tunnel, the pore water pressure at the monitoring points increases non-linearly with the increase in water head height, and the overall growth rate is relatively fixed. When the water head height increases from 90 cm to 100 cm, the water pressure at monitoring points S1, S2, and S3 increases by 6.52%, 6.82%, and 7.95%, respectively. Comparing the four monitoring points (top, bottom, left, and right) on the tunnel lining structure reveals: the water pressure at the top lining point S3 is the highest, and the water pressure at the bottom lining point S10 is the lowest. The reason is that the runoff length between S3 and the cavity is the shortest, and the pressure reduction effect of the surrounding strata is the weakest, while S10 is exactly the opposite; the pore water pressure at the left and right lining points S8 and S9 remains approximately equal and grows at the same rate under different water head heights. The reason is that the two monitoring points have the same absolute height and the same straight-line distance to the cavity, resulting in consistent pressure reduction effects during migration. Among the five longitudinally arranged measurement points, the pore water pressure at the S3 position is the highest, and the water pressure at the S5 and S7 positions is the lowest. When the cavity is located on the right side of the tunnel, the pore water pressure at each monitoring point around the tunnel lining increases with the rise in the water head of the cavity. For the three monitoring points arranged at equal horizontal intervals between the tunnel and the cavity, when the water head height increases from 90 cm to 100 cm, their water pressure increases by 10.32%, 7.69%, and 7.45%, respectively. Comparing the pore water pressure values at the top, bottom, left, and right positions of the tunnel lining cross-section shows that the maximum pressure is at S3; although monitoring points S8 and S9 are equidistant from the cavity, S8 is located at the top of the lining while S9 is at the bottom, so the water pressure at S8 is greater than that at S9; S10 is located behind the lining, and before failure, the lining has some water resistance. Water migrating from the cavity to S10 needs to bypass the lining structure, so the pore water pressure at the S10 monitoring point is the smallest. When the cavity is located at the bottom of the tunnel, the water pressure flowing to each measuring point needs to overcome gravity and soil friction, so the relative height of the measuring point has a greater impact on the water pressure. The three monitoring points arranged between the tunnel and the cavity have lower positions and are closer to the hidden cavity, so under the same water head height, their water pressure values are higher than those of other monitoring points, and the water pressure at the S1 monitoring point is the highest. Looking along the direction of the tunnel, the five monitoring points are on the same horizontal plane, so their hydrostatic pressure should theoretically be equal. However, since the straight-line distance between the S3 monitoring point and the cavity is the shortest, the distances for S4 and S6 monitoring points are next and equal. In addition, it can be seen that except for the three monitoring points between the cavity and the tunnel, the other monitoring points are all 0 under the initial water head of 90 cm. This may be due to the relatively compact compaction of the surrounding rock soil, fewer seepage fissures between strata, and slower seepage velocity. Therefore, before the water head gradient rises to the next level, water has not migrated to other monitoring points, resulting in this phenomenon. 2.2 Characteristics of the surrounding rock pressure distribution in karst strata tunnels The distribution of surrounding rock pressure in karst tunnels is influenced by multiple factors, including the degree of karst development, cavity location, groundwater activity, and rock mass structure, exhibiting significant asymmetry and dynamic characteristics (Zhang et al., 2024 ). Understanding the evolution of surrounding rock pressure under varying water pressure is crucial for the structural safety analysis of tunnels. The variation patterns of surrounding rock pressure under different water heads are presented in Fig. 6 . Figure 6 shows that when the cavity is located at the top of the tunnel, the surrounding rock pressure at various monitoring points in the tunnel shows different changing trends with the increase in water head height. When the water head height is 100cm, the surrounding rock pressures at monitoring points S1, S3, and S5 are 1.8, 8.0, and 14.5 kPa, respectively. When the water head height of the cavity on the right side increases from 90cm to 100cm, except for the S5 monitoring point at the bottom of the tunnel where the surrounding rock pressure decreases, the earth pressure at the remaining points around the tunnel increases. This is because the fluid in the cavity migrates to below the tunnel lining. Due to the light weight of the tunnel lining, the accumulation of fluid below causes the lining structure to float upward. This is also the reason for the increase in surrounding rock pressure at the S4 monitoring point at the top of the tunnel. When the cavity is located at the bottom of the tunnel, the monitoring point S1, which is closest to the cavity, experiences stronger dynamic water pressure, so its surrounding rock pressure is greater than that at the other points under the same water head height. When the water head height is 90cm, the surrounding rock pressure at this point is 3.1 kPa, and it increases to 5.4 kPa when the water head height is 100cm. The earth at the other monitoring points around the tunnel also increases due to varying degrees of compression. The surrounding rock pressure at the monitoring point above the cavity top is the smallest, which is due to the relatively thin overlying soil layer and weaker surrounding rock pressure. When the water head height increases, the surrounding rock pressure at this point increases due to the upward squeezing of the lining structure. 3 Mechanism of lining stress evolution in karst strata tunnels under water-rich conditions 3.1 Evolution of tunnel lining axial force Axial force is a key parameter for the design and safety assessment of tunnel lining structures. Excessive axial force in the lining can lead to insufficient local bearing capacity, potentially causing cracks that penetrate the entire cross-section and thus weakening the overall structural integrity (Luo et al., 2024 ). To investigate the influence mechanism of cavity position and water pressure on the tunnel lining’s axial force, evolution curves of the lining axial force were plotted, as shown in Fig. 7 . Figure 7 shows that under the same water head, when the cavity is at the top, the lining cross-section on the left and right sides are approximately symmetrically distributed. The axial force at the horizontally positioned monitoring points S2 and S3 on the lining is the largest, while the axial force value at the tunnel bottom monitoring point S4 is the smallest. The reason for this is that under the high water pressure at the top of the tunnel, the tunnel structure deforms outward at the horizontal position, and the top moves inward towards the tunnel. Comparing the lining axial force envelope values under different cavity water head heights reveals that when the water head height increases from 90cm to 100cm, the axial force values at tunnel monitoring points S1, S8, S3, S7, and S4 increase by 2.67%, 8.09%, 4.66%, 16.21%, and 13.46%, respectively. Under the action of the top cavity, the axial force at the top of the tunnel lining increases at the slowest rate with the water head height. Under the action of the right-side cavity, the axial force at monitoring point S2 at the top of the tunnel lining is the largest, while the axial force value at the bottom of the lining (S3 position) is smaller. The axial force value at the monitoring point S1 closest to the cavity is smaller than that at S2 and S3, and the axial force at the monitoring point S4 farthest from the cavity is the smallest, which is consistent with the axial force distribution pattern under the action of the top cavity. When the cavity water head height increases from 90cm to 100cm, the axial force values at S2, S5, S1, S8, and S3 increase by 1.91%, 6.62%, 14.06%, 12.39%, and 12.82%, respectively. The internal forces of the tunnel lining structure are significantly affected by the water head height of the bottom cavity. As the water head height of the bottom hidden cavity increases, the axial force experienced by each monitoring point on the lining also increases accordingly. Among these, the maximum axial force occurs at the bottom of the tunnel lining, and this axial force value is much larger than at other locations. The minimum axial force is at the top of the tunnel lining. This is because, under the action of the bottom cavity, the bottom of the lining directly bears the water pressure load and is subject to more intense foundation constraint effects, becoming a region of axial force concentration. In karst and other weak strata, the bearing capacity of the tunnel bottom structure needs to be given special attention. 3.2 Evolution characteristics of tunnel lining bending moment Bending moment is the basis for the cross-sectional design and reinforcement of tunnel lining. The presence of bending moment significantly alters the stress distribution and deformation pattern of the lining, thereby affecting its safety, durability, and waterproofing performance (Dong et al., 2023 ). To analyze the influence mechanism of cavity position and water pressure on the tunnel lining bending moment, evolution curves of the lining bending moment were plotted, as shown in Fig. 8 . Figure 8 shows that under the action of the top cavity, the bending moment values of the tunnel lining are approximately symmetrically distributed. The bending moment values at the top and bottom of the tunnel are negative, with the outer surface of the lining section under compression and the inner side under tension, while the bending moment values at the left and right monitoring points S2, S3 and their surrounding sections are positive. There are four bending moment transition points on the lining cross-section, located near monitoring points S5 to S8. The bending moment at the top monitoring point of the tunnel is the largest, followed by the bottom. When the water head height increases from 90cm to 100cm, the bending moment values at monitoring points S1, S8, S3, S7, and S4 increase by 10.17%, 4.17%, 12.5%, 0, and 10.2%, respectively. Under the action of the right cavity, the bending moment values at the two monitoring points on the right and left sides of the lining are positive. In comparison, the bending moment value at monitoring point S1 is the largest, followed by the position S2 at the top of the tunnel, while the bending moment values at other locations are generally smaller overall. The bending moment values at all monitoring points on the lining increase to varying degrees with the increase in the water head height of the hidden cavity. Under the action of the bottom cavity, the bending moment of the tunnel lining is strictly symmetric on both sides of the vertical axis of the lining section under each water head, and its distribution pattern is similar to that under the action of the top cavity. The bending moment is the largest at monitoring point S1 near the cavity location. 3.3 Tunnel lining safety factor The tunnel lining safety factor is the “threshold” for engineering safety, an important indicator for assessing the stability and reliability of the lining structure, and can evaluate the long-term safety of the tunnel lining (Wang et al., 2023 ). Based on the experimental results, the safety factors of each cross-section of the tunnel lining under different water head heights were calculated, and the results are shown in Fig. 9 . Figure 9 shows that when the cavity is located at the top of the tunnel, the stress state of the vault and arch bottom sections of the tunnel is eccentric tension, and the stress state of the remaining sections is in compression. When the cavity is located on the right side of the tunnel, the left and right haunch sections are in eccentric tension; when the cavity is located at the bottom of the tunnel, the stress state of the sections is relatively complex, the vault section is always in eccentric tension, the arch bottom section is always in eccentric compression, and the right shoulder, right arch foot, and left sidewall sections are in eccentric tension. At the same time, the cases where the safety factor does not meet the requirements are all sections in eccentric tension. In actual engineering, these sections should be closely monitored. The safety factors under different cavity positions show significant differences. In the experiment, when the cavity is above the tunnel, the vault and arch bottom sections should be given special attention. 4 Permeability characteristics of surrounding strata and structural stress evolution mechanism of karst tunnels under water-rich conditions To further study the influence mechanism of the spatial characteristics of confined-type hidden cavities on tunnel structure and surrounding rock deformation, a three-dimensional simplified calculation model of karst tunnels under water-rich conditions was constructed based on numerical simulation. This aims to clarify the influence characteristics of high-pressure cavity location, cavity water pressure, cavity scale, and the net distance between the cavity and the tunnel on the response of the tunnel lining structure and the stability of the surrounding rock. In numerical simulation, the Mohr Coulomb constitutive model is used for the surrounding rock, and the elastic constitutive model is used for the lining structure. Conventional constraints were applied to the lateral boundaries and bottom of the model. Under seepage conditions, these boundaries are designated as impermeable. The top surface of the model is set as a free surface, while the pore water pressure at the interface between the tunnel lining and the surrounding rock is fixed to zero to reflect the drainage conditions during tunnel operation. 4.1 Distribution of Mises stress on the support structure under different cavity positions and water pressures Mises stress, also known as equivalent stress, is an important indicator for assessing the degree of stress a material experiences under complex stress conditions. Assuming the net distance between the cavity and the tunnel is 2 m, the cavity radius is 1 m, and the angle between the line connecting the cavity and the tunnel and the vertical direction is α, the Mises stress at various monitoring points on the tunnel lining under different water pressures when the cavity is in different positions is shown in Fig. 10 . As Fig. 10 shows, the location of the maximum Mises stress varies with the position of the cavity, although the overall distribution pattern remains similar. For a given cavity position, the maximum Mises stress on the tunnel lining under different water pressures exhibits a “maple leaf” shape, with the outline becoming larger as the water pressure increases. Specifically, when the cavity is at the top of the tunnel and the water pressure is 3 MPa, the Mises stress at the top of the support structure reaches 21.0 MPa. This point is closest to the cavity. At the 15° and 345° positions, the Mises stresses are 19.6 MPa and 18.7 MPa, respectively. At the 30° and 330° positions, the stresses are 16.1 MPa and 14.3 MPa, respectively. At the 45° and 315° positions, the stresses are 20.2 MPa and 19.5 MPa, respectively. The distribution of Mises stress on the tunnel support structure is approximately symmetric about the line connecting the cavity and the tunnel’s center. The maximum stress occurs at the monitoring point nearest to the cavity. Moving from the vault towards the sides, the stress values at each monitoring point first decrease, then abruptly increase, before continuing to decrease until reaching the monitoring point farthest from the vault. This distribution pattern is primarily due to the presence of the hidden cavity and its interaction with the tunnel lining. Stress concentration phenomena are significant around the cavity. Due to the irregular shape of the cavity and its complex relative position to the tunnel, when stress is transferred from the cavity to the lining, stress concentration points are formed at the locations on the lining corresponding to the cavity, as well as on the sides and bottom where the cavity connects with the lining. These points, due to differences in the magnitude and direction of the forces they experience, connect to form a “maple leaf” shape. Simultaneously, the uneven deformation of the surrounding rock under the influence of in-situ stress and cavity pressure causes the pressure distribution on the lining to be uneven, further shaping the “maple leaf” stress distribution. The accumulation and flow of groundwater in the cavity generate water pressure acting on the surrounding rock and lining, intensifying the stress concentration and playing a role in promoting and refining the formation of the maple leaf shape, making the stress distribution more complex. 4.2 Influence characteristics of cavity position and water pressure on the distribution of plastic zones in the surrounding rock The distribution of plastic zones is an important parameter for determining the stability of the surrounding rock. Assuming the net distance between the cavity and the tunnel is 2m, the cavity radius is 1m, the distribution pattern of plastic zones in the surrounding rock under different cavity positions and cavity water pressure conditions is shown in Fig. 11 . Figure 11 shows that when the cavity water pressure is 0.5 MPa, plastic zones are only distributed around each cavity location, and are affected by the coupling of tensile failure and shear failure, with a relatively small area of plastic zones, most of the surrounding rock is in an elastic state. When the water pressure increases to 1 MPa, the range of plastic zones around each cavity location increases significantly. At this point, the type of surrounding rock failure around the cavity is tensile failure, while the surrounding rock far from the cavity loses stability due to large-scale shear failure. When the cavity is located at the top of the tunnel, there is a large area of plastic zones in the surrounding rock around the cavity and has extended to the tunnel support structure, indicating that under this water pressure condition, the fissure channel between the tunnel and the cavity has already been connected, and the surrounding rock between the tunnel and the cavity has been severely damaged, and the 2-meter rock layer thickness set in the numerical calculation cannot ensure the safety of the tunnel structure. When the cavity is located on the right side and bottom of the tunnel, there is a trend of connection in the karst channels between the cavity and the tunnel, indicating that the change in water pressure has a significant impact on the stability of the tunnel surrounding rock. Under the same water pressure conditions, when the cavity is located at the top of the tunnel, its plastic zone distribution range is larger, indicating that the cavity at the top of the tunnel has the greatest impact on the stability of the surrounding rock, while the bottom has the least. 4.3 Influence mechanism of cavity scale on the surrounding strata and structural stress of karst tunnels When the cavity is located at the top of the tunnel, the water pressure is 0.5 MPa, and the net distance is 2 m, different cavity radii are set to explore the influence mechanism of cavity scale on the stability of the tunnel surrounding rock, and the plastic zone distribution from the calculation results is extracted as shown in Fig. 12 . Figure 12 shows that when the water pressure inside the cavity is 0.5 MPa, tensile and shear coupling failure occurs around the cavity, leading to the formation of plastic zones. The cavity scale cannot change the form of plastic zone inducement. When the cavity radius is 0.3 m, plastic zones are only distributed in the surrounding rock of the cavity. When the cavity radius increases to 0.5 m, almost all the surrounding rock of the cavity develops plastic zones, and a small part of plastic zones appears in the surrounding rock on the side away from the tunnel. As the cavity scale continues to increase, when the radius is 1 m, larger range plastic zones are generated on the side away from the tunnel due to shear failure, while a small amount of plastic zones are produced on the side of the surrounding rock near the tunnel due to tensile failure. This indicates that the larger the cavity scale, the stronger the failure degree of the surrounding rock around the cavity. Large-scale cavities around the tunnel during operation will bring higher risks, and remedial measures should be taken according to the situation to prevent the collapse of the cavity roof, which will further affect the safety of the tunnel structure. To analyze the influence law of the scale of hidden cavities on the deformation of tunnel support structures, it is assumed that the water pressure in the cavity is 3 MPa, and the net distance L between the cavity and the tunnel is 2 m. Under the same water pressure, the displacement change curves at the most unfavorable positions of the tunnel lining caused by different cavity scales are shown in Fig. 13 . As Fig. 13 indicates, the displacement at the most critical position of the tunnel support structure, under the influence of a hidden karst cavity, consistently increases with the cavity’s size. Fundamentally, this is primarily because a larger cavity results in greater total water pressure being transmitted through the rock mass between the tunnel and the cavity onto the lining, posing a greater risk to the tunnel structure’s stability. Concurrently, an increase in cavity size causes wider and more densely distributed cracks around the tunnel. This, in turn, elevates the seepage pressure and velocity of water within the cavity, promoting the migration of fine-grained fill materials towards the tunnel. In severe cases, this material can even permeate the fissure water channels connecting the cavity and the tunnel, consequently increasing the displacement experienced by the tunnel support structure. 4.4 Influence Characteristics of the Net Distance Between the Cavity and the Tunnel on the Distribution of Plastic Zones in the Surrounding Rock Assuming the cavity is located at the bottom of the tunnel, with a water pressure of 3 MPa and a cavity radius of 1.0 m, the net distances between the cavity and the tunnel were set to 2, 4, 6, and 8 meters, respectively, to investigate the influence mechanism of the distance on the stability of the tunnel surrounding rock. The distributions of the plastic zones from the calculation results are shown in Fig. 14 . Figure 14 shows that when the net distance between the cavity and the tunnel is 2m and 4m, the plastic zone around the cavity has already extended to the position of the tunnel’s secondary lining. A completely connected karst channel has already formed between the cavity and the tunnel due to shear failure of the soil. When the net distance is 6m, the surrounding rock channel is also almost connected, with only a small portion of soil at the bottom of the tunnel not experiencing failure. When the net distance is 8m, the soil within approximately two meters around the tunnel is not subjected to failure. Therefore, it can be considered that when a high water pressure karst cavity with 3MPa exists at the bottom of the tunnel, the soil thickness between the cavity and the tunnel should be at least 8m to effectively prevent the influence on the tunnel support structure. 5 Conclusions Based on an indoor model test system, the influence mechanism of cavity position and water pressure on the water pressure distribution characteristics behind the tunnel lining was studied. The pressure distribution law of the surrounding rock around the tunnel was explored, and the stress evolution characteristics of the tunnel support structure were investigated. On this basis, the support structure and surrounding rock stress characteristics of karst tunnels were analyzed based on numerical calculations, and the specific conclusions are as follows: 1) In the early stage of the test, as the water head height increases, the water pressure increases, and the additional stress on the surrounding rock also increases accordingly. The interaction forces between the surrounding rock particles are redistributed and reach a new equilibrium, and the surrounding rock pressure tends to stabilize. As the water head height continues to increase, the rock mass structure is damaged, the force transmission path changes, and the surrounding rock pressure rises again. 2) Under the action of a cavity, the Mises stress on the tunnel lining section presents a “maple leaf” distribution. An increase in cavity water pressure will lead to an increase in Mises stress on the lining. Under the same water pressure, the influence law of cavity position on the Mises stress at the same monitoring point on the lining is: tunnel top > tunnel right side > tunnel bottom. 3) An increase in water pressure around the cavity near the tunnel will cause an increase in displacement at the corresponding monitoring points on the support structure. Under water pressure, the deformation curve of the tunnel support structure shows an overall “concave” shape distribution, with the notch pointing towards the center of the cavity. Moreover, the higher the water pressure and the higher the relative position of the cavity, the more pronounced this phenomenon becomes. 4) The mechanism of water head height affecting the axial force of the lining is different. The rate of increase in axial force at the bottom of the cavity is higher than that at the top of the tunnel. In weak geological areas such as cavities, the bearing capacity of the tunnel bottom structure needs to be closely monitored in actual engineering. Further research can involve the influence of the rate of change in cavity water pressure on the surrounding rock and structure. Declarations Conflict of interest. The authors declare no competing interests. Author Contribution Peng-Tao An: Writing - original draft, Project administration, Fundingacquisition. Liang-Dong Zhou: Writing - original draft, Data curation. Zhen Huang: Writing – review & editing. Jiabing Zhang: Writing - review & editing, Validation, Formal analysis. Helin Fu: Writing – review & editing, Project administration. Acknowledgements This paper is jointly funded by the Guangxi Youth Science Foundation (2025GXNSFBA069511), the Guangxi Science and Technology Major Program (AA23073018), the 2024 Guangxi “Qingmiao Plan” (First Batch), and the Guangxi Science and Technology Base and Talent Project (AD23026104). 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Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 31 Oct, 2025 Reviews received at journal 27 Oct, 2025 Reviews received at journal 13 Oct, 2025 Reviewers agreed at journal 13 Oct, 2025 Reviewers agreed at journal 12 Oct, 2025 Reviews received at journal 12 Oct, 2025 Reviewers agreed at journal 11 Oct, 2025 Reviewers invited by journal 11 Oct, 2025 Submission checks completed at journal 07 Oct, 2025 First submitted to journal 06 Oct, 2025 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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09:39:12","extension":"xml","order_by":31,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":97097,"visible":true,"origin":"","legend":"","description":"","filename":"963d58c429ec464c98978e737ede196a1structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7492488/v1/0f472a6573742f5c378882f5.xml"},{"id":93121715,"identity":"f18f79ba-32a2-4015-a6bd-49f6ce0e4477","added_by":"auto","created_at":"2025-10-09 09:39:11","extension":"html","order_by":32,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":104189,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7492488/v1/4418638a23024b10a98ce0d6.html"},{"id":93121691,"identity":"8602280b-7db1-438f-bfe1-7c3ea4166d95","added_by":"auto","created_at":"2025-10-09 09:39:10","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":594627,"visible":true,"origin":"","legend":"\u003cp\u003eLaboratory model test of a tunnel in karst strata\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7492488/v1/b3729dfb840362c09b83f656.png"},{"id":93120632,"identity":"c7da41c5-5eeb-4a8b-b0dc-c4cc84456054","added_by":"auto","created_at":"2025-10-09 09:31:10","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":863118,"visible":true,"origin":"","legend":"\u003cp\u003eTunnel lining fabrication\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7492488/v1/9b2a9450580e64c271be55e3.png"},{"id":93121996,"identity":"3663d731-1da0-41b1-8083-3e9212ca552c","added_by":"auto","created_at":"2025-10-09 09:47:10","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":702752,"visible":true,"origin":"","legend":"\u003cp\u003eSensors and data acquisition system\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7492488/v1/96b3063680776fa0b21a110d.png"},{"id":93122000,"identity":"3602222a-b01d-441e-b856-93f80a2cbe9e","added_by":"auto","created_at":"2025-10-09 09:47:10","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1105452,"visible":true,"origin":"","legend":"\u003cp\u003eIndoor experimental procedure\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7492488/v1/d656cf53ab53abc22891a3d9.png"},{"id":93121690,"identity":"a74563a0-6b5a-4c36-aca6-fd11ac611693","added_by":"auto","created_at":"2025-10-09 09:39:10","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":205940,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution pattern of water pressure around the tunnels\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-7492488/v1/6308199e2802fa51da5c7e76.png"},{"id":93120645,"identity":"a3a0a101-a4bf-4c0d-919f-bfba02aa7e30","added_by":"auto","created_at":"2025-10-09 09:31:10","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":199893,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution characteristics of surrounding rock pressure\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-7492488/v1/4f3c1be948f987b0a920213a.png"},{"id":93120639,"identity":"159ebd39-0fb3-4d32-b4f3-d8b93e6cc228","added_by":"auto","created_at":"2025-10-09 09:31:10","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":175469,"visible":true,"origin":"","legend":"\u003cp\u003eEnvelope diagram of axial force for tunnel lining (N)\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-7492488/v1/aa246bdc1255978fb6eabd2d.png"},{"id":93121701,"identity":"e055b252-963b-44a3-bc99-ae6917969640","added_by":"auto","created_at":"2025-10-09 09:39:10","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":128345,"visible":true,"origin":"","legend":"\u003cp\u003eEnvelope diagram of bending moment for tunnel lining (N·m)\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-7492488/v1/be41d641bef32853a0b7f62d.png"},{"id":93121696,"identity":"24644aff-5d59-400f-963a-a76cea32af80","added_by":"auto","created_at":"2025-10-09 09:39:10","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":31873,"visible":true,"origin":"","legend":"\u003cp\u003eSafety factors for different angular position of the tunnel lining\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-7492488/v1/170146354050aaafa2ad3dc3.png"},{"id":93120653,"identity":"d2c7eb79-d083-4233-b33d-4f979871e4d8","added_by":"auto","created_at":"2025-10-09 09:31:11","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":306069,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of Mises stress on the tunnel lining\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-7492488/v1/83e5b13b4e3c13e2086e1625.png"},{"id":93122910,"identity":"fbce38b2-8a09-48a2-ba38-8f8dace4b4dc","added_by":"auto","created_at":"2025-10-09 09:55:10","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":804920,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution pattern of plastic zones in the surrounding rock under different karst cavity positions and water pressures\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-7492488/v1/47e8ec126143f1c1a1f2798a.png"},{"id":93120654,"identity":"9b37d586-9609-4eee-94e1-7cceee4fab99","added_by":"auto","created_at":"2025-10-09 09:31:11","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":455583,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution pattern of plastic zones in the surrounding rock under different karst cavity sizes\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-7492488/v1/f4a7bc5ca65fda8c02006fbd.png"},{"id":93120649,"identity":"18d9bca0-18d5-4f01-9fed-fe86969a04f0","added_by":"auto","created_at":"2025-10-09 09:31:10","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":95040,"visible":true,"origin":"","legend":"\u003cp\u003eDisplacement change curves at the most critical positions of the tunnel lining under different cavity sizes\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-7492488/v1/8e0212926f3f20c3d84eaf07.png"},{"id":93121711,"identity":"7dd48d61-066f-4d5d-b61a-5aab7ba69666","added_by":"auto","created_at":"2025-10-09 09:39:11","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":120606,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution pattern of the plastic zone in the surrounding rock under varying net distances between the cavity and the tunnel\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-7492488/v1/f0ba9a687476f3a6b59f1051.png"},{"id":93123283,"identity":"e7ffaf14-a423-461e-8325-450c64b3e459","added_by":"auto","created_at":"2025-10-09 10:03:14","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":7026785,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7492488/v1/24a6f472-bd77-469e-99bd-285c7f17c095.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Investigation of Seepage Behavior and Structural Stress Evolution Mechanisms in Karst Tunnels under Water-Rich Conditions during Operation","fulltext":[{"header":"Introduction","content":"\u003cp\u003eWith the ongoing advancement of the Western Development Strategy, numerous expressways and railway tunnels are constructed through complex karst formations (Xiao et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2025a\u003c/span\u003e; Zhang et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Liu et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2024a\u003c/span\u003e). Under heavy rainfall conditions, water pressure builds up behind the tunnel lining, potentially causing seepage and leakage incidents, and in severe cases, the high water pressure may breach the tunnel lining, thereby posing a threat to operational safety (Li et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Zhua et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Hou et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2025\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe distribution characteristics of water pressure behind the lining of karst tunnels in water-rich environments are a critical factor influencing the cracking and structural failure of the tunnel lining (Sidorov, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Xiao et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2025b\u003c/span\u003e). He et al. (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) utilizing a self-developed mechanical analogue testing apparatus based on the mechanical equivalent principle, investigated the mechanism governing how the distribution of water pressure behind the tunnel lining varies with the stress state of the tunnel structure. Jiang et al. (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) employed model tests to study the evolution patterns and failure characteristics of water pressure behind the lining. Teng et al. (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) through model experiments, examined the distribution patterns of water pressure behind the tunnel lining along both the axial and radial directions of the tunnel under various drainage conditions, and analyzed the functional mechanism of the tunnel drainage system. Fang et al. (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) elucidated the distribution characteristics of water pressure behind the tunnel lining under different rainfall intensities. Wu et al. (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) applying the limit upper bound theorem and the Hoek-Brown criterion, derived a formula for calculating the critical thickness of the surrounding rock mass between the tunnel and the cavern. Xu et al. (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) grounded in structural stability theory, derived a formula for the critical thickness of the tunnel\u0026rsquo;s surrounding rock. Xiao et al. (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) leveraging the limit equilibrium method and principles of elastic mechanics, investigated the analytical solution for the minimum critical thickness of the surrounding rock. Mahmoudi et al. (2023) explored the influence mechanism of karst cavities on the stress distribution and displacement behavior of the tunnel lining. Xu et al. (\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) utilizing a self-developed tunnel geomechanical model system, investigated the stress response behavior of both the lining and surrounding rock in operating tunnels. The water pressure behind the tunnel lining is significantly influenced by the operational state of the drainage system (Chen et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Yu et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Fang et al. (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) based on model tests, uncovered the occurrence mechanism and evolutionary patterns of invert slab distress following heavy rainfall and drainage system blockage. Sun et al. (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) proposed a novel underwater tunnel drainage system designed to enhance clogging resistance. Kim et al. (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) optimized the design of the tunnel drainage system, thereby reducing the risk of tunnel lining cracking and spalling. Yu et al. (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) developed various optimized integrated waterproofing and drainage systems, effectively mitigating high water pressure hazards during the operational phase of tunnels.\u003c/p\u003e\u003cp\u003eIn summary, scholars have conducted extensive research on the sudden water inrush and gushing disasters in karst tunnels, which has effectively guided the design and construction of karst tunnels under such disasters (Tian et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Fan et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Controlling the water pressure in cavities within karst strata is highly challenging. Scholars have primarily relied on theoretical analysis and numerical calculations to study the stress and deformation evolution characteristics of tunnel linings in water-rich environments. However, the accuracy and applicability of these calculations are difficult to guarantee (Dai et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Liu et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2024b\u003c/span\u003e). To address this, this paper, based on an independently constructed indoor model test system, investigates the influence mechanism of cavity location and water pressure on the distribution characteristics of water pressure behind the tunnel lining, clarifies the distribution pattern of surrounding rock pressure, and explores the stress evolution characteristics of the tunnel support structure. On this basis, numerical calculations are employed to analyze the influence of cavity location and water pressure on the Mises stress of the support structure and the distribution of the surrounding rock plastic zone, to study the influence mechanism of cavity scale on the stress of the surrounding strata and structures, and to analyze the evolution law of the surrounding rock plastic zone with respect to the distance between the cavity and the tunnel. The aim is to provide guidance for the design and construction of support structures for karst tunnels in water-rich environments.\u003c/p\u003e"},{"header":"1 Model Experiment","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e1.1 Experimental Setup\u003c/h2\u003e\u003cp\u003eThe primary objective of this study is to reveal the stress evolution mechanisms in karst strata and tunnel structures under water-rich conditions. The model box, constructed entirely of high-strength tempered glass on all sides and the base, maximizes experimental visibility. To prevent leakage at joints, sealing strips are attached using high-strength adhesive and subsequently sealed and fixed with transparent silicone sealant. Based on experimental requirements and prior research, the model box dimensions are 80 cm (length) \u0026times; 60 cm (width) \u0026times; 80 cm (height). A circular hole (diameter 20 cm) is drilled on one long side. Adjacent to the model box, a support platform holds a 100-liter plastic bucket. A valve installed at the bucket\u0026rsquo;s base connects via tubing to a pre-embedded concealed cavity within the model box. Water pressure is controlled by adjusting the water level height in the bucket. To simulate the cavity, most of a PVC pipe wall is removed using a cutting machine, leaving a small structural frame. Additionally, a layer of stainless steel mesh is wrapped around the PVC frame to prevent surrounding soil ingress and blockage during testing. The experimental setup is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e1.2 Model test materials and structural fabrication\u003c/h2\u003e\u003cp\u003eThe material for the model lining is mainly composed of gypsum, borax, and glass fibers. 2.5% glass fibers are incorporated into the gypsum to improve the crack resistance of the lining material, and the borax content is added at 1% of the gypsum, referencing previous studies (Qian et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). The elastic modulus and strength of gypsum specimens under different similar material mix ratios are determined through unconfined compressive strength tests. Based on the experimental results, the mix ratio of the materials for the tunnel support structure is determined.\u003c/p\u003e\u003cp\u003eBased on the uniaxial compression test results, the final lining structure model for this model test was prepared using gypsum, water, glass fibers, and borax in a ratio of 1.2:1:0.025:0.012. The basic dimensions of the lining structure are: outer diameter 19.5 cm, inner diameter 16.5 cm, thickness 1.5 cm, and the lining structure length is 60 cm. Clay and fine sand were mixed in a specific ratio to create a composite soil simulating the surrounding rock. For the tests, the simulant material ratio was clay: fine sand\u0026thinsp;=\u0026thinsp;1.4:1. The lining fabrication process is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e1.3 Monitoring point layout and acquisition system\u003c/h2\u003e\u003cp\u003eVariations in structural forces within the lining and surrounding rock-soil-water pressure constituted the key focus of this experimental investigation. Lining strain was measured using BMB120-30AA bondable strain gauges suitable for materials including stone, limestone, and concrete. Pore water pressure during model testing was monitored with custom-designed BWK miniature resistive pore water pressure sensors, featuring a range of 50 kPa and an error margin below 0.5%. The data acquisition system employed was the DH3816N Static Stress-Strain Test and Analysis System manufactured by Jiangsu Donghua Testing Technology Co., Ltd. The acquisition unit was connected to a computer via crossover Ethernet cables, enabling real-time data measurement through the system\u0026rsquo;s proprietary software. The sensor configuration and data acquisition system are illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eEight measuring points were uniformly arranged in a circumferential direction along the tunnel lining cross-section, with strain gauges symmetrically placed inside and outside each measuring point. Considering the position of the hidden karst cavity in this paper, water pressure measuring points were arranged at the four vertices (top, bottom, left, right) of the tunnel. To investigate the distribution law of water pressure along the cross-sections of the tunnel under the influence of the hidden karst cavity, five water pressure monitoring points were arranged along the longitudinal direction of the tunnel. At the same time, to verify the water pressure transmission path, three water pressure monitoring points were arranged at equal intervals between the tunnel and the cavity. To determine the stress of the surrounding soil between the cavity and the tunnel lining, six earth pressure measuring points were arranged around the hidden karst cavity and the tunnel.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e1.4 Scheme design and experimental procedure\u003c/h2\u003e\u003cp\u003eConsidering the two influencing factors of the relationship between the cavity and the tunnel position and the cavity water pressure, research on the hidden karst cavity\u0026rsquo;s effect on the structural stress of the operational tunnel and the stability of the surrounding rock was carried out. The influence mechanism of the tunnel lining and stratum stress under different water pressures when the cavity is located at the top, right side, and bottom of the tunnel was simulated, and the experimental process is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"2 Evolution of water pressure and earth pressure around tunnels in karst formations under water-rich conditions","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e2.1 Characteristics of water pressure distribution behind the tunnel lining in karst formations\u003c/h2\u003e\u003cp\u003eAffected by recharge and discharge conditions, the water pressure in karst strata cavities is in a state of fluctuation. Due to the limitations of the construction technology conditions at the time of construction, the lining structure of the karst strata operational tunnel often suffers from water leakage and seepage diseases, and even the lining structure is hit by local high water pressure, resulting in water inrush, quicksand, or collapse, which threatens the safety of the tunnel structure (Bayat et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Investigating the characteristics of water pressure distribution behind the lining of karst tunnels is a prerequisite for revealing the stress and deformation of the tunnel lining. The distribution law of water pressure around the tunnel under different water heads is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows that when the cavity is located at the top of the tunnel, the pore water pressure at the monitoring points increases non-linearly with the increase in water head height, and the overall growth rate is relatively fixed. When the water head height increases from 90 cm to 100 cm, the water pressure at monitoring points S1, S2, and S3 increases by 6.52%, 6.82%, and 7.95%, respectively. Comparing the four monitoring points (top, bottom, left, and right) on the tunnel lining structure reveals: the water pressure at the top lining point S3 is the highest, and the water pressure at the bottom lining point S10 is the lowest. The reason is that the runoff length between S3 and the cavity is the shortest, and the pressure reduction effect of the surrounding strata is the weakest, while S10 is exactly the opposite; the pore water pressure at the left and right lining points S8 and S9 remains approximately equal and grows at the same rate under different water head heights. The reason is that the two monitoring points have the same absolute height and the same straight-line distance to the cavity, resulting in consistent pressure reduction effects during migration. Among the five longitudinally arranged measurement points, the pore water pressure at the S3 position is the highest, and the water pressure at the S5 and S7 positions is the lowest.\u003c/p\u003e\u003cp\u003eWhen the cavity is located on the right side of the tunnel, the pore water pressure at each monitoring point around the tunnel lining increases with the rise in the water head of the cavity. For the three monitoring points arranged at equal horizontal intervals between the tunnel and the cavity, when the water head height increases from 90 cm to 100 cm, their water pressure increases by 10.32%, 7.69%, and 7.45%, respectively. Comparing the pore water pressure values at the top, bottom, left, and right positions of the tunnel lining cross-section shows that the maximum pressure is at S3; although monitoring points S8 and S9 are equidistant from the cavity, S8 is located at the top of the lining while S9 is at the bottom, so the water pressure at S8 is greater than that at S9; S10 is located behind the lining, and before failure, the lining has some water resistance. Water migrating from the cavity to S10 needs to bypass the lining structure, so the pore water pressure at the S10 monitoring point is the smallest.\u003c/p\u003e\u003cp\u003eWhen the cavity is located at the bottom of the tunnel, the water pressure flowing to each measuring point needs to overcome gravity and soil friction, so the relative height of the measuring point has a greater impact on the water pressure. The three monitoring points arranged between the tunnel and the cavity have lower positions and are closer to the hidden cavity, so under the same water head height, their water pressure values are higher than those of other monitoring points, and the water pressure at the S1 monitoring point is the highest. Looking along the direction of the tunnel, the five monitoring points are on the same horizontal plane, so their hydrostatic pressure should theoretically be equal. However, since the straight-line distance between the S3 monitoring point and the cavity is the shortest, the distances for S4 and S6 monitoring points are next and equal. In addition, it can be seen that except for the three monitoring points between the cavity and the tunnel, the other monitoring points are all 0 under the initial water head of 90 cm. This may be due to the relatively compact compaction of the surrounding rock soil, fewer seepage fissures between strata, and slower seepage velocity. Therefore, before the water head gradient rises to the next level, water has not migrated to other monitoring points, resulting in this phenomenon.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e2.2 Characteristics of the surrounding rock pressure distribution in karst strata tunnels\u003c/h2\u003e\u003cp\u003eThe distribution of surrounding rock pressure in karst tunnels is influenced by multiple factors, including the degree of karst development, cavity location, groundwater activity, and rock mass structure, exhibiting significant asymmetry and dynamic characteristics (Zhang et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Understanding the evolution of surrounding rock pressure under varying water pressure is crucial for the structural safety analysis of tunnels. The variation patterns of surrounding rock pressure under different water heads are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows that when the cavity is located at the top of the tunnel, the surrounding rock pressure at various monitoring points in the tunnel shows different changing trends with the increase in water head height. When the water head height is 100cm, the surrounding rock pressures at monitoring points S1, S3, and S5 are 1.8, 8.0, and 14.5 kPa, respectively. When the water head height of the cavity on the right side increases from 90cm to 100cm, except for the S5 monitoring point at the bottom of the tunnel where the surrounding rock pressure decreases, the earth pressure at the remaining points around the tunnel increases. This is because the fluid in the cavity migrates to below the tunnel lining. Due to the light weight of the tunnel lining, the accumulation of fluid below causes the lining structure to float upward. This is also the reason for the increase in surrounding rock pressure at the S4 monitoring point at the top of the tunnel. When the cavity is located at the bottom of the tunnel, the monitoring point S1, which is closest to the cavity, experiences stronger dynamic water pressure, so its surrounding rock pressure is greater than that at the other points under the same water head height. When the water head height is 90cm, the surrounding rock pressure at this point is 3.1 kPa, and it increases to 5.4 kPa when the water head height is 100cm. The earth at the other monitoring points around the tunnel also increases due to varying degrees of compression. The surrounding rock pressure at the monitoring point above the cavity top is the smallest, which is due to the relatively thin overlying soil layer and weaker surrounding rock pressure. When the water head height increases, the surrounding rock pressure at this point increases due to the upward squeezing of the lining structure.\u003c/p\u003e\u003c/div\u003e"},{"header":"3 Mechanism of lining stress evolution in karst strata tunnels under water-rich conditions","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e3.1 Evolution of tunnel lining axial force\u003c/h2\u003e\u003cp\u003eAxial force is a key parameter for the design and safety assessment of tunnel lining structures. Excessive axial force in the lining can lead to insufficient local bearing capacity, potentially causing cracks that penetrate the entire cross-section and thus weakening the overall structural integrity (Luo et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). To investigate the influence mechanism of cavity position and water pressure on the tunnel lining\u0026rsquo;s axial force, evolution curves of the lining axial force were plotted, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows that under the same water head, when the cavity is at the top, the lining cross-section on the left and right sides are approximately symmetrically distributed. The axial force at the horizontally positioned monitoring points S2 and S3 on the lining is the largest, while the axial force value at the tunnel bottom monitoring point S4 is the smallest. The reason for this is that under the high water pressure at the top of the tunnel, the tunnel structure deforms outward at the horizontal position, and the top moves inward towards the tunnel. Comparing the lining axial force envelope values under different cavity water head heights reveals that when the water head height increases from 90cm to 100cm, the axial force values at tunnel monitoring points S1, S8, S3, S7, and S4 increase by 2.67%, 8.09%, 4.66%, 16.21%, and 13.46%, respectively. Under the action of the top cavity, the axial force at the top of the tunnel lining increases at the slowest rate with the water head height. Under the action of the right-side cavity, the axial force at monitoring point S2 at the top of the tunnel lining is the largest, while the axial force value at the bottom of the lining (S3 position) is smaller. The axial force value at the monitoring point S1 closest to the cavity is smaller than that at S2 and S3, and the axial force at the monitoring point S4 farthest from the cavity is the smallest, which is consistent with the axial force distribution pattern under the action of the top cavity. When the cavity water head height increases from 90cm to 100cm, the axial force values at S2, S5, S1, S8, and S3 increase by 1.91%, 6.62%, 14.06%, 12.39%, and 12.82%, respectively. The internal forces of the tunnel lining structure are significantly affected by the water head height of the bottom cavity. As the water head height of the bottom hidden cavity increases, the axial force experienced by each monitoring point on the lining also increases accordingly. Among these, the maximum axial force occurs at the bottom of the tunnel lining, and this axial force value is much larger than at other locations. The minimum axial force is at the top of the tunnel lining. This is because, under the action of the bottom cavity, the bottom of the lining directly bears the water pressure load and is subject to more intense foundation constraint effects, becoming a region of axial force concentration. In karst and other weak strata, the bearing capacity of the tunnel bottom structure needs to be given special attention.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Evolution characteristics of tunnel lining bending moment\u003c/h2\u003e\u003cp\u003eBending moment is the basis for the cross-sectional design and reinforcement of tunnel lining. The presence of bending moment significantly alters the stress distribution and deformation pattern of the lining, thereby affecting its safety, durability, and waterproofing performance (Dong et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). To analyze the influence mechanism of cavity position and water pressure on the tunnel lining bending moment, evolution curves of the lining bending moment were plotted, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e shows that under the action of the top cavity, the bending moment values of the tunnel lining are approximately symmetrically distributed. The bending moment values at the top and bottom of the tunnel are negative, with the outer surface of the lining section under compression and the inner side under tension, while the bending moment values at the left and right monitoring points S2, S3 and their surrounding sections are positive. There are four bending moment transition points on the lining cross-section, located near monitoring points S5 to S8. The bending moment at the top monitoring point of the tunnel is the largest, followed by the bottom. When the water head height increases from 90cm to 100cm, the bending moment values at monitoring points S1, S8, S3, S7, and S4 increase by 10.17%, 4.17%, 12.5%, 0, and 10.2%, respectively. Under the action of the right cavity, the bending moment values at the two monitoring points on the right and left sides of the lining are positive. In comparison, the bending moment value at monitoring point S1 is the largest, followed by the position S2 at the top of the tunnel, while the bending moment values at other locations are generally smaller overall. The bending moment values at all monitoring points on the lining increase to varying degrees with the increase in the water head height of the hidden cavity. Under the action of the bottom cavity, the bending moment of the tunnel lining is strictly symmetric on both sides of the vertical axis of the lining section under each water head, and its distribution pattern is similar to that under the action of the top cavity. The bending moment is the largest at monitoring point S1 near the cavity location.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003e3.3 Tunnel lining safety factor\u003c/h2\u003e\u003cp\u003eThe tunnel lining safety factor is the \u0026ldquo;threshold\u0026rdquo; for engineering safety, an important indicator for assessing the stability and reliability of the lining structure, and can evaluate the long-term safety of the tunnel lining (Wang et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Based on the experimental results, the safety factors of each cross-section of the tunnel lining under different water head heights were calculated, and the results are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e shows that when the cavity is located at the top of the tunnel, the stress state of the vault and arch bottom sections of the tunnel is eccentric tension, and the stress state of the remaining sections is in compression. When the cavity is located on the right side of the tunnel, the left and right haunch sections are in eccentric tension; when the cavity is located at the bottom of the tunnel, the stress state of the sections is relatively complex, the vault section is always in eccentric tension, the arch bottom section is always in eccentric compression, and the right shoulder, right arch foot, and left sidewall sections are in eccentric tension. At the same time, the cases where the safety factor does not meet the requirements are all sections in eccentric tension. In actual engineering, these sections should be closely monitored. The safety factors under different cavity positions show significant differences. In the experiment, when the cavity is above the tunnel, the vault and arch bottom sections should be given special attention.\u003c/p\u003e"},{"header":"4 Permeability characteristics of surrounding strata and structural stress evolution mechanism of karst tunnels under water-rich conditions","content":"\u003cp\u003eTo further study the influence mechanism of the spatial characteristics of confined-type hidden cavities on tunnel structure and surrounding rock deformation, a three-dimensional simplified calculation model of karst tunnels under water-rich conditions was constructed based on numerical simulation. This aims to clarify the influence characteristics of high-pressure cavity location, cavity water pressure, cavity scale, and the net distance between the cavity and the tunnel on the response of the tunnel lining structure and the stability of the surrounding rock. In numerical simulation, the Mohr Coulomb constitutive model is used for the surrounding rock, and the elastic constitutive model is used for the lining structure. Conventional constraints were applied to the lateral boundaries and bottom of the model. Under seepage conditions, these boundaries are designated as impermeable. The top surface of the model is set as a free surface, while the pore water pressure at the interface between the tunnel lining and the surrounding rock is fixed to zero to reflect the drainage conditions during tunnel operation.\u003c/p\u003e\n\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\n\u003ch2\u003e4.1 Distribution of Mises stress on the support structure under different cavity positions and water pressures\u003c/h2\u003e\n\u003cp\u003eMises stress, also known as equivalent stress, is an important indicator for assessing the degree of stress a material experiences under complex stress conditions. Assuming the net distance between the cavity and the tunnel is 2 m, the cavity radius is 1 m, and the angle between the line connecting the cavity and the tunnel and the vertical direction is \u0026alpha;, the Mises stress at various monitoring points on the tunnel lining under different water pressures when the cavity is in different positions is shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eAs Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e shows, the location of the maximum Mises stress varies with the position of the cavity, although the overall distribution pattern remains similar. For a given cavity position, the maximum Mises stress on the tunnel lining under different water pressures exhibits a \u0026ldquo;maple leaf\u0026rdquo; shape, with the outline becoming larger as the water pressure increases. Specifically, when the cavity is at the top of the tunnel and the water pressure is 3 MPa, the Mises stress at the top of the support structure reaches 21.0 MPa. This point is closest to the cavity. At the 15\u0026deg; and 345\u0026deg; positions, the Mises stresses are 19.6 MPa and 18.7 MPa, respectively. At the 30\u0026deg; and 330\u0026deg; positions, the stresses are 16.1 MPa and 14.3 MPa, respectively. At the 45\u0026deg; and 315\u0026deg; positions, the stresses are 20.2 MPa and 19.5 MPa, respectively. The distribution of Mises stress on the tunnel support structure is approximately symmetric about the line connecting the cavity and the tunnel\u0026rsquo;s center. The maximum stress occurs at the monitoring point nearest to the cavity. Moving from the vault towards the sides, the stress values at each monitoring point first decrease, then abruptly increase, before continuing to decrease until reaching the monitoring point farthest from the vault. This distribution pattern is primarily due to the presence of the hidden cavity and its interaction with the tunnel lining. Stress concentration phenomena are significant around the cavity. Due to the irregular shape of the cavity and its complex relative position to the tunnel, when stress is transferred from the cavity to the lining, stress concentration points are formed at the locations on the lining corresponding to the cavity, as well as on the sides and bottom where the cavity connects with the lining. These points, due to differences in the magnitude and direction of the forces they experience, connect to form a \u0026ldquo;maple leaf\u0026rdquo; shape. Simultaneously, the uneven deformation of the surrounding rock under the influence of in-situ stress and cavity pressure causes the pressure distribution on the lining to be uneven, further shaping the \u0026ldquo;maple leaf\u0026rdquo; stress distribution. The accumulation and flow of groundwater in the cavity generate water pressure acting on the surrounding rock and lining, intensifying the stress concentration and playing a role in promoting and refining the formation of the maple leaf shape, making the stress distribution more complex.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.2 Influence characteristics of cavity position and water pressure on the distribution of plastic zones in the surrounding rock\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe distribution of plastic zones is an important parameter for determining the stability of the surrounding rock. Assuming the net distance between the cavity and the tunnel is 2m, the cavity radius is 1m, the distribution pattern of plastic zones in the surrounding rock under different cavity positions and cavity water pressure conditions is shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eFigure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e shows that when the cavity water pressure is 0.5 MPa, plastic zones are only distributed around each cavity location, and are affected by the coupling of tensile failure and shear failure, with a relatively small area of plastic zones, most of the surrounding rock is in an elastic state. When the water pressure increases to 1 MPa, the range of plastic zones around each cavity location increases significantly. At this point, the type of surrounding rock failure around the cavity is tensile failure, while the surrounding rock far from the cavity loses stability due to large-scale shear failure. When the cavity is located at the top of the tunnel, there is a large area of plastic zones in the surrounding rock around the cavity and has extended to the tunnel support structure, indicating that under this water pressure condition, the fissure channel between the tunnel and the cavity has already been connected, and the surrounding rock between the tunnel and the cavity has been severely damaged, and the 2-meter rock layer thickness set in the numerical calculation cannot ensure the safety of the tunnel structure. When the cavity is located on the right side and bottom of the tunnel, there is a trend of connection in the karst channels between the cavity and the tunnel, indicating that the change in water pressure has a significant impact on the stability of the tunnel surrounding rock. Under the same water pressure conditions, when the cavity is located at the top of the tunnel, its plastic zone distribution range is larger, indicating that the cavity at the top of the tunnel has the greatest impact on the stability of the surrounding rock, while the bottom has the least.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\n\u003ch2\u003e4.3 Influence mechanism of cavity scale on the surrounding strata and structural stress of karst tunnels\u003c/h2\u003e\n\u003cp\u003eWhen the cavity is located at the top of the tunnel, the water pressure is 0.5 MPa, and the net distance is 2 m, different cavity radii are set to explore the influence mechanism of cavity scale on the stability of the tunnel surrounding rock, and the plastic zone distribution from the calculation results is extracted as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eFigure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e shows that when the water pressure inside the cavity is 0.5 MPa, tensile and shear coupling failure occurs around the cavity, leading to the formation of plastic zones. The cavity scale cannot change the form of plastic zone inducement. When the cavity radius is 0.3 m, plastic zones are only distributed in the surrounding rock of the cavity. When the cavity radius increases to 0.5 m, almost all the surrounding rock of the cavity develops plastic zones, and a small part of plastic zones appears in the surrounding rock on the side away from the tunnel. As the cavity scale continues to increase, when the radius is 1 m, larger range plastic zones are generated on the side away from the tunnel due to shear failure, while a small amount of plastic zones are produced on the side of the surrounding rock near the tunnel due to tensile failure. This indicates that the larger the cavity scale, the stronger the failure degree of the surrounding rock around the cavity. Large-scale cavities around the tunnel during operation will bring higher risks, and remedial measures should be taken according to the situation to prevent the collapse of the cavity roof, which will further affect the safety of the tunnel structure.\u003c/p\u003e\n\u003cp\u003eTo analyze the influence law of the scale of hidden cavities on the deformation of tunnel support structures, it is assumed that the water pressure in the cavity is 3 MPa, and the net distance L between the cavity and the tunnel is 2 m. Under the same water pressure, the displacement change curves at the most unfavorable positions of the tunnel lining caused by different cavity scales are shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eAs Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003e indicates, the displacement at the most critical position of the tunnel support structure, under the influence of a hidden karst cavity, consistently increases with the cavity\u0026rsquo;s size. Fundamentally, this is primarily because a larger cavity results in greater total water pressure being transmitted through the rock mass between the tunnel and the cavity onto the lining, posing a greater risk to the tunnel structure\u0026rsquo;s stability. Concurrently, an increase in cavity size causes wider and more densely distributed cracks around the tunnel. This, in turn, elevates the seepage pressure and velocity of water within the cavity, promoting the migration of fine-grained fill materials towards the tunnel. In severe cases, this material can even permeate the fissure water channels connecting the cavity and the tunnel, consequently increasing the displacement experienced by the tunnel support structure.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.4 Influence Characteristics of the Net Distance Between the Cavity and the Tunnel on the Distribution of Plastic Zones in the Surrounding Rock\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAssuming the cavity is located at the bottom of the tunnel, with a water pressure of 3 MPa and a cavity radius of 1.0 m, the net distances between the cavity and the tunnel were set to 2, 4, 6, and 8 meters, respectively, to investigate the influence mechanism of the distance on the stability of the tunnel surrounding rock. The distributions of the plastic zones from the calculation results are shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e14\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eFigure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e14\u003c/span\u003e shows that when the net distance between the cavity and the tunnel is 2m and 4m, the plastic zone around the cavity has already extended to the position of the tunnel\u0026rsquo;s secondary lining. A completely connected karst channel has already formed between the cavity and the tunnel due to shear failure of the soil. When the net distance is 6m, the surrounding rock channel is also almost connected, with only a small portion of soil at the bottom of the tunnel not experiencing failure. When the net distance is 8m, the soil within approximately two meters around the tunnel is not subjected to failure. Therefore, it can be considered that when a high water pressure karst cavity with 3MPa exists at the bottom of the tunnel, the soil thickness between the cavity and the tunnel should be at least 8m to effectively prevent the influence on the tunnel support structure.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"5 Conclusions","content":"\u003cp\u003eBased on an indoor model test system, the influence mechanism of cavity position and water pressure on the water pressure distribution characteristics behind the tunnel lining was studied. The pressure distribution law of the surrounding rock around the tunnel was explored, and the stress evolution characteristics of the tunnel support structure were investigated. On this basis, the support structure and surrounding rock stress characteristics of karst tunnels were analyzed based on numerical calculations, and the specific conclusions are as follows:\u003c/p\u003e\u003cp\u003e1) In the early stage of the test, as the water head height increases, the water pressure increases, and the additional stress on the surrounding rock also increases accordingly. The interaction forces between the surrounding rock particles are redistributed and reach a new equilibrium, and the surrounding rock pressure tends to stabilize. As the water head height continues to increase, the rock mass structure is damaged, the force transmission path changes, and the surrounding rock pressure rises again.\u003c/p\u003e\u003cp\u003e2) Under the action of a cavity, the Mises stress on the tunnel lining section presents a \u0026ldquo;maple leaf\u0026rdquo; distribution. An increase in cavity water pressure will lead to an increase in Mises stress on the lining. Under the same water pressure, the influence law of cavity position on the Mises stress at the same monitoring point on the lining is: tunnel top\u0026thinsp;\u0026gt;\u0026thinsp;tunnel right side\u0026thinsp;\u0026gt;\u0026thinsp;tunnel bottom.\u003c/p\u003e\u003cp\u003e3) An increase in water pressure around the cavity near the tunnel will cause an increase in displacement at the corresponding monitoring points on the support structure. Under water pressure, the deformation curve of the tunnel support structure shows an overall \u0026ldquo;concave\u0026rdquo; shape distribution, with the notch pointing towards the center of the cavity. Moreover, the higher the water pressure and the higher the relative position of the cavity, the more pronounced this phenomenon becomes.\u003c/p\u003e\u003cp\u003e4) The mechanism of water head height affecting the axial force of the lining is different. The rate of increase in axial force at the bottom of the cavity is higher than that at the top of the tunnel. In weak geological areas such as cavities, the bearing capacity of the tunnel bottom structure needs to be closely monitored in actual engineering. Further research can involve the influence of the rate of change in cavity water pressure on the surrounding rock and structure.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eConflict of interest.\u003c/strong\u003e\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003ePeng-Tao An: Writing - original draft, Project administration, Fundingacquisition. Liang-Dong Zhou: Writing - original draft, Data curation. Zhen Huang: Writing \u0026ndash; review \u0026amp; editing. Jiabing Zhang: Writing - review \u0026amp; editing, Validation, Formal analysis. Helin Fu: Writing \u0026ndash; review \u0026amp; editing, Project administration.\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e\u003cp\u003eThis paper is jointly funded by the Guangxi Youth Science Foundation (2025GXNSFBA069511), the Guangxi Science and Technology Major Program (AA23073018), the 2024 Guangxi \u0026ldquo;Qingmiao Plan\u0026rdquo; (First Batch), and the Guangxi Science and Technology Base and Talent Project (AD23026104). The authors want to acknowledge these financial assistances.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eSome or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e\n"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eBayat N, Sadeghi E, Nassery HR (2024) Evaluating the characteristics of geological structures in karst groundwater inflow, Nowsud Tunnel[J]. 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Can Geotech J 60(6):834\u0026ndash;848\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"environmental-earth-sciences","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"enge","sideBox":"Learn more about [Environmental Earth Sciences](https://www.springer.com/journal/12665)","snPcode":"12665","submissionUrl":"https://submission.nature.com/new-submission/12665/3","title":"Environmental Earth Sciences","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Karst tunnel, Tunnel lining, High water pressure, Model test, Response characteristics","lastPublishedDoi":"10.21203/rs.3.rs-7492488/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7492488/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eUtilizing a self-developed indoor model testing system for karst tunnels, the influence mechanisms of cavity location and water pressure on the water pressure distribution behind the tunnel lining, surrounding rock pressure, and lining stress were investigated. Furthermore, the impact patterns of cavity location and water pressure on the development of plastic zones in the surrounding rock of karst tunnels were determined, and the effect mechanism of the net distance between the cavity and the tunnel on structural stresses was revealed. Key findings indicate that: The presence of a cavity induces a distinctive \u0026ldquo;maple leaf\u0026rdquo; pattern in the Mises stress distribution on the tunnel lining section; Under identical water pressure, the Mises stress at a specific monitoring point on the lining is most significantly affected when the cavity is located at the tunnel crown, with minimal impact when it is at the tunnel invert; Under water pressure, the deformation curve of the tunnel support structure exhibits a generally \u0026ldquo;concave\u0026rdquo; shape, with the indentation directed towards the cavity center. This phenomenon intensifies with increasing water pressure and higher relative cavity positions; The influence mechanism of water head height on the lining axial force is complex, necessitating particular attention to the bearing capacity of the tunnel invert structure; The effect of water head on surrounding rock pressure follows a distinct pattern, and its analysis must account for the evolution characteristics of the rock mass structure under dynamic pore water pressure conditions.\u003c/p\u003e","manuscriptTitle":"Investigation of Seepage Behavior and Structural Stress Evolution Mechanisms in Karst Tunnels under Water-Rich Conditions during Operation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-09 09:31:05","doi":"10.21203/rs.3.rs-7492488/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-10-31T20:53:16+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-27T13:38:03+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-14T01:04:54+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"88292868312301903656219613255496544915","date":"2025-10-14T00:55:31+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"122046994610036294615515906494402181741","date":"2025-10-12T12:52:19+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-12T10:01:45+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"301080914410148050797415159396490043991","date":"2025-10-11T23:57:45+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-11T22:12:50+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-08T02:09:13+00:00","index":"","fulltext":""},{"type":"submitted","content":"Environmental Earth Sciences","date":"2025-10-07T01:03:35+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"environmental-earth-sciences","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"enge","sideBox":"Learn more about [Environmental Earth Sciences](https://www.springer.com/journal/12665)","snPcode":"12665","submissionUrl":"https://submission.nature.com/new-submission/12665/3","title":"Environmental Earth Sciences","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"eab970ae-5d14-4db6-ae37-7ee6c5e161ef","owner":[],"postedDate":"October 9th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-03-14T14:10:12+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-09 09:31:05","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7492488","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7492488","identity":"rs-7492488","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}