Abstract
Water-induced instability is a critical issue in water-rich and karst tunnel engineering, where seepage evolution and hydraulic loading may significantly affect the mechanical response of the lining structure. To clarify the underlying mechanism, this study establishes a numerical model under controlled idealized conditions and investigates the influence of seepage-related parameters on the hydraulic–structural response of the tunnel system. The distributions of seepage field, water pressure, and lining response are analyzed, and the causes of discrepancy between idealized simulation and practical engineering conditions are further discussed from a mechanistic perspective. The results show that the model can effectively capture the key coupling characteristics of seepage and structural response, while the variation in seepage coefficient significantly affects the internal hydraulic behavior and the resulting lining load pattern. Although the model simplifies actual working conditions, such simplification follows the principle of variable control and highlights the core mechanisms governing the problem. The study provides a theoretical basis for understanding water-related tunnel response and offers useful support for parameter adjustment and engineering assessment under complex groundwater conditions.
1 Introduction
With the continuous densification and in-depth expansion of the railway transportation network in Southwest China, tunnel projects inevitably pass through complex geological areas with intense karst development (; ; ). This region is characterized by diverse karst landforms and complex hydrogeological conditions, where there exists a close hydraulic connection between surface water, underground rivers, and karst caves. Under water-rich karst environments, karst water (or cave water) easily invades the back of tunnel linings through seepage channels such as fractures, faults, and dissolution pipelines. This not only causes issues like surrounding rock instability and cracking damage to support structures but also may induce sudden water and mud inrush disasters, which seriously threaten construction safety, result in huge economic losses, and even cause casualties—becoming a core technical bottleneck restricting tunnel construction in karst areas (; ; ). Therefore, systematically revealing the seepage evolution law of surrounding rock in karst tunnels and clarifying the mechanical and failure mechanisms of lining structures under seepage-stress coupling effects hold significant theoretical and engineering significance for disaster prevention and control (; ; ).
In recent years, scholars have conducted extensive research on the seepage of surrounding rock and the mechanical behavior of linings in karst tunnels (; ; ). carried out a systematic experiment on seepage patterns to explore the influence of surface rainfall recharge and tunnel drainage conditions on lining structure failure. They found that the invert first deforms and cracks under hydrodynamic action, and the cracking sequence of the lining follows the order of invert center, bottom of side wall, arch crown, side wall. constructed a groundwater flow field model before and after tunnel excavation using the Visual MODFLOW numerical simulation software combining geophysical exploration, hydrogeological drilling, and other methods. They quantitatively revealed the disturbance effect of tunnel excavation on the groundwater environment in karst areas, confirming that excavation leads to significant groundwater loss in both rainy and dry seasons. systematically analyzed the influence of factors such as karst cavity water pressure, pipeline filling medium, and pipeline geometric param on tunnel water inrush risk based on the mechanism of multi-physical field coupling. () adopted a combination of numerical simulation and on-site testing to study the surrounding rock deformation around the cave, mechanical behavior of support structures, and plastic zone distribution characteristics of Class-V surrounding rock under the seepage-stress coupling field, clarifying the regulatory law of different grouting circle param on seepage pressure and support deformation. () focused on key factors such as water-filled cave size, filler type, water pressure level, and grouting circle param, analyzing their sensitivity to the external water pressure of the lining and the surrounding rock seepage field. () systematically sorted out the karst geological background, distribution law, and seepage field recharge characteristics relying on the Huayingshan Extra-Long Dual-Tube Highway Tunnel project. () taken the karst tunnels of the Yiwan Railway as the research object, revealed the distribution law of the surrounding rock seepage field and the water pressure reduction effect under special geological conditions, and clarified the mechanical characteristics of the lining structure under the seepage-stress coupling effect. Mo () explored the influence mechanism of param such as water pressure, karst cavity-tunnel spacing on the internal force of the secondary lining through large-scale physical model tests, and proposed prevention and control principles for water and mud inrush disasters. () used a method of mutual verification between model tests and numerical simulations to analyze the influence law of water pressure changes in filled karst caves (located at the side, top, and bottom of the tunnel) on the internal force of the lining. Although the above studies have achieved fruitful results, most of them focus on uniform strata or conventional karst working conditions. A sudden high-pressure karst cavity in this study refers to a local water-filled karst cavity with relatively high confined hydraulic pressure. Different from general karst tunnel seepage problems, it may cause rapid pressure release, concentrated seepage, and abrupt structural damage once the tunnel lining or surrounding rock is weakened. However, for the special scenario of tunnels adjacent to sudden high-pressure karst caves, the characteristics of sudden water pressure increase, dynamic evolution process of fractures, and seepage-damage coupling mechanism are more complex. The relevant seepage evolution characteristics and disaster prevention technologies have not yet formed a unified understanding, which is difficult to meet the actual engineering needs.
This study focuses on the mechanism of seepage-induced hydraulic and structural response in water-rich/karst tunnel conditions. By using a controlled numerical framework, the work aims to identify the dominant influencing factors and clarify the applicability and limitations of the idealized model. The findings are intended to support mechanism interpretation and provide a reference for engineering analysis and model refinement in similar tunnel environments.
2 Project overview
Yesanguan Tunnel is the longest Class-I high-risk tunnel along the entire Yiwan Railway (). It comprises two single-track tunnels (Line I and Line II) with a spacing of 30 m between them. Specifically, Line I has a total length of 13,833 m, while Line II extends 13,802 m, the maximum overburden depth of tunnel reaches 684 m, and it adopts a herringbone longitudinal slope.
The study area is characterized by highly complex geological and hydrogeological conditions, which pose severe challenges to the tunnel construction. Hydrogeologically, the strata crossed by the tunnel feature extensively developed karst networks, containing six distinct karst conduit flows. Among them, the No. 3 underground river exerts the most critical impact on the project. This underground river exhibits a strip-like distribution and crosses obliquely above the tunnel alignment. Notably, the discharge base level of the No. 3 underground river is situated at an elevation of 1050 m, which is approximately 220 m higher than the tunnel elevation. This massive elevation difference generates an immense potential hydrostatic pressure. There is a strong hydraulic connection between the underground river and the tunnel, primarily facilitated by pervasive karst fissures and structural fracture zones. Structurally, the surrounding rock mass is highly fragmented, with a total of 12 faults identified within the study area. Particular attention must be paid to the F18 fault, which directly intersects and structurally connects with the No. 3 underground river. This critical fault acts as a dominant high-pressure water channel, presenting a severe risk of catastrophic water and mud inrush during the tunnel excavation process. The hydraulic conductivity of the F18 fault was preliminarily taken as 1.0 × 10−6 m/s, and the recharge rate of the No. 3 underground river was approximately taken as 2.0 × 103 m3/d. Figure 1a demonstrates the tunnel location map.
FIGURE 1
Among the rock formations traversed by the tunnel, the volcanic clastic rock segment spans 5,074 m (accounting for 37% of the total tunnel length), and the limestone segment measures 8,772 m (representing 36% of the total length). The tunnel passes through karst landscape conduit flows and fault zones, with the No. 3 underground river and F18 fault exerting the most significant impacts on the tunnel environment. The No. 3 underground river obliquely crosses above the tunnel, and its drainage datum plane is, on average, approximately 220 m higher than the tunnel. The F18 fault features well-developed karst, with fillings primarily consisting of silty fine sand and clay; it directly cuts through and connects the No. 3 underground river.
A large limestone karst cave is located obliquely above the tunnel. Specifically, this cave lies approximately 40 m to the left and 100–150 m above the DK124 + 582∼+650 section of Line I. The cave is filled with accumulations such as mud, sand, and rock blocks, and karst fissures are well-developed along the rock bedding planes. The water source of the cave mainly originates from three sources: the water catchment of the Shuidongping dissolved depression, the karst water of the No. 3 underground river, and the water of the Kutao Stream. The underground river, fault zone, and karst cave maintain a strong hydraulic connection with the tunnel, leading to a high risk of severe water and mud inrush and thus extremely high construction risks. The positional relationship among the tunnel, No. 3 underground river, and F18 fault is illustrated in Figures 1b, 2.
FIGURE 2
Because the area traversed by this tunnel contains underground rivers, fault zones, and karst caves, with strong hydraulic connections between these geological features, and on-site surveys is difficult to fully identify the detailed conditions around the tunnel. This results in significant discrepancies between on-site construction conditions and survey findings, such as unclear understanding of the hydraulic connections between the tunnel and the fissures surrounding the karst caves/underground rivers, as well as the water content of the karst caves. These uncertainties, in turn, lead to severe water and mud inrush accidents during the actual tunnel excavation, causing substantial economic losses and casualties. Photos of the accident site are provided in Figure 3.
FIGURE 3
3 Monitoring and analysis of cave water pressure and surface rainfall in the tunnel
To clarify the relationship between rainfall and karst water pressure, the monitored rainfall, underground river flow, and water pressure in the “+602” karst cavity were compared during the same period as shown in Figure 4. The results show that after rainfall events, the underground river flow increased first, followed by a rise in karst cavity water pressure with a certain time lag. The fluctuation trends of these variables were generally consistent. This indicates that rainfall infiltration recharged the karst groundwater system, and the recharge effect was transmitted through underground karst channels and fractures to the cavity water body, resulting in an increase in water pressure. Therefore, the variation of karst cavity water pressure was closely related to rainfall recharge and underground river flow response.
FIGURE 4
To quantitatively determine the hydraulic connection between surface water, the No. 3 underground river, and the “+602” karst cavity, the monitored rainfall, underground river flow, and cave water pressure were compared during the same period. The results show that the response of underground river flow and karst cavity water pressure to rainfall was not instantaneous, but exhibited a certain time lag. Specifically, rainfall events were followed first by an increase in underground river flow and then by a rise in karst cavity water pressure. Moreover, the fluctuation trends of these variables were generally consistent. This lagged response reflects the processes of rainfall recharge, groundwater migration, and pressure transmission in the karst system, and was considered in the analysis of the hydraulic connection. The observed response sequence indicates that rainfall recharge was transmitted first to the underground river and then to the karst cavity through connected karst channels and fractures. Therefore, the hydraulic connection among surface water, the underground river, and the karst cavity was confirmed based on the monitored response process and lag relationship.
The core cause of this phenomenon can be inferred as follows: a highly permeable karst fissure network exists between the “+602” cave and the surrounding surface water (water catchment in the Shuidongping dissolved depression) and the No. 3 underground river. Surface runoff from short-term heavy rainfall is quickly recharged to the underground river through dissolution fissures, then flows into the cave via the connecting channel of the F18 fault. This exceeds the cave’s own drainage capacity in a short time, leading to a sudden rise in water pressure. As the rainfall stops, the water in the cave is slowly discharged to low-potential areas through the fissure network, and the water pressure gradually returns to a dynamic equilibrium state. The above monitoring results clearly indicate that the water pressure of this cave is in dynamic change strongly coupled with regional hydrological conditions, and this feature also provides a key time window basis for water inrush risk early warning during tunnel construction.
4 Analysis of seepage evolution characteristics of tunnel surrounding rock
4.1 Establishment of the numerical model
In this study, the RFPA code was used to establish a plane strain model for simulating seepage-path evolution, surrounding rock damage, and lining failure under seepage–stress coupling near a sudden high-pressure karst cavity. RFPA is a finite element-based numerical tool that considers the mesoscopic heterogeneity of rock materials and simulates progressive failure based on fracture and damage mechanics (). Element failure is governed by the Mohr–Coulomb criterion with a tensile cut-off, and the material properties degrade after damage, allowing fracture initiation, propagation, and coalescence to be captured without predefining crack paths. Since the tunnel length is much greater than its cross-sectional dimension, the plane strain assumption was adopted.
The geometric size of the model was set to 100 m × 100 m (horizontal × vertical), and structured meshing technology was adopted to divide the model into 1,000 × 1,000 uniform elements (element size: 0.1 m × 0.1 m). This mesh density can balance calculation efficiency and the capture accuracy of fissure evolution details—it can not only avoid the distortion of seepage channel simulation caused by overly coarse elements but also prevent the surge of calculation cost due to overly fine elements. The model simplification followed the following principles: 1) The actual irregular karst cave was simplified into a circular water-bearing cavity (the diameter was set to 8 m with reference to the size of the “+602” cave measured in on-site surveys), ignoring the influence of minor geometric shapes on seepage. 2) The tunnel lining was made of C40 reinforced concrete, with a horseshoe-shaped structure. The lining thickness was 1 m, span 10 m, and clear height 12 m, which were consistent with the actual lining design parameters of the Yesanguan Tunnel. 3) An EVA (ethylene-vinyl acetate copolymer) waterproof membrane (permeability coefficient referenced the common engineering value of 1 × 10−20 m/s) was laid on the outer side of the lining to simulate the anti-seepage measures in actual engineering. 4) The surrounding rock fissures were simulated using cavity materials (only transmitting seepage without bearing mechanical loads). Based on the fissure development density (2–3 fissures per meter) measured in the on-site geological survey of the Yesanguan Tunnel, fissures were randomly generated in the surrounding rock area between the lining and the cave to restore the non-uniform distribution characteristics of fissures under real geological conditions.
The model boundary conditions were set according to the actual stress state of the project: horizontal displacement constraints were applied to the left and right boundaries (only vertical deformation was allowed, simulating the stratum constraint of the tunnel’s infinite lateral extension); fixed displacement constraints were applied to the bottom boundary (neither horizontal nor vertical movement was allowed, simulating the constraint effect of the deep stable stratum); the top boundary was a free boundary (the equivalent overlying stratum pressure was applied in subsequent calculations to simplify the influence of stratum self-weight). To systematically monitor the seepage and mechanical responses, 5 characteristic measuring points were arranged in the model: Monitoring points A–D were arranged sequentially along the connection direction between the karst cave and the tunnel lining. Point A was located 2 m away from the cave wall, and Point B was positioned close to the back of the lining. Points C and D were placed between Points A and B at an interval of 1.5 m. These points were used to monitor the real-time variation in pore water pressure at different locations. Monitoring point E was installed at the right arch waist of the lining, where field monitoring identified a key zone of water-pressure concentration, to track the stress evolution of the lining structure. The schematic diagram of the numerical simulation model is shown in Figure 5, and the physical and mechanical parameters (elastic modulus, Poisson’s ratio, permeability coefficient, etc.) of each material in the model were determined based on laboratory rock mechanics tests and engineering experience. The specific parameters are listed in Table 1. Noted that the parameter labeled Homogeneity refers to the homogeneity index of the Weibull statistical distribution. In RFPA, the mechanical properties (e.g., Young’s modulus and strength) of the mesoscopic elements are assumed to follow a Weibull distribution defined by this index. A higher value of implies a more homogeneous material, while a lower value represents a highly heterogeneous rock mass. This statistical assignment of properties is crucial for capturing the non-linear macroscopic behavior of the rock.
FIGURE 5
TABLE 1
| Material type | Elastic modulus (MPa) | Poisson’s ratio | Density (kg/m3) | Permeability coefficient (m/s) | Compressive strength (MPa) | Homogeneity |
|---|---|---|---|---|---|---|
| Surrounding rock | 50,000 | 0.3 | 2,200 | 1 × 10−8 | 60 | 10 |
| Lining | 32,500 | 0.25 | 2,430 | 1 × 10−9 | 40 | 10 |
| Flashing | 10 | 0.3 | 1,300 | 1 × 10−20 | 10 | 100 |
Material parameter.
The variable related to crack development is not treated as an independent material parameter in this study and is therefore not listed in the material parameter table. It is only used in the RFPA, simulation to indicate the local cracking/damage state during the coupled seepage–stress failure process.
To control variables and focus on the core mechanisms of seepage evolution under high-pressure karst cave conditions, several assumptions were made during the establishment of the numerical model. The model adopts an ideal working condition, assuming that the tunnel lining, particularly the secondary lining, is a continuous and intact structure. Consequently, the localized permeability variations caused by unavoidable construction joints in actual engineering practice were not considered in the initial setup. And it should be clarified that ‘cracks’ in this model are not represented by discrete geometric interfaces or joint elements. Instead, they are simulated as zones of fully damaged elements. When an element fails (representing the formation of a crack), its Young’s modulus is reduced to a residual value (close to zero, GPa), and its density is conceptually treated as negligible to reflect the loss of load-bearing capacity. This method, known as the element stiffness degradation technique, effectively mimics the physical behavior of open fractures and avoids the numerical singularity issues associated with deleting elements.
It should be noted that “crack” in the RFPA simulation does not denote a prescribed material constant. Instead, it is an output/state indicator reflecting the occurrence and development of local material damage during the numerical calculation. The key parameters in the model, including elastic modulus, Poisson’s ratio, compressive strength, and permeability coefficient, were mainly determined based on laboratory rock mechanics tests and engineering experience. The surrounding rock permeability was considered through different simulation cases. The fracture properties and damage evolution were not assigned through separate calibration, but were controlled by the built-in RFPA failure criterion and elastic-brittle-plastic damage constitutive law.
In the RFPA-based seepage–stress coupling analysis, the surrounding rock was treated as a heterogeneous elastic-brittle porous medium. Before damage, each mesoscopic element followed a linear elastic constitutive law. After damage initiation, the mechanical properties were degraded by a damage variable D, and the elastic modulus was updated as E=(1−D)E0, where E0 is the initial elastic modulus. The stress state of the rock mass was evaluated using the effective stress concept, in which pore water pressure affects the mechanical response of the medium. Seepage in the rock mass was assumed to obey Darcy’s law, and the hydraulic conductivity of each element was allowed to evolve with damage. Specifically, the permeability was updated from the initial value k0 to a damage-dependent value k = k0exp (βD), where β is the permeability enhancement coefficient. Therefore, once tensile failure or shear failure occurred according to the tensile cut-off and Mohr–Coulomb criterion, the local stiffness was reduced and the permeability was increased simultaneously, enabling the progressive evolution of crack propagation, hydraulic pathway development, and mechanical deterioration to be captured in a unified framework. The coupled calculation was performed in a stepwise iterative manner for each water-pressure loading increment. In each step, the seepage field and stress field were alternately updated until convergence was achieved. The iteration at the current loading step was considered converged when the relative changes in the principal field variables (including nodal displacement and pore pressure) between two successive iterations were less than 1 × 10−5, and no further newly damaged elements appeared in the model. If these conditions were not satisfied, the element properties were updated according to the current damage state and the next iteration was continued. This procedure ensured numerical stability and improved the reproducibility of the seepage–damage evolution process.
4.2 Simulation cases
To systematically reveal the coupled influence mechanism of surrounding rock permeability and water pressure loading rate on the damage and cracking of tunnel surrounding rock and the failure mode of lining under sudden high water pressure conditions, and clarify the primary and secondary relationships of key influencing factors, this study designed simulation experiments focusing on two core variables: surrounding rock permeability coefficient and water pressure loading rate. Among them, the surrounding rock permeability coefficient directly determines the seepage efficiency of cave water to the lining, while the water pressure loading rate corresponds to the dynamic process of sudden increase in cave water pressure after heavy rainfall on-site, both are key parameters regulating the seepage-stress coupling effect.
Referring to the measured range of surrounding rock permeability coefficient (1.0 × 10
−9∼1.0 × 10
−7m/s) and the peak cave water pressure (0.23 MPa) from on-site surveys of the Yesanguan Tunnel, three groups of variable levels were set respectively.
Water pressure loading rate: 0.1MPa/Step (low-speed loading, simulating slow water pressure rise after light rain), 0.2MPa/Step (medium-speed loading, matching moderate rain conditions), 0.3MPa/Step (high-speed loading, corresponding to sudden water pressure rise caused by short-term heavy rainfall).
Surrounding rock permeability coefficient: 1.0 × 10−7 m/s (high permeability, simulating surrounding rock with dense fissures), 1.0 × 10−8 m/s (medium permeability, consistent with the average level of the tunnel’s actual surrounding rock), 1.0 × 10−9 m/s (low permeability, representing surrounding rock after grouting reinforcement).
To reduce the experimental workload while fully covering all combinations of two factors and three levels, an L9 (32) orthogonal experimental design (i.e., 9 orthogonal schemes under 3 factor levels) was adopted, and a total of 9 simulation experiments were constructed. The influence weights of the two variables on the surrounding rock-lining failure can be quantified through range analysis or variance analysis. The specific experimental scheme is shown in Table 2.
TABLE 2
| Case ID | Permeability coefficient of surrounding rock (m/s) | Water pressure loading rate (MPa/Step) |
|---|---|---|
| 1 | 1.0 × 10−7 | 0.1 |
| 2 | 0.2 | |
| 3 | 0.3 | |
| 4 | 1.0 × 10−8 | 0.1 |
| 5 | 0.2 | |
| 6 | 0.3 | |
| 7 | 1.0 × 10−9 | 0.1 |
| 8 | 0.2 | |
| 9 | 0.3 |
Simulation group experimental plan.
4.3 Analysis of simulation results of seepage evolution characteristics of surrounding rock
Experiment Group 5 was selected as a representative case to analyze the acoustic emission (AE) characteristics during the failure process. In this group, the surrounding rock permeability coefficient was 1.0 × 10
−8m/s, corresponding to the average permeability of the actual tunnel surrounding rock, and the cave water pressure loading rate was 0.2 MPa/step, representing a medium-speed water pressure increase induced by moderate rainfall. AE is a key monitoring index for characterizing the initiation and propagation of rock micro-cracks, which can directly reflect the spatiotemporal law of surrounding rock damage evolution, the corresponding AE distribution is shown in
Figure 6. In the AE map of
Figure 6(following the default AE signal classification of the RFPA software), red signals indicate tensile failure (corresponding to tensile damage of the rock), while white signals represent compressive failure (corresponding to shear or crushing damage of the rock). The failure evolution process of this group can be divided into four stages.
Initial compaction stage (water pressure <0.1 MPa): AE signals are sparsely distributed near the cave wall, with only a few white compressive signals appearing. This indicates that the surrounding rock at the cave bottom undergoes local compaction under hydrostatic pressure, with no obvious damage.
Micro-crack initiation stage (water pressure loaded to ∼0.15 MPa): Red tensile signals start to appear at the edge of the cave bottom, marking the generation of the first damage element (i.e., micro-crack). This is because the local stress concentration at the cave wall exceeds the tensile strength of the surrounding rock.
Crack propagation and connection stage (water pressure loaded to 0.2 MPa): Tensile AE signals extend toward the lining along existing cracks, while white compressive signals increase in crack intersection areas, corresponding to the expansion of existing cracks and the initiation of new cracks. Eventually, scattered cracks gradually connect, forming a preferential seepage channel that runs directly from the cave bottom to the back of the lining.
Lining failure stage: Cave water rapidly seeps to the lining surface through the preferential seepage channel. Dense red tensile signals appear at the arch waist of the lining, indicating that this area undergoes tensile failure due to concentrated water pressure, consistent with the typical cracking location of the lining observed on-site at the Yesanguan Tunnel.
FIGURE 6
The stress variation laws of the secondary lining at Point E (a key stress-bearing area at the arch waist) under different working conditions are shown in Figures 7, 8. Figure 7 fixes the water pressure loading rate at 0.1 MPa/Step to focus on the influence of the surrounding rock permeability coefficient, while Figure 8 fixes the surrounding rock permeability coefficient at 1.0 × 10−8 m/s to analyze the effect of the cave water pressure loading rate.
FIGURE 7
FIGURE 8
Figure 7 presents the stress evolution curves of Point E in the secondary lining under different surrounding rock permeability coefficients (with a fixed water pressure loading rate of 0.1 MPa/Step). Analysis shows that the stress at Point E is significantly regulated by the surrounding rock permeability coefficient. As the permeability coefficient increases, both the growth amplitude and rate of the secondary lining stress rise, this is because a larger permeability coefficient improves the efficiency of cave water pressure transmission to the lining through surrounding rock fissures, leading to faster accumulation of water pressure loads on the lining.
The stress variation under all permeability coefficient conditions follows the law of gradual rise, peak value, rapid drop. The stress rise phase corresponds to the seepage and enrichment of cave water toward the lining; the peak point represents the critical state where the lining material reaches its ultimate bearing capacity; the sudden drop in stress after the peak is caused by stress release due to tensile/shear failure and local structural instability of the lining. Specifically, when the surrounding rock permeability coefficients are 1.0 × 10−7 m/s (high permeability), 1.0 × 10−8 m/s (medium permeability), and 1.0 × 10−9 m/s (low permeability), the stress peaks at Point E of the secondary lining reach 13.16 MPa, 10.87 MPa, and 9.21 MPa, respectively. The peak stress under the high-permeability condition exceeds the axial tensile strength of C40 concrete (approximately 1.71 MPa), indicating that the lining has undergone tensile failure at this point.
Figure 8 shows the stress variation curves of Point E in the secondary lining under different cave water pressure loading rates (with a fixed surrounding rock permeability coefficient of 1.0 × 10−8 m/s). The results indicate that the water pressure loading rate has a more significant impact on the secondary lining stress: as the loading rate increases, the growth slope of the secondary lining stress increases significantly, and the peak stress also rises notably, this is because a faster water pressure loading rate corresponds to a more intense dynamic water pressure impact, and the lining structure cannot deform sufficiently to unload, resulting in faster stress concentration.
The stress evolution under this condition also follows the rise, peak, drop characteristic: when the loading rates are 0.2 MPa/Step and 0.3 MPa/Step, the stress peaks at Point E of the secondary lining reach 15.81 MPa and 18.21 MPa, respectively. These values not only exceed the axial tensile strength of C40 concrete but also approach its axial compressive strength (19.1 MPa), indicating that the lining is prone to tension-crushing composite failure under high loading rates. In contrast, the stress peak under the 0.1 MPa/Step loading rate is significantly lower, suggesting that slow water pressure loading helps reduce the risk of stress concentration in the lining.
Combining the results of Figures 7, 8, it can be concluded that the cave water pressure loading rate has a greater impact on the stress at Point E of the secondary lining than the surrounding rock permeability coefficient: the stress peak under high loading rate (18.21 MPa) is much higher than that under high permeability coefficient (13.16 MPa), and the stress growth rate of the former is steeper. This conclusion indicates that in tunnel projects adjacent to sudden high-pressure karst caves, controlling the sudden rise rate of cave water pressure (e.g., weakening the hydraulic connection between the underground river and the cave through pre-drainage) is more effective in alleviating the stress concentration risk of the lining than simply reducing the surrounding rock permeability coefficient (e.g., local grouting).
The water pressure variation characteristics at Point B (a key seepage monitoring point at the lining-surrounding rock interface) behind the secondary lining are shown in Figures 9, 10. Figure 9 fixes the cave water pressure loading rate at 0.1 MPa/Step to focus on the regulatory effect of the surrounding rock permeability coefficient, while Figure 10 fixes the surrounding rock permeability coefficient at 1.0 × 10−8 m/s to analyze the influence of the water pressure loading rate.
FIGURE 9
FIGURE 10
It can be seen from Figure 9 that the water pressure behind the secondary lining is significantly affected by the surrounding rock permeability coefficient: before the lining fails, the water pressure increases approximately linearly with the loading step, this is because the seepage channel is in an expanding but not fully connected state at this stage, and cave water slowly seeps toward the lining through fissures, so the water pressure accumulates synchronously with the rise of cave water pressure. Among them, the larger the surrounding rock permeability coefficient, the faster the water pressure grows: a higher permeability coefficient corresponds to a more developed karst fissure network, which improves the seepage efficiency of cave water toward the lining.
Notably, the surrounding rock permeability coefficient is negatively correlated with the water pressure at lining failure: when the permeability coefficients are 1.0 × 10−7 m/s (high permeability), 1.0 × 10−8 m/s (medium permeability), and 1.0 × 10−9 m/s (low permeability), the water pressure at lining failure is 1.20 MPa, 1.33 MPa, and 1.42 MPa, respectively. The results indicate that, for the investigated parameter setting, lining failure occurred at a peak water pressure of about 1.20 MPa, 1.33 MPa, and 1.42 MPa, which should be interpreted as a case-specific result rather than a universal safety threshold. This is because denser fissures in high-permeability surrounding rock allow cave water to form connected seepage channels more easily, so the lining load reaches its ultimate bearing capacity earlier, resulting in lower water pressure at failure. After the lining fails, the water pressure decreases rapidly: the cracking of the lining forms a pressure relief channel, and the interface water pressure is quickly released as water leaks.
Results in Figure 10 show that the water pressure behind the secondary lining is also sensitive to the cave water pressure loading rate: before the lining fails, the water pressure increases approximately linearly with the loading step, and the larger the loading rate, the steeper the growth slope, this is because a faster loading rate corresponds to more intense dynamic water pressure impact; cave water rushes into the lining interface in a short time, and the water pressure cannot dissipate through surrounding rock fissures, thus accelerating accumulation.
Consistent with the influence of permeability coefficient, the water pressure loading rate is also negatively correlated with the peak water pressure at lining failure: when the loading rate is 0.3 MPa/Step, the water pressure at lining failure is only 0.98 MPa, much lower than the values under 0.2 MPa/Step (1.21 MPa) and 0.1 MPa/Step (1.35 MPa) conditions. This is because the rapid rise of water pressure under high loading rates prevents the lining from adjusting stress through deformation, leading to earlier failure, hence a lower peak water pressure at failure. After the lining fails, the interface water pressure also drops rapidly due to the formation of the pressure relief channel.
Combining the results of Figures 9, 10, it can be concluded that the cave water pressure loading rate has a greater impact on the water pressure at Point B behind the secondary lining than the surrounding rock permeability coefficient: water pressure grows faster under high loading rates, and the peak water pressure at lining failure is lower. This conclusion further confirms that the sudden rise of cave water pressure caused by heavy rainfall (corresponding to high loading rates) is the main inducement for lining crushing, which aligns with the on-site monitoring results of the Yesanguan Tunnel (cave water pressure surged to 0.23 MPa within 10 h after heavy rainfall). It should be noted that the above conclusion is based on a comparative analysis of the simulation cases in this study, rather than on a formal sensitivity analysis. Within the selected parameter range, the water pressure loading rate showed a more obvious effect on lining stress, crack propagation, and failure characteristics than the surrounding rock permeability coefficient.
Combined with the aforementioned research, the complete lining failure process can be summarized as follows: Heavy rainfall causes surface water to recharge the No. 3 underground river via the Shuidongping dissolved depression and Kutao Stream; the strong hydraulic connection between the underground river, F18 fault, and the “+602” cave allows underground river water to flow into the cave quickly along the fault-fissure network, triggering a sudden rise in cave water pressure. Subsequently, high-pressure water reaches the lining interface through existing or newly expanded seepage channels; when the water pressure exceeds the lining’s ultimate bearing capacity, the lining fails, the larger the rainfall, the faster the cave water pressure loading rate, and the earlier the lining failure. Based on this, cutting off the hydraulic connection between the underground river and the cave (e.g., grouting to seal the F18 fault) and blocking the seepage channel between the cave and the lining (e.g., adding a thickened grouting circle) are key technical measures to prevent and control such water and mud inrush disasters.
4.4 Comparative analysis of simulation results and monitoring results
To evaluate the actual influence of dynamic karst water-pressure variation on the tunnel lining and to verify the engineering applicability of the numerical simulation results, a field monitoring system was installed at section DK124 + 602 of the Yesanguan Tunnel.
Water pressure behind the secondary lining was monitored using piezometers (range: 0–2 MPa; accuracy: ±0.01 MPa).
Internal forces in the secondary lining were synchronously measured using reinforcing bar stress gauges (range: 0–300 MPa; accuracy: ±1 MPa).
Monitoring points covered typical stress-bearing parts such as the invert, arch crown, arch waist, arch foot, and side wall, the specific layout is shown in Figures 11, 12.
FIGURE 11
FIGURE 12
The stress distribution of the secondary lining at the DK124 + 602 monitoring section is shown in
Figure 13, and the stress evolution characteristics of each part exhibit significant spatial differences.
Invert area: The stress rose rapidly over time, reaching a peak of approximately 36 MPa. This is because the invert is the vertical stress core of the tunnel structure; after cave water pressure is transmitted to the lining bottom through seepage channels, the invert bears concentrated vertical water pressure loads, resulting in the most significant stress growth.
Left/right arch waist, right arch foot: The stress first increased gradually and then stabilized, finally remaining in the range of 7.8–13 MPa. These parts are located in the lateral stress area of the tunnel structure; as seepage water pressure is transmitted and structural deformation is adjusted, the load gradually reaches a state of force balance.
Left arch foot: The stress remained basically stable, fluctuating around 6.5 MPa. This part is strongly constrained by the surrounding stable rock mass, so the load transmission effect of cave water pressure is weak, resulting in insignificant stress changes.
Left/right side wall, vault: The stress gradually decreased and finally stabilized at −6.5 MPa (the negative sign indicates tensile stress). These parts bulged outward under water pressure, so the lining structure changed from a compressed state to a tensioned state. The occurrence of tensile stress also confirms the conclusion from numerical simulations that the vault and side walls are prone to tensile failure.
FIGURE 13
The water pressure changes behind the secondary lining at the DK124 + 602 monitoring section are shown in
Figure 14, and their distribution law is highly correlated with the stress characteristics.
Invert area: The water pressure grew the fastest, reaching a peak of approximately 1.62 MPa. The invert is located at the bottom of the tunnel, a natural convergence area for seepage water, so water pressure tends to accumulate rapidly here.
Left/right arch waist, right side wall, vault: The water pressure first increased gradually and then stabilized, finally remaining in the range of 0.44–1.1 MPa. The seepage channels in these parts gradually became saturated as water pressure rose, and water supply and leakage reached dynamic balance.
Left side wall: The water pressure remained at 0 MPa throughout. The lining at this part has good tightness with the surrounding rock, and no effective seepage channel was formed, so no water pressure accumulated.
Left/right arch foot: The water pressure first increased slightly and then gradually decreased to 0 MPa. The lining at the arch foot cracked locally under stress concentration, forming a pressure relief channel; the water pressure gradually dissipated after seepage water leaked out.
FIGURE 14
To verify the reliability of the elastic damage seepage model established earlier, the most representative data were selected for comparative analysis: the surrounding rock permeability coefficient of 1.0 × 10−8 m/s (matching the medium permeability level of the tunnel’s actual surrounding rock, which is the most representative in engineering practice) and the right arch waist of the secondary lining (a key area with concentrated stress and water pressure, as shown in both on-site monitoring and numerical simulation). The specific comparison results are presented in Figure 15 (stress comparison) and Figure 16 (water pressure comparison). The right arch waist was selected for comparison because the monitoring data at this location were relatively complete and continuous, and the structural response there was more evident under the studied conditions. The obtained agreement between monitoring and simulation provides preliminary support for the model, although further validation at key locations such as the vault and invert is still needed.
FIGURE 15
FIGURE 16
As shown in the stress comparison in Figure 15: under three water pressure loading rates (0.1 MPa/Step, 0.2 MPa/Step, 0.3 MPa/Step), the stresses at the right arch waist of the secondary lining obtained by numerical simulation are 11.21 MPa, 15.81 MPa, and 18.21 MPa, respectively, while the stable on-site monitoring stress is 13 MPa. The water pressure comparison in Figure 16 shows that under the same loading rates, the simulated water pressures at the right arch waist are 0.98 MPa, 1.18 MPa, and 1.33 MPa, respectively, whereas the stable on-site monitoring water pressure is only 1.11 MPa.
Both sets of data comparisons indicate that the numerical simulation results are slightly larger than the on-site monitoring results—this difference makes the simulation results conservative and safety-oriented. In tunnel engineering design, conservative simulation data can provide a conservative basis for the strength design of lining structures and disaster risk assessment, avoiding insufficient safety reserves caused by model simplification.
A further analysis of the discrepancy indicates that it may arise from multiple factors rather than a single cause. One important factor is the seepage behavior of the lining in actual engineering. In the numerical model, the lining is assumed to be continuous and intact, with a completely watertight waterproof membrane and no leakage through construction joints or other seams. In contrast, in field construction, the secondary lining may contain construction joints, expansion joints, and local defects formed during pouring, while the waterproof membrane may develop local leakage paths due to installation damage. These features can lead to partial dissipation of seepage water behind the lining, thereby reducing the monitored water pressure and stress values. In addition, the discrepancy may also be related to the heterogeneity of the surrounding rock, possible local weakness or deterioration of the grouting ring, and simplifications adopted in the numerical model, such as idealized boundary conditions and assumed material parameters. Therefore, the difference between the monitored and simulated results should be understood as the combined effect of field complexity and model idealization, rather than being attributed solely to a single identified factor.
The simulated peak water pressures are higher than the field monitoring values. This suggests that the model can capture the overall action of high-pressure karst water on the lining, although it still overestimates the local peak pressure under actual field conditions. This difference may be associated not only with the pressure-relief effect of construction joints and other local seepage paths, but also with surrounding rock heterogeneity, possible non-uniformity or local failure of the grouting ring, and the simplifications introduced in the numerical model. Nevertheless, the comparison still shows a reasonable consistency in the overall trend between the simulation and the field monitoring results.
5 Discussion
Based on the comparative analysis of the numerical simulation and on-site monitoring, the findings of this study suggest that mitigation strategies for tunnels in deep-buried, high-pressure karst environments should be formulated in a stage-specific manner according to the identified five-stage seepage evolution process.
(1) Stage I–II: Early identification and preventive control: In the initial stages of seepage evolution, when the hydraulic connection is just being established and the lining response remains limited, the main objective should be to identify potential high-risk karst structures and prevent further seepage development. At this stage, advanced geological forecasting methods, such as horizontal core drilling, transient electromagnetic detection, and seismic reflection, should be strictly implemented ahead of the tunnel face to detect hidden water-bearing cavities, faults, and underground river channels. Meanwhile, baseline monitoring of water pressure, seepage discharge, and lining stress should be established in karst-prone sections so that abnormal variations can be recognized at an early stage. (2) Stage II–III: Pressure regulation and seepage slowing-down: As seepage pathways gradually develop and water pressure begins to accumulate behind the lining, the control objective should shift to slowing seepage evolution and preventing localized pressure concentration. The results of this study indicate that construction joints can act as effective pressure-relief channels, reducing the actual hydrostatic load by approximately 40%–60%. Therefore, instead of rigidly pursuing an “absolute waterproofing” strategy, a “controlled drainage” concept should be adopted in sections exposed to high karst water pressure. Measures such as optimizing the spacing and permeability of construction joints, installing pressure-relief valves, and allowing limited drainage under controlled conditions can help safely dissipate concentrated water pressure while maintaining structural integrity. (3) Stage III–IV: Targeted intervention and structural protection: When seepage further intensifies and the lining begins to show more obvious stress concentration, leakage increase, or localized damage, more active intervention measures are required. At this stage, targeted grouting should be carried out to seal dominant seepage pathways, reduce the permeability of the surrounding rock mass, and weaken the hydraulic connection between the karst cavity and the tunnel. If necessary, drainage and grouting should be combined to achieve both pressure reduction and seepage blocking. In parallel, monitoring frequency should be increased, and dynamic warning thresholds should be adjusted according to the water pressure accumulation rate and lining response characteristics. (4) Stage IV–V: Reinforcement and emergency risk control: In the later stages of seepage evolution, when high-pressure seepage is strongly developed and the lining damage risk becomes significant, the engineering priority should be shifted to structural safety and emergency prevention. In such cases, passive resistance of the lining alone is insufficient. Reinforcement measures, such as strengthening the secondary lining, improving local support, and implementing emergency drainage and pressure-relief schemes, should be adopted in time. Construction activities in the affected section should be strictly controlled, and emergency response procedures should be activated once rapid water pressure increase, sharp seepage growth, or accelerated lining deterioration is detected. (5) Stage-based monitoring and dynamic early warning: From an engineering perspective, the five-stage seepage evolution identified in this study can provide a practical framework for dynamic risk warning and decision-making in tunnels adjacent to high-pressure karst cavities. Different stages correspond to different combinations of water pressure variation, seepage intensity, and lining response. Therefore, these indicators can be used jointly to determine the current seepage stage and to select corresponding control measures, including enhanced monitoring, controlled drainage, grouting, reinforcement, or emergency intervention. In particular, during periods of heavy rainfall, special attention should be given to the possible acceleration of seepage evolution, and preventive monitoring and emergency preparedness should be strengthened accordingly.
It should be noted that the above analysis is mainly qualitative, and quantitative hydraulic parameters such as lag time, seepage velocity, and hydraulic gradient were not further calculated in the present study. Therefore, the delayed response mechanism described here should be regarded as a preliminary hydrogeological interpretation, and a more rigorous quantitative analysis will be pursued in future work.
It is worth mentioning that there are some limitations in this paper. The RFPA-based elastic damage seepage model used in this study is based on the following assumptions: the surrounding rock is treated as a heterogeneous elastic-brittle material; seepage occurs in a porous medium; and the permeability increases progressively with material damage. At the same time, the surrounding rock and lining are simplified as continuous media, while local construction joints and the detailed geometry of karst conduits are not fully represented. These assumptions are suitable for analyzing the overall evolution of rock cracking, seepage channels, and lining failure. However, under high-pressure conditions, they may affect the local accuracy of water pressure transfer and structural response, which is also one reason for the difference between simulation and monitoring results.
6 Conclusion
To investigate the seepage evolution characteristics of tunnel surrounding rock adjacent to sudden high-pressure karst caves, this study takes the Yesanguan Tunnel project as the research background: it reveals the hydraulic connection between surface water, underground rivers, and karst caves based on long-term rainfall monitoring, establishes a surrounding rock seepage model considering elastic damage, analyzes the seepage evolution characteristics of surrounding rock and the lining failure process, and verifies the results with on-site monitoring. The main conclusions are as follows:
Under the action of sudden high-pressure karst water, seepage–stress coupling significantly promoted damage development in the surrounding rock. The seepage path gradually extended from the karst cavity toward the tunnel, causing crack initiation, propagation, and coalescence, which increased the risk of water inrush and lining failure.
The RFPA simulation reproduced the progressive failure process of the surrounding rock and lining structure. The results show that high karst water pressure and connected fractures are the main factors controlling the formation of seepage channels and the deterioration of tunnel stability.
The adopted drainage and reinforcement measures effectively reduced the karst water pressure and improved the stability of the surrounding rock–lining system. The results provide a useful reference for the risk assessment and treatment of tunnels adjacent to high-pressure karst cavities.
Statements
Data availability statement
The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.
Author contributions
HD: Writing – original draft, Methodology, Investigation, Conceptualization, Writing – review and editing. YY: Conceptualization, Writing – original draft, Investigation. LZ: Investigation, Writing – original draft, Formal Analysis, Methodology.
Funding
The author(s) declared that financial support was not received for this work and/or its publication.
Conflict of interest
The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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The author(s) declared that generative AI was not used in the creation of this manuscript.
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References
1
ChenS.MaozhuL. I.ChenZ. (2002). Study and treatment of karst water burst in huayingshan tunnel of guang'an chongqing expressway in sichuan. Chin. J. Geotechnical Eng.21 (09), 1344–1349.
2
ChenZ.LinZ.XiangC. (2022). Study on water inrush mechanism of pipeline karst tunnel based on nonlinear seepage model. Mod. Tunn. Technol.59 (01), 149–155.
3
Esmatkhah IraniA.AzadiA.NikbakhtM.AzarafzaM.BonabM. H.Behrooz SarandF. (2022). GIS-Based settlement risk assessment and its effect on surface structures: a case study for the Tabrit metro-line 1. Geotechnical Geol. Eng.40(10), 5081–5102. 10.1007/s10706-022-02201-x
4
FanH.ZhuZ.SongY.ZhangS.ZhuY.GaoX.et al (2021). Water pressure evolution and structural failure characteristics of tunnel lining under hydrodynamic pressure. Eng. Fail. Anal.130, 105747. 10.1016/j.engfailanal.2021.105747
5
FengW. (2021). Research on Seepage Characteristics of water-rich Karst Tunnels and Karst Control Technology. (dissertation). Anhui University of Science and Technology, Anhui.
6
FrenelusW.PengH.ZhangJ. (2024). Seepage actions and their consequences on the support scheme of deep-buried tunnels constructed in soft rock strata. Infrastructures9 (1), 13. 10.3390/infrastructures9010013
7
LiZ. Q.NieL.XueY.LiW.FanK. (2025). Model testing on the processes, characteristics, and mechanism of water inrush induced by karst caves ahead and alongside a tunnel. Rock Mech. Rock Eng.58 (5), 5363–5380. 10.1007/s00603-025-04414-x
8
LvY.JiangJ.ChenL.HuW.JiangY. (2022). Elaborate simulation and predication of the tunnel drainage effect on karst groundwater field and discharge based on visual MODFLOW. J. Hydrology612, 128023. 10.1016/j.jhydrol.2022.128023
9
MaD.DuanH.ZhangJ.BaiH. (2022). A state-of-the-art review on rock seepage mechanism of water inrush disaster in coal mines. Int. J. Coal Sci. and Technol.9 (1), 50. 10.1007/s40789-022-00525-w
10
MingliHUANGXiayiY. A. O.TanZ. (2022). Study on failure characteristics of deep shaft lining in water rich weathered granite stratum. Chin. J. Undergr. Space Eng.18 (S1), 433–440+447.
11
NikvandV.BonabM. H. (2024). Seismic response analysis of tunnels using a coupled polygonal finite element method. Civ. Geoengin. Lett.1(1), e100009.
12
OdintsevV. N.MiletenkoN. A. (2015). Water inrush in mines as a consequence of spontaneous hydrofracture. J. Min. Sci.51 (3), 423–434. 10.1134/s1062739115030011
13
SalehiA. N.AziziP. H. R. A. (2024). Numerical investigation on the surface settlement due to Tunneting in Strucsured Fine-grained Soilss. Civ. Geoengin. Lett.1(1), e100010.
14
TianC.XiaoZ.YeF.TongY.CaoX.SunJ.et al (2025). The impact of extreme rainfall and drainage system failure on rock tunnels: a case study of deep-buried karst tunnel. Eng. Fail. Anal.171, 109345. 10.1016/j.engfailanal.2025.109345
15
WangC.ZhangD.TanD.YeJ.WangX.RenF.et al (2024). Investigation on seepage evolution property of surrounding rock under the tunneling and water surge. Tunn. Undergr. Space Technol.153, 105970. 10.1016/j.tust.2024.105970
16
XiaoQ.LiS.YeF.QianR.LiaoH.YeB.et al (2024). Explicit analytical solution to the minimum safety thickness of waterproof-resistant slab in front of karst tunnel face. Eng. Fail. Anal.157, 107941. 10.1016/j.engfailanal.2023.107941
17
XiaomingH. U. A.FanZ.LuoC. (2021). “Analysis of influence of seepage field and stress field on support of complex karst tunnel,” in Proceedings of the 2021 National Annual Conference on Engineering Geology, 391–399.
18
XuanJ.LiM.DuY.LinJ. Q.GaoY.MaoY. C.et al (2025). Inverse analysis of surrounding rock parameters of loess tunnels and numerical simulation analysis of stress-seepage coupling under water migration. Sci. Rep.15 (1), 17694. 10.1038/s41598-025-02602-x
19
YangZ.ZhangR.JingshuX. U.YangX. l. (2017). Energy analysis of rock plug thickness in karst tunnels based on non-associated flow rule and nonlinear failure criterion. J. Central South Univ.24 (12), 2940–2950. 10.1007/s11771-017-3708-1
20
YangchunM. O. (2011). Study on the influence of water filling in the hidden cavity at the bottom of the tunnel on the internal force of the secondary lining. Hydrogeology and Eng. Geol.38 (05), 31–37.
21
ZhangM. (2008). Study on Seepage Field Distribution and Lining Water Pressure Characteristics of Karst Tunnel Surrounding Rock. Beijing: Beijing Jiaotong University.
22
ZhangM. (2011). Construction technology of deep-buried large water-rich cavity tunnel -- energy release, pressure reduction and safety construction technology of 602 cavity. Yesanguan Tunn. Yiwan Railw. Mod. Tunn. Technol.48 (03), 1–6+13.
23
ZhangS.SongD.YeF.FuW.ZhangB.XiaoQ. (2024). Research on flow field characteristics in the karst tunnel face drilling hole (conduit) under the coupling between turbulence and seepage. Tunn. Undergr. Space Technol.143, 105455. 10.1016/j.tust.2023.105455
Summary
Keywords
adjacent high-pressure caves, karst tunnel, numerical simulation, process of destruction, seepage evolution
Citation
Dong H, Yao Y and Zhang L (2026) Numerical simulation and field monitoring on seepage evolution of surrounding rock in tunnels adjacent to high-pressure karst caves. Front. Earth Sci. 14:1844727. doi: 10.3389/feart.2026.1844727
Received
01 April 2026
Revised
24 May 2026
Accepted
09 June 2026
Published
29 June 2026
Volume
14 - 2026
Edited by
Pengfei Liu, CCCC Second Harbor Engineering Co., Ltd., China
Reviewed by
Xiaonan Wang, China University of Mining and Technology, China
Yingran Fang, Henan Polytechnic University, China
Updates
Copyright
© 2026 Dong, Yao and Zhang.
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*Correspondence: Haojie Dong, donghaojie0210@126.com
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.