Study of Structural Deterioration Behavior of Mining Method Tunnels Under Steel Reinforcement Corrosion

Abstract

Tunnel lining structures, which are subjected to the combined effects of water and soil pressure as well as a water-rich erosion environment, undergo a corrosion-induced damage and degradation process in the reinforced concrete, gradually leading to structural failure and a significant decline in service performance. By introducing the Cohesive Zone Model (CZM) and the concrete damage plastic model (CDP), a three-dimensional numerical model of the tunnel lining structure in mining method tunnels was established. This model takes into account the multiple effects caused by steel reinforcement corrosion, including the degradation of the reinforcement’s performance, the loss of an effective concrete cross section, and the deterioration of the bond between the steel reinforcement and the concrete. Through this model, the deformation, internal forces, damage evolution, and degradation characteristics of the structure under the effects of the surrounding rock water–soil pressure and steel reinforcement corrosion are identified. The simulation results reveal the following: (1) Corrosion leads to a reduction in the stiffness of the lining structure, exacerbating its deformation. For example, under high water pressure conditions, the displacement at the vault of the lining before and after corrosion is 4.31 mm and 7.14 mm, respectively, with an additional displacement increase of 65.7% due to corrosion. (2) The reinforced concrete lining structure, which is affected by the surrounding rock loads and expansion due to steel reinforcement corrosion, experiences progressive degradation, resulting in a redistribution of internal forces within the structure. The overall axial force in the lining slightly increases, while the bending moment at the vault, spandrel, and invert decreases and the bending moment at the hance and arch foot increases. (3) The damage range of the tunnel lining structure continuously increases as corrosion progresses, with significant differences between the surrounding rock side and the free face side. Among the various parts of the lining, the vault exhibits the greatest damage depth and the widest cracks. (4) Water pressure significantly impacts the internal forces and crack width of the lining structure. As the water level drops, both the bending moment and the axial force diminish, while the damage range and crack width increase, with crack width increasing by 15.1% under low water pressure conditions.

1. Introduction

As the most important structure in tunnel engineering, reinforced concrete tunnel linings are expected to last for decades or even centuries. However, during service, reinforced concrete structures inevitably experience steel reinforcement corrosion [1]. Under the combined effects of load and erosive substances, reinforced concrete tunnel linings undergo a deterioration process due to corrosion damage, gradually deteriorating and ultimately failing. This leads to a situation where the mechanical properties of the lining can no longer meet the design bearing capacity, resulting in significantly reduced performance and durability issues [2,3,4]. Therefore, studying the damage and deterioration of reinforced concrete linings due to steel reinforcement corrosion is of great importance for improving the service performance of the lining.

Many researchers have employed numerical simulation methods to examine the nonlinear evolution of reinforced concrete structures from an undamaged state to failure. They have studied reinforced concrete lining structures in erosion environments, focusing on aspects such as the mechanical properties of the lining structure, service life, and safety assessment methods. The corrosion of steel reinforcement is the result of the synergistic effect of chloride ion erosion, carbonation, and electrochemical corrosion. The volume expansion of corrosion products (up to 2–6 times of the original volume) triggers the cracking of concrete, which further aggravates the medium transport and corrosion process, forming a multifactorial coupled chain deterioration effect. Lee et al. [5] found that chloride had diffused into concrete and been adsorbed onto the surface of the steel reinforcement, inducing pitting in the reinforcement. Cao et al. [6] performed numerical simulations of the coupled microporous and macroporous corrosion processes involved in typical chloride-induced corrosion. Zhu et al. [7] investigated the morphological characteristics of stray current and chloride-ion-induced corrosion pits in reinforced concrete. Jiang et al. [8] investigated the effect of chloride salt type on the corrosion threshold levels of rebar corrosion, such as corrosion current density and open circuit potential. Guo et al. [9] significantly improved the accuracy of the corrosion status monitoring of reinforcement in concrete by integrating multiple electrochemical detection indicators, including corrosion current. In addition, carbon dioxide also plays an important role in the corrosion process of reinforced concrete. Xue et al. [10] summarized and analyzed the studies related to the evolution of the chemical, structural, and mechanical properties of concrete and reinforcing bars in response to CO₂-induced reactions. Tittarelli et al. [11] compared the CO₂-induced corrosion behavior of no-fines concrete manufactured with three different strength classes and reinforcements.

The establishment of numerical mechanical models capable of characterizing the interaction and mechanical behavior of reinforced concrete is the basis for studying the damage evolution of reinforced concrete structures [12,13]. Rimkus et al. [14] addressed the limitations and uncertainty of smeared crack models applied to RC beams and provided a valuable perspective on the interpretation of numerical results in fracture-dominated regimes. De Maio et al. [15] proposed an improved cohesive crack approach to analyze degradation under mixed-mode fractures, which is applicable to tunnel linings under complex loading and environmental conditions. In the context of simulation studies investigating the effects of corrosion on reinforced concrete structures, Hu et al. [16] developed and validated a model for concrete protective layer cracking caused by the corrosion of multiple rebars, whereby the effects of rebar spacing, protective layer thickness, and ITZ fracture properties on concrete protective layer cracking were investigated. Marí et al. [17] presented a nonlinear and time-dependent step-by-step analysis model for reinforced and prestressed concrete frames that is able capture the structural effects of corrosion and the effects of strengthening interventions.

In terms of the mechanical properties of the lining, Savija et al. [18] comparatively investigated the pressure during the cracking of a concrete protective layer due to point erosion and uniform erosion. Chen et al. [19] proposed an effective method to predict concrete crack growth and estimate the residual load capacity of corroded eccentrically loaded reinforced concrete columns. Zhang et al. [20] analyzed the effect of the corrosion rate on the bearing capacity of lining structures based on a post corrosion rebar pull out test. Yousif [21] proposed a methodology for assessing the strength of corroded tunnel linings by integrating bond strength, specimen mechanical behavior, and concrete cracks. Zhang et al. [22] analyzed the structural performance of precast concrete tunnel linings in the Shanghai Metro under different loading and corrosion scenarios based on the material constitutive model obtained from static load tests and finite element simulation results. Xu et al. [23] investigated the one-sided corrosion and total corrosion of high-strength concrete with 0% and 1% volume ratios of steel fibers in sulfuric acid solution (pH = 1) to explore the changes in the physical and mechanical properties of the high-strength concrete under sulfuric acid corrosion conditions. Zhang et al. [24] investigated the effects of corrosion state and loading eccentricity on the structural behavior and failure mode of corroded lined pipe sheets based on full-scale experiments and numerical simulations. Li et al. [25] investigated the corrosion of rebars in subway tunnels constructed between 1980 and 2006 and, through theoretical analysis, revealed the nature of the corrosion potential and its relationship with the corrosion rate in different corrosion states.

With computer performance improvements and the development of numerical simulation technology, numerical simulation has become an important means for studying the damage and degradation performance of tunnel structures under steel reinforcement corrosion. However, there are several limitations in the finite element analysis of lining structure performance degradation under corrosion: (1) In most of the existing studies on the corrosion of reinforced concrete, the models do not consider the bonding properties between the reinforcement and concrete or determine the bonding performance parameters through tests. (2) There is a lack of analysis regarding the full damage process and internal force evolution, as well as the overall degradation characteristics during corrosion development. Most studies focus on the overall durability and bearing capacity of tunnels under corrosion conditions, with limited discussion on the regional degradation of the lining structure.

In light of this, this paper considers the actual service environment of the tunnel lining structure, including assessing the deterioration of the mechanical properties of the steel reinforcement, the loss of the effective cross-sectional area of concrete, and the degradation of the bond performance between the steel reinforcement and the concrete due to corrosion. A finite element model of tunnel lining corrosion degradation is established, and the changes in deformation, damage, internal force redistribution, and crack width under the combined effects of soil and water pressure and steel reinforcement corrosion are analyzed.

2. Parameter Selection and Calibration

2.1. Selection of Concrete Principal Parameters

The concrete damage plastic (CDP) model integrates damage elasticity and tensile and compressive plasticity and can accurately characterize the inelastic mechanical behavior of concrete, making it one of the most commonly used intrinsic structures for structural engineering studies [26]. Therefore, the CDP model is used to characterize the mechanical behavior of concrete materials. The stress–strain curve under uniaxial cyclic loading (tension–compression–tension) for the CDP model is shown in Figure 1.

The calculation of damage factors was carried out according to the energy equivalence method [27], and the plastic yield criterion parameters of the CDP model are shown in

Table 1. Plastic yield criterion parameters of CDP model.

Dilatancy Angle ψ/°	Flow Parameters	fb0/fc0	K	μ
30	0.1	1.16	0.6667	5 × 10−4

, where f_b0/f_c0 is the ratio of the biaxial compressive strength to the uniaxial compressive ultimate strength, K is the invariant stress ratio, and μ is the coefficient of viscous regularization.

2.2. Selection of Rebar Intrinsic Parameters

Cracks, as one of the most common issues affecting lining structures, significantly affect the mechanical properties of the material [28]. The process of concrete cracking due to the uniform corrosion of steel reinforcement is shown in Figure 2. When free face to erosive substances, the steel reinforcement within the concrete corrodes, generating corrosion products that fill the gap between the steel reinforcement and the concrete. As the degree of corrosion increases, so does the volume of corrosion products, causing the steel reinforcement to expand. With further increases in the corrosion product volume and under the restraining effect of the surrounding concrete, a corrosion expansion force is generated at the reinforced concrete interface, leading to tensile cracking of the protective layer of concrete. As the crack expands, the mechanical properties of the material are significantly reduced. The steel reinforcement in the secondary lining is not a simple straight section but consists of several circular arc segments. Most current studies suggest that the corrosion expansion displacement of steel reinforcement is not isotropic and mainly produces corrosion expansion displacement in the cross section [29]. Although it is true that the corrosion-induced longitudinal expansion of reinforcing bars occurs under the action of complex environments, previous studies have shown that the cracking mechanism of the cover is mainly controlled by the displacement of corrosion expansion in the direction of the cross section and the radial stress distribution characteristics [30,31]. Therefore, this study simplifies the longitudinal expansion effect and focuses on the main controlling factor of corrosion-induced structural deterioration, i.e., corrosion expansion within the cross section, while maintaining the rationality of the physical mechanism of the model.

When simulating the corrosion expansion of the steel reinforcement using the temperature field, the corresponding local coordinate system, the direction of the steel reinforcement material, and the anisotropic thermal expansion coefficient are set for the steel reinforcement of different circular arc segments. This ensures that the steel reinforcement produces an expansion displacement only in the cross section, as shown in Figure 3a. An HRB400 steel reinforcement was used for the secondary lining, and its mechanical characteristics of decreasing yield strength with increasing corrosion rate were characterized by setting temperature-dependent material properties. The cross section of the steel reinforcement after uniform corrosion is shown in Figure 3b.

Assuming that the length and mass of steel reinforcement are uniform and that the loss of mass corresponds to the loss of the steel reinforcement cross section, the corrosion rate and temperature field relationship is derived according to Equation (1):

$$\eta ={\displaystyle \frac{\pi [r^2-{(r-\delta )}^2]}{\pi r^2}}={\displaystyle \frac{2r\delta -r^2}{r^2}}={\displaystyle \frac{2\delta }{r}}-{\displaystyle \frac{{\delta }^2}{r^2}}$$

(1)

where r is the diameter of the steel reinforcement; δ is the corrosion depth, which satisfies Δ = (n − 1)δ; Δ is the nominal thickness of the corrosion layer; and n is taken as 2 in the calculation.

At this point, the area of the expanded cross section of the steel reinforcement is:

$$\begin{array}{cc}\hfill \Delta S_{\mathrm{cor}}& =\pi {(r+\Delta )}^2-\pi r^2\hfill \\ & =\pi [{(n-1)}^2{\delta }^2+2r(n-1)\delta ]\hfill \end{array}$$

(2)

The coefficient of linear expansion for the steel reinforcement is 1.2 × 10⁻⁵/°C, and the area of the cross section of the steel reinforcement that expands when the temperature changes by ΔT is:

$$\begin{array}{cc}\hfill \Delta S_{\mathrm{T}}& =\pi r^2[{(1+\alpha \Delta T)}^2-1]\hfill \\ & =\pi r^2(2\alpha \Delta T+{\alpha }^2\Delta T^2)\hfill \end{array}$$

(3)

Based on the fact that the temperature-induced expansion area ΔS_T is equal to the corrosion expansion area ΔS_cor, the relationship between the temperature field and the corrosion rate can be derived by substituting the steel reinforcement diameter and related parameters. By combining this with the relationship between rebar strength and corrosion rate [32], the steel reinforcement yield strength, as a function of the temperature field under corrosion conditions, can be obtained.

2.3. Selection of Intrinsic Parameters for Bonding Properties

Recent studies predominantly use nonlinear springs to characterize the bonding properties between steel reinforcement and concrete [33]; however, the force–displacement relationship of the spring unit only allows for discrete changes between analysis steps, which does not effectively simulate the gradual deterioration of bonding properties during steel reinforcement corrosion. To address this issue, the Cohesive Zone Model (CZM) is used to characterize the bonding properties between the steel reinforcement and the concrete, while cohesive unit damage degradation is used to simulate the weakening of the bonding properties due to steel reinforcement corrosion during the tunnel’s operational phase.

The interaction between the steel reinforcement and concrete can be divided into normal extrusion in the perpendicular direction (normal direction) and bond slip in the parallel direction (tangential direction). The normal and tangential key parameters of the unit need to be calibrated separately to simulate the bonding performance of the steel reinforcement and concrete using the cohesive unit. Normal parameter: Since the normal deformation produced by the extrusion action in reinforced concrete is small, the unit stiffness does not cause damage. Therefore, the normal stiffness of the cohesive unit can be assigned a large value, similar to the stiffness of concrete. Tangential parameter: The tangential parameter of the cohesive unit can be calibrated using the bond slip curve obtained from the center pull out test. By comparing the experimental data with the numerical simulation results from the pull out tests, the calculation parameters for the cohesive unit can be determined.

2.4. Central Pull Out Test

The design of the pull out test is based on the typical section dimensions of the actual tunnel lining structure, the standard geometrical parameters of which are shown in Figure 4a—a lining thickness of 300 mm and a symmetric reinforcement design. In order to calibrate the interfacial parameters, a research area (shown in Figure 4b) was identified and single rebar specimens fabricated to characterize the mechanical behavior of the steel–concrete interface.

Twelve groups of center-pulled specimens were designed, each consisting of an HRB400 steel reinforcement and C40 concrete, with an HPB300 steel reinforcement used as a hoop reinforcement to prevent splitting damage. The concrete specimen dimensions were 150 mm × 150 mm × 150 mm, with a steel reinforcement diameter of 25 mm, a bond length of 70 mm, and the non-bonded section wrapped in insulating tape. The dimensions are shown in detail in Figure 4c. The specimen fabrication process is shown in Figure 4d,e.

As shown in Figure 5, the specimen pulling device consisted of a displacement meter, a counterforce device, and a loading device. During the test, the loading rate was set to 0.1 kN/s, and the load values were recorded at intervals of 0.05 mm. The maximum load and its corresponding free end displacement were also recorded. After eliminating outlier results caused by fabrication issues, data errors, and other factors, four sets of bond slip curves with the most representative results were selected and their average values used in the final calibration curves, as shown in Figure 6.

Models with the same dimensions as the pull out specimens were established, using the damage plasticity model for concrete and the elastic–plasticity model for the main reinforcement and stirrup. The four sides of the concrete were completely fixed, and reference points were added to couple with the cross section at the pulled out end of the steel reinforcement. The 3D pull out finite element parameter calibration model is shown in Figure 7.

Among the finite element calculation parameters, the material’s tangential stiffness controls the slope of the elastic phase of the bond slip curve, the damage initiation stress governs the maximum tensile force, and the fracture energy defines the area under the bond slip curve and the x-axis. During parameter calibration, the values yielding the most similar calculation results were selected as the fracture parameters for the reinforced concrete transition region. These were determined by continuously adjusting the material’s tangential stiffness, damage initiation stress, and fracture energy to ensure that the finite element bond slip curves closely matched the average experimental curves. A comparison of the finite element and experimental bond slip curves is shown in Figure 8. The results of the maximum pull out force calculations, the corresponding slip, and the fracture parameters of the cohesive unit are presented in

Table 2. Comparison of numerical and laboratory test results.

Test Results	Experimental Value	Calculated Value	Relative Error/%
Maximum pulling force/kN	35.647	36.9561	3.672
Sliding displacement/mm	0.633	0.63563	0.415

and

Table 3. Fracture parameters of reinforced concrete interface cohesive elements.

Elastic		Fracture Criterion Maxs		Damage Evolution
Normal stiffness (MPa/mm)	Tangential stiffness (MPa/mm)	Normal damage onset stress (MPa)	Tangential damage onset stress (MPa)	Normal fracture energy (MPa·mm)	Tangential fracture energy (MPa·mm)
32.5	29.7	16.2	8.3	16.2	8.1

.

3. Tunnel Lining Performance Deterioration Analysis Model for Mining Method

Taking a water-rich mining method tunnel as an example and considering the “Code for Design of Railway Tunnels”, the selected tunnel is classified as a deep-buried tunnel. The corresponding vertical and horizontal peripheral rock pressure, as well as the uniform external water pressure and other loads, are calculated. The load pattern for the tunnel lining structure is shown in Figure 9.

The computational model that was created in ABAQUS is shown in Figure 10. The steel reinforcement has a diameter of 25 mm, with a longitudinal spacing of 200 mm, and the thickness of the concrete protective layer is 50 mm. A lining structure model with a longitudinal length of 5 m was established, in which the target section is in the middle of the model. A central 1 m section was selected for analysis. To conserve computational resources, a semi-structured approach was used for the calculation, with nonlinear springs simulating the interaction between the surrounding rock and the lining.

The mechanics model of the tunnel is based on the load structure model, which is one of the most commonly used models [34,35]. This method can simulate the interaction between the surrounding rock and the lining using nonlinear springs, incorporating appropriate simplification while ensuring the model’s rationality. This simplification enables the global stiffness of the rock–lining interface to be captured without explicitly modeling the rock mass, though it limits the analysis of the rock–structure interaction effects under localized failures. Considering the symmetry of the tunnel structure and loading, the semi-structural method is used for simulation. Symmetric constraints are set at the symmetric boundary locations, including horizontal (x-axis) displacement constraints and y-axis and z-axis rotation constraints. Based on the relevant numerical simulation studies, the mesh size is determined to be about 20 mm to facilitate the analysis of concrete deterioration behavior.

The deterioration of reinforced concrete lining structures during service arises from two main sources: the surrounding rock load and erosion. Typically, the corrosion of the steel reinforcement within the lining occurs over a prolonged period (several years or even decades), while the deformation of the lining structure under the surrounding rock load stabilizes before this stage. Therefore, the effects of the surrounding rock load and the corrosion and expansion of the steel reinforcement on the lining structure are considered in separate analysis steps.

4. Analysis

4.1. Deformation Analysis of Tunnel Lining Structures

The deformation of different parts of the lining structure caused by steel reinforcement corrosion after the stabilization of the surrounding rock load was obtained, and the relationship between deformation and the corrosion rate at each measurement point is shown in Figure 11. The lining deformed under the combined effect of the surrounding rock load and erosion, with phenomena such as the sinking of the vault, rising of the invert, and shifting of the left and right hance to the free face side, with a general inward convergence. The corrosion effect greatly increased the deformation at each location, with the deformation at measurement point A being the largest, followed by measurement points B, C, and D. This indicates that the stiffness loss in different parts of the lining structure due to corrosion is different, meaning that there are differences in corrosion-induced damage to the lining structure.

The groundwater depth at the tunnel site ranges from 2 to 6 m, and the design water level line is set to the ground elevation. As a result, when calculating the high water pressure conditions, the height of the water level was increased by 6 m, i.e., the distance between the water level and the top of the tunnel was increased from 10.55 m to 16.55 m (corresponding to an increase in water pressure from 0.1055 MPa to 0.1655 MPa) to analyze the difference in the deformation convergence of the lining structure. The deformation trend in the lining structure under high water table conditions is similar to that in Figure 12, with the most significant difference occurring in the displacement values during the first analysis step (soil and water loading). In contrast, the second analysis step showed a smaller difference in deformation. The part of the arch with the largest displacement difference, the vault (point A), was extracted for comparison, as shown in

Table 4. Comparison of deformation at point A under different water pressures (unit: mm).

Corrosion Rate/%	High Water Pressure		Low Water Pressure
	Displacement	Displacement Difference	Displacement	Displacement Difference
0	4.305	0	2.803	0
10	5.233	0.928	3.710	0.907
20	5.779	1.474	4.241	1.438
30	7.136	2.831	5.580	2.777

.

The displacement difference in Table 4 represents the variation in displacement between the corroded lining and the non-corroded lining at different corrosion rates. As shown in Table 4, the initial vault displacement of 2.803 cm for low water pressure conditions was used as a reference to analyze the effects of changes in the water pressure and corrosion rate on displacement. The initial displacement of the vault under high water pressure conditions was 4.305 cm, i.e., the difference in displacement due to the change in water pressure was 1.502 cm. The final displacement of the vault under low water pressure conditions and a corrosion rate of 30% was 5.580 cm, i.e., the difference in displacement due to corrosion was 2.777 cm. Moreover, the difference in displacement due to corrosion under the superimposed effect of high water pressure is 2.831 cm. Overall, corrosion has a more significant effect on displacement than water pressure. Water pressure affected the initial displacement and had a less pronounced effect on the corrosion rate.

4.2. Analysis of Internal Force Redistribution in Tunnel Lining Structures

The tunnel is subjected to surrounding rock loading and erosion during its long service life. These factors lead to lining structure performance deterioration. This results in phenomena such as cracks or falling blocks, causing the distribution of internal forces within the cross section to deviate from a linear elasticity relationship. This, in turn, leads to a redistribution of internal forces within the structure, ultimately bringing the structure to a new equilibrium state. Bending moments and axial force are commonly used in engineering as key indicators of structural safety. To analyze the influence of corrosion on the redistribution of internal forces, the bending moment and axial force values at different sections of the lining structure were obtained for corrosion rates ranging from 0 to 30%. The changes in bending moment and axial force during the development of corrosion are shown in Figure 12.

As seen in Figure 12a, as the corrosion rate increases, the bending moments in the different parts of the lining structure are altered in different ways. The largest changes in bending moment values occur in areas with severe damage. The bending moments at tensile positions on the free face side, such as the vault, hance, and invert, decrease, while the bending moments at tensile positions on the surrounding rock side, such as the arch spandrel and arch foot, increase. From the axial force diagram for the lining, it can be seen that as the corrosion rate increases, the axial force in each part increases by varying degrees. However, in general, the increase in axial force is minimal, with the largest increase (10.63%) occurring at the vault.

The distribution of bending moments and axial forces in the tunnel lining structures of mining method tunnels, before and after corrosion and with two different water levels, is shown in Figure 13.

As shown in Figure 13, under constant soil pressure and corrosion of the steel reinforcement, the bending moment in each part of the tunnel lining structure increases to varying degrees when the water level rises by 6 m. The changes in bending moment at the vault and spandrel are minimal, while the largest change occurs at the arch foot. Without corrosion, an increase in water pressure raises the bending moment from −130.16 kN·m to −158.30 kN·m, an increase of 21.62%. However, in the presence of corrosion (η = 30%), a higher water pressure increases the lining bending moment from −182.33 kN·m to −226.86 kN·m, an increase of 24.42%.

The distribution of axial force in the lining structure remains roughly the same, with the largest change occurring at the vault. Without corrosion, a higher water pressure increases the axial force at the vault from 2042.35 kN to 2591.06 kN, an increase of 26.87%. However, in the presence of corrosion (η = 30%), a higher water pressure increases the axial force from 2207.80 kN to 2823.44 kN, an increase of 27.88%.

To further analyze the effect of corrosion and water level on the redistribution of internal forces, the internal forces in different parts of the lining under different working conditions were extracted and the rate of change in the internal forces was calculated when the corrosion rate was increased from 0% to 30%. The lining structure monitoring points were named 1~9 from the vault to the inverted arch, and the results are shown in

Table 5. Differences in internal forces in various parts of the lining structure.

Internal Force	Working Conditions		1	2	3	4	5	6	7	8	9
Bending moment (kN·m)	Low-water level	η = 0%	90.6	28.7	−31.2	−8.2	23.4	−130.2	−71.6	96.2	139.5
		η = 30%	35.2	5.0	−53.4	−20.4	2.4	−182.3	−107.1	10.9	67.9
	Rate of change /%		61.2	82.5	71.1	148.8	89.9	40.1	49.7	88.6	51.3
	High-water level	η = 0%	98.7	31.2	−40.2	−10.6	−78.8	−158.3	−85.5	114.3	165.2
		η = 30%	39.3	5.6	−70.0	−26.9	−115.8	−226.9	−131.0	13.3	89.5
	Rate of change /%		60.2	82.0	74.1	154.1	46.9	43.3	53.2	88.4	45.8
Axial force (kN)	Low-water level	η = 0%	2042.4	1991.5	2444.3	3222.9	2348.5	1863.4	1622.7	1636.8	1792.8
		η = 30%	2207.8	2156.7	2612.6	3387.3	2500.1	2023.9	1795.1	1809.7	1969.1
	Rate of change /%		8.1	8.3	6.9	5.1	6.5	8.6	10.6	10.6	9.8
	High-water level	η = 0%	2591.1	2508.2	3040.7	3998.7	2903.4	2304.7	2015.5	2057.1	2260.0
		η = 30%	2823.4	2722.9	3290.2	4242.3	3125.8	2534.1	2249.7	2279.0	2494.0
	Rate of change /%		9.0	8.6	8.2	6.1	7.7	10.0	11.6	10.8	10.4

. The locations of measurement points 1~9 are shown in Figure 13a.

The bending moment values are small overall, and the rate of change is large. Among the nine measurement points from the vault to the inverted arch, the rate of change in monitoring point 4 (side wall) is the largest, indicating that the effect of corrosion on the redistribution of internal forces in the side wall is the largest. By comparing the bending moment rate of change between low and high water levels, it can be seen that the water level has little effect on corrosion. Nevertheless, the water level does affect the initial bending moment of the lining structure before corrosion. Overall, the effects are minor except for measurement point 5.

The rate of axial force change at each monitoring point is small. The corrosion-mediated rate of change shows a trend of decreasing and then increasing from the vault to the inverted arch. Corrosion has the greatest effect on the axial force in the inverted arch, followed by the vault and the side wall. By comparing the axial force rate of change at low and high water levels, we can see that the effect of corrosion on the axial force in the lining structure is greater when the water level is higher, but the difference is not significant. Overall, corrosion has a greater influence on the redistribution of internal forces in the structure, whereas the water pressure mainly affects the initial state of the internal forces in the structure.

To verify the correctness of the numerical model, the sensors buried in the structure during the construction period were utilized to monitor the distribution of the internal forces. The arrangement of the sensors is shown in Figure 14a; the sensors were reinforcement gauges and embedded strain gauges. The internal forces of the lining structure were calculated by testing the concrete strains and axial forces of the reinforcement on the inside and outside of the tunnel lining at different locations. At the beginning of tunnel operation, after the structural deformation and internal forces were stabilized, the axial forces and bending moments of the lining structure were tested and calculated for both the high and low water level sections. The results are shown in Figure 14.

The internal structural forces in the early stages of tunnel operation and under low water level conditions are shown in Figure 14b. The axial force in the side walls is the largest, followed by the vault; the axial force in the inverted arch is the smallest. The axial force distribution pattern is similar to that from the numerical simulation results, and the numerical differences are not significant. The bending moment values for the lining indicate that the vault, side wall, and inverted arch are tensile on the inner side and the spandrel and wall foot are tensile on the outer side, which is consistent with the numerical simulation results. The range of bending moments in the inner tensile part of the lining structure is 32.2~156.4 kN·m. The range of bending moments in the outer tensile part of the lining structure is −40.6~−129.1 kN·m.

The internal structural forces in the early stages of tunnel operation and under high water level conditions are shown in Figure 14c. The axial force in the sidewalls is the largest, followed by the vault; the axial force in the inverted arch is the smallest. Overall, the axial force is larger compared with that in low water level conditions, and the distribution pattern is similar to the numerical simulation results. The bending moment values for the lining indicate that the inner part of the vault and the inverted arch are tensile, while the outer part of the rest of the structure is tensile, which is consistent with the numerical simulation results. The bending moments in the inner part of the lining structure under tension range from 103.3 to 179.6 kN·m, while the bending moments in the outer part of the lining structure under tension range from −37.2 to −154.6 kN·m; these values are similar to those from the simulation results.

The reasonableness of the numerical model used in this study is verified by analyzing and comparing the on-site measured internal force in the tunnel lining structure. As of now, the tunnel project on which this paper is based has been built for a relatively short period of time. The tunnel will be affected by sea erosion during its long-term operation, and the trends for the axial force and bending moments in the lining structure caused by the corrosion of the steel reinforcement can be tested and analyzed in subsequent research.

4.3. Analysis of the Structural Damage Evolution of the Mining Method Tunnel

The damage to the surrounding rock side and the free face side of the lining structure differs, and the extent of damage varies across different parts. For the purpose of comparative analysis, the post treatment view of the lining structure is shown in Figure 15. Figure 16 shows the damage variation in the surrounding rock side of the lining structure during the corrosion process.

As shown in Figure 16, when the corrosion rate is 0%, meaning the lining structure is only affected by the surrounding rock and water pressure, longitudinal damage appears at the junction of the vault and spandrel, with a small and dispersed range. As the steel reinforcement inside the lining structure begins to corrode (η = 0~12%), the expansive force from the corrosion causes circumferential damage to the structure. The damage at the spandrel has gradually expanded to form intersecting longitudinal and circumferential cracks. As corrosion progresses (η = 12~21%), the damage area continuously expands in the longitudinal direction, with the spandrel developing the first large-scale damage region. At this point, significant patch-like damage occurs at the arch foot, which then develops into a damage region. As corrosion further develops (η = 21~30%), the expansion rate of the damage area reduces and eventually stabilizes.

Figure 17 shows the variation in damage on the free face side of the lining structure during the corrosion process.

As shown in Figure 17, when the corrosion rate is 0%, meaning that the lining structure is only subjected to the surrounding rock pressure and water pressure, a small amount of longitudinal damage appears at the vault on the free face side of the lining structure. As the steel reinforcement inside the lining undergoes corrosion expansion, the expansive force causes circumferential damage and spot damage on the cross section of the lining. As the corrosion progresses, the spot-distributed damage gradually connects along the longitudinal direction and continues to expand from the exterior to the interior, ultimately forming a large damage area. Additionally, the circumferential damage at the hance area in the figure has limited longitudinal expansion. At a corrosion rate of 30%, no large-scale damage area has formed in this region. The corrosion-mediated damage to the vault is more severe than that to the superelevation arch. The damage at the vault does not extend toward the spandrel. In conjunction with the development of damage in various parts of the lining, the early onset of vault damage suggests that this region may serve as a diagnostic indicator for tunnel health assessment.

From the damage contour maps for the free face side and the surrounding rock side, it can be observed that the damage caused by corrosion is more severe at the vault, spandrel, and invert. The variation in the depth of damage at these three locations and with different corrosion rates was obtained and is shown in Figure 18.

It is evident that the damage range at the tunnel vault increases progressively, with the corrosion depth continuing to grow, posing a risk of penetrating the secondary lining. The corrosion damage at the spandrel and superelevation arch expands more slowly, with limited damage areas, and damage at the spandrel is mainly found on the surrounding rock side.

The damage cloud maps for different water levels when the rebar corrosion rate is 30% are shown in Figure 19.

The damage area of the tunnel lining is reduced under high water pressure conditions compared with low water pressure conditions. The reason for this phenomenon is that when the water pressure increases, the bending moment increases to varying degrees in different parts of the tunnel lining, while the axial force increases more uniformly. In areas where the bending moment increase is small (such as the vault and spandrel), the damage area is smaller than that under low water pressure conditions, while in areas where the bending moment increase is large (such as the arch foot), the difference in the distribution of the damage area compared with the low water pressure conditions is not significant.

4.4. Analysis of Crack Width Evolution in the Mining Method Tunnel Lining Structure

Crack width is also a key factor in evaluating the durability and safety of the lining structure. The maximum crack widths in different parts of the lining structure during the development of corrosion were obtained to analyze crack width variations.

In numerical simulations, the average crack width within a certain range can be calculated using the following formula:

$$w_{\mathrm{avg}}=\Delta {\epsilon }_{\mathrm{avg}}{l}_{\mathrm{avg}}=({\epsilon }_{\mathrm{s}}-{\epsilon }_{\mathrm{c}})l_{\mathrm{avg}}=(1-{\displaystyle \frac{{\epsilon }_{\mathrm{c}}}{{\epsilon }_{\mathrm{s}}}}){\epsilon }_{\mathrm{s}}{l}_{\mathrm{avg}}$$

(4)

where w_avg is the average crack width, l_avg is the average crack spacing, Δε_avg is the strain difference between the steel reinforcement and concrete in the crack region, ε_s is the steel reinforcement unit strain, and ε_c is the concrete unit strain.

According to the experimental results from reference [36] and the “Technical Code for Waterproofing of Underground Works” [37], (1 − ε_c/ε_s)≈0.77 and the crack width amplification factor α is taken as 1.66. The formula for calculating the maximum crack width is as follows:

$$w_{\mathrm{avg}}=\alpha \Delta {\epsilon }_{\mathrm{avg}}{l}_{\mathrm{avg}}=\alpha (1-{\displaystyle \frac{{\epsilon }_{\mathrm{c}}}{{\epsilon }_{\mathrm{s}}}}){\epsilon }_{\mathrm{s}}{l}_{\mathrm{avg}}=1.66\times 0.77{\epsilon }_{\mathrm{s}}{l}_{\mathrm{avg}}$$

(5)

The maximum crack widths in the different parts of the lining structure during corrosion development were obtained, and the relationship between the maximum crack width and the corrosion rate is shown in Figure 20. The tunnel crack health assessment was performed according to the “Technical Standard for Maintenance of Tunnel Structures in Urban Rail Transit” [38]. The crack widths are categorized into four levels based on the sizes 0–0.2 mm, 0.2–0.5 mm, 0.5–1.0 mm, and 1.0–2.0 mm, with the corresponding health levels ranging from 1 to 4.

As shown in Figure 20, at the vault, spandrel, and hance, the maximum crack width increases approximately linearly with the corrosion rate during the 0–14% corrosion phase. In the 14–30% corrosion phase, the maximum crack width initially increases rapidly, then slows down and eventually stabilizes. The maximum crack width at the arch foot and inverted arch remains relatively small. The maximum crack width at the tunnel vault exhibits the fastest growth rate, followed by the spandrel and hance, with the arch foot and invert showing the slowest growth rates.

The reason that the fastest crack propagation occurs at the vault is that as the rebar corrodes, the pre-existing cracks in the tensile zone of the vault continue to expand. Although the bending moment at the vault decreases as the corrosion rate increases, the degree of cross-sectional damage continues to increase, which results in a sustained reduction in the section’s bending resistance. This leads to the deformation of the vault toward the free face side, causing the cracks to expand most rapidly at this location. When using the vault as the evaluation object, the corresponding corrosion rates for health levels 1 to 4 are 0–6%, 6–12.5%, 12.5–20%, and 20–30%, respectively.

The crack development of the lining structure under high water pressure is shown in Figure 21.

As shown in Figure 21, under high water pressure conditions, the maximum crack width of the tunnel lining structure develops more slowly than it does under low water pressure conditions. When the corrosion rate reaches 30% in low water pressure conditions, the maximum crack width at the arch top is 1.37 mm, while under high water pressure conditions, the maximum crack width is reduced to 1.19 mm, representing a 13.13% decrease. There is a noticeable difference in crack widths between the vault and spandrel under both water pressure conditions. The difference in crack width is due to the increase in water level, which reduces the bending moment, increases the axial force, and decreases the tensile stress in the concrete structure, leading to a corresponding reduction in the width of tensile cracks. Overall, a comparative analysis of the damage, internal force redistribution, and crack widths indicates that a higher water pressure can improve the durability of the tunnel lining structure to some extent.

This study mainly focuses on the effect of reinforcement corrosion and loading on the mechanical properties of the structure. In analyzing the effect of corrosion, the corrosion rate was taken as a given condition, so the method for determining the corrosion rate was not described. In fact, the method of determining the corrosion rate of the reinforcement primarily consists of destructive testing and non-destructive testing [39]. Destructive testing (GWL), such as drilling and coring, has achieved good results in evaluating the corrosion rate of reinforcing steel in concrete structures [40]. However, it is not suitable for dynamic corrosion diagnosis and assessment due to its invasive nature and the induced collateral damage. For non-destructive testing, methods such as the use of electrical resistance probes (ERPs) and half-cell potential (HCP) measurements can be used for the qualitative and quantitative analysis of reinforcement corrosion [41,42]. In subsequent studies, these methods can be used to determine the corrosion rate of steel reinforcement in tunnel lining structures and analyze the effect of corrosion on structural performance.

5. Conclusions

This study comprehensively considers the multiple effects caused by steel reinforcement corrosion, including the degradation of the reinforcement’s performance, the loss of an effective concrete cross section, and the deterioration of the bond between the steel reinforcement and the concrete. A finite element model of tunnel lining corrosion deterioration was established to analyze the deformation, damage, internal force redistribution, and crack width variation in the lining structure under the combined influence of the surrounding rock water–soil pressure and steel reinforcement corrosion. The main conclusions of this study are as follows:

• The tunnel lining structure exhibits a trend of deformation, with the vault descending, the invert rising, and the left and right hance shifting outward due to the combined effects of the surrounding soil and water pressure and steel reinforcement corrosion expansion. Corrosion reduces the stiffness of the lining structure, further exacerbating its deformation. For example, at high water pressures, when the corrosion rate is 0%, the vault displacement is 4.305 mm, while when the corrosion rate is 30%, the displacement increases to 7.136 mm, representing an increase of 65.7%.
• The performance of the reinforced concrete lining structure continuously deteriorates, leading to a redistribution of the internal forces. As the corrosion rate increases from 0% to 30%, the axial force in the lining structure slightly increases. Specifically, the axial force in the vault increases from 2042.35 kN to 2207.80 kN, representing the largest increase of 8.10%. The trends in bending moment variation differ across the various parts of the lining, with the bending moments at the vault, hance, and invert decreasing, while those at the spandrel and arch foot increase.
• The damage range of the tunnel lining structure continuously increases as corrosion progresses, with significant differences in the damage between the surrounding rock side and the free face side of the lining. The damage at the vault deepens as corrosion develops, suggesting that there is a risk of the lining being penetrated, while the corrosion depths at the spandrel and arch foot remain relatively small. Similarly, the maximum crack width develops most rapidly at the vault. When the corrosion rate reaches 30%, the crack widths at the vault, spandrel, hance, arch foot, and invert are 1.37 mm, 0.89 mm, 0.55 mm, 0.34 mm, and 0.30 mm, respectively.
• Water pressure has a significant impact on the internal forces and crack width of the lining structure. As the water level decreases, both the bending moment and the axial force decrease, while the damage range and crack width of the structure increase. When the corrosion rate is 30%, the crack widths at the vault under high and low water pressure conditions are 1.19 mm and 1.37 mm, respectively, demonstrating an increase of 15.12%.