Characteristics and control techniques of soft rock tunnel lining cracks in high geo-stress environments: Case study of Wushaoling tunnel group

2.2.1 Geological conditions

The topography of the tunnel site area can be described as a mid-high mountain and valley region. The tunnel group is located in the Wushaoling fault-fold zone, which is characterized by a stable strip-like distribution in width. The tunnel group crosses several regional faults, including the Xiaganchaigou-Xindunwan thrust fault (F7), the Shanghuangcaochuan-Hongguangou thrust fault (F6), the Tianhewan thrust fault (F5), and the Miaoergou-Dalong Village North thrust fault (F4). The fault dip angles of these faults range from approximately 55° to 70°. Wushaoling Tunnel 1# has extremely developed fault structures.

According to geological exploration data, the surrounding rocks of the Wushaoling tunnel group are predominantly categorized as Grades V and IV, based on the rock classification regulations in the code “Standard for Engineering Classification of Rock Mass GB/T 50218-2014” [35], as presented in Table 2. Rock mass is primarily classified based on two factors: the qualitative characteristics and basic quality (BQ) of rock mass. Additionally, the modification effects of groundwater, structural planes, and the initial stress state on the BQ of rock mass must be considered. The detailed rock mass classification regulations are listed in Table 3.

The lithologic composition of the tunnel through strata is complex and includes new loess, gravelly soil, cobble soil, pebble soil, sandstone, metamorphic sandstone, slate, phyllite, andesite, and mudstone. Figure 3 shows a cross-section profile of the geological layers intersected by the Wushaoling Tunnel. The multiple lithologic boundary interfaces cause significant changes to the rock phases, thus resulting in well-developed fractures. The integrity of the rock mass is extremely poor owing to the presence of faults and the high degree of weathering. Consequently, the surrounding rocks exhibit a limited self-stabilization capacity.

Figure 3

Cross-section profile of geological layers intersected by Wushaoling Tunnel.

To obtain the geo-stress condition of the Wushaoling tunnel group, geo-stress tests were conducted using the hydraulic fracturing method, which is essentially a two-dimensional method for measuring geo-stress. For the hydraulic fracturing method, high-pressure water was injected into a test section sealed by packers to induce hole wall fracturing. Subsequently, the magnitude and direction of the maximum and minimum principal stresses in the horizontal plane were determined based on the theories of elastic mechanics. The geo-stress test results of one of the boreholes for the Wushaoling tunnel group are presented in Table 4. The surrounding rock parameters obtained by drilling samples reveal that the maximum horizontal principal stress (σ _H) around the tunnel generally ranged from 3.76 to 9.82 MPa, whereas the minimum horizontal principal stress (σ _h) ranged from 2.48 to 3.74 MPa. A comparison of the magnitudes of the three principal stresses indicates that the current stress shows σ _H > σ _h > σ _v (σ _v, the vertical principal stress), thus indicating that the horizontal principal stress is the maximum and the vertical principal stress is the minimum. This suggests that tectonic stress dominates in the Wushaoling tunnel group. Based on measured geo-stress, the current σ _H in the tunnel area lies along the NNE direction.

The deep burial surrounding rock and stress characteristics of the tunnel are shown in Table 5. According to the code “Specifications for Design of Highway Tunnels JTG D70-2014” [36], when R _c/σ _max < 4, it is classified as extremely high geo-stress and 4 < R _c/σ _max < 7 is classified as high geo-stress. For σ _max set at 9.82 MPa, the R _c/σ _max values are as indicated in Table 5. Clearly, in the Triassic system sandstone, mudstone interlayers, structural belt, and other soft and weak rock layers of the tunnel section, the areas were characterized by extremely high geo-stress zone, with clear rheological deformation characteristics observed in the surrounding rock, which is susceptible to severe tunnel deformation. In the Ordovician metamorphic sandstone and slate tunnel sections, where local zones were strongly sericitized and chloritized with phyllite characteristics, the rock was soft and weak, with some sections belonging to high geo-stress areas, and the surrounding rock was primarily characterized by rheological deformation. In the Ordovician andesite basalt tunnel section, the R _c/σ _max ranged between 4 and 7, with local peeling and block dropping possible.

2.2.2 Hydrogeological conditions

The tunnel site area is within the hydrogeological zone of the eastern segment of the Qilian Mountains. The groundwater of the tunnel site can be categorized into two types: Quaternary loose pore water and bedrock fracture water. The former is discovered in the Quaternary cover layers and gravel-pebble layers at the tunnel entrances, whereas the latter is distributed in structural fractures within the bedrock and extensively developed superficial networked weathered fractures. Both groundwater types are replenished by atmospheric precipitation. The annual average precipitation in the tunnel site area is approximately 400 mm. A simple analysis of the groundwater samples obtained from the tunnel site area revealed that the pH ranges from 7.94 to 8.23 and that corrosive CO₂ does not exist. The Wushaoling mountain primarily comprises detrital rocks with extensive weathered and structural fractures. Although the high-altitude bedrock of the mountain receives abundant rainfall and has ample water supply, the presence of deep valleys and the development of surface hydrological networks typically cause groundwater to depart from the fissures, migrate downslope, and discharge into the valleys.

3.1.1 Longitudinal cracks

Cracks that are almost parallel to the longitudinal axis of the tunnel are referred to as longitudinal cracks. These longitudinal cracks are primarily caused by compressive forces on the inner edge of the arch crown and tunnel hance, which results in the squeezing, cracking, and block detachment of the inner concrete lining. Among the different types of cracks, longitudinal cracks pose the highest risk to tunnel structural safety. They can cause minor issues such as arch crown collapse or more severe consequences such as the collapse of the entire tunnel.

3.1.2 Inclined cracks

Inclined cracks are orientated at approximately 45° to the tunnel axis and occur in both the sidewalls and arch section. They typically emerge due to a combination of longitudinal and circumferential forces exerting on the tunnel lining structure. Although inclined cracks are generally less hazardous than longitudinal cracks, they are more problematic than circumferential cracks. Thus, caution should be exercised when focusing on areas where multiple inclined cracks intersect during tunnel damage treatment. This is because the intersection of multiple inclined cracks generally results in the detachment of lining blocks.

3.1.3 Circumferential cracks

Circumferential cracks are almost perpendicular to the tunnel axis. They often occur owing to the uneven settling of the structure and are primarily observed at the junction of intact rock strata and unfavorable geological zones or construction and deformation joints. Compared with the other two crack types, circumferential cracks are less hazardous.

3.1.4 Closed cracks

Closed cracks typically exhibit a form similar to a grid or network and are distributed in a continuous, dense, and relatively regular manner. This type of crack, particularly in the surrounding rock, results in an uneven stress distribution, which exerts higher stresses in the local area of the tunnel lining and causes significant deformation to the surrounding rock mass.

3.3.1 Characteristics of circumferential cracks

The up-line and downline tunnels of the Wushaoling Tunnel had 934 and 566 circumferential cracks, respectively. The stress of the surrounding rocks applied to the tunnel structure near the tunnel entrance differed significantly from that inside the tunnel. Thus, the number of circumferential cracks in the up-line and down-line within different distances from the tunnel entrance were analyzed, as shown in Figure 6.

Figure 6

Statistics on circumferential cracks in the tunnel lining of Wushaoling Tunnel. (a) Up-line. (b) Down-line.

As shown in Figure 6, the number of circumferential cracks in the up-line of the tunnel significantly exceeded that in the down-line. A total of 131 circumferential cracks were observed within the first 500 m from the tunnel entrance of the up-line. This can be attributed to the rock mass in this section, which comprised alluvial gravelly soil with a slightly cohesive silt texture and high clay content. The soil is susceptible to water loss and shrinkage deformation, and thus, the surrounding rocks must be closed promptly, and timely anchorage support must be provided after tunnel completion. The density of the circumferential cracks was the highest within 1,500–2,500 m from the tunnel entrance, which is primarily due to the geological conditions. In this area, the rock strata were of Grade IV, which comprised fragmented mudstone and carbonaceous shale and underwent deformation and damages phenomena such as rock fragmentation and block sliding/falling. Consequently, the lining deformed severely, and dense cracks emerged. The up-line section, which was beyond 2,500 m from the tunnel entrance, exhibited a balanced distribution of circumferential cracks. Meanwhile, the down-line section featured uniformly distributed circumferential cracks, with 40–50 cracks per 500 m. Dense circumferential cracks were only observed within a distance of approximately 500 m from the tunnel exit and 1,500–2,000 m from the tunnel entrance.

To further analyze the spatial distribution of circumferential cracks across the tunnel’s transverse section, the up-line was partitioned into three sections based on mileage to analyze the circumferential crack data. The resultant characteristics of the cross-sectional height distribution for circumferential cracks in the Wushaoling Tunnel are shown in Figure 7.

Figure 7

Characteristics of cross-sectional height distribution for circumferential cracks in Wushaoling Tunnel. (a) Within approximately 500 m from tunnel entrance. (b) Within approximately 1,000–1,500 m from tunnel entrance. (c) Within approximately 1,500–2,000 m from tunnel exit.

As shown in Figure 7, circumferential cracks occurred more frequently near the arch crown within the first 500 m from the tunnel entrance of the up-line, whereas fewer occurrences were observed near the sidewalls. The circumferential cracks were relatively uniformly distributed with respect to the height within 1,000–1,500 m from the tunnel entrance. Meanwhile, within 1,500–2,000 m from the tunnel entrance, the cracks were primarily concentrated near the sidewalls. In terms of the origin of the circumferential cracks, only the closed arch structure was able to withstand high pressures. If no invert exists or if construction quality of the inverted arch is low, then lining structure cannot effectively bear support pressure from the surrounding rock over the arch crown, thereby resulting in overall subsidence. When adjacent sections of the lining experience inconsistent overall settlement, circumferential cracking or even misalignment of the lining can occur.

3.3.2 Characteristics of longitudinal cracks

The up-line and down-line of the Wushaoling Tunnel had 846 and 667 longitudinal cracks, respectively. The number of longitudinal cracks in the up-line and down-line within different distances from the tunnel entrance was analyzed, as shown in Figure 8. The region with the highest number of longitudinal cracks in the up-line was 1,500–2,500 m from the tunnel entrance (369 cracks). In contrast, the down-line exhibited a uniform distribution of longitudinal cracks, with a higher number of longitudinal cracks appearing near the tunnel exit. Within a distance of approximately 500 m from the tunnel exit, 139 longitudinal cracks were observed. Areas with many longitudinal lining cracks exhibited concentration of circumferential cracks. Dense lining cracks were primarily due to severe lining deformation due to complex geological conditions.

Figure 8

Statistics on longitudinal cracks in tunnel lining of Wushaoling Tunnel. (a) Up-line. (b) Down-line.

To further analyze the spatial distribution of longitudinal cracks across the tunnel’s transverse section, the up-line was partitioned into three sections based on mileage, and the longitudinal crack data were analyzed. The resultant characteristics of the cross-sectional height distribution for longitudinal cracks in the Wushaoling Tunnel are shown in Figure 9. Within a distance of approximately 500 m from the tunnel entrance, longitudinal cracks did not exhibit a pronounced concentration in terms of height but appeared in greater quantity at the arch crown. However, within 1,500–2,000 m from the tunnel entrance, longitudinal cracks were primarily concentrated along the tunnel sidewalls, which corresponded to the region with more circumferential cracks. Moreover, longitudinal cracks tend to concentrate in the hance within 1,000–1,500 m from the tunnel exit and measured 5 m in height. Therefore, longitudinal cracks in the tunnel lining primarily occur near the tunnel crown and hance, which is consistent with the findings of the study conducted by Jiang et al. [13] on large deformation of the Jinchuan No. 2 Mine using 3D laser scanning.

Figure 9

Characteristics of cross-sectional height distribution for longitudinal cracks in Wushaoling Tunnel. (a) Within approximately 500 m from tunnel entrance. (b) Within approximately 1,000–1,500 m from tunnel exit. (c) Within approximately 1,500–2,000 m from tunnel entrance.

3.3.3 Characteristics of inclined cracks

The up-line and down-line of the Wushaoling Tunnel had 416 and 304 inclined cracks, respectively. The number of inclined cracks in the up-line and down-line within different distances from the tunnel entrance were analyzed, as shown in Figure 10. The region with the most inclined cracks in the up-line was within 2,000–2,500 m from the tunnel entrance (135 cracks). Meanwhile, the down-line had the most inclined cracks within 2,500–3,500 m from the tunnel entrance (142 cracks). Inclined cracks were primarily observed in the mid-section of the tunnel, with fewer instances near the tunnel entrance and exit.

Figure 10

Statistics on inclined cracks in the tunnel lining of Wushaoling Tunnel. (a) Up-line. (b) Down-line.

To further analyze the spatial distribution of inclined cracks across the tunnel’s transverse section, the up-line was partitioned into three sections based on mileage, and inclined crack data were sorted, as shown in Figure 11. Within 2,000–2,500 m from the tunnel entrance in the up-line, areas with the most inclined cracks were primarily along the tunnel sidewalls at a height of less than 2 m. Within a 3,000–3,500 m from the tunnel entrance in the down-line, inclined cracks were more prevalent near the tunnel arch crown.

Figure 11

Characteristics of cross-sectional height distribution for inclined cracks in Wushaoling Tunnel. (a) Within 2,000–2,500 m from the tunnel entrance. (b) Within 3,000–3,500 m from the tunnel exit.

3.3.4 Long-term development characteristics of tunnel lining cracks

Based on long-term monitoring of the Wushaoling Tunnel, the results of tunnel lining crack statistics from 2017 to 2019 were analyzed, as shown in Figure 12. The number of circumferential cracks decreased annually, which is primarily attributed to effective lining damage management. Meanwhile, the number of longitudinal cracks increased slightly in the down-line in 2018, although a decreasing trend was shown in general. By 2019, the number of longitudinal cracks in the down-line decreased to approximately 400. The increase in the number of longitudinal cracks and inclined cracks in 2018 is attributed to the continuous deformation caused by the creep characteristic of surrounding rock under the high geo-stress conditions and fault structures.

Figure 12

Annual comparison of tunnel lining crack status in Wushaoling Tunnel. (a) Circumferential cracks. (b) Longitudinal cracks. (c) Inclined cracks.

5.1.1 Crack disposal methods

For circumferential and longitudinal cracks in the lining, chiseling a “V”-shaped groove along the crack direction for a long crack is recommended. Next holes must be drilled in the groove, grouting pipes inserted into the holes, and epoxy resin-reinforced cement mortar injected for crack plugging. After the epoxy resin mortar achieves a certain strength, cement-water glass slurry or epoxy resin slurry can be injected into the crack, and the treated crack should be observed regularly during tunnel operation.

For other cracks with a width smaller than 0.3 mm, the surface is primarily sealed, and observation should be performed. For cracks with a width exceeding 0.3 mm, low-pressure injection can be employed for reparation.

5.1.2 Tunnel structure reinforcement treatment measurements

Owing to the high geo-stress environment, the tunnel lining of some sections in the Wushaoling tunnel group was severely fractured. Therefore, structural reinforcement is required after the completion of crack treatment to improve the bearing capacity of the lining structure and prevent the continuous development of cracks. Different reinforcement measures were adopted for different lining structure damages. In the Wushaoling tunnel group, four types of reinforcement measures for the tunnel-lining structure were adopted.

Method 1: Implement W-shaped steel-plate reinforcement

The implement W-shaped steel-plate reinforcement method is suitable when minor lining cracks appear. The secondary lining was strengthened by fixing a W-shaped steel plate, which was employed as a circumferential stress strip measuring 20 cm wide, 5 mm thick, and 1.5 m long, with a longitudinal spacing of 60 cm. For the longitudinal connecting steel strip, a W-shaped steel plate measuring 0.8 m long and 0.2 m wide with a ring spacing of 1.3 m was adopted. In addition to the use of a unique steel adhesive to bond the lining concrete firmly, the arch crown and side wall were securely connected to the lining using an adhesive mold expansion anchor bolt with a diameter of 16 mm and an anchorage length of 200 mm. Additionally, two lock foot anchors, each with a length of 3.5 m and a diameter of 28 mm, were added to the arch foot of the tunnel. Finally, polymer mortar was used to smooth the surface of the steel-strip-reinforcement lining.

Method 2: Grouting filling of cavity behind lining

The grouting filling method is suitable when the area and height of the cavity behind the lining are large. For the case where a cavity or an uncompacted area exists behind the lining, holes with a diameter of 50 mm were drilled on the lining within the cavity range and arranged 2 m apart in a rectangular shape. The hole depth was determined by drilling through the lining until the cavity position. When water exists in the cavity behind the hollow lining, the LB-composite (cement based) grouting material should be grouted into the lining using a steel pipe with a diameter of 50 mm. Moreover, piercing the waterproof plate should be avoided when drilling, and waterproof measures should be conducted after grouting.

Grouting was commenced from the side hole at an operating pressure not exceeding 0.1 MPa. When slurry flowed out of the middle hole, it was injected back into the middle hole, and the working pressure was maintained at 0.1 MPa until slurry flowed out of the outlet hole.

Method 3: Using bolt-anchored wire-mesh-based steel-fiber-reinforced shotcrete lining

The section with a slightly smaller lining thickness and intermediate crack damage was strengthened via a treatment method using a bolt-anchored wire-mesh-based steel-fiber-reinforced shotcrete lining, which is shown in Figure 21. For this treatment method, the following rules should be followed.

Figure 21

The treatment method using bolt-anchored wire-mesh-based steel-fiber-reinforced shotcrete lining.

The original secondary lining’s cracks should be repaired, the voids behind the lining backfilled, and the principle of first treating and then reinforcing followed. For local components of the side wall that are extremely thin and thus susceptible to splitting, local replacement should be performed.

The mechanical chiseling anchorage zone concrete lining was brushed or sprayed with a 2 mm interface agent that satisfies type-I index requirements. To enhance the structural integrity and stability of the reinforced lining, a bonded bolt with an expanded bottom was used for anchorage. The anchor bolt was made of stainless steel and featured a nominal diameter of 12 mm. To ensure effective anchorage, the embedment depth was ensured to be at least 100 mm. Additionally, the plum-blossom layout with an anchor distance of 60 cm × 60 cm was adopted to uniformly distribute the anchorage load and minimize stress concentration.

After the anchor bolt installation was completed and had successfully passed the acceptance criteria, a φ12 steel mesh was suspended, with a spacing of 20 cm × 20 cm between each grid. The steel mesh and anchor bolt were cross-bonded with iron wire or spot-welded securely in place. To ensure stability during the lapping process, a U-shaped fixture was set in the lap area to provide a secure fixation.

C30 steel fiber-reinforced concrete (under a standard 28-day curing period with a compressive strength of 30 MPa) was used to achieve a 10 cm-thick spray layer. The volume fraction of steel fiber in the steel fiber-reinforced concrete was 1.0%.

Finally, polymer mortar was used to flatten the surface from the side wall to the hance, and a tunnel fire retardant coating was sprayed on the entire section.

Method 4: Treatment method using lining steel rail and hanging net sprayed concrete lining

For the section with the thin lining thickness, although the cracking damage is serious under the condition of high ground stress, the structure has not lost the bearing capacity, which can be reinforced by steel rail and hanging net sprayed concrete lining. The profile of the lining reinforced by this treatment method is shown in Figure 22.

Figure 22

Treatment method using lining steel rail and hanging net sprayed concrete lining.

The treatment method should meet the following parameter design requirements.

The rail was configured with a longitudinal spacing of 60 cm and was reliably fixed with the existing lining using a φ16U stirrup. The steel rail was made of 55Q15 grade light steel (with a tensile strength of at least 685 MPa), which satisfies the requirements of the code “Hot-rolled light rails GB/T 11264-2012” [41]. The arch foot of the rail was firmly connected to the existing invert by anchorage steel bars. Additionally, it was anchored by a lock foot anchor pipe measuring 3 m in length, 60 mm in diameter, and 5 mm in thickness. Longitudinal connecting bars with a diameter of 22 mm were set between the rails at a circumferential spacing of 1 m. C30 steel fiber-reinforced concrete was sprayed via wet spraying to achieve a spray layer measuring 12 cm thick.

5.2.1 Numerical model

A numerical model was established using the Midas/GTS NX program to analyze the lining crack treatment effect. The Wushaoling tunnel group was modeled as a single-line double-hole tunnel, and the distance between the left and right tunnels was set as 42 m. The interaction between the tunnels was addressed. Considering the complex conditions in the actual project, the section and stratum of the Wushaoling tunnel were simplified in the numerical study.

The buried depth of the tunnel at the calculated section was approximately 130 m. Based on the tunnel excavation’s influence range, the finite element model was designed to measure 120 and 170 m in the horizontal and vertical directions [42], respectively. A self-weight stress field was imposed on the basic model of the Wushaoling tunnel. When tectonic stress was not considered, the boundary conditions of the model were as follows: the vertical boundary constrains the horizontal displacement, the bottom surface constrains the horizontal and vertical displacement, and the upper surface boundary is the free boundary. These geotechnical materials in the numerical model were simulated using quadrilateral and triangular mixed meshes, with 5,264 nodes and 5,231 elements. Additionally, a local refined mesh was adopted in the calculation area of interest. The calculation model of Method 4 is shown in Figure 23.

Figure 23

Schematic diagram of numerical model (Method 4).

In the numerical model, the anchor bolt reinforcement for improving the mechanical properties of the tunnel lining structure was comprehensively considered [43]. Based on the literature, the elastic modulus of a lining subjected to anchor bolt reinforcement increased by 20% [29,44]. Additionally, the thickness of the lining was increased to simulate the spray layer thickness of the steel fiber concrete. The retaining structure of the tunnel was regarded as an elastic material. The nonvolume, linear elastic beam elements, which can provide bending resistance, were used to simulate the behavior of the primary and secondary linings of the tunnel. The primary and secondary linings of the tunnel measured 0.24 and 0.45 m thick, respectively, and were composed of C25 and C30 concrete, respectively [17]. The embedded truss element was set to simulate the anchor bolts in the initial support of the tunnel. A circular section was adopted for the element section, and the axial stiffness of the latter was equivalent to that of the original anchor bolt of a steel pipe with a diameter of 42 mm and a thickness of 3.25 mm. The mechanical parameters of the supporting structure in the model are listed in Table 6. In the numerical model of Method 4, the light rail was simulated using a beam element, and the elastic constitutive model was adopted. The elastic modulus and Poisson’s ratio were 200 GPa and 0.3, respectively. The standard size of the No. 15 light rail was adopted for the rail section. Based on the example of SVb lining, this study examined the reinforcement mechanism of rail-lining reinforcement treatments. The surrounding-rock grade and mechanical parameters are listed in Table 7.

To verify the accuracy of the finite element model and the selected parameters, the calculated values of both treatment methods were compared with the measured values obtained from the treated tunnel section. During the operation of the Wushaoling tunnel group from 2013 to 2017, structural damages such as cracking and pavement heave occurred. However, monitoring data were not recorded in this period, affecting the assessment of the structural health of the tunnel. Therefore, during the tunnel reinforcement projects carried out from 2017 to 2018, the tunnel floor heave was monitored using fiber Bragg grating settlement meters. Based on different reinforcement treatment methods, monitoring results from section XK1866 + 280 to XK1866 + 645 of the down-line of Wushaoling Tunnel 1# (Method 3) and section SK1878 + 393 to SK1878 + 720 of the up-line of Wushaoling Tunnel 2# (Method 4) were selected for comparative analysis (Figure 24). As shown in the figure, the bottom heave values of the tunnel resulting from Methods 3 and 4 did not exceed 5 mm, indicating effective deformation control. Additionally, the tunnel floor heaves in treatment Methods 3 and 4 obtained using finite element method (FEM) were compared. Figure 24 indicates that the measured values of the tunnel floor heave are in good agreement with the calculated values. Based on the above analysis, the accuracy of the finite element model in predicting the mechanical behavior of the treated tunnel was validated.

Figure 24

Comparison between measured and calculated values of tunnel floor heave.

5.2.2 Analysis results

5.2.2.1 Displacement analysis

Figure 25 shows the displacement contours yielded by Methods 3 and 4. As shown in Figure 24, the vertical deformation of the secondary lining structure of the tunnel was effectively controlled. After using treatment Methods 3 and 4 to reinforce the lining, the maximum values of the arch-crown settlement and tunnel floor heave by the secondary lining structure decreased as compared with those before the treatment. Among them, the values of the arch-crown settlement and tunnel floor heave in Method 3 were 1.5 and 4.3 mm, respectively. Owing to the overall reinforcement of the secondary lining structure and the sprayed fiber concrete, the vertical deformation of the tunnel was controlled more effectively compared with the case before the reinforcement. For Method 4, the values of the arch-crown settlement and tunnel floor heave were 1.3 and 4.2 mm, respectively. The treatment via steel rail-lining reinforcement effectively restrained the vertical deformation of the secondary lining structure.

Figure 25

Displacement contour for Methods 3 and 4. (a) Vertical displacement contour for Method 3. (b) Horizontal displacement contour for Method 3. (c) Vertical displacement contour for Method 4. (d) Horizontal displacement contour for Method 4.

The horizontal displacement of the secondary lining caused by tunnel excavation primarily occurred at the side wall and hance of the tunnel. After Method 3 was adopted to reinforce the secondary lining structure, the horizontal displacement at the hance of the secondary lining was 4.9 mm, which was approximately 20.7 mm lower than the horizontal displacement before reinforcement. After the secondary lining structure was reinforced via Method 4, the horizontal displacement at the hance was 5.5 mm, i.e., approximately 20.1 mm lower than the horizontal displacement before reinforcement, which effectively limited the lateral deformation of the tunnel under high geo-stress.

5.2.2.2 Stress analysis

Figure 26 shows the stress contours yielded by Methods 3 and 4. When the steel rail lining reinforcement was adopted for the lining structure, the maximum vertical tensile stress of the secondary lining structure appeared at the hance position. The vertical tensile stresses at the hance for Methods 3 and 4 were approximately 1.4 and 1.6 MPa, respectively, and longitudinal tensile cracks generated easily in the tunnel. The stress mode of the original lining structure improved by adopting the steel rail lining to reinforce the upper section of the tunnel, and the tensile stress of the tunnel hance was shared by the steel rail.

Figure 26

Stress contours for Methods 3 and 4. (a) Vertical stress contour for Method 3. (b) Horizontal stress contour for Method 3. (c) Vertical stress contour for Method 4. (d) Horizontal stress contour for Method 4.

The horizontal stress of the tunnel lining structure reduced significantly, and the internal force in the lining was more reasonable. Because of the treatment, the maximum horizontal compressive stress was transferred from the arch crown to the arch foot. The minimum horizontal tensile stress yielded by Method 3 was 0.70 MPa, which appeared at the hance of the tunnel, whereas the maximum horizontal compressive stress was 10.9 MPa, which appeared in a small area at the arch foot. The horizontal stress of the secondary lining was within the strength of the concrete material presented in the specifications after the treatment using bolt-anchored wire-mesh-based steel-fiber-reinforced shotcrete lining. In Method 4, the upper stress of the tunnel-lining structure improved owing to the steel rail-lining reinforcement. The maximum compressive stress of the tunnel crown reduced from 35 to 12.5 MPa at the arch foot, which effectively overcame the low bearing capacity of the tunnel structure.

5.2.2.3 Comparative analysis of treatment methods

To further analyze the treatment and reinforcement effects of Methods 3 and 4, several critical parameters of the secondary lining structure were analyzed. Subsequently, the numerical calculation results of Methods 3 and 4, as well as the conditions before treatment, were compared. The comparison diagram of the treatment method is shown in Figure 27.

Figure 27

Comparison of different treatment measures (S _{arch crown} is the arch crown settlement; S _{tunnel floor} is the tunnel floor heave; S _h-hance is the horizontal displacement at hance; σ _h-t-max is the maximum horizontal tensile stress; σ _h-c-max is the maximum horizontal compressive stress; σ _v-t-max is the maximum vertical tensile stress; σ _v-c-max is the maximum vertical compressive stress.).

As shown in Figure 27, Methods 3 and 4 significantly affected the treatment of the tunnel-lining structure, which rendered the stress distribution along the tunnel lining more reasonably, thus enabling deformation and stress reductions by 80–90% and 64–95%, respectively. In particular, for the tunnel floor heave control of the secondary lining structure, the tunnel floor heave measured as high as 48.7 mm before treatment, whereas the tunnel floor heave was only 4.2 mm high after treatment using Method 4.

Compared with the conditions before and after treatment, the difference in the treatment effect between Methods 3 and 4 after treatment was slight. At the hance of the tunnel, the maximum horizontal displacement yielded by Method 4 was 5.5 mm, whereas that yielded by Method 3 was only 4.9 mm. Method 3 reduced the maximum horizontal displacement by 10.9% compared with Method 4. The two methods exerted similar limiting effects on the arch crown settlement and tunnel floor heave, with differences of approximately 0.2 and 0.1 mm, respectively. Compared with Method 3, Method 4 significantly reduced the lining stress. The maximum vertical compressive stress yielded by Method 4 was only 1.3 MPa, which was 43% lower than 2.3 MPa yielded by Method 3.