Mechanical response of large-span variable-cross-section tunnels: insights from numerical simulation and field monitoring

1 Introduction

Global transportation infrastructure in mountainous regions necessitates large-span variable-cross-section tunnels. These structures are essential for expressway interchanges and complex terrain engineering. Cross-section variations and complex stress redistribution increase tunnel vulnerability (Zhang and He, 2026; Li et al., 2023). Stress concentrations during excavation trigger plastic deformation and crack propagation. Loosening zone evolution also occurs under these conditions. Limestone strata are prevalent across South and Southwest China. This rock type displays brittle failure behavior and well-developed structural planes. Stability control for large-span variable-cross-section limestone tunnels presents a major technical bottleneck. This constraint affects the safety and efficiency of construction projects (Jing et al., 1999).

Surrounding rock pressure, displacement, and loosening zone distribution serve as core indicators for stability evaluation and support design. Inadequate coordination between support parameters and deformation laws causes rock instability or collapse. Such failures lead to substantial economic losses and construction safety risks (Wang et al., 2025; Li et al., 2021). Therefore, comprehensive investigations of rock pressure, displacement, and loosening zones offer significant theoretical and engineering value. Displacement sensitivity analysis at critical positions under various excavation conditions is equally essential. This research ensures the structural integrity of large-span variable-cross-section limestone tunnels.

Surrounding rock deformation and loosening zone development reflect stress redistribution after tunnel excavation. Multiple factors influence these evolutionary processes, including rock mass properties, tunnel span, excavation length, and construction method (Shen and Chen, 2015; Lai et al., 2009). Extensive research has been conducted on tunnel surrounding rock deformation and loosening zones over recent decades. Ma et al. (2025) statistically analyzed rock pressure distributions in large-section high-speed railway tunnels. This analysis identified stress concentration patterns at key positions. Yu et al. (2018) conducted in-situ pressure tests for mechanically constructed large-section tunnels. Their research provided a basis for support parameter optimization.

Jing et al. (1999) performed field measurements of loosening zones in deep mine roadways and proposed corresponding control technologies. Huang et al. (2016) investigated rock loosening zone development through field tests and theoretical analysis and established a theoretical calculation method for loosening zone thickness. Xiao et al. (2026) analyzed loosening zone distribution in deep tunnels using acoustic detection and numerical simulation. They verified the rationality of the testing method. Discrete element and finite element methods are widely used to analyze the influence of excavation parameters on surrounding rock deformation and identify the sensitive positions under different engineering conditions (Jing et al., 2020; Zhao and Wu, 2024). Studies have also clarified a correlation between loosening zone thickness and surrounding rock deformation. The loosening zone serves as the boundary for plastic zone (Yang et al., 2021; Liu et al., 2022). These collective findings provide a theoretical foundation for the stability evaluation of conventional uniform-cross-section tunnels.

However, significant limitations persist regarding large-span variable-cross-section limestone tunnels:

• Existing studies primarily focus on uniform-cross-section tunnels. Systematic studies on pressure-displacement evolution in large-span variable-cross-section tunnels remain limited. Comparative data for three-lane and four-lane sections under identical geological conditions are scarce. Brittle limestone strata specifically lack comprehensive field-measured support (Terron-Almenara et al., 2023; Luo et al., 2020; Yan et al., 2017; Xue, 2012).
• Studies often overlook the spatial inconsistency between maximum surrounding rock pressure and maximum displacement. This phenomenon occurs in large-section tunnels but lacks systematic documentation. Existing engineering literature provides insufficient analysis of this specific behavior (Xie et al., 2025; Wang, 2019; Yang, 2013; Xia et al., 2010; Dong, 1980).
• Specific impacts of tunnel span and excavation step lengths on the crown and inverted arch require more research. This knowledge gap hinders the development of targeted construction control measures (Gai et al., 2026; Lin, 2025; Zhang et al., 2024; Wang et al., 2018a).

Research gaps result in insufficient theoretical and practical data support for surrounding rock stability control. This limitation specifically affects large-span variable-cross-section limestone tunnels.

The Qingshan Tunnel on the Ren-Zun Expressway served as a representative variable-cross-section tunnel case. Both three-lane and four-lane sections are located within Grade III limestone surrounding rock stratum. These sections share a buried depth of 220 m and consistent geological conditions, as shown in Tables 1, 2. Field measurements and numerical simulations were performed on the Qingshan Tunnel to address the identified research gaps.

TABLE 1. Physical and mechanical properties of Grade-III surrounding rock.

LS, limestone; ρ = Density; Rc = Uniaxial compressive strength; BQ, Rock mass quality index;

K = bulk modulus; G = shear modulus; ν = Poisson’s ratio; φ = Internal friction angle; c = Cohesion.

TABLE 2. Mechanical parameters of rock joints.

Kn = Normal stiffness; Ks = Shear stiffness; φ = Internal friction angle; σt = Tensile strength.

Firstly, the surrounding rock pressure, peripheral convergence, vault settlement and loose zone thickness were monitored during the construction of three-lane and four-lane tunnel sections. A 3DEC discrete element numerical model was subsequently established to evaluate the displacement of key monitoring points and the sensitivity of plastic zones under different excavation spans and step lengths. The numerical simulation results were compared with the field measured data to analyze their evolution and distribution characteristics. The novelty of this paper lies in the quantitative comparison between the three-lane and four-lane sections and the identification of the influence of excavation span on the deformation and loose zone of surrounding rock. These results aimed to expand the field-measured database for large-span variable-cross-section limestone tunnels and provide reliable data support for stability evaluation in similar tunnel projects.

2 Engineering overview

The Qingshan Tunnel is located on the Zunyi–Renhuai section in Guizhou Province. The tunnel traverses soluble rock formations. Bedrock consists of limestone, siltstone, and marl. The left tunnel spans from ZK51 + 092 to ZK53 + 510. This segment has a total length of 2418 m. The right tunnel extends from K51 + 072 to K53 + 499. The total length of the right tunnel is 2427 m. The maximum buried depth is 225 m. A 399-m segment (K53 + 100 to K53 + 499) at the Zunyi end of the right tunnel features a four-lane cross-section. This design fulfills exit interchange layout requirements. All other sections employ a three-lane cross-section. Figure 1 illustrates the location and general layout of the tunnel. The surrounding is classified as Grade III, IV, and V (Ministry of Transport of the People’s Republic of China, 2018). The selected three-lane and four-lane transition sections consist of Grade III surrounding rock at a buried depth of 220 m. Table 1 provides the physical and mechanical parameters of Grade III surrounding rock. The inner radii of the three-lane and four-lane sections are 8.745 m and 11.581 m, respectively.

3 In-situ measurement scheme

3.1 Monitoring contents and sections

Monitoring during tunnel excavation focused on surrounding rock pressure, deformation (rock convergence and crown settlement), and loosening zone thickness. These parameters were measured using total stations, pressure cells, and ultrasonic testers. The objective was to characterize the development of stress, displacement, and the loosening zone within the surrounding rock during variable cross-section construction.

Two typical monitoring sections were established in the right tunnel. These sections were located within 40 m of the variable-cross-section position at K53 + 100. Table 3 lists the detailed specifications for these sections. Figure 2 illustrates the layout of monitoring sections.

TABLE 3. Field test locations for the surrounding rock loosening zone.

3.2 Installation and monitoring of surrounding rock pressure sensors

Pressure cells were installed between the surrounding rock and the primary support. These instruments tracked pressure variations throughout the construction phase. Sensors were installed at the vault, haunch and sidewall foot of the tunnel cross-section. Surrounding rock pressure was measured using equipment manufactured by Changzhou Jintan Tengfei Engineering Instrument Co., Ltd. The sensor adopted was a vibrating wire pressure cell (TYJ-2020) with a measuring range of 0–1.0 MPa and an accuracy of ±0.5% FS. Figure 3 depicts the specific arrangement of these measuring elements.

On-site installation utilized welding techniques. Pressure cells were mounted on smoothed rock surfaces. Steel bars were welded between the sensor edge and the steel arch of the primary support. This configuration ensured continuous contact. An intelligent data logger recorded the baseline readings immediately after installation. Subsequent measurements were performed every 2 days until the surrounding rock became stable. Figures 4–6 illustrate the on-site installation process.

3.3 Rock convergence measurement

Rock convergence measurements were performed at each monitoring section to investigate the time-dependent deformation behavior at the variable cross-section. Measuring points were embedded approximately 0.5–1.0 m from the excavation face. These points received protection prior to blasting. Two measuring lines, an upper line (DE) and a lower line (FG), were established. As shown in Figure 3 at lines DE and FG. The total station used was model NTS-362R10, with an angular accuracy of 1″and a distance accuracy of 1 mm + 1 ppm. The monitoring frequency is listed in Table 3.

The spatial distance between two rock convergence points was measured using the side-side function of a total station. Rock convergence was calculated as the difference between the current and previous measurements. Initial measurements occurred within 12 h of excavation. Subsequent monitoring followed the frequency outlined in Table 4 (Ministry of Transport of the People’s Republic of China, 2020).

TABLE 4. Monitoring frequency for rock convergence and crown settlement.

3.4 Crown settlement measurement

Crown settlement measurements were conducted at the same two sections. The measurement frequency remained identical to that of rock convergence. Three settlement monitoring points (A, B, C) were installed at the tunnel crown and adjacent areas. Installation occurred immediately following excavation. As shown in Figure 3 at points A, B and C.

Stable reference points were established inside and outside the tunnel. These points served as backsights for cross-verification of the data. Individual displacement measurements for points A, B, and C yielded settlement values and rates. Time-history curves for settlement and settlement rate were generated. These curves enabled the assessment of surrounding rock stability.

3.5 Loosening zone measurement

Loosening zone thickness was determined using the acoustic wave detection method. An RSM–SYS5 ultrasonic detector was employed for these measurements. Five boreholes were drilled at each testing section. Preliminary trial testing established a borehole depth of 3 m.

Boreholes were cleaned with water following drilling. This process removed crushed stones and rock powder. The ultrasonic probe was positioned at the borehole base. The boreholes were filled with water. An air bag was used to seal the opening. The probe was retracted gradually during the test. Measuring points were spaced at 20 cm intervals (Wang, 2019; Xia et al., 2010; Dong, 1980). Figure 7 illustrates the single-hole test schematic. Figure 8 illustrates the borehole arrangement and the single-hole ultrasonic testing protocol.

Sensors were installed before shotcrete application, and the installation time was strictly controlled within 2 h after excavation. The on-site testing scenario for the loose area is shown in Figure 9.

4 On-site measurement data and analysis

4.1 Field measured data

4.1.1 Surrounding rock pressure

Figures 10, 11 present the measured surrounding rock pressure before lower bench excavation for both sections.

Surrounding rock pressure increased rapidly during the first 6 days of excavation. All monitoring points reached a stable state following this initial period. Stress levels were highest at the spandrels and lowest at the side walls. Monitoring Section I showed a pressure difference of approximately 0.02 MPa among the monitoring points. Maximum pressures occurred at the left and right spandrels. These values reached 0.08 MPa and 0.07 MPa, respectively. Monitoring Section II recorded a maximum pressure of 0.36 MPa at the left spandrel. Pressures at the remaining points were significantly lower. This distribution pattern is consistent with established research findings (Wang, 2019; Xia et al., 2010).

The final contact pressure between the surrounding rock and the primary support measured at Monitoring Section I is 0.32 MPa, and that at Monitoring Section II is 0.69 MPa. Due to the influence of on-site construction factors, detailed data during the construction stage from lower bench excavation to invert completion were not obtained.

4.1.2 Rock convergence results

Field measurements provided the time-dependent characteristics of rock convergence in the Qingshan Tunnel. Figures 12, 13 display these monitoring results.

The upper measuring line (DE) exhibited the highest cumulative rock convergence. Monitoring Section I recorded a maximum cumulative displacement of 11.32 mm for line DE. The maximum deformation rate for this line reached 1.41 mm/d. The lower line FG in Section I showed a cumulative convergence of ∼3.80 mm. The final deformation rate for line FG remained below 0.20 mm/d. Monitoring Section II exhibited a maximum cumulative displacement of 15.63 mm for line DE. The peak deformation rate was 1.60 mm/d. Line FG in Section II reached a cumulative displacement of 5.36 mm. Its maximum deformation rate was 1.47 mm/d. The cumulative convergence for line DE in the four-lane section was 1.38 times that in the three-lane section. The cumulative convergence for line FG in the four-lane section was 1.41 times that in the three-lane section.

The rock convergence curves for the upper measuring line exhibited a stepwise evolution. This process consists of four distinct stages:

• Rapid growth stage: This stage occurred during the first 5 days. The average deformation rate reached approximately 1.00 mm/d.
• Approaching stabilization stage: This period lasted from day 5 to day 20. The average deformation rate decreased to less than 0.50 mm/d.
• Secondary growth stage: Lower bench excavation caused secondary disturbance to the surrounding rock. This event led to a noticeable increase in convergence. This stage lasted three to 4 days. Deformation rate generally remained below 1.00 mm/d.
• Re-stabilization stage: The effect of lower bench excavation disturbance dissipated rapidly. Convergence deformation stabilized again. The final deformation rate remained below 0.20 mm/d.

The lower measuring line exhibited an approximately arc-shaped deformation pattern. This behavior could be characterized by two main stages:

• Rapid growth stage: Significant surrounding rock deformation occurred during the initial 5 days.
• Gradual stabilization stage: Rock convergence gradually stabilized. The average change rate remained below 0.20 mm/d.

Comprehensive analysis showed that upper bench excavation required approximately 20 days. Deformation was significant during the first 5 days. The average daily convergence rate was 1.00 mm/d. Subsequent convergence values increased slowly. Lower bench excavation commenced on the 20th day. This activity caused secondary disturbance to the surrounding rock. Measuring line DE recorded a corresponding increase in deformation. Stability returned rapidly after this event.

Overall deformation rate curve followed a sawtooth pattern. The upper measuring line DE exhibited an inverted L-shaped curve with stepwise characteristics. The lower measuring line FG demonstrated an arc-shaped curve.

Figures 11, 12 indicated consistent trends between displacement and pressure. Both parameters first increased rapidly and then stabilized. The rapid growth period for pressure lasted approximately 6 days. Rock convergence showed a rapid growth period of approximately 5 days. These results demonstrated strong temporal synchronization. The one-day difference was mainly attributed to the two-day monitoring interval for pressure measurements. The actual rapid growth period likely approached 5 days.

4.1.3 Crown settlement

Figures 14, 15 present the crown settlement and settlement rate data for the two monitoring sections. Monitoring point B at section K53 + 090 reached a maximum cumulative crown settlement of 19.2 mm. All final deformation rates remained below 0.2 mm/d. The specific maximum rate was 0.15 mm/d. Monitoring point B at section K53 + 120 recorded a maximum cumulative settlement of 34.2 mm. The final deformation rate for this section was 0.82 mm/d.

Analysis of cumulative crown settlement and deformation rates indicated significant spatial variations. Crown settlement in the four-lane monitoring section was significantly larger than that in the three-lane section. Both sections achieved stability after approximately 1 month of monitoring. Cumulative crown settlement followed a stepwise increasing trend over time. Deformation rate curves exhibited a zigzag pattern throughout the monitoring period.

First half of vault settlement trend consistent with pressure variation in Figure 10. Settlement in the four-lane section reached 1.78 times the value observed in the three-lane section. The relationship between deformation rate and monitoring time defines three distinct stages of crown settlement:

• Rapid deformation stage: The deformation rate reached a maximum of 2.80 mm/d. Initial surrounding rock disturbance from upper bench excavation and subsequent stress release drove this acceleration. Secondary and tertiary disturbances from middle and lower bench excavation further increased crown settlement. This stage typically persisted for 5 days after each excavation disturbance.
• Slow deformation stage: The deformation rate decreased significantly during this period. Continuous deformation occurred at rates below 1.20 mm/d. These intervals occurred between successive disturbances and lasted approximately 1 week.
• Deformation convergence stage: The crown settlement rate dropped below 0.15 mm/d. The surrounding rock reached a stable state. Inverted arch excavation and primary support closure caused minor settlement increase. The four-lane section experienced a brief rate increase to 1.20 mm/d during these activities. The formation of a closed ring by the primary support enhanced the overall loadbearing capacity. Consequently, the deformation rate fluctuated and stabilized. Since deformation rates in the four-lane section reached stability 4 days after the recorded period, graphical constraints prevented the inclusion of these final data points.

After tunnel excavation, stress redistribution occurs in the surrounding rock. The haunches are the main load-bearing points of the pressure arch, bearing most of the load from the overlying surrounding rock; while the vault is located at the neutral axis of the pressure arch, where the radial stress is most fully released, resulting in the minimum compressive stress. Meanwhile, the rock mass above the vault subsides downward under the action of gravity. Without lateral confinement, its displacement develops most freely, leading to the maximum settlement.

4.1.4 Loose zone

Figure 15 displays the surrounding rock wave velocity results for the three-lane and four-lane sections. Previous studies (Xie et al., 2025; Yang, 2013) and field tests have established specific thresholds for these measurements. A measured wave velocity below 3.0 km/s indicates the loosening zone. Velocities exceeding 3.0 km/s indicate a transitional zone to intact rock.

Wave velocity increased with borehole depth in the three-lane section (Figure 16a). This section consisted of Grade III surrounding rock. Intact rock levels occurred at a depth of 1.40 m for boreholes 3 and 4 at the wall foot. Boreholes 1, 2, and 5 reached this level at a depth of 1.60 m. Borehole 5 exhibited a slightly thicker loosening zone. Velocity differences between boreholes remained minimal. The loosening zone thickness measured approximately 1.40 m at the wall foot and 1.60 m at the crown and spandrels.

Figure 16b presents the data for the four-lane section. Wave velocity reached stability at different depths. Boreholes 1 and 2 stabilized at 2.0 m. Borehole 5 reached stability at 2.20 m. Boreholes 3 and 4 stabilized at 1.80 m. The loosening zone thickness varied by position. The crown exhibited the greatest thickness, followed by the spandrel. The wall foot showed the smallest thickness. Stabilized wave velocities also differed between boreholes. The arch springing generally recorded lower values. Table 5 summarizes the inferred loosening zone thicknesses for the three-lane and four-lane sections.

TABLE 5. Inferred loosening zone thicknesses from ultrasonic testing.

The inferred data demonstrated spatial variations in loosening zone thickness within each section. The three-lane section exhibited a thickness of 1.60 m at the crown and spandrels. The wall foot in this section recorded a thickness of 1.40 m. The loosening zone thickness in the four-lane section reached a minimum of 1.8 m at the wall foot. The crown exhibited a maximum thickness of 2.2 m. Spandrel measurements indicated intermediate values.

The loosening zone thickness correlated directly with rock convergence and crown settlement. The maximum deformation occurred at the crown. This location corresponded to the greatest loosening zone thickness. Moderate deformation and thickness occurred at the spandrels. Both deformation and loosening zone thickness were minimal for the wall foot.

The four-lane section exhibited a significantly thicker loosening zone than the three-lane section. The thickness ratios reached 1.38 at the crown, 1.25 at the spandrel, and 1.29 at the wall foot.

4.2 Numerical simulation and sensitivity analysis

The sensitivity value of surrounding rock displacement or plastic zone defined in this paper refers to the maximum difference in surrounding rock change effects induced by the construction of three-lane and four-lane cross-sections under specific excavation conditions.

During tunnel excavation, different factors exert varying degrees of influence on surrounding rock displacement and plastic zone distribution. In this study, the 3DEC discrete element analysis software was employed to obtain the displacement or plastic zone at typical positions including the vault, haunch, arch foot and invert by varying the tunnel span and excavation step length while controlling all other variables. The sensitivity of surrounding rock displacement or plastic zone to tunnel span variation was then calculated. A larger sensitivity value indicates that the corresponding position requires more attention.

4.2.1 Sensitivity analysis of surrounding rock displacement

• 1. Numerical Calculation Model

A discrete element model was established using 3DEC software, with a tunnel overburden depth of 220 m. The cross-sectional dimensions adopted the actual three-lane and four-lane cross-sections from the engineering project. Parameters such as in-situ stress, lateral pressure coefficient and Poisson’s ratio were kept constant. The rock mass integrity coefficient K _*v* was adjusted by varying the joint spacing and increasing the joint density.

According to existing research (Li et al., 2026; He et al., 2025; Sun et al., 2021), the influence range of tunnel excavation on the surrounding rock mass is approximately 3–5 times the tunnel diameter. The study section covers about 50 m before and after the variable cross-section. The excavation width of the three-lane section is approximately 17 m, and that of the four-lane section is approximately 21 m. Therefore, the left and right boundaries of the model were set 80 m away from the tunnel centerline, the lower boundary 50 m below the tunnel invert, and the upper boundary 220 m above the vault. The overall model dimensions were adjusted according to the actual excavation width.

A constant excavation step length of 40 m was adopted, and the cross-section at Y = 5 in the model was designated as the monitoring section. The tunnel was excavated using the three-bench method. Using the single-variable control method (where all other variables were set to their minimum values), the influence of variations in surrounding rock parameters on rock mass deformation was simulated at an excavation step length of 40 m, thereby determining the magnitude of sensitivity of surrounding rock parameters to excavation step length.

The excavation sequence was as follows: the upper bench was excavated first, and after advancing 10 m, excavation of the middle bench commenced with an advance per cycle of 2 m. The model is shown in Figure 17.

• 2. Selection of Surrounding Rock Parameters

The variable cross-section section of this tunnel is located in Grade III surrounding rock, with a rock mass integrity index (K _*v*) of 0.42 and an internal friction angle of 37°.

The Mohr-Coulomb constitutive model was adopted in the numerical simulation of this study. The parameters of the surrounding rock and joint planes in the variable cross-section section were mainly obtained from the geological investigation report and Ministry of Transport of the People’s Republic of China (2018). The calculation parameters are shown in Tables 1, 2, 6. The three-dimensional geological model was partitioned by tunnel joints using the built-in modeling commands of the 3DEC software. Joint sets with specified dip angles and dip directions were defined to enable the rock mass to undergo sliding along the predefined joint structural planes.

• 3. Stress Release Coefficient and Lateral Pressure Coefficient

According to Ministry of Transport of the People’s Republic of China (2018) and considering construction safety, the stress release coefficient was set to 0.8 in this simulation. The lateral pressure coefficient in the numerical simulation was determined based on the Poisson’s ratio of the surrounding rock, with a value of 0.26.

• 4. Model Boundary Conditions

The model boundaries were set mainly through two aspects: stress boundary conditions and displacement boundary conditions. The stress boundary conditions were defined using the BOUNDARY command in 3DEC. For the displacement boundary conditions, the left and right boundaries of the model were constrained in the X-direction, the front and rear boundaries were constrained in the Y-direction, the bottom boundary was constrained in the Z-direction, and the top boundary was set as a free surface.

• 5. Analysis of Displacement Simulation Results

TABLE 6. Mechanical parameters of primary support of qingshan tunnel.

Numerical simulations were conducted to evaluate the effects of span and excavation step length on surrounding rock deformation. Figure 18 shows the deformation contours for both sections at a 50 m step length (A 50 m excavation step length was adopted in the actual project). Vertical deformation and horizontal convergence varied significantly with changes in step length. Deformation contours for 50–70 m step lengths were omitted due to space constraints.

Figure 18 revealed that surrounding rock deformation in the four-lane section was significantly larger than that in the three-lane section. Displacement data for both tunnel configurations under different excavation step lengths were extracted from the 3DEC model for comparative analysis. Tables 7–10 present post-excavation displacements and sensitivity values at critical monitoring points, including crown, spandrel, arch springing, and inverted arch. The data encompass various tunnel spans and excavation step lengths.

TABLE 7. Crown displacement results for three-lane and four-lane tunnels across different excavation step lengths (mm).

TABLE 8. Spandrel displacement results for three-lane and four-lane tunnels across different excavation step lengths (mm).

TABLE 9. Arch springing displacement results for three-lane and four-lane tunnels across different excavation step lengths (mm).

TABLE 10. Inverted arch displacement results of three-lane and four-lane tunnels across different excavation step lengths (mm).

Data analysis indicates specific displacement patterns across the monitoring sections. X-direction displacements at the crown and inverted arch were negligible. The model featured a horizontal boundary with uniform forces.

Z-direction displacements at the crown and inverted arch increased with tunnel span. The four-lane section exhibited significantly higher displacements than the three-lane section at equivalent excavation step lengths. Greater spans necessitate stricter control of excavation step length under identical geological conditions. Reduced step lengths are essential for maintaining surrounding rock stability. The spandrel exhibited vertical settlement and horizontal inward convergence across all spans and excavation step lengths.

Table 9 illustrates the displacements at the arch springing. Both horizontal and vertical displacements increased with excavation step length. The four-lane section showed significantly higher displacement values than the three-lane section.

Figure 19 presents the displacement sensitivity values for different monitoring points in the X and Z directions. Analysis of these curves indicated several key trends.

X-direction displacement sensitivities were negligible at the crown and inverted arch. The spandrel exhibited the highest sensitivity. Sensitivity values reached 27.86 mm for the three-lane section and 45.33 mm for the four-lane section. The arch springing followed the spandrel in sensitivity level. Z-direction displacement sensitivities were highest at the crown and inverted arch. The three-lane section recorded values of 24.73 mm and 37.45 mm. The four-lane section showed values of 49.37 mm and 61.87 mm. Sensitivities at the spandrel and arch springing were comparatively lower. However, these values exceeded 34 mm in the four-lane section.

All monitoring points in the four-lane section exhibited higher displacement sensitivities at the same excavation step lengths. Z-direction sensitivities at the crown and inverted arch were particularly prominent. Z-direction displacements at the spandrel and arch springing were also significant.

Therefore, four-lane tunnel spans necessitate increased focus on crown settlement and inverted arch uplift. Deformations at the spandrel and arch springing also require close monitoring. Timely implementation of engineering measures ensures surrounding rock stability.

4.2.2 Sensitivity analysis of surrounding rock plastic zone

During tunnel excavation, stress redistribution occurs, leading to the formation of plastic zones around the tunnel opening, which are unevenly distributed. The distribution and extent of plastic zones at different excavation step lengths for a given tunnel span, based on the approximate estimation of plastic zone volume using 3DEC, are presented in Table 11.

TABLE 11. Distribution and extent of tunnel plastic zones.

It can be seen from Table 11 that the plastic zone distributions of three-lane and four-lane tunnels under different excavation step lengths are relatively similar.

Affected by joint cutting, the entire rock mass becomes a discontinuous medium with rock blocks interlocked with each other. During tunnel excavation, blocks around the tunnel opening move under external forces, and part of the rock mass undergoes plastic shear slip along structural planes. This leads to an uneven distribution of plastic zones around the tunnel opening, with plastic stress zones appearing in some rock mass not adjacent to the tunnel periphery.

Overall, under the same tunnel span, the extent of the plastic zone gradually increases as the excavation step length increases. While under the same excavation step length, the plastic zone extent of four-lane tunnels is larger than that of three-lane tunnels. The difference increases from 0.2 m to 3.2 m, and the ratio of the two increases from 1.07 to 1.62.

Overall, under the same tunnel span, the extent of the plastic zone gradually increases as the excavation step length increases. For three-lane and four-lane spans, the plastic zone extents at an excavation step length of 50 m are 2.2 m and 2.8 m respectively, and the comparison with the field-measured loosened zones is presented in Table 4. While under the same excavation step length, the plastic zone extent of four-lane tunnels is larger than that of three-lane tunnels. The difference increases from 0.2 m to 3.2 m, and the ratio between the two increases from 1.07 to 1.62.

4.3 Discussions

Field-measured data show certain discrepancies with the numerical simulation results. However, the ratios of the measured deformations at the vault and haunch to the numerical simulation deformations at an excavation step length of 50 m are basically consistent, as presented in Tables 5, 12.

TABLE 12. Comparison of field-measured and numerical simulation data.

According to the variation range of the plastic zone obtained from numerical simulation, the plastic zone extent is relatively small when the excavation step length is 30 m and 40 m. When the excavation step length is 50 m, statistical calculations show that the plastic zone thickness is approximately 2.8 m for three-lane tunnels and 3.3 m for four-lane tunnels.

As presented in Table 12, except for the arch foot, the ratios of numerical simulation values to field-measured values at other positions are approximately 3, showing good consistency. The arch foot is affected by actual field conditions, with a ratio of approximately 7–8.

The ratios of the calculated plastic zone thickness to the field-measured loose zone thickness at each position are presented in Table 5. It can be seen that the ratios range from 1.75 to 2.00 for three-lane tunnels and from 1.50 to 1.83 for four-lane tunnels.

As presented in Table 12, except for the arch foot, the ratios of numerical simulation values to field-measured values at other positions are approximately 3, showing good consistency. The arch foot is affected by actual field conditions, with a ratio of approximately 7–8.

The consistency of these ratios indicates that the numerical simulation is in good agreement with the field conditions. Nevertheless, the ratio at the arch foot is abnormal, which is attributed to the fact that the FG measuring line is positioned at a lower elevation and is significantly affected by the benches during the field benched excavation.

Due to the complex construction conditions and limited access to the tunnel face, only one complete monitoring dataset was obtained for this specific section.

All relevant monitoring equipment was strictly calibrated, and data collection was performed by trained professionals. Nevertheless, the measured values are consistent with the statistical ranges reported in previous studies of similar Grade III surrounding rock tunnels.

The maximum vault settlements observed in this study were 19.2 mm (three-lane) and 34.2 mm (four-lane), which fall within the range of 8–62 mm for Grade III rock mass reported by Sun et al. (2021) and Wang et al. (2018b). Generally speaking, deep-buried tunnels exhibit smaller maximum vault settlements. The tunnel section studied in this paper has an overburden depth of 220 m, which is a deep-buried tunnel, and thus the vault settlement values are relatively small.

The maximum cumulative convergence values at the three-lane and four-lane monitoring sections were 11.32 mm and 15.63 mm respectively. The convergence value of the four-lane tunnel is slightly larger than the range of 5.9–12.07 mm reported by Wang et al. (2018b) and Shen et al. (2018). In general, the larger the span, the greater the horizontal convergence, which is related to the ultra-large width of the four-lane monitoring section.

The pressure values between the surrounding rock and shotcrete varied significantly. The maximum surrounding rock pressure measured at the three-lane section was 0.32 MPa, and that at the four-lane section was 0.69 MPa. The observed variation trend of the pressure values is basically consistent with that of Grade III surrounding rock tunnels reported by Wang et al. (2018b), which initially increases, then decreases slightly, and finally stabilizes. The maximum values are within the limit of 0.8 MPa reported by Zhou et al. (2023) and Zhou et al. (2020), showing good agreement. These comparisons confirm that our monitoring data are reasonable and represent the typical behavior of Grade III rock mass under similar engineering conditions.

The main limitation of the present study resides in the insufficient number of monitoring sections available for robust statistical analysis. Further investigations are warranted to accumulate additional field monitoring data, which will enable a more comprehensive quantification of the variability in surrounding rock responses across varying geological conditions.

5 Conclusion

Comprehensive field monitoring, ultrasonic testing, and 3DEC numerical simulation of the variable-cross-section Qingshan Tunnel yielded the following conclusions:

• Surrounding rock pressure stabilized after 6 days of excavation. The maximum pressures in the three-lane and four-lane sections were 0.32 MPa and 0.69 MPa, respectively. Both occurred at the spandrels. Displacement trends mirrored these pressure variations. Rock convergence reached stability after 5 days of excavation. The maximum displacement values reached 11.32 mm in the three-lane section and 15.63 mm in the four-lane section.
• Cumulative deformation in the four-lane section was 1.38–1.78 times that in the three-lane section. Notably, maximum pressure occurred at the spandrels, while maximum displacement occurred at the crown. This observed inconsistency is predominantly attributed to the differential release of radial stress.
• Loosening zone thickness distribution correlated with deformation magnitude. The thickness hierarchy followed the order: crown > spandrel > wall foot. Measured thicknesses at the crown ranged from 1.60 m to 2.20 m. Loosening zones in the four-lane section were 1.25–1.38 times thicker than those in the three-lane section.
• Numerical simulations confirmed higher displacement sensitivities in the four-lane section. Vertical deformations at the crown, inverted arch, spandrel, and arch springing were particularly sensitive. Larger spans require shorter excavation step lengths to maintain surrounding rock stability.

These findings characterize the span effect on deformation and loosening zone distribution in variable-cross-section limestone tunnels. The results provide valuable guidance for stability control and support optimization in similar tunnel projects.

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Footnotes

Edited by: Wenling Tian, China University of Mining and Technology, China

Reviewed by: Aizhong Luo, Guizhou University of Engineering Science, China

Zhengyang Su, Wuhan University, China