Numerical Simulation of Large-Span Bifurcated Tunnels with Large Cross-Sections in Urban Underground Interchanges

Abstract

The stress distribution after excavation becomes highly complex in large-span bifurcated tunnel sections commonly found in urban underground interchanges. This study investigates the stress evolution induced by the excavation of large-span and bifurcated tunnel, focusing on the 32.17 m maximum-span section of the Shenzhen Baopeng–Shahe Underground Interchange. The results show that stress concentration near the tunnel walls of large-span sections is greater than that in sections with bifurcated tunnels. Adjusting the burial depth of the large-span tunnel, the influence of stiff layer thickness on the redistribution of surrounding rock stress was analyzed. When the tunnel is buried at a shallow depth and the stiff layer thickness is small, the maximum tangential stress of the surrounding rock occurs at the stiff layer boundary, and the surrounding rock remains entirely elastic. In large-span tunnels, as the thickness of the stiff layer increases from 5 m to 20 m, the stress relaxation zone grows from 0 m to 8 m, and the stress-bearing zone expands from 10 m to 27 m. As the burial depth increases and the stiff layer thickness grows, the maximum tangential stress shifts to within the stiff layer. In this case, the tangential stress distribution at the stiff layer boundary becomes non-smooth. Therefore, an appropriate stiff layer thickness must be selected to prevent the surrounding rock from entering a plastic state. The findings provide theoretical guidance and technical support for the design of large-scale underground interchange bifurcated tunnels, advancing the intelligent and scientific development of urban underground transportation facilities and offering significant practical and social benefits.

1. Introduction

With the accelerating pace of urbanization, urban transportation faces increasingly severe challenges, particularly in large cities, where traffic congestion and land resource constraints are becoming increasingly prominent [1,2]. Underground interchanges—as key urban road transportation facilities—can effectively conserve surface land resources, alleviate urban traffic congestion, and improve traffic flow. However, analyzing the stability of surrounding rock during the construction of urban underground transportation facilities is crucial for the safe and rational design of underground interchanges.

Currently, research on the stability of surrounding rock in ultra-large cross-section tunnels mainly includes theoretical analytical methods, numerical calculations, and model experiments [3]. The main drawback of using theoretical analytical methods to calculate stability is that they cannot reflect the true constitutive characteristics of the rock mass and have a limited consideration of factors, thus possessing certain limitations. Model experiments are an effective research method, commonly used in the stability research of large and ultra-large cross-section tunnels. Model experiments are mostly conducted indoors, obtaining experimental models based on similarity ratios to simulate the construction process of underground structures, and combining measurement results to analyze the stress and rock mass variation patterns of the surrounding rock and support structures. However, model experiments have disadvantages such as high cost, poor repeatability, insufficient theoretical depth, and uncontrollable errors in experimental results. The greatest advantage of numerical calculation methods is that they can realistically simulate the displacement and stress field variations during tunnel construction to the greatest extent possible, and are characterized by repeatability and ease of operation. Therefore, more and more researchers are applying numerical calculation methods to stability research. Fang et al. proposed an empirical formula based on the Peck-Fujuta method to estimate the surface settlement of parallel double-tunnel shield tunnels [4,5]. The applicable condition is that the ratio of the tunnel center distance to the tunnel diameter is less than 2.7. Ghaboussi et al. conducted a two-dimensional finite element analysis based on the linear elastic model and comprehensively studied the influence of the net distance on the stability of the surrounding rock of parallel tunnels [6]. The study found that as the net distance decreases, the vertical stress and horizontal stress of the interbedded rock gradually increase. Chehade and Shahrour believed, based on the finite element analysis results, that when the net distance between the two tunnels is greater than three times the tunnel diameter, the excavation of the first tunnel will not affect the excavation of the second tunnel [7]. Kim et al. used kaolin to simulate soft soil strata and conducted a study on the close-proximity construction of parallel tunnels through five sets of similar model tests [8]. They used secondary lining deformation and bending moment as evaluation indicators to analyze the influence of the clearance on the safety and stability of the two tunnels. Wen et al. also studied the reasonable spacing of parallel tunnels with a small-clearance section through experimental methods [9]. When the clearance is greater than one times the tunnel diameter, the mechanical state of the two tunnels can be kept unaffected by close-proximity construction. Osman et al. focused on the stability problem of unlined parallel tunnel excavation in soft soil strata based on the upper limit analysis method [10]. Vlachopoulos et al. used 2D and 3D numerical models to explore the influence of the clearance between parallel tunnels on the surrounding rock deformation, surrounding rock stress, and the size of the plastic zone in soft strata [11]. Lu and Tian summarized the minimum reasonable clearance values of parallel double tunnels under different surrounding rock grades based on numerical analysis and model test results [12,13]. Wang et al. studied the Kuiqi large-section small-clearance section tunnel through numerical simulation. Based on the surrounding rock displacement, plastic zone distribution and safety factor, they determined that the minimum reasonable clearance value was 0.55 times the tunnel diameter [14].

Large-span sections and bifurcated sections constitute essential components of urban underground interchanges. Each section requires different construction methods and has different disturbance effects. Furthermore, the close proximity of these sections significantly influences each other during construction [15,16,17]. At present, numerous studies have been performed on the stability of large-span tunnels. Liu et al. used the Ganggou Tunnel on the Jinan Link of the Beijing-Shanghai Expressway, which passes through a fractured and shattered area, as a case study to investigate the mechanical response of the surrounding rock under construction in complex strata [18]. They found that displacement changes can be divided into three stages: “slow increase-rapid increase-to-stable state,” and stress changes can be divided into three stages: “stress accumulation-stress release-to-stable state.” Yang et al. studied the bearing modes of composite middle walls in continuous arch tunnels by embedding monitoring elements [19]. They presented the changes in surrounding rock stress under different construction steps and summarized three typical middle wall bearing modes: distributed symmetrical bearing mode, distributed eccentric bearing mode, and concentrated eccentric bearing mode. Gao et al. derived a process load structure calculation formula for deep asymmetric multi-arch tunnels based on the process load structure design method and the Prokhorov arch theory assumption, considering the complex mechanical behavior of deep asymmetric multi-arch tunnels, including geometric asymmetry, structural asymmetry, and left–right load asymmetry [20]. Zhang et al. used the discrete element method to analyze the overall vertical stress distribution of the middle rock wall at different clearances [21]. They found that the vertical stress in the core of the middle rock wall decreases with increasing clearance. When the clearance reaches 0.6 B, the vertical stress in the core and the two sides is close. When the clearance exceeds 0.6 B, the vertical stress in the core is lower than that on the two sides. Zhang et al. used a three-dimensional geomechanical model test method to study a large, bifurcated tunnel on the Shanghai-Chengdu West Expressway [22]. They revealed the stress and displacement variation patterns around the bifurcated tunnel and the failure mechanism of the surrounding rock of the bifurcated tunnel. They also obtained the design and ultimate bearing safety of the bifurcated tunnel, providing suggestions and conclusions with engineering guidance for the optimized design and construction of bifurcated tunnels.

A major challenge in the research of large-section interchanges is the complex geological conditions and unique construction environments of tunnels. This is particularly true when tunnel clusters are closely spaced and the maximum span of a single tunnel is large. These characteristics significantly increase the difficulty of tunnel construction. In some areas, the surrounding rock mass along the tunnels is poor, and the geological conditions are complex and variable. These factors directly impact tunnel stability and construction safety [23]. Against this backdrop, there are no similar large-section highway tunnel projects in China, resulting in a lack of case studies to reference and a lack of established design specifications to follow. This situation presents significant technical challenges in the design and construction of such tunnels, necessitating the urgent need for innovative solutions.

In summary, to address the complex load transfer and excavation-induced disturbance in urban underground interchanges where an extra-large cross-section segment is spatially adjacent to a bifurcated small-clearance section, this study takes the Qiaocheng East Road North Extension underground interchange in Shenzhen as a representative case and investigates the stress redistribution of surrounding rock through refined numerical simulations. The main contributions are as follows: a unified 3D FLAC3D model is established under consistent geological and construction settings, simultaneously covering the extra-large cross-section segment and the adjacent bifurcated small-clearance section, enabling a direct and comparable assessment; the redistribution characteristics of principal stresses as well as radial/tangential stresses and principal stress rotation are comparatively quantified to identify distinct stress concentration zones and to discuss the interaction induced by spatial proximity; a 2D parametric model based on borehole #25 is developed to isolate the effect of stiff layer thickness above the crown, clarifying its control on peak tangential stress migration, deformation response, and the tendency of yielding; and design-oriented quantitative references and practical implications (e.g., stress level, critical locations, and the coupled consideration of burial depth and stiff layer thickness) are provided for similar urban interchange tunnels under complex stratigraphic conditions.

2. Engineering Background

The Qiaocheng East Road North Extension is a fully interchanged underground interchange. As a unique tunnel layout, it gradually transitions from a large-span portal tunnel and a small-clearance section tunnel to a conventional separated tunnel within a relatively short distance. The flat mountain has a “Y”-shaped bifurcation, and there are also spatial cross-crossings (Figure 1). However, the excavation span of interchange tunnels varies greatly, the construction process is complex, and excavation and support are intertwined. The surrounding rock stress changes and lining load conversion are very complex, especially the stress on the center wall, which is subject to tension, compression, bending, torsion, and shear. In addition, the stress distribution of the surrounding rock and the stress and deformation of the lining are unclear during the construction process, and the impact of the left and right tunnel construction on the middle wall is difficult to grasp, which increases the difficulty of controlling deformation and stability during tunnel construction. Any carelessness may cause engineering accidents such as surrounding rock instability, lining cracking or middle partition wall damage, which cause safety hazards.

According to the design data, the maximum span of the long-span section at the intersection of Baopeng Channel and Qiaocheng East Road (right line mileage K3+695) is approximately 32 m, and the longitudinal length of the maximum span section is approximately 120 m, which is the longest longitudinal length among the maximum spans. The tunnel surrounding rock here was assessed as Class V surrounding rock, and the stratum conditions are poor. When the tunnel enters the bifurcated section, the surrounding rock grade was assessed as even reaching Class IV, so this section was selected as the most unfavorable section for analysis. Based on the strata at the tunnel site at the most unfavorable node and the surrounding rock parameters provided by the geological survey report, the mechanical parameters of each stratum are selected and shown in

Table 1. Formation parameters [24].

Formation Name	Gravity/kN·m−3	Young’s Modulus/N·m−2	Poisson’s Ratio	Cohesion /kPa	Friction Angle/°
Plain Fill	18.70	7.50 × 106	0.38	20.00	15.00
Earthy Strongly Weathered Medium-Grained Granite	19.50	1.80 × 108	0.33	27.00	32.00
Massive Strongly Weathered Medium-Grained Granite	23.00	3.00 × 108	0.32	39.00	35.00
Completely Weathered Medium-Grained Granite	19.20	8.00 × 107	0.35	32.00	28.00
Moderately Weathered Medium-Grained Granite	26.00	7.50 × 109	0.30	3.40 × 103	36.00
Slightly Weathered Medium-Grained Granite	26.20	3.00 × 1010	0.23	8.00 × 103	40.00

.

3. Three-Dimensional Numerical Simulation of Extra-Large Cross-Section Bifurcated Tunnels

3.1. Numerical Model

The 3D simulation of this extra-large cross-section bifurcated tunnel was performed using FLAC 3D version 6.0 software. The modeling area spanned from stakes K3+545 to K3+845, with a longitudinal length of 300 m, a height of 200 m, and a width of 300 m, as shown in Figure 2. The long span was 150 m long, and the short-span section was 150 m long. The strata were simplified, and the entire model used the parameters of a 25# borehole. The tunnel’s shallowest depth was approximately 65 m, and the excavation span of the long-span section was approximately 32 m. To reduce boundary effects, the model boundary is set sufficiently far away from the tunnel span (with a model width of 300 m and a maximum excavation span of approximately 32 m). The bottom boundary is fixed in all directions. The four lateral boundaries and longitudinal end boundaries limit the normal displacement of each boundary plane and allow tangential displacement. The top boundary is considered as a free surface that is only affected by its own weight. Before excavation, an initial stress field was established by applying gravitational acceleration to the entire model and running the calculation to a static equilibrium state. In this way, the vertical stress is mainly controlled by the cover layer, and the related lateral stress state is uniformly generated by the equilibrium process under the boundary constraints mentioned above. This assumption applies to the current work, which focuses on conducting consistent comparative evaluations of large-span sections and adjacent forked small gap sections within the same modeling framework. The potential impact of this hypothesis was discussed in the discussion/limitation section.

The 3D model was discretized using FLAC3D zones, with local mesh refinement around the tunnel perimeters, the middle-wall/rock pillar region between adjacent openings, and the intersection area where steep stress gradients are expected. The zone size increases gradually away from the excavations toward the far-field boundaries. The mesh layout is shown in Figure 2, and the same meshing strategy was applied to all excavation stages to maintain comparability across sections and construction steps. The initial in situ stress field was generated by coupling gravity stress and horizontal tectonic stress. Gradient meshing was used, and mesh sensitivity analysis was performed to verify the stability of the results. Specifically, key parameters (e.g., rock mass mechanical properties, seepage coefficients, in situ stress) were selected based on site-specific geological survey data and ISRM classification standards. Boundary conditions of the numerical model were determined according to the study area’s actual engineering geological conditions. For input value assumptions, parameters with insufficient field data were assigned ranges based on adjacent engineering statistics.

Excavation was carried out using a three-step method with a 2 m step, as shown in Figure 3. The simulation process excavated the large span first, followed by the smaller clear-spacing sections. The bifurcated tunnel face lagged 20 m behind the mainline tunnel face, approximately twice the bifurcated tunnel span. The surrounding rock mass adopts the Mohr–Coulomb constitutive model. The surrounding rock mass is represented by the Mohr–Coulomb elastoplastic model, which is widely used in tunnel analysis on an engineering scale to capture the first-order yield trend and stress redistribution under excavation. Based on the geological survey report and design documents of the most unfavorable node, the mechanical parameters of each layer were selected, and the geological profile and parameter set of borehole #25 were used for consistency in the entire model. Table 1 summarizes the parameters used. As the purpose of this study is to compare and evaluate the stress evolution between different cross-sections and to study the parameters of stiff layer thickness, the Mohr–Coulomb model provides a robust and transparent baseline representation. Due to the different longitudinal configurations of the two monitoring sections, this cannot simply be considered a plane strain problem and requires special attention. In this study, the main focus is on the stress redistribution caused by excavation, as well as the comparative response between large-span and bifurcation sections under the same geological background and construction sequence. Therefore, the response of the surrounding rock was evaluated under the assumption of unsupported excavation (i.e., without explicitly modeling shotcrete, anchor rods, or lining elements). This simplification allows for consistent comparisons of stress concentration locations and stress path evolution, and provides a conservative envelope for deformation and yield trends in the near-field. This model has two monitoring sections: one in the extra-large span section (Figure 3c), and one in the small-clearance section (Figure 3d). Both the monitoring section of the long-span section and bifurcated section are located at the interface where the long-span section and the bifurcated section intersect. It should be noted that the large-span segment and the bifurcated small-clearance section segment are simulated within one integrated 3D model and are excavated in close proximity; therefore, the response reported here inherently includes the coupling effect induced by the adjacent bifurcated excavation (see Section 3.4). For clarity, a side-by-side quantitative comparison is provided to explicitly highlight how the spatial proximity and excavation sequence influence the stress concentration characteristics of the two segments.

3.2. Analysis of Monitoring Results of the Large Span Section

Figure 4a shows the distribution of the maximum principal stress in the surrounding rock of the large-span tunnel. After excavation, the maximum principal stress was mainly concentrated in the upper part of the haunch, with a peak value of approximately 7.24 MPa, while the minimum value of maximum principal stress was concentrated at the invert and was nearly 0 MPa.

Figure 4b illustrates the reorientation of the principal stresses surrounding the tunnel. The streamlines of the maximum principal stress exhibit a ring-like configuration, as is highlighted within the solid elliptical box. In the regions directly above the vault and directly below the invert, the orientation of the maximum principal stress undergoes a 90° rotation, aligning horizontally. The two solid squares in the figure denote the locations where the maximum principal stress reverts to a vertical orientation. The location where the principal stress above the vault undergoes a 90° rotation coincides with the boundary of the stiff strata. This indicates that in large-span tunnels, due to the horizontally elongated elliptical shape of the excavation and the presence of stiff strata, the load-bearing zone of the surrounding rock manifests as a vertically elongated ellipse.

To investigate the characteristics of stress redistribution in the surrounding rock of the large-span section after excavation, Figure 5 shows the radial and tangential stress distribution curves for the surrounding rock mass along the left haunch (Figure 5a), right haunch (Figure 5b) and vault (Figure 5c). At the left haunch, the radial stress first increases and then decreases with increasing distance from the tunnel wall, and the radial stress at the model boundary is approximately 0.5 MPa. Tangential stress, however, is concentrated at the tunnel wall, reaching a maximum value of approximately 5 MPa and exhibiting a gradual decrease with distance from the tunnel wall, indicating an elastic state of the surrounding rock mass. The stress distribution at the right arch shoulder is nearly identical to that at the left arch shoulder. At the vault, the radial stress initially increases and then decreases with increasing distance from the tunnel wall, due to the gradual reduction in the overlying rock weight. Between the interface of the stiff layer and the tunnel wall, the surrounding rock is relatively weak, with low bearing capacity. As the distance to the stiff layer decreases, the bearing capacity of the surrounding rock gradually increases, resulting in a progressive rise in the tangential stress. The tangential stress exhibits a similar trend, with its maximum value occurring within the thickness of the stiff layer. During tunnel excavation, radial stress initially increases and then decreases. The core issue is the dynamic adjustment of the surrounding rock stress field from equilibrium to imbalance and then back to a new equilibrium. Before excavation, the rock mass is in a triaxial equilibrium state due to its own weight and tectonic stress. After excavation creates a free face, the constraints are suddenly released. In the elastic stage, stress concentration occurs in the surrounding rock mass because stress cannot be transferred to the free face, resulting in a temporary increase in radial stress. When the tangential stress exceeds the compressive strength of the rock mass, the surrounding rock enters the plastic stage. Crack expansion and particle slippage lead to a decrease in bearing capacity, and the concentrated stress is transferred to the distant elastic zone, releasing and reducing the radial stress. Without support, the radial stress in the tunnel wall eventually returns to zero; with support, it stabilizes at the support reaction force level. The geometry (e.g., a circular cross-section with uniform stress distribution) and rock mass stiffness (stress concentration is more pronounced in hard rock masses) affect the rate and magnitude of this process.

3.3. Analysis of Monitoring Results of the Bifurcated Tunnel Section

Figure 6 illustrates the distribution of the maximum principal stress in the surrounding rock of the bifurcated tunnel section, along with the corresponding stress vector diagram. Compared to the large-span section, the peak value of the maximum principal stress decreases to approximately 6.72 MPa, occurring at the haunch of the bifurcated tunnel. However, the minimum value of the maximum principal stress near the tunnel occurs at the vault and invert of the main tunnel. Similarly to the large-span section, the streamlines of the maximum principal stress exhibit a ring-shaped pattern. Near the vault and the invert, the orientation of the maximum principal stress rotates by 90°, becoming horizontal.

Figure 7 summarizes the stress redistribution of the surrounding rock at various locations in the bifurcated tunnel sections. At the left waist Figure 7a, the radial stress gradually decreases with distance from the tunnel wall and eventually stabilizes. The radial stress at the tunnel wall is larger than 0, which can be attributed to the finite element mesh discretization. The tangential stress exhibits a clear concentration at the tunnel wall, reaching a maximum of approximately 5.8 MPa, and then gradually decreases to a stable value, indicating that the surrounding rock remains in an elastic state in this region. At the left arch (Figure 7b), the tangential stress initially increases with distance from the tunnel wall and then decreases, with the turning point corresponding to the location of the stiff layer. At the tunnel wall, the tangential stress is lower than the pre-excavation vertical stress at the crown, while the radial stress nearly drops to zero after excavation. As the distance from the wall increases, the radial stress first rises and then gradually decreases, and it aligns with the pre-excavation vertical stress once the horizontal stress at the crown reaches equilibrium with the initial ground stress. In interbedded rock sections (Figure 7c), the radial stress generally remains low, around 0.3 MPa, whereas the tangential stress maintains a higher level of approximately 4 MPa. Due to weak longitudinal constraints, the surrounding rock behaves approximately under uniaxial compression, highlighting the need to prioritize the strength design of interbedded rock. In the arch of the bifurcated section (Figure 7d), both radial and tangential stresses decrease compared to their initial levels. The radial stress first increases and then decreases with distance, ultimately approaching the initial vertical stress before tending to zero, while the tangential stress initially decreases and then increases, eventually coinciding with the initial horizontal stress. In the right waist of the bifurcated section (Figure 7e), the radial stress first increases and then decreases with distance from the tunnel wall, eventually stabilizing, with the radial stress at the wall approaching zero. The tangential stress gradually decreases with distance and finally stabilizes.

3.4. Interaction Between the Large-Span and Bifurcated Sections

The motivation for this study is that in urban underground interchanges, the spatial distance between the ultra large section and large-span section and the adjacent bifurcation small gap section is relatively close, so it cannot be regarded as two completely independent excavation processes. In the modeling strategy of this study, two sections of the structure were included in a unified 3D FLAC3D numerical model and excavated in a predetermined order under the same geological conditions and construction assumptions, with a lag between the bifurcation face and the main face. Therefore, the results presented in Section 3.2 and Section 3.3 should be understood as a coupled response, and the interaction can be explained through a unified indicator system and direct comparison.

A first indication of coupling is the difference in peak stress levels and stress-path characteristics between the two segments under the same modeling framework. The peak maximum principal stress in the large-span segment is higher than that in the bifurcated segment (approximately 7.24 MPa versus 6.72 MPa, respectively), reflecting the larger excavation span and the associated redistribution demand in the surrounding rock mass. Meanwhile, the bifurcated section exhibits a pronounced stress reorientation, with the maximum principal stress trajectory showing a marked rotation (up to about 90° in the representative case), which is consistent with the complex load-transfer and confinement conditions created by the adjacent openings and the middle-wall/rock-pillar region. In addition, the tangential stress response in the bifurcated section indicates that stress concentration may localize at the haunch adjacent to the middle wall, where the reported peak tangential stress reaches about 5.8 MPa in the representative monitoring profile, implying stress transfer and confinement amplification caused by the proximity of the neighboring excavation.

4. Comparative Study on Bearing Mechanism of Surrounding Rock with Different Stiff Layer Thickness

As shown by the analysis in Section 3, large spans are the most critical because they exhibit greater displacement and a higher degree of stress concentration. The thickness of the stiff layer has a significant impact on large-span sections. To investigate the influence of the thickness of the stiff layer above the tunnel arch on the bearing mechanism of the surrounding rock, a parameter sensitivity analysis was conducted on the stiff layer thickness. Two-dimensional numerical simulations were established under different stiff layer thicknesses to analyze the disturbance of surrounding rock stress during tunnel excavation, revealing the variation in the bearing mechanism of the surrounding rock with changes in stiff layer thickness.

Based on the geological conditions of borehole #25, we adjusted the burial depth of the long-span tunnel to simulate different stiff layer thicknesses. This two-dimensional numerical simulation used the stratum parameters from borehole No. 25. Numerical calculations were performed on models of ultra-long-span tunnels under four different stiff layer thicknesses (distance from the tunnel arch to the stiff layer boundary), as shown in

Table 2. Operating Condition Description Table.

Number	Simulated Stratum	Simulated Stiff Layer Thickness
1	No. 25	5 m
2	No. 25	10 m
3	No. 25	20 m
4	No. 25	30 m

. Solid elements were used for the strata, all based on the Mohr–Coulomb elastoplastic constitutive model.

4.1. Analysis of Stress Variation Under Different Stiff Layer Thicknesses

Figure 8 presents the stress cloud diagrams of the surrounding rock after excavation for different stiff layer thicknesses. When the stiff layer thickness is 5 m, the maximum vertical stress is concentrated at the haunch, while the arch crown and bifurcate exhibit relatively low vertical stress. The maximum horizontal stress appears at the arch shoulder (Figure 8a,b). For a stiff layer thickness of 10 m, the vertical stress distribution remains similar, with peak values at the haunch and lower values at the crown and bottom. However, the maximum horizontal stress is observed at both the arch shoulder and the arch foot (Figure 8c,d). With a stiff layer thickness of 20 m, the vertical stress continues to concentrate at the haunch, and the crown and bottom still experience smaller vertical stresses. In this case, the maximum horizontal stress shifts to the invert (Figure 8e,f). When the stiff layer thickness increases to 30 m, the vertical stress pattern remains consistent, with the highest values at the haunch. The maximum horizontal stress is again concentrated at the invert (Figure 8g,h).

To quantitatively analyze the bearing mechanism of the surrounding rock under different stiff layer thicknesses, Figure 9 summarizes the radial and tangential stresses of the surrounding rock for various stiff layer thicknesses at the arch and waist. For a stiff layer thickness of 5 m (Figure 9a,b), the radial stress increment at the tunnel arch is negative, whereas the tangential stress increment is positive. With increasing distance from the tunnel wall, the radial stress gradually rises back to the in situ stress. At the hard boundary, the radial stress exhibits local fluctuations, while the tangential stress increases to a peak and then decreases to the original rock stress, with the maximum tangential stress occurring at the stiff layer boundary—consistent with the behavior under thin stiff layer confinement. Based on the stress distribution characteristics, the size of the stress loss zone is 0, the size of the stress bearing zone is approximately 10 m. At the tunnel waist, both the radial and tangential stress increments are positive and decrease gradually with distance.

For a stiff layer thickness of 10 m (Figure 9c,d), the radial and tangential stress increments at the tunnel arch are both negative. The radial stress increases continuously to the in situ level, while the tangential stress rises to a maximum at the stiff layer boundary before declining. The size of stress loss zone and stress bearing zone is approximately 2 m and 8 m, respectively. At the tunnel waist, the radial stress increment is positive; the radial stress first increases and then decreases to the in situ stress with increasing distance. The tangential stress increment is also positive and gradually decreases, similar to the behavior observed for the stiff layer thickness of 5 m.

For a stiff layer thickness of 20 m (Figure 9e,f), the radial and tangential stress increments at the tunnel arch are negative. After an initial disturbance, the radial stress gradually returns to the in situ stress, while the tangential stress increases to a peak at the stiff layer boundary and then decreases. The size of the stress loss zone and the stress bearing zone is approximately 5 m and 11 m, respectively. At the tunnel waist, the radial stress increment is positive, showing a pattern of first increasing and then decreasing with distance from the wall. The tangential stress increment is also positive and decays gradually.

For a stiff layer thickness of 30 m (Figure 9g,h), the radial stress increment at the tunnel arch remains negative, whereas the tangential stress increment becomes positive. The radial stress increases steadily toward the in situ level, and the tangential stress first rises and then decreases; however, unlike the thinner-layer cases, the maximum tangential stress occurs within the stiff layer, resembling the redistribution pattern in homogeneous strata. The size of the stress loss zone and the stress bearing zone is approximately 8 m and 27 m, respectively. At the tunnel waist, both radial and tangential stress increments are positive and gradually decrease to the in situ stress with increasing distance from the tunnel wall.

4.2. Analysis of Displacement Variation Under Different Stiff Layer Thicknesses

For stiff layer thickness of 5 m, to analyze the settlement of the arch crown and the convergence of the haunch after excavation, the vertical and horizontal displacement values of the surrounding rock were extracted and analyzed (Figure 10a,b). It was found that the vertical displacement of the main tunnel arch crown is the largest at 5.77 mm, while the horizontal displacement of the haunch is smaller, but both are directed towards the outside of the tunnel. For stiff layer thickness of 10 m, to analyze the settlement of the arch crown and the convergence of the haunch after excavation, the vertical and horizontal displacement values of the surrounding rock were extracted and analyzed (Figure 10c,d). It was found that the vertical displacement of the main tunnel arch crown is the largest at 4.147 mm, while the horizontal displacement of the haunch is smaller, but both are directed towards the outside of the tunnel. For stiff layer thickness of 20 m, to analyze the settlement of the arch crown and the convergence of the haunch after excavation, the vertical and horizontal displacement values of the surrounding rock were extracted and analyzed. It was found that the vertical displacement of the main tunnel arch crown is the largest at 3.23 mm, while the horizontal displacement of the haunch is smaller, but both are directed towards the outside of the tunnel (Figure 10e,f). For stiff layer thickness of 30 m, to analyze the settlement of the arch crown and the convergence of the haunch after excavation, the vertical and horizontal displacement values of the surrounding rock were extracted and analyzed (Figure 10g,h). It was found that the vertical displacement of the main tunnel arch crown is the largest at 3.06 mm, while the horizontal displacement of the haunch is smaller, but both are directed towards the outside of the tunnel.

Overall, this work integrates the extra-large cross-section segment and the adjacent bifurcated small-clearance section of a real urban underground interchange within a unified 3D framework, and further clarifies the controlling role of crown stiff layer thickness through a complementary parametric study. From an engineering perspective, monitoring and reinforcement should prioritize the haunch/sidewall zones and the crown region affected by the stiff layer, and burial depth should be selected together with stiff layer thickness to mitigate the risk of yielding under stiff layers at a greater depth.

5. Conclusions

This study investigates the stress redistribution characteristics of the surrounding rock in large-span bifurcated urban underground tunnels and examines the influence of stiff layer thickness on the stability of surrounding rock in large-span tunnels. The main conclusions are as follows:

(1)

During tunnel excavation, the stress distribution of the surrounding rock differs between large-span and bifurcated sections. The maximum principal stress is more concentrated in the large-span sections, while in the interbedded rock, the surrounding rock exhibits an approximately uniaxial stress state.

(2)

Both radial and tangential stresses in the surrounding rock exhibit distinct patterns of change after excavation. Radial stress typically increases first, then decreases, eventually stabilizing. Tangential stress, on the other hand, is concentrated at the tunnel wall and gradually decreases, eventually returning to pre-excavation ground stress levels in areas farther from the wall, with this trend being particularly pronounced at the vault.

(3)

In large-span tunnels, as the thickness of the stiff layer increases from 5 m to 20 m, the stress relaxation zone grows from 0 m to 8 m, and the stress-bearing zone expands from 10 m to 27 m; when the stiff layer thickness is less than 20 m and the tunnel burial depth is relatively shallow, the maximum tangential stress typically occurs at the stiff layer boundary, whereas when the stiff layer thickness reaches 30 m and the tunnel burial depth increases, the maximum tangential stress shifts to within the stiff layer, leading to the development of a plastic zone in the surrounding rock, which means that both the stiff layer thickness and tunnel burial depth must be considered simultaneously in the design process.

Overall, the innovations of this study are the following: First, this study breaks through the traditional single-cross-section research paradigm, establishing a unified 3D model covering two types of key cross-sections, achieving for the first time a direct quantitative assessment of stress interaction between adjacent sections, and clarifying the unique stress concentration patterns caused by spatial proximity. Second, it incorporates the coupling effect of burial depth and stiff layer thickness into the analysis system, accurately revealing the change mechanism of peak tangential stress migration and surrounding rock yielding trend under their synergistic effect through a 2D parametric model, making up for the shortcomings of existing studies that rely on multiple single-factor analyses, and providing more practical theoretical support for the design of tunnels with complex spatial combinations.