Research on the Optimization of Reinforcement Measures and the Deformation Mechanism of the Lower Tunnel in the Construction of the Overlapping Tunnels

Abstract

Taking a completely stacked section of Beijing Metro Line 22 as the research background, a three-dimensional finite element model was established to study and analyze the displacement and stress variation laws of the existing lower tunnel under different working conditions. The results show that the combined reinforcement measures of radial grouting and trolley support can effectively reduce the adverse effects of the upper tunnel on the lower tunnel during the construction of the overlapping tunnel. It cut the vault vertical displacement from 5.31 mm to 2.67 mm and reduced the stress range from 2.30 MPa to 0.71 MPa, reducing vertical displacement by 50% and maximum principal stress changes by 40% compared to the unreinforced condition. Furthermore, a parametric study indicated an optimal grouting scheme with a 2 m thickness, 120° angle, and 200 MPa modulus, which achieved similar reinforcement effectiveness with a 50% reduction in grout volume.

1. Introduction

With the acceleration of urbanization and the continuous improvement of metro networks in China, the interchange and undercrossing between different metro lines have become increasingly frequent. At the same time, the spacing between metro tunnels and other buildings, as well as between metro tunnels themselves, has been reduced. Through this approach, the tunnel can effectively avoid surrounding buildings and roads, saving underground space resources. Consequently, many tunnels are arranged in stacked or slightly overlapping configurations, known as stacked tunnels.

China’s metro construction is in a phase of rapid development, and the construction of stacked tunnels is gradually increasing. However, alongside the expansion of metro networks and the spatialization of metro lines, issues such as structural safety hazards in tunnels have emerged. The construction of stacked tunnels can cause multiple construction disturbances to the ground and surrounding structures. The construction of the upper tunnels will have a greater impact on the stress and displacement fields of the soil around the lower tunnels that have already been formed during the same period [1,2,3]. Then, it can increase stress concentration and deformation of the tunnel structure, which greatly affects the structural safety of the tunnels. Therefore, it is vital to take appropriate control reinforcement measures to ensure the safety of the structure.

Prior studies compared grouting or mechanical support in isolation; few quantified how a trolley support plus radial grouting jointly affects the existing lower tunnel during upper-tunnel excavation. Radial grouting reinforcement is a common measure during the construction process of overlapping tunnels. Trolley support is a movable support installed at the upper shield to increase the structure’s stability and rigidity. Both reinforcement methods can be employed simultaneously, which may impact the lower tunnel. In this paper, we model a fully stacked section on Beijing Metro Line 22 and test four working cases to measure lower-vault displacement and stress during construction, with and without grouting and trolley support. At the same time, the parameters of the grouting reinforcement measure (thickness, angle, and modulus of elasticity) were analyzed to determine the better grouting reinforcement scheme.

2. Project Profile, Methods and Model

2.1. Project Profile

The shield tunnel between Guanzhuang Station and Yongshun Station of Beijing Metro Line 22 is east–west oriented, the design starting point of the section is at right K115+200.851, and the design ending point is at right K118+334.574. Due to the constraints of Guanzhuang Station form and Yongshun Station form, both of them are completely stacked form, and in the middle section of the tunnel show parallel form or partially stacked form. The total length of the completely stacked section is about 800 m, and the clear distance between the upper and lower tunnels is 3.4–6 m. This article selects the fully overlapping shield tunnel segment near the Yongshun Station as the research object for simulated reinforcement measures, with a tunnel spacing of around 5 m, predominantly composed of sandy soil and clay. The right line of the shield tunnel in the stacked section is located below the left line, with the excavation sequence of the right line (the lower tunnel) followed by the left line (the upper tunnel). The geological profile is shown in Figure 1, and the calculated parameters of the soil layer are shown in

Table 1. Soil layer calculation parameters table.

Name	Soil Thickness (m)	Unit Weight (kN/m3)	The Angle of Internal Friction (°)	Cohesion (kPa)	Poisson Ratio	Modulus of Elasticity E (MPa)
① Miscellaneous fill	3	18	8	5	0.3	4
② Silty clay	6	19	11	34	0.3	9
④ Fine to medium sand	10	20	30	0	0.26	30
⑤ Silty clay to fat clay	3	19.5	9	32	0.32	12
⑥ Medium dense fine-medium sand	14	20	32	0	0.26	40
⑦ Clayey silt to heavy clay	6	19.5	9	36	0.32	13
⑧ Dense fine-medium sand	18	20	36	0	0.26	50

. One point needs to be clarified: the soil characteristics of layers ③ and ④ are similar. For the convenience of calculation, they have been combined into soil layer ④.

Control Standards

During the construction of overlapping tunnels, two indicators are critical for controlling the structural integrity of the lower tunnel: strength control and deformation control. Excessive deformation directly threatens overall stability, necessitating strict deformation control standards to ensure operational safety.

In this study, the deformation control standards for the lower tunnel are based on the “Code for Monitoring of Urban Rail Transit Engineering” (GB50911-2013) [4] and previous project cases [5,6]. The cumulative uplift deformation of the lower tunnel segments caused by the upper tunnel construction was set as the control value, with a limit of less than 5 mm.

2.2. Methods

To mitigate the impact of construction-induced settlements on the prior tunnels, auxiliary methods such as radial grouting and trolley support are often used in the construction of stacked tunnels. Radial grouting reinforcement of the surrounding soil can effectively enhance the integrity and strength of the surrounding rock, thereby increasing ground stiffness and reducing the disturbance caused by shield tunneling. When the upper shield passes through the segments of the lower tunnel, timely trolley support can improve stress distribution and constrain deformation of segments.

2.2.1. Radial Grouting Reinforcement

To reduce soil settlement and ensure the structural safety of the lower tunnel, grouting is performed in the soil layer near the interlayer. Grouting pipes with a certain length are installed in the reserved grouting holes on the vault of the lower tunnel segments, extending into the surrounding soil. After the passage of the shield in the lower tunnel, the soil around the tunnel is grouted by these pipes [7,8]. Radial grouting enhances tunnel bearing capacity by filling rock fissures and improving soil compaction.

After the construction of the right-line tunnel, additional reserved secondary grouting holes are added to the vault segments. The lower tunnel segments B1 and B2 each have three reserved grouting holes, while the K-block has one. The upper tunnel segment A2 has three reserved grouting holes, and A1 and A3 each have two. Grouting is performed through these holes to reinforce the soil within a 3.0 m radius of the tunnel vault, covering a 180° range. The special design of the stacked tunnel segments is shown in Figure 2, and the radial grouting cross-section is illustrated in Figure 3.

2.2.2. Trolley Support Reinforcement

Internal support structures are typically installed within the lower tunnel, covering an area 10 m ahead and behind the upper shield in order to prevent excessive deformation or structural damage to the lower tunnel segments caused by the weight of the upper shield or construction activities. Common support structures include cross-shaped, star-shaped, gate-type, and mobile hydraulic trolley supports. The first three types suffer from high material consumption, low overall stiffness, difficulty in controlling support force, and inability to move with the upper shield, making them less effective for protecting the lower tunnel. In contrast, mobile hydraulic trolleys overcome these shortcomings and have been widely adopted in recent stacked tunnel projects. The trolley support has a high strength, which not only directly bears part of the maximum principal stress originally borne by the surrounding rock, but also limits the deformation of the surrounding rock, improving overall stability.

The trolley support arrangement must align with the progress of the upper tunnel construction, ensuring that the trolley remains within the lower tunnel in the area affected by the upper shield. Typically, the trolley is positioned approximately 10 m ahead of the deck and 3 m behind the shield to ensure the structural safety of the lower tunnel. Based on previous cases, the preliminary design parameters for the support trolley are as follows [9,10].

The trolley consists of five sections with a total length of about 30 m. Each section has two frames, and each frame is equipped with five wheeled supports. The trolley moves on steel rails, and the sections are connected by hinges. The trolley head always remains 5 m ahead of the upper shield deck and advances at the same speed as the shield tunneling machine. The longitudinal section of the trolley support is shown in Figure 4.

In the numerical simulation, eight sets of trolley meshes were established, each of which was 6 m long. After the lower tunnel was completed, the first trolley mesh group was activated. After two excavation steps of the upper tunnel, the second trolley mesh group was activated. Following two more excavation steps, the third trolley mesh group was activated while the first was deactivated. This process continued, ensuring that two active trolley mesh groups always supported the lower tunnel as the upper shield advanced, simulating the movement of the trolley with the shield.

2.3. Model Establishment

2.3.1. Constitutive Model

The modified Mohr–Coulomb model is an extended version of the Mohr–Coulomb model. It features numerical coupling and is more suitable for frictional sandy soil foundations. It enables reasonable calculation of stratum deformation caused by the shield tunnel excavation. Therefore, the modified Mohr–Coulomb constitutive model is selected as the soil constitutive model.

The modified Mohr–Coulomb model requires numerous material parameters in numerical simulation process. Among these, the three stiffness parameters E_50ref, E_refur, and E_refoed—which significantly influence model calculations—are determined based on triaxial compression tests and one-dimensional compression tests. Within the model, these parameters are typically established using equivalent values and conversion ratios. The reference secant modulus E_50ref is typically set equal to the deformation modulus E₀. For sandy soils, the unloading–reloading modulus E_refur is taken as (3–5)E_50ref, and the reference tangent stiffness E_refoed is generally set at (0.5–1.3) E_50ref. In this study, the sand layer uses E₀:E_50ref:E_refoed:E_refur = 1:1:1:3, while the silty clay layer uses 1:1:1:5.

2.3.2. Model Establishment

To accurately simulate the effects of trolley and grouting reinforcement, the meshes were optimized. The 3D model was generated by extending a 2D mesh, with the 2D meshes divided using the Delaunay method for computational efficiency and data export convenience (Figure 5). The 2D meshes were then replicated along the tunnel excavation direction to form the 3D meshes (Figure 6). The shield tunnel area was finely meshed, with element sizes of 0.5 m for the lower tunnel and 1 m for the upper tunnel. The boundary meshes were 2 m, and the rest were transitional sizes. The model comprised 89,702 elements and 88,935 nodes. Each mesh is independent during the numerical simulation process and peak uplift changes by less than five percent between different meshes.

The boundary conditions for the model are as follows: the upper surface is free, the bottom is subjected to vertical constraint in the y-direction, and the side boundaries are applied with normal constraints. The soil mass and grouting layer are simulated using 3D solid elements, while the segments and shield shell are modeled with 2D plate elements. The segments were obtained by extracting the outer soil meshes of the tunnel, the shield shell was derived from the outer surface of the grouting layer, and the trolley support was simulated using 1D beam elements. The above steps ensured that the contact points between the dolly model and the tube sheet model are co-nodes. During the construction phase, the properties of the grouting mass were converted to the properties of grouting reinforcement mass at the corresponding locations, and the grouting mass follows the structural strength criterion. As the strength of the grouting mass is greatly affected by the grouting materials and construction, the mechanical indexes of the grouting reinforcement mass are determined with the existing engineering cases [11,12,13,14]. The material parameters for structural units are listed in

Table 2. Structure material parameter table.

Structural Material	Unit Weight (kN/m3)	Poisson Ratio	Modulus of Elasticity (MPa)
Trolley (rolled steel)	78.5	0.2	206,000
Grouting reinforcement mass	22	0.25	150

. The radial grouting model and trolley modeling are illustrated in Figure 7 and Figure 8, respectively.

2.3.3. Model Assumptions

In researching shield tunneling construction, the excavation process is simulated by activating and deactivating mesh groups, boundary groups, and load groups. For earth pressure balance shield tunneling, a tunneling pressure is usually applied to the soil at the tunnel face in simulations to restrict the displacement of the soil in front of it. Grouting pressure is applied to the segments to simulate the pressure exerted by grout during synchronous grouting. The shield tunnel excavation process is defined as a discontinuous, jump-type advancement. The specific assumptions for the three-dimensional numerical model are as follows:

• Homogeneous layered soil: In numerical simulations, soil layers are approximated as homogeneous elastoplastic bodies, assuming the soil is isotropic and conforms to the modified Mohr–Coulomb criterion.
• Initial soil stress: In actual engineering, soil stress includes self-weight stress and tectonic stress. However, since this paper does not address rock mass failure, the initial soil stress is solely considered as the self-weight stress. The initial stress field is therefore analyzed based on the self-weight stress field. In the software, self-weight is applied to the initial stratum, and the displacement reset function is used to achieve the effect of constructing the initial ground stress field.
• Neglecting groundwater influence: In actual projects, dewatering measures may be adopted according to specific construction methods before excavation, which weakens the impact of groundwater on the project. To simplify simulation calculations, groundwater effects are disregarded in this study.
• Shield machine stepwise advancement: The simulation models shield machine excavation as sequential construction steps, with each step corresponding to the width of a segment ring.
• Simplified treatment of loads and grouting: During excavation, the support pressure at the working face is simulated by applying tunneling pressure, with horizontal stress at the tunnel centerline serving as the reference. The equivalent layer is used to simulate the construction process of synchronous grouting, and the equivalent layer is treated as an elastic body with a uniformly distributed and constant-thickness circular ring.

2.3.4. The Load Value of the Construction Stage

In this paper, the grouting pressure of the upper and lower tunnels is simulated by 0.4 MPa and 0.5 MPa, which acts radially on the outer ring surface of the segment in the form of uniformly distributed load. The upper tunnel tunneling pressure is 0.15 MPa, and the lower tunnel tunneling pressure is 0.25 MPa. The jack thrust is considered the annular uniform load acting on the segment longitudinally, and the jack thrust on the previous segment is “passivated” after the jack thrust is applied to the next segment.

2.3.5. Reinforcement Conditions

To evaluate the impact of different reinforcement measures on the deformation and stress of the lower tunnel during upper tunnel construction, four working conditions are considered:

• Condition 1 (grouting only): After the lower shield tunnel was constructed and the pipe sheet was applied, the lower tunnel was grouted radially upwards to a depth of 3 m. The upper tunnel was then excavated until it was completed.
• Condition 2 (trolley only): After the lower shield tunnel was constructed and the pipe sheet was applied, trolley support was first set up in the lower tunnel diameter, after which the upper tunnel was excavated to completion. The lower trolley was always kept 5 m ahead of the upper shield during the upper tunnel driving.
• Condition 3 (grouting + trolley): After the lower tunnel was constructed, both radial grouting and trolley support were applied before excavating the upper tunnel. Then, the upper tunnel was excavated to completion.
• Control condition (no reinforcement): No measures were taken; the upper tunnel was excavated directly after the lower tunnel.

To isolate the deformation of the lower tunnel caused by upper tunnel excavation, a displacement reset step is added after the lower tunnel excavation in all conditions. Each working condition is carried out independently and does not affect the other.

2.3.6. Shield Tunneling Process

Earth pressure balance shield excavation process: Excavation is achieved by the rotating cutter head at the front of the shield machine, which cuts the soil on the tunnel face. The sealed soil chamber behind the cutter head provides thrust pressure to maintain balance between water and soil pressures on the excavation face. Forward momentum is generated by the thrust force from jacks applied to the longitudinal sides of the segment rings. After segment assembly, synchronous grouting is performed in the annular gap between the segments and the surrounding soil to stabilize the soil around the tunnel. During the process from excavation to segment lining assembly, the shield shell bears the water and soil pressure around the tunnel, serving as temporary support.

3. Results and Discussion

3.1. Displacement and Stress Variation

3.1.1. Displacement Variation in the Lower Tunnel

Referring to the previous engineering examples, it is known that the change in value of displacement at the vault of the lower tunnel is the largest [15,16,17]. The vertical displacement change in the lower tunnel vault is selected to plot a time history curve like Figure 9.

From Figure 9, it can be observed that all four curves exhibit a consistent behavioral trend: as the upper tunnel excavation face approaches, passes, and moves away from the monitoring section, the vertical displacement curve gradually steepens before stabilizing. This indicates that reinforcement measures do not alter the displacement trend but effectively reduce its magnitude. The final vertical deformations under the four conditions are 5.31 mm (no reinforcement), 4.42 mm (grouting only), 4.14 mm (trolley only), and 2.67 mm (grouting + trolley). Among them, the combined reinforcement is the most effective in controlling vertical displacement. The vertical deformation values of the combined reinforcement are reduced by about 50% compared to the unreinforced case, with a much smoother curve. This is because radial grouting enhances the parameters of the surrounding rock, thereby improving its self-supporting capacity and fundamentally reducing its own deformation. The trolley support directly bears the load through its high strength and rigidity, effectively limiting structural deformation. Using both measures simultaneously can achieve better results.

3.1.2. Stress Variation in the Lower Tunnel

The curve of the maximum principal stresses in the lower tunnel vault as it varies with the tunneling process on the upper line is shown in Figure 10.

As the excavation face of the upper tunnel approaches and then moves away from the monitoring face, the maximum principal stress at the vault first increases and then decreases. The overall variation trends of the four curves are relatively consistent. Therefore, reinforcement measures do not change this trend. The maximum principal stresses, from highest to lowest, are 2.30 MPa, 2.14 MPa, 1.94 MPa, and 1.85 MPa. The minimum principal stresses, from lowest to highest, are 1.07 MPa, 1.11 MPa, 1.14 MPa, and 1.14 MPa. The stress variations under the four conditions are 1.23 MPa (no reinforcement), 1.12 MPa (grouting only), 0.8 MPa (trolley only), and 0.71 MPa (grouting + trolley). Detailed information of the maximum principal stress value is shown in

Table 3. Detailed list of maximum principal stress values.

Reinforcement Condition	Maximum Value (MPa)	Minimum Value (MPa)	Difference (MPa)
Unreinforced	2.30	1.07	1.23
Only grouting	2.14	1.11	1.03
Only trolley	1.94	1.14	0.8
Grouting + trolley	1.85	1.14	0.71

. From Table 3, we can see the above data more clearly. The data indicates that the reinforcement measures are effective in minimizing the impact of the upper shield construction on the change in maximum principal stress in the lower tunnel. The combined reinforcement reduces stress variation by about 40%, with trolley support showing a more apparent effect on vertical displacement control.

In this process, tunnel reinforcement measures serve distinct functions. Radial grouting significantly enhances the mechanical properties of the surrounding rock, enabling it to withstand higher maximum principal stresses without failure. Simultaneously, it optimizes stress distribution by forming a “load-bearing arch,” thereby indirectly alleviating stress concentration. The support structure possesses high strength, allowing it to directly bear a portion of the maximum principal stress originally sustained by the surrounding rock. The combined application of both measures yields superior results.

3.1.3. Validation [9]

The overlapping section of Guangzhou Metro Line 12 was constructed using the shield method, with excavation proceeding from bottom to top. The tunnel diameter is 6.4 m. During excavation of the upper tunnel, the maximum vertical deformation of the lower tunnel occurred at the vault, reaching 4.02 mm. Compared to an unreinforced condition, the use of trolley support reduced vault vertical displacement by 1.72 mm, representing approximately 42%.

In summary, the combination of radial grouting and trolley support significantly reduces vertical deformation and principal stress variation in the lower tunnel, effectively mitigating the adverse effects of upper tunnel construction.

3.2. Analysis of the Displacement of Lower Tunnel

Factors such as geological and hydrological conditions, types of grouting fluids, grouting pressure, grouting reinforcement parameters, and construction techniques can affect the effectiveness of radial grouting reinforcement in tunnels. This simulation focused on three aspects of grouting reinforcement parameters: the thickness, the grouting angle, and the elastic modulus. The standard group is based on the original grouting reinforcement design for the overlapping tunnel section, with a grouting radius thickness of 3 m, a grouting angle of 180°, and an elastic modulus of 150 MPa. An unreinforced condition is added as the control group. All other factors remain unchanged, and only a single variable is altered to analyze the displacement and stress changes in the lower tunnel.

3.2.1. Influence of Grouting Reinforcement Mass Thickness on Vertical Displacement

A simulation was conducted with the radial thickness of the grouting reinforcement mass as the single variable. In the numerical simulation design, only the thickness was changed. Since the radial grouting thickness in actual engineering generally does not exceed 3 m, the thicknesses were set to 1 m, 2 m, and 3 m, while other factors remained the same as the standard group. Based on the vertical displacement change at the vault of the lower tunnel, time course curves of vertical deformation at the vault for different grouting thicknesses and a curve of maximum vertical displacement at the vault of the lower tunnel with different grouting thicknesses were plotted, as shown in Figure 11 and Figure 12.

The maximum vertical displacements of the vault, from largest to smallest, are 5.31 mm, 4.87 mm, 4.58 mm, and 4.42 mm. From Figure 11, it can be observed that the maximum vertical deformation and displacement values at the vault of the lower tunnel significantly increase as the grouting reinforcement thickness decreases during the excavation of the upper tunnel. From the perspective of the tunnel excavation direction, it leads to larger differences in longitudinal displacements in the lower tunnel segments, which can easily cause uneven settlement.

The thickness of reinforcement is an important factor in determining reinforcement capacity. The greater the thickness, the greater the radial support force provided, which can more effectively resist deformation of the surrounding rock. However, economic benefits also need to be considered. From Figure 12, it can be seen that the maximum vertical displacement of the lower tunnel decreases as the thickness of the grouting reinforcement mass increases, but the trend of reduction is gradually slowing down. Using a grouting reinforced thickness of 2 m, the vertical displacement changes noticeably with the radial grouting thickness when the grouting thickness is less than 2 m. When the grouting thickness exceeds 2 m, the trend in displacement changes slows down. Therefore, from the perspective of economic benefits, choosing a reinforcement thickness of 2 m is more reasonable.

3.2.2. Influence of Grouting Angle on Deformation of Lower Tunnel

Simulation of different working conditions with the grouting angle as a single variable; only the grouting angle was changed. In actual projects, grouting angles of 120° and 180° are commonly used. Therefore, the grouting angles for the tunnel arch were set to 90°, 120°, 180°, and 360°, while other factors remained the same as the standard group. The time course curves of vertical deformation of lower tunnel vaults with different grouting angles and the curve of maximum vertical displacement of the lower tunnel with different grouting angles are shown in Figure 13 and Figure 14.

The maximum vertical displacements of the vault, from largest to smallest, are 5.31 mm, 4.85 mm, 4.62 mm, 4.42 mm and 4.16 mm. From Figure 13, it can be observed that the vertical displacement at the vault of the lower tunnel decreases as the grouting angle increases. Figure 14 shows that the rate of decrease gradually slows. Considering the reinforcement effect and economic efficiency, a grouting angle of around 120° is deemed reasonable.

3.2.3. Influence of Elastic Modulus of Grouting Reinforcement Mass on Deformation

The elastic modulus of the grouting reinforcement mass is significantly influenced by construction techniques and grout mix ratios. In most projects, the elastic modulus of the grouting reinforcement mass typically ranges from 150 MPa to 250 MPa. Therefore, elastic moduli of 100 MPa, 150 MPa, 200 MPa, 250 MPa, and 300 MPa were selected for modeling analysis, while other factors remained the same as the standard group. The time course curves of vertical deformation of lower tunnel vaults with different modulus of elasticity are shown in Figure 15. And the curve of maximum vertical displacement of lower tunnel with different modulus of elasticity is shown in Figure 16.

The maximum vertical displacements of the vault, from largest to smallest, are 5.31 mm, 4.69 mm, 4.42 mm, 4.19 mm, 3.98 mm, and 3.84 mm. From Figure 15 and Figure 16, it can be seen that the vertical displacement at the vault of the lower tunnel decreases as the elastic modulus of the modulus of elasticity increases, but the trend of reduction slows. A sufficiently high elastic modulus can enable the reinforcement ring to withstand greater loads, but attention must be paid to coordinating with the stiffness of the surrounding rock to avoid generating new stress concentrations due to excessive rigidity. When the elastic modulus is less than 200 MPa, the displacement changes noticeably with the elastic modulus. When the elastic modulus exceeds 200 MPa, the changes in displacement become less pronounced. Considering both the reinforcement effect and economic efficiency, an elastic modulus of 200 MPa is considered reasonable.

3.2.4. Optimal Grouting Reinforcement Design Scheme

Based on the above analysis of the changes in grouting thickness, grouting angle, and elastic modulus, the optimal grouting reinforcement parameters were determined as follows: grouting thickness of 2 m, grouting angle of 120°, and elastic modulus of 200 MPa. A corresponding model was established to analyze the reinforcement effect, as shown in Figure 17. The results of the calculations were analyzed in comparison with the original design scheme and the control group, and the vertical displacement time history curve of the lower tunnel vault during the excavation of the upper tunnel was plotted, as shown in Figure 18.

In the optimal combination scheme, the maximum vertical displacement at the vault of the lower tunnel is 4.55 mm, compared to 4.42 mm for the original design scheme and 5.31 mm for the control group. In terms of grouting reinforcement effectiveness, compared to the unreinforced condition, the vertical displacement of the vault is reduced by 17% in the original design scheme and 14% in the optimal combination scheme, showing close results. From the perspective of material usage (grouting volume), the optimal combination scheme reduced the grouting volume by nearly half compared to the original scheme, which is more significant in terms of economics.

Due to limitations such as grouting diffusion, hardening strength of the grout, and practical construction conditions, as well as potential discrepancies between numerical simulations and actual conditions. The actual grouting reinforcement design tends to be relatively conservative and requires adjustments based on actual construction situations.

4. Conclusions

Through three-dimensional numerical simulations, this paper compares and analyzes the law of the displacement and stress of the lower tunnel during the excavation of the upper tunnel under radial grouting, trolley support, and combined reinforcement measures. The results show that the above three reinforcement conditions can reduce the vertical deformation and principal stress changes in the lower tunnel structure. Among them, the combined reinforcement measure of radial grouting and trolley support yielded the best control effect. It cut the vault vertical displacement from 5.31 mm to 2.67 mm and reduced the stress range from 2.30 MPa to 0.71 MPa, reducing vertical displacement by 50% and maximum principal stress changes by 40% compared to the unreinforced condition. This effectively mitigates the adverse effects of upper tunnel construction on the lower tunnel in overlapping tunnel projects.

Numerical simulations were also conducted to analyze the influence of different grouting reinforcement parameters on the vertical deformation of the lower tunnel under grouting reinforcement measures. The data indicates that increasing the thickness, angle, and elastic modulus of the grouting reinforcement mass reduces the maximum vertical deformation of the lower tunnel, but the rate of reduction gradually slows as these parameters increase. The original design proposal was rather conservative. By comparing the results, an optimal grouting reinforcement scheme was derived. In terms of reinforcement effectiveness, the optimized scheme was comparable to the original scheme. From the viewpoint of grouting volume, the optimized scheme used significantly less material, demonstrating that the optimized grouting scheme is safe and reasonable.