Parametric Analysis of Static–Dynamic Characteristics of Adjacent Tunnels in Super-Large Twin Tunnels by DEM

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The parametric analysis of super-large-diameter twin tunnels under train-induced vibrations provides scientific guidance for the design, construction, and operation of super-large twin tunnel engineering.

Abstract

The dynamic characteristics of super-large-diameter twin tunnels under train vibration loads have become a critical issue affecting not only the engineering safety of their own tunnels but also adjacent tunnels. A numerical model of super-large-diameter (D = 15.2 m) twin tunnels was established by the discrete element method (DEM) to analyze the static and dynamic responses of adjacent tunnel structures and surroundings under train-induced vibrations. Three parameters were considered: internal walls, absolute and relative spacing, and water pressure. The results indicate that internal walls in super-large twin tunnels can significantly reduce the static and dynamic responses in both the structures and surroundings of the adjacent tunnel. The vehicular lane board (wall2) plays a determinative role, followed by the smoke exhaust board (wall1), while the left and right partition walls (wall3 and wall4) exhibit the least effectiveness. The static–dynamic responses of the liners and surroundings of adjacent tunnels in super-large twin tunnels are significantly greater than those in smaller twin tunnels when the absolute spacing is identical. Moreover, the significant differences in displacement and velocity between the liners and surroundings can lead to cracks, leakage, or even instability. Appropriate water pressure (149 kPa) can effectively mitigate dynamic responses in adjacent tunnel structures and surroundings. The dynamic characteristics of super-large-diameter twin tunnels differ markedly from those of small-diameter twin tunnels, with internal walls, twin tunnel spacing, and water pressure all influencing their static and dynamic behaviors. This study provides theoretical guidance for the design and operation of super-large-diameter twin tunnels.

1. Introduction

With the rapid development of urban rail transit, super-large-diameter twin tunnels designed for combined highway and railway use are being extensively constructed due to their advantages in conserving underground space [1,2]. Subway train operations cause vibrations in their own and adjacent tunnel structures and surrounding soil, impacting stability, durability, and the safety and comfort of adjacent tunnels. As a result, research on the dynamic behavior of super-large-diameter twin tunnels is gaining more attention.

For small-diameter tunnels (d = 6.0–6.2 m), Heidary et al. [3] found ground vibration increases with higher axle loads when two trains pass in opposite directions inside twin tunnels (d = 6.0 m). Zhou et al. [4] conducted a 50× g centrifuge test on parallel tunnels (d = 6.0 m) under train and sweeping frequency loads. Their results showed that twin-tunnel interaction significantly amplifies dynamic responses. Li et al. [5] found the influence range of shield driving, and the interaction between the twin tunnels (d = 6.2 m) with different axis spacings in shield driving. Pang et al. [6] established a robust methodological framework for assessing tunnel face stability and offers valuable guidance for the design and construction of shield tunnels (d = 6.0 m) in analogous geological and operational contexts. Li et al. [7] demonstrated that the calculated displacement settlement trends align closely with the numerical simulation and are consistent with field monitoring data when new tunnels (d = 6.2 m) are excavated above existing tunnels. These studies demonstrate that research on standard-diameter tunnels (d = 6.0–6.2 m) under train-induced vibrations has been relatively thorough.

In research on large-diameter tunnels (D = 10.0–15.0 m), Wang et al. [8] found that wider faults significantly increase plastic zone expansion in the lining of a fault-crossing tunnel (D = 10 m). Zhang et al. [9] have identified “horizontal duck egg” deformation patterns and butterfly-shaped moment distributions under ultimate loads, crucial data for assessing the capacity of large tunnels (D = 11.6 m). Liu et al. [10] demonstrated that shield speed directly affects subgrade settlement, informing construction parameter optimization in sensitive areas in twin shield tunnels (D = 12.8 m). Zhang et al. [11] conducted long-term monitoring of segment loads and structural internal forces in a large-diameter shield tunnel (D = 14.5 m) and found that actual earth pressures are just 48–60% of theoretical values, which provides an empirical basis for the load calculation of large-diameter tunnels. These studies collectively demonstrate that large-diameter tunnels exhibit distinct dynamic characteristics compared to conventional sizes, warranting further investigation.

In research on super-large-diameter tunnels (D ≥ 15.0 m) [12,13,14,15], Shi et al. [16] defined the longitudinal ground settlement patterns of twin tunnels (D = 15 m), combining the three-dimensional random finite element methods and Monte Carlo simulation. Kou et al. [17] provided critical design guidelines of large-diameter tunnel (D = 15 m) joints for high-pressure environments. Wu et al. [18] compared vibration characteristics between ultra-large (D = 15.2 m) and small (d = 6.2 m) river-crossing twin tunnels using DEM models, demonstrating larger tunnels’ superior stability when the relative spacing is the same (l/d = 0.25, l/D = 0.25). Wang et al. [19] proved that thicker secondary linings enhance load capacity by optimizing segment-lining interaction in 15.2 m shield tunnels. Guo et al. [20] found that internal structures effectively reduce dynamic responses by physical model tests (D = 15.2 m). Li et al. [21] studied the impact of 15.4 m shield tunnel construction on adjacent existing subway tunnels by finite element model, measuring 17.9 mm displacements in adjacent subway tunnels and evaluating isolation pile effectiveness. Xue et al. [22] revealed that excavation of super-large-diameter tunnels (D = 15.56 m) causes the maximum compressive stress in the existing tunnel lining at the haunch and the maximum tensile stress at the crown. From the above research results, it can be seen that current research on super-large-diameter tunnels primarily examines single-tunnel configurations, with limited studies on the dynamic response of twin tunnels.

In this paper, the factors affecting the static and dynamic response of the ultra-large-diameter twin tunnels (D = 15.2 m) are further investigated by DEM based on the previous research of our group [18]. Three parameters with different internal walls, different spacings, and different water pressures are set up, and the static and dynamic responses of sleepers, segments, and surroundings of super-large twin tunnels under train vibration are investigated. This research provides scientific guidance for the design, construction, and operation of super-large-diameter twin tunnel projects.

2. Modeling Procedure

2.1. Project Overview

This study is based on the Sanyang Road combined road-rail twin tunnels of Wuhan Metro Line 7, the cross section of this super-large-diameter (D = 15.2 m) twin tunnels as shown in Figure 1. The burial depth of twin tunnels is 0.5 D, and the water depth varies between 0.5 D and 1.5 D, with a minimum clear spacing of l = 0.25 D between the twin tunnels. The geometric dimensions of the tunnels and the physical–mechanical parameters of the surroundings (silty sand) are summarized in

Table 1. Basic dimensions of twin tunnels model.

Model Parameter	Diameter	Thickness of Liner	Thickness of Wall1	Thickness of Wall2	Thickness of Wall3 and Wall4	Size of Sleeper (Length × Height)
Dimension (m)	15.2	0.65	0.65	1.0	0.65	1.2 × 0.2

and

Table 2. Physical–mechanical parameters of silty sand.

Silty Sand	w/%	Es/MPa	c/kPa	φ/°	v	γ/kN/m3
Physical and mechanical parameters	20.4	21.9	7.0	31.9	0.49	20

Note: w is the water content; Es is the compression modulus; c is the cohesion; φ is the friction; v is the Poisson’s ratio; γ is the bulk density.

. The Type A train, which operates in Wuhan Metro Line 7, and its corresponding train-induced vibration loads are illustrated in Figure 2. Detailed derivations of these loads can be found in the prior research [18].

2.2. Basic Model Information

The discrete element method (DEM) establishes a physical and mechanical model of contact based on Newton’s second law and the force-displacement equation to simulate discontinuous and discrete elements. This method has wide applicability and has been applied in fields such as mining [23,24], civil engineering, petroleum [25], chemical engineering [26,27], waste material isolation, agriculture [28,29], and materials science [30,31].

In this paper, the two-dimensional model recommended in the user manual is adopted for modeling. The modeling process is detailed in the literature [14]. The summary of mesoscopic parameters adopted for the surroundings and C60 segments is shown in

Table 3. Micro-parameters of silty sand in the DEM model.

Parameters	Radius of Particles (m)	Density (kg/m3)	Normal Stiffness (N/m)	Tangential Stiffness (N/m)	Coefficient of Friction
Silty sand①	R1 = 0.12–0.2	2000	2.05 × 107	2.05 × 107	0.62
Silty sand②	R2 = r1 = 0.06–0.1	2000	2.19 × 107	2.19 × 107	0.62
Silty sand③	r2 = 0.03–0.05	2000	2.27 × 107	2.27 × 107	0.63

and

Table 4. Micro-parameters of C60 segments in the DEM model.

Parameters	C60①	C60②	Parameters	C60①	C60②
Radius of particles (m)	r3 = 0.009–0.012	R3 = 0.02–0.03	Normal strength of parallel bond (Pa)	7.1 × 109	6.9 × 109
Density (kg/m3)	2500	2500	Tangential strength of parallel bond (Pa)	7.1 × 109	6.9 × 109
Normal stiffness (N/m)	9 × 108	9 × 108	Normal stiffness of parallel bonding (N/m)	9 × 108	8.6 × 108
Tangential stiffness (N/m)	9 × 108	9 × 108	Parallel bonding tangential stiffness (N/m)	9 × 108	8.6 × 108
Coefficient of friction	1.98	1.98	Parallel bonding radius	1.0	1.0

Note: C60① for small-diameter twin tunnels and C60② for large-diameter twin tunnels.

.

Three sets of numerical models were established to investigate the influencing factors of the dynamic response of super-large-diameter twin tunnels under train-induced vibrations. These models analyze the static and dynamic characteristics of adjacent tunnel liners and surroundings under different conditions, including internal wall configurations, absolute and relative spacings between tunnels, and varying water pressures. The model details are summarized in

Table 5. Summary of model information.

No.	Objective	Condition	Explanation
1	Comparison of inner wall effects	A1 (T2)	Super-large-diameter twin tunnels
		A2 (W234)	Super-large twin tunnels with wall2, wall3, and wall4
		A3 (W12)	Super-large twin tunnels with wall1 and wall2
		A4 (W2)	Super-large twin tunnels with wall2
		A5 (NW)	Super-large twin tunnels with no internal walls
2	Comparison of absolute and relative spacing	B1	Small-diameter twin tunnels with 0.25 d spacing
		B2	Super-large twin tunnels with 0.25 d spacing
		B3	Super-large twin tunnels with 0.25 D spacing
3	Comparison of water pressure	C1	0.5 D water pressure
		C2	1.0 D water pressure
		C3	1.5 D water pressure

.

The first set comprises five models (T2, W234, W12, W2, and NW), and the cross-section of T2 is illustrated in Figure 3. The analysis primarily addresses the displacement and velocity of adjacent tunnel sleepers, liners, and surroundings under train loads.

The second set of models, comprising three conditions (B₁, B₂, and B₃), aiming to compare the absolute and relative spacing, are illustrated in Figure 4. The absolute spacing is defined as maintaining identical distances between the small and super-large twin tunnels, while relative spacing refers to controlling the ratio of the tunnel spacing to their respective diameters to be consistent.

The comparison between B₁ and B₂ aims to evaluate the influence of train-induced vibrations on adjacent tunnels under identical absolute spacing (0.25 d), whereas the comparison between B₁ and B₃ focuses on the effects under identical relative spacing. The spacing of the twin tunnel in B1-B3 conditions is calculated by Equations (1) and (2).

l₁ = l₂ = 0.25 d = 0.25 × 6.2 m = 1.55 m

(1)

l₃ = 0.25 D = 0.25 × 15.2 m = 3.8 m

(2)

where d is the diameter of small twin tunnels, and D is the diameter of super-large twin tunnels.

The third set of models includes three conditions, comparing the static and dynamic responses of the adjacent tunnel of super-large-diameter twin tunnels under train-induced vibrations at different water pressures. The water pressures on the top surface of the model for conditions C₁, C₂, and C₃ are 0.5 D, 1.0 D, and 1.5 D, respectively, and they are calculated by the following Equations (3)–(5):

C₁: P₁ = ρgh₁ = 1 × 10³ × 9.81 × 0.5 × 15.2 = 74.6 kPa

(3)

C₂: P₂ = ρgh₂ = 1 × 10³ × 9.81 × 1.0 × 15.2 = 149 kPa

(4)

C₃: P₃ = ρgh₃ = 1 × 10³ × 9.81 × 1.5 × 15.2 = 223 kPa

(5)

where ρ is the density of water, 1 g/cm³; g is gravitational acceleration, 9.81 m/s²; and h_i (i = 1,2,3) is the depth of groundwater from the top surface of the model.

Taking the C₂ condition as an example, a schematic diagram of water pressure calculation for the C₂ condition in the third set of models can be seen in Figure 5. The length and height of the model are 64.6 and 38.0 m. The lateral pressure coefficient is specified as 0.4 [18]. The water pressures on all sides of the model are calculated as follows: Equations (6)–(8):

P_w1 = ρgh₂ = 149 kPa

(6)

P_w2 = P_w1 + ρgH = 149 + 1 × 9.81 × 38.0 = 522 kPa

(7)

P_w3 = P_w4 = (P_w1 + P_w2) × 0.5 × 0.4 = 134 kPa

(8)

where P_w1 is the water pressure on the top surface of the model; P_w2 is the water pressure on the bottom surface of the model; and P_w3 and P_w4 are the water pressures on the left and right sides of the model.

3. Results and Discussion

This chapter is divided into three subsections. Firstly, the vibration characteristics of adjacent super-large-diameter tunnels under train-induced vibrations under A₁–A₅ conditions (Figure 3), focusing on the analysis of displacement and velocity in tunnel sleepers, liners, and surroundings. Secondly, we compare the responses of liners and surroundings in adjacent tunnels under train-induced vibrations when the absolute and relative spacings between super-large and small twin tunnels are identical (Figure 4). Finally, we compare the maximum displacement and velocity of adjacent tunnel liners and surroundings under varying water pressure conditions (74.6 kPa, 149 kPa, 223 kPa) on the top face of super-large twin-tunnel models during train-induced vibrations.

3.1. Inner Walls

Super-large-diameter tunnels contain various inner walls: wall1 denotes the smoke exhaust board, wall2 represents the vehicular lane board, while wall3 and wall4 correspond to the left and right partition walls, respectively. This section focuses on investigating the static–dynamic response levels of these walls on adjacent tunnel sleepers, liners, and surroundings.

3.1.1. Sleeper

The horizontal displacement and velocity patterns of adjacent tunnel structures and surroundings are similar to their vertical counterparts, though the vertical displacement and vertical velocity (D_V and V_V) values consistently exceed horizontal measurements based on previous comparative studies [18]. Therefore, this study emphasizes the vertical responses of Tunnel 2 structures and surroundings.

Figure 6 illustrates the time–history curves of vertical displacement (D_V) and velocity (V_V) at the mid-point S₃ of Tunnel 2 sleepers under conditions A₁–A₅. S₁ and S₅ are the left and right endpoints, and S₂ and S₄ are the points of application of the train load. As train-induced vibrations propagate, the D_V and V_V values at S₃ exhibit oscillatory behavior under A₁–A₅ conditions, with the NW condition demonstrating significantly greater D_V and V_V compared to other conditions.

The D_V of point S₃ in T2 sleepers is shown in Figure 6a. The minimum and maximum values were −1.52 mm and 0.79 mm, respectively. The absolute values of negative D_V for S₃ were significantly larger than the positive values, indicating that the sleepers in adjacent tunnels primarily experience downward pressure under train loads.

The differences between maximum and minimum D_V values under the five conditions were 1.19 mm (T2), 1.31 mm (W234), 1.3 mm (W12), 1.34 mm (W2), and 2.31 mm (NW). The NW condition exhibited the largest amplitude, with a 94.12% increase compared to T2. At 2.13 s, the D_V reached −1.52 mm, showing distinct behavior from other conditions.

The D_V trends for W234, W12, W2, and T2 were similar, with nearly overlapping curves. Compared to T2, the amplitude increases for these conditions were 10.08%, 9.24%, and 12.61%, respectively. The absence of wall2 in NW led to its significantly higher D_V, confirming that wall2 plays a critical role in mitigating train-induced vibrations and maintaining tunnel stability.

The V_V of point S₃ in T2 sleepers is shown in Figure 6b. Under T2, W234, W12, and W2, the V_V curves overlapped, with maximum positive and negative peaks at 7.78 mm/s and −9.39 mm/s, respectively. In contrast, the NW condition showed an outstanding V_V trend, peaking at −21.35 mm/s (t = 2.05 s) and 20.87 mm/s (t = 2.22 s), followed by gradual stabilization.

The differences between maximum and minimum V_V values at A₁–A₅ conditions are 16.17 mm/s (T2), 16.99 mm/s (W234), 16.81 mm/s (W12), 16.95 mm/s (W2), and 42.35 mm/s (NW). Compared to T2, the increases were 5.07%, 3.96%, 4.82%, and 161.90%, respectively. This indicates that the internal walls of super-large tunnels significantly reduce the V_V of adjacent tunnel sleepers, with wall2 playing a decisive role in mitigating the dynamic response of Tunnel 2 sleepers.

As shown in Figure 6a,b, the V_V curves largely overlap under A₁–A₄ conditions, while D_V exhibits some differences. This indicates that inner walls exert a greater influence on D_V than on V_V. Adjacent tunnel sleepers oscillate vertically under these vibrations because metro train-induced vibrations induce pronounced dynamic disturbances in closely spaced tunnels. Internal walls in super-large-diameter tunnels markedly reduce the static–dynamic responses of sleepers, with wall2 playing a decisive role. Notably, the NW condition exhibits the most severe sleeper disturbances, significantly exceeding other conditions.

To further investigate the displacement patterns of Tunnel 2 sleepers, Figure 7 compares the D_V and V_V variations in A₁–A₅ conditions. The calculation formulas are provided in Equations (9) and (10).

$${D_V=D}_{Vmax}-D_{Vmin}$$

(9)

$$V_V=V_{Vmax}-V_{Vmax}$$

(10)

where D_Vmax is the maximum value of vertical displacement; D_Vmin is the minimum value of vertical displacement; V_Vmax is the maximum value of vertical velocity; and V_Vmin is the minimum value of vertical velocity.

The D_V variations at monitoring points of Tunnel 2 sleepers are shown in Figure 7a. The maximum and minimum D_V variations are 2.36 mm and 1.12 mm, respectively. Under the NW condition, D_V variations (2.27–2.36 mm) significantly exceed those of the other four conditions (1.12–1.43 mm), further confirming the decisive role of wall2 in reducing D_V. Comparing W12 and W234, the differences between S₁-S₅ monitoring points are 0.02, 0.02, 0.02, 0.03, and 0.03 mm, respectively. The slightly higher D_V variations in W234 indicate that horizontal wall1 contributes more to D_V reduction than vertical wall3 and wall4.

The V_V variations at monitoring points are shown in Figure 7b. The V_V curves nearly overlap (15.40–17.85 mm/s) under A₁–A₄ conditions, while NW exhibits significantly higher values (41.61–42.99 mm/s). Compared to T2, NW shows V_V variation increases of 152.97% (S₁), 155.48% (S₂), 161.10% (S₃), 166.75% (S₄), and 170.13% (S₅). This underscores wall2’s dominant role in suppressing V_V, while wall1, wall3, and wall4 have negligible effects.

Compared to Figure 7a,b, point S₁ exhibits the largest D_V and V_V values, while point S₅ shows the smallest under A₁–A₅ conditions. This indicates that sleeper regions closer to T1 experience greater vertical vibration impacts. The effectiveness of internal walls in reducing D_V and V_V for Tunnel 2 sleepers is ranked as wall2 > wall1 > wall3 = wall4, with wall2 playing a decisive role.

As shown in Figure 6 and Figure 7, adjacent tunnel sleepers oscillate vertically with train loads under metro train-induced vibrations. The D_V and V_V of Tunnel 2 sleepers under NW condition are significantly higher than other conditions, confirming that internal walls markedly reduce both static and dynamic responses. The stabilizing effect of Tunnel 2 internal walls follows the hierarchy: wall2 > wall1 > wall3 + wall4. Wall2 is critical for suppressing the static–dynamic characteristics of Tunnel 2 sleepers.

3.1.2. Liner

As shown in Figure 8, the maximum resultant displacements (D_R) and velocities (V_R) values at four monitoring points (0°, 90°, 180°, and 270°) of the Tunnel 2 liner vary significantly across the A₁–A₅ conditions. D_R and V_R are calculated by Equations (11) and (12).

$$D_R=\sqrt{D_h^2+D_v^2}$$

(11)

$$V_R=\sqrt{V_h^2+V_v^2}$$

(12)

where D_H is the maximum horizontal displacement; D_V is the maximum vertical displacement; V_H is the maximum horizontal velocity; and V_V is the maximum vertical velocity.

As shown in Figure 8a, the maximum D_R values at the 0°, 90°, 180°, and 270° monitoring points of the Tunnel 2 liner vary significantly under A₁–A₅ conditions. D_R magnitudes follow the order 180° > 90° > 270° > 0° across all conditions, reflecting distinct vibration impacts at each angle. The largest D_R consistently occurs at 180° (closest to T1), while the smallest D_R is observed at 0° (farthest from T1). D_R attenuates progressively from the vibration source (180°) toward the opposite side (0°), demonstrating a clear distance-dependent decay pattern. Notably, D_R at 270° is slightly smaller than at 90°, indicating that deeper burial depth enhances structural restraint from the surroundings, thereby improving the liner’s resistance to disturbances and reducing displacements. This highlights two key factors influencing D_R: (1) proximity to the vibration source and (2) burial depth, with deeper sections benefiting from stronger soil support to mitigate displacement.

The maximum V_R values of the Tunnel 2 liner are shown in Figure 8b. Under conditions with internal walls, the V_R trends align with the D_R patterns in Figure 8a, following the order 180° > 90° > 270° > 0°, further confirming that V_R increases with proximity to the vibration source (T1). However, under the NW condition, the V_R ranking shifts to 180° > 270° > 0° > 90°. This anomaly likely stems from the reduced structural stability of the liner without internal walls, making it more susceptible to vibrations from T1 and resulting in markedly different velocity patterns compared to wall-equipped conditions.

Under train-induced vibrations, both D_R and V_R at the four monitoring points of Tunnel 2 liner correlate strongly with distance from the vibration source and burial depth. The NW condition exhibits distinct D_R and V_R patterns (e.g., reversed ranking at 270° and 0°) and significantly higher magnitudes compared to other conditions, emphasizing the critical role of internal walls in stabilizing dynamic responses.

3.1.3. Surroundings

The surroundings play a critical role in supporting tunnel structures to maintain stability under dynamic loads. Analyzing the dynamic characteristics of the surroundings provides essential insights to complement the dynamic behavior of Tunnel 2 liners.

Figure 9 shows the D_R and V_R of Tunnel 2 surroundings under A₁–A₅ conditions. Figure 9a compares the maximum D_R values of the T2 surroundings. The D_R magnitudes at four monitoring points follow the order 180° > 90° > 270° > 0°, consistent with the trends observed in Figure 8a. This confirms that the D_R of surroundings is similarly influenced by propagation distance from the vibration source and burial depth.

Figure 8a and Figure 9a reveal minimal differences in D_R between Tunnel 2 liners and surroundings across A₁–A₅ conditions. Notably, the D_R values at four angles (0°, 90°, 180°, 270°) are identical for both liners and surroundings under W2 and NW conditions, indicating that the displacement patterns of tunnel structures and surroundings are closely aligned under metro train-induced vibrations, signifying a structurally safe state.

Comparing T2 and NW conditions, the differences of D_R in surroundings at 180° and 0° are 0.65 mm and 0.71 mm under the T2 condition are increased by 48.15% and 151.06% when compared to the NW condition. These results demonstrate that internal walls significantly reduce D_R in surroundings, with effectiveness varying by proximity to the vibration source.

Figure 9b compares the maximum V_R values of the Tunnel 2 surroundings under A₁–A₅ conditions. Similar to the D_R trends in Figure 9a and the liner V_R patterns in Figure 8b, the V_R magnitudes under A₁–A₅ conditions follow 180° > 90° > 270° > 0° which is consistence with the D_R trends in Figure 9a and the liner V_R patterns in Figure 8b, confirming that V_R increases with proximity to the vibration source, consistent with findings from liner analysis.

Under the NW condition, the V_R ranking shifts to 180° > 0° > 270° > 90°, deviating from the established patterns observed in wall-equipped conditions. This indicates that the vibration transmission law identified in Figure 8b does not apply to NW condition.

Compared to the most stable condition T2, the V_R differences in surroundings at 180° and 0° under NW condition are 11.79 mm/s and 15.03 mm/s, increased by 93.57% and 230.30% when compared to the value in the most stable condition T2. This indicates that the absence of internal walls (NW) leads to significantly amplified and complex dynamic responses in both liners and surroundings under dynamic loads, further proving the critical role of internal walls in stabilizing the surroundings.

As shown in Figure 9a, b, the D_R and V_R patterns in the surroundings at four monitoring points align closely with those of the liners, governed by their position, proximity to the vibration source, and burial depth. Additionally, the T2 condition exhibits the highest stability, and the internal walls significantly reduce the D_R and V_R of the surroundings when comparing T2 and NW conditions. Notably, wall2 contributes most prominently to maintaining the stability of the surroundings.

Figure 10 shows the coordination of the surroundings at various angles of Tunnel 2 under T2 and NW conditions. Coordination is defined as the average number of particles in contact with a central particle within a measurement circle, which can reflect structural stability. A higher coordination means greater stability. Each tunnel is monitored via eight measurement circles (0°, 45°, 90°, 135°, 180°, 215°, 270°, and 315°) to assess coordination at different angles. Changes in the coordination of Tunnel 2 surroundings indicate the disturbance level induced by train-induced vibrations from the adjacent tunnel.

Under the NW condition, coordination variations at all monitoring points are greater than those under T2. The most significant coordination changes occur at the vault (90°), followed by 180°, indicating that coordination changes in the Tunnel 2 surroundings correlate with monitoring distance and position. At the vault, train-induced vibrations cause particles to slide downward along the liners, leading to a decrease in coordination and stability, which also shows that the vault is the focus of dynamic characteristics.

Overall, the Tunnel 2 surroundings exhibit greater fluctuations in coordination under NW condition due to the absence of internal walls when compared to the T2 condition. Under T2 condition, the surroundings with greater burial depth demonstrate higher coordination, which remains nearly constant throughout the testing period. This indicates that the lower-right region of the Tunnel 2 surroundings is less affected by vibrations and maintains greater stability.

Combined with Figure 9 and Figure 10, the static–dynamic responses of Tunnel 2 surroundings are influenced by the position of liners and surroundings, proximity to the vibration source, and burial depth. Internal walls enhance surroundings stability, while coordination is governed by distance from the vibration source and burial depth. The T2 condition demonstrates higher and more stable coordination, highlighting the structural benefits of internal walls.

3.2. Absolute and Relative Spacing

It is well-known that the spacing between parallel twin tunnels significantly influences the dynamic characteristics of the adjacent tunnel [32,33,34]. Figure 11 compares the D_R and V_R of adjacent tunnel liners and surroundings under varying spacing conditions to investigate the effects of absolute and relative spacing.

As shown in Figure 11a, the maximum and minimum differences of D_R of liners and surroundings under B₁–B₃ conditions occur at 180° (closest to T1), confirming that proximity to the vibration source dominates displacement patterns. The maximum liner-surroundings D_R differences for B₁, B₂, and B₃ are 0.49 mm, 0.33 mm, and 0.12 mm. Such discrepancies possibly destabilize the surroundings due to insufficient structural support.

The liners D_R ranking is as follows: B₂ > B₁ > B₃. For the surroundings, all other monitoring points align with the same ranking of the liners except at the vault (90°), where the D_R of the small-diameter tunnels is slightly lower than that of the 0.25 D super-large-diameter tunnels. This indicates that super-large-diameter tunnels exhibit greater static–dynamic responses under the same absolute spacing while showing slightly lower responses under relative spacing equivalence. Additionally, the granular nature of the surroundings leads to distinct displacement patterns at the vault compared to other monitoring points, necessitating focused stability assessments in this region.

As shown in Figure 11b, the V_R of liners and surroundings for the 0.25 D super-large-diameter twin tunnels (B₃) is significantly smaller than those under B₁ and B₂ conditions. This indicates that the dynamic characteristics of super-large-diameter tunnels with equivalent relative spacing (B₃) are markedly lower compared to small-diameter tunnels (B₁) and super-large-diameter tunnels with 0.25 d (B₂). Additionally, the V_R of surroundings and liners align closely across all monitoring points, suggesting that the surroundings effectively support the tunnel structure, placing the super-large-diameter tunnel in a safer state.

Comparing B₁ and B₂ conditions, significant V_R differences exist between surroundings and liners. In the 45–135°, the V_R in surroundings is smaller than the value in liners, while in the 180–270°, the V_R in surroundings exceeds the value in liners. This opposing dynamic behavior in the upper-right and lower-left regions of Tunnel 2 disrupts the support mechanism between surroundings and liners, potentially leading to liner cracking, leakage, or instability.

The V_R in liners for super-large and small-diameter tunnels overlap at most monitoring points, with minor differences at 0°, 45°, and 315°. However, the V_R in surroundings exhibits substantial disparities. In the 0–135° interval (upper half), super-large-diameter tunnels (B₂) show higher V_R than small-diameter tunnels (B₁), while in the 180–270° interval (lower-left corner), small-diameter tunnels (B₁) exhibit higher V_R. This demonstrates that under equivalent absolute spacing, liner displacements are comparable between super-large and small-diameter tunnels, but the V_R differences in surroundings are pronounced, highlighting distinct dynamic behaviors in super-large-diameter tunnel surroundings that warrant further investigation.

As shown in Figure 11a,b, the D_R and V_R of liners and surroundings follow the order B₂ > B₁ > B₃. For twin tunnels with equivalent relative spacing, super-large-diameter tunnels exhibit smaller static–dynamic responses in both liners and surroundings compared to small-diameter tunnels, likely attributed to the vibration-damping effect of internal walls discussed in Section 3.1. In contrast, under equivalent absolute spacing, super-large-diameter tunnels demonstrate significantly enhanced dynamic responses, accompanied by increased discrepancies in displacements and velocities between liners and surroundings. Regardless of whether absolute or relative spacing is maintained, the static–dynamic characteristics of super-large-diameter tunnel liners and surroundings fundamentally differ from those of small-diameter tunnels. This highlights the complex interactions between structural and surroundings in super-large-diameter tunnels, necessitating further research to address their unique challenges in stability and dynamic performance.

3.3. Water Pressure

Under train-induced vibrations, the surrounding water pressure of super-large-diameter twin tunnels exerts varying influences on adjacent tunnel liners and surroundings. This section investigates the static–dynamic responses of liners and surroundings under different water pressures (P₁ = 74.6 kPa, P₂ = 149 kPa, P₃ = 223 kPa).

Figure 12a compares the maximum D_R values under different water pressures (C₁–C₃ conditions). The D_R of liners and surroundings at C₂ condition is slightly smaller than at C₁ condition, while D_R at C₃ condition exceeds that at C₂ condition. This suggests that moderate water pressure (P₂ = 149 kPa) can mitigate train-induced vibrations in adjacent tunnels, whereas excessive water pressure (P₃ = 223 kPa) possibly amplifies displacements.

Figure 12b compares the maximum V_R values. Across all monitoring points (0–315°), V_R initially increases and then decreases, peaking at 180° and 225°. The higher V_R in the central tunnel region (90–270°) correlates with proximity to the vibration source. From 0° to 180°, the liner V_R exceeds the surroundings V_R, while the reverse occurs from 180 to 315°, indicating that the distance to the vibration source significantly influences velocity distributions.

As shown in Figure 12a, b, the D_R and V_R of liners and surroundings remain similar for most monitoring points under C₁–C₃ conditions, with only minor variations observed at specific points such as 180° and 225°. The maximum displacement occurs at 180°, while peak velocity appears at 225°, indicating a spatial shift between the locations. Both displacement and velocity patterns are closely tied to proximity to the vibration source. Moderate water pressure (P₂ = 149 kPa) effectively reduces the static–dynamic responses of adjacent tunnel liners and surroundings under train-induced vibrations.

Figure 13a compares the average coordination of the surroundings. The results show significantly lower coordination under the C₁ condition compared to the C₂ and C₃ conditions. This demonstrates that increasing water pressure from 74.6 kPa to 149 kPa substantially enhances surroundings stability, particularly in the central tunnel region, where coordination at 180° increases by up to 9.81%. Under the C₃ condition, coordination improvements over the C₂ condition are marginal, indicating comparable stability levels between these two pressure conditions.

The coordination variation rate is defined as in Equation (13), and its change rate of the surroundings is shown in Figure 13b. Under the C₃ condition, the variation rate reaches its maximum at 180°, indicating significant instability in this region. The higher variation rate at the C₃ condition reflects reduced stability in the tunnel and surroundings due to excessive water pressure, which increases stress in the twin tunnel structure and compromises stability.

$$\mathrm{A}={\displaystyle \frac{M1-M2}{M1}}\times 100\%$$

(13)

where M₁ is the maximum coordination, and M₂ is the minimum coordination.

As shown in Figure 13a,b, the C₂ condition exhibits the highest stability among the three conditions. The central region of the twin tunnels (particularly at 180°) experiences the greatest impact. Optimal water pressure (P₂ = 149 kPa) effectively enhances the stability of super-large-diameter tunnels.

The displacements and velocities at the vault of super-large-diameter tunnels are significantly larger and exhibit distinct patterns compared to other monitoring points, necessitating focused investigation from Figure 11a and Figure 12a. Figure 14a compares the vertical strain at the vault under different water pressures. The vertical strain curves oscillate with metro train-induced vibrations but remain positive, indicating vertical elongation of particles and soil loosening. This phenomenon arises because the surroundings at the vault tend to slide laterally due to the structural features of the liners under vibrations. Under C₂ and C₃ conditions, the vertical strains at the tunnel crown are similar and smaller than those at the C₁ condition, likely due to higher confining pressure in this region, which restricts particle movement and reduces strain.

Figure 14b compares the maximum and minimum values of vertical strain at the vault. Under C₁–C₃ conditions, the maximum vertical strain differences occur at 90° (0.015%, 0.014%, and 0.014%), while the minimum differences appear at 180° (0.004%, 0.002%, and 0.002%). This is likely due to the structural constraints of the twin tunnels at 180°, which limit lateral particle movement, resulting in minimal vertical strain. At 135°, strain differences are slightly smaller than at 90°, possibly because this region is closer to both the vibration source (T1) and the vault. These points are experiencing stronger disturbances and weaker resistance to sliding, leading to higher vertical strain.

As shown in Figure 14a,b, the structural features of the vault liners cause significant positive vertical strain in the surroundings. Larger differences in maximum-minimum strains at 90° and 135° indicate lower stability in these regions.

As shown in Figure 12, Figure 13 and Figure 14, increasing water pressure from C₁ to C₂ condition reduces the static–dynamic responses in super-large-diameter tunnels reduced when water pressure increase from C₁ to C₂ condition, while the static–dynamic responses increase when the water pressure further increases to C₃ condition. Optimal water pressure (P₂ = 149 kPa) is critical for maintaining stability. Displacement and velocity in the surroundings depend on proximity to the vibration source, with the central tunnel region (especially 180°) most affected. Vertical strain peaks at 90° and 135° require special attention due to their instability.

4. Conclusions

This study conducted a parametric analysis of the static–dynamic characteristics of adjacent tunnels for super-large-diameter twin tunnels under train-induced vibrations using the DEM. Three sets of models were developed to investigate the effects of internal walls, absolute and relative spacing, and water pressure on the static–dynamic responses of adjacent tunnel structures and surroundings. The main conclusions are as follows:

• The NW condition (no internal walls) of T2 exhibits significantly greater static–dynamic responses in both liners and surroundings compared to other conditions. Internal walls in super-large tunnels markedly reduce these responses, with their stabilizing effectiveness ranked as wall2 > wall1 > wall3 = wall4. Wall2 plays a particularly decisive role. D_R and V_R in liners and surroundings correlate strongly with the burial depth and distance to the vibration source.
• Under equivalent relative spacing, super-large twin tunnels show smaller static–dynamic responses in liners and surroundings than small twin tunnels. However, under equivalent absolute spacing, super-large twin tunnels exhibit significantly enhanced dynamic responses and larger discrepancies in liner and surroundings displacements and velocities. The static–dynamic characteristics of super-large twin tunnels fundamentally differ from those of small twin tunnels under any spacing.
• Optimal water pressure (P₂ = 149 kPa) effectively suppresses displacements and velocities in liners and surroundings, while excessive pressure (P₃ = 223 kPa) amplifies static–dynamic responses. Critical monitoring points requiring attention include the central tunnel region (180°), vault (90°), and 135°, where responses are most pronounced due to proximity to the vibration source and the surroundings easily sliding.

The static–dynamic characteristics of super-large-diameter twin tunnel liners and surroundings differ fundamentally from those of small twin tunnels, highlighting the complex interactions between their liners and surroundings. Future research will employ the scale model to explore the dynamic behavior of super-large twin tunnels under train-induced vibrations.