Full-scale experimental investigation of structural effects in existing shield tunnel linings induced by a new tunnel crossing

Abstract

The construction of new tunnels induces additional/unloading pressures on existing tunnels, subsequently affecting structural integrity. To assess tunnel response, a full-scale multiring test was conducted, simulating water/soil and additional/unloading pressure from a new undercrossing tunnel. Key parameters analyzed included additional/unloading pressure, tunnel axis distance, longitudinal forces, and loading levels to evaluate structural deformations and joint behavior. Results showed that additional/unloading forces significantly impact structural ring convergence during tunnel crossing stage. These forces vary nonlinearly with distance from the crossing point, but their influence is linear. Further, joint opening and dislocation not only depend on external load but also on the staggering effect and segment geometry. Reducing the tunnel axis distance meaningfully upsurges unloading forces, leading to higher strains at joints and the segment body. Longitudinal force, directly proportional to the staggering effect, reduces structural deformations; for instance, even a 1% force mitigates up to 32.05% joint dislocation. Lifecycle analysis revealed the tunnel crossing stage is far more vulnerable than the construction/operation stage, and tunnel axis distances of twice or more of the diameter can be considered safe. This study provides practical insights for engineers to mitigate risks during tunnel crossings and enhances safety guidelines for life cycle management.

Graphical abstract

Keywords

segmental tunnel lining / full-scale test / tunnel crossing / additional/unloading pressure / tunnel safety / life cycle of segmental lining

1 Introduction

The establishment of an underground transportation system has been a goal for many large cities in China, aimed at mitigating surface traffic congestion. The growing use of underground space presents considerable hurdles to the development of new shield tunnels. As the density of subway lines increases, an increasing number of shield tunnels are necessarily created to cross with existing tunnels, whether situated above or below them. It may result in structural defects such as dislocation between rings, segment opening, segment cracking, and disengagement of the track bed, jeopardizing tunnel safety [1–9]. These issues mentioned, including the risk of structural failure in tunnel construction, necessitate immediate attention due to their potential for catastrophic consequences, such as collapse, ground settlement, and significant project delays. Excavation adjacent to existing tunnels compromises ground stability, redistributes stress, and may induce fissures, necessitating real-time monitoring and full-scale experimental investigation. Therefore, during the construction of a new tunnel, forecasting the stress and deformation responses of the existing tunnel and proactively instituting a series of control measures poses a considerable challenge for modern geotechnical engineering designers.

Two categories of new tunnels crossing with existing tunnels are identified: above-crossing tunnels and below-crossing tunnels. Numerous researchers have conducted extensive investigations into the response of existing tunnels to above-crossings and have proposed various control measures to substantially reduce the risks to these tunnels [10–18]. An example of a case study is the Chongqing rail transit line 5, which is located above the Renhechang tunnel of the Shanghai-Chengdu China railway, inducing upward dislocation in the existing tunnel [19]. Another case study of twin tunnels undercrossing the existing twin subway line 4 in Beijing, China, induced downward settlement of up to 7 mm [20]. Nevertheless, the crossing mechanism between the existing tunnel and the newly built tunnel beneath it is insufficiently delineated, and practical solutions for addressing the deformation of the existing tunnel require additional investigation.

Recent studies have recorded the additional deformations of existing tunnels caused by nearby tunnels crossing below, as measured through empirical field data [20–23], numerical analysis [24–29], and physical model tests [30–33]. The construction of new metro lines inevitably necessitates tunneling beneath existing facilities, such as shield tunnels and pipelines. As a result, the growing apprehensions about the effects of below-crossing tunneling on existing structures have been extensively studied by specialists [14,34]. As the below-crossing tunneling alters the already balanced stress field due to the removal and replacement of soil with new concrete lining, it instigates unloading weight. This weight’s influence propagates through the stratum to the existing tunnel, referred to as additional/unloading pressure. The below-crossing tunneling will alter the already balanced stress field and induce settlements, resulting in bending moments, on the existing structures, which may adversely affect their normal operation [35,36]. Consequently, accurately predicting the deformation behaviors of existing tunnels is imperative for ensuring their safety, stability, and durability. Additionally, due to the inherent complexities of soil-structure interaction, investigating this phenomenon presents a substantial challenge.

Based on the preceding elaboration, it is evident that researchers have attained a comprehensive and integrated understanding of the deformation and mechanical responses of existing tunnels. However, these studies have involved small-scale testing, field measurements, and numerical simulations, which entail several assumptions and simplifications concerning the responses of existing tunnels. This results in an insufficient real-time response to elevated additional/unloading pressure generated by a tunnel situated below. However, no research has been undertaken to examine the effects on existing tunnel structures stemming from a below-crossing tunnel, attributed to the higher costs and restricted access to advanced testing systems. To gain a comprehensive understanding of the performance of an existing shield tunnel lining, a meticulously designed full-scale experimental study has been conducted. The multi-ring shield tunnel test yields more authentic structural behavior by precisely replicating soil−structure interaction and joint mechanics under actual stress scenarios. These tests provide the secure validation of failure scenarios, such as overloads or new construction events, which would be too hazardous or costly to execute in actual tunnels. Figure 1 illustrates the below-crossing tunnel perpendicularly and elaborates the impact on the existing tunnel in the form of additional/unloading pressure developed by unbalancing underneath strata.

In this study, the Longshui-South Road Tunnel project in Shanghai was analyzed for the additional/unloading pressure induced by the new tunnel, calculated under various conditions. In this investigation, the structural mechanics of tunnel linings subjected to varying additional or unloading pressures, tunnel axis distance (TAD), and longitudinal forces have been carefully elucidated, thereby enhancing the understanding of their role in practical engineering applications. Following the introduction, the present work is organized as follows: Section 2 presents the experimental specimens, TC conditions, design of load, and monitoring of response. Structural behavior of lining rings, inter-ring dislocations, and response of lining components in Section 3. A detailed analysis including characteristics and structural mechanics of the existing tunnel lining during operation and the TC stage in Section 4. Moreover, a safety guide for the design of the below-crossing tunnel and the structure analysis of factors that affect the shield tunnel during its life cycle is provided in Section 5. Finally, conclusions are concise in Section 6.

2 The experiment

This experimental plan includes three rings of segmental tunnel linings with segment and radial joints subjected to circumferential and tunnel boring machine (TBM) jack forces [37,38]. Figure 2 explains experimental methodology. Subsection 2.1 delineates the specifics of the test specimen, while Subsection 2.2 emphasizes the diverse components of the testing system. Subsection 2.3 discusses the design of deformations and strain monitoring of test specimens.

2.1 Design of test apparatus

2.1.1 Experimental specimens

Segments were cast in C60 concrete, hydrated in water, and conveyed to the Shanghai Shield Tunnel center. Reinforcement (HRB400E) maintains uniformity throughout segments, with slight modifications in neighboring and critical parts. Materials properties of various components of shield tunnel are given in Table 1. Joint configuration, segment and bolt geometry, and placement orientation are shown in Fig. 3. The test specimens comprise three rings: two outer rings (750 mm in width) and a middle one that spans the full width (1500 mm). Eight segments (seven standard plus one key) constitute a ring with an outer diameter of 11360 mm and an inner diameter of 10360 mm. Each section possesses a width of 1500 mm and a thickness of 500 mm. Five standard segments (B1–B5) and two adjacent segments (L1–L2) each possess a central angle of 49.091°, but the key segment has a central angle of 16.364°.

2.1.2 Testing system

Figure 4 displays the complete loading equipment for the multiring test, comprising a test frame, a hydraulic pump system, hydraulic jacks, and a data acquisition system. Further, the hydraulic system has a pressure capacity of 63 MPa, a flow rate of 1.5 L/min, and a sampling cycle of 10 s at each station, with an accuracy of 0.10 mm in dislocation measurement. The data acquisition system also records the deformation and strain values every second. Furthermore, the top and bottom rings (half width) utilize 24 jacks each, spaced at 15° intervals in a 360° configuration, and the middle ring (full width) comprises two jack rows, amounting to 48 jacks and totaling 96 in number for three rings. Each hydraulic jack has a capacity of 981 kN, with stroke lengths of up to 300 mm. Moreover, 12 pairs of hydraulic jacks replicate the longitudinal force of the TBM jack shoe with intervals of 30° around the ring, with each pair having a capacity of 200 kN. Additionally, a test system has some limitations, including roller support at the bottom, hydraulic jacks for a uniform load, and the residual longitudinal force of 5% has been selected to accommodate test equipment constraints. Convincingly, three rings are considered a real situation of joints and segmental lining, which not only gives real stress distribution but also considers the spatial effect of tunnels.

2.2 Design of test load

2.2.1 Crossing of tunnels and test conditions

Figure 5(a) illustrates the crossing of the new tunnel under the existing shield tunnel perpendicularly, and Fig. 5(b) elaborates the impact of the new tunnel on the existing tunnel in the form of additional/unloading pressure developed by unbalancing underneath strata. Figure 5 displays the complete geometrical configuration and unloading weight ‘p’, which produces the additional/unloading pressure ‘q(x)’ at the top side of the precast concrete segmental tunnel lining (PCTL) of the existing tunnel [4,39,40].

The existing tunnel has a diameter of 11.36 m, and the new tunnel’s diameter is also the same. The existing tunnel has (x,y,z) coordinates, and the new tunnel coordinates are (λ,η,z). The origin meets at O, where both tunnel coordinates are (0,0,z), while the z-axis has various values based on the TAD between tunnels, e.g., ‘H₁’. The unloading weight ‘p’ of the new tunnel has been calculated based on material and geometric parameters. A theoretical model (Eq. (1)) is then used to compute the unloading pressure on the existing tunnel, taking into account material parameters, distances from the unloading point, and the TBM excavation location [39]. Further, MATLAB calculates the additional/unloading pressure at the origin point O (0,0,z). ‘L₁’ and ‘L₂’ are the distances of the starting point of the new tunnel to the origin and the distance of the cutting face of the new tunnel from the origin, respectively. Furthermore, this unloading pressure is applied in addition to the prevailing radial pressure on the existing tunnel.

Only the origin point O (0,0,z) is considered for the calculations with various heights between tunnels and multiple positions of the cutting face from the origin at one height. A negative value of ‘L₁’ and ‘L₂’ indicates that points are behind the origin point, and a positive value indicates that points are ahead of the origin.

(1)\begin{array}{rl}q\left(x\right)=& {\int }_{-D/2}^{D/2}{\int }_{L_1}^{L_2}\frac{P\mathrm{d}\lambda \mathrm{d}\eta }{8\pi (1-\nu )}\times [-\frac{(1-2\nu )({\mathrm{z}}_0-H)}{R_1^3}\\ & +\frac{(1-2\nu )({\mathrm{z}}_0-H)}{R_2^3}-\frac{3({\mathrm{z}}_0-H{)}^3}{R_1^5}\\ & -\frac{3(3-4\nu ){\mathrm{z}}_0({\mathrm{z}}_0+H{)}^2-3H({\mathrm{z}}_0+H\left)\right(5{\mathrm{z}}_0-H)}{R_2^5}\\ & -\frac{30H{\mathrm{z}}_0({\mathrm{z}}_0+H{)}^3}{R_2^7}],\end{array}

(2)p=\frac{{\gamma }_{\mathrm{s}}{A}_{\mathrm{e}}-{\gamma }_{\mathrm{l}}{A}_{\mathrm{l}}}{D},

(3)R_1=\sqrt{(x-\lambda {)}^2+(y-\eta {)}^2+({\mathrm{z}}_0-H{)}^2},

(4)R_2=\sqrt{(x-\lambda {)}^2+(y-\eta {)}^2+({\mathrm{z}}_0+H{)}^2},

where ν is the Passion’s ratio of soil and q(x) additional/unloading pressure. D is the outer diameter of the new tunnel. γ_s and γ_l are the unit load of soil and PCTL. A_e and A_l are the cross-sectional areas of the excavation and PCTL, respectively.

It was discovered that TCs lead to various structural deformations, which require investigation in multiple scenarios. Therefore, an experimental investigation was conducted on Longshui South Road in Shanghai, utilizing several loading conditions. The TAD while crossing tunnels was a key factor in using literature to establish experimental conditions [39]. Further, a second key factor was the residual longitudinal force caused by the TBM jack shoe thrust, and the analysis of the TBM jack shoe thrust was conducted based on actual monitoring of tunnel construction [41]. In this experiment, the TC condition, in addition to the operation stage condition, and the longitudinal force are converted into residual longitudinal force. Table 2 summarizes the experimental conditions that were convincingly developed based on the literature and experimental equipment limitations.

2.2.2 Calculation of additional/unloading pressure

Some studies investigate key parameters such as the distance between tunnels [39,42]. The impact of the distance between tunnels was analyzed in a range of 0.1D to 4D in the literature, which stated that vertical displacement reduced substantially at 2D [42]. Considering the influence of TAD on the existing tunnel, analysis was conducted for the unloading pressure induced by the new tunnel on the existing tunnel, as illustrated in Table 3. This analysis clearly indicates that the TAD doubles from 1D to 2D, yet the corresponding unloading pressure diminishes to a third of its original value. Consequently, the authors have selected a maximum TAD of 2D for experimental investigation because of marginal variations in structural deformations from the operation stage. The Additional/unloading force is calculated by dividing the circumferential length by the total number of jacks and multiplying by the area covered by ten jacks of the middle ring. Based on the internal force analysis, the load calculations for the experimental conditions were completed in the previous section.

2.2.3 Calculations of jack load

The load-structure method is used to calculate radial pressure on the tunnel, which is based on the buried depth (this study is 1D). Further, with the aid of input pressure on the tunnel, a widely known modified routine method adopting the elastic foundation approach is applied to compute the tunnel lining internal force followed by various studies in Refs. [37,43]. This load is applied for the top, middle and bottom rings in the experimental investigation.

Figures 6(a) and 6(b) illustrate the internal forces acting on the segmental linings at a depth equal to the tunnel diameter. Traditionally, for symmetric bending moments, three jack-loading groups are sufficient. However, the tunnel under examination is shallow, and the bending moment is asymmetrical. Consequently, the number of jack-loading groups has been increased to 22 to enhance the accuracy of test bending moments. Each group consists of three jacks; the load of one jack is regarded as a unit, while the loads of the other two jacks must be balanced within the system of equations. In this manner, all 22 groups achieve self-balance and accurately replicate the internal force following the actual loads. Figure 6(c) compares internal forces under actual and experimental loads. The loading principle ensures equivalence between the load and the internal force distribution on the lining structures in both the test design and the experimental study. In agreement, Fig. 6 depicts the numerical calculations’ outcome of the internal force and test design load.

2.2.4 Arrangements of loading jack’s forces and loading scheme

Subsubsections 3.4.1 and 3.4.2 computed the jack load for the top, middle, and bottom rings. Figures 7(a) and 7(b) illustrates the plan view of the top, middle, and bottom rings and the positions of the longitudinal joints on the lining ring. The Cartesian system is established with the crown at 0° and positions quantified clockwise. At the crown (0°) and the invert (180°) of the ring, 30° on either side is the area of influence by the unloading pressure. This area dominantly exhibited the vertical component of radial pressure, making it more vulnerable to structural deformations. Figure 7(c) depicts the elevation of the ring configurations in the multiring test system, highlighting the radial jack loading, water/soil force with additional/unloading force (P + SL), water/soil force (P), and longitudinal force locations.

Further, 25 hydraulic pumps are combined with 96 hydraulic jacks to apply loads on top, middle, and bottom rings, thereby replicating radial forces. One pump is connected to a maximum of 4 hydraulic jacks, and every jack in the group applies the same force. The top and bottom rings have 24 jacks, as their width is half that of the middle ring.

During the operation stage of the tunnel, a longitudinal force termed as residual longitudinal force due to dissipation over time, which stays for a more extended period [44]. Based on the TBM jack force analysis, a maximum of 50000 kN is employed during construction, and the residual longitudinal force of 5% has been selected to accommodate test equipment constraints and how the impact of longitudinal force influences segmental tunnel lining, and this value of longitudinal force will also reduce the tunnel lining’s bearing capacity [41]. Therefore, a range of 5%, 2.5%, and 0% has been introduced to analyze the tunnel lining’s more challenging behavior. Subsequently, three distinct TC conditions are amalgamated for each longitudinal force interval, reducing the overall conditions to three.

Figure 8 displays the loading scheme, which states that in step 0, the sole longitudinal force is applied, and onward, the radial force is applied sequentially. At load step 14, the design load under the operation stage is applied at 1D buried depth without TC phenomenon, and load steps 15, 16, and 17 use the load of TCs at TADs of 2D, 1.5D, and 1D, respectively.

2.3 Monitoring design

The experimental measuring technique encompasses the observation of structural ring convergence, joint opening and dislocation, bolt strain, and strain in lining concrete and reinforcing steel, as illustrated in Table 4. Figure 9 demonstrates various measuring devices at the intrados of testing specimens. The middle ring convergence is quantified at 22.5°, whereas the top and bottom rings are positioned at 90° intervals utilizing linear variable differential transformer (LVDT). The joint opening on the middle ring is monitored by four LVDT sensors placed at the intrados and extrados, although the top and bottom rings utilize half that quantity. Circumferential joint dislocation is quantified in 15° increments using LVDT sensors. Strain gauges on joint bolts and concrete/reinforcement steel quantify loads at 10°.

3 Results of experimental investigation

Upon completion of the load at design and various conditions of TC, experimental results for deformations and material behavior are explained in the upcoming sections. Generalized load P is a reference for plotting, defined as P = 2 × (P₀ – P₉₀), where P₀ (load at ring crown, 0°) and P₉₀ (load at ring waist, 90°) at the middle ring.

3.1 Structural behavior of segmental tunnel linings rings

3.1.1 Structural ring convergence

Figure 10 compares structural ring convergence under external load in the 0°–180° and 90°–270° directions in the presence of longitudinal force. A positive value indicates an increased diameter, while a negative value indicates a decreased diameter. Up to loading step 13, the convergence slope was steeply varied. At design load (step 14), lining structural ring convergence reached 3.73 mm. After crossing the new tunnel below the existing one, structural ring convergence increased to 16.62% and 21% at 2D (step 15), with further increases of 25% and 40% at 1.5D (step 16) and surges of 3.86 and 5.36 times (step 17) compared to the design load under conditions without crossing in both directions. MR (middle ring) outperformed TR (top ring) and BR (bottom ring) in most scenarios due to higher additional/unloading pressure. While TR and BR have identical loads, their responses differ in structural ring convergence; BR’s behavior is affected by support on one end. Further, convergences were higher in the ring waist direction than in the crown/invert direction, regardless of longitudinal force and ring location. Additionally, varying LF (longitudinal force) from 5%–2.5% structural ring convergence increased 1.30 and 1.34 times, and in a 2.5%–0% LF structural ring convergence increased by 1.84 and 2.25 times, respectively. Reducing longitudinal force enhances structural ring convergence, as rings behave as individual entities with lower stiffness. The tunnel-crossing phenomenon may induce structural deformations in lining structures, making the TAD and longitudinal force crucial for lining safety.

Also, in this experimental investigation, vertical displacement at the center of the tunnel was observed as 6.23 mm at 5% longitudinal force, which may increase up to 7.98 mm at 2.5% longitudinal force. Similarly, it was observed that the vertical displacement of the existing tunnel due to volume loss is 6.40 mm via theoretical analysis, and field monitoring showed it 6.25 mm at the tunnel center [42]. This shows that experimental results are very close to actual monitoring data and theoretical analysis in the literature, and displacement is one of the key indicators of investigation for easy assessment of the tunnel.

3.1.2 Response of longitudinal joints

Figure 11 compares the longitudinal joint opening of three rings, top, middle, and bottom, upon variation of LF from 5%–0%. Three locations were under consideration based on the openings, e.g., 114.55° (TR), 245.46° (MR), and 114.55° (BR). Figure 11 results revealed that longitudinal and radial forces are applied. Longitudinal joint opening increased minimally until step 3 due to initial joint adjustments. Further, steps 4–14 load versus joint opening linearly vary. In steps 15–16, the joint opening was increased with a steep slope irrespective of rings. From steps 16–17, the longitudinal joint opening increased linearly in TR and BR, while MR showed a lesser joint opening.

The longitudinal joint opening was observed significantly near the haunch of the ring, and TR has maximum, followed by BR and MR, respectively. At the same time, BR exhibited higher fluctuations in response to variations in parameters. Joint opening increased up to 5% at 2D TAD, which amplified up to 13% when TAD was reduced to 1.5D, and it crucially enlarged up to 78% compared to the design load under operation conditions without crossing phenomenon at 114.55° (BR). Further, the variation of LF from 5%–2.5%, opening increased upon reduction of LF in most cases, was up to 4%, which further enhanced up to 27% when LF is in the range of 2.5%–0%.

3.2 Inter-rings structural behavior

Figure 12 compares the circumferential joint dislocation between top-middle ring (TMR) and middle-bottom ring (MBR) at the design load under the operation stage without TC. TMR and MBR joint exhibited the most disturbed zone around the ring’s waist (65.45°–114.55° and 245.46°–294.55°) and invert (163.64°–180°). It was observed that TMR showed peak circumferential joint dislocation (CJD) at 165° compared to other locations. Further, it is stated that the ring invert is under the influence of the reaction force against the vertical load at the crown. In contrast, the waist of the ring expressed more CJD due to the presence of a key segment, as it offered lesser shear stiffness due to the shape and assembly sequence. Furthermore, there is a difference between the outcomes of both ring waists (90° and 270°) regarding the CJD, as one waist (90°) had a key segment in the middle ring, and another waist (270°) had a key segment in the TR in this experimental investigation. The TR key segment was directly in contact with a longitudinal force jack, which enhanced its shear stiffness against sliding compared to the MR key segment; therefore, at 90°, it showed superior CJD.

Additionally, upon TC, at 120°, CJD rose to 6.86% (TMR) and 3.64% (MBR) at 2D TAD, increasing to 8%/14.55% (1.5D) and 60.57%/36.36% (1D). At 165°, CJD reached 6.73%/4.64% (2D), 9.87%/9.27% (1.5D), and 36.77%/24.5% (1D). Maximum dislocation (3.05 mm) occurred in TMR at 165° due to crown loading, while MBR remained stable. Structural convergence and inter-ring forces drove TMR/MBR joint dislocation.

3.3 Response of segments and joint devices

Figure 13(a) shows (LJB) strain in TR, MR, and BR under 5%–0% LF variation. Strain increases moderately until load step 9, then sharply peaks. At 2D TAD, strain reaches 2.28%, rising to 4.62% (1.5D) and 7.64% (1D). MR consistently exhibits the highest strain, followed by BR and TR. Reducing LF from 5%–2.5% increases strain by 30.01%, while 2.5%–0% LF causes a 70.49% surge. Figure 13(b) shows circumferential joint bolt (CJB) strain in TMR and MBR at 122.73° and 171.82° under 5%–0% LF variation. Strain initially rises steeply, then mildly until step 14, before sharply increasing again. At 2D TAD, strain reaches 2%, climbing to 5% (1.5D) and 65% (1D). MBR consistently exhibits higher strain than TMR. Reducing LF from 5%–2.5% increases strain by 62% in TMR, while 2.5%–0% LF causes a 2.59 times surge, confirming LF’s inverse proportionality to bolt strain—higher LF reduces stress via increased friction, and vice versa.

Figure 13(c) shows steel reinforcement strain (90° waist location) in three rings under 5%–0% LF variation. Strain increases linearly until step 14, then steeply rises (steps 15–17), peaking at 157.98 × 10^–6 without yielding, and reinforcement plays a significant role in the internal force of the segment [45]. Strain amplifies with reduced TAD: 14.58% (2D), 25% (1.5D), and 45.83% (1D) versus operational loads. BR exhibits the highest strain, followed by MR and TR. Reducing LF from 5%–2.5% decreases strain by 19.63%, while 2.5%–0% LF further reduces it by 38.17%, confirming LF’s direct correlation with strain mitigation. Figure 13(d) shows concrete strain in TR (294.55°), MR (114.55°), and BR (294.55°) under 5%–0% LF variation. Strain rises slightly until step 14, then steeply increases. At 2D TAD, strain grows by 9.39%, escalating to 13.42% (1.5D) and 19.46% (1D). BR exhibits the highest strain, peaking at −231.85 × 10^–6 (MR) without crushing. Higher LF reduces strain: at BR’s 294.55°, strain decreases from −231.95 × 10^–6 (5% LF) to −204.96 × 10^–6 (2.5% LF) and −197.96 × 10^–6 (0% LF), confirming LF’s role in mitigating deformation.

4 Analysis of structural behavior

4.1 Characteristics of structural behavior

4.1.1 Structural ring convergence

Upon TC, the soil was removed underneath the existing tunnel and replaced with new tunnel linings, introducing additional/unloading pressure at the top of the existing tunnel. Therefore, a novel full-scale multiring experimental investigation has been designed and conducted to assess the response of lining structures and existing tunnels, which are considered to have three rings. At the crown of the rings, the MR has maximum load upon TC, while TR and BR rings have half of MR, as it is considered precisely at the center of the crossing. In contrast, ring inverts are believed to respond equally to rings while balancing forces.

Figure 14 compares structural ring convergence at the operation stage and when a new tunnel crosses below an existing tunnel at a TAD of 1D in the absence of longitudinal force. The ring crown/invert exhibited outstanding convergence in operation, as well as the TC stage, because of the enormous vertical load. Still, there was a considerable augmentation of convergence from the operation stage to TCs in the waist/waist direction of the ring in response to deformation caused by vertical load and joint stiffness. Further, in the operation stage (plain color), convergence is peaked in MR, followed by TR and BR, respectively. Similarly, this trend was also observed in the TC phenomenon, which resulted from the lack of staggering effect and the massive load. Furthermore, deformations by TC decreased upon getting away from the cause of the phenomenon on both sides (TR and BR) of the existing tunnel. However, it was observed that TR and BR exhibit differential convergence, despite having the same external load, due to differences in shear stiffness and the BR support on one side.

4.1.2 Longitudinal joint

From the analysis of outcomes, it was revealed that the TAD greatly influenced joint opening and showed an inverse relationship with it. While comparing joint openings between rings, it was revealed that TR outperformed in most circumstances, followed by BR and MR, as a result of TR being confined on one side, which introduces more opening in TR compared to the other rings, which are on both sides. Maximum longitudinal joint opening was observed irrespective of the ring at the haunch of the ring, while BR exhibited higher fluctuations upon variations in parameters, which are shown in Table 5. Further, LF also showed a similar relation with opening and caused more opening in the absence of LF; however, the maximum longitudinal joint opening, having a value of 2.45 mm, did not exceed the code value of 6 mm [46]. Furthermore, TC also induced severe bolt strain, but the strain in the bolt was significantly lower than the yield limit. Convincingly, it’s stated that TAD greatly influenced the longitudinal joint opening based on additional/unloading force which induces more load at crown and cause convergence cum joint opening.

4.1.3 Circumferential joint

Figure 15 depicts the TMR and MBR circumferential joint dislocation at various locations around the ring, e.g., 120° and 165°. A positive (+ve) value means the middle ring is displaced outward, and a negative (–ve) value means it is displaced inward, with other rings with which it shares the joint. The external load versus dislocation varied with a mild to steep slope in both joints up to load step 14, after which it transitioned into a steep slope until the peak load was reached.

At 120°, CJD increased to 6.86% and 3.64% at 2D TAD, which increased to 8% and 14.55% when the TAD was reduced to 1.5D in TMR and MBR joint, respectively. It increased significantly to 60.57% and 36.36% compared to the design load under operational conditions without the TC phenomenon in TMR and MBR, respectively, when the TAD was reduced to 1D. Further, at 165°, CJD increased to 6.73% and 4.64% at 2D TAD, which increased to 9.87% and 9.27% when TAD was reduced to 1.5D in TMR and MBR, respectively. It increased significantly to 36.77% and 24.50% compared to the design load under operational conditions without the TC phenomenon in TMR and MBR, respectively, when the TAD was reduced to 1D. The maximum dislocation was observed in TMR at 165° in response to the additional/unloading force at the crown of the ring, and MBR did not show any significant CJD due to support at the other end of the bottom ring. TMR/MBR joint dislocation is caused by structural ring convergence and inter-ring differential force. However, the maximum CJD value of 3.05 mm did not exceed the Chinese code for the shield tunneling method; the maximum allowable CJD is 9 mm to avoid leakage issues [46].

Additionally, upon variation of LF from 5%–2.5% and then further to 2.5%–0%, CJD was increased up to 44.44% and 80.13%, respectively, at 120°, irrespective of TMR/MBR. In contrast, upon variation of LF from 5%–2.5% and then further to 2.5%–0%, CJD was increased up to 20.87% and 63.48%, respectively, at 165°, irrespective of TMR/MBR. It was revealed that the ring waist direction exhibited more CJD variation. Upon reduction in longitudinal force, the upward trend was observed in CJD, as rings behaved as individual entities that offered shear stiffness. At the same time, the absence of LF boosted the dislocation, and this phenomenon was more evident near the invert/waist of the ring.

4.1.4 Segments and joint devices

Table 6 shows peak strain change in lining components upon unit variation of key parameters, e.g., TAD and LF. During TCs, segmental lining materials undergo excessive loading, which induces extreme strain in some components. There are four components, e.g., LJBs, CJBs, segment reinforcement, and segment concrete strain, which are discussed in this section.

Table 6 results indicate that reducing TAD results in a higher unloading force on the existing tunnel, leading to a higher bending moment. This moment peaks at longitudinal joints, where rotation occurs, causing additional LJB strains. Furthermore, it has been revealed that staggering effect reduction causes higher internal force with more strain at LJB. Convincingly, LF revealed a dominating change in strain while TAD shows less in bolts of both joints, and the peak was observed near the ring waist in the middle ring. Moreover, Table 6 results for the CJB case reveal that as TAD reduces, the asymmetric load on the circumferential joint increases, and the CJB bolt with higher shear force leads to more strain, which is inversely proportional to TAD. Similarly, lessening of LF also reduces shear stiffness, causing more shear force to resist the same level of dislocation.

Additionally, reinforcement and body strain vary linearly with external load until the design load in the operational stage (Opt.), and then transition to a steep slope upon TC. Reinforcement and segment strain inversely fluctuate upon variations of TAD, as reducing TAD increases asymmetric load, which directly increases internal force and strain. Also, LF directly influences circumferential joint shear stiffness as LF reduction causes more joint dislocation and less segment strain, and vice versa.

It’s convincingly revealed that the TAD and longitudinal force influence the strain behavior of materials. Both factors have different impacts on segmental lining, which triggers either internal force or joint stiffness, further inducing higher strain. However, no failure occurred in either joint devices or segment bodies, as the strain was significantly lower than the strain limit.

4.2 Structural mechanics during tunnel crossings

4.2.1 Structural effect of stagger joints

Subsection 4.1 elaborated that structural deformations depend not only on external loads but also on the configuration of the segmental linings; for example, the staggering of longitudinal joints significantly affects the lining behavior upon load application. There are two kinds of loads that segmental lining take: a radial load comprised of water and soil pressure, and a residual longitudinal force induced by a TBM jack shoe during construction. Further, in Subsubsection 4.1.1, structural ring convergence was observed 1.30 times higher at 2.5% LF compared to 5% LF presence, which significantly enhanced to 1.84 times in the absence of LF, and a similar trend was observed in Subsubsection 4.1.4 for joint bolts however, the opposite behavior in the case of reinforcement steel and segment body strains, which is better for maximum utilization of the material’s capacity to make construction more sustainable and economical. Convincingly, the investigation revealed that structural deformations and strains of segmental lining components were significantly reduced when the staggering effect of joints prevailed. This indicates that LF and staggering of joints are directly proportional; for example, higher LF produces lower structural deformations and strains in lining segments.

4.2.2 Additional/unloading pressure corresponding to tunnels axis distance

A positive (+ve) value means the middle ring is displaced outward, and a negative (–ve) value means the middle ring is displaced inward, with other rings with which it shares the joint. Figure 16 depicts the outcomes of circumferential joint dislocation around segmental lining rings at various stages of experimental investigation. A comparison is made for CJD at key locations without longitudinal force. To begin with, Fig. 16(a) expresses the CJD at load step 14 of the multiring test without TCs in the operation stage, e.g., 0.01, −0.48, 0.28, and −0.26 mm at 0°, 90°, 180°, and 270° positions, respectively between TMR, in contrast CJD was −0.12, 0.33, −0.03, and 0.13 mm at 0°, 90°, 180°, and 270° positions, respectively, between MBR.

Further, Fig. 16(b) shows experimental outcomes at load step 15, when the tunnel crosses at 2D, CJD revealed at key locations as −0.14, −0.07, 0.25, and −0.08 mm at 0°, 90°, 180°, and 270° locations, respectively among TMR, while CJD was −0.12, 0.38, −0.03, and 0.12 mm at 0°, 90°, 180°, and 270° positions respectively among MBR. Furthermore, Fig. 16(c) displays test results at load step 16, when the tunnel crosses at 1.5D, CJD revealed at key positions as 0, −0.54, 0.39, and −0.26 mm at 0°, 90°, 180°, and 270° positions, respectively between TMR meanwhile, CJD was −0.12, 0.39, 0.01, and 0.12 mm at 0°, 90°, 180°, and 270° positions, respectively, between MBR. Moreover, Fig. 16(d) demonstrates multiring test findings at load step 17, when the tunnel crosses at 1D, CJD revealed at key positions as −0.19, −0.11, 0.41, and −0.08 mm at 0°, 90°, 180°, and 270° positions, respectively in the joint of TMR, similarly CJD was −0.3, 1.62, 0.19, and 0.05 mm at 0°, 90°, 180°, and 270° positions between MBR.

Additionally, investigation findings revealed that TCs impact segmental tunnel linings at key locations, especially from the waist to the invert of the ring. It was also discovered that the crown is under the influence of unloading forces, while their impact was more evident at reaction positions, such as in the ring invert and ring waist. The top/bottom ring waists (270°) exhibited more shear stiffness than middle ring (90°) not only because of asymmetric load but also due to two reasons behind this phenomenon: first, the position of the key segment in the testing setup, which alters the mechanics of joints due to direct or indirect contact with the longitudinal force beams/specimen supports, and is the source of differential dislocation between ring waists, e.g., the top ring key segment was directly in contact with a longitudinal force beam while bottom ring key segment with specimen support, which enhanced shear stiffness against rotation/dislocation compared to the middle ring key segment without direct contact. Secondly, the trapezoidal geometry of key segments causes joint rotation/dislocation at lower asymmetric loads, and the middle key segment has a higher chance of dislocation than other key segments due to the size effect. Further, even having the same asymmetric load among top/bottom ring waists (270°), the top ring exhibited higher dislocation than the bottom ring waist because the loading beam only enhanced shear stiffness due to longitudinal force. In contrast, the bottom ring specimen supports enhanced shear stiffness due to longitudinal force and the self-weight of the lining specimen. Also, longitudinal joints are the weakest zones of the ring, offering lower stiffness against sliding and aiding more CJD. Conclusively, two positions over the ring were chosen based on unloading force and more distressing with higher CJD, e.g., 120° and 165°, for deeper analysis of CJD influenced by TAD (Fig. 17) and longitudinal force (Fig. 18).

Figure 17 explains the loading level of a multi-ring full-scale test incorporating unloading force on TR, MR, and BR and the influence of loading level on segmental linings. From 0°–360° of TMR, the most distressing positions were chosen to analyze the loading level and their impact on CJD, e.g., 120° and 165°. A positive (+ve) value means the middle ring is displaced outward, and a negative (–ve) value means the middle ring is displaced inward, with other rings with which it shares the joint.

At 120°, CJD increased to 2.23 mm when there was a design load in the operation stage without crossings of tunnels; meanwhile, at 2D TAD crossing of tunnels, CJD enlarged to 2.38 mm (+6.73%), which further boosted to 2.45 mm (+9.87%) at 1.5D. It critically increased to 3.05 mm (+36.77%) at 1D compared to the design load. Further, in a similar fashion at 165°, CJD was noted as −1.75 mm at design load in the operation stage without crossings of tunnels. Furthermore, CJD augmented to −1.87 mm (+6.86%), −1.89 mm (+8%), and −2.81 mm (+60.57%) at 2D, 1.5D, and 1D TAD of crossing of tunnels, respectively. Additionally, outcomes revealed that 120° and 165° circumferential joint dislocations were within 2% of the difference. Still, when the tunnel axis is reduced to 1D, then around the ring invert (165°), CJD is boosted because of the weak zone via the presence of a longitudinal joint.

Convincingly, the loading level is the leading factor because fluctuating the load step caused higher CJD. However, up to step 14, CJD smoothing altered, and TCs amplified CJD when the load level reached steps 15 (2D TAD) and onward.

4.2.3 Longitudinal force

Figure 18 depicts the impact of LF on circumferential joint dislocation between the TMR and MBR joints and it has vital importance in joint stiffness [47]. From 0°–360° of TMR/MBR, the most distressing locations were chosen to analyze LF influence over CJD of the circumferential joint, e.g., 120° and 165°.

Further, upon dissimilarity of LF from 5%–2.5% and then further to 2.5%–0%, CJD was augmented up to 26.92% and 80.13% for TMR, and similarly, MBR observed 44.44% and 66.67% increment respectively at 120°. In contrast, upon the distinction of LF from 5%–2.5% and then further to 2.5%–0%, CJD was enlarged up to 13.17% and 25.51% for TMR, and similarly, MBR pragmatic 20.87% and 63.48% rose respectively at 165°. It was discovered that the ring waist unveiled additional CJD differences, and upon lessening in LF, the ascending trend was observed in CJD, as rings act as discrete objects that present shear stiffness. At the same time, the absence of LF enhanced CJD, and this phenomenon was more evident near the inner/waist of the ring. Furthermore, a 1% alteration in LF instigated up to 17.18% and 32.05% oscillation in CJD at 120° in the 5%–2.5% segment and 2.5%–0%, respectively. In comparison, a 1% amendment in LF initiated up to 8.35% and 25.30% fluctuation in CJD at 165° in the segments of 5%–2.5% and 2.5%–0%, respectively.

Conclusively, the investigation’s results demonstrated that LF boosted joint stiffness. Even a minute quantity of LF stabilized the CJD, while absenteeism meaningfully amplified it. A residual longitudinal force is necessary for sealing and protecting the tunnel during its Opt.

4.2.4 Influence of key parameters

Figure 19 elaborates on how two key parameters, TAD and longitudinal force, influence the structural ring convergence of the segmental linings. The TAD is a critical safety factor for segmental linings, varying from 1D to 2D (with a change interval of 2.84 m) for TCs. Additionally, longitudinal force is vital as it induces stiffness in the lining joints, reducing structural deformation. In this research, the longitudinal force varies widely within a range of 5% to 0% (with a change interval of 1.25%). Initially, the TAD has a significant impact on the structural ring convergence of the rings. This section will focus on the convergence of the middle ring, which demonstrates peak results compared to other rings. By maintaining a constant longitudinal force, TAD enhanced structural ring convergence by as much as 24.93% within the range of 2D to 1.5D; moreover, the increase in structural ring convergence was particularly notable, reaching 158.18% within the range of 1.5D to 1D.

Also, the LF influenced segmental lining behavior, significantly impacting structural ring convergence. No surrounding phenomenon, such as TCs, was present during the Opt. (1D). Concurrently, LF increased structural ring convergence from 10.21% to 28.62% in the interval of 3.75% to 0% LF, compared to 5% LF. Further, during TCs at TAD 1.5D to 1D, structural ring convergence boosted from 19.40% to 55.85% within the LF 3.75% to 0% interval.

Convincingly, a thorough analysis of the per-meter change attributed to TAD revealed that within a diameter range of 2D to 1.5D, the maximum increase in structural ring convergence was documented at 1.51%. Meanwhile, a range of 1.5D to 1D resulted in a 25.02% increase in structural ring convergence. In contrast, to deeply analyze the unit change in LF and its influence on structural ring convergence, e.g., in the operation stage, a maximum of 10.48%, and at the same time, a peak change was noted, having a value of 15.78% in the section of 1.5D to 1D of TAD.

Figure 20 illustrates the circumferential joint dislocation of the top-middle ring when subjected to an external load, considering variations in TAD and longitudinal force at an angle of 165° of the ring. Initially, the LF is maintained at a constant level. The CJD results are derived from a comparison with a buried depth of 1D in the Opt. without cross-sections. The TAD is treated as a variable. The maximum value of CJD was 18.44% and 45.51% greater than the Opt. in moving from TAD 2D to 1.5D and from 1.5D to 1D, respectively. Additionally, when LF is considered as a variable while maintaining the TAD constant, there is a maximum increase of 33.53% in CJD during the Opt. Further, the CJD exhibited variation between 6.53% and 25.51%, whereas the LF fluctuated between 3.75% and 0% during the adjustments.

It can be convincingly asserted that unit change elucidates the significance of the interplay between variables; consequently, a change of one meter in TAD results in a 4.74% CJD, whereas a 1% alteration in LF incurs a maximum of 5.27%.

In conclusion, the variation in structural ring convergence changed hugely in the case of TAD, while CJD remained nearly similar in both scenarios at peak values. Consequently, TAD plays a more significant role in the tunnel-crossing phenomenon when a new tunnel is constructed beneath an existing one. However, the presence of LF considerably influenced the behavior of the segmental linings.

5 Factors that influence segmental tunnel linings during life cycle

5.1 Safety of tunnel crossings

In soft soils like Shanghai, tunnels are more prone to structural deformations upon excessive load, and any construction nearby existing tunnel can cause severe damage to tunnel linings; it was proved in a current investigation that TAD had massive impact on existing tunnel linings e.g., variation of TAD 1D–2D resulted in lessening of additional/unloading pressure at existing tunnel linings from 19.13–6.37 kPa (−66.70%), similarly structural ring convergence condensed from 3.86 times to 7% in same bracket of distance. Further, circumferential joint dislocation varied from 60.57%–6.86% at 165° when distance varied from 1D to 2D, while just a 1% alteration in longitudinal force caused 8.35% and 25.30% modification in circumferential joint dislocation from 5%–2.5% and 2.5%–0%, respectively.

Furthermore, experimental findings proved that additional/unloading pressure, structural deformations, and strain are reduced to a single digit at the 2D TAD at the existing tunnel. Moreover, it was also revealed that a reduction of just 1% in longitudinal force can decrease circumferential joint dislocation by up to 25.30%. Convincingly, it is stated that TADs of 2D and greater between new and existing tunnels can be considered safe. Meanwhile, longitudinal force in the ring joint can also be a plus point by prestressing CJBs or changing the circumferential joint design.

5.2 Analysis of structural deformation during the life cycle of segmental linings

The life cycle of segmental tunnel linings encompasses three distinct stages: construction, operation, and any subsequent development that impacts the structural integrity of the tunnel linings. Thus, an extensive study necessitates monitoring synchronous grouting forces (GF) during the construction stage (Cons.) [48] analyzing and calculating internal forces in the Opt., and studying additional/unloading forces encountered during TCs alongside their application in full-scale testing procedures. In the Cons., there are some cases when longitudinal force is approaching a minimum, e.g., segment installation, TBM maintenance, steering, and alignment. Further, unexpected conditions can arise when the longitudinal force is also low, such as in low resistance strata, over excavation, and failure of the propulsion system [49]. After construction, the longitudinal force turned into a residual force with the dissipation over time [44]. The residual longitudinal force of 5% has been selected to accommodate test equipment constraints and how the impact of longitudinal force influences segmental tunnel lining, and this value of longitudinal force will also reduce the tunnel lining’s bearing capacity. It is reasonable to choose an extreme condition (0% longitudinal force) for comparison of various stages.

Figure 21 presents the structural deformations observed during various stages in the life cycle of segmental tunnel structures. This comparison is undertaken without longitudinal forces to elucidate the impact of external loads and CJD and structural ring convergence (TAD: 1D) indicated at the peak locations. Initially, CJD is compared to the Opt. in construction and TCs, recorded at 1.45 and 1.37 times higher, respectively. Conversely, structural ring convergence was documented at higher values, specifically 1.69 and 3.32 times the convergence observed during the Opt.

Additionally, a comprehensive analysis revealed that the Opt. poses a higher level of risk than the other two stages. Moreover, when comparing the CJD in construction with that of TCs, it was observed that CJD was somewhat elevated (by 8%) in construction. Conversely, the structural ring convergence in TCs was meaningfully greater, reaching up to twice that of construction. It is thus convincingly concluded that TCs may present greater dangers than the Cons. to segmental tunnel lining structures.

Convincingly, Figs. 21(a) to 21(c) highlights that asymmetric loading under the influence of staggered joints and boundary conditions impacts the global deformation pattern, e.g., under asymmetric loading, staggered joints between adjacent rings redistribute stresses unevenly, leading to complex global deformation patterns. Further, shear and moment transfer at the joints cause coupled ring interactions, resulting in phase-shifted ovalisation rather than uniform distortion, and boundary conditions amplify (TR) or mitigate (BR) these effects.

6 Conclusions

An innovative experimental investigation involves a multiring in the presence of the longitudinal force from the TBM jack shoe, an external radial load (such as water or soil force), and an unloading force due to TC over on segmental linings. This study examines the impact of the tunnel-crossing phenomenon, which generates unloading forces that affect segmental linings, particularly at circumferential and longitudinal joints. Furthermore, it also included strain analysis of various key locations susceptible to structural deformations, such as joint bolts and lining segments. Moreover, it also included the assessment of the impression of longitudinal forces and loading levels on the circumferential joint of PCTL to gain a deeper insight into the lining structure. Based on the analysis of the study, the following conclusion has been drawn.

1) The TC phenomenon caused structural deformations to the existing tunnel linings. Structural ring convergences were enormously enhanced upon crossing the new tunnel below. TAD and joint staggering are key factors in controlling convergence. It was proved that the additional/unloading pressure by this phenomenon significantly affects the tunnel linings.

2) The middle ring pragmatically lowers longitudinal joint opening due to confinement by the top and bottom rings, and the ring’s haunch exhibited less radial stiffness, causing joint openings. Further, it was evidenced that the dominance of the staggering effect diminished joint opening, circumferential joint dislocation, structural ring convergences, and vice versa.

3) Circumferential joint dislocation is a key factor for the structural integrity of tunnel linings, and structural ring convergence, along with TCs, induces more dislocations between rings. It was revealed that the top-middle ring joint dislocates higher than the middle-bottom ring, as the bottom ring had support on one side, which offered resistance against dislocation. A key segment and unloading force reaction are the defining moments for the ring waist and invert for enormous circumferential joint dislocation, respectively.

4) The analysis shows that decreased TAD intensifies unloading forces, increasing bending moments and LJB strains, especially near the middle ring’s waist. Reducing the staggering effects raises internal forces, while the longitudinal force primarily governs strain. For circumferential joints, smaller TADs amplify asymmetric loading, boosting shear-related strain inversely with distance. Lower longitudinal force reduces joint shear stiffness, worsening dislocation. Reinforcement and segment strains grow inversely following TAD.

5) Tunnel crossings involved complex behavior, and investigation revealed that segmental linings underwent huge structural deformations around weaker zones, especially from the waist to the invert of rings. Circumferential joints near the invert observed peak dislocations depending upon TAD, caused by reactional forces and longitudinal joints.

6) Residual longitudinal force lessened structural deformations and was directly proportional to the staggering effect, which altered lining ring behavior to homogenous units; in contrast, segment body discovered opposite effects utilizing maximum capacity. Even 1% longitudinal force mitigates up to 32.05% dislocations between rings.

7) Structural ring convergences are 4.54, 2.68, and 8.9 mm in construction, operation, and TC stage, respectively. It is thus convincingly concluded that TCs may present greater dangers than the Cons. to segmental tunnel lining structures. Convincingly, it is stated that TADs of 2D and greater between new and existing tunnels can be considered safe.

This novel investigation has shown that TCs have a detrimental effect on the lining structure, posing challenges during the operational phase. Joint openings/dislocations did not exceed the code limit but may damage the gasket, leading to water leakage and cracking due to stress concentration at the intrados.

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