Weakening behavior of waterproof performance in joints of shield tunnels under adjacent constructions

Abstract

Groundwater leakage in shield tunnels poses a threat to the safety and durability of tunnel structures. Disturbance of adjacent constructions during the operation of shield tunnels frequently occurs in China, leading to deformation of tunnel lining and leakage in joints. Understanding the impact of adjacent constructions on the waterproofing performance of the lining is critical for the protection of shield tunnels. In this study, the weakening behavior of waterproof performance was investigated in the joints of shield tunnels under transverse deformation induced by adjacent construction. First, the relationship between the joint opening and transverse deformation under three typical adjacent constructions (upper loading, upper excavation, and side excavation) was investigated via elaborate numerical simulations. Subsequently, the evolution of the waterproof performance of a common gasket with a joint opening was examined by establishing a coupled Eulerian–Lagrangian model of joint seepage, and a formula describing the relationship between waterproof performance and joint opening was proposed. Finally, the weakening law of waterproofing performance was investigated based on the results of the aforementioned studies. It was determined that the joints with the greatest decline in waterproof performance were located at the tunnel shoulder in the upper loading case, tunnel crown in the upper excavation case, and tunnel shoulder in the side excavation case. When the waterproof performance of these joints decreased to 50% and 30%, the transverse deformations were 60 and 90 mm under upper loading, 90 and 140 mm under upper excavation, and 45 and 70 mm under side excavation, respectively. The results provide a straightforward reference for setting a controlled deformation standard considering the waterproof performance.

Graphical abstract

Keywords

shield tunnel / waterproof performance / horizontal transverse deformation / joint opening / weakening behavior

1 Introduction

Shield tunneling has become an essential method for the development of urban underground transportation systems because of its small disturbance and safe and rapid excavation [1–3]. For the tunnel lining, several arc-shaped reinforced concrete segments are combined to form a segmental ring via longitudinal joints, and the adjacent segmental rings are then assembled into a lining structure by circumferential joints. To maintain the tunnel watertight, rubber sealing gaskets affixed to the joints between adjacent segments were utilized. During tunnel operation, structural deformation of the shield tunnel lining often occurs under the disturbance of adjacent construction (e.g., surcharge, over-lying excavation, and nearby excavation) [4–7]. As an assembled structure, structural deformation leads to significant deformation in joints, resulting in weakening of the waterproof performance of the joints and further occurrence of groundwater leakage [6,8]. Groundwater leakage due to joint deformation induces deterioration of the tunnel structure (e.g., segment deterioration and bolt corrosion), aging of utilities, or even lead to further deformation of the tunnel itself [9,10]. Therefore, it is significantly important to fully understand the weakening behavior of the waterproof performance in the joints of shield tunnels under deformation.

Many theoretical calculation models have been proposed for circumferential joint deformation, and the existing literature provides a reasonable longitudinal structural model based on the Timoshenko beam theory, which can truly reflect the circumferential joint deformation due to the longitudinal deformation of the shield tunnel [11,12]. For longitudinal joint deformation owing to segmental ring deformation, considerable research has been conducted on full-scale tests and numerical model experiments. Full-scale experiments have been conducted on segmental rings to determine the mechanical behavior and failure mechanism of the entire segment ring and joint [13–16]. These experiments can accurately reflect the deformation of the segmental ring to a certain extent. Nevertheless, the experimental cost is high, and given the limitations of the measuring instrument, certain important results may not be successfully detected. Numerical simulations have been widely used by an increasing number of scholars to examine the mechanical behavior of tunnel linings because of the advantages of low cost and comprehensive data [17]. In previous simulations, joints were usually set as linear springs or joint elements in the model [17]. However, this method does not accurately reflect the mechanical behavior. Recently, an elaborate numerical model considering the detailed structure of the segment ring was established [18], which significantly expresses the deformation rule of the segmental ring and joint.

In the shield tunnel, an elastic sealing gasket was pasted on the sealing groove around the segment and used as a structure to prevent groundwater leakage. Generally, in China, an ethylene-propylene-diene monomer (EPDM) gasket is selected as the waterproof material for good contact stress after compression. Currently, some laboratory tests are used to explore the laws of mechanical performance and waterproof performance of gaskets with different configurations [19–23]. These results reflect the waterproof capacity of the gasket under the general deformation mode of the joint to a certain extent. Furthermore, the aging performance and service life of rubber gaskets should be considered. The hydrothermal accelerated aging test is the main method used to explore the aging performance of rubber, and some models that can reflect the aging behavior of rubber gaskets have been proposed [24,25]. Furthermore, numerous numerical simulation methods have been developed to investigate the failure behavior of sealing gaskets. The relationship between the waterproof performance and contact stress of gaskets has been established [26]. The stress variation and waterproof capacity of the joint during the seepage process have been investigated [27]. The leakage mechanism of the tunnel joint was analyzed based on the effective contact stress of the gasket [28,29]. Although existing studies significantly promote the understanding of the waterproof performance of sealing gaskets under a given opening and dislocation of the joint, the relationship between the weakening behavior of the waterproof performance in joints and deformation of the tunnel remains unknown.

In this study, we aim to investigate the weakening behavior of waterproof performance in the joints of shield tunnels under transverse deformation induced by adjacent construction. For this purpose, the relationship between the deformation of joints and transverse deformation of the segmental ring under different adjacent construction conditions was first obtained via elaborate numerical simulations. Second, by establishing a coupled Eulerian–Lagrangian model of joint seepage, the evolution of the waterproof performance of a common gasket with joint deformation was captured, and a formula reflecting the relationship between waterproof performance and joint opening was proposed. Finally, the relationship between the deformation of the segmental ring and waterproof performance of each joint was established, and the weakening performance in the joints of shield tunnels under transverse deformation induced by adjacent construction was determined.

2 Observed leakage through joints under external disturbance

The disturbance of adjacent construction can generally be classified into three categories: i) vertical loading via surcharge, ii) vertical unloading via upper excavation, and iii) side unloading via side excavation. Under different loading/unloading conditions, the segmental ring of the shield tunnel leads to significant differences in deformation based on a large number of field investigations [6,30–32]. Fig.1 illustrates the transverse deformation modes under different loading/unloading conditions. Under upper loading, the segmental ring presents a horizontal and zygomorphic ellipse shape, with stretching in the horizontal axis and shortening in the vertical axis [18]. Under upper unloading, the segmental ring presents a vertical and symmetric ellipse shape, with stretching in the vertical axis and shortening in the horizontal axis [33]. Under side unloading, the segmental ring presents a horizontal and asymmetric ellipse shape, with stretching in the horizontal axis and shortening in the vertical axis [34]. Under the influence of the deformation mentioned above, longitudinal joints are vulnerable to leakage, and leakage phenomena are more likely observed at the waist and above the lining as shown in Fig.1.

When transverse deformation occurs in the segmental ring, the segments on both sides of the longitudinal joint rotate around their intersection, resulting in two deformation modes of the joint (e.g., positive joint rotation {\theta }^{+} and negative joint rotation {\theta }^{-}). Then, the opening appears at the sealing groove. The sealing gaskets change from the perfect state of complete compression to the state of stress relaxation when the joint is opened, as depicted in Fig.2, which leads to the contact stress relaxation of gaskets, and the waterproof performance of the joint decreases to a certain extent. Therefore, to investigate the change rule of waterproof performance with the transverse deformation of the segmental ring, first, the relationship between the transverse deformation and joint opening should be determined.

3 Relationship between transverse deformation and joint opening

3.1 Numerical model

Fig.3 shows the geometric dimensions of the segmental ring investigated in this study. The segment ring consists of six reinforced concrete segments, including a key segment (K) with a central angle of 21.5°, two segments (B1 and B2) with a central angle of 68°, and three segments (A1, A2, and A3) with a central angle of 67.5° are connected by prestressed bolts. The external diameter, thickness, and width of the segment ring were 6200, 350, and 1500 mm, respectively.

According to the geometry shown in Fig.3, an elaborate numerical model of a segmental ring is established. To consider the interaction between the soil and tunnel, the ground is also established, and Fig.4 shows the 3D finite element model. As depicted in Fig.4, the length and width of the soil layer are programmed to 80 and 60 m, respectively. Considering that the buried depth of the tunnel crown is approximately 10–20 m in most of the existing operation shield tunnels, the buried depth of the tunnel crown is set to 15 m. The transverse deformation of the segmental lining corresponds to a plane strain problem. Hence, the length of the soil ground can be smaller along the longitudinal direction of the tunnel. The width of the entire model was set as the width of a single segmental ring (1.5 m).

The segmental ring model incorporated reinforced concrete, connecting bolts, and reinforcing bars, in which the quantity and distribution of the reinforcing bars corresponded to the actual reinforcement diagram. Nevertheless, detailed structures, such as sealing grooves and caulking grooves, which have no effect on the structural response, were not considered. In the numerical model, X-, Y-, and Z-direction displacements of the left and right sides, front and rear sides, and bottom of the soil layer model are limited. The interaction between the tunnel and soil was modelled by Yan et al. [35]. The Mohr–Coulomb constitutive model is applied to represent the mechanical behavior of soils, and the basic parameters of the soil are listed in Tab.1 [36]. The concrete grade of the segments was C50, and the concrete damaged plasticity model was applied to simulate the mechanical behavior of concrete [37]. Tab.2 lists the parameters of the concrete damage plasticity model. The types of circumferential rebar and other rebars are HRB400 (hot-rolled ribbed bar) and HPB300 (hot-rolled plain bar), respectively, and the yield limit and ultimate strength of the high-strength bolt are 640 and 800 MPa, respectively. The specific parameters of the rebars and bolts are listed in Tab.3. Furthermore, Tab.4 presents the interaction parameters of the interface models.

To investigate the relationship between the transverse deformation and longitudinal joint deformation of the shield tunnel under the influence of different disturbances, upper loading, upper excavation, and side excavation were simulated. The models and loading modes are shown in Fig.5. Detailed simulation methods for these three cases are as follows.

i) In upper loading, overloading is applied through the displacement boundary, and the boundary curve of the stratum corresponds to the Peck curve. The simulation of the loading mode is to continuously increase the surface settlement until the segmental ring is deformed to failure, and the maximum value of the surface settlement is set to a larger value (0.5 m).

ii) In the upper excavation, the foundation pit is set directly above the tunnel. The excavation width of the foundation is selected as twice the diameter of the tunnel (12.4 m), which is common in engineering applications. The loading mode continuously increases the excavation depth until the segmental ring is deformed to failure, and the maximum value of the excavation depth is set as a deeper value (11.9 m).

iii) In the side excavation, to make the tunnel closer to the foundation, the horizontal distance between the tunnel axis and left boundary of the foundation is set to 1.5 times the tunnel diameter (9.3 m). The excavation width of the foundation is selected as the diameter of the tunnel, which is 6.2 m. The loading mode of side excavation is simulated by the deformation mode of “deep inward movement” of the retaining wall [38], and the excavation depth is set as 24.3 m. Hence, the maximum lateral wall deflection and tunnel center are at the same depth. In the simulation, the maximum lateral wall deflection is gradually increased until the segment ring is deformed to failure. Before the segmental ring is loaded, the initial excavation of the tunnel and assembly of segments are included in the numerical simulation.

3.2 Analysis of horizontal transverse deformation and opening of joints

In the calculated results, the displacements in X and Y directions of the node in the middle of the Y direction of the sealing groove on both sides of the joint are extracted, and the joint opening of the sealing groove is obtained using Eq. (1) as follows:

(1)\mathrm{\Delta }=\sqrt{{\left(u_{11}-u_{12}\right)}^2+{\left(u_{31}-u_{32}\right)}^2}.

In this equation, u_mn denotes the direction displacement of the node, where m denotes the displacement direction, 1 and 3 denote X and Z directions, respectively, n is the node number, and u₁₁ denotes the displacement in the X direction of node 1. Fig.6 shows a schematic diagram in which the red node represents the location of the sealing groove.

Fig.7 shows the deformation nephogram of the tunnel with the center of the undeformed segmental ring as the origin of the coordinate axis. Fig.8 shows the diagrammatic drawing and relationship between the joint opening at the sealing groove and converging deformation of the segmental ring under different external disturbances. In Fig.8, a positive value indicates that the opening appears on the external surface of the segment, whereas negative values correspond to the internal surface. It should be noted that the initial joint opening considering the excavation of the shield tunnel is greater than 0 mm, and the transverse deformation at this stage is also greater than 0 mm.

Next, the relationships between the transverse deformation of the segment ring and deformation of the longitudinal joint at the sealing groove under different disturbances are discussed.

3.3 Upper loading

As depicted in Fig.7(a), the tunnel deformation is a horizontal ellipse, and the joints at the tunnel crown (349.25°, 10.75°) and springline (213.75°, 146.25°) are in a state of external compression and internal tension, whereas joints at tunnel shoulder (281.25°, 78.75°) are in a state of external tension and internal compression. Therefore, joints at 349.25°, 10.75°, 213.75°, and 146.25° are opened on the inside and pressed on the outside; joints at 73° and 287° are open on the outside and compressed on the inside.

Under the influence of upper loading, the transverse deformation of the tunnel is symmetrical; therefore, only data on the deformation of the left side of the tunnel are provided. As shown in Fig.8(a), the joint deformation at tunnel crown (349.25°, 10.75°) and springline (213.75°, 146.25°) increases nonlinearly, whereas the joint deformation at tunnel shoulder (281.25°, 78.75°) approximately increases linearly albeit its value is not obvious. When the joint opening is increased to 5 mm, the horizontal transverse deformation is 60 mm; when the joint opening is 10 mm, the horizontal transverse deformation is 110 mm and slope of this line is close to 0.1. When the horizontal transverse deformation is increased to 160 mm, the joint at the tunnel shoulder is fully opened.

3.4 Upper excavation

As shown in Fig.7(b), the tunnel deformation is a vertical ellipse. The joints at the tunnel shoulder (281.25°, 78.75°) are in a state of external compression and internal tension, whereas joints at the tunnel crown (349.25°, 10.75°) and tunnel springline (213.75°, 146.25°) are in a state of external tension and internal compression. Therefore, the joints at the tunnel shoulder are opened on the inside and pressed on the outside; the joints at the tunnel crown and tunnel springline are opened on the outside and compressed on the inside.

Given that the tunnel deformation shows the stretching of the vertical axis and compression of the horizontal axis, the variation in the vertical axis when compared to an appropriate circle is selected as the standard for the transverse deformation. It should be noted that after completion of the tunnel construction, the tunnel deformation presents the shape of a horizontal ellipse, and thus the vertical transverse deformation shows some negative values. As shown in Fig.8(b), the joint opening at the tunnel shoulder (281.25°, 78.75°) is small; when the vertical transverse deformation increases to 160 mm, the joint opening is only 2 mm. With the increase in vertical transverse deformation, the joint opening of the joints at the tunnel crown and spring line cannot be ignored, and the maximum opening occurs at the joints (349.25°, 10.75°) on both sides of the key segment, corresponding to the tunnel crown. For the curve with the largest slope, when the joint opening is increased to 5 mm, the vertical transverse deformation is 80 mm; when the joint opening is 10 mm, the vertical transverse deformation is 160 mm and slope of this line is close to 0.0625.

3.5 Side excavation

As shown in Fig.7(c), the tunnel deformation is a horizontal ellipse, which is similar to the shape rotated 90° clockwise in Fig.7(b). The joints at the tunnel shoulder (281.25°, 78.75°) are in a state of external tension and internal compression, whereas the joints at the tunnel crown (349.25°, 10.75°) and springline (213.75°, 146.25°) are in a state of external compression and internal tension. Therefore, joints at the tunnel shoulder (281.25°, 78.75°) are open on the outside and compressed on the inside, and other joints are opened on the inside and pressed on the outside.

As shown in Fig.8(c), under the influence of side excavation, with the increase in horizontal transverse deformation, the joint opening basically increases linearly, whereas joint deformation at tunnel crown (349.25°, 10.75°) and tunnel springline (146.25°, 213.75°) is negligible. This can be explained by the fact that the sealing groove at these joints is near the concrete pressured region. The opening of the two joints at the tunnel shoulder (281.25° and 78.75°) is greater than other joints. Furthermore, the joint at the tunnel right shoulder near the excavation range (78.75°) has a maximal deformation. In this joint, when the horizontal transverse deformation is 47 mm, the joint opening is approximately 5 mm. Furthermore, when the horizontal transverse deformation is 80 mm, the joint opening is approximately 10 mm, the slope is close to 0.15, which is the highest change rate in all the aforementioned conditions. When the horizontal transverse deformation increases to 120 mm, the joint at the right shoulder of the tunnel is fully opened.

4 Waterproof performance of the gasket

4.1 Numerical model

4.1.1 Model size

The gasket used in this study is composed of an EPDM. The height of the gasket is 21.5 mm and depth of the sealing groove is 14 mm. By using a simple calculation, it can be concluded that the maximum compression of gaskets on both sides is 15 mm when the joint is fully closed. The detailed dimensions of the sealing gaskets and grooves are shown in Fig.9.

4.2 Method

To investigate the relationship between the waterproof performance of the gasket and joint opening, a coupled Eulerian−Lagrangian model was established. This method can simulate the dynamic process of water infiltration into a gasket, and the accuracy of the calculated waterproof performance has been proven to be effective [27]. Fig.10 shows the fluid–structure coupled model in water and gasket. The parts of the model can be classified into Lagrangian and Eulerian bodies. The Lagrangian body includes the segment groove and gasket and Eulerian body consists of the reference part and Eulerian part. Furthermore, the reference part defines the entity of water, and the Eulerian part coincides with the flowable space of water.

The process of numerical simulation is divided into two stages. In the first stage, the process of joint compression during segment assembly is simulated, and the joint opening is determined in this procedure. In the second stage, the process of water penetrating the sealing gasket at the joint during the tunnel operation period is simulated.

4.3 Model materials

The sealing gasket is a material with hyperelastic mechanical behavior, and to truly reflect its characteristics of high deformability, the Mooney–Rivlin model is used to simulate the rubber gasket [39,40]. The formula for the strain energy is as follows:

(2)E_0=6C_{10}\left(1+\frac{C_{01}}{C_{10}}\right),

where E₀ denotes Young’s modulus, and C₀₁ and C₁₀ denote material parameters that fit the equation as follows:

(3)C_{01}=0.25C_{10}.

Based on the existing studies [41], the relationship between hardness H_A and Young’s modulus E₀ of rubber gasket material can be expressed as follows:

(4)E_0=\frac{15.75+2.15H_{\text{A}}}{100-H_{\text{A}}}.

According to Eqs. (2)–(4), the material parameters of the rubber gasket used in this study are listed in Tab.5. The gasket hardness values listed in Tab.5 are typically used in the waterproof design of shield tunnels.

The water is modeled using the Eulerian formulation, and the behavior of the fluid material is defined by the U_S−U_P Hugoniot equation [42], which can be expressed as follows:

(5)P=\frac{{\rho }_0{c}_0^2\eta }{{(1-s\eta )}^2}\left(1-\frac{{\mathrm{\Gamma }}_0\eta }{2}\right)+{\mathrm{\Gamma }}_0{\rho }_0{E}_{\text{m}},

(6)U_{\text{s}}=c_0+s{U}_{\text{p}},

where P denotes pressure (MPa), η denotes nominal volumetric compressive strain, ρ₀ denotes the density of the fluid (t/mm³), Γ₀ denotes material constant, E_m denotes energy per unit mass (J/t), U_s denotes the velocity of the stress wave propagation (mm/s), U_p denotes the velocity of the particle (mm/s), c₀ denotes the water wave speed (mm/s), and s denotes the coefficient that defines the linear relationship between the shock velocity. The parameters values are as follows: ρ₀ = 1 × 10⁻⁹ t/mm³, c₀ = 1.45 × 10⁶ mm/s, s = 0, η = 0, and U_p = 1.00 × 10⁻⁹ mm/s.

4.4 Boundary conditions and interaction

Water seepage can occur at the interface between the gaskets and interface between the gasket and groove; however, the gasket and groove are connected by adhesive, and the interface between the gaskets is more permeable to leakage. Therefore, binding constraints are used between the gasket foot and groove in this simulation. The other interactions, including the interactions between the Lagrangian and Eulerian bodies, are set as general contacts.

Given that the rigidity of the reinforced concrete segment is significantly greater than that of the rubber gasket, the groove is set as discrete rigid, and reference points are set to control the displacement of the groove as shown in Fig.10. The bottom groove is fixed as the boundary condition, and displacement is applied to the upper groove to simulate gasket compression. In the stage of water seepage, the grooves are fixed, and a rigid body with an initial velocity along the X-direction is set to the left of the entity of water to promote the movement of water. To ensure that water flows in the Eulerian grid, the velocity boundaries of each face of the reference body are fixed.

4.5 Contact stress

Fig.11 depicts the contact stress along the contact surface between gaskets when the joint openings are 2, 6, and 10 mm, and the hardness of the rubber gasket used in this analysis is 73 Shore A. It should be noted that in the simulated compression process, the deformation of the gasket is symmetrical, and the gasket–gasket interface increases as compression increases; consequently, the curves in Fig.11 are described with the midpoint of the contact path as the origin. Given that there are some holes in the gasket, the distribution of the contact stress fluctuates with different structural stiffnesses corresponding to the interface. The parts with a larger structural stiffness coincide with the peak stress, whereas parts with a smaller structural stiffness correspond to the valley stress, which can also be concluded from the contact path between the gaskets in the stress nephogram (the joint opening is 6 mm) in Fig.11. When the opening is large (10 mm), the peaks in the middle of the curve are larger than those on both sides. With the decrease in opening, all peaks on the curve increase significantly, and maximum peaks appear at both ends of the curve. The seepage process can be understood as the process by which pressurized water breaks through the peak stress on the contact surface at the cost of the potential energy of pressurized water. Therefore, considering the development of peak stress as an explanation, as the joint opening decreases, the peak stress increases, and the sealing gasket at the joint exhibits a higher waterproof performance.

Fig.12 shows the development of the average contact stress along the contact surface of the gaskets with different joint openings. An increase in the hardness of the gasket material has a positive effect on the contact stress, and this effect is more obvious when the compression is at a higher level. Based on the change in the slope of the curve in Fig.12, the development of the average contact stress with the joint opening can be divided into three stages. The characteristics of these stages and the reasons for dividing them are as follows.

Stage I: The first stage starts from the beginning of the compression (opening is 15 mm) to the state that the compression is 4 mm (opening is 11 mm). At this stage, the contact stress increases almost linearly as the joint opening decreases. During the process of joint deformation, the gasket is at the initial stage of compression, and the compression force is borne by the entire solid skeleton of the gasket.

Stage II: The second stage coincides with an opening in the range of 11–6 mm. The slope of the curve in this stage is lower than that in the first stage. This phenomenon can be interpreted as follows: The deformation at this stage is mainly reflected in the compression of the gasket hole, and the stiffness of the part with holes is relatively small. Compared with the first stage, when the same displacement is compressed, a smaller load is exerted.

Stage III: The final stage (phase III) lasted until full compression of the sealing groove (opening is 6–0 mm). The deformation graphs of the gasket with the joint openings of 6 and 0 mm in Fig.12 show that as the joint opening continues to shrink, the holes are basically completely closed. Furthermore, there is an obvious lateral deformation on the gasket owing to the incompressibility of rubber. Therefore, at this stage, the stiffness of the gasket increases, and the result shows that the average contact stress increases in a nonlinear manner with a decrease in the joint opening.

4.6 Waterproof performance under opening

Fig.13 shows four stages of water breaking through the contact surface of the gaskets when the joint opening is 6 mm. In Fig.14, the red solid line denotes the stress variation of the initial adjacent gasket contact path in the four stages, and the blue dotted line denotes the stress distribution of the contact path when there is no water flow. When the water seeps to the contact surface between the gaskets, the stress at the extreme left of the contact path increases, and the average contact stress reaches 0.72 MPa, which is slightly higher than the initial value. With the development of the seepage process, the peak value of the contact stress continuously shifts to the right along the contact path. When the water completely breaks through the contact surface of the gaskets, the average contact stress increases from 0.72 to 1.48 MPa. Specifically, average contact stress of 1.48 MPa corresponds to the waterproof performance of the gasket when the joint opening is 6 mm. This phenomenon implies that as the water flow breaks through the contact surface, the contact stress between the gaskets increases; thus, a higher water pressure is required to complete the seepage process.

The relationships between the waterproofing performance of gaskets with different hardnesses and joint openings are shown in Fig.15. In the process of increasing the hardness of the gasket from 60 to 73 Shore A, the waterproof behavior is improved. However, this increase is not as significant as the increase in the average contact stress as shown in Fig.12. This phenomenon indicates that if it is necessary to improve the hardness of the gasket material to guarantee waterproof performance. Hence, crushing of the concrete segment should be avoided because of the high jacking force. The waterproofing performance of joints is closely related to the contact stress at the gasket–gasket interface [26]. Therefore, the contact stress of the gaskets and waterproof performance of the joint continues to increase as the joint opening decreases. It can be observed from the curves in Fig.15 that the waterproof performance increases approximately in a nonlinear trend with a decrease in the joint opening. The waterproof performance curve of the gasket with a hardness of 60 Shore A is considered as a case study to explain the aforementioned phenomenon. When the joint opening is high, the slope of the curve is gentle. Under the influence of water flow extrusion, the vertical deformation of the gasket is mainly reflected by the closure of the hole based on the comparison of seepage before and after the opening of 8 mm. The aforementioned process is similar to Stages I and II shown in Fig.12. The slope of the curve increases with a decrease in the joint opening. In Fig.15, the seepage before and after the opening corresponds to 4 mm is compared. When the gasket–gasket interface is penetrated by water, the holes of the gasket are nearly completely closed; thus, there is a transverse deformation in the gasket, which results in an increase in gasket stiffness. The aforementioned state of complete closure of the hole appears in advance as the joint opening continues to decrease, which implies that the stiffness of the gasket increases, and afterwards, it is more difficult for water to penetrate the gasket–gasket interface.

To facilitate the following analysis, according to the numerical simulation results and existing conclusion that the waterproof performance changes nonlinearly with the joint opening [20], a formula for joint waterproof performance, incorporating the opening and rubber hardness, is proposed as follows:

(7)P_{\text{w}}=\left(a+b{E}_0\right)\left({\text{e}}^{c\left({\mathrm{\Delta }}_0-\mathrm{\Delta }\right)}-1\right),

where E₀ denotes Young’s modulus obtained by Eq. (4); ∆₀ denotes the maximum compression of the gasket at the sealing groove; and ∆ denotes the joint opening. Furthermore, a, b, and c are constants. In this simulation, when the joint opening is maximum (the compression of the gasket is 0 mm), under the impact of the water flow, the gasket still has a degree of deformation, which leads to an increase in the contact stress and exhibits a weak waterproof performance. Similarly, when the joint opening is relatively large, the calculated contact stress of the gasket can be higher than the actual value because of the impact of water flow. To correct for the phenomenon that is inconsistent with the actual situation, the exponential function in Eq. (7) is subtracted by “1”.

A comparison between the fitted curve and numerical simulation results, including the fitted Eq. (7), and the corresponding R-squared values are shown in Fig.15. The results indicate that most of the data are consistent when the hardness of the gasket does not exceed 70 Shore A. When the hardness of the gasket is 73 Shore A, the consistency of the fitting curve is poor. This can be due to the impact of water flow mentioned above and the greater contact stress at higher hardness. When the joint opening is relatively large, the phenomenon in which the waterproof performance is greater than the actual value is more obvious. Therefore, in Fig.15, there are some errors in the data of the larger joint opening, which is slightly different from the result obtained using Eq. (7).

4.7 Waterproof performance considering rotation

In an actual project, the deformation of the longitudinal joint is generally reflected in the form in which the segments on both sides of the joint rotate around the internal or external intersection of the segments. However, in the previous numerical simulation and analysis, it is assumed that the deformation of the joint is a parallel opening, and the rotation angle is not considered. This section shows the rationality of the assumptions in the previous section by analyzing the calculation example considering the rotation angle.

The joint opening with rotation is shown in Fig.2, \mathrm{\Delta } denotes the joint opening represented by the ordinate in Fig.8, which is defined as the opening at the midpoint of the sealing groove, {\theta }^{+} indicates that the rotation angle appears on the external surface of the segment, and {\theta }^{-} indicates that the rotation angle appears on the internal surface. Based on Fig.8, under each operating condition, the joint opening under negative rotation is much smaller than that under positive rotation. Therefore, joint opening under negative rotation is not discussed in this study. Considering the influence of rotation, the rotation angles corresponding to different joint openings are not constant, and their correspondence can be obtained by simple geometric calculations. The rotation angles corresponding to the different joint openings are listed in Tab.6. The seepage process of the joint is numerically simulated under the conditions that the rubber hardness is 73 Shore A and joint openings are 4, 6, 8, and 10 mm with rotation.

A comparison of the results of the waterproof performance with and without rotation is obtained, and the discrepancies between the above results are shown in Fig.16 and Tab.7. The results show that the tendency of waterproof performance is similar in the two sets of data, and the discrepancies are not obvious. The maximum error is 10.6%, which occurs when the joint opening is 10 mm. Therefore, considering the error due to the numerical simulation, the assumption that the deformation of the longitudinal joint is regarded as a parallel opening seems reasonable.

5 Weakening behavior of waterproof performance in joints under transverse deformation

In this section, the relationship between the waterproof performance of the joint and transverse deformation of the segmental ring under various working conditions is obtained by combining the fitting curve of the variation in the waterproof performance with respect to different joint openings and relationship between the transverse deformation of the segment ring and joint opening as shown in Fig.17. It should be noted that the transverse deformation of most segmental rings is within 200 mm in the actual project. Hence, the data corresponding to the transverse deformation between 0 and 200 mm are shown in Fig.17.

5.1 Upper loading

As shown in Fig.17 (a), in the process of upper loading, a relatively high waterproof performance is always maintained on joints (349.25°, 213.75°, 146.25°, 10.75°), which are located at the tunnel crown and tunnel springline. Among the joints, the waterproof performance of the joint at the tunnel crown decreases more obviously; however, when the horizontal transverse deformation increases to 200 mm, the waterproof performance of the rubber gaskets with four hardnesses is still above 1.4 MPa, and the waterproof performance of the gasket is reduced to 78%. Compared with the above joints, the waterproofing performance of the joints at the tunnel shoulder (281.25° and 78.75°) decreases more sharply. When the horizontal transverse deformation of the segment ring increases to 60 mm, the waterproofing performance of the joints decreases by 50%. The waterproof performance of the rubber gasket with a hardness of 60 Shore A is 0.9 MPa, less than 1.0 MPa, and the waterproof performance of the rubber gasket with a hardness of 73 Shore A is 1.33 MPa. With an increase in transverse deformation, the waterproofing performance continues to decline. When the horizontal transverse deformation is 90 mm, the waterproofing performance is reduced to 30% of its original performance. While in this form, the waterproof performance of the joints at the tunnel shoulder significantly weakenes, and the waterproof performance with four hardness ranges from 0.5 to 0.9 MPa. As the transverse deformation expandes from 90 to 160 mm, the waterproof performance is completely lost.

5.2 Upper excavation

The waterproofing performance under the influence of the upper excavation is shown in Fig.17(b). After completion of the tunnel construction, a transverse deformation occurrs with joint opening and an associated small weakening of the waterproof performance. With the upper excavation, the transverse deformation changes from a horizontal ellipse to a proper circle, and there is a slight increase in waterproof performance. With a continuous upper excavation, the transverse deformation changes from a proper circle to a vertical ellipse. Given that the sealing gasket of the joint at the tunnel shoulder (281.25°, 78.75°) is near the concrete pressured region of the segment, the waterproof performance of the joints decreases relatively slowly, and when the vertical transverse deformation is 200 mm, the waterproof performance of the gasket is weakened to 72% of its initial performance. For the two joints at the tunnel crown (349.25°, 10.75°), when the vertical transverse deformation of the segment ring increases to 90 mm, the waterproof performance of this joint decreases to 50%, and when the vertical transverse deformation continues to develop to 140 mm, the waterproof performance is reduced to 30%. Until the vertical transverse deformation increases to 200 mm, the waterproofing performance remains at 10%. When compared with the waterproof performance of joints that are most likely penetrated by water under upper loading at the tunnel shoulder, the process of weakening the waterproof performance of the joint is prolonged. However, the decline in the waterproofing capacity of the joints at the tunnel springline (213.75°, 146.25°) cannot be ignored. When the vertical transverse deformation increases to 200 mm, the waterproofing performance of these joints decreases to 23%.

5.3 Side excavation

Fig.17(c) shows the downward trend of the waterproof performance with respect to horizontal transverse deformation under side excavation. When the horizontal transverse deformation increases to 200 mm, the waterproofing performance of the joints at the tunnel springline (213.75°, 146.25°) and tunnel crown (349.25°, 10.75°) is still at a high level. The decline in the waterproofing performance of the joints at the tunnel shoulder is evident, and the waterproof performance of the joint at the tunnel right shoulder (78.75°) is weakened more severely. In this joint, when the waterproof performance decreases to 50% and 30% of its original performance, the corresponding horizontal transverse deformations are 45 and 70 mm, respectively, and when the horizontal transverse deformation continues to increase to 120 mm, the waterproof performance decreases to 0 MPa. This process exhibits the fastest decline rate of waterproofing performance among all the aforementioned joints under different operating conditions. Similarly, the joint at the tunnel left shoulder (281.25°) also exhibits a rapid downward trend when the waterproof performance decreases to 50%, 30%, and 4% of its original performance, and the corresponding horizontal transverse deformation is 80, 125, and 200 mm, respectively, which is not shown in Fig.17(c).

The decline process of the waterproofing performance of all joints under the different working conditions mentioned above is summarized in Tab.8. It can be concluded that the leakage of the longitudinal joint of the segmental ring generally does not occur at the tunnel springline, and the probability of leakage at the tunnel shoulder is higher. This is followed by the probability of leakage at the tunnel crown.

6 Conclusion and recommendation

In this study, the weakening behavior of a shield tunnel was investigated under transverse deformation induced by adjacent construction. The relationships between the joint opening and transverse deformation under different adjacent constructions were obtained in an elaborate numerical simulation, and the variation rules of the contact stress and waterproof performance of a common gasket with the opening were captured by establishing a coupled Eulerian–Lagrangian model of joint seepage. Subsequently, a formula for waterproof performance incorporating the hardness of the gasket and joint opening was proposed. The relationship between the joint waterproofing performance and transverse deformation was established, and the decline process of the joint waterproofing performance was summarized in stages. The main conclusions and suggestions are as follows.

1) The relationship between the joint opening and transverse deformation under three typical deformation modes is clarified. Under upper loading and excavation, the joints with the maximum joint opening are at the tunnel shoulder and tunnel crown, respectively. When the transverse deformation of the segmental ring reaches 60 and 110 mm in the upper loading and 80 and 160 mm in the upper excavation, the joint opening of the above joints expands to 5 and 10 mm, respectively. Under the action of side excavation, there is an obvious deformation at the two joints of the tunnel shoulder, and the joint opening at the tunnel right shoulder near the excavation is the largest. For this joint, when the tunnel transverse deformation is 47 and 80 mm, the joint opening reaches 5 and 10 mm, respectively.

2) The process of compression and seepage of the gasket can be considered as the process in which the holes are compressed first, and then the entire gasket is laterally deformed; thus, the stiffness of the gasket increases continuously. This corresponds to the phenomenon in which the waterproof performance increases nonlinearly with the decrease in opening, and a formula reflecting the relationship between waterproof performance and joint opening is proposed. In practical engineering, the deformation at the longitudinal joint is generally due to the rotation of the segments; however, when calculating the waterproof performance, it can be regarded as a parallel opening at the sealing groove. Comparing the waterproofing performance of the joints under the two deformation modes, the maximum error is 10.6%.

3) In the three typical deformation modes, the segmental ring with transverse deformation under side excavation exhibits the worst waterproofing performance. In side excavation, the joint with the worst waterproof performance is located at the right shoulder of the tunnel, and when the waterproof performance decreases to 50%, 30%, and 0% of the initial value, the corresponding horizontal transverse deformations are 45, 70, and 120 mm, respectively. In the upper loading, the joint with the worst performance is located at the tunnel right shoulder, and when the waterproof performance decreases to 50%, 30%, and 0%, the corresponding horizontal transverse deformations are 60, 90, and 160 mm, respectively. In the upper excavation, the joint with the worst performance is at the tunnel crown, and when the waterproof performance decreases to 50%, 30%, and 10%, the corresponding vertical transverse deformations are 90, 140, and 200 mm, respectively. The aforementioned analysis provides a quantitative evaluation of waterproof weakening behavior under different deformation modes and straightforward reference for setting the controlled standard of deformation considering waterproof performance.

References

[1] Cheng W C, Ni J C, Shen S L. Investigation into factors affecting jacking force: A case study. ICE Proceedings Geotechnical Engineering, 2017, 170(4): 322–334

[2] Zhang P, Chen R P, Wu H N. Real-time analysis and regulation of EPB shield steering using Random Forest. Automation in Construction, 2019, 106(Oct): 102860

[3] Liu M B, Liao S M, Yang Y F, Men Y Q, He J, Huang Y. Tunnel boring machine vibration-based deep learning for the ground identification of working faces. Journal of Rock Mechanics and Geotechnical Engineering, 2021, 13(6): 1–18

[4] Meng F Y, Chen R P, Liu S L, Wu H N. Centrifuge modeling of ground and tunnel responses to nearby excavation in soft clay. Journal of Geotechnical and Geoenvironmental Engineering, 2020, 147(3): 04020178

[5] Meng F Y, Chen R P, Wu H N, Xie S W, Liu Y. Observed behaviors of a long and deep excavation and collinear underlying tunnels in Shenzhen granite residual soil. Tunnelling and Underground Space Technology, 2020, 103: 103504

[6] Huang H W, Shao H, Zhang D M, Wang F. Deformational responses of operated shield tunnel to extreme surcharge: A case study. Structure and Infrastructure Engineering, 2017, 13(3): 345–360

[7] Meng F Y, Chen R P, Xu Y, Wu K, Wu H, Liu Y. Contributions to responses of existing tunnel subjected to nearby excavation: A review. Tunnelling and Underground Space Technology, 2022, 119: 104195

[8] Liu D, Wang F, Hu Q, Huang H, Zuo J, Tian C, Zhang D. Structural responses and treatments of shield tunnel due to leakage: A case study. Tunnelling and Underground Space Technology, 2020, 103: 103471

[9] Wu H N, Huang R Q, Sun W J, Shen S L, Xu Y S, Liu Y B, Du S J. Leaking behavior of shield tunnels under the Huangpu River of Shanghai with induced hazards. Natural Hazards, 2014, 70(2): 1115–1132

[10] Wu H N, Shen S L, Chen R P, Zhou A N. Three-dimensional numerical modelling on localised leakage in segmental lining of shield tunnels. Computers and Geotechnics, 2020, 122: 103549

[11] Wu H N, Shen S L, Liao S M, Yin Z Y. Longitudinal structural modelling of shield tunnels considering shearing dislocation between segmental rings. Tunnelling and Underground Space Technology, 2015, 50(AUG): 317–323

[12] Wu H N, Shen S L, Yang J, Zhou A N. Soil-tunnel interaction modelling for shield tunnels considering shearing dislocation in longitudinal joints. Tunnelling and Underground Space Technology, 2018, 78: 168–177

[13] Molins C, Arnau O. Experimental and analytical study of the structural response of segmental tunnel linings based on an in situ loading test. Part 1: Test configuration and execution. Tunnelling and Underground Space Technology, 2011, 26(6): 764–777

[14] Liu X, Bai Y, Yuan Y, Mang H A. Experimental investigation of the ultimate bearing capacity of continuously jointed segmental tunnel linings. Structure and Infrastructure Engineering, 2016, 12(10): 1364–1379

[15] Liu X, Ye Y, Liu Z, Huang D. Mechanical behavior of Quasi-rectangular segmental tunnel linings: First results from full-scale ring tests. Tunnelling and Underground Space Technology, 2018, 71(SEP): 440–453

[16] Wang Q, Geng P, Guo X Y, Zeng G X, Chen C, He C. Experimental study on the tensile performance of circumferential joint in shield tunnel. Tunnelling and Underground Space Technology, 2021, 112(June): 103937

[17] Li Z, Soga K, Wright P. Behaviour of cast-iron bolted tunnels and their modelling. Tunnelling and Underground Space Technology, 2015, 50(AUG): 250–269

[18] Chen R P, Chen S, Wu H N, Liu Y, Meng F Y. Investigation on deformation behavior and failure mechanism of a segmental ring in shield tunnels based on elaborate numerical simulation. Engineering Failure Analysis, 2020, 117: 104960

[19] Shalabi F I, Cording E J, Paul S L. Concrete segment tunnel lining sealant performance under earthquake loading. Tunnelling and Underground Space Technology, 2012, 31: 51–60

[20] Ding W Q, Gong C J, Mosalam K M, Soga K. Development and application of the integrated sealant test apparatus for sealing gaskets in tunnel segmental joints. Tunnelling and Underground Space Technology, 2017, 63(MAR): 54–68

[21] Li X, Zhou S H, Di H G, Wang P. F W P. Evaluation and experimental study on the sealant behaviour of double gaskets for shield tunnel lining. Tunnelling and Underground Space Technology, 2018, 75(MAY): 81–89

[22] Zhang D M, Liu J, Huang Z K, Yang G H, Jiang Y, Jia K. Waterproof performance of tunnel segmental joints under different deformation conditions. Tunnelling and Underground Space Technology, 2022, 123: 104437

[23] Zhang G L, Zhang W J, Li H L, Cao W Z, Gao P. Waterproofing behavior of sealing gaskets for circumferential joints in shield tunnels: A full-scale experimental investigation. Tunnelling and Underground Space Technology, 2020, 108(3): 103682

[24] Shi C H, Cao C Y, Lei M F, Shen J J. Time-dependent performance and constitutive model of EPDM rubber gasket used for tunnel segment joints. Tunnelling and Underground Space Technology Incorporating Trenchless Technology Research, 2015, 50(AUG): 490–498

[25] Kömmling A, Jaunich M, Wolff D. Effects of heterogeneous aging in compressed HNBR and EPDM O-ring seals. Polymer Degradation & Stability, 2016, 126(Apr): 39–46

[26] Gong C J, Ding W Q, Soga K, Mosalam K M, Tuo Y F. Sealant behavior of gasketed segmental joints in shield tunnels: An experimental and numerical study. Tunnelling and Underground Space Technology, 2018, 77: 127–141

[27] Zhou W F, Liao S M, Men Y Q. A fluid-solid coupled modeling on water seepage through gasketed joint of segmented tunnels. Tunnelling and Underground Space Technology, 2021, 114: 104008

[28] Li P, Xie H M, He C, Zhou Z Y, Wang S M. Waterproof performance analysis of water sealing gasket of large open shield tunnel based on effective contact stress. Tunnel Construction, 2019, 39(12): 1993–1999

[29] Xie H M, Wang S M, He C, Ma T Y, Peng X Y, Li P. Performance of a new waterproof system with double sealing gaskets outside bolt hole of segment. Tunnelling and Underground Space Technology, 2022, 119: 104206

[30] Chen R P, Meng F Y, Li Z C, Ye Y H, Ye J. Investigation of response of metro tunnels due to adjacent large excavation and protective measures in soft soils. Tunnelling and Underground Space Technology, 2016, 58(SEP): 224–235

[31] Shi C H, Cao C Y, Lei M F, Peng L M, Ai H J. Effects of lateral unloading on the mechanical and deformation performance of shield tunnel segment joints. Tunnelling and Underground Space Technology, 2016, 51(JAN): 175–188

[32] Zhang X H, Wei G, Lin X B, Xia C, Wei X J. Transverse force analysis of adjacent shield tunnel caused by foundation pit excavation considering deformation of retaining structures. Symmetry, 2021, 13(8): 1478

[33] Meng F Y, Chen R P, Liu L, Wu H N, Xie S W. Centrifuge modeling of ground and tunnel responses to nearby excavation in soft clay. Journal of Geotechnical and Geoenvironmental Engineering, 2021, 147(3): 04020178

[34] Su D, Chen W J, Wang X T, Huang M L, Pang X C, Chen X S. Numerical study on transverse deformation characteristics of shield tunnel subject to local soil loosening. Underground Space, 2022, 7(1): 106–121

[35] Yan Q X, Sun M H, Qing S Y, Deng Z X, Dong W J. Numerical investigation on the damage and cracking characteristics of shield tunnel upon derailed impact of high-speed train. Engineering Failure Analysis, 2019, 108(8): 104205

[36] Zhang Z G, Huang M S. Geotechnical influence on existing subway tunnels induced by multiline tunneling in Shanghai soft soil. Computers and Geotechnics, 2014, 56(MAR): 121–132

[37] Lee J, Fenves G L. Plastic-damage model for cyclic loading of concrete structures. Journal of Engineering Mechanics, 1998, 124(8): 892–900

[38] Ou C Y, Hsieh P G, Chiou D C. Characteristics of ground surface settlement during excavation. Canadian Geotechnical Journal, 1993, 30(5): 758–767

[39] Mooney M. A theory of large elastic deformation. Journal of Applied Physics, 1940, 11(9): 582–592

[40] Rivlin R S. Large elastic deformation of isotropic materials IV. Further development of general theory. Philosophical Transactions of the Royal Society, 1948, 241(835): 379–397

[41] GentA N. Engineering with Rubber-How to Design Rubber Components. Munich: Hanser, 2001

[42] GraczykowskiCHolnicki-SzulcJ. Adaptive inflatable structures for impact absorption. In: III ECCOMAS Thematic Conference on Smart Structures and Materials. Gdansk: ECCOMAS, 2007

RIGHTS & PERMISSIONS

Higher Education Press