Effects of Jack Thrust on the Damage of Segment Lining Structure during Shield Machine Tunnelling

Abstract

Constructing a tunnel with a large longitudinal slope and a small-radius sharp curve is challenging. During the construction process, it necessitates a series of intricate operations, including adjusting the horizontal and vertical posture of the shield machine, controlling the tunnelling thrust, and consistently ensuring the appropriate over-excavation amount inside and outside of the turn. Improper operations can easily induce undue stress on the segments. This study establishes a finite element numerical model of lining segments subjected to jacking force under various construction conditions. The concrete damage plasticity (CDP) constitutive model was used to characterize the mechanical behavior of concrete under load. The mechanical characteristics and damage behavior of segments under construction conditions, such as significant thrust escape, vertical attitude adjustment of the shield machine, excavation in soft and hard interbedded strata, line turning, sudden failure of the propulsion system, and eccentricity of brace boots, were analyzed. The results revealed that, when advancing according to the maximum thrust design value (50 MPa), cracks in the tensile plastic damage zone near the brace boot plate and the edges of the segment can develop. This can lead to localized corner failure of the concrete at the lining’s edge. Therefore, it is recommended that the jack’s thrust value should not surpass 30 MPa. Maintaining the usual uneven jack thrust state of shield tunnelling along the design axis is unlikely to result in segment concrete cracking. Damage to the segment caused by the eccentricity of the brace boot plate is the most severe; hence, avoiding the eccentricity of the brace boot plate during construction is crucial. The findings of this research can guide the control of jack thrust during shield tunnelling construction and offer insights into the design of segment parameters.

1. Introduction

With the rapid advancement of modern construction and manufacturing technologies, the associated technology and expertise in shield construction have matured considerably. However, due to the ongoing utilization of urban above-ground and underground spaces, the selection of rail transit lines is constrained by urban planning and nearby buildings. Consequently, the complexity of these line types has increased, leading to progressively more challenging shield construction environments. Complex engineering problems frequently arise during the construction of subway projects [1,2,3]. For instance, during the shield tunnelling of approximately 10 km under intricate conditions, such as a mudstone composite stratum; a 37.5‰, lengthy, and substantial longitudinal slope; and a 310 m minimum radius curve, within the civil engineering bid 3 of the initial phase of Chengdu Rail Transit Line 9, challenges like difficulty in controlling the shield axis, segment dislocation, severe cracking and damage, and water leakage were encountered.

Constructing tunnels with a substantial longitudinal slope and a small-radius sharp curve presents difficulties [4,5,6]. Complex procedures are always required throughout the construction process, including adjusting the shield machine’s horizontal and vertical position, controlling the tunnelling thrust, and ensuring the over-excavation amount inside and outside the turn. Improper operations can cause tunnel axis deviations, surface subsidence, excessive uplift values, or inadequate stress on segments [7,8,9]. During shield tunnel excavation, damage such as outer arc surface ruptures, corner impairments, concrete collapse at the bolt and positioning holes, shallow segmental cracks, and through-segment cracks frequently occur [10,11,12]. Currently, there are no fully effective methods to prevent these issues, and the impact of construction load on segment quality remains a research focus.

Throughout shield tunnel construction, besides recognizable jack thrust, surrounding rock pressure, and buoyancy, unpredictable challenges such as adverse assembly load, subpar contact force of the shield shell, and various impact loads can arise [13,14]. The jack’s reaction force represents the peak external load on the segment’s axial direction during construction [15]. Particularly in curved construction sections, factors such as the eccentricity of the jack thrust, overpowering thrust, brace boot eccentricity, and sudden jack failures can subject the segment to intense localized stress concentrations, leading to segment cracking and damage. If pre-assembly segment defects exist, the cracking and damage phenomena become even more probable under the adverse force of the jack. Multiple damage forms to the lining segment can result in tunnel water leakage affecting the tunnel’s structural safety and durability [16]. Factors such as surrounding rock pressure and buoyancy remain uncontrollable, contingent on formation conditions. Thus, this study concentrates on analyzing the influence of jack thrust on segment damage.

Among the published research results, Idris et al. [17] and Sandrone et al. [18] analyzed the mechanisms of cracks and deformation diseases in highway tunnel lining structures. Yahagi examined the mechanical response characteristics of lining segments under construction loads during excavation. Yan et al. [19] proposed a damage identification method for shield tunnel lining based on back analysis. Arnau et al. [20,21] applied loads on the tunnel’s top using three hydraulic jacks to analyze the displacement, joint closure, and crack morphology of the lining under various load conditions. Wells et al. [22] employed the viscous crack model to simulate the fracturing of quasi-brittle heterogeneous materials, highlighting that the finite element model can accurately represent the nonlinear cracking of materials. Belytschko [23] confirmed the efficacy of the extended finite element method by numerically simulating concrete viscous crack propagation, demonstrating its capacity to illustrate the growth of arbitrary viscous cracks. Takeuchi et al. [24] explored the impact of jack thrust on segment stress using field tests, fundamental laboratory experiments, and three-dimensional finite element analysis methods. Lu [25] elucidated the damage mechanisms of diseased segments and ascertained and validated the crack distribution and propagation patterns of lining segments under various construction loads. Yang et al. [26] examined the damage mechanisms of shield tunnel segments on three scales: a single segment, two segments (including joints), and a whole-ring lining structure. Lai et al. [27] developed a three-dimensional nonlinear model to assess the crack propagation patterns of segments.

Various research methodologies exist to study the mechanical response patterns of shield tunnel lining segments under stratum and construction loads, including field investigations, field tests, and analogous model tests. A large number of research findings have been accumulated using these methods. However, in numerical simulation, earlier researchers predominantly employed the extended finite element method based on fracture mechanics to simulate segmental crack evolution under construction loads. Given the significant variability in the extended finite element crack calculation outcomes and the substantial influence of element meshing quality on these results, there remains room for refining simulation accuracy. It thus becomes imperative to investigate other constitutive models to characterize the material attributes of the lining segment concrete. This will enable a more precise understanding of the effects of construction loads on segment damage.

This study develops a finite element analysis model of lining segments under jacking force across varied construction scenarios, incorporating the concrete damage plastic constitutive model in ABAQUS. The stress patterns and damage behavior of segments under construction situations, such as extensive thrust relief, vertical adjustments of shield machines, tunnelling in mixed soft and hard strata, line turning, sudden propulsion system failures, and the eccentricity of brace boots, are analyzed. Such insights will guide the regulation of jack thrust during shield tunnelling construction and offer references for pivotal parameters in segment design.

2. On-Site Investigation of Segment Damage

Based on a subway project, an extensive field investigation was undertaken regarding the cracking and damage of the lining segment during the construction stage of the entire line, as shown in Figure 1. The crack distribution characteristics, cracking conditions, and causes of these segments were analyzed [28]. A total of 443 segment defects were recorded. These defects can be categorized into three types: longitudinal cracks, arch roof shedding, and corner cracks, constituting 45.8%, 41.3%, and 12.9% of the defects, respectively. Longitudinal cracks and arch roof shedding represent the majority, significantly impacting the quality of segments during construction.

Longitudinal cracks refer to those that propagate along the axis of the tunnel and are among the most prevalent forms of segment fracture. Typically, these are one or more parallel cracks spaced at 10–30 cm intervals. The investigation identified two crack types, anterior and posterior, based on their direction. Of the 203 longitudinal cracks discovered, 153 were anterior, while 50 were posterior. The crack distribution is listed in

Table 1. Statistical table of longitudinal crack distribution.

Crack Location and Segment Blocks		Anterior Crack		Posterior Crack
		Numbers	Proportion	Numbers	Proportion
Crack location	Arch roof	20	13.07%	3	6.00%
	Arch waist	111	72.55%	23	46.00%
	Arch bottom	22	14.38%	24	48.00%
Segment block	Capping block (F)	0	0.00%	0	0.00%
	Adjacent block (L1)	47	30.72	4	8.00%
	Adjacent block (L2)	27	17.65%	24	48.00%
	Standard block (B1)	32	20.91%	13	26.00%
	Standard block (B2)	27	17.65%	4	8.00%
	Standard block (B3)	20	13.07%	5	10.00%

.

Table 1 reveals that only a few longitudinal cracks are situated at the arch roof of the tunnel. The distribution ratio of longitudinal cracks at the arch waist exceeds that at the arch bottom. Along the tunnel’s axis, the formation of longitudinal cracks in the segment correlates with the stratum’s complexity, indicating a pronounced regional concentration. For instance, within this tunnel section, most of the longitudinal cracks manifest in areas with intricate stratum conditions, such as where the shield traverses soft and hard interbedded strata. No longitudinal cracks were observed in the capping block (F), and the highest distribution ratio occurred in the adjacent block (L2).

Crack length, width, and depth were statistically analyzed and are illustrated in Figure 2. The length of the anterior cracks predominantly falls within the [500, 600) range, while the posterior cracks are primarily within the [300, 400) range. This indicates that the anterior cracks exhibit a more pronounced fracture degree. Overall, the distribution of the two crack types is consistent; however, the anterior cracks surpass the posterior cracks in value and concentration range. Longitudinal cracks in the segment structure can compromise the shield tunnel’s waterproofing system and significantly diminish the mechanical performance of the segment structure. Among the two crack types, the anterior cracks, whether in length, depth, or width, are more numerous, have a broader distribution, and exhibit a more severe degree of defect. Consequently, they have a more pronounced impact on the shield tunnel’s load-bearing capacity and pose a considerable risk to the tunnel structure’s safety and longevity.

3. Numerical Model

3.1. Material Constitutive Model

To study the stress damage of pipe segments, selecting a reasonable constitutive model of concrete materials is the key to finite element numerical analysis. Through comprehensive comparison of a large number of constitutive model theories currently used to describe concrete materials [29], this article chooses to use the concrete plastic damage (CDP) mechanical model. The CDP model characterizes the gradual decrease in material unloading stiffness due to damage accumulation and crack development by introducing damage factors into the stress–strain constitutive relationship of concrete in tension and compression. It can accurately and clearly describe the material damage and stiffness degradation caused by cracks, and is very consistent with the stress characteristics of materials. Therefore, it is widely used in finite element numerical analysis. When using this model, we make the following assumptions: (1) The elastic behavior of concrete materials is isotropic and linear; (2) The damage of concrete materials is isotropic, and we combine isotropic tensile and compressive plasticity to represent the inelastic behavior of concrete; (3) The two main failure modes of concrete materials are tensile cracking and compressive crushing; (4) Under alternating loads, the material stiffness is allowed to recover. By default, the stiffness is restored from tensile stress to compressive stress, and the stiffness remains unchanged from compressive stress to tensile stress.

Selecting an appropriate constitutive model for concrete material is crucial for finite element numerical analysis when investigating the stress damage of segments. This study adopts the CDP model to delineate the mechanical behavior of segments under stress [30,31]. The CDP model elucidates the attributes of material-unloading stiffness degradation attributable to damage accumulation and crack development. It introduces damage factors into the tensile and compressive stress–strain constitutive equation of concrete [32,33,34], providing an accurate and precise depiction of the material damage and stiffness degradation instigated by cracks.

Based on the Chinese Code for Design of Concrete Structures (GB 50010–2010) [35], the stress–strain curve for concrete under uniaxial tension, as shown in Figure 3, can be ascertained using Equations (1)–(4).

$$\sigma =(1-{\beta }_{\mathrm{t}})E_{\mathrm{c}}\epsilon ,$$

(1)

$${\beta }_{\mathrm{t}}=\left\{\begin{array}{ll}1-{\rho }_{\mathrm{t}}\left[1.2-0.2x^5\right]\hfill & x⩽1\hfill \\ 1-\frac{{\rho }_{\mathrm{t}}}{{\alpha }_{\mathrm{t}}{(x-1)}^{1.7}+x}\hfill & x>1\hfill \end{array},\right.$$

(2)

$$x=\frac{\epsilon }{{\epsilon }_{\mathrm{t},\mathrm{r}}},$$

(3)

$${\rho }_{\mathrm{t}}=\frac{f_{\mathrm{t},\mathrm{r}}}{E_{\mathrm{c}}{\epsilon }_{\mathrm{t},\mathrm{r}}},$$

(4)

where ${\alpha }_{\mathrm{t}}$ is the parameter related to the descending section of the stress–strain curve of concrete under uniaxial tension, ${\alpha }_{\mathrm{t}}=0.312\times f_{\mathrm{t},\mathrm{r}}^2$; $f_{\mathrm{t},\mathrm{r}}$ is the standard value for uniaxial tensile strength of concrete; $\epsilon$ is the strain of concrete; ${\epsilon }_{\mathrm{t},\mathrm{r}}$ is the peak tensile strain of concrete corresponding to the standard value of uniaxial tensile strength, ${\epsilon }_{\mathrm{t},\mathrm{r}}=f_{\mathrm{t},\mathrm{r}}^{0.54}\times 65\times {10}^{-6}$; ${\beta }_{\mathrm{t}}$ is the parameter related to the tensile stress–strain curve; and $E_{\mathrm{c}}$ is the elastic modulus of concrete.

Similarly, the stress–strain curve for concrete under uniaxial compression can be determined based on Equations (5)–(9).

$$\sigma =(1-{\beta }_{\mathrm{c}})E_{\mathrm{c}}\epsilon ,$$

(5)

$${\beta }_{\mathrm{c}}=\left\{\begin{array}{cc}1-\frac{{\rho }_{\mathrm{c}}n}{n-1+x^n}& x⩽1\\ 1-\frac{{\rho }_{\mathrm{c}}}{{\alpha }_{\mathrm{c}}{(x-1)}^2+x}& x>1\end{array}\right.,$$

(6)

$${\rho }_{\mathrm{c}}=\frac{f_{\mathrm{c},\mathrm{r}}}{E_{\mathrm{c}}{\epsilon }_{\mathrm{c},\mathrm{r}}},$$

(7)

$$n=\frac{E_{\mathrm{c}}{\epsilon }_{\mathrm{c},\mathrm{r}}}{E_{\mathrm{c}}{\epsilon }_{\mathrm{c},\mathrm{r}}-f_{\mathrm{c},\mathrm{r}}},$$

(8)

$$x=\frac{\epsilon }{{\epsilon }_{\mathrm{c},\mathrm{r}}},$$

(9)

where ${\alpha }_{\mathrm{c}}$ is the parameter related to the descending section of the concrete stress–strain curve under uniaxial compression, ${\alpha }_{\mathrm{c}}=0.157f_{\mathrm{c},\mathrm{r}}^{0.785}-0.905$; $f_{\mathrm{c},\mathrm{r}}$ is the standard value for concrete uniaxial compressive strength; ${\epsilon }_{\mathrm{c},\mathrm{r}}$ is the peak compressive strain of concrete corresponding to the standard value for uniaxial compressive strength, ${\epsilon }_{\mathrm{c},\mathrm{r}}=(700+172\sqrt{f_{\mathrm{c},\mathrm{r}}})\times {10}^{-6}$; and ${\beta }_{\mathrm{c}}$ is a parameter related to the compressive stress–strain curve.

Figure 4a illustrates that the portion of concrete surpassing the elastic range under uniaxial compression is called compressive damage. The compressive stress data can be articulated as a function of non-elastic strain. The compressive stress–strain data beyond the elastic portion is entered as a positive value. The relationship between compressive plastic strain, compressive inelastic strain, and the damage factor is described subsequently.

$${\tilde{\epsilon }}_{\mathrm{t}}^{pl}={\tilde{\epsilon }}_{\mathrm{t}}^{ck}-\frac{d_{\mathrm{t}}}{(1-d_{\mathrm{t}})}\frac{{\sigma }_{\mathrm{t}}}{E_0}.$$

(10)

Figure 4b indicates that the part of concrete that exceeds the elastic range under uniaxial compression is defined as compressive damage, and the compressive stress data can be expressed as a function of non-elastic strain ${\tilde{\epsilon }}_{\mathrm{c}}^{in}$. The compressive stress–strain data beyond the elastic part is input as a positive value in the form of ${\sigma }_{\mathrm{c}}-{\tilde{\epsilon }}_{\mathrm{c}}^{in}$. The following describes the relationship between compressive plastic strain, compressive inelastic strain, and the damage factor:

$${\tilde{\epsilon }}_{\mathrm{c}}^{pl}={\tilde{\epsilon }}_{\mathrm{c}}^{in}-({\epsilon }_{\mathrm{c}}^{el}-{\epsilon }_{0\mathrm{c}}^{el})={\tilde{\epsilon }}_{\mathrm{c}}^{in}-\frac{d_{\mathrm{c}}}{(1-d_{\mathrm{c}})}\frac{{\sigma }_{\mathrm{c}}}{E_0}.$$

(11)

The damage factors represent the properties of the concrete damage plasticity model d_t and d_c. Based on the energy equivalence principle [36], the elastic residual energy of damaged and undamaged materials under stress is $W_{\mathrm{d}}^{\mathrm{e}}=\frac{{\overline{\sigma }}^2}{2E_{\mathrm{d}}}=W_0^{\mathrm{e}}=\frac{{\sigma }^2}{2E_{\mathrm{c}}}$. The relationship between the equivalent stress acting on the damaged material and the stress acting on the non-destructive material is as follows:

$$\overline{\sigma }=(1-d)\sigma .$$

(12)

The equivalent elastic modulus of the damaged material can be obtained:

$$E_{\mathrm{d}}=E_{\mathrm{c}}{(1-d)}^2.$$

(13)

Multiplying both sides by strain ε:

$$\sigma ={(1-d)}^2{E}_{\mathrm{c}}\epsilon .$$

(14)

Substituting Equation (14) into the tensile and compressive constitutive equations of concrete, the damage factors d_t and d_c can be derived as follows:

$$d_{\mathrm{t}}=\left\{\begin{array}{l}1-\sqrt{{\rho }_{\mathrm{t}}(1.2-0.2x^5)}\hspace{1em}(x\le 1)\\ 1-\sqrt{\frac{{\rho }_{\mathrm{t}}}{{\alpha }_{\mathrm{t}}{(x-1)}^{1.7}+x}}\hspace{1em}\hspace{1em} (x>1)\end{array}\right..$$

(15)

$$d_{\mathrm{c}}=\left\{\begin{array}{l}1-\sqrt{\frac{{\rho }_{\mathrm{c}}n}{n-1+x^n}}\hspace{1em}\hspace{1em}(x\le 1)\\ 1-\sqrt{\frac{{\rho }_{\mathrm{c}}}{{\alpha }_{\mathrm{c}}{(x-1)}^2+x}\hspace{1em}}(x>1)\end{array}\right.$$

(16)

In the CDP model, it is necessary to exclude the difference between the elastic stage and input relevant values to describe the tensile and compressive characteristics of concrete in the plastic stage (curve fitting). After calculation and conversion according to the specifications, the input parameters are shown in Figure 5.

The compression damage factor d_c > 0.2 and tensile damage factor d_t > 0 are the criteria for the development and damage of concrete cracks, and the greater the damage factor, the more severe the cracking of concrete materials. The parameters of concrete and steel bar materials in the numerical model are listed in

Table 2. Concrete strength parameters.

Concrete Grade	Strength Standard Value (MPa)		Strength Design Value (MPa)		Elastic Modulus (MPa)	Density (kg·m−3)	Poisson’s Ratio
	Tension	Compression	Tension	Compression
C50	2.64	32.4	1.89	23.1	34.5	2420	0.2

and

Table 3. Steel material parameters.

Types of Steel Bars	A10, A12	C16
Design value of tensile strength (MPa)	270	360
Design value of compressive strength (MPa)	270	360
Elastic modulus (GPa)	210	200
Poisson’s ratio	0.3	0.3

, respectively.

3.2. Geometry and Meshing

The lining ring comprises a capping block (F), two adjacent blocks (L1 and L2) and three standard blocks (B1, B2, and B3). The partition of the jacks is shown in Figure 6. The segment’s thickness is 350 mm, its width is 1500 mm, and its outer diameter measures 6700 mm. The design includes 32 longitudinal hand holes and 24 circumferential hand holes. One hoisting hole (also a grouting hole) and two more grouting holes are present. Figure 7 depicts the established standard block segment entity and the numerical calculation model. The burial depth of the vault ranges from 10.5 to 25 m, and the primary crossing interval consists of substantial and medium-weathered mudstone strata.

The segment and jack brace shoe models are consistent with the project’s dimensions. The bolt, hand, hoisting, and grouting holes reduce the segment’s section and significantly impact its stress, so accurate modeling is paramount. Since the bolt remains unlocked during the initial phase of segment assembly, its effect on segment stress can be disregarded; hence, the joint bolt model is omitted. The enhancement of concrete’s stress state due to the steel mesh skeleton is noteworthy, so this model is incorporated.

Given the meshing feasibility and calculation continuity, the four-node linear tetrahedral element (C3D4) in ABAQUS is designated for the bolt hand hole, bolt hole, hoisting hole, and grouting hole. The remaining parts of the segment and the brace boot plate use the eight-node linear hexahedron reduced integral element (C3D8R). The steel skeleton employs the two-node linear three-dimensional truss element (T3D2). The regular grid part is divided using a sweeping method, while the remaining parts are divided freely.

3.3. Boundary Conditions

The research object pertains to the lining segment interacting directly with the jack. The stress state of this segment within the shield shell is well-defined, and the impact of gravity can be disregarded. It is considered that the segment is solely influenced by the thrust force of the jack in the width direction, as depicted in Figure 8.

During the construction process, the longitudinal contact surface of the segment undergoes compression and separation from its adjacent segment on multiple occasions. Consequently, this longitudinal contact surface cannot be directly hinged or assigned a fixed displacement. Regardless of the joint bolts, a fixed displacement concrete base is established on either side of the longitudinal segment. The boundary conditions of this longitudinal contact surface are simulated by specifying both normal and tangential contact conditions. The circumferential contact surface of the segment, which remains unaffected by the jacking force, can be designated as a fixed constraint. Normal and tangential contact conditions are implemented between the jack brace boots and the segments. This study considers the friction coefficient between concrete and concrete or the brace boot plate to be 0.35. In addition, steel bars are integrated and constrained with the concrete through embedding.

3.4. Modeling Scheme

Under varying construction conditions, disparities emerge in the pressure across each partition of the propulsion system as well as the thrust state of the jack. This study primarily investigates the damage state of the segment under construction conditions, such as significant thrust relief, vertical orientation adjustments of the shield machine, tunnelling within interbedded soft and hard strata, line deviations, abrupt malfunctions of the propulsion system, and eccentric positioning of brace boots.

When the shield machine encounters hard strata, boulders, or weak self-stability of the surrounding rock and becomes trapped during the shutdown, an increase in thrust and cutterhead torque is essential for troubleshooting. Consequently, the segment’s thrust also rises, and excessive jack thrust during construction might damage the segment. The target segment 1 (B2 block) should be selected, and the scenario is presented in

Table 4. Excessive jack thrust cases.

Cases	Load (MPa)			Construction State	Target Segment
	Brace Boot 1	Brace Boot 2	Brace Boot 3
1–1	11	11	11	Common thrust	B2
1–2	14	14	14	Increased thrust
1–3	18	18	18
1–4	23	23	23
1–5	30	30	30	Large thrust escape
1–6	40	40	40
1–7	50	50	50	Ultimate thrust escape

.

If the shield tunnelling machine requires thrust adjustments in diverse tunnel face areas due to soft and hard interbedded strata or while altering the excavation direction, it must progress in line with the design axis. Furthermore, a sudden malfunction in the shield tunnelling machine propulsion system during construction can result in varying jack thrusts for the same oil cylinder zone. In these scenarios of unpredictable, extreme non-uniform jack thrust, the segments face a higher risk of damage from excessive stress concentration. Target segments 1 (B2 block), 2 (L2 block), and 3 (B1 block) should be selected, with cases presented in

Table 5. Uneven jack thrust cases.

Cases	Load (MPa)			Construction State	Target Segment
	Brace Boot 1	Brace Boot 2	Brace Boot 3
2–1	30	20	20	Adjusting the posture of raising and lowering the head	L2, B1
				Excavation in soft and hard interbedded strata	B1
2–2	10	20	20	Excavation in soft and hard interbedded strata	L2
2–3	15	20	20	Turning right	B1
2–4	15	10	10	Turning right	L2
2–5	50	10	10	Propulsion system sudden failure	B2
2–6	10	50	10
2–7	50	50	10
2–8	50	10	50

. In the table, uneven jack thrust from cases 2–1 to 2–4 maintains the regular driving thrust of the shield tunnelling machine along the design axis. However, the highly uneven jack thrust from cases 2–5 to 2–8 represents an irregular driving thrust following a propulsion system failure.

In general, deviations from the excavation axis can occur during the process. Adjusting the shield machine’s attitude can cause the center of the jack brace boot to shift from the segment’s center, leading to a bending moment in the segment, a primary contributor to segmental damage. As illustrated in Figure 9, an eccentric distance of ±3 cm suggests that the brace boot plate remains within the concrete ring section; an eccentricity of ±6 cm indicates that, while the brace boot plate exceeds the concrete ring section, the jacking force range remains intact; an eccentricity of ±10 cm denotes an exceedance of the jacking force on the brace boot plate beyond the concrete ring section. One should choose target segment 1 (B2 block) and consider the jack boots’ eccentricity, with the scenarios displayed in

Table 6. Cases of eccentric distance of jack brace boot plate.

Cases	Eccentric Distance (cm)	Load (MPa)			Construction State	Target Segment
		Brace Boot 1	Brace Boot 2	Brace Boot 3
3–1	+3 (outside)	30	30	30	Eccentricity of jack brace boot plate caused by adjustment of shield tunnelling posture	B2
3–2	+6 (outside)
3–3	+10 (outside)
3–4	−3 (inside)
3–5	−6 (inside)
3–6	−10 (inside)
1–5	0 (control group)

.

4. Model Validation

Zhang et al. [11] utilized a multi-functional three-dimensional loading test platform to perform full-scale structural load tests on critical super-large-diameter shield tunnel sections, examining their corresponding mechanical properties and failure processes. It is necessary to conduct a more in-depth analysis of the key segments using the finite element method and fully reveal the mechanical properties of the key segments. This study conducts a numerical simulation of the tests above to affirm the CDP model’s validity.

Figure 10 depicts the relationship between the specimen’s maximum vertical displacement and the vertical load under a compressive bending load. Under varying longitudinal force conditions, the segment’s maximum vertical displacement follows a similar trend. With an increasing vertical load, the maximum vertical displacement rises almost linearly, and a positive correlation exists between the two. These observations validate the experimental results’ reliability. The numerical simulation results closely match the measured values, with the highest error being under 8%. Discrepancies can arise due to: (1) gaps between distinct segments in the actual model leading to stress concentration; (2) manufacturing variability in segments; and (3) minor differences between the experimental loading apparatus and the model’s constraint configuration.

5. Results Analysis

5.1. Excessive Jack Thrust

5.1.1. Plastic Damage Analysis of Segments

The damage situation of the segment is illustrated in Figure 11 and Figure 12. Under the commonly used jack thrust in the construction ledger (case 1–1), the concrete material of the segment does not undergo plastic damage; in other words, local damage does not occur. Under the maximum jack thrust in the construction ledger (case 1–4), the segment’s maximum compression damage is 0.01779, which falls short of the crack damage criterion d_c > 0.2 noted previously. However, the maximum tensile damage stands at 0.3206, satisfying the criteria for concrete material tensile cracking. Thus, at this juncture, the segment begins to exhibit local microcracks. Although these microcracks emerge due to the tensile plastic damage to the concrete, their distribution is virtually indistinguishable on the cloud map. Hence, it may be concluded that these microcracks do not penetrate or instigate local block failure.

For cases 1–5 to 1–7, as the jack thrust escalates to its utmost design value, the maximum compressive and tensile plastic damages can reach 0.1627 and 0.8485, respectively. This suggests that cracks within the tensile plastic damage zone near the segment’s inner and outer edges surrounding the brace boot, as depicted in Figure 11d, have expanded, resulting in the lining concrete’s corner failure. The compressive plastic damage zone, shown in Figure 11c, is somewhat extensive. Nonetheless, its value does not surpass 0.2, which indicates it does not prompt concrete materials to crack or deteriorate.

Figure 12 depicts the fluctuation of the maximum damage factor under various scenarios. Once tensile and plastic damages manifest, augmenting the jacking force progressively intensifies the concrete’s cracking until it completely breaks down. The probability of tensile cracking damage in concrete materials is greater than compressive damage. When the pipe jack’s thrust is evenly spread, the customary jack thrust (11 MPa) in the construction ledger does not induce microcracks within the segment. The apex jack thrust utilized in the construction ledger (23 MPa) can trigger local microcracks in the concrete due to tensile plastic damage, yet these cracks remain unconnected. Should the maximum thrust design value be employed, the cracks in the tensile plastic damage region near the segment’s inner and outer boundaries adjacent to the brace boot plate will progress, culminating in the lining’s local corner failure. Concrete fractures are predominantly instigated by tensile plastic damage. The jack thrust value should not surpass 30 MPa.

Considering that the segment’s plastic damage factor is predicated on the ultimate tensile and compressive failure stress and strain, these serve as the benchmark for scrutinizing the concrete materials’ cracked region. During the segment’s design phase, there is also a requirement to assess the concrete strength design value meticulously. This must be paired with the highest principal stress to better forecast the segment cracking based on the plastic damage region.

5.1.2. Maximum Principal Stress of Segments

The distribution of principal stress in the segment is depicted in Figure 13 and Figure 14. As the jacking force increases within the range of 10–40 MPa, the maximum compressive principal stress of the concrete demonstrates a linear rising trend. When the jacking force escalates to 50 MPa, the growth rate for the maximum compressive principal stress also rises. However, numerically, this is substantially smaller than the concrete’s design compressive strength value of 23.1 MPa. Thus, it can be inferred that, within the range of the maximum thrust design value, the concrete will not experience compression failure. Even at the minimal jacking force of 10 MPa, the maximum tensile principal stress of the segment surpasses the designed tensile strength value of 1.89 MPa. This indicates that, should the concrete material of the pipe segment undergo tension leading to cracks, such incidents are likely. Furthermore, it can be deduced that cracks and damage in concrete segments due to tension are prone to happen.

A decline in the maximum tensile stress under conditions 1–2 is posited to result from decreased material stiffness after the onset of plastic damage in the concrete. The inability of the maximum tensile principal stress, under all conditions, to attain the standard tensile strength value of 2.64 MPa can also be attributed to the diminished stiffness of the concrete material following the commencement of plastic damage.

Based on Figure 11 and Figure 13, the subsequent damage trend of the segment can be outlined as follows: cracks propagate from the initial damage point along the longitudinal depth and develop toward the bolt hand hole on the inner diameter side, with the circumferential hand hole being the first to incur damage. In the circumferential section, cracks proximate to the longitudinal joint will swiftly penetrate along the segment’s radial direction. Between the two brace boot plates, the initial failure point first emerges at the segment’s edge and the section’s center and subsequently connects with and is penetrated by the initial failure point.

5.2. Uneven Jack Thrust

5.2.1. Plastic Damage Analysis of Segments

Based on Figure 15, in case 2–1, the tensile plastic damage zone cracks manifested at both the inner and outer edges of the segment near the brace boot plate and the position of the longitudinal crack, leading to concrete damage at the lining edge due to missing corners. However, both the damage factor and the damage area remain minimal. Moreover, from cases 2–4 to 2–4, even though the segment has begun to exhibit local microcracks owing to tensile plastic damage, their distribution location is virtually imperceptible on the cloud map. Thus, it is assessed that the microcracks are unlikely to penetrate and result in localized block falling and damage. Consequently, barring the potential minor angular damage to some segments caused by adjusting the shield tunnelling machine’s vertical orientation, inducing concrete cracking and damage to the segments is challenging.

Comparing cases 2–5 and 2–6, it is observed that, when the fault jacking force is concentrated near the longitudinal joint, the segment suffers greater damage than when it is centered within the segment. Comparing cases 2–7 and 2–8, the plastic damage inflicted by two distinct fault thrusts acting separately on the segment is more pronounced than that caused by their continuous action on the segment.

5.2.2. Maximum Principal Stress of Segments

Figure 16 demonstrates that, for cases 2–1 to 2–4, even though the plastic damage is insufficient to induce significant cracking in each condition, the maximum tensile principal stress consistently surpasses the design value for tensile strength, which is 1.89 MPa. Within these, conditions 2–1 to 2–3 demonstrate a tendency toward bolt hand hole failure, with conditions 2–1 being the most pronounced (as evidenced by the stress at the bolt hand hole exceeding the design value for strength).

In comparing cases 2–1 and 1–5, one observes that, although the jack thrust exerted on brace boot plate 1 is 30 MPa in both situations, uneven thrust results in stress concentration. The maximum tensile principal stress in condition 2–1 is notably higher, rendering it more susceptible to material damage. Comparing cases 2–1 and 2–2, during excavation in the mixed soft and hard interbedded strata, it is evident that block B1 is more vulnerable than block L2. Similarly, when contrasting cases 2–7 and 2–8, block B1 exhibits more susceptibility to damage than block L2 during a right turn. Additionally, upon contrasting cases 2–5 to 2–8 with 1–7, one can discern that, in contrast to a uniformly distributed significant thrust, when a singular set of jack thrusts is focused, the damage tends to progress more profoundly along the axial direction, predominantly near the corner of brace boot plate 2.

5.3. Eccentricity of the Jack Brace Boot Plate

5.3.1. Plastic Damage Analysis of Segments

According to Figure 17, relative to the brace boot plate acting on the central portion of the segment’s section (as in cases 1–5), when the brace boot plate is located eccentrically, the segment’s plastic damage zone and intensity manifest in an eccentric manner. This is specifically evident in the following ways.

Concerning compressive plastic damage, when the brace boot plate is eccentrically positioned outwards, the compressive plastic damage on the segment’s outer diameter corner intensifies with the increment of the eccentric distance. Conversely, the damage on the inner diameter side diminishes. The inverse occurs when the brace boot plate’s position is eccentric inwards. In the realm of tensile plastic damage, the pattern of eccentricity contrasts with that of compressive damage. Moreover, with increased eccentric distance, the concrete shifts from angular damage at the peripheries to more pervasive crack penetration along the edge of the brace boot plate.

Considering the extent as illustrated by the damage cloud map, one observes that the compressive plastic damage on the inner diameter side (resulting from the inward eccentricity of the brace boot plate) and the tensile plastic damage (due to the outward eccentricity of the support shoe plate) are marginally more acute than those on the outer side. This heightened susceptibility can be attributed to side bolt holes and handholes on the inner diameter side. Analyzing the numerical values of the damage factor (as depicted in Figure 18), the discrepancy between the damage factors on the segment’s inner and outer diameter sides, caused by the brace boot plate’s eccentricity, is relatively minor. Nonetheless, both values are considerably higher than when the brace boot plate is centrally positioned on the segment section (as in case 1–5). The peak tensile plastic damage factor reaches 0.9833, indicating that the concrete is nearing complete failure.

5.3.2. Maximum Principal Stress of Segments

Figure 19 shows that the compression area and numerical values vary with the displacement of the brace boot plate position. The closer the compression area is to the inner and outer diameter corners of the segment, the more pronounced the increase in tensile and compressive stress of the concrete due to concentrated stress. Additionally, in the area depicted on the cloud map that surpasses the design value of concrete strength, indicating imminent or already present corner damage, it is observed that, when the brace boot plate is eccentric either inwardly or outwardly, the tensile zone increasingly envelops the compression zone. It can be inferred that, if the brace boot plate continues its displacement or the jacking force escalates, the tensile (shear) failure stress will induce microcracks to evolve and join along this area’s periphery, leading to significant block failing and damage.

6. Conclusions

A mechanical model of a segment under varied construction conditions is constructed. The CDP model in ABAQUS is utilized to analyze the damage state of the segment under diverse adverse jacking forces during distinct scenarios. The pertinent conclusions are as follows:

(1)

If the segment’s jack thrust is uniformly spread, the commonly employed jack thrust (11 MPa) in construction will not induce microcracks. The maximal jack thrust (23 MPa) used in construction can result in sporadic microcracks in the concrete due to tensile plastic damage, but these will not fully extend, leading to localized fracturing. However, if the ultimate thrust design value (50 MPa) is employed, cracks will proliferate in the tensile plastic damage region adjacent to the segment’s inner and outer borders around the brace boot plate, causing local angular failure at the lining’s edge. Most concrete cracks are attributed to the tensile plastic damage of materials. It is advised that the jack’s thrust value should not surpass 30 MPa.

(2)

Besides the potential minor angular failure in some segments due to the shield’s vertical alignment adjustments, the customary uneven jack thrust, intended to maintain the shield machine tunnelling in line with the design axis, is unlikely to inflict segment crack damage. When the jack malfunctions, the uneven fault jacking force concentrates near the longitudinal joint, inflicting more substantial segment damage than at the segment’s center. Furthermore, the uneven and focused distribution of jacking force can lead to more pronounced segment damage.

(3)

Among all kinds of adverse jacking force, the damage to the segment caused by the brace boot plate’s eccentricity is the most severe. Regardless of the brace shoe plate’s positioning, either inwards or outwards, the plastic damage at the inner and outer diameter corners and the brace shoe plate’s edge is significantly exacerbated. This damage primarily stems from the shear stress concentration at the brace shoe plate’s boundary, and the cracks traverse the affected zone, resulting in extensive corner damage.

(4)

This article focuses on the influence of the controllable factor of the jack on the force acting on the pipe segment. Subsequent research will continue to analyze the further damage behavior of the damaged pipe segment under loads such as formation pressure and buoyancy in the formation after assembly.