Mechanical Response Characteristics of Prefabricated Utility Tunnel Joints Considering Jacking Load Imbalance

Featured Application

The proposed numerical approach can be used to assess the mechanical performance of segmental joints in prefabricated utility tunnels during jacking construction. By quantifying joint stress-deformation responses under thrust imbalance and interface friction, it helps identify critical leading-end regions and provides practical references for defining acceptable imbalance levels. The outcomes can support design verification, construction monitoring, and decision-making in similar utility-tunnel jacking projects.

Abstract

During jacking construction of prefabricated utility tunnels, asynchronous jack output and interface friction may induce internal force redistribution and deformation amplification at the leading end. Taking a triple-cell prefabricated utility tunnel in Xiong’an New Area as a case study, a three-dimensional finite element model was established considering inter-segment contact, equivalent bolted connections, and bottom-slab-bedding friction. Jack asynchrony was idealized as a quasi-static thrust imbalance, and a synchronous case, asynchronous cases with thrust differences of 5–30%, and varying friction coefficients were analyzed. For the 30% thrust-difference condition, structural responses were examined at both the gasket-compression stage and the maximum jacking-force stage. The results show that jacking loads attenuate along the tunnel length in a staged manner, with the leading end acting as the primary load-transfer zone. Increasing thrust imbalance drives the response from axial compression toward eccentric compression-bending, accompanied by monotonic increases in principal stresses and vertical displacement. Higher friction further amplifies the leading-end response; nevertheless, for the investigated configuration, stresses and deformations under a 30% thrust imbalance remain within engineeringly acceptable limits. The findings provide a basis for identifying critical leading-end locations, arranging monitoring schemes, and supporting construction control under asynchronous jacking.

1. Introduction

With the acceleration of urbanization, underground utility tunnels, as a critical component of urban lifeline infrastructure, play an essential role in enhancing urban operational safety and sustainable development. Owing to their high construction efficiency, controllable quality, and reduced environmental impact, prefabricated utility tunnel construction technologies have been widely adopted in urban infrastructure projects [1,2,3]. However, during jacking construction, the transfer of jacking loads and the frictional behavior at the bottom-slab-bedding interface significantly influence the structural stress state. In particular, under asynchronous jacking conditions, uneven thrust output can induce additional internal forces and amplified deformations, thereby posing potential risks to structural safety and stability [4,5,6]. A systematic investigation of the stress and deformation responses of utility tunnel structures under asynchronous jacking is therefore of considerable engineering significance.

Current research on synchronous and asynchronous jacking has largely focused on theoretical analysis and numerical modeling [7,8,9]. Under synchronous jacking, loads are transmitted more uniformly along the tunnel axis and the structural response is typically near-symmetric. In contrast, asynchronous jacking leads to uneven thrust distribution, making the leading end prone to eccentric loading and localized deformation, which may compromise global stability. Existing studies still emphasize synchronous behavior, while the redistribution of internal forces at the leading end and its engineering implications under asynchronous jacking remain insufficiently quantified [10,11]. Moreover, joints and end components are widely recognized as structural weak links whose mechanical performance is highly sensitive to asymmetric or eccentric actions. Experimental studies, including pseudo-static, cyclic, and shaking-table tests, have demonstrated the governing role of joint behavior under complex loading conditions [12,13,14,15], yet quantitative insights into end-joint response during asynchronous jacking remain limited.

Compared with synchronous jacking, asynchronous jacking better reflects the complex boundary conditions encountered in practice. Nevertheless, existing studies remain fragmented and are mostly concerned with how construction-parameter deviations in shield tunneling or pipe jacking affect surrounding ground behavior or local structural responses. Engineering-oriented research on prefabricated utility tunnels—particularly tensile-compressive force redistribution, amplification of differential displacement, and safety margin evaluation at end joints under asynchronous jacking—remains scarce [16,17,18]. More broadly, underground structures are known to exhibit pronounced asymmetric stress responses under earthquakes, explosions, heterogeneous strata, or construction-induced unloading [19]. Numerical investigations further indicate that, for large-section rectangular tunnels constructed by jacking, uneven thrust distribution and frictional variability are key drivers of eccentric deformation and localized stress concentration, and that refined finite element modeling provides an effective tool for elucidating these mechanisms [20,21,22,23,24,25].

Recent studies on smart monitoring and control systems have shown that real-time identification of load non-uniformity and threshold-based indicators can effectively support process controllability in complex engineering operations. Although such approaches have been widely explored in drilling engineering and vibration control, their methodological framework is also relevant to prefabricated utility tunnel jacking, where thrust imbalance and joint response can be continuously monitored and regulated through intelligent control strategies. Accordingly, this study investigates prefabricated utility tunnels constructed by jacking, with a systematic analysis of stress and deformation responses under asynchronous jacking conditions. Particular emphasis is placed on the roles of thrust imbalance and interface friction in governing the mechanical behavior of leading-end joints. Using field-representative jacking forces, typical cases are analyzed to provide quantitative support for structural safety assessment and construction control under asynchronous jacking.

2. Project Overview and Structural Characteristics

2.1. Project Overview

The study focuses on an urban underground utility tunnel project in Xiong’an New Area. The project location, terrain, and construction layout are shown in Figure 1. Located in Rongcheng County, Baoding, Hebei Province, the tunnel adopts a prefabricated assembly system and is constructed using the jacking method. Although the geological conditions along the alignment are generally stable, alternating backfilled and unbackfilled sections locally introduce complexity to the load transfer and structural response during jacking.

The standard segment adopts a three-cell rectangular cross-section composed of a roof slab, invert slab, sidewalls, and a central partition. Compared with double- and single-cell configurations, the three-cell tunnel has greater self-weight and a more complex stiffness distribution, making it more sensitive to thrust imbalance and eccentric effects; it is therefore both conservative and representative and is selected for this study. Each segment is a precast reinforced concrete unit, with adjacent segments connected by bolts and joints to ensure composite action. The concrete is C55 with a permeability grade of P8 and waterproofing grade II, and the reinforcement is HRB500. For subsequent assessments of compressive safety, the concrete design compressive strength is consistently adopted as the governing criterion to ensure analytical consistency.

During construction, the jacking force is applied by the end-mounted jack system and is transferred backward through inter-segment joints and bolted connections, while being progressively dissipated by friction mobilized at the bottom-slab-bedding interface. As a result, the effective influence of the jacking load is largely confined to a limited number of segments near the advancing end. Consequently, the leading segments experience relatively unfavorable loading conditions during jacking and constitute the critical region for analyzing both synchronous and asynchronous jacking effects.

2.2. Structural Characteristics of the Three-Cell Prefabricated Segment

As shown in Figure 2, the project adopts a three-cell prefabricated segment with a rectangular cross-section, consisting of a roof slab, invert slab, sidewalls, and two internal partition walls arranged symmetrically. The partition walls subdivide the roof and invert into several relatively short spans, enabling the segment to maintain functional requirements while providing high global stiffness and favorable continuity of force transfer. The structure is manufactured by China Railway Engineering Equipment Group Co., Ltd. (Zhengzhou, Henan).

From a structural standpoint, the roof and invert are connected through the sidewalls and internal partitions to form multiple closed load paths, which helps distribute the axial jacking force and reduce the demand on individual components. However, the intersections between the partition walls and the roof/invert constitute typical stiffness discontinuities and are therefore sensitive to internal force redistribution under external loading. During jacking, in particular, unequal thrusts applied to the upper and lower slabs can introduce additional bending moments at these locations, leading to localized tensile and compressive stress concentrations.

Moreover, the multi-cell cross-section provides the leading end with bending resistance in both the vertical and transverse directions, while simultaneously increasing its sensitivity to eccentric loading. These sectional characteristics establish the structural basis for subsequent analyses of internal force transfer, identification of stress concentration zones, and selection of control indicators under synchronous and asynchronous jacking conditions.

3. Numerical Modeling and Computational Method

3.1. Mechanical Characteristics of the Jacking Process

During jacking, the axial thrust is applied by end-mounted jacks through a loading plate to the leading segment and is transmitted successively through inter-segment joints and tie bolts. Concurrently, tangential friction is progressively mobilized at the bottom-slab-bedding and sidewall-soil interfaces under normal pressure, dissipating the jacking load along the alignment. As the number of jacked segments increases, cumulative friction grows and confines the effective load-transfer range to a limited zone near the advancing end, while the response of distant segments stabilizes. Consequently, load transfer exhibits a front-concentrated, longitudinally attenuating pattern.

Under synchronous jacking, equal thrusts on the upper and lower slabs produce a predominantly axial compression at the leading section with near-symmetric internal forces. When thrusts differ, the resultant shifts off the neutral axis, introducing additional bending; the response evolves from axial compression to eccentric compression-bending, with internal forces and deformations redistributing as eccentricity increases. This eccentric effect is concentrated in the leading segments and is a primary driver of end-force redistribution and local response amplification. In addition, the friction level at the bottom-slab-bedding interface governs the rate and distribution of friction mobilization along the alignment, thereby influencing bolt force convergence and the effective range of jacking load transfer.

Accordingly, within a unified three-dimensional numerical framework, a synchronous jacking case (S1) is defined as the baseline, an asynchronous jacking case (S2) is introduced to examine thrust-imbalance-induced eccentric effects at the leading end, and a friction-sensitivity case (S3) is employed to assess the influence of friction parameters on load-transfer extent and convergence behavior. The cases and corresponding objectives are summarized in

Table 1. Jacking analysis cases and research objectives.

Case	Description	Control Variables	Loading Sequence	Objective
S1	Synchronous jacking	Total thrust N * (uniform over section); friction μ *; bolt preload	Dead load → preload → synchronous jacking	Load transfer pattern and effective transfer length (m *)
S2	Asynchronous jacking	N fixed; thrust difference δ * = 5%, 10%, 15%, 20%, 30%	Dead load → preload → unequal top-bottom jacking	End response under eccentric jacking: σ1,max/σ3,max, U2 *, and relative U2 *
S3	Friction sensitivity	Only μ * varied (others as S1/S2)	Same as S1/S2	Effect of friction level on transfer length scale and axial-force convergence

* N = total jacking thrust; δ = ratio of top–bottom thrust difference; μ = friction coefficient at the bottom-slab-bedding interface; m = friction-balance segment number (when thrust ≈ cumulative friction); U₂ = end vertical displacement; relative U₂ = vertical relative displacement between roof and invert slabs.

.

3.2. Geometric Model and Meshing

The geometric model was established based on the actual dimensions of the three-cell prefabricated segment. A three-dimensional solid model was constructed in Rhino 7.0 to explicitly represent the roof slab, invert slab, sidewalls, and partition walls. A segment length of 3.0 m was adopted as the geometric reference to define joint locations and end loading boundaries. The model was subsequently imported into HyperMesh 12.0 for finite element meshing. Considering component thickness characteristics and computational efficiency, the global element size was controlled at approximately 80–100 mm, with local mesh refinement applied in regions with geometric discontinuities, such as slab-wall intersections, opening corners, and joint vicinities. Finite element analyses were performed in ABAQUS 6.14 using C3D8R solid elements for concrete, with default hourglass control activated to ensure numerical stability.

During the model setup stage, an engineering-level mesh sensitivity check was performed to examine the influence of mesh resolution on the numerical response, with particular attention to joint regions where stress concentration is expected. Local mesh refinement was applied in these regions to examine the sensitivity of representative response quantities, including peak compressive stress, peak tensile stress, and displacement indicators, to mesh resolution. The observations indicate that, under the adopted mesh configuration, further mesh refinement does not lead to notable changes in the overall response trends, while computational efficiency can be maintained. Accordingly, the selected mesh resolution was considered suitable for the numerical analyses presented in this study, as shown in Figure 3, the finite element model of the utility tunnel.

3.3. Material Constitutive Models, Boundary Conditions, and Connections

Concrete was modeled using the Concrete Damaged Plasticity (CDP) formulation available in ABAQUS 6.14. The main CDP parameters, including compressive post-peak behavior and fracture-energy-based tensile softening, are summarized in

Table 2. CDP model parameters.

Category	Plasticity Parameters	Compression Behavior	Tension Behavior
CDP plasticity	φ = 30°; ε = 0.10; σbo/σco = 1.16; Kc = 0.67	Post-peak softening included; stress-inelastic strain formulation	Fracture-energy-based softening; ft = 4.0 MPa; Gf = 0.265 N/mm
Damage evolution	-	Compressive damage Dc defined	Tensile damage Dt defined

Note: All parameters follow the ABAQUS CDP formulation, and the fracture energy is determined according to fib Model Code recommendations.

. The model incorporates post-peak softening under compression together with a fracture-energy-regularized tensile softening law, reducing mesh sensitivity and improving the objectivity of crack energy dissipation. Parameter selection follows the ABAQUS CDP theory and user documentation, as well as commonly used fib Model Code recommendations for fracture energy. The damage evolution behavior of concrete is illustrated in Figure 4. The compressive and tensile damage factors are defined as functions of the corresponding inelastic strain to describe the progressive stiffness degradation of concrete under compression and tension.

For inter-segment joint modeling, a combined surface-to-surface contact and equivalent bolt formulation was used to approximate the dominant mechanical characteristics of prefabricated segment joints during jacking. Normal contact was employed to describe joint closure and compressive force transfer, while tangential contact with friction represented shear transfer and potential slip. Local compliance associated with joint gaps, sealing elements, and construction tolerances was reflected in an equivalent manner through the selected contact stiffness and the axial stiffness of the equivalent bolts governing the global joint response. The joint parameters were selected and checked with reference to commonly used design codes and engineering specifications for prefabricated concrete structures.

The joint region was reinforced with steel rebars and prestressed bolts. In the numerical model, the reinforcement layout, geometric properties, and bolt preload conditions were explicitly defined and are summarized in

Table 3. Reinforcement and bolt parameters used in the numerical model.

Component	Parameter	Value	Description
Rebar	Layout	Longitudinal + transverse	Joint reinforcement configuration
	Diameter	Φ 12 mm	Uniform rebar diameter
	Spacing	150 mm	Center-to-center spacing
Bolt	Length	1.20 m	Effective bolt length
	Installation position	Through joint region	Consistent with joint configuration
	Preload magnitude	100 kN	Applied pretension force
	Preload method	Bolt-load (pretension)	ABAQUS pretension method

Note: The reinforcement and bolt parameters were explicitly defined in the numerical model to ensure a realistic representation of joint stiffness and load-transfer behavior.

. Bolt preload was applied using the bolt-load (pretension) method in ABAQUS 6.14 to simulate construction tightening and to provide a realistic representation of joint stiffness and load-transfer behavior.

Regarding jack asynchrony, it was idealized as a quasi-static thrust imbalance to isolate the mechanical effects of force non-uniformity. The actual jacking process may involve stepwise advancement, joint seating, short-term force fluctuations, and interface stick-slip, which can locally amplify stress and deformation responses. Therefore, the results presented herein should be interpreted as an envelope response under asynchronous jacking conditions, rather than a complete transient or dynamic analysis. The contact behavior between the bottom slab and the bedding layer was modeled using a surface-to-surface contact formulation. Normal contact pressure was determined from the self-weight of the structure and applied external loads obtained from global equilibrium. A hard contact formulation was adopted in the normal direction, while a penalty-based formulation was used in the tangential direction with a Coulomb friction model. Explicit stick-slip or rate-dependent frictional behavior was not modeled, consistent with the adopted quasi-static contact assumption.

For the surrounding soil, it was not explicitly modeled as a continuum medium but was idealized through frictional contact interfaces at the bottom slab and lateral boundaries. This friction-only boundary representation focuses on the load-transfer mechanisms within the tunnel structure and its joints, avoiding the introduction of uncertain, site-dependent soil parameters. This simplified assumption does not capture stress diffusion, deformation compatibility, or nonlinear soil behavior; therefore, quantitative results should be interpreted within the scope of the adopted boundary modeling assumptions. However, the comparative trends and relative influences of the investigated parameters remain informative for mechanism-oriented analysis.

Inter-segment connections were modeled using a combined surface-to-surface contact and equivalent bolt-spring approach. Contact interfaces were defined with normal contact and tangential friction, with an adjustable friction coefficient μ to represent different interface conditions. The frictional force transfer between adjacent segments during jacking is expressed as:

$$F_f=\mu N_n,$$

(1)

where μ is the friction coefficient and N_n is the normal contact force.

The axial stiffness of the bolts is calculated as

$$k_b={\displaystyle \frac{E\pi d^2}{4l}},$$

(2)

where E is the elastic modulus, d is the bolt diameter, and l is the effective bolt length. This expression ensures effective load transfer across the joints while preventing excessive joint deformation.

For reproducibility, the main material parameters, constitutive laws, contact definitions, and loading conditions adopted in the numerical simulations are reported in the manuscript in a structured and tabulated form, which allows the model to be implemented in ABAQUS 6.14.

3.4. Loading Cases and Application

The jacking scenarios consider the combined effects of self-weight, overburden, groundwater pressure, and construction jacking loads. Vertically, the roof slab carries the dead load from approximately 2.5 m of overburden; surface traffic is represented by an equivalent load of 4.0 kN/m² and transferred to the roof through the soil cover. The anti-uplift design groundwater level is about 2.5 m, generating uplift on the invert and hydrostatic pressure on the sidewalls, which also sustain lateral earth pressure. During construction, when leading segments are not yet fully backfilled, vertical support is provided primarily by friction at the bottom-slab-bedding interface. As backfilling progresses, vertical support and lateral confinement stabilize, friction is progressively reduced, and the jacking thrust is transferred rearward.

(1) Synchronous Jacking Analysis (S1)

The jacking thrust is applied to the leading segment through an end loading plate and transmitted segment by segment, until it is balanced by the cumulative friction at the bottom-slab-bedding interfaces. When the advance reaches the m-th segment, the equilibrium between the jacking thrust and segmental friction is given by Equation (3):

$$N={\displaystyle \sum _{i=1}^m{f}_{ui}},$$

(3)

where N is the total jacking thrust and f_ui is the friction force acting on the i-th segment. Equation (3) describes the frictional equilibrium governing longitudinal load transfer during jacking.

(2) Asynchronous Jacking Analysis (S2)

In the asynchronous jacking analysis, the total thrust N is kept constant, and different jacking forces are applied to the upper and lower slabs of the first segment. The thrust difference δ is set to 5%, 10%, 15%, 20%, and 30%. The varying thrust differences result in different load distributions between the segments, and this process is described by Equation (4):

$$M=(N-{\displaystyle \sum _{i=1}^v{f}_{ui}})e_{i-1},$$

(4)

where M is the additional bending moment and e_i is the moment arm of the i-th segment. This expression characterizes the formation of additional bending moments induced by thrust imbalance and quantifies their effects.

(3) Friction-Coefficient Sensitivity Analysis (S3)

In the friction sensitivity analysis (S3), the friction coefficient μ at the bottom-slab- bedding interface is varied to examine its effect on jacking load transfer. Changes in μ directly modify segmental friction and bolt axial forces, thereby affecting joint deformation. The friction level has a pronounced influence on the stress and deformation of the leading segment: higher friction increases frictional resistance, intensifies compressive stress on the loaded side, and confines the load-transfer range. It also affects the vertical displacement of the leading segment, with more pronounced deformation under higher friction, particularly at larger jacking forces. Figure 5 illustrates the model responses under different friction coefficients, highlighting the impact of friction on stress and deformation.

4. Results and Analysis

4.1. Load Transfer and Segment Response Under Synchronous Jacking

Under synchronous jacking, all jacks operate uniformly and the thrust is transmitted segment by segment along the tunnel axis. To clarify the load-transfer path and attenuation behavior, the longitudinal evolution of bolt pretension was examined. Figure 6 shows the variation in bolt pretension with increasing segment number. Overall, the pretension exhibits a pattern of rapid increase in the leading segments followed by gradual stabilization toward a plateau, which can be well described by an exponential-type function:

$$F=311.35+88.82\left[1-e^{\left(-n/8.33\right)}\right],$$

(5)

The fit achieves a high coefficient of determination (R² = 0.9960), indicating strong consistency and representativeness of the empirical expression. With increasing segment number, the preload rises rapidly from an initial value of about 311 MPa, with pronounced growth over the first few segments. As the number of segments reaches 15–20, the increase becomes markedly slower, and by 20–25 segments the preload approaches a plateau of approximately 390–400 MPa. As advancement proceeds, the jacking thrust is progressively dissipated by bottom-slab-bedding friction, and the influence of local end deformation and contact redistribution on preload diminishes, resulting in the observed rapid-rise-plateau convergence behavior [26].

Mechanistically, the jacking thrust introduced at the leading end is transferred rearward through joints and bolts and continuously dissipated by friction at the bottom-slab-bedding interface. Consequently, the effective load-transfer range is confined to a limited number of segments near the advancing end, while the response of subsequent segments stabilizes. Based on the quantitative results in Figure 6, the load evolution under synchronous jacking can be divided into distinct stages; the corresponding segment ranges, response characteristics, and engineering implications are summarized in

Table 4. Stage characteristics of bolt-preload response under synchronous jacking.

Segment Range	Preload Response	Engineering Implication
1–15	Rapid increase; large growth rate	Main load-transfer and restraint redistribution zone near the advancing end; end response most sensitive
15–20	Growth rate weakens; transition toward plateau	Friction/contact mobilization progressively strengthens; boundary effects start to decay
20–25	Approaches plateau (390–400 MPa)	Response stabilizes; provides an empirical basis for selecting model length/convergence criterion

. Overall, the leading segments constitute the primary load-transfer zone, the middle segments form a transition zone, and the rear segments enter a stable zone. This indicates a localized and stage-wise attenuation of jacking loads along the alignment, consistent with field observations showing larger bolt-force fluctuations near the front and smaller variations farther back. These findings provide a load-transfer scale and baseline response for subsequent analyses of end-force redistribution and critical control locations under asynchronous jacking and varying friction conditions.

4.2. Stress–Displacement Response Considering Thrust Imbalance

The primary trigger for the transition to eccentric compression–bending behavior is the non-uniform jacking force between the upper and lower slabs, which shifts the resultant force away from the neutral axis and introduces an additional bending moment. Base friction and geometric characteristics of the cross-section play secondary roles by influencing load redistribution and stiffness distribution, thereby amplifying the eccentric response rather than initiating it. In this study, the transition to the eccentric regime is identified based on the emergence of asymmetric stress concentration in the maximum principal compressive stress field, together with a pronounced increase in vertical displacement at the leading end.

Figure 7, Figure 8 and Figure 9 provide quantitative evidence for the above mechanism. Under asynchronous jacking, increasing the thrust difference from 5% to 30% leads to monotonic increases in the maximum principal tensile stress, maximum principal compressive stress, and end vertical displacement of the leading segment. Accordingly, the end-section response evolves from near-axial compression to eccentric compression biased toward the loaded side. In light of the load-transfer scale established in Section 4.1, the effects of asynchronous jacking are mainly confined to a limited number of segments near the advancing end. Mechanistically, unequal upper–lower thrusts shift the resultant force away from the neutral axis, superimposing an additional bending moment on the axial thrust and inducing internal force redistribution at the leading end [27].

Figure 7 indicates that at low thrust differences (5–10%), the principal tensile stress remains low, with peak values mainly confined to geometric and stiffness discontinuities such as roof-sidewall intersections and opening corners, and a relatively symmetric distribution across the section. As summarized in

Table 5. Peak end responses under asynchronous jacking.

Thrust Difference δ/%	Max Principal Tensile Stress σ1,max/MPa	Max Principal Compressive Stress σ3,max/MPa	Max End Vertical Disp. U2/mm	Compressive Utilization ηc	Safety Reserve γ	Peak Location
5	+0.394	−2.874	0.052	0.114	8.803	Loaded-side invert; partition-wall root
10	+0.436	−3.111	0.103	0.123	8.132	Loaded-side invert; end partition wall
15	+0.503	−3.587	0.155	0.142	7.053	Mid-span of invert; partition-wall root
20	+0.570	−4.063	0.207	0.160	6.227	Loaded-side invert; corner region
30	+0.691	−5.490	0.311	0.217	4.608	Loaded-side invert; partition-wall root

, the maximum principal tensile stress ranges from 0.394 to 0.436 MPa. When the thrust difference increases to 15% or higher, the tensile stress concentration consistently shifts toward the loaded side, forming a continuous band along the loaded roof edge and near inter-segment joints. The maximum principal tensile stress further rises to 0.691 MPa at 30%, indicating that under eccentric loading the loaded-side joints and roof edge become tensile-stress-governing regions.

Figure 8 shows that the leading end remains predominantly in compression, while the compressive stress evolves from a dispersed to a concentrated pattern as the thrust difference increases. At 5–10%, the compressive stress is relatively uniform, with localized peaks only at the invert bearing zones and the roots of partition walls; accordingly, the maximum principal compressive stress is 2.874–3.111 MPa (Table 5). When the thrust difference reaches 15% or higher, compressive stress at the loaded-side invert bearing zone and partition-wall roots is markedly amplified and becomes increasingly concentrated. The maximum principal compressive stress increases from 3.587 MPa (15%) to 5.490 MPa (30%), indicating that the controlling compression zones progressively localize at the loaded-side supports and stiffness-discontinuity regions at the leading end.

Figure 9 further shows that the vertical displacement at the leading end increases steadily with thrust difference, with the loaded side exhibiting markedly larger displacement than the unloaded side, indicating progressively enhanced sectional rotation. As listed in Table 5, the maximum end vertical displacement increases from 0.052 mm at 5% to 0.311 mm at 30%. The displacement pattern is consistent with the stress concentrations shifting toward the loaded side in Figure 7 and Figure 8, indicating that the structure accommodates internal force redistribution under eccentric loading primarily through bending deformation.

To quantitatively evaluate compressive safety at the leading end, the compressive stress utilization ratio η_c and the safety reserve factor γ are introduced. The compressive stress utilization ratio is defined as the ratio of the maximum principal compressive stress at the leading end to the design compressive strength of concrete:

$${\eta }_c={\displaystyle \frac{\left|{\sigma }_{3,\max }\right|}{f_{cd}}},$$

(6)

Accordingly, the safety reserve factor is defined as its reciprocal:

$$\gamma ={\displaystyle \frac{1}{{\eta }_c}},$$

(7)

where σ_3,max is the maximum principal compressive stress at the leading end, and f_cd is the design compressive strength of C55 concrete, taken as 25.3 MPa.

Based on Table 5, increasing thrust difference leads to a continuous rise in η_c and a corresponding reduction in γ, indicating that asynchronous jacking progressively reduces the compressive safety margin at the leading end. Nevertheless, even at the most unfavorable case of a 30% thrust difference, the compressive stress remains below the design strength, and the leading-end structure retains a certain compressive safety reserve. Notably, the increase in η_c becomes more pronounced once the thrust difference exceeds about 15%, consistent with the evolution in Figure 8 where compressive stress concentrations shift from a dispersed pattern to stable localization at the loaded-side invert bearing zone and partition-wall roots. This suggests that a thrust difference of approximately 15% marks a critical transition from predominantly axial compression to eccentric compression-bending control at the leading end.

Synthesizing Figure 7, Figure 8, Figure 9 and Table 5, asynchronous jacking does not alter the overall attenuation trend of jacking loads along the alignment, but it markedly reshapes the internal force and deformation patterns within the limited segment range near the advancing end. The loaded-side roof edge and inter-segment joints govern tensile stress, while the loaded-side invert bearing zone and partition-wall roots concentrate compressive stress, accompanied by larger vertical displacements and sectional rotation. These locations should therefore be prioritized for monitoring and control at the leading end, together with strengthened control of jack output uniformity and the working condition of end joints and bolts, to mitigate adverse eccentric effects on the structure.

4.3. Effect of Friction Coefficient on the Evolution of Bolt Preload

To further clarify how interface friction modulates load transfer during jacking, four friction coefficients (μ = 0.15, 0.20, 0.25, and 0.30) were considered under the same jacking framework, and the segment-wise evolution of bolt preload was compared (Figure 10). Overall, the curves exhibit similar shapes across all μ values, showing the typical pattern of a rapid increase in the front segments followed by a gradual stabilization. This agrees with the “finite influence length + stage-wise attenuation” behavior identified for synchronous jacking in Section 4.1.

Based on the slope variations in Figure 10, the preload evolution can be divided into three stages. For n = 1–15, a rapid-growth stage is observed, with preload increasing markedly as segment number rises, indicating that jacking loads are mainly transferred and accumulated within the front segments near the advancing end. For n = 15–20, the response enters a transition/convergence stage with a substantially reduced growth rate. When n ≥ 20, a quasi-plateau stage is reached, where the marginal contribution of additional segments to preload becomes limited. The locations of these stages are essentially identical for different μ values, indicating that variations in friction do not alter the spatial scale of load transfer but primarily affect the magnitude of the end load transfer.

Integrating the load-transfer scale established in Section 4.1 with the critical end regions identified in Section 4.2 indicates that, within practical ranges, μ mainly affects bolt and joint demand by regulating the rate of thrust dissipation within the limited front segments, while the governing control zone remains stably confined to the segments near the advancing end. Therefore, under lower-friction conditions, monitoring of bolt forces and joint performance in the front segments should be strengthened to prevent excessive connection demand due to enhanced load transfer. Under higher-friction conditions, attention should be paid to the stability of end friction to avoid abnormal local friction that could induce uneven load transfer and, when coupled with asynchronous jacking, further amplify stress concentrations at the leading end.

5. Discussion

5.1. Load Transfer and Friction Mobilization Under Synchronous Jacking

During synchronous jacking, bolt preload evolves non-linearly along the segments, showing a rapid increase near the advancing end followed by a plateau, indicating that load transfer is not uniformly distributed but jointly governed by inter-segment force transmission and friction at the bottom-slab-bedding interface [28]. As illustrated in Figure 11, friction is initially carried by only a few leading segments; with increasing jacking distance, subsequent segments progressively engage and the system approaches force equilibrium with the applied thrust, thereby forming a stable, finite influence length.

From the thrust-friction equilibrium perspective, the jacking load applied at the leading end is transmitted rearward through joints and bolts, while frictional resistance at the bottom-slab-bedding interface progressively increases with advancement and dissipates the axial thrust [29]. Once friction mobilization approaches saturation, the growth of bolt preload along the alignment markedly diminishes, and the response of subsequent segments weakens, yielding a load-transfer pattern characterized by front-concentrated transmission and stabilized response downstream. This behavior indicates that the leading segments constitute the critical zone for load transfer and dissipation, and are also the most sensitive region to the effects of asynchronous jacking and parameter variations.

Based on these mechanisms, construction monitoring and process control should prioritize the first few segments near the advancing end, with focused tracking of bolt axial forces, joint opening/closure, and bottom-slab interface responses. Such real-time monitoring enables timely identification of abnormal load transfer and frictional changes, ensuring structural safety and controllability during jacking.

5.2. Leading-End Stress Evolution and Control Thresholds Under Asynchronous Jacking

Figure 12 shows that as the thrust difference between the upper and lower jacks increases from 5% to 30%, both the maximum principal tensile and compressive stresses at the leading segment increase monotonically. Asynchronous jacking introduces additional eccentric effects that amplify the end response. Overall, the increase in principal compressive stress exceeds that of tensile stress, indicating that the compressive zone is more sensitive to thrust imbalance.

The fitted curves further confirm this trend: principal tensile stress increases relatively gradually with thrust difference, whereas principal compressive stress shows a more concentrated and stable response, indicating that the leading-end behavior is more readily governed by compressive stress levels. Mechanistically, thrust imbalance shifts the resultant force away from the neutral axis, superimposing additional bending on axial compression and intensifying stress concentration on the loaded side. As a result, the invert and partition-wall roots on the loaded side are more prone to develop high compressive stresses, while tensile stresses—mainly at the loaded-side roof edge and inter-segment joints—also increase but at a comparatively moderate rate. Accordingly, compressive zones at the leading end should be treated as the priority control regions under asynchronous jacking.

From a control perspective, the primary risk of asynchronous jacking lies in the concentrated amplification of compressive zones rather than the widespread expansion of tensile regions. A thrust difference of approximately 15% can be regarded as a control threshold marking the transition of the leading-end response from axial compression- dominated to eccentric compression-bending-dominated behavior. Beyond this level, enhanced monitoring and control are warranted, with priority given to stresses at the loaded-side invert and partition-wall roots, together with joint opening/closure and bolt axial forces for integrated assessment. At lower thrust differences, mitigating eccentricity to promote a more uniform end response is the preferred strategy. These insights clarify the governing regions and sensitive indicators at the leading end, providing a basis for stress and deformation checks under the most unfavorable conditions.

5.3. Process Response and Safety Assessment Under the Most Unfavorable Condition

To further assess the safety of asynchronous jacking at practical construction thrust levels, Figure 13 presents the instantaneous responses of the leading-end structure at two representative stages of the jacking process—namely, the seating stage and the maximum jacking-force stage—under a 30% thrust difference. The analysis is conducted using realistic loading levels during jacking and aims to determine whether the stresses and deformations at the leading end remain within an engineeringly controllable range under extreme asynchronous conditions [30].

At the seating stage, the overall jacking force is relatively low, and the tensile and compressive stresses in the leading segment remain limited. The results indicate a maximum principal compressive stress of approximately −5.490 MPa and a maximum principal tensile stress of about 0.6905 MPa. Stress concentrations are mainly located near the jacking plate and at the invert-partition wall intersections, with magnitudes well below the design compressive strength of C55 concrete (f_cd = 25.3 MPa) and without the formation of continuous tensile stress bands. At this stage, the relative vertical displacement between the roof and invert is about 1 mm, and deformation is dominated by slight sectional rotation, indicating good structural continuity. As the jacking force increases to the maximum value during construction (approximately 20,698 kN), the tensile and compressive stresses within the leading segment further rise. The tensile stress at the loaded-side roof edge and inter-segment joints increases, and the compressive stress at the invert-partition wall root extends. However, the maximum principal compressive stress is about −11.142 MPa, and the maximum principal tensile stress is approximately 1.851 MPa, still well below the design strength control threshold. The corresponding relative vertical displacement between the roof and invert is about 3 mm, with deformation primarily in the form of overall deflection. No significant misalignment or joint opening is observed.

From the combined stress and deformation responses, it can be concluded that under the most unfavorable asynchronous jacking condition with a 30% thrust difference, the stresses and deformations in the leading segment remain within an acceptable range, and the structure retains a certain safety margin. The results at this stage, from the perspective of extreme conditions, support the assessment of the asynchronous jacking load evolution and provide a quantitative basis for phased safety control and key monitoring point placement during jacking construction based on varying degrees of thrust imbalance.

From an engineering perspective, the admissible thrust non-uniformity threshold identified in this study should be interpreted within the context of the investigated structural configuration and boundary conditions, rather than as a universally transferable value. The threshold is derived from prefabricated utility tunnels with similar cross-sectional proportions, joint configurations, and reinforcement schemes, under jacking conditions where base friction governs resistance to movement. Although variations in geometry, joint type, reinforcement layout, or ground conditions may alter the quantitative value of the threshold, the underlying mechanical mechanism—namely, the transition from axial compression to eccentric compression-bending induced by non-uniform jacking forces—remains applicable. Accordingly, the analytical framework and response indicators adopted herein can be used to re-evaluate an appropriate admissible range for other engineering conditions.

6. Conclusions

This study systematically analyzes the stress and deformation characteristics of utility tunnel structures under asynchronous jacking conditions, focusing on the impact of frictional effects and thrust imbalance on segmental stress and deformation. Based on realistic thrust difference conditions, structural safety assessment and construction control strategies are proposed. The results show that:

(1)

Asynchronous jacking significantly alters structural load distribution. As the thrust difference increases from 5% to 30%, both maximum principal tensile and compressive stresses rise, with the compressive stress reaching 5.49 MPa and tensile stress 1.85 MPa. The stress state transitions from axial compression to eccentric compression-bending, with more pronounced stress and deformation concentration at a 30% thrust difference, highlighting the significant impact of asynchronous jacking on the tunnel structure’s load distribution.

(2)

Frictional effects play an important role in the jacking process. Variations in the friction coefficient influence the load-transfer range and stress distribution. As the friction coefficient increases, frictional resistance increases, leading to a more localized load transfer and higher stress concentration on the loaded side. Numerical results indicate that when the friction coefficient increases from 0.15 to 0.30, compressive and tensile stresses increase by approximately 20% and 15%, respectively, highlighting the significance of frictional effects during jacking.

(3)

The leading segment of the tunnel retains a safety margin under the most unfavorable conditions. At a 30% thrust difference, the maximum principal compressive and tensile stresses in the leading segment do not exceed the design compressive strength of concrete (25.3 MPa), and both stress increases remain within the allowable design limits. This indicates that, even under extreme conditions, the structure can maintain sufficient safety margin and exhibits strong safety and stability.

(4)

A safety control strategy for asynchronous jacking is proposed based on the research findings. During construction, it is essential to monitor the changes in compressive and tensile stresses at the loaded-side roof edge, inter-segment joints, and invert-partition wall roots. Measures to control the friction coefficient and thrust difference should be implemented to reduce the impact of eccentricity. Additionally, real-time monitoring of bolt forces, joint opening/closure, and invert deformation at key segments is necessary to ensure overall structural safety.