Research on Axial Stress and Strain Characteristics of Reinforced-Concrete Curved Pipe Jacking in Power Tunnels

Abstract

Joint deflection during curved pipe jacking in power tunnels poses a significant risk of structural failure due to the resulting eccentric and diagonal loading on the pipes. This study investigated the axial stress and strain characteristics of reinforced-concrete pipes under varying joint deflection angles and jacking forces, using a combined approach of experimental model testing and finite element method (FEM) numerical simulations. The experimental setup replicated curved pipe jacking conditions, allowing for the measurement of strains and deformation under controlled loading. Numerical simulations, validated against experimental data, provided detailed insights into the stress distribution patterns. The results revealed distinct stress states in different pipe sections. The pipe closest to the jacking force (3# pipe) experienced eccentric loading, leading to localized stress concentrations and inelastic strain on the inner wall at the point of eccentricity, indicating vulnerability to compressive failure. The middle pipe section (2# pipe) underwent complex diagonal loading, resulting in the development of inelastic strain on both the inner and outer walls at specific orientations, highlighting a risk of both compressive and shear failure modes. The study also demonstrated that the magnitude of the axial jacking force and the degree of joint deflection significantly influence the stress distribution and the extent of inelastic strain. These findings provide important information for optimizing the design and construction of curved pipe jacking projects in power tunnels. The identified failure mechanisms and the influence of key parameters on pipe behavior can inform strategies to mitigate the risk of structural failure, improve the resilience of pipe systems, and enhance the overall safety and reliability of underground power tunnel infrastructure.

1. Introduction

Large-diameter, reinforced-concrete pipe jacking is a primary technology for constructing urban power tunnels. This method offers several benefits: rapid construction, minimal impact on the surrounding environment, cost effectiveness, and adherence to environmentally friendly practices. These advantages contribute to the advancement of underground power tunnel construction in urban areas.

The pipe jacking process involves pushing a series of connected pipe sections into a tunnel created by a tunnel boring machine. This is achieved through the application of a jacking force. Each pipe section is subjected to a complex and dynamic spatial force system. These forces include the axial jacking force, head-on resistance, surrounding soil and water pressure, lubricating grouting pressure, pipe–soil friction, the weight of the pipe itself, and potential surface traffic loads. Additionally, the jacking force is cyclic, meaning that the pipe sections undergo repeated loading and unloading throughout the process.

In curved pipe jacking, the joints between adjacent pipes have eccentric angles. This results in the axial jacking force acting as an eccentric load on the pipes. In many cases, pipe failures during curved pipe jacking construction are attributed to the concentration of axial stress caused by this eccentricity. Consequently, understanding the pipe force characteristics under varying axial jacking forces and joint eccentricities is essential for the successful execution of curved pipe jacking projects.

Current research on the stress characteristics of pipe jacking joints primarily focuses on two approaches, as follows:

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Theoretical analysis: Researchers have employed various theoretical frameworks to investigate the internal forces and deformations of pipe joints under different conditions. These frameworks include the cross-section kernel theory of material mechanics [1,2], thin-walled cylinder stability theory of elastodynamics [3], thick-walled cylinder models of elastodynamics [4], and shell theory [5]. Studies have examined both straightline jacking and curvilinear deflection scenarios for thick-walled steel-reinforced concrete, glass fiber-reinforced plastic, and thin-walled steel pipe joints. These analyses have led to the development of calculation models for the internal forces and wall thickness of pipe joints;

(2)

Internal force monitoring tests: Researchers have also conducted field tests to monitor the internal forces within pipe joints during construction. Milligan and Norris [6] performed on-site monitoring to gather data on pipe–soil contact pressure and reinforcement stress in reinforced-concrete pipe jacking. Pan [7] conducted an experimental study on stress, contact pressure, and soil deformation, during the construction of large-caliber, sharply curved, reinforced-concrete pipe jacking. Wei et al. [8] used similar methods to monitor the contact pressure and reinforcement stress on linear reinforced-concrete pipe jacking joints, establishing stress patterns for both curved and straightline jacking. Yang [9] monitored and analyzed the stress in terms of large-diameter, linear, steel pipe jacking using a pipe curtain preconstruction method, revealing that the pipe section was predominantly under pressure;

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Numerical simulation: Numerical methods, particularly finite element analysis, have been employed to investigate the stress behavior of pipe joints. Huang et al. [10] used finite element simulation to study the dynamic jacking process of large-diameter FRP-sandwiched pipes, highlighting the tendency for stress concentration at pipe joints. Chen [1] employed the ABAQUS 6.14 software to analyze the stresses in glass fiber-reinforced plastic pipe joints under deflection conditions, demonstrating a rapid increase in the stresses with increasing deflection angles, beyond the free deflection angle.

In a recent study of the construction and operation of curved pipe jacking, Pan et al. [11] introduced an automatic guidance system for long-distance curved pipe jacking based on single-prism technology, with further advancements in multivariate data fusion that enabled 3D orientations of the tunnel boring machine (TBM) to be obtained. Choo et al. [12] assessed the non-linear rock strength parameters to estimate the pipe-jacking forces through numerical modeling, emphasizing the importance of an equivalent tangential cohesion and friction angle in the finite element analysis. Zhou et al. [13] explored the static equilibrium configuration and non-linear dynamics of slightly curved, cantilevered pipes, conveying fluid, highlighting the unique behavior of nonconservative systems in fluid–structure interactions. Zhong et al. [14] addressed the frictional characteristics and contact properties of pipe strings to understand and verify solutions for pipe sticking issues encountered during rock pipe-jacking projects. Zhang et al. [15] discuss field monitoring and analysis of soil deformation during curved steel pipe jacking in the Gongbei Tunnel, emphasizing the importance of monitoring and analyzing soil behavior during construction. Zhou et al. [16] and Zu et al. [17] focused on predicting jacking forces in curved pipe roofs using different algorithms and de-noising methods, highlighting the significance of accurate force estimation in ensuring the success of pipe-jacking projects.

While substantial research has been conducted on the forces in linear jacking pipes using theoretical analysis, field monitoring, and numerical simulation, the investigation of forces in regard to curved jacking pipes has primarily relied on theoretical analysis and a limited number of field tests. Consequently, the relationship between pipe stress, joint deflection, and the axial jacking force remains unclear. To address this gap, this study utilizes a test system and a three-dimensional finite element model, comprising three sections of reinforced-concrete pipes. This setup simulates joint deflection in curved pipe jacking under various axial jacking forces. By analyzing the resulting axial stress changes under different deflection angles and axial forces, this research aims to elucidate the underlying relationships.

2. Methodology

2.1. Curved Pipe Jacking Test

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Test pipes

The test utilized C50 reinforced-concrete jacking pipes, with an inner diameter of 600 mm, an outer diameter of 740 mm, and F-type socket joints. Each pipe section had a length of 2000 mm. A single layer of steel cage reinforcement was embedded within the pipe wall. The rebar had a diameter of 5 mm and was arranged longitudinally at 45° intervals, totaling eight bars. The ring bar pitch was 60 mm. At the pipe joints, a 10 mm thick pad plate was bonded to the socket end. The inner and outer diameters of the pad plate were 610 mm and 730 mm, respectively.

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Test setup

Figure 1 and Figure 2 show the schematic diagram and actual picture of the test setup. Three test pipes were connected in a straightline. One end of the assembly was fixed to a reaction wall, while the other end was connected to loading jacks. The jacks applied force parallel to the axial direction of the pipe, with the combined force centered on the pipe.

Moreover, 1# pipe was restrained by the reaction wall, limiting its vertical displacement. In addition to this, 3# pipe was connected to an axial jack. Joint deflection was achieved by raising a jack positioned beneath 2# pipe. During testing, 2# pipe was deflected relative to pipes 1# and 3#, by the jack beneath it. Subsequently, the axial jack at the end of 3# pipe applied the jacking force, simulating the axial force conditions during curved pipe jacking construction.

The pipe joint deflection test setup is shown in Figure 3. The distance between the centerline of the jacking jack and 1# pipe joint was maintained at 1500 mm throughout the test. When the jacking jack extended by Δh, the pipe 2# was deflected upwards by an angle of θ/2. Due to the constraint imposed by the joint between pipes 2# and 3#, alongside the proximity of the jacking jack to the pipe 3# joint, pipe 2# lifted upwards as pipe 3# was deflected upwards by θ/2. Consequently, the relative deflection angle between pipes 2# and 3# was θ.

To monitor axial force changes in the pipe sections at different stages, strain gauges were affixed to the middle of the inner wall of pipes 2# and 3#. The gauges were positioned to ensure that the direction of the tensile stress was parallel to the axial direction of the pipe sections. Each monitoring section had eight strain gauges, evenly distributed along the circumference and numbered 1–8, as depicted in Figure 4. The static stress–strain test and analysis system acquired and stored real-time strain data from the gauges.

Figure 1 presents a schematic diagram of the test setup. Three test pipes were connected in a straightline. One end was fixed to a reaction wall, while the other end was connected to loading jacks. The jacks applied force parallel to the pipe’s axial direction, with the combined force centered on the pipe. During testing, 1# pipe was restrained by the reaction wall, restricting its vertical movement. Additionally, 3# pipe was connected to an axial jack, and joint deflection was achieved by raising a jack positioned beneath 2# pipe. This configuration simulated the axial force state during curved pipe-jacking construction.

The pipe joint deflection test setup is detailed in Figure 2. The distance between the jacking jack’s centerline and the pipe 1# joint was maintained at 1500 mm throughout the test. When the jacking jack extended by Δh, 2# pipe was deflected upwards by an angle of θ/2. Due to the joint constraint between pipes 2# and 3# and the proximity of the jacking jack to the pipe 3# joint, 2# pipe lifted upwards as 3# pipe was deflected by θ/2. This resulted in a relative deflection angle of θ between pipes 2# and 3#.

During testing, the jacking jack lifted 2# pipe by 26 mm, resulting in a deflection angle θ/2 of 1.0°. Subsequently, the main jack applied axial loads of 50 kN, 100 kN, 150 kN, 200 kN, and 250 kN to the socket end of the pipe 3# section in sequence.

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Test steps

The test procedure followed these steps:

(i)

With the axial jack unloaded, the jacking jack was activated, and the jacking displacement was set. Once the set value was reached, 2# pipe was lifted 26 mm upwards, and the jacking jack extension was maintained;

(ii)

The axial jack was activated, extending and gradually making contact with the end of 3# pipe. The jacking force was increased to 50 kN and held for 60 s, while strain data were collected;

(iii)

The axial jack load was controlled and then incrementally increased to 100 kN, 150 kN, 200 kN, and 250 kN, with a 60 s hold at each load level for strain data collection;

(iv)

The axial jack and jacking jack were fully unloaded, restoring the pipe joint deflection angle to 0°.

2.2. FEM Numerical Simulation

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Pipe model

To further investigate the influence of varying joint deflection angles on pipe stress, a three-dimensional pipe model was constructed using the ABAQUS simulation software, with 14,544 continuum 3D 8-node reduced integration (C3D8R) elements and 4776 2-node 3D truss (T3D2) elements, as shown in Figure 5. The dimensions of the pipes and the wooden cushion plate in the model matched those used in the physical test.

In the model, the reaction wall and rail restrained the movement in three directions. The end of pipe #1 was constrained to simulate its connection to the reaction wall. The contact pairs between the rail and the outer surface of the pipe was established. Deflection was achieved by applying an upward displacement at pipe joint #2, incrementally deflecting it upwards by 0.5°, 1.0°, 1.5°, 2.0°, 2.5°, and 3.0° around the socket end. At each deflection angle, axial loads equivalent to 50 kN, 100 kN, 150 kN, 200 kN, and 250 kN, were sequentially applied to the end of pipe joint #3.

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Material parameters

The concrete used to make the pipe was modeled with a modulus of elasticity of 34,500 MPa, a density of 2400 kg/m³, and a Poisson’s ratio of 0.2. The concrete damage plasticity (CDP) model was employed within the ABAQUS software and the parameters were the same as applied by Younis et al. [18].

The steel reinforcement and steel collar were modeled using an elastic model, with a modulus of elasticity of 200,000 MPa, a density of 7850 kg/m³, and a Poisson’s ratio of 0.3. The wooden mat boards were also modeled using an elastic model, with a modulus of elasticity of 100 MPa, a density of 600 kg/m³, and a Poisson’s ratio of 0.2.

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Validation of simulation results

To ensure the accuracy of the numerical simulation results, the simulated pipe strain under a joint deflection of 1.0° was compared with the experimental results, as shown in Figure 5. The figure demonstrates that the distribution of the strain in the simulation closely matches that of the test across the range of applied axial loads, indicating that the numerical simulation accurately reflects the changes in pipe joint forces observed in the physical test.

As shown in Figure 6a, when the axial load on pipe #2 is less than 150 kN, the compressive strain at the top and bottom are greater in the simulation results, while the compressive strain at points 6 and 8 are relatively smaller. In contrast, the compressive strain at each point in the test is more uniform. Once the axial load reaches 200 kN, the compressive strain at points 1, 2, 4, and 5 in the simulation results increases rapidly, with the compressive strain at the bottom approaching zero. During the test, the changes in compressive strain at these points is generally smaller than in the simulation, and the compressive strain at the bottom remains around 20 με.

Figure 6b reveals a more pronounced eccentric strain phenomenon in the simulation results for pipe #3. The compressive strain at the top approaches zero and the compressive strain at the bottom is generally larger than the experimental values.

3. Analysis of the Numerical Simulation Results

3.1. Effect of Jacking Force on Axial Stress Distribution in Pipes

To illustrate the effect of the jacking force on the axial stress distribution, the numerical simulation results with a pipe deflection angle of 1.5° and axial jacking force of 50 kN and 250 kN were analyzed. Figure 7 presents cloud diagrams illustrating the distribution of axial stress in pipe #3 and pipe #2 under the different axial loads.

Figure 7a,c shows that as the axial jacking force increases, the area of compressive stress concentration at the end of pipe #3 expands significantly, and the maximum compressive stress increases substantially from 5.1 MPa to 15.1 MPa. In Figure 7b,d, the diagonal compressive area in the pipe #2 section also enlarges with increasing axial stress, accompanied by a significant increase in the maximum compressive stress. These findings indicate that, under a constant deflection angle, increasing axial loads enlarge the contact area between the pipe joints, thereby mitigating compressive stress concentration.

3.2. Effect of Deflection Angle on Axial Stress Distribution in Pipes

To examine the effect of the deflection angle on the axial stress distribution, the axial stresses in pipe #2 and pipe #3 were analyzed under varying deflection angles at an axial jacking force of 150 kN, as shown in Figure 8.

In Figure 8a,c, after the relative deflection in terms of pipes 3# and 2#, the pipe 3# section experiences eccentric compression, with a significant concentration of compressive stress in the bottom area of the joint. This stress concentration extends backwards, along the pipe body. In contrast, the compressive stress in the upper part of the pipe is significantly reduced, and tensile stress may even occur. As the deflection angle increases, the area of compressive stress concentration at the joint decreases, but the maximum compressive stress increases notably, from 8.6 MPa at 0.5° to 13.8 MPa at 2.5°. Simultaneously, the tensile area above the pipe expands backwards, along the pipe body, and the maximum tensile stress also increases, from 0.26 MPa at 0.5° to 0.48 MPa at 2.5°.

Figure 8b,d reveals that, due to the constraint on the vertical displacement of the pipe 1# section, the pipe 2# section experiences diagonal compression after deflection. Compressive stress concentration areas emerge at the top and bottom of both ends of the pipe. The stress distribution in the pipe 2# section is complex, with multiple tensile stress zones appearing. The maximum tensile stress reaches 1.3 MPa when the deflection angle is 2.5°.

3.3. Plastic Strain Analysis of the Pipes

The concrete material in the numerical simulation model was assigned a plastic damage constitutive model to assess the degree of pipe damage due to loading. Figure 9 illustrates the distribution of inelastic strain in pipe joints under various deflection angles, when subjected to an axial jacking force of 250 kN. For reference, the direction facing the right side of the loading direction is designated as 0° azimuth, with the counterclockwise azimuth angle increasing (as depicted in Figure 9a). The strain cloud exhibits approximate symmetry at about 90° and 270° of the pipe circumference.

At a deflection angle of 0.5°, inelastic strain areas emerge on the inner wall of the joint at 90° and 270° in pipe section #2. Long strip-shaped inelastic strain concentration areas develop on the outer wall of the joint at approximately 30° and 150°, with a maximum inelastic strain of about 3531 με. When the deflection angle increases to 1.5°, the inelastic strain areas at 90° and 270° expand, while the long strip-shaped strain concentration areas on the outer wall do not extend along the pipe body but spread towards the lower area. The maximum inelastic strain at this stage is approximately 6049 με. Upon reaching a deflection angle of 2.5°, the extent of the previous inelastic strain areas expands considerably, showing a tendency to connect and rapidly extend along the pipe body. The maximum inelastic strain at this point reaches 8037 με.

The inelastic strain in pipe #3 initially emerged near the inner wall of the socket end at 270°, forming a peach-shaped strain concentration area, with a maximum inelastic strain of approximately 128 με. When the deflection angle increased to 1.5°, this area developed into a long strip, extending along the inner wall of the pipe section. Concurrently, inelastic strain areas appeared near the outer wall of the socket end at 225° and 315°, with a maximum strain of about 1649 με. With a further increase in the deflection angle to 2.5°, the elongated strain concentration area at the 270° inner-wall position continued to extend and new inelastic strain zones emerged on both sides, reaching a maximum inelastic strain of approximately 2297 με.

As indicated in the CDP model, the peak compressive strength of the concrete is reached at an inelastic strain of 676 με. This implies that yielding has already occurred in the pipe joints under most of the aforementioned conditions. For the pipe 2# section, the stress state is notably inferior to that of the pipe 3# section, resulting in a larger yield region. The inelastic strain in the inner wall at 90° and 270°, as well as the outer wall at 30° and 150°, exceeds the yield strain. For the pipe 3# section, yielding first appears on the inner wall on the side experiencing eccentric strain, making it susceptible to compressive damage in that location.

4. Conclusions

In this study, a combined approach involving model tests and numerical simulations was employed to comprehensively analyze the strain distribution in pipes subjected to varying deflection angles and axial jacking forces during curved pipe jacking. The experimental observations revealed distinct stress states in different pipe sections. In the pipe 3# section, a state of eccentric strain was observed, characterized by higher compressive strain in the lower part, compared to the corresponding upper part. Furthermore, as the deflection angle increased, the closing circle representing the strain values shifted downwards. This shift suggests a redistribution of stresses within the pipe section, highlighting the dynamic nature of stress distribution in curved pipe-jacking scenarios.

The pipe 2# section exhibited a more complex stress state, identified as diagonal compression. This was evidenced by the occurrence of extreme compressive strain values at specific orientations, namely 45° and 135°. The complex nature of diagonal compression underscores the importance of considering multiple stress components when assessing the structural integrity of pipes in curved configurations.

The numerical simulations provided further insights into the inelastic strain behavior of the pipes. The pipe 2# section, subjected to diagonal compression, displayed inelastic strain on both the inner and outer walls at specific orientations. Specifically, inelastic strain emerged on the inner wall at 90° and 270° and on the outer wall at 30° and 150°. This distribution of inelastic strain suggests that the pipe section is susceptible to damage at multiple locations under diagonal compression.

Conversely, the pipe 3# section, experiencing eccentric compression, showed inelastic strain predominantly on the inner wall, particularly on the side exposed to eccentric strain. This observation indicates a higher vulnerability to localized damage in this region due to the concentration of stress.

The study also revealed a clear relationship between the magnitude of the axial load and the potential for damage. With increasing axial loads, the risk of localized stress damage on the inner wall of the pipe 3# section intensified, especially on the side subjected to eccentric stress. Additionally, the pipe 2# section faced a dual threat of both localized stress damage and diagonal shear damage, underscoring the importance of considering combined loading effects in curved pipe-jacking design and analysis.