Experimental investigation of the effect of ground surcharge on the structural behavior of a quasi-rectangular tunnel

Abstract

The infrastructure in the urban core area is becoming increasingly dense, leading to restrictions on intensive development; however, there is a lack of adequate research on the structural mechanics of quasi-rectangular pipe jacking tunnels. This paper presents an experimental investigation that was conducted to analyze the impact of ground surcharge on the structural behavior of a quasi-rectangular tunnel located at Jing’an Temple station of Shanghai Rail Transit Line 14. The experimental setup included a scaled-down model of a quasi-rectangular tunnel, which was considered to be typical of underground structures. A series of tests were carried out by applying varying surcharge loads and eccentricities on the ground surface located above the tunnel. The tunnel structure’s response was monitored and analyzed through the use of earth pressure gauges, displacement sensors, and strain gauges. The experimental results revealed that ground surcharge on existing tunnels is mainly influenced by eccentricity and depth, with distinct effects at zero eccentricity and increasing eccentricity. Shallow tunnel burial depths intensify the impact of ground surcharge on the tunnel structure.

Graphical abstract

Keywords

quasi-rectangular pipe jacking / ground surcharge / model test / safety assessment / intensive construction technology

1 Introduction

The increasing development of urban underground space has resulted in a notable rise in the density of pedestrian passages, vehicle tunnels, subways, and other related facilities in the urban core areas. As a consequence, there have been tighter restrictions on continuous and intensive development, leading to a surge in the construction activities of neighboring underground structures. For instance, in 2014 alone, there were 16 recorded close-range constructions along the subway in Shanghai, China [1]. These construction behaviors can impose detrimental external loads on the pre-existing tunnel structure, including ground surcharge and eccentric overload, leading to added stress and deformation. In extreme cases, it can result in substantial deformation and harm to the segments, along with the collapse of the adjacent soil. Conversely, there’s a growing preference for the pipe-jacking method in numerous urban short-distance tunnel projects [2]. Its technology has advanced to the point where the cross-sectional shape of the segment has transitioned from circular to rectangular or quasi-rectangular. Although the circular shape is characterized by excellent mechanical performance, mature design, and construction methods, its cross-sectional utilization remains low. The rectangular shape has the potential to enhance cross-sectional utilization, but it is susceptible to concentrated stress at the corners and substantial internal force at the mid-span of the segment. With its quasi-rectangular shape that combines the advantages of both circular and rectangular, this design has found wide usage [3–6]. Therefore, it is imperative to carry out in-depth research on the effects of ground surcharge and eccentric overload on current pipe jacking tunnels involved in practical engineering, particularly the large cross-section quasi-rectangular pipe jacking tunnels.

Numerous scholars have researched to investigate the influence of ground loading on existing tunnels and have obtained specific findings. The research methods can be summarized as follows: on-site monitoring, theoretical analysis, numerical simulation, and model testing.

Most of the existing research on on-site monitoring has primarily focused on circular shield tunnels. For instance, Mohamad et al. [7] monitored the effect of a recently constructed tunnel on the deformation of an existing tunnel. Zhang et al. [8] undertook a series of full-scale experiments to examine the failure characteristics of the key segment within a super-large cross-section shield tunnel under general loading conditions. Wei et al. [9] conducted an indoor scaled model test method in conjunction with three-dimensional finite element simulation and theoretical calculations to investigate multiple aspects. The lateral and vertical convergence deformation, tunnel settlement, and deep soil settlement of an existing shield tunnel were included, which were caused by a sudden ground surcharge. Zhang et al. [10,11] elaborated on the cracking elements method, which is a numerical approach used for simulating quasi-brittle fractures, method designed to accurately model the behavior of quasi-brittle fracture. Shao et al. [1] examined the structural damage caused by soil accumulation above a subway tunnel in Shanghai and recommended appropriate repair and reinforcement techniques. Huang and Zhang [12] developed a resilience evaluation model for shield tunnels and compared it with the measured data. The aforementioned research primarily unveils the emergence of ground settlement, tunnel deformation, and diseases in pipe segments, which are caused by ground surcharge. However, due to its unpredictable nature, monitoring is only conducted following the occurrence of a ground surcharge, leading to a delay. Additionally, due to measurement points being exclusively positioned on the inner side of existing tunnels, monitoring fluctuations in external additional earth pressure poses a challenge. Consequently, analyzing the influence of ground surcharge on the tunnels from the standpoint of structural stress changes becomes problematic.

In terms of theoretical analysis, several studies have been conducted on the mechanical properties of pipe-jacking tunnels. However, the primary focus has been on circular and rectangular cross-sectional shapes, with the load-structure model being the main approach used [13–18]. At present, there is a lack of theoretical research on novel cross-sectional shapes for pipes, including rectangles and arches. Further enhancement is needed to fill the gap in research regarding the impact of ground surcharge. While numerical simulation is still focused on circular shield tunnels. For instance, Wang et al. [19] analyzed the surface settlement characteristics of the soft soil layer above the Dalian Metro Line 5 subway tunnel construction site, evaluating the impact of seismic action through ABAQUS finite element analysis. Gan et al. [20] introduced an analytical method to investigate the response of longitudinal tunnels to asymmetric ground movements resulting from new tunneling operations under crossings at different skew angles. Zhang et al. [21,22] proposed a micropolar peridynamics approach with a non-uniform horizon, showing effective failure criteria and weak mesh dependency, while discrete and continuum-based crack models, like the cracking element method, effectively capture crack initiation and propagation without remeshing, aligning well with interface element method results in crack openings and energy dissipation. Sun et al. [23] analyzed that shallow tunnels subjected to fire loading may experience stability loss due to thermal spalling and mechanical degradation, necessitating thermo-hydro-chemo-mechanical models for accurate simulation. Dutta and Bhattacharya [24] examined the stability of unsupported elliptical tunnels subjected to uniformly distributed ground loads and introduced a set of analysis indicators to assess the influence of ground surcharge. It can be considered that numerical simulation has increasingly become one of the primary techniques for examining the effects of ground surcharge on existing tunnels. Nonetheless, creating large-scale, three-dimensional refined finite element models is immense, especially for tunnels with non-continuous structures such as joints. This process is also prone to calculation convergence issues, which impede its rapid application in practical engineering.

Until now, when researchers utilize indoor model tests to explore tunnel deformations, the tunnel model tends to be simplified. The connecting bolts between tunnel segments are often represented through a reduction approach. However, no study has thoroughly explored the degree of impact caused by convergence deformation, settlement, and deep soil settlement of shield tunnels under different ground surcharge conditions [25–30]. Regarding model tests, Guo et al. [31] performed a series of loading tests on the circumferential joint to examine its shear behavior and damage mechanism. Zhang et al. [32] conducted full-scale experiments on a stagger-jointed shield circular tunnel reinforced with a new carbon fiber shell reinforcement. Furthermore, Zhang et al. [33] conducted full-scale tests on segments of the shield circular tunnel to assess the ultimate bearing capacity under unloading. Wu and Du [34] conducted a study on the effects of tunnel burial depth and ground surcharge position on the deformation of existing shield tunnels using scaled indoor model tests. Huang et al. [35] conducted a reduced-scale indoor model test to investigate the deformation of the tunnel structure and the associated changes in earth pressure surrounding the tunnel, caused by surface overloads.

To clarify, it’s currently common to conduct ground surcharge model tests using circular shield tunnels as specimens, while giving limited consideration to the influence of joints, bolts, and other factors on the model’s reliability. In particular, the model tests for quasi-rectangular pipe jacking tunnels have been less thoroughly studied. Simultaneously, the primary method of stacking is uniformly distributed overload, whereas there is a dearth of research on eccentric overload. Although experimental monitoring primarily concentrates on convergence deformation and joint opening, research on the distribution of extra internal forces in tunnel structures is lacking.

It is evident that despite the widespread use of the quasi-rectangular pipe jacking tunnel in recent years, research on its structural mechanics performance remains relatively scarce. The impact of adverse load conditions, such as ground surcharge and eccentric overload caused by close construction, on the internal force and deformation of existing tunnel structures has not been fully studied, especially. Hence, drawing from the Jing’an Temple station engineering project of Shanghai Rail Transit Line 14, a model test study was carried out to investigate the quasi-rectangular pipe jacking tunnel’s underground surcharge and eccentric overload conditions. The study further analyzed the development law of additional internal forces, convergence deformation, and the surrounding strata response of this type of structure under adverse load conditions. This endeavor aims to serve as a valuable reference for the structural design and safety assessment of similar projects in the future.

The paper’s structure is arranged as follows. Section 2 provides the comprehensive experimental program and methodology for the quasi-rectangular pipe-jacking tunnel. Section 3 presents the complete experimental results regarding earth pressure and convergences. Section 4 pertains to evaluating the internal forces of the pipe segment from measured strains. Section 5 deals with the impact of the surcharge’s relative position on the structural behavior of the tunnels. Consequently, Section 6 provides a summary of the study’s conclusions.

2 Experimental program

2.1 Prototype of the quasi-rectangular pipe-jacking tunnel

The tunnel under consideration is comparable to the pipe-jacking tunnel of Jing’an Temple station on Shanghai Rail Transit Line 14. For more information, please refer to Appendix A in the Electronic Supplementary Material. The model test is designed to replicate the corresponding engineering prototype, which is the pipe section of the platform layer located in Zone B. The pipe has a cross-sectional size of 9.9 m × 8.7 m and a thickness of 525 mm. The design utilizes a composite structure that comprises an outer steel structure and an inner concrete lining. The outer steel structure boasts an overall thickness of 400 mm. On the inner side, a layer of C35 concrete with a maximum thickness of 125 mm is poured. Specifically, during the construction process, the steel pipe joint is inserted and then concrete is poured over it, creating a composite pipe. Tab.1 displays the material parameters of the prototype tunnel.

As shown in Fig.1, the quasi-rectangular tunnel cross-section is symmetric about both the horizontal centerline H1H2 and vertical centerline V1V2. The intersection of the two mutually perpendicular symmetry axes is the center O. Each 1/4 curve segment divided by the horizontal and vertical centerlines is symmetric to each other. Here, the 1/4 curve segment A1B1C1D1 located in the first quadrant (V1OH2) is taken for explanation.

This 1/4 curve segment consists of an arc segment A1B1 with a radius R1 = 5.792 m, a central angle of 22°, a center O1, and an arc segment B1C1 with a radius R2 = 1.593 m, a central angle of 68°, a center O2, and a straight line segment C1D1 with a length L1 = 1.227 m. A1 is the upper vertex of this 1/4 curve segment, B1 is the junction point of the arc segment with radius R1 and the arc segment with radius R2, C1 is the junction point of the arc segment with radius R2 and the straight line segment, and D1 is the right vertex. The tangent line of the 1/4 curve segment at A1 is perpendicular to the vertical symmetry axis V1V2; the tangent line at C1 is perpendicular to the horizontal symmetry axis H1H2.

The composite segment jacking pipe is actually constructed by first pushing in the steel segment, followed by pouring the secondary concrete. As a result, model specimens are designed to be steel-mortar composite segment specimens.

The Jing’an Temple Station Project of Shanghai Rail Transit Line 14 is situated in a typical soft soil region, however, it encompasses numerous soil layers. Considering the limitations of the experimental conditions, simplify the soil layer of the original site to match the soil layer through which the tunnel passes. The upper soil layer of the tunnel was designated as muddy clay ④, while the lower soil layer was identified as silty clay ⑤. The corresponding physical and mechanical parameters are displayed in Tab.2.

2.2 Similarity relationship and scaled model

In this paper, the model test is categorized under linear elasticity, implying that the similarity criteria and ratio should be chosen according to the pertinent theory of elasticity. Specifically, both the elastic modulus and Poisson’s ratio should meet a certain level of similarity, while also considering the similarities in geometry and load. Taking into account the model test site conditions and materials, it has been determined that the similarity ratio between the specimen and prototype tunnel is determined by the geometric dimension of S_l = 1:20.

For the steel−mortar composite segment, the similarity relationship of physical quantities between the model and prototype is demonstrated in Tab.3, based on the similarity ratio of geometric dimensions of S_l = 1:20 and the similarity ratio of density between the mortar used in the specimens and the prototype C35 concrete of S_ρ = 1:1.29.

2.3 Model tunnel and soil

The steel segment primarily comprises a panel and a T-shaped vertical and horizontal partition, which function as a stiffener during the jacking construction. The T-shaped partition serves as a vital connection between the steel and concrete throughout the operation period, ensuring seamless integration and functionality.

To streamline the production of the steel segment specimen and the pouring of the concrete lining, a similar approach that incorporates dual control of strength and stiffness is implemented to simplify the T-shaped partition. This equivalent simplification allows for efficient management of both strength and stiffness. The equivalent strength is demonstrated by the panel of the steel segment, which does not cause local instability, and the prototype’s 58 T-shaped partitions have been reduced to just 20 straight-shaped partitions in the model. The straight-shaped partition and panel are 2 mm thick, and the partition is 14 mm long. In this way, the bending stiffness of the steel segment specimen is equivalent to the prototype, which can be proved by the comparative analysis of the model segment and the prototype segment, as shown in Fig.2.

First, as depicted in Fig.3(a), a 2 mm thick cold-rolled steel plate is cut and cold welded to create a steel segment. Then, splice these steel segments into a jacking pipe tunnel using ϕ3 diameter bolts, as illustrated in Fig.3(b). Secondly, to facilitate the pouring of the concrete lining, a steel jacking pipe tunnel is erected, and the formwork inside the model for pouring is illustrated in Fig.3(c). The mortar is prepared following the ratio of cement: sand: lime: water = 1:5:0.8:1.16.

The model soil is made of sawdust and medium sand, and the elastic modulus of the model soil is adjusted by changing the mass ratio of sawdust and medium sand. Sawdust has strong water absorption and is a flammable material, it can be dried by the hot air drying method. The average particle size of medium sand is 0.25–0.5 mm, the mass of particles which is larger than 0.25 mm should exceed 50% of the total mass, and the moisture content is 2%. Through the comparative experimental study of four groups of mass ratios (sawdust:sand) of 1:5, 1:3, 1:2.5, and 1:2, the mass ratio 1:2.5 is selected, with which the elastic modulus of model soil is closest to the target modulus. Consequently, the material parameters of the model soil used in the test are shown in Tab.4.

2.4 Test conditions

The influence of buried depth, and ground surcharge location are the main factors that are taken into account while designing the test procedure. The tunnels are classified into three test series, I, II, and III, corresponding to buried depths of 2.0D, 1.5D, and 1.0D, respectively. Tab.5 displays the test number and every test condition. To ensure that the model tunnel remains in a state of plane strain, the longitudinal ends are secured during the test. In the test series I, II, and III, each model tunnel comprises 10 segments that are loaded in stages of 9, 18, 9, and 0 kPa.

The test at the maximum tunnel buried depth in three test series, I, II, and III, was conducted first. These correspond to test number I with a tunnel buried depth of 2.0D, which includes test conditions with three eccentricities: no eccentricity, 0.5D eccentricity, and 1.0D eccentricity, respectively. Afterward, remove a 250 mm thick soil layer and proceed with the subsequent set of tests, which correspond to condition II with a buried depth of 1.5D. Continue unloading and conclude the test corresponding to condition III with a buried depth of 1.0D.

2.5 Measurement scheme design

Set the middle two of the ten longitudinally distributed segments as observation segments, and arrange measuring points at the same position on them. Therefore, it is possible to obtain the average value of the two segments. The measurement schemes encompass additional earth pressure, tunnel convergence deformation, segment strain, and other related factors.

The membrane earth pressure gauge is affixed to the exterior of the segment to gauge the contact stress between the soil layer and the tunnel. A Linear Variable Differential Transformer (LVDT) has been installed inside the tunnel to measure convergence deformation. The resistance strain gauge is adhered to the corresponding positions of the outer and inner arc surfaces of the segment, enabling the calculation of the segment’s internal force distribution.

3 Experimental results

To provide a more accurate description of the test data for each measuring point, the angular coordinates θ are defined. The segment’s center point O serves as the origin, the vertical upward direction through the center point O as the positive Y axis, and the clockwise direction as the angle θ growth direction, with \theta \in[0,360°). The direction of the surcharge’s eccentricity is on the right side of the Y axis, which corresponds to the positive direction of the X axis.

3.1 Earth pressure

Fig.4 illustrates the distribution of additional earth pressure beyond the model segment. A positive value indicates an increase in earth pressure at the monitoring position compared to that without a surcharge, while a negative value indicates a decrease. Using burial depths of H = 500 mm and surcharge eccentricities of e = 0, 250, and 500 mm as examples, this section analyzes the variation and distribution characteristics of additional soil pressure. Section 5 details the variations in soil cover conditions.

When e = 0, the additional earth pressure on the outside of the segment exhibits left-right symmetry characteristics, primarily intensifying around the top and bottom of the segment, with the maximum value appearing directly beneath it, and smaller values on both sides. In other words, the soil layers on either side of the segment tend to deviate from the structure. Under these conditions, the maximum increase in additional earth pressure, corresponding to a maximum surcharge of 18 kPa, is 15.84 kPa, with an increase ratio of 88.0%.

When e = 250 mm, the additional earth pressure on the exterior of the segment is inclined toward the eccentric side of the surcharge, with the highest value occurring at the point beneath the segment and away from the surcharge. The additional earth pressure above the segment away from the surcharge side is minimal, with the soil mass there tending to deviate from the segment, and the deformation of the soil around the segment exhibiting characteristics of an oblique ellipse. Under these conditions, the maximum increase in additional earth pressure, corresponding to a maximum surcharge of 18 kPa, is 15.36 kPa, with an increase rate of 85.3%.

When e = 500 mm, the distribution of additional earth pressure on the outside of the segment continues to shift toward the eccentric side of the surcharge, exhibiting marked oblique elliptic features. The highest value is observed at a location near the surcharge side above the segment, indicating that the soil and segment near the surcharge area are subjected to the most intense compression. In this scenario, the rise in extra earth pressure, corresponding to the maximum surcharge of 18 kPa, is 11.42 kPa, with a rising ratio of 63.4%.

On the other hand, when eccentricity e is kept constant, the maximum additional earth pressure σ of the segment shows an approximate linear relationship with ground surcharge p. This can be observed from the parallel connecting lines of earth pressure at each measuring point, indicating that the interaction between soil and segment remains in the elastic range during the loading and unloading process. Meanwhile, as eccentricity e increases, σ/p decreases, indicating that the influence of ground surcharge on the structure decreases with the increase of surcharge eccentricity. This is demonstrated in Tab.6.

3.2 Convergences

Fig.5 illustrates the additional convergence deformation of the model segment. A positive deformation indicates an outward expansion of the monitoring position, while a negative deformation indicates an inward shrinkage. Using burial depths of H = 500 mm and surcharge eccentricities of e = 0, 250, and 500 mm as examples, during loading and unloading, it is evident that the convergence deformation of the segment is relatively close under the same ground surcharge p, suggesting the absence of significant plastic deformation. Section 5 details the variations in soil cover conditions.

Tab.7 displays the maximum value of convergence deformation for various ground surcharge eccentricities and magnitudes. The results indicate that, given the same ground surcharge eccentricity e, the convergence deformation is significantly greater for a surcharge magnitude of p = 18 kPa compared to p = 9 kPa. This suggests that as the ground surcharge increases, so does the convergence deformation of the segment. Meanwhile, as the eccentricity e increases, the convergence deformation of the tunnel decreases, suggesting that the effect of the eccentric load on the convergence deformation is weakening. However, the location of the peak convergence deformation shifts from the initial horizontal and vertical sections to the oblique sections, indicating a transition from transverse to oblique ellipse.

4 Evaluation of the internal forces of pipe segment from measured strains

The axial force N per unit width on the cross-section of the pipe joint can be calculated according to Eq. (1). In Eq. (1), A is the cross-sectional area of the pipe joint, E is its Elastic modulus, and \overline{\sigma } is the average normal stress in the normal direction of the section.

(1)N=A\overline{\sigma }=AE\overline{\epsilon }.

The bending moment M per unit width on the cross-section of the pipe joint can be calculated according to Eq. (2). In Eq. (2), I_x is the moment of inertia about the position of the cross-section centroid, y_1 is the distance from the outer curved surfaces of the pipe joint to the centroid axis of the section, and {\sigma }_1 is the stress calculated on the outer curved surface of the pipe joint.

(2)M=\frac{I_x}{y_1}({\sigma }_1-\overline{\sigma }).

Fig.6 and Fig.7 show the distribution of tunnel bending moment M and axial force N under all working conditions, respectively.

The internal force distribution can be obtained by converting the strain values of the outer arc surface and the inner arc surface of the segment, mainly including the bending moment and axial force. During the loading and unloading process, the strain recorded at each measuring point remains within the elastic strain limits of the material. This observation confirms that the model structure remains within an elastic state during the testing phase. Additionally, the internal forces within the test specimens are below the values corresponding to their elastic limits. When the stacking level is doubled, the distribution of internal forces also doubles, indicating a linear relationship between the ground stacking value and the tunnel internal forces. Under the operational scenario where the eccentricity of the pile load is e = 0, the distribution of internal forces in the model structure under symmetric loads also approximates symmetry. The distribution of bending moments closely resembles a scenario where uniform pressure is applied at the top of the structure. This observation aligns with the “transverse elliptical” deformation pattern exhibited by the structure. With the escalation of loading eccentricity, the tunnel’s bending moment control section shifts from the midpoint to the corner. This change illustrates the transition of the ground loading’s impact on the tunnel, moving from the load directly above to the load positioned on the inclined 45° angle section. The impact on the internal force of the structure decreases with the increase of eccentricity.

5 Effects of the relative position of the surcharge on the structural behavior of the tunnels

To further analyze the effect of ground surcharge on an existing tunnel, the main variable factors in the test process should be considered: ground surcharge magnitude p, surcharge eccentricity e, and tunnel buried depth H, as shown in Tab.8. A dimensionless method is adopted to define κ as the buried depth coefficient, which indicates the ratio of the buried depth H to the horizontal span D_x of the tunnel; definition λ as the eccentricity coefficient, which represents the ratio of ground surcharge eccentricity e to the horizontal span D_x of the tunnel. The calculation method is shown in Eqs. (3) and (4). Thus, it is more intuitive to reflect the position relationship between the ground surcharge and the tunnel, which is conducive to the comprehensive analysis of the influence of these variable factors.

(3)k=\frac{H}{D_x},

(4)\lambda =\frac{e}{D_x}.

5.1 Additional external load on the structure

To comprehensively evaluate the additional earth pressure, two main characteristics are selected: one is the strength and the other is the spatial distribution symmetry. Therefore, the average value of the additional earth pressure on the outer side of the segment is quantitatively defined as the average additional earth pressure P, which can be calculated by Eq. (5).

According to the test results in Section 4, when the eccentricity e = 0.0D, the ground surcharge is symmetric about the vertical centerline of the segment, so the distribution of additional earth pressure outside the segment is correspondingly symmetric; and when e increases, the earth pressure on the inclined section of the segment increases. Therefore, the ratio between the sums of the earth pressure D-value at the symmetric positions on both sides of the segment’s vertical centerline to the average additional earth pressure P is defined as the inclined concentration Q for the additional earth pressure outside the segment, and the calculation method is given by Eq. (6):

(5)P=\frac{{\displaystyle \sum _{i=1}^n{S}_i}}{n},n=12,

(6)Q=\frac{\lceil S_{30}-S_{330}\rceil +\lceil S_{60}-S_{300}\rceil +\lceil S_{90}-S_{270}\rceil +\lceil S_{120}-S_{240}\rceil +\lceil S_{150}-S_{210}\rceil }{P},n=12,

where S_i is the additional earth pressure measured at each measuring point. 12 measuring points are arranged along the circumferential direction, so n = 12. Hence, S_{30},S_{60},S_{90},…,S_{330} refer to the additional earth pressure on the section of 30°, 60°, 90°, and 330°, respectively.

The relationship among buried depth coefficient κ, eccentricity coefficient λ, and average additional earth pressure P is shown in Fig.8. When the eccentricity coefficient λ remains unchanged, with the buried depth coefficient κ increases, or when the buried depth coefficient κ remains unchanged, with the eccentricity coefficient λ increases, the average additional earth pressure P decreases, which indicates that with the increase of buried depth H or ground surcharge eccentricity e, the influence on the additional earth pressure outside the segment becomes smaller and smaller.

The relationship among buried depth coefficient κ, eccentricity coefficient λ, and inclined concentration Q for the additional earth pressure outside the segment is shown in Fig.9. It can be concluded that Q is mainly controlled by the surcharge eccentricity e and has less relationship with the tunnel depth H. With the increase of eccentricity e, the additional earth pressure gradually transfers from horizontal symmetric distribution to oblique symmetric distribution manifested as the increases of Q.

5.2 Convergence deformation

Unlike the circular tunnel, the quasi-rectangular tunnel has curvature change and no fixed radius, so its convergence deformation evaluation should not use the corresponding index of the circular tunnel. Therefore, combined with the measuring data of additional convergence deformation at each angle of the segment, the average convergence deformation rate T is defined, and the calculation method is given by Eq. (7):

(7)T=\frac{{\displaystyle \sum _{i=1}^n\left|\mathrm{\Delta }{D}_i\right|/D_i}}{n},n=6,

where D_i is the span of the measuring point, \mathrm{\Delta }{D}_i is the convergence deformation, n is the number of measuring points, n = 6.

The relationship among buried depth coefficient κ, eccentricity coefficient λ, and average convergence deformation rate T is shown in Fig.10. When the eccentricity coefficient λ remains unchanged, with the buried depth coefficient κ increase, or when the buried depth coefficient κ remains unchanged, with the eccentricity coefficient λ increase, the average convergence deformation rate T decreases, which once again indicates that with the increase of buried depth H or ground surcharge eccentricity e, the influence on the mechanic’s characteristic of the segment becomes smaller and smaller.

5.3 Internal forces of the pipe segment

To quantitatively compare and analyze the magnitude of the additional internal force, the average additional bending moment M and the average additional axial force N are defined, to characterize the mechanical response of the segment under the ground surcharge. The calculation method is given by Eqs. (8) and (9):

(8)M=\frac{{\displaystyle \sum _{i=1}^n\left|M_i\right|}}{n},n=12,

(9)N=\frac{{\displaystyle \sum _{i=1}^n\left|N_i\right|}}{n},n=12,

where M_i is the bending moment at the measuring point, N_i is the axial force, n is the number of measuring points, and n = 12.

Fig.11 and Fig.12 illustrate the correlation among the buried depth coefficient κ, eccentricity coefficient λ, average additional bending moment M, and average additional axial force N. First, as the eccentricity coefficient λ remains constant and the buried depth coefficient κ increases, or vice versa, the average additional bending moment M decreases. This suggests that the influence on the bending moment diminishes as the buried depth H or surcharge eccentricity e increases. In contrast, there is no significant correlation with the average additional axial force N.

5.4 Comprehensive analysis of variable factors

Based on the analysis conclusion from the previous section, it is generally observed that the additional responses P, T, M, and N of the segment under the ground surcharge will decrease as the tunnel depth H and surcharge eccentricity e increase. Additionally, a dimensionless relative position coefficient μ has been defined, which serves to characterize the relative relationship among the tunnel depth, surcharge eccentricity, and tunnel horizontal span. This coefficient is to be calculated using Eq. (10):

(10)\mu =k+3\lambda =\frac{H+3e}{D_x}.

Define the standard test condition for a buried depth of H = 500 mm, a ground surcharge of p = 18 kPa, and a surcharge eccentricity of e = 0. Divide the data from other test conditions by that of the standard test condition to perform dimensionless analysis. The standard test condition corresponding to the relative position coefficient μ = 1 is κ = 1 and λ = 0. Record the additional responses under standard test conditions as P₀, T₀, M₀, N₀, and calculate the ratios of the additional responses under each test condition to the standard test condition, denoted as P/P₀, T/T₀, M/M₀, N/N₀. In Fig.13, plot the correlation between the response ratio mentioned above and the relative position coefficient μ.

As the relative position coefficient μ increases, there is a notable decrease in the ratios of the additional responses to the standard test condition. Moreover, the maximum values of average additional earth pressure and average convergence deformation outside the segment were observed in all tests under standard test conditions, suggesting that these conditions correspond to the most unfavorable stress state of the tunnel. In other words, in the current quasi-rectangular tunnel, the impact of the ground surcharge is greater when the tunnel is buried deeper and when the ground surcharge position is closer to the vertical centerline of the tunnel.

Secondly, the influence of tunnel depth is found to be more significant than that of ground surcharge eccentricity, as indicated by the value of the response ratio.

Finally, the convergence deformation serves as an indicator that is comparatively easy to monitor, while also being a more responsive and perceptive reaction to the segment’s mechanical properties. Hence, it is recommended in engineering practice to evaluate the influence of adverse load conditions, such as ground surcharge, on the current tunnel by monitoring convergence deformation and taking into account the spatial correlation between the ground surcharge and the tunnel.

6 Conclusions

Drawing upon the engineering background of the quasi-rectangular pipe jacking tunnel in Jing’an Temple Station of Shanghai rail transit line 14, and leveraging the practical construction process of jacking steel pipe segments first and pouring concrete lining second, this paper introduces steel-mortar composite segments to investigate the impact of surcharge on the tunnel. Subsequently, three sets of model tests were conducted involving ground surcharge and eccentric overload. The conclusions are as follows.

1) Once the magnitude of the ground surcharge is confirmed, the additional response of the existing tunnel structure is primarily linked to the eccentricity of the ground surcharge and the buried depth of the tunnel. When the eccentricity is zero, several characteristics are observed.

• The peak value of the additional earth pressure on the outside of the segment is observed at the top and bottom of the structure.

• The convergence deformation is characterized by a symmetric transverse ellipse.

• The peak value of the convergence deformation is observed in both the horizontal and vertical sections of the structure.

• The internal force is approximately symmetric.

As the eccentricity increases, several changes occur.

• The peak value of the extra earth pressure outside the segment shifts from the perpendicular to the oblique section.

• The convergence deformation shifts from a transverse ellipse to an oblique ellipse.

• The distribution of internal force is no longer symmetric about the vertical centerline.

2) Furthermore, as the tunnel is buried at shallower depths, the ground surcharge position becomes closer to the vertical centerline of the tunnel, resulting in a greater impact from the ground surcharge.

3) The Internal force conversion was carried out using strain test data. It is evident that there is a significant correlation between convergence deformation and the internal force state of the pipe-jacking structure.

However, in engineering practice, due to the unpredictability of not reserving strain monitoring conditions and the irreversibility of the soil-facing surface, measuring points can be arranged on the inner side only, it is impossible to rely on strain data measurements to assess the internal force state of the structure as in experiments. Therefore, based on the convergence deformation measurement data of the inner arc surface, establishing a hybrid calculation method to achieve the internal force analysis of the quasi-rectangular pipe-jacking tunnel, can provide a scientific basis for its safety assessment during operation. This is also the key achievement of the subsequent papers after this experimental study provides conceptual and data support.

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