Pre-supporting mechanism and supporting scheme design for advanced small pipes in the silty clay layer

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Pre-supporting mechanism and supporting scheme design for advanced small pipes in the silty clay layer ⁎

Keqi Liua, Shucai Lia, Wantao Dinga,b, , Minglei Houa, Yingjie Gongc, Huiliang Lic a

Geotechnical and Structural Engineering Research Center, Shandong Univ., 17923 Jingshi Road, Jinan 250061, China School of Qilu Transportation, Shandong Univ., Jinan 250002, China c Harbin Metro Group Co., Ltd, 65 Xuefu Road, Harbin 150080, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Silty clay Pre-support Numerical calculation Tunnel face stability

This study presents a design method for the advanced support of subway tunnels for different water content conditions in the silty clay layer. The influence of particle size distribution and water content on the mechanical properties of silty clay is studied through laboratory tests. In addition to the actual construction of the Harbin subway with a silty clay layer, a numerical calculation model is established to study the surface settlement, crown settlement, and supporting structure internal force during the tunnel excavation and support process under different working conditions. Furthermore, the mechanism of action of the advanced small pipe support is clearly defined, and a stability analysis model of the top and bench excavation in a silty clay layer is proposed to evaluate the stability of the tunnel face. The necessity and rationality of the pre-support is quantitatively analysed using the stability coefficient. The laboratory tests illustrate that within a certain range of clay content, the shear strength of silty clay decreases with an increase in water content. The silty clay was further divided into subgrades. The pre-support transfers the loose soil load to the initial support, which improves the early utilization of the lining structure. The advanced small pipe grouting increases the range of the bearing arch, shortens the interval distance of the supporting arch feet, and reduces the vertical load acting on the tunnel face. For the condition of subgrade V in silty clay strata, the stability of the tunnel face can be maintained without the advanced small pipe support. For the condition of subgrade VI1, the advanced small pipe support must be applied to ensure the stability of the tunnel face, but the grouting reinforcement measures are not required. For the condition of subgrade VI2, the advanced small pipe support and grouting reinforcement must be used simultaneously to ensure the stability of the tunnel face.

1. Introduction As urban rail transit construction becomes large scale, the types of strata encountered in the civil construction process are diverse and complex. Therefore, it is crucial to research the tunnel excavation and support technology under different strata conditions. However, existing research on supporting technology mainly focuses on mine tunnel excavations, especially for tunnels under harsh geological conditions, such as extremely weak broken rock masses, high tectonic stresses, and other mine lanes (Kang et al., 2018; Li et al., 2018). Current studies on tunnel excavations and support for soil tunnels are inadequate, especially those with a focus on the Quaternary depositional layer, in which the urban rail transit is located. At present, the planned construction lines for urban rail transit are all round and large. A rationally optimized design for the supporting structure will provide significant

economic and social benefits by ensuring construction safety. In soil strata, the effect of water content on the strength and stability of the formation is evident (Estabragh et al., 2015; Wang et al., 2016), especially in the clay layer. While significantly influencing the physical and mechanical properties of soil, such as the permeability coefficient, porosity, cohesive force, and friction angle, the water content even necessitates a nonlinear influence law. The study of remoulded clay illustrated that the cohesive force increases with the increase in water content (Naser and Al-Shayea, 2001). When the water content is higher than the critical value, the cohesive force and friction angle gradually decrease with an increase in water content. It is worth noting that different contents of clay particles correspond to different distribution laws between particles (Horpibulsuk et al., 2010). Therefore, the influence of the clay content on the physical and mechanical parameters is highly significant for clay soil. As a typical clay soil, silty clay is

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Corresponding author at: Geotechnical and Structural Engineering Research Center, Shandong Univ., Jinan 250061, China. Tel.: +08613698610960. E-mail addresses: [email protected] (K. Liu), [email protected] (S. Li), [email protected] (W. Ding), [email protected] (M. Hou), [email protected] (Y. Gong), [email protected] (H. Li). https://doi.org/10.1016/j.tust.2019.103259 Received 17 July 2018; Received in revised form 12 September 2019; Accepted 20 December 2019 0886-7798/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Keqi Liu, et al., Tunnelling and Underground Space Technology, https://doi.org/10.1016/j.tust.2019.103259

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scheme of advanced small pipe support is proposed for the benching of tunnelling construction in silty clay strata under different subgrade conditions.

extensively used in practical engineering. However, because of the combined effect of different powder and clay contents and the influence of the water content (Wang et al., 2018), the physical and mechanical properties of silty clay are extremely complex, which often makes engineering design and construction difficult. For silty clay strata, the range of variation of the water content in engineering is large, and the influence of water and clay content on the physical and mechanical parameters of silty clay are unclear. There is a lack of detailed studies on the subgrade classifications of silty clay. Existing design methods for tunnel support structures primarily include the distributed ground pressure approach, subgrade reaction approach, and convergence-confinement method (Carranza and Engen, 2017). The convergence-confinement method considers the interaction of the surrounding rock and support structure and is extensively used in the design of tunnel structures. However, using this method presents certain problems in the process of tunnel structure design; for example, the shape of the tunnel is limited to a circular tunnel (Carranza and Diederichs, 2009), and the results of the analysis largely depend on the selection of the constitutive relation of rock and soil (Mousivand and Maleki, 2017; Ochmański et al., 2015), so practical engineering is often performed using numerical calculations (Cui et al., 2015; Mousivand et al., 2017). Simultaneously, auxiliary construction design is often required in order to ensure the safety of the construction in weak strata. However, the design generally depends on similar engineering construction experience, so the design scheme is occasionally inapplicable. Determining the necessity and rationality of the pre-support is key to ensuring the construction’s safety and economy. The model test (Juneja et al., 2010) illustrated that the effect of the advanced support on the stability of the tunnel occurs before the excavation of the face, and the stability of the tunnel depends not only on the length of the excavation steps but also on the parameters of the pre-support structure. The existing research mainly treats the pre-support design as being equal to the reinforcement of the tunnel face or soil parameters (Dias, 2011) in the optimization design of the pre-support structure (Basirat et al., 2016) and does not consider the necessity of a quantitative analysis of the pre-support. Based on the complexity of the formation parameters and the flexible diversity of the schemes, a mechanical analysis of the pre-support scheme needs to be verified by numerical calculation (Funatsu et al., 2008; Kamata and Mashimo, 2003; Oke et al., 2014). In addition, it is necessary to modify the calculation parameters according to the field tests (Oke et al., 2016) for most cases. However, there are limited studies on the fine numerical simulation and field support effect of advanced small pipe supports, and the accuracy of the numerical calculations is difficult to verify. More importantly, there is currently no quantitative method to evaluate the supporting effect of advanced small pipes. Therefore, it is crucial to obtain a reasonable quantitative evaluation method for the pre-supporting effect, thereby guiding engineering solutions. This study involved laboratory tests to define the primary factors influencing the mechanical properties of the silty clay, starting from the particle size distribution and water content of the silty clay. Furthermore, a subgrade classification standard of silty clay was established. On this basis, the finite difference numerical model was established to analyse the stability of the surrounding soil and support structure in the tunnel excavation and supporting process. Through a comparison with the field monitoring data, the rationality of the calculation model and parameters is clarified. The influence of the advanced small pipe support on the settlement of the tunnel crown and the stress model of the initial support were further analysed, and the supporting mechanism of the pre-support in the different silty clay layers was clarified. Finally, the stability analysis model of the tunnel face under the effect of the pre-support in a clay layer was established, and the necessity and rationality of the pre-support were quantitatively analysed by introducing the stability coefficient of the tunnel face. Finally, a method is established for evaluating the effect of pre-supporting in silty clay strata for engineering applications. The design

2. Geomechanical properties and sub-classification of silty clay 2.1. Engineering survey Harbin, a significant provincial capital in the northeast of China, is famous for its long history and rich culture of ice and snow. Economic development has promoted the metro as a preferred traffic mode, due to its convenience and space efficiency. The planning of Harbin Metro's long-range network included 19 lines, with a total length of 720 km. Currently, only sections of Metro Lines #1 and #3 are operational, while the remaining parts of these two lines are still under construction. Harbin is located in the southeast part of the Songnen Plain, which has a complex terrain. It consists of three landform units: the Gangfu plain area, Songhua River terrace landform, and Songhua River floodplain. The plain area in these landforms comprises silty clay with medium compressibility and in a plastic state. In addition, the engineering is located above the ground water, but some upper stagnant water may exist as a result of pipeline leakage. The shallow tunnelling method was used because of the intervals in variable sections and obstructions in the structure range. Fig. 1 displays the ground stratification of a tunnelling section in phase III of Harbin Metro Line #1, and the horizontal distance of this section is 871 m. The shallow tunnelling method in the hilly and flat plain area of Harbin Metro combines the use of the bench method and advanced small pipe grouting. The shape of the section is composed of three core circles and an inverted arch. The height of the excavation is 3.0 m, and the length of the step is 5.0~6.0 m. The width and height of the tunnel are 4.88 m and 5.15 m, respectively. Fig. 2(a) and (b) illustrate the transverse and longitudinal sections of the metro tunnels, respectively. The support system consists of a pre-support using advanced small pipes, primary lining with steel grids, steel meshes, and sprayed concrete and a secondary lining with cast-in concrete. The advanced small pipe is 42 mm in diameter and 3 m in length, as depicted in Fig. 2(c). The small pipes are deployed every two cycles of the circulating footage, with a length of 1.5 m. The application range is 120°–150° along the centre angle of the vault. The steel grid is 22 mm in diameter for the main bar and 0.75 m for the spacing. The steel meshes are 8 mm in diameter and 200 mm for the spacing for both the longitudinal and axial directions. The sprayed concrete has a thickness of 250 mm, and the uniaxial compression strength is 25 MPa. According to the national code for the design of metros (GB501572013), the silty clay is generally identified as class V without specific details, and the pre-support with advanced small pipes is required for the construction of metro tunnels. However, in the actual construction process, the mechanical properties of silty clay are different under different conditions of water content, and the mechanical parameters of silty clay vary widely as the water content changes. The specific performance is as follows. (1) When the water content of the silty clay is low and the soil presents a hard plastic state, the tunnel face is stable and the soil is dense. In this case, the small pipe is inefficient. Simultaneously, the advanced small pipe grouting slurry does not spread according to the field test. (2) However, when the water content in the silty clay layer is relatively high, there is a serious drop phenomenon in the tunnel face; moreover, the seepage phenomenon is obvious. In this case, a reasonable advanced support method is especially important, and the advanced small pipe grouting generates obvious pulp veins, and the reinforcement effect on the tunnel face is remarkable. Therefore, it is necessary and reasonable to study the mechanics of the pre-support structure and deformation characteristics of the surrounding soil in silty clay layers with different water contents. It proves to be extremely helpful to the rational design and construction of tunnels. 2

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Fig. 1. Ground stratification of a tunneling section.

to 12, and the liquid index is between 0.07 and 0.22, which belongs to the hard plastic state of silty clay. Harbin Metro Line #3 has a natural water content ranging from 25 to 28%, plasticity index from 11.46 to 14.33, and liquid index from 0.28 to 0.71, which belongs to the plastic state of silty clay. To further confirm the mechanical parameters of silty clay under different water contents, triaxial compression tests were carried out on the hard plastic, plastic, and soft plastic clay, in which the soft plastic state clay was artificially remoulded. Three different states of silty clay samples were prepared into standard samples with a diameter of 39.1 mm and a height of 80 mm. The confining pressures of the test loading were 100 kPa, 200 kPa, and 400 kPa. Fig. 3 displays the relationship between the deviatoric stress and axial strain for three different silty clay specimens at a confining pressure of 400 kPa. The silty clay was assumed to be an isotropic elastic-perfectly plastic material complying with the Mohr-Coulomb failure criteria. The experimental data were fitted with the linear elastic-perfectly plastic material behaviour using the solid lines to obtain the constitutive relation of different states of silty clay under a specific confining pressure. The research primarily considered the stability of the surrounding soil and the initial lining structure at the early stage of excavation, and as a result the effect of the long-term creep was neglected (Wang, 2016; Wang and Wong, 2015). It is known that when the confining pressure is 400 kPa,

2.2. Sub-classification of silty clay Due to differences in particle size and clay content, silty clay with the same water content may display different physical and mechanical properties (Wang, 2016; Wang and Wong, 2015). Therefore, water content cannot be used as the sole indicator of the mechanical properties of the silty clay. The plastic index is selected as an aggregative indicator to consider the influence of the water content and particle size on the physical properties of silty clay. The plastic limit of silty clay increases with the increase in clay content. Soil samples were obtained from the tunnel excavation face at the construction site, and laboratory tests were carried out to measure their physical and mechanical parameters. To study the mechanical response of the surrounding soil and support structure during tunnel excavation, it is essential to define the physical and mechanical properties of the silty clay under different water contents. Liquid and plastic limit tests were conducted with the soil samples obtained from the field. The water content of the pattern was measured using the heating method, and the plastic and liquid limits of the soil samples were measured using liquid-plastic combined equipment. The operational criterion of the specific test was strictly implemented according to the specification for soil tests (SL237-1999). According to the test results, the natural water content of Harbin Metro Line #1 ranges from 18% to 27%. The plasticity index ranges from 10.1

Fig. 2. Schematic diagram of tunnel standard section for excavation and support structure design. 3

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the effect of the upper stagnant water and pipe leaks can be neglected due to the special treatment of those areas. The model of a tunnel standard section was chosen as the engineering background to establish the numerical model. A standard section consisting of three core circles and an inverted arch was selected to establish the numerical model. In the process of numerical modelling, the size of the model should avoid the influence of a boundary effect; that is, the boundary range of the model must be larger than 3 times the tunnel diameter. The projection point of the starting point on the tunnel centre line at the ground surface was considered to be the coordinate origin, and the left and right boundaries were set at 30 m, the lower boundary was 25 m, the ground surface was a free boundary for displacement, and the length along the axis direction of the tunnel was 50 m. Therefore, the surrounding soil was modelled by a hexahedral mesh solid element, with dimensions of 70 m × 50 m × 60 m (length × width × height), and the thickness of the overlying soil is 20 m. No vertical displacement was permitted on the bottom surface, and no horizontal displacement was permitted on the left, right, front, and backward surfaces of the model. The finite difference model was divided into 106,157 nodes and 98,160 units. Furthermore, numerical models must fully consider the actual construction conditions, especially for the key construction procedures. The excavation part of the tunnel was divided into three parts, i.e., the upper step, the lower step, and the core soil part. Fig. 4 displays half the numerical calculation model.

Fig. 3. Triaxial test simulation of silty clay for σ3 = 400 kPa.

the shear strength of silty clay decreases with the increase in water content (Mitchell and Soga, 2005). Compared with the hard plastic state, the strength of the plastic clay in the plastic state is reduced by 25%, and the strength of the silty clay in the soft plastic state is reduced by 41%. To further clarify the mechanism of the pre-support and carry out the parameter design of the pre-support in silty clay strata under the condition of different water contents, sub-classification of the silty clay in the Harbin metro tunnels is required. Therefore, the silty clay has been sub-classified, and the mechanical parameters presented in Table 1 under different subclass conditions have been suggested according to the laboratory test results and geological surveying.

3.2. Simulation of the support structure In this project, the bench method was adopted in the construction of the interval tunnel, and the core soil was reserved for the surface of the tunnel. The initial supporting structure consists of a steel grid, steel meshes, and sprayed concrete. The steel grid is 22 mm in diameter in the main bar and 0.75 m in spacing. The steel meshes are 8 mm in diameter and 200 mm in spacing for both the longitudinal and axial directions. The sprayed concrete has a thickness of 250 mm, and the early uniaxial compression strength is 25 MPa. After completion of the tunnel excavation, the steel grid is erected, the steel mesh piece is laid, the advanced small pipes and locking anchor pipes are applied, and the concrete is sprayed. The small pipes are made of common steel pipes with a diameter of 42 mm, thickness of 3.25 mm, and length of 3.0 m. The circumferential spacing is 30 cm in the 120° of the crown, with the camber angle of 15°. When the lower step surface advances a step length, then the erection of the steel grid is completed and the concrete is sprayed. Fig. 5 shows the simulation model of the initial lining structure. The composite supports of steel grids and sprayed concrete completely develop the deformation capacity of the soil around the tunnel in the process of excavation and supporting by using the bench method in the silty clay strata. Therefore, unlike the traditional numerical modelling method, the support structure cannot be simply simulated by an entity unit or a single structural unit. In the early stage of the initial support, the strength of the sprayed concrete is relatively low, and the surrounding rock load is mainly borne by the steel grid. Meanwhile, the front end of the advanced small pipe is also linked with the steel grid. Therefore, it is evident that the stress characteristics of the steel grid at

3. The establishment of a numerical model Numerical simulations, using the code FLAC (Itasca Inc, 2000), were performed to clarify the mechanism of an advanced small pipe support, simulate the working conditions under different sub-grade conditions, and further determine the advanced support scheme of silty clay under different sub-grade conditions. Typical construction sections in practical engineering were selected as the prototypes for the numerical models, and field test were carried out to verify the rationality and accuracy of the numerical results. 3.1. Numerical simulation model The numerical model was established based on the site construction interval, and the chainage 1 from DK13+950 to DK14+050 of Harbin Metro Line #1 was selected, where the average buried depth of the overlying soil on the top of the tunnel is approximately 20 m. The surrounding soil of chainage 1 belongs to class V, in which the formation is mainly silty clay in the hard plastic state. The surrounding soil of chainage 2 belongs to class VI1, in which the formation is mainly silty clay in the plastic state. Additionally, the stable groundwater is approximately 10–30 m deeper than the tunnel, which means that the tunnel construction will be unaffected by the groundwater. In addition, Table 1 Parameters of silty clay in different subgrade. Parameters Subgrade

Void ratio, e

Density, g (cm3)

Water content, w (%)

Plastic limit, PL (%)

Liquid index, IL

Cohesion, c (kPa)

Friction angle, φ(°)

Poisson’s ratio, μ

Deformation modulus, E0 (MPa)

Ⅴ VI1 VI2

0.6–0.7 0.7–0.8 0.8–0.9

1.95 1.90 1.85

21–24 24–29 30–34

18.5–22.4

0.05–0.25 0.25–0.75 0.75–1

40 25 20

20 19 18

0.33–0.35 0.35–0.38 0.38–0.43

33 19 13

4

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Fig. 4. Three-dimensional numerical calculation model.

following section). In view of this, the simulation unit of steel grid should not only meet the requirements of a geometric structure to generate a reasonable and effective stiffness and strength response, but also be able to reflect the complex mechanical characteristics, such as the steel axial stress, shear force, and bending moment. Therefore, the equivalent box beam is used to simulate the steel grid structure, as illustrated in Fig. 6. An equivalent method of strength and stiffness is used to simulate the sprayed concrete and steel meshes using solid units. The advanced small pipe is simulated by a pile element. The diffusion radius of the grouting reinforcement area is 0.25 m, and the strength enhanced solid element is used to simulate the grouting reinforcement area. The geometric parameters of the equivalent box girder and the mechanical parameters of the initial support structure of the grid arch are displayed in Tables 2 and 3, respectively.

4. Analysis of numerical results 4.1. Checking of numerical calculation model To verify the rationality of the numerical calculation model and accuracy of the calculation results, the ground and crown settlement data were monitored on the site of phase III in Metro Line #1. In addition, steel grid stress meters were installed in the grid main bar to monitor the internal force of the initial lining structure. Earth pressure boxes were embedded between the lining structure and the surrounding

Fig. 5. Initial lining structure simulation.

the initial stage of supporting must be analysed in detail. Field tests must also focus on monitoring the stress characteristics of the steel grid in the entire tunnel excavation and supporting process (see the

Fig. 6. Cross section of grid arch and the equivalent box beam. 5

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Table 2 Geometric parameters table of equivalent section of steel grid. Parameters

h (mm)

H (mm)

b (mm)

B (mm)

A (mm2)

Iz (mm4)

Iy (mm4)

HRB400

126

170

178

222

15,312

61,218,256

95,780,784

Table 3 Initial support structure parameters. Parameters Catalogue

Young’s modulus E (GPa)

Poisson’s ratio μ

Stiffness L (MPa/m)

Cohesion c (kPa)

Friction angle φ(°)

Steel grid Small pipe Reinforced zone Spray concrete

210 106 0.03 20

0.3 0.3 0.3 0.2

180 180 – –

– – 60 –

– – 30 –

Table 4 Field monitoring scheme used for this study. NO.

Monitoring items

Instrument

Monitoring sections

1

Ground surface

Total station

2 3 4

Crown settlement Steel grid axial stress Surrounding earth pressure

Total station Stress meter Pressure box

DK14+011, DK14+026, DK13+971, DK14+011, DK14+026,

Fig. 8. Ground surface settlement versus dimensionless distance to monitoring section from numerical results compared to the field monitoring data.

DK14+017, DK14+033 DK13+977, DK14+017, DK14+036

of the numerical calculation model and the calculation results. Furthermore, the field-measured values and numerical results of the tunnel excavation in hard plastic state silty clay with and without advanced small pipe support were later compared and analysed. Fig. 8 displays the ground settlements of four monitoring sections in DK14+011, DK14+017, DK14+026, and DK14+033. It can be seen that the ground settlement above the soft soil tunnel has a larger range of influence according to the field-measured data. In addition, an initial displacement of was generated in front of the tunnel face approximately 5 times the hole diameter. The numerical results predicted the variation and size of the ground settlement well compared with the measured data. The numerical calculation results were used to analyse the effect of the advanced small pipe support on the ground settlement because of the uncontrollable factors and measurement errors during the process of on-site monitoring. Compared with the results of the numerical calculation, it was found that the effect of the advanced small pipe on the surface subsidence was less than 1 mm, and it can be ignored, which is also a distinct difference between the advanced small pipe and the advanced pipe shed. In the actual construction, the initial monitoring value of the crown settlement was usually obtained from a certain distance behind the tunnel face due to the limited space during construction and the progress requirements of the project. The comparative analysis of the

soil to monitor the surrounding soil pressure of the initial lining structure. The test monitoring project is presented in Table 4. Due to the large difference in stiffness between the surrounding soil and the earth pressure box, the contact between the soil and the earth pressure box may be poor during the earth pressure monitoring process. Therefore, a “sandwich” type testing device is used to bury the earth pressure box in the middle of the two steel pallets. The inside pallet was fixed on the whole plane of the surrounding soil, while the outside pallet was welded onto the steel grid. The field tests exhibited that the method not only effectively solved the problem of poor soil stiffness and the flow of extrusion, but also prevented the possibility of the shotcrete inclining to the working face of the pressure box, thereby improving the test precision. The monitoring instruments were installed at the crown, arch shoulder, and arch waist at each monitoring section. The schematic and actual installations are shown in Fig. 7. The data from each monitoring instrument corresponding to the field tests were numerically extracted and used to verify the rationality

Fig. 7. Arrangement sketch and actual installation effect of monitoring element. 6

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Fig. 9. Crown settlement versus propelling distance of the tunnel face from numerical results compared to the field monitoring data.

measured data and numerical results of the vault settlement is shown in Fig. 9. It is worth noting that the crown settlement occurred before the tunnel face reached the monitoring section, which is the same as the ground settlement. However, it is impossible to monitor the initial settlement in the actual construction process. In other words, the monitored crown settlement value of the project site is only a part of the actual settlement value. According to the discovered rule of crown settlement, many scholars (Panet, 1995; Hoek, 1999) obtained the full time curve of the crown settlement by fitting the monitored values and retrieving the surrounding soil parameters. Sun (2014) pointed out that the actual monitoring value of the crown settlement of the soft surrounding rock is only 30%–50% of the total settlement value. Furthermore, the field-measured data can be described by curves in a full time subsidence diagram as shown in Fig. 9. Although the measured crown settlement curve has great discreteness, the numerical calculation results reflect the rule and size of the actual crown settlement well. In addition, the control effect on the crown settlement of the advanced small pipe is more obvious in the initial stage of the excavation. Compared with the data without the pre-support, the pre-support measures could reduce the settlement value in the initial stage of the excavation by approximately 22%, and the control effect on the crown settlement occurred before the excavation of the tunnel face. To verify the rationality of the supporting structure in the numerical model, the axial stress of the beam element in the numerical model at the crown, the arch shoulder, and the arch waist were extracted for a comparison with the field-measured data. Because of the installation of the monitoring elements and many uncontrollable factors in the process of the steel grid installation, the monitoring data for the axial stress of the steel grid were discrete. Due to the limited to the length of this article, only two groups of monitoring data in DK13+971 and DK13+977 were selected for analysis (see Fig. 10). From Fig. 10, it can be seen that the stress of the steel grid tends to be stable when the tunnel face is approximately 5 times the diameter of the tunnel. Based on Fig. 10(a) and (b), the numerical results could be better in accordance with the change law of the axial stress of the grid in the actual engineering process with pre-support. As shown in Fig. 10(c), the average axial stress of the grid with pre-support is approximately 1.5 times higher than the average stress without the pre-support. This shows that the steel grid can bear a greater pressure on the surrounding soil under the pre-support of the advanced small pipes. The application of advanced small pipes could impact the stress pattern of the initial support structure, so that the initial support structure could play a supporting role as early as possible, which is equivalent to shifting the initial support structure to an earlier time. The axial stress on the steel grid at the crown and the arch shoulder without pre-support is obviously lower than that with the pre-support, but the axial stress at the arch waist is not changed much. This is because the setting of the locking anchor pipes can meet the strength requirements during the numerical calculation, and the steel grid of the upper step took the main pressure of the surrounding soil with the action of the locking anchor

Fig. 10. Steel grid axial stress versus dimensionless distance to monitoring section. (a) Numerical results without pre-support compared to the field monitoring data in DK13+971; (b) numerical results with pre-support compared to the field monitoring data in DK13+977; (c) numerical results without presupport compared to numerical results with pre-support.

pipes when the initial support was not closed in a ring. Therefore, in the actual construction process, the quality of the anchor bolts must be ensured to guarantee the effectiveness of the pre-support. It should be noted that in the numerical calculation, it is difficult to monitor the interaction resistance between the initial support structure and the surrounding soil. Therefore, the support structure was regarded as a uniform elastic body by means of the strength equivalent method (see Appendix A), and the support resistance was calculated by the internal force of the supporting structure from the numerical 7

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Table 5 Design table of numerical calculation working condition. Subgrade Pre-support scheme

V1

VI2

VI2

Without pre-support Advanced small pipes Grouting reinforcement

Case1-1 Case1-2 –

Case2-1 Case2-2 Case2-3

Case3-1 Case3-2 Case3-3

4.2. Calculation results analysis The rationality of the numerical model was verified by comparing it with the field monitoring data. It was observed that the pre-support primarily altered the bearing mode of the primary support, which caused the primary support to bear more surrounding soil load earlier (Dias, 2011). To further study the influence of the advanced small pipe support structure in front of the tunnel face in a silty clay layer under different subclass conditions, the numerical simulation of the tunnel excavation and supporting process was carried out for different subgrade conditions with different advanced support schemes. The specific calculation conditions considered are shown in Table 5. The crown settlement and the horizontal displacement of the tunnel face were analysed in silty clay layers under different subgrade conditions (Figs. 12 and 13). As shown in Fig. 12, the control effect of the pre-support on the crown settlement is not evident for the condition of subgrade V in silty clay strata, while the control effects of the advanced small pipe on the crown settlement for subgrades VI1 and VI2 reached 14% and 18%, respectively. Furthermore, when the advanced small pipe was combined with the grouting reinforcement, the control effects on the crown settlement reached 24% and 34%. Fig. 13 shows that the horizontal displacement of the tunnel face began from an area that is double the hole diameter of the tunnel face. In addition, the weaker the surrounding soil is, the greater the horizontal displacement of the tunnel face will be. The same rule holds for the crown settlement; the worse the condition of the formation is, the more obvious the effect of the pre-support on the horizontal displacement of the tunnel face will be. Table 6 presents the final value of the axial stress on the steel grid under different conditions. Table 6 shows that under the same supporting scheme, the state of the silty clay has a negligible influence on the stress characteristics of the steel grid, but the different pre-support methods in the same stratum have a great influence on the force form of the grid. This is because the stress release rate of the surrounding soil was identical under the same excavation support scheme. However, the

Fig. 11. Earth pressure acted on the support structure versus dimensionless distance to monitoring section. (a) Calculated results without pre-support compared to the field monitoring data in DK13+971; (b) calculated results with pre-support compared to the field monitoring data in DK13+977.

calculation. Fig. 11(a) and (b) show the measured results of the supporting resistance and the calculated values with and without the presupport, respectively. It can be seen that the measured values of the surrounding soil pressure are discrete. When there was no pre-support of the advanced small pipes, the pressure changes in the surrounding soil at different monitoring points were basically the same as they were with the pre-support. When the advanced small pipe was used, the earth pressure at the crown decreased significantly, and the earth pressure at the arch shoulder increased significantly. However, the actual monitored pressure in the surrounding soil was unaffected by the pre-support measure. The pre-support structure first carried the load of the soil in front of the tunnel face and passed it to the initial lining grid, so the internal force of the grid increased at the initial stage of supporting. It should be noted that the pre-support structure did not change the surrounding soil pressure in the excavation section, but only the interaction between the surrounding soil and the initial support structure. In general, the back calculation of the numerical steel grid stress can reflect the change process of the support resistance to a certain extent, but the calculation results are greater than the actual monitoring values of the support resistance.

Fig. 12. Crown settlement versus propelling distance of the tunnel face from numerical results in different cases. 8

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Fig. 14. The axial force of the advanced small pipes at the crown.

Fig. 13. Horizontal displacement versus propelling distance of the tunnel face from numerical results in different cases.

4.3. Analysis of the mechanism of the pre-support deformation produced by the surrounding soil during stress release was quite different in silty clay layers under different subclass conditions. The load acting on the steel grid increased obviously after the application of the advanced small pipe, especially in the crown and the arch shoulder of the grid. The stress of the grid increased by 32% for the condition of subgrade V in silty clay strata. Furthermore, the stress of the grid shaft increased by 51% and 42% with the grouting reinforcement for subgrade VI1, as well 67% and 53% for subgrade VI2. It is worth noting that the pre-grouting reinforcement reduced the axis stress of the grid, which means a reduction in the load acting on the initial lining structure. In addition, the grouting reinforcement is effective in controlling the crown settlement and horizontal displacement of the tunnel face (see Figs. 12 and 13). Therefore, it could be considered that the advanced grouting reinforcement formed an advanced support arch in front of the tunnel face, which bore the stratum load. To further analyse the mechanism of the small pipes in the silty clay layer, the data on the axial force of the pipe at the crown were extracted and analysed in the numerical calculation as shown in Fig. 14. The axial stress of the small pipe increased with the propelling of the tunnel face. However, the growth rate of the force on the small pipes under different subgrade conditions is different: the worse the soil condition is, the faster the increase in the axial force is, and the peak axial force on the advanced small pipes for the condition of subgrade VI2 in silty clay stratum is approximately twice that of subgrade V. When the circulating footage is greater than the length of the pipe in front of the tunnel face, the axial force on the small pipe reduces, finally stabilising under the initial lining support. If the grouting reinforcement was applied combined with the advanced small pipe, the axial force on the advanced pipe will become smaller after the propelling of the head. The supporting arch, formed by the advanced grouting, is considered to support a larger part of the load, thus further reducing the load acting on the pipes.

Through the analysis of the crown settlement, the horizontal displacement of the tunnel face, the axis stress of the steel grid, and the force of the small pipes, it is known that the advanced small pipe made the stress state change after the excavation in front of the tunnel face, transferring the load acting on the tunnel face to the initial support structure. After the grouting was completed through the small pipes, the soil above the tunnel face could be reinforced, and a continuous and stable arched shell was formed ahead of the tunnel face. To further clarify the effect of the advanced small pipe support and the pregrouting reinforcement on the stability of the tunnel face, the canopy frame model of the advanced small pipe and the arch model of the grouting reinforcement were constructed (Muraki, 1997) as shown in Fig. 15(a) and (b). The single pipe was regarded as an elastic foundation beam (see Appendix B) applied to the soil between the initial lining structure and the tunnel face. The axial strain was calculated based on the axial force on the pipe. Thus, we can calculate the load of the foundation, which is eventually applied to the front of the tunnel face. It can be seen from Fig. 15 that the advanced small pipe grouting reinforcement can fill and compact the loose zone in front of the tunnel face after excavation, promoting the soil mass in the loose zone to form a balanced arch in a short duration. The advanced small pipe plays the role of a scaffolding beam in the longitudinal direction of the tunnel. In general, the pre-support transferred the loosening soil load in front of the tunnel face to the initial support structure and improved the early utilization ratio of the initial lining structure. Furthermore, the grouting measure reinforced the bearing arch, which reduced the distance between the two supporting arch feet. This further reduced the vertical load of the tunnel face and ensured the safety and stability of the tunnel face. 5. Advanced small pipe support design Determining reasonable leading support parameters for the silty clay stratum provides significant benefits in terms of construction safety and the economic gain, by clarifying the supporting mechanism of the

Table 6 Stress statistics table of grid shaft under different working conditions. Position

case1-1

case1-2

case2-1

case2-2

case2-3

case3-1

case3-2

case3-3

Crown Arch shoulder Arch waist Average value

70.50 40.51 40.27 50.43

96.28 63.67 39.83 66.60

59.78 33.24 40.77 44.60

101.21 60.98 39.83 67.34

95.49 53.68 40.49 63.22

59.51 30.88 47.98 46.12

123.84 60.41 46.41 76.89

109.24 57.25 44.72 70.40

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Fig. 16. Calculation model of tunnel face stability.

to transfer the excavation stress to the steel grid that has been erected in the rear. Therefore, the stability of the tunnel face is regarded as a problem of slope stability under the transmission and release load. The plastic shear limit state of the tunnel face was treated as the critical failure state considering the influence of the surrounding soil, geometry size of the tunnel, and depth of the buried tunnel. The calculation model of the tunnel face stability is presented in Fig. 16. To simplify the calculation, it is assumed that the sliding region in front of the tunnel face is three prismatic wedge-shapes ABCDEF. According to the force characteristics of the slider, the following assumptions are established: (1) When the sliding region is in the limit equilibrium state, the two sides of ABF and CDE are subjected to static earth pressure, the bottom face of ADEF is subjected to active earth pressure, and the failure of the sliding surface meets the Mohr-Coulomb failure criterion. (2) The shape of the fracture surface is symmetric along the central axis of the tunnel, and the top surface BCEF is horizontal. The angle of the sliding surface ADEF is equal to the angle of the rupture of the Rankine's active state, that is: θ = 45° + π/2. (3) The sliding tracks on the side of the region are AG and DH, where G and H are the midpoints of BF and CE, respectively. According to these assumptions, the force acting on the three prismatic wedge-shape sliding regions is deduced as follows.

Fig. 15. Schematic of supporting mechanism of pre-support. (a) The arch model (A-A section); (b) the canopy frame model of small pipes.

(1) Normal pressure on the bottom surface:

advanced small pipe. Therefore, it is necessary to quantitatively judge the necessity and rationality of advanced small pipe support under different subgrade conditions in silty clay strata, in order to rationally design the pre-support parameters. The pre-support structure must be set to ensure the stability of the surrounding rock during tunnel construction in soft and weak strata, especially the stability of the tunnel face. The instability of the tunnel face directly affects construction safety and project progress, and an instability can cause secondary disasters. The current research on the stability of the tunnel face is significant (Lü et al., 2018; Zingg and Anagnostou, 2018). However, in actual engineering construction, the displacement is often used as the control standard for the stability of the tunnel face, which leads to large errors. In the process of auxiliary construction with advanced small pipes, the effect of the pipe will be weakened or even lost, and the tunnel face is prone to collapse when the excavation step is long, or the soil quality is poor. In severe cases, the overall tunnel face will collapse, so it is necessary to analyse the stability of the face.

N1 =

∫h

h2

1

K a γzadz =

1 K a γa (h22 − h12), 2

(1)

where Ka, γ, and z are the active soil pressure coefficient, bulk density (kN/m3), and buried depth (m), respectively. The width of the tunnel face (m) is represented by a, and h1 and h2 are the buried depths (m) on the top and bottom of the tunnel face, respectively. Area of the bottom surface ADEF:

A1 =

ab , sin θ

(2)

where b is the height of the tunnel face (m). (2) Tangential force on the bottom surface:

T1 = cA1 + N1 tan φ ,

(3) 2

where A1 and N1 are the area (m ) and the normal pressure (kN) of the bottom surface ADEF. Substituting Eqs. (1) and (2) into Eq. (3) yields:

T1 = 5.1. Analysis model of the pre-supporting effect

abc 1 + K a γa (h22 − h12) tan φ sin θ 2

(3) The normal pressure on the lateral surface

In the advanced small pipe support system, the effect of the pipe is 10

(4)

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h2 − z π b tan ⎛ − θ⎞ dz h2 − h1 ⎝2 ⎠ K γb π = 0 tan ⎛ − θ⎞ (h2 − h1 )(h2 + 2h1), 6 ⎝2 ⎠

N2 =

∫h

h2

1

strata, the stability of the tunnel face can be maintained without the advanced small pipe support. For the condition of subgrade VI1, the presupport must be applied to ensure the stability of the tunnel face, but the grouting reinforcement measures are not needed. For the condition of subgrade VI2, the advanced small pipe support and grouting reinforcement must be used at the same time to ensure the stability of the tunnel face. The advanced small pipe support schemes in silty clay strata under different sub-grade conditions have now been defined, and the ‘Application’ is adopted in Table 7 for the marking and illustration of different working conditions. It is worth noting that the displacement of the tunnel wall for the condition of subgrade VI2 in a silty clay stratum is too large, and the overall deformation value of the surrounding soil is larger than 100 mm (see Fig. 12). Therefore, it is necessary to consider the advanced pipe shed support or deep hole grouting reinforcement technology to reinforce the tunnel face when the tunnel excavation is under the pile foundations, the existing pipelines, and other risk sources. In this way, the surrounding soil deformation during tunnel excavation can be effectively controlled.

K 0 γz

(5)

where K0 is the static soil pressure coefficient of the soil. The area of lateral surface CDE:

A2 =

b2 π tan ⎛ − θ⎞ 2 ⎠ ⎝2

(6)

(4) Lateral tangential force:

T2 = cA2 + N2 tan φ

(7)

Substituting Eqs. (5) and (6) into Eq. (7) yields:

T2 =

K γb π b 2c π tan ⎛ − θ⎞ + 0 tan ⎛ − θ⎞ (h2 − h1 )(h2 + 2h1)tanφ 2 6 ⎝2 ⎠ ⎝2 ⎠

(8)

(5) The supporting force of the core soil in front of the tunnel face is represented by:

N3 = cA3 + W3 tan φ ,

6. Conclusion

(9)

where A3 is the area of the core soil bottom surface, and W3 is the weight of the core soil. Therefore, the stability coefficient of the tunnel face can be expressed as:

K=

T1 + 2T2cosα + N3cosθ , (W + P )sinθ

This study involves laboratory tests to investigate the effect of changes in clay and water content of silty clay on its physical and mechanical parameters. Subsequently, the subgrade classification of silty clay was completed. Comprehensive analysis of numerical calculations and field tests clarifies the mechanism of the advanced small pipe support. An analysis model of the pre-supporting effect was established to determine the design of pre-supporting schemes in silty clay strata under different subgrade conditions. The laboratory tests illustrate that the percentage of grains with diameters less than 0.075 mm is greater than 90% for the Harbin metro soil mass, and the plastic index ranges from 10.1 to 14.3, which classifies it as silty clay. Within a certain range of clay content, the shear strength of silty clay decreases with the increase in water content. The suggested parameters of silty clay for different sub-classifications were used in numerical simulations to study the mechanism of advanced small pipe support. The rationality of the numerical calculation model and the accuracy of the calculation parameters were verified through the field test data. With the existence of the advanced small pipe, the loose soil load in front of the tunnel face was transferred to the initial support structure, which improved the early utilization of the lining structure. In addition, the advanced small pipe grouting increased the range of the bearing arch, shortened the distance between the supporting arch feet, and reduced the vertical load acting on the tunnel face. To clarify the action effect of the advanced small pipe, an evaluation and analysis model of the advanced support was established. Thereafter, a reasonable pre-supporting design scheme was provided in silty clay strata under different subgrade conditions. For the condition of subgrade V in silty clay strata, the stability of the tunnel face can be maintained without the advanced small pipe support. For the condition of subgrade VI1, the advanced small pipe support must be applied to ensure the stability of the tunnel face, but the grouting reinforcement measures are not required. For the condition of subgrade VI2, the advanced small pipe support and grouting reinforcement must be used simultaneously to ensure tunnel face stability.

(10)

where

cotθsinθ ⎞, α = arctan ⎛ ⎝ 2 sinθ − cotθcosθ ⎠

(11)

where W and P are the weights of the sliding region and the upper overload (kN), respectively. When the advanced small pipes were applied in front of the tunnel face, the calculation of the upper load was determined according to the force analysis of the advanced pipes in Appendix B. When the small pipes were not applied, the overloading was determined using the empirical formula of the vertical uniform pressure from the surrounding rock according to the code for the design of rode tunnels (JTGD702004).

q = 0.41 × 1.79 s × γ ,

(12) 2

where q is the vertical uniform pressure in the tunnel vault (kN/m ), s is the grade of the surrounding soil, referring to the GB 50307-2012, and γ is the bulk density (kN/m3) of the surrounding soil. According to the technical code for building slope engineering (GB50330-2002), the stability coefficient K for a grade I slope cannot be less than 1.30. If K is greater than 1.30, it indicates that the soil of the tunnel face meets the strength requirements; conversely, if K is less than 1.30, the strength requirements are not satisfied. Therefore, the excavation plan must be optimized, stiffness of the initial support should be strengthened, and time of the initial support should be accelerated. The tunnel was excavated by the bench method, so the stability of the upper face was particularly important in the actual engineering. The step span and step height were considered in the calculation to be the width and height of the slip mode, respectively. Thus, a = 6.2 m, and b = 3.1 m. The dimensions of the core soil were 3.2 m × 3.2 m × 1.4 m (length × width × height). The stability coefficient of the tunnel face was calculated under different working conditions as displayed in Table 7.

Acknowledgements The authors are grateful to the editor and reviewers for critically reviewing and suggesting improvements for the manuscript. This research was financially supported by the National Natural Science Foundation of China (Grant No. 41572275), and the Natural Science Foundation of Shandong Province (Grant No. ZR2012EEM006).

5.2. Advanced support design scheme Table 7 illustrates that for the condition of subgrade V in silty clay 11

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Table 7 The stability coefficient of the tunnel face under different working conditions. Working conditions

Resistant coefficient, k (MPa/m)

Shear modulus, Gp(kN/ m)

Unit weight, γ(kN/ m3)

Axial force, F (kN)

Overlying load, P (kN)

Stability coefficient, K

Remarks

Case1-1 Case1-2

200

1200

19.5

– 17.46

1.97 1.30

2.05 3.09

Application

Case2-1 Case2-2 Case2-3

150

1000

19.0

– 23.01 22.42

3.51 1.67 1.53

0.96 2.00 2.18

Case3-1 Case3-2 Case3-3

80

– 41.38 33.85

3.48 2.49 2.04

0.89 1.24 1.51

800

18.5

Application

Application

Fig. A1. Sketch map of the equivalent cross section.

Appendix A. Equivalent calculation of support resistance In this project, the initial support structure adopted the combined support of a grid arch frame and sprayed concrete. The equivalent section method (Carranza and Diederichs, 2009) was used to treat the different support forms of the support members with uniform thickness, and the equivalent diagram of the cross section is shown in Fig. A1. After the equivalent treatment, the equivalent elastic modulus Eeq and thickness teq of the supporting structure can be expressed as follows:

Eeq =

(D1 + D2 ) bteq

teq =

12

(A1)

K1 + K2 , D1 + D2

(A2)

where D and K are the compressive stiffness and flexural rigidity of a single supporting member, respectively. When the single component is calculated, the stiffness can be expressed as follows:

D = EA (1 − μ2 )

(A3)

μ2 ),

(A4)

K = EI (1 −

where E is the Young’s modulus of the support material, μ is the Poisson ratio of the support material, I is the moment of inertia of the supporting component, and A is the cross sectional area of the supporting component. When studying the load of the grille support in the composite support structure, it is necessary to treat the steel grid equally as an elastic support with uniform width of b1 (b1 = 0.75 m), the same as the equivalent treatment of a combined support (see Fig. A1). Furthermore, Eqs. (A1) and (A2) should be calculated using a single value. The force calculation formula of single supporting member in a combined support system can be expressed as

Pl =

As (D1 + D2 ) σ , 2rl D1

(A5)

where As is the cross sectional area of the steel grid, D1 and D2 are the compressive stiffnesses of the steel grid and sprayed concrete, respectively, σ is the internal force of the steel grid, which is taken as the value of the grid axis force measured in the field during the calculation, and rl is the radius of the tunnel equivalent to a circular section, which is taken as 3.25 m during the calculation. The supporting parameters of the lining structure are Table A1 Support structure parameters. Steel grid

Spray concrete

Es(GPa)

As(cm2)

Is(m4)

μs

tseq(cm)

Ec(GPa)

Ac(cm2)

Ic(m4)

μc

tc(cm)

210

15

9.78e−6

0.3

28

20

1680

9.67e−4

0.2

25

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Fig. B1. Axial force analysis model of the advanced small pipe.

presented in Table A1. Appendix B. Analysis model of the advanced small pipe The results of the numerical calculation illustrate that the stress of the advanced small pipe near the tunnel face was maximum. The single steel pipe was considered the research object, and the elastic foundation beam was used to simulate the stress of the steel pipe as shown in Fig. B1. The A end located on the initial support structure was regarded as an elastic fixed end with a vertical displacement of ω0 and corner θ0. For the AB section that has been excavated but not supported, the surrounding soil pressure q(x) is entirely borne by the pipes. In the BC section of the slack area in front of the tunnel face, the pipe was subjected both to the pressure of the surrounding soil q(x) and the elastic resistance of the foundation p(x). In the analysis model shown in Fig. B1, the elastic resistance of the foundation p(x) can be calculated by Pasternak’s (1954) method as Eq. (B1):

p(x ) = kω(x )− Gp

dω2(x) dx 2

(B1)

The flexural control differential equation of the elastic foundation beam in the BC segment can be expressed as:

dω4 (x) dω2(x) EI − Gp b2 + kb2 ω(x ) = b2 q(x ), dx 4 dx 2

(B2) -8

4

where E is the Young's modulus of the pipe (see Table 3), I is the moment of inertia of the pipe (I = 7.48 * 10 m , and b2 is the width of the elastic foundation beam, which is taken as the diameter of the pipe (b2 = 42 mm). Gp and k are the shear modulus and resistance coefficient of the foundation, respectively, as displayed in Table 7. According to the geometric equation of beam bending (Sun et al., 1994), the formula for calculating the longitudinal strain of the steel pipe inner wall can be expressed as:

D dω2(x) ε (x ) = ⎛ − δ ⎞ , ⎝2 ⎠ dx 2

(B3)

where D and δ are the outer diameter and the thickness of the small pipe, respectively. Therefore, it is possible to further deduce the deflection differential equation by using the expression for the axial strain of pipes as Eq. (B4):

ω(x ) =

ε (x ) 2 x + c1 x + c2 D − 2δ

(B4)

Because the range of influence of the tunnel excavation is limited in a short time, it is considered that the end part of the pipe inserted into the soil has not been displaced and rotated after the tunnel face has just been excavated. Therefore, the boundary condition of the differential equation was obtained:

ωC |x → l = 0 ⎫ θC |x → l = 0 ⎬ ⎭

(B5)

The expression of the coefficient can be obtained by introducing the boundary condition into Eq. (B4):

c1 = c2 =

−6ε (x) ⎫ D − 2δ 9ε (x) ⎬ D − 2δ ⎭

(B6)

Therefore, we can determine the deflection equation ω(x), elastic resistance equation p(x) (see Table 7), and pressure equation q(x) of the surrounding soil in the BC segment of the pipe can be determined. The value of the axial strain ε(x) was calculated according to the maximum axial force during the process of small pipe supporting (see Fig. 14) to verify the calculation results.

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