Numerical simulation and analysis of the three-step excavation of an extra-large cross section and a low flat-ratio railway tunnel

The Xinbaishiyan tunnel in the reconstruction Chengdu–Kunming railway Ermeishan-Mipan section mainly runs through dolomite with dolomitic limestone, with an excavation area of 260 m2, a maximum span of 22.3 m, a maximum height of 14.4 m, a vector height of 7 m, and a rise-span ratio of 0.31. The tunnel has an extra-large cross section, and it is a low flat-ration railway tunnel. This paper mainly describes the finite element analysis for this tunnel excavation that was used to guide the construction. Finite element software was used to model the tunnel according to the engineering geological conditions of the tunnel. These engineering geological conditions included the rock mass, system bolts, middle pipe shed, steel arch and shotcrete, grouting layer, second lining and so on. Nonlinear construction phase analysis was adopted. The results showed that the maximum vertical deformation of the tunnel vault and the middle of the invert was about 34 mm. The vertical deformation of the tunnel could be divided into an acceleration deformation section, linear deformation section, deceleration deformation section, and stable deformation section. The maximum horizontal deformation in the middle of the side wall was about 12.3 mm. Under the effect of the initial support, the equivalent stress of the side wall gradually increased with the excavation of the steps and the increase in the support structure. The axial force of the bolt in the middle of the side wall was larger than that in other places and the axial force of the middle pipe shed went along with the excavation of the tunnel in waves. The steel arch and the shotcrete had the maximum effective stress at the arch shoulder, which played the role of the deformation and pressure for the surrounding rock. During the construction, the length and height of the three-step method had to be set reasonably. The middle pipe shed and the system bolt supported the rock mass together. In the construction of the extra-large cross section and the flat tunnel, there was no need to set up temporary support, which was convenient for mechanical excavation.


Introduction
The stability of surrounding rock is very important during tunnel construction. To ensure the stability of surrounding rock excavation, appropriate excavation methods should be selected according to the surrounding rock grade and water seepage. After selecting the construction methods based on engineering experience during large-span tunnel construction, the selected excavation methods should be analyzed to ensure the stability of the tunnel excavation. For rail tunneling, there are many other excavation processes available, some of which have been addressed. The median septum method is also known as the CD method. This approach requires excavating each portion of the tunnel directly, followed by the middle diaphragm. After that, the Communicated by Vicente Garcia Diaz.
& Shifeng Xue xuesf@126.com drilling is from the other portion is completed. This process uses a steel supports and formwork as a center diaphragm to divide tunnel space. Method of the middle cross-diaphragm (CRD) is a long-span tunnel with weak surrounding rock. The cross section of the tunnel is divided into left and right sections with the center diaphragm. The left and right sections are divided into two or more sections. First, the upper part of one side of the tunnel is excavated, and the center diaphragm and the transverse diaphragm are applied. Then, the upper part of the other side of the tunnel is excavated to complete the transverse diaphragm construction. Finally, the transverse diaphragm and the center diaphragm are dismantled in an orderly way. The extra-large cross-section tunnels always include a tunnel with more settings in the import and export as station tunnels and a tunnel with surrounding rock breakage due to import and export and complicated geological conditions. This produces construction difficulty and the need to adopt a numerical simulation and field test the reliability of the tunnel construction. China has produced certain achievements in the study of such tunnels. Xi et al. (2015) conducted a comparative study on the three-step excavation method and the double-side wall diversion pit method of a long-span tunnel and concluded that the double-side wall diversion pit method produced less ground settlement than the step-method and that the double-side wall diversion pit method was safer than the stepmethod. Zhang et al. (2018) studied the demolition of the temporary support of a secondary lining. They pointed out the evolution of the safety factor in each stage of the demolition and support, and they pointed out that the reasonable length of the one-time demolition and support of the double side wall diversion pit method was about 9 m. Wang and Mei (2017) made a comparative analysis of the step method, the center cross diagram (CRD), and double side-wall drift pilot excavation, and they proposed the excavation method of a three-step temporary invert plus vertical support. A border region to boundary proportion of a cross-sectional area to perimeter level of a cross-sectional area to perimeter average of a cross-sectional area. The stream is held at the necessary self-cleaning speed by the smaller cross box at the bottom. Attempting to control the structural deformation of the initial pillar as well as the residual stress of the starlight structure was easier with the ''cross path perpendicular shaft construction'' process. The actual construction showed that this method was efficient and fast.
China has built several extra-large cross-section tunnels. The exit section of the Xinkaotang tunnel of the Ganlong railway, completed in 2014, is the third-line tunnel of ''2 main lines ? 1 tie line.'' The maximum excavation width of the tunnel is 30.26 m, the maximum height is 16.94 m, and the maximum excavation area exceeds 390 m 2 . For the New Zhijiawan tunnel of the Yuxiang railway line II, the largest span is 22 m and the largest excavated area is 250 m 2 . The maximum excavation width of the Gongbei tunnel (Kontogianni and Stiros 2015) of the Zhuhai connecting line of the Hong Kong-Zhuhai-Macao bridge is 19 m, the maximum height is 21 m, and the excavation area is 337 m 2 . The Yingpan road tunnel (Shi et al. 2017) in Changsha city adopts advanced full-section pre-reinforcement, double-layer steel pre-support, and reasonably organized shallow excavation. The ultra-deep and largesection underwater tunnel was successfully excavated with a depth span ratio of only 0.46 and an area of 376 m 2 , which overcame the difficulties of multi-process and multisection in the construction of the ultra-large-section underwater tunnel. With the development of tunnel and underground space engineering, the number of long-span tunnels is increasing.
The construction of a large-section tunnel generally adopts the method of step excavation, and the main construction methods are: step method, middle wall engineering method [center diagram method (CD), CRD], single side-wall drift pilot method, double side-wall drift pilot excavation, cylinder hole method, wall hole method, etc. A drift is a tiny shaft that is drilled further into stone and whose segment is gradually expanded until it equals that about the tunnel. The pilot tunnel's representative sample is normally measured and guided adjacent to the goes deeper, with crossover splits at several places connecting this to the central pipeline's center line. It contributes to adequate sunlight to generate in the goes deeper. Cylinder-cut usually contains open spaces with just a circumference which are less active at dampening vibration. The smaller the blasting capacity, the longer the drilling period, and the higher the blasted efficiency, the greater the open space. Moreover, cylinder-cut usually contains open spaces with just a circumference which are less active at dampening vibration. The smaller the blasting capacity, the longer the drilling period, and the higher the blasted efficiency, the greater the open space. Further, the wall hole approach aids in the removal of rocky terrain from the crown and walls. The primary idea of developing a tunnelling drill template is to attain the highest amount of simple recognition and appropriately drilled holes. Its core principle is reliance on the auxiliary construction methods to translate a large section into a small cross section. The arch department is constructed first. Then the construction wall or wall arch construction occurs as soon as possible to have a better section tunnel closed loop. Then the excavation and inverted arch core soil occur, dismantling the temporary support. The conversion system forms the large cross-section tunnel. The main construction problem is a complex process of cohesion that is unfavorable to mechanization construction. The temporary support is difficult to remove, and the system conversion time is long.
The tunnel studied in this research was the Xinbaishiyan tunnel in the Reconstruction Chengdu-Kunming railway Ermeishan-Mipan section. The tunnel has an excavation area of 260 m 2 , a maximum span of 22.3 m, a maximum height of 14.4 m, a vector height of 7 m, and a rise-span ratio of 0.31. Because the three-step method was simpler than the double-wall guide pit method and mechanical excavation was available, there was no problem of system transformation caused by the removal of temporary supports. According to the engineering geological conditions of the Xinbaishi tunnel, the finite element method was used to analyze and study the three-step construction (Dammyr et al. 2017).

Project summary
The Xinbaishiyan tunnel in the reconstruction Chengdu-Kunming railway Ermeishan-Mipan section mainly runs through dolomite with dolomitic limestone, and the maximum depth is about 470 m. The lithology is mainly light gray, off-white middle thick block dolomite mixed with dolomitic limestone. Thin layers and bands of siliceous rocks are occasionally encountered, the rock strata affected by faults are broken, and the overall stability is poor. The tunnel inlet side is around 1200 m for the three-line tunnel station. The V level of the surrounding rock, rock trends, and oblique line was up to the angles of 45-56. The section of the tunnel is shown in Fig. 1. The components include: C30 shotcrete, 350 mm thick, section steel HW300 9 300 9 10 9 15 arch frame, with a spacing of 1000 mm, middle pipe shed, adopting a U76 steel pipe wall thickness of 7 mm, 8 m long, 400 mm spacing, self-drilling bolt adopting a U28 steel tube wall thickness of 6 mm, 4 m long, according to a 1000 mm 9 1000 mm arrangement, and C40 concrete lining thickness of about 900 mm. Groundwater types of bedrock fissure water, karst water, and covering layer pore water mainly occur in the dolomite and the fault fracture zone along the rock level and fault fracture zone to the next to the river discharge, narrow tunnel buried depth, and displacement for the tunnel construction. The finite element analysis did not consider the water. FEA is a method of understanding and quantifying the impact of realistic circumstances on a component or assembly using statistical formulas. Technicians may use these simulations, that are run using sophisticated software, to find possible problems in a layout, such as places of stress and problem areas. The finite element method (FEM) is a computational process of performing finite element analysis (FEA) on almost any natural entity. To fully comprehend and measure any physical phenomenon, along with systemic or fluid activity, thermal transport, acoustic waves, and biologically cell proliferation, mathematical function is needed. Partial differential equations are used to explain the majority of these systems.

Brief description of three-step tunnel excavation
As shown in Fig. 2, the three-step method was divided into three steps: the upper, middle, and lower steps and four parts of the invert. Each step was 5 m long and the distance from one step to the invert was 15 m. The construction process was: first the middle pipe shed was hit, and then the upper step À was excavated. After the upper excavation was completed, the initial support was applied for the upper hole body, namely the initial shotcrete. The steel arch was erected, and the rock bolt was hit. After the construction of the upper step reached 5 m, the left side`of the middle step and the upper core soilẃ ere excavated in order to provide the initial support for the step structure in the left side of the cave body with the same supporting structure À. After`construction to 1 m, the right part of the middle step was excavated in order to provide the initial support for the step structure in the right hole body. Afterˆ, the construction to 3 m, excavation occurred˜in the step of the core soil. After the˜was excavated 1 m, excavation occurred in accordance with thè andˆconstruction methods for the lower steps Þ þ. Then the excavation of the lower step of the core soil ¼, the upper, middle, and lower steps, retained a distance of 5 m. Finally, during the excavation of invert ½, the support structure had to be closed. The support structure closure and invert excavation and support had to be carried out in time. The excavation footage had to be 1 m. Midas GTS NX finite element software was used for modeling and analysis. The surrounding rocks were assumed to be continuous interstitium. GTS NX is specialized geotechnical research tool for 2D and 3D soil and rock fracture and strength, and also some surface runoff, complex movements, and soil-structure interactions. Software also offers, structural, and mine experts utilizing TS NX for research, evaluation, and modelling. It's developed to function with every geotechnical venture. The userfriendly interface would make it simple for existing customers to incorporate the app into their workflow. The shotcrete and the steel arch were simulated by the shell element with equal stiffness. The middle pipe shed was simulated by an implantable beam unit. The self-drilling bolt was simulated by an implantable truss element. The grouting layer and the second lining were simulated by the body element. The time-dependent creep of the surrounding rock was not considered, and the linear elastic constitutive model was adopted for the support system and the secondary lining. The linear elastic model is used to characterize materials which react to low strain in such a predictable way, with the strain relative to the stress. The constitutive theory of elastic deformation necessitates the specification of two boundary conditions based on experimental results. There seem to be a variety of compounds which contain pairs to choose from, all of which are generally clear. The most popular material parameters, as well as transformation equations amongst them are mentioned.

Plastic yield criterion
The Mohr-Coulomb yield criterion was applied, and the yield was based on the maximum shear stress. The Mohr-Coulomb (MC) failure mechanism is a collection of basic functions in shear stresses space that describe the constraints under which an isotropic material can fail, while ignoring the influence of transitional stress field. On the fault plane, MC can indeed be defined as a function of minor and major applied stress, or normal stress and shear stress. See Formula 1 for the yield function, where the range of the Lode angle was 0 ( h ( 60 . The yield failure surface is shown in Fig. 3.
In the formula, is the Lode angle, that is, the angle between the first principal stress and the deviatoric stress components in the principal stress space, J 3 ¼ s x s y s z þ 2s xy s yz s zx À s x s 2 yz À s y s 2 zx À s z s 2 xy is the third invariant of the stress tensor, and s x ; s y ; s z À Á is the stress deviation (¼ r À r mean ).

Related flow law
According to Mises's plastic potential theory, the components of the plastic strain increment were determined by the differential of the plastic potential function to the stress components. When the octahedral compressive force reaches a threshold value, the Mises criterion predicts gain. Von Mises parameters are dynamic viscosity autonomous and can be used to construct metallic cognitive function. However, fluid pressure has a significant influence on resources like rock, soils, and asphalt.
Or the matrix form In the formula, de p ij is plastic and should be an incremental tensor, og r ij À Á is the stress tensor, and dk is the proportionality constant.
There were two kinds of flow rules: correlation and discorrelation. The plastic potential function was assumed to be consistent with the failure function g r ij À Á ¼ f 0 r ij À Á of the flow law. The fact that the failure surface and the plastic potential energy surface coincided was called the correlative flow law. The plastic strain increment de p ij was orthogonal to the failure surface (plastic potential surface). All of the points of the initial stress r Ã ij of the soil had be within the plastic potential surface.

Elastic-plastic stress-strain equation
According to the failure criterion, the relationship between plastic stress and strain was: where f r ð Þ is the failure function and F ¼ f H ð Þ is the function of the hardening parameter H.
Equation (4) was substituted into Eq. (5), and the flow rule Eq. (3) was substituted into Eq. (5) to obtain: Equation (6) was substituted into Eq. (3): The corresponding relationship between the components of the plastic strain increment and the total strain component was given, and Eq. (7) was substituted into Eq. (4) to obtain: The solution method of the common nonlinear equation was adopted, and the convergence criterion was satisfied.

Model establishment
The rock parameters were selected according to the geological exploration data of the Xinbaishiyan tunnel in the reconstruction Chengdu-Kunming railway Ermeishan-Mipan section. The element material properties of the middle pipe shed, bolt support, steel arch, and shotcrete composite shell are shown in Table 1.
The width boundary of the calculated model was selected to be four times the tunnel span, with the height boundary reaching 100 m at the top of the tunnel, the bottom boundary reaching 50 m at the bottom of the tunnel, and a span of 22.3 m. Therefore, the total length of the established model boundary was 142 m, the total height was 164.4 m, and the tunnel depth was 60 m. The boundary conditions of the calculation model were as follows: the bottom surface was the vertical constraint, the upper boundary was the free boundary, a vertical pressure of 1400 kPa was loaded, the left and right boundaries were

Surrounding rock deformation analysis
The nonlinear construction stage analysis was applied to the model, which was divided into 49 construction stages, each of which was 1 m in depth. The tunnel support and excavation surface after 49 steps of excavation are shown in Fig. 5, and the tunnel deformation results are shown in Fig. 6. The challenge of surface settlement and deflection of surrounding rock triggered by construction operations, that can be solved by using dynamic monitoring and assessment of cavern surrounding material, which would be an effective tool for determining if the surrounding rock is secure and stable. The seismic activity of the tunnel and ground settling are primarily controlled based upon this curvature of the tunnel's surrounding rock. The simple process for measuring the supporting impact, directing the construction process, verifying the strength of the surrounding rock, and guaranteeing the quality of the project for deep tunnels is to use the dome dipping calculation. The soil excavation surface deformation trend was upward, and the excavation of the lateral and maximum deformation occurred in the second step in the central core soil surface. The maximum deformation was 42 mm (Zhou et al. 2019). The upper tunnel deformation was down, the lower deformation was upward due to the large span, and the tunnel was under the load. The deformation of the excavation face during the early supporting small, and the left side of the excavation face had far greater deformation. The early stage of the two lining concrete inverted arch deformations was small.

Vertical deformation
The vertical deformation cloud diagram of the tunnel after the 49th excavation step is shown in Fig. 7. The maximum settlement at the vault was 34.2 mm, and the upward deformation in the middle of the invert was 34.0 mm. In the process of the excavation of the tunnel, all of the parts of the initial excavation face of the tunnel settled down with the excavation step, as shown in Fig. 8. The vault in the tunnel had an excavation length of 15 m before the settling velocity was larger. For 15-40 m, the excavation subsidence speed was slow. At 40 m and 50 m, there was settlement stabilization in the excavation. The excavation face was about two times the hole diameter measuring point distance, there was deformation stability, and the maximum subsidence value was 33.63 mm.
The soil mass of the invert ½ was excavated at Step 25, but the middle part of the invert was rapidly raised with the excavation of the upper core soil´and the uplift tended to be stable at the 25 m elevation. When excavated at 50 m, the maximum uplift value was 34.04 mm. The settlement of the other parts was relatively small and the settlement increased with the increase of the excavation length. In the fourth position, the volume of the uplift gradually decreased with the excavation of the lower step Þ in the Step 14.
The vertical deformation of the tunnel vault every 5 m along the length of the tunnel with the tunnel excavation step is shown in Fig. 9. The settlement value of the soil body before excavation gradually increased with the approach of the excavation face, and the settlement speed was small. The settlement value of the arch soil directly above the excavation face increased rapidly with the increase in the excavation footage. Since the excavation face was further away, the settlement value tended to be stable, and the settlement point of each part gradually tended toward consistency. See Fig. 8 for Step 50 in the lower right corner. This step could be divided into the accelerated deformation section, linear deformation section, deceleration deformation section, and stable deformation section (Zuo et al. 2018).

Horizontal deformation
The horizontal deformation of the tunnel at the 49th excavation step is shown in Fig. 10. Due to the rock mass inclination during soil modeling, the horizontal deformation was not symmetrical. All of the parts of the initial excavation face horizontal deformation with the excavation steps In the process of excavation of the tunnel are shown in Fig. 11. The deformation was the largest in three parts. The maximum deformation value increased with the excavation step. To the left`of Step 7, the slope of the deformation increased after excavation. To the lower step left Þ of Step 13, the slope of the deformation increased rapidly after excavation, to the maximum value of 12.28 mm in Step 33. Finally, the deformation converged to 12.07 mm. Position 2 was at the top of the middle step, and the slope of the deformation increased rapidly after the excavation to the left`of Step 7 and to the lower step left`of Step 12. At position 4, the slope of the deformation increased slightly after excavation and the maximum value was 4.50 mm at Step 33. Position 1 had a smooth curve compared with other parts, and the maximum value was 3.07 mm at Step 33. Combined with the analysis of the excavation steps, the deformation increased with adjacent soil excavation. The second lining was applied in Step 34, and the deformation of each part decreased slightly after reaching the maximum value in Step 33. After the vertical deformation of the second lining, it was extruded to both sides, so there was a reaction to the horizontal deformation of both sides.
The central tunnel side wall was located down the lower steps to the left of side Þ. The horizontal deformation every 5 m along the depth of the tunnel with the excavation step is shown in Fig. 12. With the upper step À excavation the deformation increased, and with the middle stepè xcavation the deformation was gentle, increasing slowly until the lower step left Þ excavation of the deformation slope increased rapidly. After three steps, the deformation tended to be smooth. The final deformation was concentrated in the range of 11-13 mm.
There were two stationary segments in the deformation curve. The first stable stage was caused by the extrusion effect of the left side of the step on the middle of the tunnel side wall, and the deformation in the middle of the side wall stagnated during the excavation of the middle step, indicating that the lower step played a protective role in the rock mass of the side wall. With the excavation of the soil in the middle of the lower step of the side wall, the horizontal deformation of the side wall increased rapidly and finally tended to be stable. After the construction of the second lining, the horizontal deformation of the tunnel was reduced and the horizontal deformation of the part without the second lining was greater than that of the adjacent part with the second lining. The second lining had a greater inhibition on the horizontal deformation of the tunnel rock mass.

Equivalent stress analysis
The equivalent stress distribution of the surrounding rock is shown in Fig. 13. Under the action of the support structure, the effective stress at a certain distance from the lateral side wall reached the maximum value of 5.67 MPa. The effective stress on both sides of the invert was relatively large, about 4.0 MPa. The stress of the soil at the back of As shown in Fig. 14, the equivalent stress changed for each part of the initial tunnel excavation face with the length of tunnel excavation. At Position 4, the equivalent stress increased gradually with the excavation of the tunnel. After the excavation of the first cycle invert, the stress growth curve tended to be smooth, and the maximum equivalent stress was 5.65 MPa. The effective stress at Arches 1 and 6 in the middle of the invert was released with the tunnel excavation, and this stress was lower than the initial effective stress. With the arch foot support after the excavation of the upper step À, Position 3 increased sharply when the excavation reached 3 m. However, when the excavation stress was rapidly released on the left side of the middle step`, the stress slightly increased with the excavation of the left side of the lower step Þ. The change trend of Position 5 was the same as that of Position 4. When the increase in the tunnel excavation stress gradual increased, the maximum value was 2.93 MPa. After stress release, the stress of Position 2 increased slightly and tended to be gentle. With the increase in the excavation of the steps and the support structure, the equivalent stress changed with the transformation of the stress system. The gravity of the arch roof was transferred to both sides of the tunnel with the initial support, and the equivalent stress in the middle of the tunnel side wall increased gradually. During construction, the arch legs of the arch frame had to be firmly supported, and the bolts with locking legs had to be arranged. If there is indeed a multiaxial action items in the system with several stress components operating at about the same moment, equivalent stress has been used. In this case, we could use a set of criteria to convert the entire boundary conditions into a parallel combination part that can be interpreted as a tensile stress and therefore quickly transferred to the strength of the material.

Primary stress analysis
Because the tunnel was relatively flat, under the action of the initial support structure, the main tensile stress appeared to have a positive value (about 0.07 MPa) at some parts of the tunnel vault, on both sides, and in the middle of the invert, while no tensile stress appeared on the side wall, as shown in Fig. 15.   The main tensile stress of each part of the tunnel increased with the excavation of the tunnel. The increase trend of the horizontal deformation at Position 3 was similar to the horizontal deformation shown in Fig. 11. With the excavation of the left part of each step, a stagnation state appeared for Positions 1, 2, and 3. With the excavation of the tunnel, the main tensile stress first increased rapidly and then decreased slightly with the initial support gradually closed and without any tensile stress. Tensile stress appeared at Positions 4 and 5, with a maximum value of 0.07 MPa. With the second lining, the tensile stress gradually reduced to compressive stress, as shown in Fig. 16. Due to the lack of a smooth arch, the tunnel invert and the foot of the arch were prone to failure due to tensile stress. High attention had to be paid to the construction, which had be closed early with a precocious ring. Induced mechanical loading (forces) creates predominant primary stress, which is most often caused by load and pressure. Massive plastic deformation and break are caused by increased primary stress. Primary stress is not selfcontained.

Plastic zone analysis
The plastic zone development zone is shown in Fig. 17. The color red represents the plastic zone formed by the single disturbance, blue represents the plastic zone formed by the secondary disturbance, and green represents the plastic zone formed by tensile stress. In Step 15, the plastic zone of the secondary disturbance appeared on the top and core soil, and the plastic zone of the single disturbance appeared on both sides of the invert. In Step 25, the plastic zone formed by tensile stress appeared at the location where the invert met the side wall. In Step 30, the plastic zone generated by the bottom tensile stress disappeared due to the secondary lining. The plastic zone at the bottom of the side wall was large, and the plastic zone of the tensile stress appeared. The pressure transferred to this zone by the Initial support of the tunnel was large, and the surrounding rock was vulnerable to disturbance. Therefore, support had to be provided at the bottom of the side wall and on both sides of the invert during construction. A microcomputerimplementable technique for the material properties variational study of plane steel frames. Use of pseudo joint forces resulting from the structural finite element of the system accounts for geometric nonlinearity in the context of participant and framework disturbances. As the tunnel was excavated, the vertical deformation of the pipe shed gradually increased and tended to be stable, with a maximum deformation of about 30 mm. Since the tail of the pipe shed in the front section of the tunnel was located below the front of the pipe shed in the rear section, and because there were superimposed parts in the front and rear middle sections, the vertical deformation of the front of the pipe shed in the rear section was slightly reduced. The bending moment of the pipe shed at the face of the tunnel was the largest, and the maximum value (0.23 kNm) was about three times the maximum value at other locations. The bending resistance of the pipe shed bought time for the bolting and shotcrete support of the steel arch frame erected after tunnel excavation. A representative middle pipe shed steel pipe 13 m from the initial excavation surface was selected in order to extract its axial force, as shown in Fig. 18. With the excavation of the tunnel, the variation of the axial force of the pipe shed was complicated. When the excavation face was at the end of the pipe shed, the axial force of the pipe shed was as shown in excavation Step 13. The front end of the pipe shed was pulled, and the tail was compressed. As the excavation face moved to the middle of the pipe shed, the pipe shed was in the middle of the axial pressure, and the front tension reached a maximum at the same time. The excavation Step 17 of the pipe shed steel tube axial force was carried out, the excavation face continued to move forward, and the pressure peak of the pipe shed moved forward (Geng et al. 2016). When the excavation face reached the front of the pipe shed, the pipe shed was under overall axial pressure and the front-end pressure was greater than the end. Since the excavation face was far away from the front end of the pipe shed, the axial force at the back end of the pipe shed experienced little change, the pressure at the front end decreased, and the tension state was gradually restored. In the process of excavation, the axial force of the pipe shed changed in a complicated but regular way. The axial force changed in a wave shape (Ki-Il et al. 2013) with the tunnel excavation step. After the excavation surface left the pipe shed, the change in the axial force of the pipe shed became smaller and smaller as the distance increased. The stress on the front and rear pipe sheds was continuous, and the deformation at the joints was coordinated (Jiang et al. 2019).

Tunnel bolt
The axial force of the bolt at Step 15 generally increased with the excavation of the tunnel, as shown in Fig. 19. The axial force at the end of the arch roof bolt was slightly lower than the middle, the tail of the bolt at the bottom of the side wall was greater than that at the front, and the axial force of the other bolts was greater than that at the end. The axial force of the bolt tended to be stable with the excavation of the tunnel. The maximum axial force of the bolt rod in the middle of the side wall was about 90 kN. The maximum axial force of the bolt rod at the foot of the arch of the upper step was 70 kN. The maximum axial force of the bolt rod at the vault was 40 kN, and the maximum axial force of the bolt rod at the bottom of the side wall was 19 kN. With the large horizontal deformation and equivalent stress in the middle of the side wall, the corresponding rock bolt axial force was also large (Huo et al. 2012). When the rock mass in the middle of the side wall was excavated, the protection had to be strengthened. Since the rock bolt axial force increased gradually with the excavation step, the supporting effect became stronger and stronger.

Composite shell of the shotcrete and steel arch
The steel arch and the shotcrete in the initial support were converted into a single material according to the principle of equivalent compressive stiffness (Janin et al. 2015).
In the formula,E c , E s , and E 0 represent the sprayed concrete, steel arch shelf, and equivalent modulus of It can be seen from the analysis results that the equivalent stress of the shell at the arch shoulder reached the maximum value of 27.4 MPa, as shown in Fig. 20, and the bending moments of the vault and side wall were larger.
With the excavation of the tunnel, the annular compressive stress, equivalent stress, and circumferential bending moment of the shell generally increased, as shown in Fig. 21. After the middle step excavation, the Position 3 stress increase rate was obvious. The pressure increased, the bending moment remained essentially stable, and the gravity of the vault was transferred to the middle of the side wall through the initial support. The stress of the shotcrete at the bottom of the invert was much less than that of other parts, and the stress was smaller.  In the process of tunnel excavation, the steel arch and the shotcrete formed a closed-loop structure that played a role in transferring and redistributing the surrounding rock stress, and the timely erection of the steel arch and the shotcrete played a good role in the surrounding rock support.

Conclusions
The three-step method was not necessary to set up temporary support and there was convenient mechanical excavation, which was a great advantage. The middle pipe shed, system bolt, steel arch frame and shotcrete joint support rock mass were set up, and the three-step method's step length and step height were set reasonably to stabilize the excavation surface. The following conclusions were drawn through the finite element analysis.
1. The vertical deformation of the arch roof and the arch bottom was relatively large, reaching 34 mm. According to the analysis in this study, the vertical deformation could be divided into four sections: The accelerated deformation section, linear deformation section, deceleration deformation section, and stable deformation section. The point that was about twice the diameter of the excavation edge made the vertical deformation tend to be stable. The horizontal deformation was the largest in the middle of the side wall, reaching 12.28 mm. With the excavation of the soil on the lower steps in the middle of the side wall, the horizontal deformation of the side wall increased rapidly and finally became stable, indicating that the lower steps excavated after the excavation played a protective role on the side wall. The horizontal deformation of the tunnel at the position of the second lining decreased slightly. Under the vertical pressure of Numerical simulation and analysis of the three-step excavation of an extra-large cross section… 12129 the surrounding rock, the middle of the second lining of the side wall would extrude to the rock and soil. 2. With the increase in the excavation of the steps and the support structure, the equivalent stress of the rock mass changed with the transformation of the stress system. The gravity of the arch roof was transferred to both sides of the tunnel with the initial support, and the equivalent stress in the middle of the side wall of the tunnel gradually increased. During the construction, the arch legs needed to be firmly supported, and bolts with locking feet had to be arranged. Pressure was transferred to the inverted arch and the foot of the tunnel through the Initial support, the surrounding rocks of which were susceptible to disturbance. At the same time, due to the failure of the tunnel section to form a smooth arch at the inverted arch position, tensile stress occurred in some construction stages. Rock and soil damage could easily occur, and the support at the bottom of the side wall and on both sides of the invert had to be done well in the construction. It was thus advisable to close the ring early. 3. During the process of excavation, the axial force of the pipe shed changed in a complex and regular manner.
Since the axial force of pipe shed changed in a waveform with the tunnel excavation, the change of the axial force of the pipe shed became smaller and smaller with the increase of the distance after the excavation surface left the pipe shed. The front and rear pipe sheds were under continuous stress, and the joint deformation was coordinated. 4. The horizontal deformation and the equivalent stress in the middle of the side wall were large, and the corresponding axial force of the bolt was large. The protection in the middle of the side wall had to be strengthened. As the axial force of rock bolt increased gradually with the excavation steps, the supporting effect became stronger and stronger. 5. The steel arch and shotcrete formed a closed-loop structure in the process of tunnel excavation, which played a role in transferring and redistributing the surrounding rock stress, and the timely erection of the steel arch and shotcrete played a good role in supporting the surrounding rock.
Authors' contribution WXH, SFX, ZZZ, ZYG and MYS have all participated in the designing framework, collecting data, analysis and interpretation of data, drafting, reviewing and approving the manuscript.
Funding No funding is received.
Availability of data and material The data in this paper include calculation result data and finite element analysis data. All the data used to support the findings of this study are included within the article. There are not any restrictions on data access.
Code availability Not Applicable.

Declarations
Conflicts of interest The authors declare that they have no conflicts of interest.