Calculation method for equivalent modulus of tunnel double-layer support

Abstract

The invention discloses a tunnel double-layer support equivalent modulus calculation method, which belongs to the technical field of road traffic engineering, and comprises the following steps: S1, analyzing environmental conditions, geological factors and construction conditions of a tunnel through field investigation to obtain influence factors generated in a tunnel collapse field, and carrying out sensitivity analysis on the influence factors; s2, researching common influence factors aiming at the elastic modulus of the double-layer primary support through a refined numerical simulation method, and calculating the equivalent elastic modulus of the double-layer support structure; s3, verifying the reliability of the refined numerical simulation method and proposing a modulus correction formula; according to the calculation method for the equivalent modulus of the tunnel double-layer support, provided by the invention, a refined numerical simulation method is adopted; the interaction between the reinforcing steel bars and concrete materials, the interaction between the double-layer preliminary bracing structure and the stratum and the influence of different space structures of the reinforcing steel bar components on the elastic modulus of the double-layer preliminary bracing structure can be fully considered.

Description

Technical Field

[0001] The invention relates to the technical field of highway traffic engineering, and in particular to a method for calculating an equivalent modulus of a double-layer support of a tunnel. Background Art

[0002] The terrain in the western region is mainly mountainous and hilly, so tunnel engineering plays a vital role. The construction and operation of tunnels are directly related to the smooth flow of urban traffic, so the attention to the safety and stability of tunnels is increasing. Existing statistics show that my country's tunnel construction mileage and the number of tunnel projects currently rank first in the world, and more and more tunnel projects are being built in sandy loess areas. Loess is a common but special type of stratum. Its characteristics include collapsibility and easy sedimentation. It is widely distributed in the northwest of my country, accounting for about 6.3% of my country's land area. my country's loess can be subdivided into sandy, silty and clay loess according to its characteristics. It is mainly distributed in bands in the central and western regions. From the northwest to the southeast, the sand content in the loess gradually decreases, and the clay content gradually increases. Sandy loess refers to loess with a fine sand content of more than 30%. The sensitivity of sandy loess means that during the construction of the tunnel, factors such as changes in groundwater and soil may cause major changes in the strata around the tunnel, thereby causing landslides. Tunnel collapse may cause project stagnation, damage existing tunnel structures, and even cause serious harm to the surrounding environment. Understanding the corresponding causes of engineering disasters and taking targeted measures to address engineering problems are crucial to ensuring the stability and safety of tunnels during construction and operation.

[0003] In order to effectively prevent and control tunnel collapse, initial support in tunnel engineering is particularly critical. The rationality and effectiveness of initial support are directly related to the later stability of the entire project. In view of the particularity of sandy loess areas, double-layer support as a means of strengthening support is particularly worthy of study. By optimizing the design of double-layer support, it can better adapt to complex geological conditions, improve the overall stability of the tunnel, ensure that the tunnel can remain stable during excavation, and avoid the occurrence of collapse.

[0004] A highway tunnel passes through sandy loess strata, and the shallow buried section of the tunnel entrance passes under existing highways, flood drainage channels, irrigation channels and other important structures. The construction is difficult and risky. During the construction process, a large area of ​​landslides occurred in the shallow buried section of the tunnel entrance, resulting in engineering problems such as deformation and limit intrusion of the initial support structure, cracking of the double-layer initial support, and distortion of the steel arch. Through on-site investigation and analysis, it is believed that insufficient initial support strength is the main cause of tunnel collapse. Therefore, it is necessary to conduct research and analysis on the initial support design method. The existing initial support design system includes single-layer support, double-layer support and advance support. The engineering analogy method is often used, and the elastic modulus of the initial support structure is determined by the conversion method. However, the conversion method has disadvantages and cannot consider the interaction between the support structure and the surrounding rock, and the mechanical response between the steel bar and the concrete. This paper proposes a refined numerical simulation method for the design of double-layer tunnel support structure. Considering the interaction between initial support and surrounding rock, the bonding effect between steel components and concrete, and the spatial distribution of steel bars, the influence of different influencing factors on the change law of the equivalent elastic modulus of the double-layer initial support structure is studied. Finally, based on the conversion method, an empirical formula considering these influencing factors is proposed, which provides a scientific reference for future support structure design and provides certain reference significance for solving practical problems in similar projects. Summary of the invention

[0005] The purpose of the present invention is to provide a method for calculating the equivalent modulus of double-layer support of a tunnel to solve the problems existing in the above-mentioned background technology.

[0006] To achieve the above object, the present invention provides a method for calculating the equivalent modulus of double-layer support of a tunnel, comprising the following steps:

[0007] S1. Analyze the environmental conditions, geological factors and construction conditions of the tunnel through on-site investigation, obtain the influencing factors of tunnel collapse, and conduct sensitivity analysis on these influencing factors;

[0008] S2. Use refined numerical simulation methods to study the common influencing factors of the elastic modulus of the double-layer initial support, and calculate the equivalent elastic modulus of the double-layer support structure;

[0009] S3. Propose a refined numerical simulation method for reliability verification and a modulus correction formula.

[0010] Preferably, the influencing factors in step S1 include rainfall infiltration depth, excavation cycle footage and initial support strength, specifically including:

[0011] a. Analysis of the impact of rainfall infiltration depth on tunnel stability, including

[0012] The stratum-tunnel model was established by using the numerical simulation software MIDAS GTS / NX. First, the collapse phenomenon of tunnel engineering involves multiple complex factors, such as geological conditions, hydrogeology, support structures, etc. Numerical simulation can simulate these complex engineering systems to help understand the overall behavior of the project. Secondly, numerical simulation predicts potential risks in advance, allowing engineers to take necessary measures before design and construction to reduce the risk of tunnel collapse. In addition, by simulating the impact of different design schemes, the engineering design can be optimized and the stability and safety of the tunnel can be improved. Numerical simulation can also detect problems before actual construction, reduce engineering costs, and improve construction efficiency, thereby achieving cost and time benefits. Most importantly, this method deeply analyzes the mechanism of tunnel collapse, providing strong support for scientifically explaining the causes of collapse and providing valuable lessons for future projects;

[0013] The tunnel collapse occurred in the shallow buried section of the tunnel entrance, and the secondary lining has not yet been constructed. Therefore, the secondary lining structure is not considered in the numerical model. Both the double-layer initial support structure and the temporary middle wall are composite double-layer initial support structures. The elastic modulus value is determined using the conversion method. The conversion method is the principle that the initial support structure is equivalent to the original and the strength of the steel component is converted to concrete. The calculation formula is:

[0014]

[0015] Among them, E is the initial support elastic modulus of the conversion method; E c is the elastic modulus of plain concrete; E s A is the elastic modulus of steel; w A is the cross-sectional area of ​​the steel mesh; g A is the cross-sectional area of ​​the I-beam; gs A is the cross-sectional area of ​​the grid steel frame; c is the concrete cross-sectional area;

[0016] The elastic modulus of temporary support is:

[0017]

[0018] Among them, E 临 is the elastic modulus of temporary support after conversion;

[0019] b. Analysis of the impact of excavation cycle footage on tunnel stability, by simulating the stratum stress state and soil deformation under different footages, to understand the risk of geological disasters that may occur;

[0020] c. Analysis of the influence of initial support strength on tunnel stability. The elastic modulus E of the single-layer support is calculated by the conversion method. d .

[0021] Preferably, a sensitivity analysis is performed on the factors affecting the rainfall infiltration depth, excavation cycle footage and initial support strength in S1, specifically including:

[0022] Since the units of the three influencing factors, namely rainfall infiltration depth, excavation cycle advance, and initial support strength, are inconsistent and cannot be directly compared, a variable sensitivity coefficient M with a dimension of 1 is defined to quantitatively describe their influence on tunnel collapse; the sensitivity coefficient formula of each influencing factor is:

[0023] M l =(Δσ / σ) / (ΔH / H);

[0024] M m =(Δσ / σ) / (ΔL / L);

[0025] M n =(Δσ / σ) / (ΔE / E);

[0026] Among them, M>0 means that the tunnel collapse is positively correlated with the influencing factors, and M<0 means that the tunnel collapse is negatively correlated with the influencing factors; M l M is the sensitivity coefficient of rainfall infiltration depth to tunnel collapse; m M is the sensitivity coefficient of excavation cycle advance to tunnel collapse; n is the sensitivity coefficient of initial support strength to tunnel collapse; Δσ is the difference between the maximum tensile stress of the initial support arch of tunnel excavation and the maximum tensile stress of the reference initial support arch; σ is the maximum tensile stress of the tunnel arch of reference tunnel excavation; ΔH is the difference between the rainfall infiltration depth and the reference rainfall infiltration depth; H is the reference rainfall infiltration depth; ΔL is the difference between the tunnel excavation cycle footage and the reference tunnel excavation footage; L is the reference tunnel excavation footage; ΔE is the difference between the elastic modulus of the initial support strength and the elastic modulus of the reference initial support strength; E is the elastic modulus of the reference initial support strength.

[0027] Preferably, the refined numerical simulation method in S2 specifically includes:

[0028] S21. Determination of constitutive parameters of double-layer support structure unit, including:

[0029] The double-layer initial support model was established using the numerical simulation software ABAQUS. The concrete plastic damage model (CDP) in ABAQUS was used to simulate the interaction between the double-layer initial support structure and the ground, the interaction between the steel bars and concrete, and the spatial structure of the steel bar components.

[0030] Establish a finite element model. In the process of establishing the double-layer initial support finite element model, the structure is divided into concrete, steel mesh, I-beam arch frame, and steel grille for modeling, and they are assembled into initial support units in the assembly module. According to the unit library provided by ABAQUS, concrete uses solid units, and because steel bars mainly play a tensile role in the component, steel bars use line units. The constitutive model used for concrete is the plastic damage model, and the steel bars use the elastic model;

[0031] The elastic modulus E of the double-layer initial support elastic stage obtained by the refined numerical simulation method eq ;

[0032] The factors affecting the stiffness of the double-layer initial support structure are studied to find the changing rules of the equivalent elastic modulus of the double-layer initial support structure with different influencing factors; as a reinforced concrete structure, the factors affecting the elastic modulus of the double-layer initial support structure mainly include: concrete strength, concrete thickness, steel mesh diameter, steel mesh spacing, grid steel frame diameter, grid steel frame spacing, I-beam arch frame model, and I-beam arch frame spacing;

[0033] S22. The equivalent elastic modulus of the double-layer support structure is studied using the stratum-structure method.

[0034] Preferably, the influence of different influencing factors on the initial support elastic modulus is as follows:

[0035] A. The influence of concrete strength q on the elastic modulus of initial support. By changing the strength of concrete materials, under the same load conditions, the concrete strength and the elastic modulus E calculated by the refined numerical simulation method are obtained. eq The change law of elastic modulus E calculated by the conversion method and the refined numerical simulation method are both positively correlated with the elastic modulus of the double-layer initial support and the concrete strength, thus obtaining the relative difference δ=|E eq -E| / E×100%, the linear relationship between the relative difference and the concrete strength is: δ=-0.0179q+0.7888;

[0036] Concrete strength and E eq The linear function relationship is: E eq =1.3679q+3.0728;

[0037] The linear function relationship between concrete strength and E is E = q + 25.17;

[0038] B. The influence of concrete thickness d on the initial support elastic modulus. The double-layer support elastic modulus is negatively correlated with the concrete thickness. The fitting formula of relative difference and concrete thickness is: δ = 0.0002d + 0.2029;

[0039] Concrete thickness and E eq The linear function relationship is: E eq =-0.0375d+59.171;

[0040] The linear function relationship between concrete thickness and E is: E = -0.0418d + 73.082;

[0041] C. The influence of steel mesh diameter s1 on the initial support elastic modulus. The initial support equivalent elastic modulus is positively correlated with the steel mesh diameter. The fitting formula between the relative difference and the steel mesh diameter is: δ = 0.0017s1 + 0.2744;

[0042] Steel mesh diameter and E eq The linear function relationship is: E eq =0.01s1+41.22;

[0043] The linear function relationship between the steel mesh diameter and E is: E = 0.0824s1 + 52.529;

[0044] D. The influence of the steel mesh spacing l1 on the initial support elastic modulus. The double-layer initial support elastic modulus is negatively correlated with the steel mesh spacing, and the fitting formula is: δ = -0.000017l1 + 0.289680;

[0045] Steel mesh spacing and E eq The linear function relationship is: E eq =-0.0002l1+41.33;

[0046] The linear function relationship between the steel mesh spacing and E is: E = -0.001l1 + 53.302;

[0047] E. The influence of grid steel frame diameter s2 on the initial support elastic modulus. The initial support elastic modulus is positively correlated with the grid steel frame diameter, and the fitting relationship is:

[0048] δ=-0.0034s2+0.3744;

[0049] Diameter of grid steel frame and E eq The linear function relationship is: E eq =0.2206s2+35.713;

[0050] The linear function relationship between the diameter of the grid steel frame and E is: E = 0.1484s2 + 49.443;

[0051] F. The influence of grid steel frame spacing l2 on the initial support elastic modulus. The initial support elastic modulus is negatively correlated with the grid steel frame spacing, and the fitting relationship is:

[0052] δ=-0.0003l2+0.3082;

[0053] Grid steel frame spacing and E eq The linear function relationship is: E eq =-0.0252l2+53.51;

[0054] The linear function relationship between the grid steel frame spacing and E is: E = -0.0417l2 + 68.648;

[0055] G. The influence of I-beam model a on the initial support elastic modulus. The double-layer initial support elastic modulus is positively correlated with the I-beam model, and the fitting formula is:

[0056] δ=-0.0043a+0.4798;

[0057] I-beam model and E eq The linear function relationship is: E eq =0.2212a+31.325;

[0058] The linear function relationship between the I-beam model and E is: E = 0.1094a + 48.081;

[0059] H. The influence of the spacing between I-beam arch frames on the initial support elastic modulus. The initial support elastic modulus is negatively correlated with the spacing between I-beam arch frames. The fitting formula is:

[0060] δ=0.0002l3+0.1651;

[0061] I-beam arch spacing and E eq The linear function relationship is: E eq =-0.0108l3+47.26;

[0062] The linear function relationship between the I-beam arch spacing and E is: E = -0.0068l3 + 55.375.

[0063] Preferably, step S3 specifically comprises:

[0064] The formula for calculating the reinforcement ratio of reinforced concrete structures is:

[0065] Among them, A s is the cross-sectional area of ​​the steel bars in the reinforced concrete structure;

[0066] The calculation formula for the double-layer initial support reinforcement ratio is:

[0067] The calculation formula of the change rate of double-layer support elastic modulus is:

[0068] Among them, Eeq is the elastic modulus of the double-layer support structure under different reinforcement ratios;

[0069] Determine the equivalent elastic modulus of double-layer initial support with different reinforcement ratios using a refined numerical simulation method;

[0070] The elastic modulus E of the double-layer initial support structure under different reinforcement ratios ρ obtained by the refined numerical simulation method eq The following relationship is established between the converted elastic modulus E:

[0071]

[0072] Therefore, the present invention adopts the above-mentioned method for calculating the equivalent modulus of the double-layer support of a tunnel, which has the following beneficial effects:

[0073] (1) Based on the plastic damage model (CDP) and the stratum structure method, a refined numerical simulation method for the mechanical response of the double-layer support structure in the tunnel is proposed. This method can take into account the interaction between the steel mesh, I-beams, grid steel frame and concrete in the double-layer support structure, as well as the interaction between the double-layer support structure and the surrounding rock and the timing of support.

[0074] (2) By studying the changing rules of the equivalent elastic modulus of the double-layer initial support structure due to different influencing factors, an empirical formula considering these influencing factors is proposed based on the conversion method, which provides a scientific reference for the design of support structures in the future and provides a certain reference significance for solving practical problems in similar projects;

[0075] (3) By proposing a modified conversion method for the elastic modulus of the double-layer support structure and consulting relevant literature, the change rate of the elastic modulus with the reinforcement ratio calculated by the refined numerical simulation method is within the range of the measured value. Therefore, it can be considered that the refined numerical simulation method can effectively calculate the equivalent elastic modulus of the double-layer support.

[0076] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 A flow chart of a method for calculating the equivalent modulus of double-layer support of a tunnel according to the present invention;

[0078] Figure 2 A schematic diagram of sensitivity analysis of factors affecting tunnel collapse according to an embodiment of the present invention;

[0079] Figure 3Schematic diagram of CDP damage parameter change curve of an embodiment of the present invention, wherein (a) is a schematic diagram of concrete compressive stress-inelastic strain curve, (b) is a schematic diagram of concrete tensile stress-cracking strain curve, (c) is a schematic diagram of concrete compressive stress-inelastic strain curve, and (d) is a schematic diagram of concrete tensile stress-inelastic strain curve;

[0080] Figure 4 It is a schematic diagram of the stress-strain curve of the initial support of an embodiment of the present invention;

[0081] Figure 5 Schematic diagram of the relationship between elastic modulus and concrete strength according to an embodiment of the present invention;

[0082] Figure 6 This is a schematic diagram of the relationship between the elastic modulus and the concrete thickness according to an embodiment of the present invention;

[0083] Figure 7 Schematic diagram of the relationship between the elastic modulus and the diameter of the steel mesh according to an embodiment of the present invention;

[0084] Figure 8 Schematic diagram of the relationship between elastic modulus and steel mesh spacing in an embodiment of the present invention;

[0085] Fig. 9 Schematic diagram of the relationship between the elastic modulus and the diameter of the grid steel frame according to an embodiment of the present invention;

[0086] Fig.10 Schematic diagram of the relationship between the elastic modulus and the grid steel frame spacing in an embodiment of the present invention;

[0087] Fig.11 Schematic diagram of the relationship between the elastic modulus and the I-beam model according to an embodiment of the present invention;

[0088] Fig.12 Schematic diagram of the relationship between the elastic modulus and the I-beam arch spacing in an embodiment of the present invention;

[0089] Fig.13 Schematic diagram of the relationship between the reinforcement ratio and the measured elastic modulus change rate according to an embodiment of the present invention;

[0090] Fig.14 It is a schematic diagram comparing the elastic modulus and the fitting value of the refined numerical simulation method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0091] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0092] See also Figure 1 , a calculation method for the equivalent modulus of double-layer support of a tunnel, taking a highway tunnel as the research background, and targeting the landslide accident that occurred during the construction of the shallow sandy loess tunnel as the research object, through field research, literature research, numerical analysis and other methods, the main causes of tunnel landslides were analyzed and studied, including:

[0093] (1) Through on-site investigation, the environmental conditions, geological factors, construction conditions, etc. of the tunnel are analyzed to obtain the main influencing factors of tunnel collapse. Sensitivity analysis is performed on these influencing factors to find the most unfavorable influencing factors.

[0094] (2) Aiming at the problem of selecting the elastic modulus of the double-layer initial support structure, the interaction between the steel bars and concrete in the double-layer initial support structure was simulated using ABAQUS finite element software. The interaction between the double-layer initial support structure and the stratum was considered, and the influence of the spatial structure of the steel bar components was considered. A refined numerical simulation method was proposed to study the variation law of the elastic modulus of the double-layer initial support structure under different influencing factors. The literature on the selection of the elastic modulus of reinforced concrete structures was consulted, and the reliability of the refined numerical simulation method for the design of the double-layer support structure of the tunnel was verified by the measured value of the elastic modulus. A correction conversion method for the elastic modulus of the double-layer support structure was proposed.

[0095] (3) In order to ensure the safety of shallow sandy loess tunnel construction, the elastic modulus of the double-layer initial support structure was determined based on a refined numerical simulation method. The numerical simulation software MIDAS GTS / NX was used to study the effects of different excavation schemes, the timing of double-layer initial support application, and different excavation advances on tunnel excavation. The surrounding rock displacement, double-layer initial support, and mechanical responses of surface structure channels under different working conditions were analyzed. A construction process for rapid entry of shallow sandy loess tunnels and prevention of cracking of surface channels was proposed.

[0096] 1. Analysis of the collapse mechanism of a highway tunnel

[0097] Tunnel Design Overview

[0098] A highway tunnel is a key control project of the entire project. The exit section is located on the I-level terrace, with a relatively flat terrain and well-developed surface vegetation, mainly crops and low shrubs, and poor slope consolidation. The tunnel exit underground excavation section passes under the expressway, flood drainage channels, irrigation channels, etc. The surrounding rock is relatively unstable, the construction is difficult and risky, and landslides are prone to occur during the tunnel construction process.

[0099] In principle, the tunnel plan design follows the route direction, but it also fully considers the engineering geology and hydrogeology conditions of the tunnel site, avoids large unfavorable geological sections, and considers the difficulty of tunnel opening.

[0100] The highway grade of a certain highway tunnel is a two-way six-lane first-class highway, the design speed of the tunnel is 60km / h, the tunnel construction limit width is 14.00m, and the height is 5m; the one-way slope of the tunnel pavement is 2%, and the superelevation is not more than ±3%; the maximum allowable longitudinal slope in the tunnel is ±3%, and the minimum allowable longitudinal slope is ±0.5%; the design load of the tunnel is highway grade I, the tunnel waterproof grade is grade II, and the secondary double-layer initial support concrete anti-seepage grade is not less than P8; the main structure of the tunnel is designed for a service life of 100 years, and the design service life of replaceable and repairable components is 30 years.

[0101] Analysis on the Causes of Sandy Loess Tunnel Collapse

[0102] During the construction of this large-section shallow sandy loess tunnel, landslides and other engineering disasters occurred in the shallow buried section of the tunnel entrance (the tunnel arch is buried at a depth of about 14m), and multiple collapses, roof falls, cracks, and structural damage occurred on the surface of the exit section. Specifically, the exit section surface collapsed, the surface ramp cracked and sunk, the surface cracked, and the surface water channel failed (structural cracks, foundation hollowing).

[0103] Through field investigation, it was found that the tunnel exit section experienced large-scale rainfall during the rainy period, the slope was seriously flooded, the sandy loess in the tunnel site area was softened due to wetness, and the drainage of the channel above the tunnel was not smooth, which may be the environmental cause of the tunnel collapse and roof fall. In addition, in order to meet the construction schedule, the construction party had a fast construction progress on site and the initial support strength of the support factor was insufficient, which also had an adverse effect on the stability of the tunnel construction. In summary, the sandy loess was deformed by humidification after rainfall, and the unreasonable excavation method and support timing led to engineering problems such as local instability of the tunnel surrounding rock and damage to surface structures. Therefore, it is necessary to further analyze the causes of tunnel collapse, ensure the stability of the support structure and cavern during tunnel construction, prevent structural deformation and damage, prevent and control the occurrence of tunnel disasters and operational diseases, and provide effective guidance for the construction of the sandy loess tunnel. A numerical simulation research plan was formulated for the main causes of tunnel collapse: rainfall infiltration, excavation cycle footage, and initial support strength. See Table 1 for details.

[0104] Table 1 Numerical simulation scheme

[0105]

[0106]

[0107] Analysis of the influence of rainfall infiltration on the stability of shallow buried sandy loess tunnels

[0108] 1. Numerical analysis methods

[0109] In order to study the causes of tunnel collapse in shallow sandy loess, a stratum-tunnel model was established using the numerical simulation software MIDAS GTS / NX. First, the phenomenon of tunnel collapse involves multiple complex factors, such as geological conditions, hydrogeology, and support structures. Numerical simulation can simulate these complex engineering systems and help understand the overall behavior of the project. Secondly, numerical simulation predicts potential risks in advance, allowing engineers to take necessary measures before design and construction to reduce the risk of tunnel collapse. In addition, by simulating the impact of different design schemes, the engineering design can be optimized and the stability and safety of the tunnel can be improved. Numerical simulation can also detect problems before actual construction, reduce engineering costs, and improve construction efficiency, thereby achieving cost and time benefits. This method deeply analyzes the mechanism of tunnel collapse, providing strong support for scientifically explaining the causes of collapse and providing valuable lessons for future projects.

[0110] (1) Calculation parameters

[0111] The parameter values ​​of surrounding rock and support structure in the numerical model refer to the "Highway Tunnel Design Code" and tunnel engineering investigation report. The tunnel collapse occurred in the shallow buried section of the tunnel entrance, and the secondary lining has not yet been constructed. Therefore, the secondary lining structure is not considered in the numerical model. The double-layer initial support structure and the temporary middle wall are both composite double-layer initial support structures. The elastic modulus value is determined using the conversion method. The conversion method is the principle of the initial support structure being equivalent before and after, and the strength of the steel component is converted to concrete. The specific calculation formula is:

[0112]

[0113] The initial support of the shallow buried tunnel entrance is a composite double-layer initial support, with a shotcrete thickness of 48cm and a concrete design grade of C25; the steel mesh is double-layer, with a size of φ8 and a spacing of @15*15; the steel arch frame is I22b I-beam and H18 grid, with a spacing of 60cm. Based on the above formula, the initial support elastic modulus is:

[0114]

[0115] The temporary support of the shallow buried section of the tunnel entrance is made of 20cm thick C25 shotcrete, with I18 I-beams inside, with a spacing of 60cm. The elastic modulus of the temporary support is:

[0116]

[0117] According to engineering experience and related research results, the grouting effect is mainly achieved by enhancing the E, C, reflect.

[0118] (2) Model size and boundary conditions

[0119] A highway tunnel is a two-way six-lane tunnel with a tunnel diameter of 17m and a height of 12m. According to the Saint-Venant principle and the simulation of tunnel excavation by domestic and foreign researchers, it is believed that the disturbance range of tunnel excavation on the surrounding rock is 3 to 5 times the tunnel diameter, so the model size is finally determined to be 84m×30m×61m (length×width×height). The left and right boundary conditions of the numerical model are X-direction displacement constraints, the longitudinal boundary conditions are Y-direction displacement constraints, and the lower boundary conditions are Z-direction displacement constraints. The mesh size of the tunnel excavation part is set to 1m, the mesh size of the surface stratum is 2m, and the mesh size of the lower sandstone stratum is 4m. The mesh attribute is set to a mixed mesh, mainly hexahedral units. The initial support, temporary support and other structures are generated by extracting the geometric surface of the tunnel structure to ensure the coupling of the grid nodes. The displacement is reset to zero in the initial stress stage, and the self-weight stress is applied at the same time.

[0120] (3) Construction process simulation

[0121] The surrounding rock of a tunnel collapse section is V-level surrounding rock, mainly sandy loess layer, with low strength and poor stability. It is easy to collapse during construction. At the same time, tunnel excavation will have an adverse impact on the surface structures such as the highway under the tunnel and the flood drainage channel and irrigation channel. Therefore, the design scheme uses the double side wall pilot pit method to reduce the deformation of the surrounding rock. This excavation method is divided into two steps, upper and lower, and three pilot pits on the left, middle and right, and excavation and support are carried out along the longitudinal direction of the tunnel.

[0122] In the finite element software MIDAS GTS / NX, the mesh group and boundary group are operated through the "Active" and "Remove" functions. The specific construction steps are:

[0123] ①STEP1: Activate all mesh elements in the initial stage, including the original soil and channel structure before tunnel excavation, activate boundary conditions and gravity, and clear displacement;

[0124] ②STEP2: Passivate part of the units on the upper step of the left pilot pit and activate part of the initial support and temporary support;

[0125] ③STEP3: Passivate the two units of the lower step of the left pilot pit and activate the two initial supports and temporary supports;

[0126] ④STEP4: Passivate the 3-part unit on the upper step of the right pilot pit and activate the initial support and temporary support of the 3 parts;

[0127] ⑤STEP5: Passivate the 4 units of the lower step of the right pilot pit and activate the initial support and temporary support of the 4 parts;

[0128] ⑥STEP6: Passivate the 5-part unit on the upper step of the middle pilot pit and activate the 5-part initial support;

[0129] ⑦STEP7: Passivate the 6-part unit of the lower step of the middle pilot pit and activate the 6-part initial support;

[0130] ⑧ Repeat the excavation steps until the excavation of the entire model tunnel is completed.

[0131] (4) Tunnel stability analysis under rainfall infiltration conditions

[0132] This section mainly studies the impact of rainfall infiltration on tunnel excavation. Rainfall infiltration will cause the sandy loess to saturate and soften, which will in turn weaken the tunnel arching effect, which may cause deformation and collapse of underground engineering structures, and induce surface subsidence and damage to surface buildings. In addition, the rise in water level directly lifts the support structure and has an adverse effect on the mechanical response of the support structure.

[0133] When using the finite element software MIDAS GTS / NX to simulate the effect of rainfall infiltration, the strata at 2m, 6m, 10m, and 14m below the surface are considered to be saturated until the loess strata where the tunnel is located are all saturated. In order to simulate the effect of rainfall infiltration, the original stratum parameters of the corresponding thickness are directly replaced with the saturated stratum parameters. In order to analyze the stability of the tunnel excavation process under different rainfall infiltration conditions, the section at the model Y=26m is selected as the research object.

[0134] The greater the rainfall infiltration depth, the greater the maximum tensile stress of the double-layer initial support structure. When the rainfall infiltration depth of the double-layer support structure increases from 0m to 14m, the maximum tensile stress of the double-layer initial support structure at the arch position at Y=26m changes from 2.3MPa to 2.8MPa, an increase of 21.7%.

[0135] Analysis of the influence of excavation cycle advance on the stability of shallow buried sandy loess tunnels

[0136] This section studies the impact of different cycle advances on tunnel excavation in order to gain a deeper understanding of the changes and challenges in the construction process. By simulating the stratum stress state and soil deformation at different advances, we can better understand the risks of possible geological disasters, such as landslides and caving. In addition, the simulation is also helpful to evaluate the adaptability of the support structure at different advances, optimize the design, and improve the support effect. Numerical simulation of different cycle advances can also provide a scientific basis for planning the construction process, adjusting construction methods, and selecting support measures to reduce tunnel construction risks and improve efficiency and safety. This study studied the impact of cycle advances of 1.5m, 2m, and 3m on tunnel excavation.

[0137] When the tunnel excavation cycle advance is 1.5m, the maximum tensile stress of the double-layer initial support structure is 17.2MPa, located at the arch shoulder position of the shallow buried section of the tunnel entrance, and the maximum compressive stress is 19.3MPa, located at the arch foot position of the shallow buried section of the tunnel entrance; when the tunnel excavation cycle advance is 2m, the maximum tensile stress of the double-layer initial support structure is 16.2MPa, and the maximum compressive stress is 17.7MPa, which are 5.8% and 8.3% lower than those when the advance is 1.5m respectively; when the tunnel excavation cycle advance is 3m, the maximum tensile stress of the double-layer initial support structure is 15.8MPa, and the maximum compressive stress is 16.7MPa, which are 8.1% and 13.5% lower than those when the advance is 1.5m respectively.

[0138] Analysis of the influence of initial support strength on the stability of shallow loess tunnels

[0139] This section mainly studies the influence of different initial support strengths on tunnel excavation stability. It is crucial to study the influence of initial support strength on tunnels. This study can directly guide and optimize the design and construction of support structures, ensuring that problems such as ground deformation and collapse are effectively mitigated or resisted in the early stages of construction. Reasonable initial support is directly related to the subsequent construction process. If the strength is insufficient, it may lead to excessive displacement, affect subsequent processes, and even cause accidents. Therefore, in-depth research on the influence of initial support strength will help to discover problems in advance, take technical measures to adjust and reinforce, and ensure the continuity and efficiency of construction. In addition, systematic research on initial support strength can also provide experience and reference for similar projects in the future, summarize lessons learned, promote the continuous improvement and innovation of engineering technology, and ensure the quality and safety of tunnel projects.

[0140] The design parameters of single-layer support are shotcrete thickness of 28cm, concrete design grade of C25; steel mesh is single-layer, size is φ8, spacing is @15*15; steel arch is I22b I-beam, spacing is 60cm. Therefore, the elastic modulus of single-layer support calculated by the conversion method is:

[0141]

[0142] The double-layer support elastic modulus E=53.17GPa calculated by the conversion method.

[0143] The initial support structure of the tunnel is changed from single-layer support to double-layer support, and the maximum tensile stress of the initial support is reduced from 16.3MPa to 15.8MPa, a decrease of 3.1%. This shows that the double-layer support structure can improve the stress condition of the support structure.

[0144] Sensitivity analysis of different influencing factors on tunnel collapse causes

[0145] Based on the above numerical simulation analysis of the cause of sandy loess tunnel collapse, in order to find the main cause of the collapse, a sensitivity analysis of the factors that cause the three collapse phenomena was carried out. Since the units of the three influencing factors, namely rainfall infiltration depth, excavation cycle advance, and initial support strength, are inconsistent, direct comparison is impossible. Therefore, a variable sensitivity coefficient M with a dimension of 1 is defined to quantitatively describe its influence on tunnel collapse.

[0146] M l =(Δσ / σ) / (ΔH / H);

[0147] M m =(Δσ / σ) / (ΔL / L);

[0148] M n =(Δσ / σ) / (ΔE / E);

[0149] In the formula, M>0 means that the tunnel collapse is positively correlated with the influencing factors, and M<0 means that the tunnel collapse is negatively correlated with the influencing factors.

[0150] The calculation results show that the sensitivity coefficient of the initial support strength of the design parameter to tunnel collapse is 5.547, the sensitivity coefficient of the external condition rainfall infiltration to tunnel collapse is 0.023, and the sensitivity coefficient of the construction influencing factor excavation advance to tunnel collapse is 0.003. The relationship between the three is as follows: Figure 2 As shown in the figure, it can be seen that the initial support strength has the greatest impact on the occurrence of tunnel collapse, followed by the impact of rainfall infiltration on tunnel collapse, and finally the construction factor excavation progress. Therefore, it is necessary to analyze and study the value of the initial support strength of the tunnel to avoid the occurrence of tunnel collapse from the design aspect.

[0151] Through the sensitivity analysis of the influencing factors of sandy loess tunnel collapse, it is known that the size of the sensitivity index M is: initial support strength > rainfall infiltration > influence of excavation advance. Therefore, it is necessary to analyze and discuss the value of the strength of the double-layer initial support, that is, the elastic modulus.

[0152] Refined numerical simulation method for the design of double-layer tunnel support structure

[0153] A certain tunnel is a double-hole, six-lane, large-span highway tunnel that passes through the sandy loess layer in Qinghai. The shallow buried section of the tunnel entrance passes under important structures such as existing highways and power transmission lines. The construction is difficult and risky. The tunnel support structure adopts a composite double-layer initial support. In the composite double-layer initial support structure, the initial support bears most of the load during the tunnel construction and operation stages. In this tunnel, double-layer initial support is used to ensure the stability of the surrounding rock. The elastic modulus is the most important indicator reflecting the safety and strength of the initial support structure, and determines the surrounding rock pressure that the initial support bears during the design.

[0154] The initial support of the composite double-layer initial support is a reinforced concrete structure. Currently, the commonly used calculation methods for the elastic modulus of reinforced concrete structures include: elastic theory method, empirical formula method, and numerical simulation method.

[0155] Elasticity theory method. It mainly calculates the deformation of the material through the stress-strain relationship based on the elastic modulus and stress conditions of the material. For reinforced concrete structures, its elastic modulus can be calculated through parameters such as the elastic modulus of concrete and steel bars, the volume fraction of steel bars, and the arrangement of steel bars;

[0156] Empirical formula method. It is mainly to calculate the elastic modulus of the material through a formula obtained from a large amount of experimental data. For reinforced concrete structures, commonly used empirical formulas include Euler-Bernoulli beam theory formula, Timoshenko beam theory formula, etc.

[0157] Numerical simulation method. It refers to the use of numerical calculation methods such as finite element analysis to simulate the deformation of materials after being subjected to force and calculate the elastic modulus of the material. This method can more accurately calculate the elastic modulus of reinforced concrete.

[0158] In previous numerical simulation analysis of initial tunnel support, researchers often use conversion methods to simplify calculations, converting the elastic modulus of steel components such as I-beams, grid steel frames, and steel meshes to the elastic modulus of shotcrete. This method only considers the steel structure as a rigid body, without considering the bonding effect between the steel bars and concrete and the influence of the layout method, and has certain shortcomings. This embodiment proposes a refined numerical simulation and auxiliary design method for a double-layer support structure for a large-section collapsible loess tunnel similar to a highway tunnel, explores the difference between the conversion method of the elastic modulus of the double-layer support and the refined numerical simulation method, and further applies it to the construction of tunnels and the design of support schemes.

[0159] Structural design concept of double-layer support structure

[0160] Through the analysis of the influence of rainfall infiltration, different cycle advances, and initial support strength on the initial support structure of the tunnel, it can be seen that the most important cause of tunnel collapse is the insufficient initial support strength. The large deformation problem of shallow buried large-section sandy loess tunnels is a difficult problem in the tunnel construction process. The sandy loess has low shear strength and high collapsibility. It is very easy to have large deformation problems during tunnel excavation, resulting in common engineering problems such as deformation intrusion of the initial support structure, cracking of the double-layer initial support, and distortion of the steel arch frame.

[0161] In order to solve this type of engineering problem, double-layer initial support, as a commonly used construction method, plays an extremely important role in stabilizing tunnel construction and controlling surrounding rock deformation. Therefore, it is necessary to discuss the design method of double-layer support structure. The selection of materials and the determination of size in the design of double-layer initial support structure are key design parameters, which need to be reasonably determined according to specific geological conditions, engineering requirements and construction technology. There is no standard design method. In the design, it is mainly based on engineering experience and relevant standards and specifications, but the empirical method is usually a "one-size-fits-all" method, which is difficult to cope with the particularity of each specific project. It may not take into account special geological conditions or engineering environment, resulting in inaccurate design and difficulty in accurately reflecting the risks of specific projects. Therefore, when engineering designers use the empirical method to design double-layer initial support structures, they will use numerical simulation methods to improve the scientificity and accuracy of the design.

[0162] Based on the relevant literature on double-layer support structure and reference to the "Highway Tunnel Design Code", it can be seen that the design parameters of double-layer support do not change much. The general parameters of double-layer support are: shotcrete strength is C20, C25, C30, C35; shotcrete thickness is 480, 510, 550, 600mm; steel mesh diameter is 6, 8, 10, 12mm; steel mesh spacing is 150, 200, 250, 300mm; grid steel frame diameter is 18, 20, 22, 25mm; grid steel frame spacing is 300, 400, 500, 600mm; I-beam arch frame model is I18, I20b, I22b, I25b; I-beam arch frame spacing is 300, 400, 500, 600mm.

[0163] The tunnel excavation progress is strictly controlled according to the designed steel frame spacing to control the excavation step. After each step and each cycle of excavation is completed, the face is immediately closed and the initial support construction is carried out. After the tunnel excavation is completed, the cross-sectional dimensions of the excavation face are checked, and high-pressure water or high-pressure air is used for flushing before the initial spraying. The pre-buried steel bars control the thickness mark of the shotcrete. The shotcrete operation should follow the excavation working face. The initial spraying thickness is 40mm, followed by the installation of the steel mesh. The steel mesh should be processed in the factory or on-site. The second layer of steel mesh is laid together with the I-beam arch frame. The displacement of the arch foot is fixed with a locking foot anchor rod. The U-shaped clip is welded firmly with the I-beam arch frame and filled with mortar. The adjacent two steel frames are connected with longitudinal steel bars to ensure the rigidity and stability of the steel frame along the longitudinal direction of the tunnel. Then the grid steel frame is installed and the concrete is sprayed again.

[0164] Refined numerical simulation method for double-layer support structure

[0165] The elastic modulus is an important mechanical property of reinforced concrete structure, and it is known that the strength of the initial support is the most sensitive to tunnel collapse. In previous studies, the model test method or theoretical calculation method was generally used to determine the elastic modulus of similar reinforced concrete structures. This embodiment aims to propose a refined numerical simulation method for double-layer support of shallow loess tunnels, and uses the numerical simulation software ABAQUS to simulate the actual structure of the initial support structure in the project, including the spatial distribution of steel mesh, I-beam, and grid steel frame, the mutual bonding between steel bars and concrete, and the boundary constraints of the initial support. The common influencing factors of the elastic modulus of the double-layer initial support: concrete strength and thickness, diameter and spacing of the steel mesh, diameter and spacing of the grid steel frame, I-beam arch frame and spacing and the law between the elastic modulus are discussed and studied. The following simulation methods are mainly used as refined numerical simulation methods: double-layer initial support unit method, load-structure method, stratum-structure method, theoretical method.

[0166] Determination of constitutive parameters of double-layer support structure unit

[0167] Previous studies on composite materials similar to reinforced concrete mainly used the homogenization theory method, taking the unit cell of the microstructure of the material as the basic unit, assuming that the unit cell has periodicity, and describing the macrostructure properties through the microstructure. In order to determine the equivalent elastic modulus of the double-layer initial support, a unit body with a size of 1000mm×1000mm×480mm (length×width×height) was selected, and the equivalent elastic modulus of the initial support as a whole was predicted by the elastic modulus of the unit body. In the finite element analysis of reinforced concrete structures, ABAQUS can effectively simulate the mechanical response characteristics of reinforced concrete structures, so ABAQUS is used to establish a double-layer initial support model.

[0168] 1. Numerical simulation parameters

[0169] The concrete uses the unique plastic damage model (CDP) in ABAQUS to simulate the interaction between the double-layer initial support structure and the ground, the interaction between the steel bars and concrete, and the spatial structure of the steel bar components, such as Figure 3 The specific values ​​of the simulation parameters are shown in Table 2-Table 3.

[0170] Table 2 Model parameters

[0171] Material Name Density / kg.m-3 Elastic modulus / GPa μ Constitutive model C25 2500 28 0.2 CDP steel 7850 210 0.25 elasticity

[0172] Table 3 CDP parameters

[0173] Dilation Ecc fb0 / fc0 K Vis 40 0.1 1.16 0.6667 0

[0174] Note: Dilation is the expansion angle; Ecc is the eccentricity; Vis is the viscosity coefficient.

[0175] 2. Establishment of finite element model

[0176] Based on the above considerations, the size of the finite element model is determined to be 1000mm×1000mm×480mm (length×width×height). In the process of establishing the double-layer initial support finite element model, the structure is divided into concrete, steel mesh, I-beam arch frame, and steel grille for modeling, and assembled into initial support units in the assembly module. According to the unit library provided by ABAQUS, concrete uses solid units, and because the steel bar mainly plays a tensile role in the component, the steel bar uses line units. The constitutive model used for concrete is the plastic damage model, and the steel bar uses the elastic model.

[0177] The specific modeling process is as follows:

[0178] In the part module, build component models. First, build models of concrete, steel mesh, grid steel frame, and I-beam arch frame respectively. When modeling concrete components, select "deformable" for type, "solid" for shape, and "stretch" for type. Draw the cross-sectional dimensions of the concrete structure in the drawing interface, and use the stretch command to form components. For steel mesh, grid steel frame, and I-beam arch frame components, you only need to create one component. Select "deformable" for type, "line" for shape, and "plane" for type, and create a 1000mm long line component.

[0179] In the Property module, first create the steel and concrete material properties based on the selected concrete and steel constitutive models. Concrete is C25, and the constitutive model is a plastic damage model; steel mesh, grid steel frame, I-beam arch frame and other steel components use an elastic model without considering plasticity.

[0180] After the material definition is completed, define the required cross-sectional shape of the steel bar component, including circular cross-sections with diameters of 8mm, 10mm, 12mm, and 25mm, as well as I-beam sections. Then create the cross-section, select "solid" for the concrete cross-section category, "homogeneous" for the type, and concrete for the material; select "beam" for the steel bar component cross-sectional category, "beam" for the type, select the corresponding steel bar size for the cross-section, and select the defined steel bar material for the material. Finally, assign the cross-section of the corresponding component and the direction of the beam unit component, and give the cross-sectional attributes to the steel bar component.

[0181] In the Assembly module, the actual spatial structure of the initial support is created by using functions such as translation, rotation, and array, and then the steel mesh, I-beam arch, and grid steel frame components are formed separately through the merge function. This ensures that common nodes can be formed at the joints of the steel components, ensuring that the deformation of the components is coordinated and consistent. Finally, the steel components and concrete components are assembled into a complete initial support unit.

[0182] The analysis step is defined in the Step module. The main purpose of creating the analysis step is to load the double-layer initial support unit components in stages, obtain the stress-strain curve of the reinforced concrete components, and thus obtain the equivalent elastic modulus of the initial support elastic stage. A total of two analysis steps are set. The Initial analysis step considers the influence of the structure's self-weight. Based on the existing Initial analysis step, a second analysis step (Step-1) is created. This stage realizes the application of surface loads on the top surface of the structure.

[0183] In the Interaction module, in order to simulate the interaction between steel bars and concrete structures, the steel bar components are embedded into the concrete components using the Embedded region constraint function.

[0184] In the load module, first create boundary conditions. Because the initial support in the tunnel structure is under the condition of constraints on all sides, fixed constraints are applied on all sides of the model in the Initial analysis step, and no settings are made on the upper and lower sides. Then, the load condition of the initial support is simulated. Because the elastic modulus is taken in the elastic stage of the structure, the applied load should not be too large to ensure that the structure is in the elastic stage. After consulting relevant literature and specifications, the load size is finally determined to be 1MPa. The load is applied to the upper top surface to simulate the surrounding rock pressure on the initial support.

[0185] In the Mesh module, the quality of mesh division is crucial to the accuracy of the calculation results. The mesh is divided according to the components. In order to ensure the convergence of the calculation results, the approximate division size of the concrete unit is 50mm, and the approximate division size of the steel component unit is 25mm. The unit type of concrete adopts three-dimensional eight-node linear hexahedron unit (C3D8R), and the steel bar adopts two-node spatial linear beam unit (B31).

[0186] 3. Obtaining the elastic modulus obtained by refined numerical simulation method

[0187] In the operation module, create a new job. After the calculation is completed, enter the visualization module to view the results. By extracting the vertical stress (σ 22 ) and strain (ε 22 ), and the stress-strain curve of the initial support under the surface load of 1MPa is obtained, as shown in Figure 4 As shown, according to this curve, the elastic modulus of the double-layer initial support elastic stage is 41.11 GPa, while the elastic modulus calculated by the conversion method is 55.63 GPa. The elastic modulus obtained by the refined numerical simulation method is reduced by nearly 35% compared with it.

[0188] 4. Numerical simulation scheme

[0189] After determining the preliminary calculation method of the equivalent elastic modulus of the double-layer initial support, the main influencing factors of the stiffness of the double-layer initial support structure were studied in order to find the variation law of different influencing factors and the equivalent elastic modulus of the double-layer initial support structure. As a reinforced concrete structure, the main influencing factors of the elastic modulus of the double-layer initial support structure include: concrete strength and thickness, steel mesh diameter and spacing, grid steel frame diameter and spacing, I-beam model and spacing. The values ​​of the influencing factors are mainly determined by referring to the "Highway Tunnel Design Code", "Highway Tunnel Construction Technical Code" and the commonly used specifications in construction. The numerical simulation scheme is shown in Table 4.

[0190] Table 4 Numerical simulation research plan

[0191]

[0192] Stratigraphic-structural method

[0193] In the analysis of double-layer support structure, the load-structure method simplifies the load and boundary conditions. Therefore, based on the above research, the stratum-structure method is considered to study the equivalent elastic modulus of the double-layer support structure. The size of the finite element model is 100m×80m×1.2m (length×width×height). In order to ensure the quality of the grid, it is divided into four parts at the center of the model. The analysis step is divided into two steps, the first step is the ground stress balance, and the second step is the tunnel excavation.

[0194] (1) Influence of concrete strength on initial support elastic modulus

[0195] The initial support construction phase of shallow loess tunnels bears most of the surrounding rock pressure. Generally, a composite double-layer initial support is used, which is a reinforced concrete composite structure. The equivalent elastic modulus of reinforced concrete structure is greatly affected by the mechanical properties of both steel and concrete. The elastic modulus of steel is generally fixed at 210GPa, so only the change in the elastic modulus of concrete is considered. The higher the concrete grade, the greater the equivalent elastic modulus, and the greater the elastic modulus of the double-layer initial support. By changing the strength of the concrete material, under the same load conditions, the concrete strength and the elastic modulus E calculated by the refined numerical simulation method are obtained. eq The change law of elastic modulus E is calculated by conversion method, such as Figure 5 shown.

[0196] The elastic modulus of the double-layer initial support obtained by the refined numerical simulation method and the conversion method are positively correlated with the concrete strength. The higher the concrete grade, the greater the initial support elastic modulus. The elastic modulus of the refined numerical simulation method is smaller than the elastic modulus of the conversion method. The relative difference δ = |E eq-E| / E×100%, the relative difference is 28% to 31% within the range of concrete strength, and the average error is 27.46%. The relative difference gradually converges with the increase of concrete strength, and the linear relationship between it and concrete strength is:

[0197] δ=-0.0179q+0.7888;

[0198] For the refined numerical simulation method, when the concrete grade increases from C20 to C25, the elastic modulus increases from 38GPa to 41.3GPa, an increase of 8.68%; when the concrete grade increases from C25 to C30, the elastic modulus increases from 41.3GPa to 44.1GPa, an increase of 6.78%; when the concrete grade increases from C30 to C35, the elastic modulus increases from 44.1GPa to 46.2GPa, an increase of 4.76%. Through the curves of concrete grade and elastic modulus, it can be seen that the two conform to a linear function relationship:

[0199] E eq =1.3679q+3.0728;

[0200] For the conversion method, when the concrete grade increases from C20 to C25, the elastic modulus increases from 50.67GPa to 53.17GPa, an increase of 4.93%; when the concrete grade increases from C25 to C30, the elastic modulus increases from 53.17GPa to 55.17GPa, an increase of 3.76%; when the concrete grade increases from C30 to C35, the elastic modulus increases from 55.17GPa to 56.67GPa, an increase of 2.72%. Through the curves of concrete grade and elastic modulus, it can be seen that the two conform to a linear function relationship:

[0201] E = q + 25.17;

[0202] (2) Influence of concrete thickness on initial support elastic modulus

[0203] In the initial stage of shallow loess tunnel excavation, the surrounding rock pressure is mainly borne by I-beam arches and grid arches. After a period of time after the initial support is completed, the strength of the concrete gradually increases. At this time, the arch and concrete provide surrounding rock support pressure as a composite. The thickness of shotcrete is directly related to the size of the support pressure. Its thickness is almost equal to the cross-sectional height of the steel arch. The equivalent elastic modulus of the double-layer initial support and the thickness of the concrete change law are as follows: Figure 6 shown.

[0204] The elastic modulus calculated by both methods decreases with the thickness of concrete. The equivalent elastic modulus calculated by the refined numerical simulation method is generally smaller than the calculation result of the conversion method. The elastic modulus of the double-layer initial support is negatively correlated with the thickness of concrete. The greater the thickness of the concrete, the smaller the initial support elastic modulus. The relative difference δ varies from 23% to 26%, with an average error of 29.72%. It gradually converges with the increase of concrete thickness, and the fitting formula with the concrete thickness is:

[0205] δ=0.0002d+0.2029;

[0206] For the refined numerical simulation method, when the concrete thickness increases from 480mm to 510mm, the elastic modulus decreases from 41.3GPa to 40GPa, a decrease of 3.15%; when the concrete grade increases from 510mm to 550mm, the elastic modulus decreases from 40GPa to 38.4GPa, a decrease of 4.00%; when the concrete grade increases from 550mm to 600mm, the elastic modulus decreases from 38.4GPa to 36.8GPa, a decrease of 4.17%. Through the curves of concrete grade and elastic modulus, it can be seen that the two conform to a linear function relationship:

[0207] E eq =-0.0375d+59.171;

[0208] For the conversion method, when the concrete thickness increases from 480mm to 510mm, the elastic modulus increases from 53.17GPa to 51.69GPa, a decrease of 2.78%; when the concrete grade increases from 510mm to 550mm, the elastic modulus decreases from 51.69GPa to 49.97GPa, a decrease of 3.33%; when the concrete grade increases from 550mm to 600mm, the elastic modulus decreases from 49.97GPa to 48.14GPa, a decrease of 3.66%. Through the curves of concrete grade and elastic modulus, it can be seen that the two conform to a linear function relationship:

[0209] E = -0.0418d + 73.082;

[0210] From the stiffness of the steel bars and concrete materials in the composite double-layer initial support structure, it can be seen that the steel bar structure contributes relatively greatly to the overall elastic modulus of the composite, and the concrete material mainly plays the role of protecting the steel bar structure. Therefore, the thickness of the concrete only needs to leave enough protective layer thickness for the steel bar structure to meet the requirements of the specification.

[0211] (3) Influence of steel mesh diameter on initial support elastic modulus

[0212] The factors affecting the equivalent elastic modulus of double-layer initial support by steel mesh include the diameter of the steel mesh and the spacing between the steel bars in the steel mesh. This section mainly studies the influence of the diameter of the steel mesh on the elastic modulus of initial support. The change rules between the two are as follows: Figure 7 shown.

[0213] The initial support equivalent elastic modulus is positively correlated with the diameter of the steel mesh. The larger the diameter of the steel mesh, the larger the initial support elastic modulus, which is consistent with construction experience and the researchers' cognition. The relative difference δ ranges from 28% to 30%, with an average error of 28.95%. The fitting formula is:

[0214] δ=0.0017s1+0.2744;

[0215] For the refined numerical simulation method, when the diameter of the steel mesh increases from 6mm to 8mm, the elastic modulus increases from 41.28GPa to 41.3GPa, an increase of 0.05%; when the concrete grade increases from 8mm to 10mm, the elastic modulus increases from 41.3GPa to 41.32GPa, an increase of 0.05%; when the concrete grade increases from 10mm to 12mm, the elastic modulus increases from 41.32GPa to 41.34GPa, an increase of 0.05%. Through the curve law of the equivalent elastic modulus of the double-layer initial support and the diameter of the steel mesh, it can be seen that the two conform to the linear function relationship:

[0216] E eq =0.01s1+41.22;

[0217] For the conversion method, when the diameter of the steel mesh increases from 6mm to 8mm, the elastic modulus increases from 53.04GPa to 53.17GPa, an increase of 0.24%; when the concrete grade increases from 8mm to 10mm, the elastic modulus increases from 53.17GPa to 53.34GPa, an increase of 0.31%; when the concrete grade increases from 10mm to 12mm, the elastic modulus increases from 53.34GPa to 53.54GPa, an increase of 0.38%. Through the curve law of the equivalent elastic modulus of the double-layer initial support and the diameter of the steel mesh, it can be seen that the two conform to a linear function relationship:

[0218] E = 0.0824s1 + 52.529;

[0219] (4) Effect of steel mesh spacing on initial support elastic modulus

[0220] The previous section studied the effect of the diameter of the steel mesh on the equivalent elastic modulus of the double-layer initial support. This section mainly studies another effect of the steel mesh structure, the steel mesh spacing. The relationship between the steel mesh spacing and the equivalent elastic modulus is as follows: Figure 8 shown.

[0221] The elastic modulus of the double-layer initial support is negatively correlated with the spacing of the steel mesh. The larger the spacing of the steel mesh, the smaller the initial elastic modulus. The relative difference δ ranges from 28% to 29%, with an average error of 28.59%. It gradually becomes discrete with the increase of concrete thickness, and the fitting formula with the concrete thickness is:

[0222] δ=-0.000017l1+0.289680;

[0223] For the refined numerical simulation method, when the spacing of the steel mesh increases from 150mm to 200mm, the elastic modulus decreases from 41.3GPa to 41.29GPa, a decrease of 0.02%; when the spacing of the steel mesh increases from 200mm to 250mm, the elastic modulus decreases from 41.29GPa to 41.28GPa, a decrease of 0.02%; when the spacing of the steel mesh increases from 250mm to 300mm, the elastic modulus decreases from 41.28GPa to 41.27GPa, a decrease of 0.02%. Through the curves of the spacing of the steel mesh and the equivalent elastic modulus of the double-layer initial support, it can be seen that the two conform to a linear function relationship:

[0224] E eq =-0.0002l1+41.33;

[0225] For the conversion method, when the spacing of the steel mesh increases from 150mm to 200mm, the elastic modulus decreases from 53.17GPa to 53.10GPa, a decrease of 2.5%; when the spacing of the steel mesh increases from 200mm to 250mm, the elastic modulus decreases from 53.10GPa to 53.06GPa, a decrease of 0.07%; when the spacing of the steel mesh increases from 250mm to 300mm, the elastic modulus decreases from 53.06GPa to 53.02GPa, a decrease of 0.07%. Through the curves of the spacing of the steel mesh and the equivalent elastic modulus of the double-layer initial support, it can be seen that the two conform to a linear function relationship:

[0226] E = -0.001l1 + 53.302;

[0227] (5) Influence of grid steel frame diameter on initial support elastic modulus

[0228] When the surrounding rock conditions of the tunnel are relatively good, the initial support is generally single-layer support, and the I-beam arch frame mainly bears the surrounding rock pressure. However, the surrounding rock conditions of a highway tunnel are poor, and the settlement requirements of the surface structures are high, so double-layer initial support is adopted. The I-beam arch frame and the grid steel frame jointly bear the surrounding rock pressure. The two provide most of the support resistance, so it is necessary to discuss and study the influence of the grid steel frame on the equivalent elastic modulus of the double-layer initial support. This section mainly studies the steel bar diameter among the influencing factors of the grid steel frame. The relationship between the equivalent elastic modulus and the grid steel frame diameter is as follows: Fig. 9 shown.

[0229] As can be seen from the figure, the initial support elastic modulus is positively correlated with the grid steel frame diameter. The larger the grid steel frame diameter, the larger the initial support elastic modulus. The relative difference δ ranges from 28% to 31%, with an average error of 30.20%. The fitting formula is:

[0230] δ=-0.0034s2+0.3744;

[0231] For the refined numerical simulation method, when the diameter of the grid steel frame increases from 18mm to 20mm, the elastic modulus increases from 39.8GPa to 40GPa, an increase of 0.5%; when the concrete grade increases from 20mm to 22mm, the elastic modulus increases from 40GPa to 40.5GPa, an increase of 1.25%; when the concrete grade increases from 22mm to 25mm, the elastic modulus increases from 40.5GPa to 41.3GPa, an increase of 1.98%. Through the curves of concrete grade and elastic modulus, it can be seen that the two conform to a linear function relationship:

[0232] E eq =0.2206s2+35.713;

[0233] For the conversion method, when the diameter of the grid steel frame increases from 18mm to 20mm, the elastic modulus increases from 52.13GPa to 52.40GPa, an increase of 0.50%; when the concrete grade increases from 20mm to 22mm, the elastic modulus increases from 52.40GPa to 52.68GPa, an increase of 0.55%; when the concrete grade increases from 22mm to 25mm, the elastic modulus increases from 52.68GPa to 53.17GPa, an increase of 0.92%. Through the curves of concrete grade and elastic modulus, it can be seen that the two conform to a linear function relationship:

[0234] E = 0.1484s2 + 49.443;

[0235] (6) Influence of grid steel frame spacing on initial support elastic modulus

[0236] Based on the above-mentioned influence of grid steel frame diameter on the equivalent elastic modulus of double-layer initial support, this section mainly studies the relationship between grid steel frame spacing and elastic modulus. The changing rules between the two are as follows: Fig.10 shown.

[0237] It can be seen from the figure that the initial support elastic modulus is negatively correlated with the grid steel frame spacing. The larger the grid steel frame spacing, the smaller the initial support elastic modulus. The relative difference δ varies from 14% to 22%, with an average error of 18.98%. The fitting formula is:

[0238] δ=-0.0003l2+0.3082;

[0239] For the refined numerical simulation method, when the grid steel frame spacing increases from 300mm to 400mm, the elastic modulus decreases from 44.4GPa to 44.3GPa, a decrease of 0.23%; when the grid steel frame spacing increases from 400mm to 500mm, the elastic modulus decreases from 44.3GPa to 41.5GPa, a decrease of 6.32%; when the grid steel frame increases from 500mm to 600mm, the elastic modulus decreases from 41.5GPa to 41.3GPa, a decrease of 0.48%. Through the curves of concrete grade and elastic modulus, it can be seen that the two conform to a linear function relationship:

[0240] E eq =-0.0252l2+53.51;

[0241] For the conversion method, when the grid steel frame spacing increases from 300mm to 400mm, the elastic modulus does not change; when the grid steel frame spacing increases from 400mm to 500mm, the elastic modulus decreases from 53.17GPa to 50.19GPa, a decrease of 5.60%; when the grid steel frame increases from 500mm to 600mm, the elastic modulus decreases from 50.19GPa to 47.22GPa, a decrease of 5.93%. Through the curves of concrete grade and elastic modulus, it can be seen that the two conform to a linear function relationship:

[0242] E = -0.0417l2 + 68.648;

[0243] (7) Influence of I-beam type on initial support elastic modulus

[0244] I-beam is the most commonly used steel arch frame in tunnel initial support. The selection of I-beam model is related to the safety of tunnel construction quality, as well as the construction cost, and also determines the size of the equivalent elastic modulus of the double-layer initial support. The relationship between the equivalent elastic modulus of the two methods and the I-beam model (i.e. the size of the cross-sectional area) is as follows: Fig.11 shown.

[0245] As can be seen from the figure, the elastic modulus of the double-layer initial support is positively correlated with the type of I-beam (section area). The larger the section area of ​​the I-beam, the larger the initial support elastic modulus. The relative difference δ ranges from 23% to 34%, with an average error of 29.60%. The fitting formula is:

[0246] δ=-0.0043a+0.4798;

[0247] For the refined numerical simulation method, when the I-beam model changes from I18 to I20b, the elastic modulus increases from 38.4GPa to 39.8GPa, an increase of 3.65%; when the I-beam model changes from I20b to I22b, the elastic modulus increases from 39.8GPa to 41.3GPa, an increase of 3.77%; when the I-beam model changes from I22b to I25b, the elastic modulus increases from 41.3GPa to 43.5GPa, an increase of 5.33%. Through the curve law of the I-beam model (cross-sectional area) and the elastic modulus, it can be seen that the two conform to the linear function relationship:

[0248] E eq =0.2212a+31.325;

[0249] For the conversion method, when the I-beam type changes from I18 to I20b, the elastic modulus increases from 51.45GPa to 52.41GPa, an increase of 1.88%; when the I-beam type changes from I20b to I22b, the elastic modulus increases from 52.41GPa to 53.17GPa, an increase of 1.45%; when the I-beam type changes from I22b to I25b, the elastic modulus increases from 53.17GPa to 56.67GPa, an increase of 1.44%. Through the curve law of the I-beam type (cross-sectional area) and the elastic modulus, it can be seen that the two conform to a linear function relationship:

[0250] E = 0.1094a + 48.081;

[0251] (8) Influence of I-beam arch spacing on initial support elastic modulus

[0252] The previous section studied the relationship between the I-beam type and the equivalent elastic modulus of the double-layer initial support. This section mainly studies the influence of the I-beam arch spacing on the initial support elastic modulus. The specific curve law is as follows: Fig.12 shown.

[0253] As can be seen from the figure, the initial support elastic modulus is negatively correlated with the I-steel arch spacing. The larger the I-steel arch spacing, the smaller the initial support elastic modulus. The relative difference δ ranges from 21% to 26%, with an average error of 22.93%. The fitting formula is:

[0254] δ=0.0002l3+0.1651;

[0255] For the refined numerical simulation method, when the I-beam arch spacing increases from 300mm to 400mm, the elastic modulus decreases from 43.8GPa to 43.6GPa, a decrease of 0.46%; when the I-beam arch spacing increases from 400mm to 500mm, the elastic modulus decreases from 43.6GPa to 41.2GPa, a decrease of 5.50%; when the I-beam arch spacing increases from 500mm to 600mm, the elastic modulus decreases from 41.2GPa to 41GPa, a decrease of 0.49%. Through the curves of the I-beam arch spacing and the elastic modulus, it can be seen that the two conform to a linear function relationship:

[0256] E eq =-0.0108l3+47.26;

[0257] For the conversion method, when the I-beam arch spacing increases from 300mm to 400mm, the elastic modulus does not change; when the I-beam arch spacing increases from 400mm to 500mm, the elastic modulus decreases from 53.17GPa to 51.47GPa, a decrease of 3.19%; when the I-beam arch spacing increases from 500mm to 600mm, the elastic modulus does not change. Through the curves of the I-beam arch spacing and the elastic modulus, it can be seen that the two conform to a linear function relationship:

[0258] E = -0.0068l3 + 55.375;

[0259] Reliability verification of refined numerical simulation method and modulus correction formula

[0260] In order to verify the reliability of the refined numerical simulation method of double-layer support for shallow loess tunnels, the research literature on the elastic modulus of reinforced concrete structures was consulted. Existing literature 1 used experimental methods to study the elastic modulus of reinforced concrete components and test blocks with different reinforcement ratios. The test results showed that the elastic modulus of reinforced concrete structures increased with the increase of reinforcement ratio. Literature 2 used model test methods to study the equivalent elastic modulus of reinforced concrete structures under different stress states, different boundary conditions, and different reinforcement ratios. The conclusion showed that there was a positive correlation between the equivalent elastic modulus of reinforced concrete and the reinforcement ratio. In previous analyses of reinforced concrete structures, the role of steel bars was often ignored in the equivalent elastic modulus, and the elastic modulus of plain concrete was directly used as the elastic modulus of the entire component. Literature 3 studied the elastic modulus of 11 groups of reinforced concrete test blocks with different reinforcement ratios. The research results showed that the reinforcement ratio had a great influence on the equivalent elastic modulus of reinforced concrete structures. If the role of steel bars was ignored in the calculation of internal forces, the calculation results would have a large error. Reference 4 draws on the calculation method of the composite elastic modulus of composite materials, uses the numerical simulation software ANSYS in combination with experimental data, obtains the elastic modulus and reinforcement ratio law of reinforced concrete structures during the construction period, and accurately calculates the elastic modulus of reinforced concrete structures.

[0261] The formula for calculating the reinforcement ratio of reinforced concrete structures is:

[0262]

[0263] The calculation formula for the double-layer initial support reinforcement ratio is:

[0264]

[0265] The calculation formula of the change rate of double-layer support elastic modulus is:

[0266]

[0267] The specific values ​​of the equivalent elastic modulus of double-layer initial support with different reinforcement ratios under the refined numerical simulation method are shown in Table 5:

[0268] Table 5 Equivalent elastic modulus of double-layer initial support with different reinforcement ratios under refined numerical simulation method

[0269]

[0270]

[0271] The measured values ​​of elastic modulus and reinforcement ratio of reinforced concrete structure, and the measured values ​​of elastic modulus and reinforcement ratio of double-layer initial support structure under refined numerical simulation method, the relationship between the two is as follows Fig.13 shown.

[0272] Depend on Fig.13 It can be seen that the values ​​of reinforcement ratio and elastic modulus change rate of different numerical simulation schemes calculated by the refined numerical simulation method are within the range of model test data, and the refined numerical simulation method can be considered feasible.

[0273] In order to facilitate the design, the elastic modulus E of the double-layer initial support structure under different reinforcement ratios ρ obtained by the refined numerical simulation is eq The following empirical relationship is established between the elastic modulus E calculated using the traditional calculation method (conversion method):

[0274]

[0275] Compare the calculated value obtained by the above formula with the elastic modulus value calculated by the refined numerical simulation method, such as Fig.14 As shown, the correlation coefficient between the calculated value obtained by the empirical formula and the calculated value obtained by the refined numerical simulation reaches 90%, which can basically meet the engineering accuracy.

[0276] Therefore, the present invention adopts the above-mentioned method for calculating the equivalent modulus of the double-layer tunnel support. Through a refined numerical simulation method, it can fully consider the interaction between the steel bars and concrete materials, the interaction between the double-layer initial support structure and the stratum, and the influence of different spatial structures of the steel bar components on the elastic modulus of the double-layer initial support structure.

[0277] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for calculating the equivalent modulus of double-layer support of a tunnel, characterized in that: The following steps are involved: S1. Analyze the environmental conditions, geological factors and construction conditions of the tunnel through on-site investigation, obtain the influencing factors of tunnel collapse, and conduct sensitivity analysis on these influencing factors; S2. Use refined numerical simulation methods to study the common influencing factors of the elastic modulus of the double-layer initial support, and calculate the equivalent elastic modulus of the double-layer support structure; S3. Propose a refined numerical simulation method for reliability verification and a modulus correction formula.

2. The method for calculating the equivalent modulus of double-layer support of a tunnel according to claim 1, characterized in that: The influencing factors in step S1 include rainfall infiltration depth, excavation cycle footage and initial support strength, specifically including: a. Analysis of the impact of rainfall infiltration depth on tunnel stability, including Establish the stratum-tunnel model through the numerical simulation software MIDAS GTS / NX; The double-layer initial support structure and the temporary middle wall are both composite double-layer initial support structures. The elastic modulus value is determined using the conversion method. The conversion method is the principle that the initial support structure is equal before and after, and the strength of the steel member is converted to concrete. The calculation formula is: Among them, E is the initial support elastic modulus of the conversion method; E c is the elastic modulus of plain concrete; E s A is the elastic modulus of steel; w A is the cross-sectional area of ​​the steel mesh; g A is the cross-sectional area of ​​the I-beam; gs A is the cross-sectional area of ​​the grid steel frame; c is the concrete cross-sectional area; The elastic modulus of temporary support is: Among them, E 临 is the elastic modulus of temporary support after conversion; b. Analysis of the impact of excavation cycle footage on tunnel stability, by simulating the stratum stress state and soil deformation under different footages, to understand the risk of geological disasters that may occur; c. Analysis of the influence of initial support strength on tunnel stability. The elastic modulus E of the single-layer support is calculated by the conversion method. d .

3. The method for calculating the equivalent modulus of double-layer support of a tunnel according to claim 1 is characterized in that: A sensitivity analysis was conducted on the factors affecting rainfall infiltration depth, excavation cycle footage and initial support strength in S1, including: Since the units of the three influencing factors, namely rainfall infiltration depth, excavation cycle advance, and initial support strength, are inconsistent and cannot be directly compared, a variable sensitivity coefficient M with a dimension of 1 is defined to quantitatively describe their influence on tunnel collapse; the sensitivity coefficient formula of each influencing factor is: M l =(Δσ / σ) / (ΔH / H); M m =(Δσ / σ) / (ΔL / L); M n =(Δσ / σ) / (ΔE / E); Among them, M>0 means that the tunnel collapse is positively correlated with the influencing factors, and M<0 means that the tunnel collapse is negatively correlated with the influencing factors; M l M is the sensitivity coefficient of rainfall infiltration depth to tunnel collapse; m M is the sensitivity coefficient of excavation cycle advance to tunnel collapse; n is the sensitivity coefficient of initial support strength to tunnel collapse; Δσ is the difference between the maximum tensile stress of the initial support arch of tunnel excavation and the maximum tensile stress of the reference initial support arch; σ is the maximum tensile stress of the tunnel arch of reference tunnel excavation; ΔH is the difference between the rainfall infiltration depth and the reference rainfall infiltration depth; H is the reference rainfall infiltration depth; ΔL is the difference between the tunnel excavation cycle footage and the reference tunnel excavation footage; L is the reference tunnel excavation footage; ΔE is the difference between the elastic modulus of the initial support strength and the elastic modulus of the reference initial support strength; E is the elastic modulus of the reference initial support strength.

4. The method for calculating the equivalent modulus of double-layer support of a tunnel according to claim 1, characterized in that: The refined numerical simulation method in S2 specifically includes: S21. Determination of constitutive parameters of double-layer support structure unit, including: The double-layer initial support model was established using the numerical simulation software ABAQUS. The plastic damage model in ABAQUS was used to simulate the interaction between the double-layer initial support structure and the ground, the interaction between the steel bars and concrete, and the spatial structure of the steel bar components. Establish a finite element model, divide the structure into concrete, steel mesh, I-beam arch frame, and steel grille, and then assemble them into initial support units in the assembly module; The elastic modulus E of the double-layer initial support elastic stage obtained by the refined numerical simulation method eq ; The factors affecting the stiffness of the double-layer initial support structure are studied to find the changing rules of the equivalent elastic modulus of the double-layer initial support structure with different influencing factors; as a reinforced concrete structure, the factors affecting the elastic modulus of the double-layer initial support structure mainly include: concrete strength, concrete thickness, steel mesh diameter, steel mesh spacing, grid steel frame diameter, grid steel frame spacing, I-beam arch frame model, and I-beam arch frame spacing; S22. The equivalent elastic modulus of the double-layer support structure is studied using the stratum-structure method.

5. The method for calculating the equivalent modulus of double-layer support of a tunnel according to claim 2, characterized in that: The influence of different influencing factors on the initial support elastic modulus is as follows: A. The influence of concrete strength q on the elastic modulus of initial support. By changing the strength of concrete materials, under the same load conditions, the concrete strength and the elastic modulus E calculated by the refined numerical simulation method are obtained. eq The change law of elastic modulus E calculated by the conversion method and the refined numerical simulation method are both positively correlated with the elastic modulus of the double-layer initial support and the concrete strength, thus obtaining the relative difference δ=|E eq -E| / E×100%, the linear relationship between the relative difference and the concrete strength is: δ=-0.0179q+0.7888; Concrete strength and E eq The linear function relationship is: E eq =1.3679q+3.0728; The linear function relationship between concrete strength and E is E = q + 25.17; B. The influence of concrete thickness d on the initial support elastic modulus. The double-layer support elastic modulus is negatively correlated with the concrete thickness. The fitting formula of relative difference and concrete thickness is: δ = 0.0002d + 0.2029; Concrete thickness and E eq The linear function relationship is: E eq =-0.0375d+59.171; The linear function relationship between concrete thickness and E is: E = -0.0418d + 73.082; C. The influence of steel mesh diameter s1 on the initial support elastic modulus. The initial support equivalent elastic modulus is positively correlated with the steel mesh diameter. The fitting formula between the relative difference and the steel mesh diameter is: δ = 0.0017s1 + 0.2744; Steel mesh diameter and E eq The linear function relationship is: E eq =0.01s1+41.22; The linear function relationship between the steel mesh diameter and E is: E = 0.0824s1 + 52.529; D. The influence of the steel mesh spacing l1 on the initial support elastic modulus. The double-layer initial support elastic modulus is negatively correlated with the steel mesh spacing, and the fitting formula is: δ = -0.000017l1 + 0.289680; Steel mesh spacing and E eq The linear function relationship is: E eq =-0.0002l1+41.33; The linear function relationship between the steel mesh spacing and E is: E = -0.001l1 + 53.302; E. The influence of grid steel frame diameter s2 on the initial support elastic modulus. The initial support elastic modulus is positively correlated with the grid steel frame diameter, and the fitting relationship is: δ=-0.0034s2+0.3744; Diameter of grid steel frame and E eq The linear function relationship is: E eq =0.2206s2+35.713; The linear function relationship between the diameter of the grid steel frame and E is: E = 0.1484s2 + 49.443; F. The influence of grid steel frame spacing l2 on the initial support elastic modulus. The initial support elastic modulus is negatively correlated with the grid steel frame spacing, and the fitting relationship is: δ=-0.0003l2+0.3082; Grid steel frame spacing and E eq The linear function relationship is: E eq =-0.0252l2+53.51; The linear function relationship between the grid steel frame spacing and E is: E = -0.0417l2 + 68.648; G. The influence of I-beam model a on the initial support elastic modulus. The double-layer initial support elastic modulus is positively correlated with the I-beam model, and the fitting formula is: δ=-0.0043a+0.4798; I-beam model and E eq The linear function relationship is: E eq =0.2212a+31.325; The linear function relationship between the I-beam model and E is: E = 0.1094a + 48.081; H. The influence of the spacing between I-beam arches on the initial support elastic modulus. The initial support elastic modulus is negatively correlated with the spacing between I-beam arches. The fitting formula is: δ=0.0002l3+0.1651; I-beam arch spacing and E eq The linear function relationship is: E eq =-0.0108l3+47.26; The linear function relationship between the I-beam arch spacing and E is: E = -0.0068l3 + 55.

375.

6. The method for calculating the equivalent modulus of double-layer support of a tunnel according to claim 1, characterized in that: Step S3 is specifically as follows: The formula for calculating the reinforcement ratio of reinforced concrete structures is: Among them, A s is the cross-sectional area of ​​the steel bars in the reinforced concrete structure; The calculation formula for the double-layer initial support reinforcement ratio is: The calculation formula of the change rate of double-layer support elastic modulus is: Among them, E eq is the elastic modulus of the double-layer support structure under different reinforcement ratios; Determine the equivalent elastic modulus of double-layer initial support with different reinforcement ratios using a refined numerical simulation method; The elastic modulus E of the double-layer initial support structure under different reinforcement ratios ρ obtained by the refined numerical simulation method eq The following relationship is established between the converted elastic modulus E:

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