A method for determining the comprehensive stiffness of tunnel composite support systems

Abstract

The present invention discloses a method for determining the comprehensive stiffness of a tunnel composite support system, comprising the following steps: step 1, establishing a large three-dimensional model, simulating construction to obtain a curve of convergence displacement of characteristic points as excavation progresses; step 2, excavating the tunnel in the model once, applying an initial virtual support force on the tunnel wall, and obtaining a relationship curve between the convergence displacement of the characteristic points and the virtual support force; step 3, establishing a corresponding curve diagram of the distance between the tunnel face and the monitoring surface and the virtual support force of the tunnel wall; step 4, drawing a relationship curve between the distance between the tunnel face and the monitoring surface and the displacement completion rate of the monitoring point under the support action; step 5, combining the relationship curve between the displacement completion rate and the virtual support force and the relationship curve between the distance between the tunnel face and the monitoring surface and the displacement completion rate of the characteristic point under the support action, and calculating the actual comprehensive stiffness value of the composite support system. The present invention has the advantages of quantitatively evaluating support stiffness, good simulation effect, and convenient construction.

Description

Technical Field

[0001] The invention belongs to the technical field of tunnel simulation construction, and in particular relates to a method for determining the comprehensive stiffness of a tunnel composite support system. Background Art

[0002] The LDP (Longitudinal Deformation Curve) and GRC (Gross Displacement Characteristic Curve) together form the basis of the tunnel convergence constraint method. They can be used to analyze the surrounding rock deformation and support structure response caused by tunnel excavation, providing important theoretical basis and practical guidance for tunnel support design. ‌‌‌With the rapid development of rock theory and numerical simulation methods, numerical simulation calculation methods have become an important method for the calculation, analysis and design of tunnels. At the same time, with the innovation of support structure forms and the continuous improvement of the construction monitoring level of the New Austrian Tunneling Method, the convergence constraint method came into being in the development of support design to intuitively express the relevant effects of surrounding rock and support. Although the convergence constraint method can simply estimate the load borne by a simple support structure installed in a tunnel, for a complex tunnel support system containing multiple support structures and different layout forms, it is also necessary to consider the influence of the time effect caused by the different construction timing of each support. It cannot reflect the interaction mechanism between surrounding rock and structure based on the excavation process, the collaborative working characteristics of the tunnel-support system, and the role of the support structure in the system. However, this deficiency is indeed something that designers urgently need to understand. To answer the above questions, experts and scholars use theoretical analysis and numerical calculation methods to study the confining pressure-support system and extract support characteristic curves to represent the support stiffness, because the support stiffness can directly reflect the support capacity of the support structure.

[0003] Existing research on the collaborative working characteristics and support stiffness of support systems has many deficiencies: (1) Theoretical studies often assume that the support structure is laid uniformly in the circumferential direction of the entire section, but in actual projects, sprayed concrete, anchor rods, and steel arch frames are often only applied within a certain range in the circumferential direction of the tunnel. At the same time, the theoretical assumptions cannot fully consider the uneven stress conditions of the support structure; (2) Numerical methods can better make up for the shortcomings of the above theoretical methods, but the composite support stiffness in numerical studies is less studied than the single support stiffness. At the same time, the actual stiffness evolution process of the composite support system after considering the support application time effect is unclear, and the actual stiffness contribution value of the composite support system is difficult to calculate. Therefore, no effective and feasible calculation process and method have been proposed. Summary of the Invention

[0004] The purpose of the present invention is to address the problems existing in the prior art and provide a method for determining the comprehensive stiffness of a tunnel composite support system. This solution has the advantages of quantitatively calculating support stiffness, good simulation effect, and convenient construction.

[0005] To achieve the above object, the present invention adopts a technical solution: a method for determining the comprehensive stiffness of a tunnel composite support system, comprising the following steps:

[0006] Step 1: Build a large 3D model containing the tunnel, select a monitoring surface, select feature points on the monitoring surface, excavate the model in steps without any support measures, monitor the selected feature points, and simulate the construction process to obtain the evolution curve of the convergence displacement of the feature points as the excavation progresses;

[0007] Step 2: Based on the principle of virtual support force, the support force of the rock mass of the excavated tunnel on the surrounding rock is first obtained. Then, the tunnel in the model is excavated once, and an initial virtual support force is applied to the tunnel wall. The virtual support force is then gradually reduced proportionally. The selected feature points are monitored to obtain the corresponding mathematical relationship curve between the convergence displacement of the feature points and the virtual support force.

[0008] Step 3: Normalize the convergence displacements of the characteristic points in steps 1 and 2 to calculate the displacement completion rate. This results in a relationship curve between the distance between the tunnel face and the monitoring surface and the displacement completion rate, and a relationship curve between the displacement completion rate and the virtual support force. Based on these two relationship curves, a corresponding curve diagram is established between the distance between the tunnel face and the monitoring surface and the virtual support force of the tunnel wall.

[0009] Step 4: Determine the distance between the application section and the tunnel face of each support structure in the composite support system. The virtual support force provided by the tunnel face at each position can be obtained by the corresponding graphical relationship between the distance between the tunnel face and the monitoring surface and the virtual support force of the tunnel wall. The tunnel face advancement process is simulated by stress release. Support is applied, and monitoring points are set on the support section. The displacement completion rate of the monitoring points at each support section is calculated. Finally, a curve is drawn showing the relationship between the distance between the tunnel face and the monitoring surface and the displacement completion rate of the monitoring points under the support effect.

[0010] Step 5: Use the displacement completion rate as the horizontal coordinate, combine the relationship curve between the displacement completion rate and the virtual support force, and the relationship curve between the distance between the tunnel face and the monitoring surface and the displacement completion rate of the characteristic point under the support action, and distribute them up and down. Connect the intersection of the relationship curve between the displacement completion rate and the virtual support force and the displacement asymptote, and the perpendicular point of the support starting point on the horizontal axis. The product of the slope of the line segment and the final convergent displacement of the characteristic point in the unsupported case is the actual comprehensive stiffness value of the composite support system.

[0011] In the above scheme, in step 1, a large three-dimensional model is established to simulate the construction process, and the evolution curve of the convergence displacement at the feature point with the excavation progress is monitored, that is, the relationship curve between the distance between the tunnel face and the monitoring surface and the convergence displacement at the feature point; in step 2, the tunnel is excavated once, and an initial virtual support force is applied, and then the virtual support force is reduced proportionally, and the convergence displacement of the selected feature points is monitored to obtain the relationship curve between the convergence displacement of the feature point and the virtual support force; in step 3, the convergence displacement of the feature point is normalized to obtain the relationship curve between the distance between the tunnel face and the monitoring surface and the displacement completion rate, and the relationship curve between the displacement completion rate and the virtual support force. The two formulas are combined through the displacement completion rate to obtain the relationship between the distance between the tunnel face and the monitoring surface and the virtual support force of the tunnel wall. The corresponding curve diagram of the pseudo support force; in step 4, according to the position of the support structure in the composite support system, combined with the corresponding graphical relationship between the distance between the tunnel face and the monitoring surface and the virtual support force of the tunnel wall, the virtual support force at each tunnel face is obtained, the advancement process is simulated, the displacement completion rate of the monitoring point of each support section is calculated, and the relationship curve between the distance between the tunnel face and the monitoring surface and the displacement completion rate of the monitoring point under the support effect is obtained; in step 5, with the displacement completion rate as the horizontal coordinate, the relationship curve between the displacement completion rate and the virtual support force, and the relationship curve between the distance between the tunnel face and the monitoring surface and the displacement completion rate of the characteristic point under the support effect are combined, and the actual comprehensive stiffness value of the composite support system is obtained by multiplying the line segment slope and the final convergence displacement of the characteristic point under the unsupported condition through the graphical relationship.

[0012] Furthermore, in step 3, the convergence displacement of the characteristic points in the step-by-step excavation condition of the model is converted into the displacement completion rate using formula (1)

[0013] (1)

[0014] Where: The distance from the tunnel face to the monitoring surface; is the convergence displacement of the feature point when the tunnel face reaches the monitoring surface.

[0015] The convergence displacement of the feature point when the tunnel face reaches the monitoring surface is calculated Convergence displacement of the characteristic point when the full longitudinal excavation of the model is completed By comparison, we can get the displacement completion rate and perform conversion calculations.

[0016] Furthermore, in step 3, the fitting process of the displacement completion rate in the step-by-step excavation condition of the model adopts formula (2)

[0017] (2)

[0018] Where: is the displacement completion rate of the feature point when the tunnel face and the monitoring surface coincide; x is the distance from the tunnel face to the monitoring surface, and X is an undetermined constant.

[0019] The LDP curve fitting calculation of the displacement completion rate is performed using formula (2), which makes it easy to intuitively understand the changing trend of the displacement completion rate.

[0020] Furthermore, in step 2, the virtual support force is calculated using formula (3)

[0021] (3)

[0022] Where: is the stress release coefficient, which increases evenly from 0 to 100% in this calculation, with a step size of 10%. F0 is the initial virtual support force.

[0023] By adjusting the stress release coefficient to gradually reduce the virtual support force, it is convenient to obtain the corresponding relationship curve between the convergence displacement of the characteristic point and the virtual support force.

[0024] Furthermore, in step 3, the displacement completion rate of the feature point is calculated using formula (4)

[0025] (4)

[0026] Where: The stress release coefficient of the characteristic point P is Convergence displacement when ; is a feature point Converged displacement at completion of load release.

[0027] The calculation formulas corresponding to the displacement completion rate and virtual support force under various stress release coefficients are obtained through formula (4).

[0028] Furthermore, in step 4, the spacing between the sections of each support structure in the composite support system is used to determine the distance between the sections of each support structure and the tunnel face.

[0029] The positions of the support structures and their distances from the tunnel face are simulated based on the actual spacing of the support structures in the composite support system to improve the simulation effect and provide more accurate data for actual construction.

[0030] Furthermore, the cross section of the tunnel is horseshoe-shaped or circular.

[0031] The horseshoe-shaped tunnel has a horseshoe-shaped or circular cross-section, which is convenient for construction.

[0032] Furthermore, the monitoring point is selected from the vertex of the support section.

[0033] The monitoring point is selected at the top of the support section, where deformation is significant and detection is convenient.

[0034] Furthermore, the monitoring surface is located at the axial middle position of the tunnel, and the characteristic point is located at the vertex of the monitoring surface.

[0035] The monitoring surface is set at the middle position of the tunnel axis. The force and convergence displacement there are representative and can be used to simulate the overall situation of the tunnel. The characteristic points are selected from the vertices of the monitoring surface, where deformation is significant and detection is convenient.

[0036] Furthermore, the stress release in step 4 is calculated using formula (3). Increase evenly from 0 to 100% in steps of 10%.

[0037] In step 4, stress release calculation is performed to gradually strengthen the support as the stress is released until the stress disappears and the final support strength is reached.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] 1. By establishing a large three-dimensional model, the convergence displacement curves of characteristic points during unsupported construction were simulated and calculated, as well as the relationship curves between the convergence displacement of characteristic points and the virtual support force. Combined with the simulated construction of the composite support system, the relationship curve between the distance between the tunnel face and the monitoring surface and the displacement completion rate of the monitoring point under the support effect was obtained. After data processing, the actual comprehensive stiffness value of the composite support system was finally obtained. The support stiffness value was quantitatively calculated, facilitating an intuitive understanding of the stiffness of the composite support system and quantitatively evaluating the support system's ability to maintain surrounding rock stability.

[0040] 2. The heterogeneity of the support structure is taken into account in the comprehensive stiffness assessment of the support system. Feature points and monitoring points are selected at the top of the tunnel section to reflect the actual working characteristics of the support system and achieve good simulation results.

[0041] 3. By calculating the comprehensive stiffness value of the support system, it provides a reference for the support system design process, facilitating design and construction;

[0042] 4. The present invention can demonstrate the convergence and deformation process of the surrounding rock and the stiffness evolution process of the support system during the construction process of the composite support system. The calculation principle is clear and easy to accept. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 1 is a corresponding curve diagram of the distance between the tunnel face and the monitoring surface and the virtual supporting force of the tunnel wall in Example 1 of the present invention;

[0044] Figure 2 This is a combined graph of the relationship curve between the displacement completion rate and the virtual support force in Example 1 of the present invention and the relationship curve between the distance between the tunnel face and the monitoring surface and the displacement completion rate of the characteristic point under the support effect. DETAILED DESCRIPTION

[0045] The technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. In the description of the present invention, it should be noted that the terms front, back, left, right, etc. indicate directions or positional relationships based on the directions or positional relationships shown in the drawings, or the directions or positional relationships in which the invented product is usually placed when used. They are only for the convenience of describing the present invention or simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed or operated in a specific direction, and therefore cannot be understood as a limitation on the present invention.

[0046] Example 1

[0047] like Figure 1-2 As shown, a method for determining the comprehensive stiffness of a tunnel composite support system includes the following steps:

[0048] Step 1: Build a large 3D model containing the tunnel, select a monitoring surface, select feature points on the monitoring surface, excavate the model in steps without any support measures, monitor the selected feature points, and simulate the construction process to obtain the evolution curve of the convergence displacement of the feature points as the excavation progresses;

[0049] Step 2: Based on the principle of virtual support force, the support force of the rock mass of the excavated tunnel on the surrounding rock is first obtained. Then, the tunnel in the model is excavated once, and an initial virtual support force is applied to the tunnel wall. The virtual support force is then gradually reduced proportionally. The selected feature points are monitored to obtain the corresponding mathematical relationship curve between the convergence displacement of the feature points and the virtual support force.

[0050] Step 3: Normalize the convergence displacements of the characteristic points in steps 1 and 2 to calculate the displacement completion rate. This results in a relationship curve between the distance between the tunnel face and the monitoring surface and the displacement completion rate, and a relationship curve between the displacement completion rate and the virtual support force. Based on these two relationship curves, a corresponding curve diagram is established between the distance between the tunnel face and the monitoring surface and the virtual support force of the tunnel wall.

[0051] Step 4: Determine the distance between the application section and the tunnel face of each support structure in the composite support system. The virtual support force provided by the tunnel face at each position can be obtained by the corresponding graphical relationship between the distance between the tunnel face and the monitoring surface and the virtual support force of the tunnel wall. The tunnel face advancement process is simulated by stress release. Support is applied, and monitoring points are set on the support section. The displacement completion rate of the monitoring points at each support section is calculated. Finally, a curve is drawn showing the relationship between the distance between the tunnel face and the monitoring surface and the displacement completion rate of the monitoring points under the support effect.

[0052] Step 5: Use the displacement completion rate as the horizontal coordinate, combine the relationship curve between the displacement completion rate and the virtual support force, and the relationship curve between the distance between the tunnel face and the monitoring surface and the displacement completion rate of the characteristic point under the support action, and distribute them up and down. Connect the intersection of the relationship curve between the displacement completion rate and the virtual support force and the displacement asymptote, and the perpendicular point of the support starting point on the horizontal axis. The product of the slope of the line segment and the final convergent displacement of the characteristic point in the unsupported case is the actual comprehensive stiffness value of the composite support system.

[0053] In the above scheme, in step 1, a large three-dimensional model is established to simulate the construction process, and the evolution curve of the convergence displacement at the feature point with the excavation progress is monitored, that is, the relationship curve between the distance between the tunnel face and the monitoring surface and the convergence displacement at the feature point; in step 2, the tunnel is excavated once, and an initial virtual support force is applied, and then the virtual support force is reduced proportionally, and the convergence displacement of the selected feature points is monitored to obtain the relationship curve between the convergence displacement of the feature point and the virtual support force; in step 3, the convergence displacement of the feature point is normalized to obtain the relationship curve between the distance between the tunnel face and the monitoring surface and the displacement completion rate, and the relationship curve between the displacement completion rate and the virtual support force. The two formulas are combined through the displacement completion rate to obtain the relationship between the distance between the tunnel face and the monitoring surface and the virtual support force of the tunnel wall. The corresponding curve diagram of the pseudo support force; in step 4, according to the position of the support structure in the composite support system, combined with the corresponding graphical relationship between the distance between the tunnel face and the monitoring surface and the virtual support force of the tunnel wall, the virtual support force at each tunnel face is obtained, the advancement process is simulated, the displacement completion rate of the monitoring point of each support section is calculated, and the relationship curve between the distance between the tunnel face and the monitoring surface and the displacement completion rate of the monitoring point under the support effect is obtained; in step 5, with the displacement completion rate as the horizontal coordinate, the relationship curve between the displacement completion rate and the virtual support force, and the relationship curve between the distance between the tunnel face and the monitoring surface and the displacement completion rate of the characteristic point under the support effect are combined, and the actual comprehensive stiffness value of the composite support system is obtained by multiplying the line segment slope and the final convergence displacement of the characteristic point under the unsupported condition through the graphical relationship.

[0054] In step 1, a large three-dimensional model including the tunnel is established considering the boundary effect of the numerical model. The distance between the center of the tunnel and the upper and lower and left and right boundaries of the model is not less than 7 times the tunnel diameter, and the longitudinal length of the model is not less than 10 times the tunnel diameter. Feature points are selected and the model is excavated step by step without support measures. The selected feature points are monitored. Get the convergence displacement of the feature points , convergence displacement of feature points Normalized and converted into displacement completion rate , and then the displacement completion rate The longitudinal deformation curve (LDP) of the surrounding rock is obtained by fitting, as shown in line ① in the figure.

[0055] In step 2, based on the principle of virtual support force, the support force of the rock mass of the excavated tunnel on the surrounding rock is first obtained. Then, the tunnel in the model is excavated once and an initial virtual support force is applied to the tunnel wall. , select feature points in the model , and then gradually reduce the virtual support force in proportion , get the feature points Convergence displacement of and virtual support The corresponding relationship, the same feature point convergence displacement Normalized and converted into displacement completion rate Post-drawing displacement completion rate With virtual support Relationship curve②.

[0056] Step 3, line ① in the figure represents the displacement completion rate Distance from the tunnel face and monitoring surface The relationship curve of displacement completion rate is shown in line ②. With virtual support The relationship curve of the two curves is the displacement completion rate The distance between the bridge and the tunnel face and monitoring surface can be established Virtual support force of cave wall The corresponding relationship is as follows Figure 1 shown.

[0057] Step 4: Determine the distance between the construction section of each support structure and the tunnel face based on the distance between the construction sections of each support structure in the composite support system. 、 、 ; The virtual support force provided by the tunnel face at each position can be obtained through the corresponding relationship in step 3 By simulating the tunnel face advancement process through stress release, applying support, calculating the tunnel wall convergence displacement at each support application point, and calculating the displacement completion coefficient, the point 、 、 , and finally draw the surrounding rock deformation curve under the support effect③.

[0058] Step 5, see Figure 2 , connect support starting point The corresponding horizontal axis (displacement completion rate ) is the intersection point J of point I on the surrounding rock deformation curve ③ displacement asymptote and GRC curve, as shown in the figure, the slope of line segment ④IJ The final convergent displacement of the characteristic point in the case of no support The product of is the actual comprehensive stiffness value of the composite support system.

[0059] Furthermore, in step 3, the convergence displacement of the characteristic points in the step-by-step excavation condition of the model is converted into the displacement completion rate using formula (1)

[0060] (1)

[0061] Where: The distance from the tunnel face to the monitoring surface; is the convergence displacement of the feature point when the tunnel face reaches the monitoring surface.

[0062] The convergence displacement of the feature point when the tunnel face reaches the monitoring surface is calculated Convergence displacement of the characteristic point when the full longitudinal excavation of the model is completed By comparison, we can get the displacement completion rate and perform conversion calculations.

[0063] Furthermore, in step 3, the fitting process of the displacement completion rate in the step-by-step excavation condition of the model adopts formula (2)

[0064] (2)

[0065] Where: is the displacement completion rate of the feature point when the tunnel face and the monitoring surface coincide; x is the distance from the tunnel face to the monitoring surface, and X is an undetermined constant.

[0066] The LDP curve fitting calculation of the displacement completion rate is performed using formula (2), which facilitates an intuitive understanding of the changing trend of the displacement completion rate. The positive and negative values ​​of x represent the direction relative to the detection surface. Formula (2) corresponds to line ① in the figure.

[0067] Furthermore, in step 2, the virtual support force is calculated using formula (3)

[0068] (3)

[0069] Where: is the stress release coefficient, which increases evenly from 0 to 100% in this calculation, with a step size of 10%. F0 is the initial virtual support force.

[0070] By adjusting the stress release coefficient to gradually reduce the virtual support force, it is convenient to obtain the corresponding relationship curve between the convergence displacement of the characteristic point and the virtual support force.

[0071] Furthermore, in step 3, the displacement completion rate of the feature point is calculated using formula (4)

[0072] (4)

[0073] Where: The stress release coefficient of the characteristic point P is Convergence displacement when ; is a feature point Converged displacement at completion of load release.

[0074] The calculation formulas corresponding to the displacement completion rate and virtual support force under various stress release coefficients are obtained through formula (4).

[0075] Furthermore, in step 4, the spacing between the sections of each support structure in the composite support system is used to determine the distance between the sections of each support structure and the tunnel face.

[0076] The positions of the support structures and their distances from the tunnel face are simulated based on the actual spacing of the support structures in the composite support system to improve the simulation effect and provide more accurate data for actual construction.

[0077] Furthermore, the cross section of the tunnel is horseshoe-shaped or circular.

[0078] The horseshoe-shaped tunnel has a horseshoe-shaped or circular cross-section, which is convenient for construction.

[0079] Furthermore, the monitoring point is selected from the vertex of the support section.

[0080] The monitoring point is selected at the top of the support section, where deformation is significant and detection is convenient.

[0081] Furthermore, the monitoring surface is located at the axial middle position of the tunnel, and the characteristic point is located at the vertex of the monitoring surface.

[0082] The monitoring surface is set at the middle position of the tunnel axis. The force and convergence displacement there are representative and can be used to simulate the overall situation of the tunnel. The characteristic points are selected from the vertices of the monitoring surface, where deformation is significant and detection is convenient.

[0083] Furthermore, the stress release in step 4 is calculated using formula (3). Increase evenly from 0 to 100% in steps of 10%.

[0084] In step 4, stress release calculation is performed to gradually strengthen the support as the stress is released until the stress disappears and the final support strength is reached.

[0085] You can reduce the step size as needed to get more accurate data.

[0086] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A method for determining the comprehensive stiffness of a tunnel composite support system, characterized in that: The steps include: Step 1: Build a large 3D model containing the tunnel, select a monitoring surface, select feature points on the monitoring surface, excavate the model in steps without any support measures, monitor the selected feature points, and simulate the construction process to obtain the evolution curve of the convergence displacement of the feature points as the excavation progresses; Step 2: Based on the principle of virtual support force, the support force of the rock mass of the excavated tunnel on the surrounding rock is first obtained. Then, the tunnel in the model is excavated once, and an initial virtual support force is applied to the tunnel wall. The virtual support force is then gradually reduced proportionally. The selected feature points are monitored to obtain the corresponding mathematical relationship curve between the convergence displacement of the feature points and the virtual support force. Step 3: Normalize the convergence displacements of the characteristic points in steps 1 and 2 to calculate the displacement completion rate. This results in a relationship curve between the distance between the tunnel face and the monitoring surface and the displacement completion rate, and a relationship curve between the displacement completion rate and the virtual support force. Based on these two relationship curves, a corresponding curve diagram is established between the distance between the tunnel face and the monitoring surface and the virtual support force of the tunnel wall. Step 4: Determine the distance between the application section and the tunnel face of each support structure in the composite support system. The virtual support force provided by the tunnel face at each position can be obtained by the corresponding graphical relationship between the distance between the tunnel face and the monitoring surface and the virtual support force of the tunnel wall. The tunnel face advancement process is simulated by stress release. Support is applied, and monitoring points are set on the support section. The displacement completion rate of the monitoring points at each support section is calculated. Finally, a curve is drawn showing the relationship between the distance between the tunnel face and the monitoring surface and the displacement completion rate of the monitoring points under the support effect. Step 5: Use the displacement completion rate as the horizontal coordinate, combine the relationship curve between the displacement completion rate and the virtual support force, and the relationship curve between the distance between the tunnel face and the monitoring surface and the displacement completion rate of the characteristic point under the support action, and distribute them up and down. Connect the intersection of the relationship curve between the displacement completion rate and the virtual support force and the displacement asymptote, and the perpendicular point of the support starting point on the horizontal axis. The product of the slope of the line segment and the final convergent displacement of the characteristic point in the unsupported case is the actual comprehensive stiffness value of the composite support system.

2. The method for determining the comprehensive stiffness of a tunnel composite support system according to claim 1, characterized in that: In step 3, the convergence displacement of the characteristic points in the step-by-step excavation condition of the model is converted into the displacement completion rate using formula (1) （1） Where: The distance from the tunnel face to the monitoring surface; is the convergence displacement of the feature point when the tunnel face reaches the monitoring surface; is the convergence displacement of the feature point when the full longitudinal excavation of the model is completed.

3. The method for determining the comprehensive stiffness of a tunnel composite support system according to claim 1, characterized in that: In step 3, the fitting process of the displacement completion rate in the step-by-step excavation condition of the model adopts formula (2) （2） Where: is the displacement completion rate of the feature point when the tunnel face and the monitoring surface coincide; x is the distance from the tunnel face to the monitoring surface, and X is an undetermined constant.

4. The method for determining the comprehensive stiffness of a tunnel composite support system according to claim 1, characterized in that: In step 2, the virtual support force is calculated using formula (3) （3） Where: is the stress release coefficient.

5. The method for determining the comprehensive stiffness of a tunnel composite support system according to claim 4, characterized in that: In step 3, the displacement completion rate of the feature point is calculated using formula (4) （4） Where: is a feature point The stress release coefficient is Convergence displacement when ; is a feature point Converged displacement at completion of load release.

6. The method for determining the comprehensive stiffness of a tunnel composite support system according to claim 1, characterized in that In step 4, the spacing between the sections of each support structure in the composite support system is used to determine the distance between the sections of each support structure and the tunnel face.

7. The method for determining the comprehensive stiffness of a tunnel composite support system according to claim 1, characterized in that ,The cross section of the tunnel is horseshoe-shaped or circular.

8. The method for determining the comprehensive stiffness of a tunnel composite support system according to claim 1, characterized in that ,The monitoring point is selected from the vertex of the support section.

9. The method for determining the comprehensive stiffness of a tunnel composite support system according to claim 1, characterized in that ,The monitoring surface is located in the axial middle position of the tunnel, and the characteristic point is located at the vertex of the monitoring surface.

10. The method for determining the comprehensive stiffness of a tunnel composite support system according to claim 4, characterized in that ,The stress release in step 4 is calculated using formula (3). Increase evenly from 0 to 100% in steps of 10%.

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