Analytical design method for lining stress sharing ratio based on allowing tensile strain

Abstract

This invention belongs to the field of tunnel engineering technology and relates to an analytical design method for lining stress sharing ratio based on allowable tensile strain. The method includes: simulating the initial support-secondary lining stress system using an elastic double-layer thick-walled cylinder model, where the model consists of the secondary lining and the initial support from the inside out; assuming continuous interlayer radial stress and radial displacement, and setting an allowable tensile strain limit for the secondary lining; obtaining the radial displacements of the inner wall of the initial support, the outer wall of the secondary lining, and the inner wall of the secondary lining based on the continuity of interlayer radial stress; obtaining the interface pressure between the secondary lining and the initial support based on the continuity of interlayer radial displacement; calculating the circumferential tensile strain of the secondary lining; and calculating the stress sharing ratio of the secondary lining based on the analytical formula for obtaining the secondary lining thickness. This invention, by establishing an elastic double-layer thick-walled cylinder model and coupling it with the allowable tensile strain constraint of the secondary lining, obtains the analytical formula for the minimum thickness of the secondary lining and quantifies the stress sharing ratio. This allows for efficient and accurate determination of the minimum thickness of the secondary lining without repeated trial calculations, thus providing a reliable theoretical tool for secondary lining design.

Description

Technical Field

[0001] This invention belongs to the field of tunnel engineering technology, specifically relating to an analytical design method for lining stress sharing ratio based on allowable tensile strain. Background Technology

[0002] Deeply buried circular tunnels are widely used in major projects such as water conservancy, transportation, and energy. Their long-term service safety is highly dependent on the mechanical properties of the secondary lining. As a permanent load-bearing structure, the secondary lining must withstand internal water pressure (in water conveyance tunnels) or residual loads after construction. Its thickness design directly affects the project cost and structural durability.

[0003] Tunnel lining design theory has always revolved around the synergistic effect of "surrounding rock-lining". Early Lame solutions laid the theoretical foundation for stress calculation of thick-walled tubes, but only considered the stress of a single elastic body, failing to reflect the mutual constraints between the primary support and the secondary lining. The double-layer thick-walled tube model realized the analysis of the joint action of the primary support (i.e., initial support) and the secondary lining (i.e., secondary lining) through displacement coordination conditions, but its core focus was on internal force calculation, without incorporating tensile strain control indicators. Some scholars have found through indoor experiments and field monitoring that the bearing capacity of the primary support mainly depends on its elastic modulus and Poisson's ratio—the larger the elastic modulus, the stronger the primary support capacity, and the lower the load share of the secondary lining. However, existing studies have paid insufficient attention to the coupling relationship of "allowable tensile strain-secondary lining thickness-stress sharing ratio".

[0004] For the design of secondary linings in deeply buried circular tunnels, current methods require repeated calculations of thickness to meet tensile strain control requirements. This method has two key limitations: First, based on the traditional approach of "stress control," it requires repeated calculations of "assumed thickness - stress verification - thickness adjustment" to meet design requirements, without directly relating to material tensile strain constraints, resulting in low efficiency in secondary lining design. Second, the stress sharing relationship between the initial support and the secondary lining relies heavily on numerical simulations, lacking analytical expressions, making it difficult to quantify their load-bearing contributions, leading to unclear stress sharing relationships and potentially causing redundancy or insufficiency in the secondary lining thickness.

[0005] For concrete secondary lining materials, tensile strain is the core indicator for controlling crack formation. Taking commonly used C40 concrete as an example, its allowable tensile strain usually does not exceed 0.0015. If the tensile strain exceeds the limit, it is easy to cause through cracks, leading to water seepage, steel corrosion and other defects, and shortening the structural life.

[0006] In view of this, establishing an analytical method that directly correlates allowable tensile strain with secondary lining thickness and quantifying the stress sharing ratio between the initial support and the secondary lining is of great engineering significance for improving the accuracy and efficiency of tunnel design. Summary of the Invention

[0007] In view of the shortcomings of the related technologies, the present invention provides an analytical design method for lining stress sharing ratio based on allowable tensile strain, so as to solve the technical problems mentioned in the background art.

[0008] This invention provides an analytical design method for lining stress sharing ratio based on allowable tensile strain, comprising the following steps: S1. An elastic double-layer thick-walled cylinder model is used to simulate the initial support-secondary lining stress system, establishing the tunnel stress model. The elastic double-layer thick-walled cylinder model consists of the secondary lining and the initial support from the inside out. It is assumed that the secondary lining and the initial support satisfy the interlayer contact condition where both radial stress and radial displacement are continuous. The allowable tensile strain limit of the secondary lining is set to be... ; S2. Based on the continuity of radial stress between the secondary lining and the primary support, and according to the thick-walled cylinder theory and Hooke's law, the radial displacement of the inner wall of the primary support is obtained. Radial displacement of the outer wall of the secondary lining Radial displacement of the inner wall of the secondary lining ; S3. Based on the continuity of radial displacement between the secondary lining and the primary support, the interfacial pressure between the secondary lining and the primary support is obtained. , expressed as equation (1), where, The original rock stress borne by the outer wall of the initial support. This refers to the internal water pressure borne by the inner wall of the secondary lining. , The radial stiffness coefficients of the secondary lining and the primary support are respectively calculated according to equation (2); (1); (2); In equation (2), , These are the elastic moduli of the secondary lining and the initial support, respectively. , The Poisson's ratios for the secondary lining and the primary support, respectively. Let be the radius of the inner wall of the secondary lining. The radius of the inner wall of the initial support and the outer wall of the secondary lining; S4. Calculate the circumferential tensile strain of the secondary lining according to equation (3). ;according to And in combination with the thickness of the secondary lining To obtain the secondary lining thickness The analytical expression of is expressed as equation (4); (3); (4); S5. Calculate the minimum thickness of the secondary lining obtained in step S4. Then calculate according to equations (1) to (2). Then, the stress sharing ratio of the secondary lining is calculated according to equation (5). ; (5).

[0009] In some embodiments, the tunnel stress model in step S1 is also based on the following assumptions: The axisymmetric plane strain condition is as follows: the axial dimension of the tunnel is much larger than the radial dimension, and the stress and displacement only change radially, while the influence of axial stress is ignored. The material properties are as follows: both the secondary lining and the primary support are homogeneous isotropic elastic materials.

[0010] In some embodiments, in step S2, the obtained radial displacement of the inner wall of the initial support is... The radial displacement of the outer wall of the secondary lining is expressed as equation (6); The radial displacement of the inner wall of the secondary lining is expressed as equation (7); , expressed as equation (8); (6); (7); (8).

[0011] In some embodiments, step S6 is further included, which involves calculating the circumferential tensile strain of the secondary lining at the minimum thickness by referring to typical tunnel engineering parameters and the set minimum thickness of the secondary lining according to equations (8) and (3). And compare it with the allowable tensile strain limit of the secondary lining. A comparison was conducted to verify the minimum thickness of the secondary lining.

[0012] In some embodiments, step S7 is further included, specifically, using the controlled variable method to analyze the sensitivity of key parameters to the minimum thickness of the secondary lining and the stress sharing ratio of the secondary lining; the key parameters include the original rock stress. Internal water pressure , initial support elastic modulus The elastic modulus of the secondary lining .

[0013] Based on the above technical solution, the analytical design method for lining stress sharing ratio based on allowable tensile strain in this embodiment of the invention takes the coordinated stress of the primary support and the secondary lining as the core. By establishing the displacement coordination equation of the elastic double-layer thick-walled cylinder and coupling it with the allowable tensile strain constraint of the secondary lining, the analytical formula for the minimum thickness of the secondary lining is obtained, and the stress sharing ratio between the secondary lining and the primary support is quantified. Therefore, the minimum thickness of the secondary lining can be determined efficiently and accurately using the analytical formula, without the need for repeated trial calculations to determine the thickness of the secondary lining as in traditional methods. This improves the design efficiency of the secondary lining and has high calculation accuracy, avoiding redundancy or insufficiency in the design of the secondary lining thickness. It has important engineering significance for improving the accuracy and efficiency of tunnel design. Attached Figure Description

[0014] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings: Figure 1 This is a flowchart of the analytical design method for lining stress sharing ratio based on allowable tensile strain according to the present invention; Figure 2 This is a schematic diagram of the tunnel stress model in this invention. Detailed Implementation

[0015] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0016] In the description of this invention, it should be understood that the terms "center", "lateral", "longitudinal", "upper", "lower", "top", "bottom", "inner", "outer", "left", "right", "front", "rear", "vertical", "horizontal", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0017] The terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature.

[0018] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0019] refer to Figures 1-2 As shown, the present invention provides an analytical design method for lining stress sharing ratio based on allowable tensile strain, including the following steps S1 to S5.

[0020] Step S1: A stress model of the tunnel is established by simulating the initial support-secondary lining stress system using an elastic double-layer thick-walled cylinder model. The tunnel is theoretically assumed to be circular. The elastic double-layer thick-walled cylinder model consists of the secondary lining and the initial support from the inside out. The outer wall of the secondary lining is in contact with the inner wall of the initial support, and the outer wall of the initial support is in contact with the surrounding rock. The radii of the inner and outer walls of the secondary lining are denoted as... , Let the inner and outer radii of the initial support be denoted as... , , This refers to the tunnel excavation radius. Assuming the secondary lining and the initial support satisfy the interlayer contact condition of continuous radial stress and radial displacement, let the allowable tensile strain limit of the secondary lining be... Its allowable tensile strain limit It usually does not exceed 0.0015.

[0021] Furthermore, the tunnel stress model is based on the following assumptions: axisymmetric plane strain condition, specifically, the axial dimension of the tunnel is much larger than the radial dimension, stress and displacement only change radially, and the influence of axial stress is ignored; material property condition, specifically, the secondary lining and the primary support are both homogeneous isotropic elastic materials, and the secondary lining and the primary support are both linear elastic bodies; load condition, specifically, the inner wall of the secondary lining is subjected to internal water pressure (or construction load). The outer wall of the initial support bears the stress of the original rock. .

[0022] Step S2: Based on the continuity of radial stress between the secondary lining and the primary support, and according to the thick-walled cylinder theory and Hooke's law, the radial displacement of the inner wall of the primary support is obtained. Radial displacement of the outer wall of the secondary lining Radial displacement of the inner wall of the secondary lining .

[0023] To further explain, the secondary lining is a linear elastic body. Based on the theory of thick-walled cylinders in elastic mechanics, the radial stress of the secondary lining... Satisfying the Lamé equation, expressed as equation (11), where, , The integral constant is determined by the boundary conditions. Radial coordinates, ; (11); Based on boundary conditions, when At this time, the inner wall of the secondary lining is subjected to internal water pressure, and the radial stress of the secondary lining is... ;when At this time, the outer wall of the secondary lining is in contact with the inner wall of the initial support. Because the radial stress between the two is continuous, the radial stress of the secondary lining is... ,in, The radial stress of the initial support, The boundary condition is the interfacial pressure between the secondary lining and the initial support; substituting this boundary condition into equation (11), the integral constant can be solved simultaneously. , , expressed as equation (12); (12); According to Hooke's Law, the radial displacement of the secondary lining... The relationship between stress and force is expressed by equation (13), where, The elastic modulus of the secondary lining is given by [value]. The Poisson's ratio of the secondary lining is given; substituting equations (11) and (12) into equation (13) and simplifying, we obtain the outer wall of the secondary lining ( Radial displacement and the inner wall of the secondary lining ( Radial displacement , respectively expressed as equation (7) and equation (8), where, The elastic modulus of the secondary lining is given by [value]. The Poisson's ratio for the secondary lining; (13); (7); (8).

[0024] To further explain, the initial support is a linear elastic body. Combining the Lamé equation and Hooke's law, the inner wall of the initial support can be derived ( Radial displacement , expressed as equation (6), where, The elastic modulus of the initial support. The Poisson's ratio of the initial branch; (6).

[0025] Step S3: Based on the continuity of radial displacement between the secondary lining and the initial support, utilize... Substituting equations (6) and (7) into the relational expression, the interface pressure between the secondary lining and the primary support is obtained by simplification. , expressed as equation (1), where, is the radial stiffness coefficient of the secondary lining. The radial stiffness coefficient of the initial support is... and The calculation is performed according to equation (2); equation (1) shows the interfacial pressure between the secondary lining and the primary support. The radial stiffness of the secondary lining and the primary support are jointly determined. The greater the radial stiffness, the higher the proportion of the load it bears. (1); (2).

[0026] Step S4: The circumferential tensile strain of the secondary lining is the core indicator controlling crack formation. According to the definition of strain in elastic mechanics, the circumferential tensile strain of the secondary lining... Calculate according to equation (3); (3).

[0027] Tunnel secondary lining design constraints include It is understandable that the thickness of the secondary lining... The definition of ,according to Combining the definition of secondary lining thickness, equations (8) and (3) are substituted into the relation to simplify and obtain the secondary lining thickness. The analytical expression is expressed as equation (4); the result calculated based on equation (4) is... The minimum value is the minimum thickness of the secondary lining; further explanation: if the right side of equation (4) is less than 0, it indicates that the initial support stiffness is sufficient to control the tensile strain of the secondary lining, and the thickness of the secondary lining can be taken as the structural thickness. (4).

[0028] Step S5: Using the minimum thickness of the secondary lining obtained in step S4, according to... calculate Then calculate according to equations (1) to (2). Then, the stress sharing ratio of the secondary lining is calculated according to equation (5). It is understandable that the stress distribution ratio of the initial support is equal to... ; Defined as the ratio of the load borne by the secondary lining to the total load. The larger the value, the higher the proportion of the load borne by the secondary lining. The smaller the value, the stronger the self-supporting capacity of the primary support, which can quantify the load-bearing contribution of the secondary lining and the primary support. (5).

[0029] The above illustrative embodiment, based on the principle of coordinated stress of "initial support-secondary lining", establishes an elastic double-layer thick-walled cylinder model and uses the radial displacement continuity condition to realize the joint action analysis of the initial support and secondary lining. Allowable tensile strain constraints for the secondary lining are designed. Based on the elastic double-layer thick-walled cylinder model, the allowable tensile strain constraints of the secondary lining are coupled to obtain the analytical formula for the minimum thickness of the secondary lining. This directly correlates the secondary lining thickness with the allowable tensile strain and quantifies the stress sharing ratio between the secondary lining and the initial support. Furthermore, a coupling relationship of "allowable tensile strain of secondary lining - secondary lining thickness - stress sharing ratio" is established. Thus, the minimum thickness of the secondary lining can be efficiently and accurately determined using the analytical formula, eliminating the need for repeated trial calculations as in traditional methods. This improves the efficiency and accuracy of secondary lining design, avoids redundant or under-design, and provides a precise, efficient, and reliable theoretical tool for tunnel secondary lining design in fields such as water conservancy and transportation.

[0030] In some embodiments, the analytical design method based on the allowable tensile strain lining stress sharing ratio further includes step S6, specifically, referring to typical tunnel engineering parameters and the set minimum thickness of the secondary lining, calculating the circumferential tensile strain of the secondary lining at the minimum thickness according to equations (8) and (3). And compare it with the allowable tensile strain limit of the secondary lining. A comparison was conducted to verify the minimum thickness of the secondary lining.

[0031] To further explain, typical parameters for tunnel engineering are shown in Table 1. The initial minimum thickness of the secondary lining is set at 0.45m. Therefore, the outer wall radius of the secondary lining... It is 5.45m.

[0032] Table 1: Typical Parameters of Tunnel Engineering

[0033] Substituting the parameters from Table 1 into equation (2), we obtain the radial stiffness coefficient of the secondary lining. Pa, initial support radial stiffness coefficient Pa; will , Substituting the parameters from Table 1 into equation (1), we obtain the interfacial pressure between the secondary lining and the primary support. Pa; Substituting all the above parameters into equation (8), we obtain the radial displacement of the inner wall of the secondary lining. m; will Substituting into equation (3), we obtain the circumferential tensile strain of the secondary lining. Compare it with the allowable tensile strain limit of the secondary lining. In comparison, the error was only 0.67%, meeting the engineering design accuracy requirements. Therefore, the minimum thickness of the secondary lining was determined to be 0.45m, consistent with the initial setting, verifying the correctness of the analytical formula for the minimum thickness of the secondary lining. Based on this, and Substituting into equation (5), the stress sharing ratio of the secondary lining based on the allowable tensile strain can be calculated. .

[0034] To clarify the influence of key parameters on the minimum thickness and stress sharing ratio of the secondary lining, in some embodiments, the analytical design method based on the allowable tensile strain lining stress sharing ratio further includes step S7, specifically, using the controlled variable method to analyze the sensitivity of key parameters to the minimum thickness and stress sharing ratio of the secondary lining; key parameters include the original rock stress. Internal water pressure , initial support elastic modulus The elastic modulus of the secondary lining In the controlled variable method, a single parameter is varied by 20%, while the other parameters are kept at their original values, to calculate the minimum thickness of the secondary lining. and its rate of change, stress sharing ratio of the secondary lining The results of the calculation of the rate of change are shown in Table 2.

[0035] Table 2: Results of parameter sensitivity analysis

[0036] As can be seen from Table 2, the internal water pressure and the elastic modulus of the secondary lining The minimum thickness of the secondary lining is a highly sensitive parameter and a core factor affecting the thickness of the secondary lining. When these two parameters change by 20%, The rate of change exceeds 15%, and the elastic modulus of the secondary lining... That is, the proportion of its own stiffness to the load it bears. The impact of internal water pressure is greater than that of external water pressure, and precise value selection is crucial in the design. Under elastic conditions, the original rock stress... Only the total load scale is changed, but the load distribution ratio between the secondary lining and the primary support is not changed; that is, the original rock stress... It only affects the thickness, not the load-sharing ratio. Initial support elastic modulus. That is, its own stiffness has little impact on the thickness of the secondary lining and the load sharing ratio, which is different from the understanding that "the current method mainly relies on the elastic modulus of the initial support to adjust the load sharing ratio".

[0037] Through the description of several embodiments of the analytical design method for lining stress sharing ratio based on allowable tensile strain of the present invention, it can be seen that the present invention has at least one or more of the following advantages: 1) This invention addresses the problems of low design efficiency and unclear stress sharing relationship in secondary lining of deep-buried tunnels. Based on the principle of "primary support-secondary lining" synergistic stress, and with the synergistic stress of primary support and secondary lining as the core, it establishes the displacement coordination equation of elastic double-layer thick-walled cylinder, couples the allowable tensile strain constraint of secondary lining, derives the analytical formula for the minimum thickness of secondary lining, and quantifies the stress sharing ratio between secondary lining and primary support. This solves the problem of design efficiency and accuracy of tunnel secondary lining, and provides a theoretical basis for quantifying the support capacity of primary support and avoiding redundancy or insufficiency in secondary lining thickness design. 2) This invention also verifies through numerical examples that the calculation results are in high agreement with theoretical expectations; through parameter sensitivity analysis, the internal water pressure is clarified. and the elastic modulus of the secondary lining It has a significant impact on the thickness of the secondary lining, providing a theoretical reference for the design of the minimum thickness of the secondary lining; 3) This invention can efficiently and accurately determine the minimum thickness of the secondary lining using analytical formulas, eliminating the need for repeated trial calculations as in traditional methods. This improves the efficiency of secondary lining design and provides high calculation accuracy. Thus, it solves the problem of low efficiency in determining the secondary lining thickness using existing stress control methods. 4) This invention directly constrains crack generation by allowing tensile strain in the secondary lining, ensuring the durability of the support structure; at the same time, it uses analytical formulas to accurately determine the minimum thickness of the secondary lining, avoiding redundant or under-design of the secondary lining, providing a precise, efficient and reliable theoretical tool for the design of tunnel secondary linings in water conservancy, transportation and other fields, and can effectively balance structural safety and economy.

[0038] Finally, it should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0039] The above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them; although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications can still be made to the specific implementation of the present invention or equivalent substitutions can be made to some technical features without departing from the spirit of the technical solutions of the present invention, and all such modifications and substitutions should be covered within the scope of the technical solutions claimed in the present invention.

Claims

1. An analytical design method for lining stress sharing ratio based on allowable tensile strain, characterized in that, Includes the following steps: S1. An elastic double-layer thick-walled cylinder model is used to simulate the initial support-secondary lining stress system, establishing a tunnel stress model. The elastic double-layer thick-walled cylinder model consists of the secondary lining and the initial support from the inside out. It is assumed that the secondary lining and the initial support satisfy the interlayer contact condition where both radial stress and radial displacement are continuous. The allowable tensile strain limit of the secondary lining is set to be... ; S2. Based on the continuity of radial stress between the secondary lining and the primary support, and according to the thick-walled cylinder theory and Hooke's law, the radial displacement of the inner wall of the primary support is obtained. Radial displacement of the outer wall of the secondary lining Radial displacement of the inner wall of the secondary lining ; S3. Based on the continuity of radial displacement between the secondary lining and the primary support, the interfacial pressure between the secondary lining and the primary support is obtained. , expressed as equation (1), where, The original rock stress borne by the outer wall of the initial support. This refers to the internal water pressure borne by the inner wall of the secondary lining. , The radial stiffness coefficients of the secondary lining and the primary support are respectively calculated according to equation (2); (1)； (2)； In equation (2), , These are the elastic moduli of the secondary lining and the initial support, respectively. , The Poisson's ratios for the secondary lining and the primary support, respectively. Let be the radius of the inner wall of the secondary lining. The radius of the inner wall of the initial support and the outer wall of the secondary lining; S4. Calculate the circumferential tensile strain of the secondary lining according to equation (3). ;according to And in combination with the thickness of the secondary lining To obtain the secondary lining thickness The analytical expression of is expressed as equation (4); (3)； (4)； S5. Calculate the minimum thickness of the secondary lining obtained in step S4. Then calculate according to equations (1) to (2). Then, the stress sharing ratio of the secondary lining is calculated according to equation (5). ; (5)。 2. The analytical design method for lining stress sharing ratio based on allowable tensile strain according to claim 1, characterized in that, In step S1, the tunnel stress model is also based on the following assumptions: The axisymmetric plane strain condition is as follows: the axial dimension of the tunnel is much larger than the radial dimension, and the stress and displacement only change radially, while the influence of axial stress is ignored. The material properties are as follows: both the secondary lining and the primary support are homogeneous isotropic elastic materials.

3. The analytical design method for lining stress sharing ratio based on allowable tensile strain according to claim 2, characterized in that, In step S2, the obtained radial displacement of the inner wall of the initial support is... The radial displacement of the outer wall of the secondary lining is expressed as equation (6); The radial displacement of the inner wall of the secondary lining is expressed as equation (7); , expressed as equation (8); (6)； (7)； (8)。 4. The analytical design method for lining stress sharing ratio based on allowable tensile strain according to claim 3, characterized in that, The process also includes step S6, which involves, with reference to typical tunnel engineering parameters and the set minimum thickness of the secondary lining, calculating the circumferential tensile strain of the secondary lining at the minimum thickness according to equations (8) and (3). And compare it with the allowable tensile strain limit of the secondary lining. A comparison was conducted to verify the minimum thickness of the secondary lining.

5. The analytical design method for lining stress sharing ratio based on allowable tensile strain according to claim 4, characterized in that, The method also includes step S7, which involves using the controlled variable method to analyze the sensitivity of key parameters to the minimum thickness of the secondary lining and the stress sharing ratio of the secondary lining; the key parameters include the original rock stress. Internal water pressure , initial support elastic modulus The elastic modulus of the secondary lining .

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