A method for calculating structural stress sharing ratio considering plastic strain of surrounding rock

Abstract

This invention belongs to the field of tunnel engineering technology and relates to a method for calculating the stress sharing ratio of a structure considering the plastic strain of the surrounding rock. The method includes: simulating the tunnel's stress system using a three-layer thick-walled cylinder model, where the model consists of a secondary lining, an initial support, and a loosened ring of surrounding rock from the inside out; assuming continuous radial stress and displacement between the initial support and the loosened ring, and continuous radial stress but discontinuous radial displacement between the secondary lining and the initial support; setting the radial relative displacement between the outer wall of the secondary lining and the inner wall of the initial support as ; calculating the interface pressure between the initial support and the surrounding rock; obtaining the radial displacements of the inner wall of the initial support and the outer wall of the secondary lining; and calculating the interface pressure between the secondary lining and the initial support based on ; and calculating the stress sharing ratio of the secondary lining, the initial support, and the surrounding rock using and the original rock stress. This invention establishes a stress sharing ratio calculation model coupled with displacement discontinuity and plastic strain of the surrounding rock, which can be used for secondary lining design and construction timing optimization, providing a quantitative tool for dynamic support of soft rock tunnels.

Description

Technical Field

[0001] This invention belongs to the field of tunnel engineering technology, specifically relating to a method for calculating the structural stress sharing ratio considering the plastic strain of the surrounding rock. Background Technology

[0002] Due to the low strength and significant plastic deformation of the surrounding rock, soft rock tunnels are prone to forming large-scale loosening zones after excavation. The coordinated stress relationship between the secondary lining, the initial support, and the surrounding rock directly determines the safety and economy of the support structure. Engineering practice shows that after the excavation of soft rock tunnels, the initial support needs to undergo a process of "rapid deformation - slow stabilization." However, the timing of the secondary lining construction is often limited by the construction period and the stability of the surrounding rock, resulting in the inability to achieve deformation coordination between the inner wall of the initial support and the outer wall of the secondary lining, i.e., discontinuous displacement, which mainly occurs in the radial direction of the tunnel. For example, in the construction of the Yuanliangshan Tunnel of the Chongqing-Huaihua Railway, the secondary lining was constructed 30 days later than the initial support, and the relative displacement of the interface reached 3.5 mm. The secondary lining load-sharing ratio calculated by the traditional displacement continuity model deviated by 28% from the actual measured value, leading to circumferential cracks in the secondary lining.

[0003] Currently, there are two major limitations in the calculation of stress sharing ratio in soft rock tunnels: First, existing three-layer thick-walled tube models all assume continuous displacement between the initial support and the secondary lining, which does not match the actual working conditions on the construction site, where the initial support deforms in advance and the secondary lining passively bears the load. This leads to conservative or underestimated results in the calculation of interface pressure and stress sharing ratio. Second, although some studies have focused on the problem of displacement discontinuity, they are mostly aimed at double-layer structures (only the initial support and the secondary lining) and do not consider the load sharing effect of the plastic loosening zone of the surrounding rock, thus failing to fully reflect the collaborative stress mechanism of the support and the surrounding rock.

[0004] Currently, research on tunnel stress sharing ratio by scholars both domestically and internationally can be divided into three categories, each with its own shortcomings: 1) Analytical methods based on the assumption of displacement continuity, such as establishing a three-layer thick-walled cylinder model based on the Mohr-Coulomb criterion (MC criterion) and deriving the formula for the initial support-secondary lining sharing ratio, do not consider displacement discontinuity; the calculation of the loosening zone radius based on this theory is only applicable to scenarios where the secondary lining and the initial support are constructed simultaneously. 2) Numerical simulation-based analysis method: FLAC3D simulation analysis is used to analyze the numerical relationship between the relative displacement increment of the primary support-secondary lining and the reduction of the secondary lining sharing ratio, but no analytical expression can be given; considering the creep characteristics of the surrounding rock, the sharing ratio curves at different times are simulated, but it depends on complex parameter input and is difficult to extend to engineering design. 3) Based on the two-layer model of displacement discontinuity, although the formula for the initial support-secondary lining sharing ratio under displacement discontinuity is derived, the loosening zone of the surrounding rock is ignored, and it is only applicable to elastic surrounding rock or shallow buried tunnels.

[0005] As can be seen from the above, existing research has two main shortcomings: first, it fails to couple "displacement discontinuity" with "surrounding rock plastic loosening zone," thus failing to fully reflect the stress mechanism of soft rock tunnels; second, the three-layer model under the MC criterion lacks analytical derivation of the displacement discontinuity condition, making it difficult to quantify the influence of relative displacement on the load sharing ratio. For soft rock tunnels with MC constitutive model, the presence of the surrounding rock loosening zone significantly alters the load transfer path. Due to the deterioration of rock mass strength within the loosening zone, part of the load must be borne through the primary support and secondary lining, and the displacement difference between the primary support and secondary lining further reconstructs the interface pressure distribution. Therefore, it is urgent to develop a structural stress sharing ratio calculation method that couples displacement discontinuity and surrounding rock plastic strain. Summary of the Invention

[0006] In view of the shortcomings of the related technologies, the present invention provides a method for calculating the stress sharing ratio of structures that takes into account the plastic strain of the surrounding rock, so as to solve the technical problems mentioned in the background art.

[0007] This invention provides a method for calculating the stress sharing ratio of a structure considering the plastic strain of the surrounding rock, comprising the following steps: S1. A three-layer thick-walled cylinder model is used to simulate the tunnel's stress system, establishing the tunnel stress model. From the inside out, the three-layer thick-walled cylinder model consists of the secondary lining, the initial support, and the loosened surrounding rock zone. It is assumed that the initial support and the loosened surrounding rock zone satisfy the interlayer contact condition of continuous radial stress and continuous radial displacement. It is also assumed that the secondary lining and the initial support satisfy the interlayer contact condition of continuous radial stress but discontinuous radial displacement. The radial relative displacement between the outer wall of the secondary lining and the inner wall of the initial support is set as... ; S2. Based on the continuity of radial stress between the initial support and the loosened zone of the surrounding rock, calculate the interfacial pressure between the initial support and the surrounding rock. , expressed as equation (1), where, The stress borne by the original rock on the outer wall of the loosened zone of the surrounding rock. Let be the radius of the outer wall of the loosened zone of the surrounding rock. Let be the radius of the inner wall of the loosened zone of the surrounding rock and the outer wall of the initial support. The cohesion of the rock mass, The internal friction angle of the rock mass; (1); S3. Based on the continuity of radial stress between the secondary lining and the primary support, the radial displacement of the inner wall of the primary support is obtained according to the thick-walled cylinder theory and Hooke's law. radial displacement of the outer wall of the secondary lining Based on the discontinuity of radial displacement between the secondary lining and the primary support, utilizing... Solve the interfacial pressure between the secondary lining and the primary support. , expressed as equation (2), where, This refers to the internal water pressure borne by the inner wall of the secondary lining. The elastic modulus of the initial support. The elastic modulus of the secondary lining is given by [value]. For the Poisson's ratio of the initial branch, For the Poisson's ratio of the secondary lining, Let be the radius of the inner wall of the secondary lining. The radius of the outer wall of the secondary lining and the inner wall of the initial support; (2); S4. Calculate the stress sharing ratio of the secondary lining according to equation (3). Stress sharing ratio of initial support Stress sharing ratio of surrounding rock ; (3).

[0008] 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: the secondary lining and the primary support are both homogeneous isotropic elastic materials, the plastic deformation of the surrounding rock follows the Mohr-Coulomb criterion, and the rock mass within the loosened zone enters a plastic state.

[0009] In some embodiments, the radius of the outer wall of the loosened zone of the surrounding rock is calculated according to Equation (4) based on the Mohr-Coulomb criterion. ,in, The initial support reaction force is set to 0. (4).

[0010] In some embodiments, in step S2, equation (4) is substituted into equation (1) to obtain the interfacial pressure between the initial support and the surrounding rock. The solution is expressed as equation (5); (5).

[0011] In some embodiments, in step S3, 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); , expressed as equation (7); (6); (7).

[0012] In some embodiments, step S5 is further included, specifically, calculating different parameters based on typical parameters for soft rock tunnel engineering. Stress sharing ratio of the lower lining Stress sharing ratio of initial support Stress sharing ratio of surrounding rock In order to carry out Impact Analysis

[0013] In some embodiments, step S6 is further included, specifically, using the controlled variable method to analyze the impact of key parameters on the stress sharing ratio of the secondary lining. Sensitivity; key parameters include in-situ stress. Rock mass cohesion , initial support elastic modulus The elastic modulus of the secondary lining Radial relative displacement between the outer wall of the secondary lining and the inner wall of the primary support .

[0014] Based on the above technical solution, the structural stress sharing ratio calculation method considering the plastic strain of the surrounding rock in this embodiment of the invention takes into account the interface displacement discontinuity caused by the difference in the timing of the initial support and secondary lining construction in soft rock tunnels, as well as the calculation deviation of the stress sharing ratio caused by the traditional three-layer thick-walled tube model ignoring this displacement difference. A three-layer thick-walled tube model coupled with "secondary lining-initial support displacement discontinuity + surrounding rock plastic strain (loosening zone)" is established. Based on the Mohr-Coulomb criterion and the three-layer thick-walled tube model, the radial relative displacement between the secondary lining and the initial support is introduced, and the analytical formulas for the stress sharing ratio of each structure under displacement discontinuity are derived, breaking through the traditional assumption of displacement continuity. This invention overcomes the limitations of conventional design, better reflects on-site construction conditions, quantifies the stress sharing ratio among the secondary lining, primary support, and surrounding rock, clarifies the influence of key parameters such as radial relative displacement on the stress sharing ratio of the secondary lining, and improves the theoretical system of stress distribution in soft rock tunnel support structures. In actual construction, the radial relative displacement between the secondary lining and primary support, monitored on-site, can guide and optimize the design and timing of secondary lining construction in soft rock tunnels, ensuring a reasonable stress sharing ratio, reducing support defects, and improving the design accuracy of soft rock tunnel support. Therefore, this invention provides a more practical and accurate quantitative tool for dynamic support of soft rock tunnels and has high engineering application and promotion value. Attached Figure Description

[0015] 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 structural stress sharing ratio calculation method considering the plastic strain of surrounding rock according to the present invention; Figure 2 This is a schematic diagram of the three-layer thick-walled cylinder model in this invention. Detailed Implementation

[0016] 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.

[0017] 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.

[0018] 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.

[0019] 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.

[0020] refer to Figure 1 , Figure 2 As shown, the present invention provides a method for calculating the stress sharing ratio of a structure considering the plastic strain of the surrounding rock, including the following steps S1 to S4.

[0021] Step S1: A three-layer thick-walled cylinder model is used to simulate the tunnel's stress system, establishing the tunnel stress model. The tunnel is theoretically considered circular. The three-layer thick-walled cylinder model, from the inside out, consists of the secondary lining, the primary support, and the loosened zone of the surrounding rock. The outer wall of the secondary lining is in contact with the inner wall of the primary support, and the outer wall of the primary support is in contact with the inner wall of the plastic deformation zone of the surrounding rock, i.e., the loosened zone. 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... , Let the inner and outer radii of the loosened zone of the surrounding rock be denoted as... , .

[0022] Assuming that the primary support and the loosened zone of the surrounding rock satisfy the interlayer contact condition of continuous radial stress and continuous radial displacement, and assuming that the secondary lining and the primary support satisfy the interlayer contact condition of continuous radial stress but discontinuous radial displacement, the radial relative displacement between the outer wall of the secondary lining and the inner wall of the primary support is set as... .

[0023] 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 primary support are both homogeneous isotropic elastic materials, the secondary lining and primary support are both linear elastic bodies, the plastic deformation of the surrounding rock follows the Mohr-Coulomb criterion, and the rock mass within the loosened zone enters a plastic state; load condition, specifically, the inner wall of the secondary lining is subjected to internal water pressure (or construction load). The outer wall of the loosened zone of the surrounding rock bears the stress of the original rock. .

[0024] To further explain, based on the Mohr-Coulomb criterion, the radius of the outer wall of the loosened zone of the surrounding rock is calculated according to equation (4). ,in, The initial support reaction force is set to 0. The cohesion of the rock mass, The internal friction angle of the rock mass; This is the excavation radius of the tunnel, which is also the radius of the initial support outer wall; (4).

[0025] Step S2: Based on the continuity of radial stress between the initial support and the loosened zone of the surrounding rock, calculate the interfacial pressure between the initial support and the surrounding rock. To further explain, based on the Mohr-Coulomb criterion, the radial stress of the loosened zone of the surrounding rock... Represented as equation (11), where, Radial coordinates, ; (11); Based on the continuity of radial stress between the initial support and the loosened zone of the surrounding rock, when hour, , The radial stress of the initial support is given. Substituting this boundary condition into equation (11) allows us to calculate the interfacial pressure between the initial support and the surrounding rock. This can be expressed as equation (1); further, substituting equation (4) into equation (1) can eliminate... The item obtains the interfacial pressure between the initial support and the surrounding rock. The solution is expressed as equation (5); (1); (5).

[0026] Step S3: 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, obtain the radial displacement of the inner wall of the primary support. radial displacement of the outer wall of the secondary lining .

[0027] 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 (21), where, , The integral constant is determined by the boundary conditions. Radial coordinates, ; (twenty one); 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; by substituting this boundary condition into equation (21), the integral constant can be solved simultaneously. , , expressed as equation (22); (twenty two); According to Hooke's Law, the radial displacement of the secondary lining... Represented as equation (23), where, The elastic modulus of the secondary lining is given by [value]. Let be the Poisson's ratio of the secondary lining; substituting equation (22) into equation (23) and simplifying, we obtain the outer wall of the secondary lining ( Radial displacement , expressed as equation (7); (twenty three); (7).

[0028] Similarly, the initial support is a linear elastic body. Based on the thick-walled cylinder theory of elasticity, the radial stress of the initial support... Satisfying the Lamé equation, expressed as equation (31), where, , The integral constant is determined by the boundary conditions. Radial coordinates, ; (31); Based on boundary conditions, when At this time, the inner wall of the initial support is in contact with the outer wall of the secondary lining. Because the radial stress between them is continuous, the radial stress of the initial support is... ;when At this time, the outer wall of the initial support is in contact with the inner wall of the loosened zone of the surrounding rock. Because the radial stress between the two is continuous, the radial stress of the initial support is... ,in, The radial stress of the loosened zone of the surrounding rock; substituting this boundary condition into equation (31), the integral constant can be solved simultaneously. , , expressed as equation (32); (32); According to Hooke's law, the radial displacement of the initial support... Represented as equation (33), where, The elastic modulus of the initial support. Let be the Poisson's ratio of the initial support; substituting equation (32) into equation (33) and simplifying, we obtain the inner wall of the initial support ( Radial displacement , expressed as equation (6); (33); (6).

[0029] Furthermore, based on the discontinuity of radial displacement between the secondary lining and the primary support, utilizing... Substituting equations (6) and (7) into the relation, we obtain the following: The linear equation is then used to solve for the interfacial pressure between the secondary lining and the initial support. , expressed as equation (2); (2).

[0030] Step S4: Define the stress sharing ratio of the secondary lining, primary support, and surrounding rock as the ratio of their respective bearing pressure to the original rock stress. The stress sharing ratio of the secondary lining is calculated according to equation (3). Stress sharing ratio of initial support Stress sharing ratio of surrounding rock It is understandable that ; (3).

[0031] The above illustrative embodiment, considering the discontinuity of interface displacement caused by the difference in the timing of the initial support and secondary lining construction in soft rock tunnels, and the calculation deviation of the sharing ratio caused by the traditional three-layer thick-walled cylinder model ignoring this displacement difference, couples the radial displacement discontinuity between the secondary lining and the initial support with the plastic strain (loosening zone) of the surrounding rock to fully reflect the stress mechanism of soft rock tunnels. By establishing a three-layer thick-walled cylinder model, the radial displacement expression of the outer wall of the secondary lining and the inner wall of the initial support is derived, and the radial relative displacement relationship between the two is substituted to solve the interface pressure between the secondary lining and the initial support. Based on the loosening zone of the initial support and the surrounding rock... By solving the interfacial pressure between the primary support and the surrounding rock, the analytical formula for the stress sharing ratio of the secondary lining, primary support, and surrounding rock is derived, thus establishing a calculation model for the stress sharing ratio of each structure under displacement discontinuity. This breaks through the limitations of the traditional assumption of displacement continuity and improves the stress theory system of soft rock tunnel support structure. In practical engineering applications, the support parameters can be dynamically adjusted by combining the radial relative displacement between the outer wall of the secondary lining and the inner wall of the primary support with on-site monitoring, thereby providing a more practical and accurate theoretical tool for optimizing the design and construction timing of the secondary lining of soft rock tunnels.

[0032] In some embodiments, the method for calculating the structural stress sharing ratio considering the plastic strain of the surrounding rock further includes step S5, specifically, calculating different... Stress sharing ratio of the lower lining Stress sharing ratio of initial support Stress sharing ratio of surrounding rock In order to carry out Impact analysis.

[0033] To further illustrate, typical parameters for soft rock tunnel engineering are shown in Table 1. Substituting the parameters in Table 1 into equations (2), (5), and (3), different... interfacial pressure between the secondary lining and the primary support interfacial pressure between the primary support and the surrounding rock Stress sharing ratio of secondary lining Stress sharing ratio of initial support Stress sharing ratio of surrounding rock The calculation results are shown in Table 2.

[0034] Table 1: Typical parameters for soft rock tunnel engineering

[0035] Table 2: Differences Calculation results of lower interface pressure and stress sharing ratio

[0036] Impact Analysis: As can be seen from Table 2, when At that time, the radial displacement of the outer wall of the secondary lining is greater than the radial displacement of the inner wall of the initial support. If the secondary lining is constructed in advance, it will have to bear additional pressure. Follow Decrease and increase; when When mm, , Comparison Increased by 44.9% at that time; When mm, , Comparison Increased by 26.6% at that time; At that time, the radial displacement of the outer wall of the secondary lining is less than the radial displacement of the inner wall of the primary support. The primary support deforms earlier, the secondary lining is constructed later, and the primary support releases part of the load. Follow Increase and decrease; when When mm, , Comparison It decreased by 26.6% at that time; When mm, , Comparison It decreased by 44.6% at that time; When the radial displacement between the primary support and the secondary lining is continuous, This indicates that the analytical formula for the structural stress sharing ratio considering the plastic strain of the surrounding rock in this invention can degenerate into a classical model when the displacement is continuous.

[0037] In addition, as shown in Table 2, in soft rock tunnels, the surrounding rock bears 10% to 12% of the load, the primary support bears 37% to 69% of the load, and the secondary lining bears 20% to 52% of the load. When designing, it is necessary to pay attention to the temporary bearing capacity of the primary support and the self-supporting capacity of the surrounding rock, avoid over-reliance on the secondary lining, and at the same time, achieve the coordinated force bearing of the support and the surrounding rock by controlling the timing of the secondary lining construction.

[0038] To clarify the stress sharing ratio of key parameters in the secondary lining To determine the degree of influence, in some embodiments, the method for calculating the structural stress sharing ratio considering the plastic strain of the surrounding rock further includes step S6, specifically, using the controlled variable method to analyze the impact of key parameters on the stress sharing ratio of the secondary lining. Sensitivity; key parameters include in-situ stress. Rock mass cohesion , initial support elastic modulus The elastic modulus of the secondary lining Radial relative displacement between the outer wall of the secondary lining and the inner wall of the primary support In the controlled variable method, a single parameter changes by 20%, while the remaining parameters are taken as baseline values. , , , , ), calculate the stress sharing ratio of the secondary lining. rate of change ,Will The calculation results are shown in Table 3, which serves as the baseline sharing ratio for the secondary lining.

[0039] Table 3: Results of parameter sensitivity analysis

[0040] As shown in Table 3, the radial relative displacement between the outer wall of the secondary lining and the inner wall of the initial support can be seen. Original rock stress Rock mass cohesion All of these are highly sensitive parameters. For every 1mm change, The change is approximately 0.032 to 0.036. It is a key control parameter in dynamic design, and can be monitored on-site during engineering. Adjusting the timing of secondary lining construction is recommended. Controlled within -3 to 3 mm, avoid mm This can lead to cracking of the secondary lining, or mm This results in excessive concentration of initial support loads, thereby preventing load imbalance in the support structure. (Original rock stress) Each increase Pa, An increase of 0.036, because Increasing the thickness of the secondary lining expands the loosened zone, increasing the pressure transmitted from the primary support to the secondary lining. Therefore, high-stress tunnels require increased secondary lining thickness and strengthened primary support stiffness. Rock mass cohesion. For every 0.1 increase Pa, An increase of 0.032, because Increasing the resistance to the expansion of the loosened zone enhances the self-supporting capacity of the surrounding rock and reduces the load shared by the secondary lining; therefore, precise exploration is required for soft rock tunnels. The value was determined using a combination of borehole elastic mode testing and acoustic wave testing to avoid errors caused by... The underestimation of the value led to a conservative approach in the support design.

[0041] initial support elastic modulus This is a moderately sensitive parameter; Increase by 20%, The load distribution can be optimized by adjusting the properties of the initial support material, as the increased initial support stiffness allows it to withstand more loads. This is particularly suitable for soft rock tunnels. Pa's initial support material, when When Pa, the lag time for secondary lining construction should be appropriately reduced to control... mm.

[0042] The elastic modulus of the secondary lining It is a parameter with extremely low sensitivity. Changes No impact, because Determined by the stress balance between the primary support and the surrounding rock, the stiffness of the secondary lining only affects its own deformation. Therefore, economy can be given priority in the design of the secondary lining. In the project, C30 to C40 concrete can be selected according to economy. Under the premise of meeting the strength requirements, low elastic modulus concrete should be given priority to reduce the internal stress of the secondary lining.

[0043] In summary, the structural stress sharing ratio calculation method of this invention, which considers the plastic strain of the surrounding rock, takes into account the discontinuity of interface displacement caused by the difference in the timing of the initial support and secondary lining construction in soft rock tunnels, as well as the calculation deviation of the stress sharing ratio caused by the traditional three-layer thick-walled tube model neglecting this displacement difference. A three-layer thick-walled tube model coupled with "discontinuity of secondary lining-initial support displacement + plastic strain of surrounding rock (loosening zone)" is established. The Mohr-Coulomb constitutive model is coupled with the condition of discontinuity of initial support-secondary lining displacement, and an analytical formula for the stress sharing ratio of the secondary lining under discontinuous displacement is derived, ultimately quantifying the stress sharing ratio of the initial support, secondary lining, and surrounding rock. This invention also verifies the rationality of the analytical formula for stress sharing ratio through numerical examples and sensitivity analysis. The study investigated the effectiveness and impact of key parameters such as radial relative displacement on the stress sharing ratio of the secondary lining, thus improving the theoretical system of stress distribution in soft rock tunnel support structures. Results showed that the radial relative displacement between the secondary lining and the primary support, the original rock stress, and the rock mass cohesion significantly affect the stress sharing ratio. Therefore, in practical engineering applications, the radial relative displacement between the outer wall of the secondary lining and the inner wall of the primary support, obtained from on-site monitoring, can guide and dynamically adjust the design and construction timing of the secondary lining, avoiding load imbalance in the support structure, improving the design accuracy of soft rock tunnel support, and reducing engineering defects. Furthermore, the Mohr-Coulomb criterion parameters can be further optimized using on-site monitoring data (e.g., considering the effect of rock mass creep on cohesion). The invention improves calculation accuracy and extends to the calculation of stress sharing ratio for non-circular cross-section tunnels. Therefore, this invention provides a theoretical tool for dynamic support optimization of soft rock tunnels, which has high engineering application and promotion value and can reliably guide actual engineering construction.

[0044] 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.

[0045] 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. A method for calculating a structural stress sharing ratio taking into account plastic strain of surrounding rock, characterized by, Includes the following steps: S1, a three-layer thick-walled cylinder model is used to simulate a tunnel stress system, and a tunnel stress model is established; the three-layer thick-walled cylinder model is sequentially two linings, primary support and a surrounding rock loose circle from inside to outside; it is assumed that the primary support and the surrounding rock loose circle satisfy the interlayer contact condition of continuous radial stress and continuous radial displacement, it is assumed that the two linings and the primary support satisfy the interlayer contact condition of continuous radial stress but discontinuous radial displacement, and the radial relative displacement between the outer wall of the two linings and the inner wall of the primary support is set as ; S2, based on the continuity of the radial stress between the primary support and the surrounding rock loose circle, the interface pressure between the primary support and the surrounding rock is solved , is expressed as formula (1), wherein, is the in-situ rock stress borne by the outer wall of the surrounding rock loose circle, is the radius of the outer wall of the surrounding rock loose circle, is the radius of the inner wall of the surrounding rock loose circle and the outer wall of the primary support, is the cohesion of the rock mass, is the internal friction angle of the rock mass; (1)； S3. Based on the continuity of radial stress between the secondary lining and the primary support, the radial displacement of the inner wall of the primary support is obtained according to the thick-walled cylinder theory and Hooke's law. radial displacement of the outer wall of the secondary lining Based on the discontinuity of radial displacement between the secondary lining and the primary support, utilizing... Solve the interfacial pressure between the secondary lining and the primary support. , expressed as equation (2), where, This refers to the internal water pressure borne by the inner wall of the secondary lining. The elastic modulus of the initial support. The elastic modulus of the secondary lining is given by [value]. For the Poisson's ratio of the initial branch, For the Poisson's ratio of the secondary lining, Let be the radius of the inner wall of the secondary lining. The radius of the outer wall of the secondary lining and the inner wall of the initial support; (2)； S4. Calculate the stress sharing ratio of the secondary lining according to equation (3). Stress sharing ratio of initial support Stress sharing ratio of surrounding rock ; (3)。 2. The method for calculating the structural stress sharing ratio considering the plastic strain of surrounding rock 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: the secondary lining and the primary support are both homogeneous isotropic elastic materials, the plastic deformation of the surrounding rock follows the Mohr-Coulomb criterion, and the rock mass within the loosened zone enters a plastic state.

3. The method for calculating the structural stress sharing ratio considering the plastic strain of surrounding rock according to claim 2, characterized in that, Based on the Mohr-Coulomb criterion, the radius of the outer wall of the loosened zone of the surrounding rock is calculated according to equation (4). ,in, The initial support reaction force is set to 0. (4)。 4. The method for calculating the structural stress sharing ratio considering the plastic strain of surrounding rock according to claim 3, characterized in that, In step S2, substitute equation (4) into equation (1) to obtain the interfacial pressure between the initial support and the surrounding rock. The solution is expressed as equation (5); (5)。 5. The method for calculating the structural stress sharing ratio considering the plastic strain of surrounding rock according to claim 4, characterized in that, In step S3, 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); , expressed as equation (7); (6)； (7)。 6. The method for calculating the structural stress sharing ratio considering the plastic strain of surrounding rock according to any one of claims 1 to 5, characterized in that, It also includes step S5, which specifically involves calculating different parameters based on typical parameters for soft rock tunnel engineering. Stress sharing ratio of the lower lining Stress sharing ratio of initial support Stress sharing ratio of surrounding rock In order to carry out Impact analysis.

7. The method for calculating the structural stress sharing ratio considering the plastic strain of surrounding rock according to claim 6, characterized in that, The process also includes step S6, which involves using the controlled variable method to analyze the impact of key parameters on the stress distribution ratio of the secondary lining. Sensitivity; the key parameters include in-situ stress. Rock mass cohesion , initial support elastic modulus The elastic modulus of the secondary lining Radial relative displacement between the outer wall of the secondary lining and the inner wall of the primary support .

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