Calculation method of secondary lining thickness of water conveyance tunnel considering plastic deformation of surrounding rock

Abstract

The present application belongs to the technical field of water conveyance tunnel, and relates to a method for calculating the thickness of the second lining of a water conveyance tunnel considering the plastic deformation of surrounding rock, which comprises the following steps: a three-layer thick-walled cylinder model is used to simulate the stress system of the water conveyance tunnel, and the model comprises, from inside to outside, the second lining, the primary support and the surrounding rock loose circle; it is assumed that the plastic deformation of the surrounding rock complies with the H-B criterion, and the rock mass in the loose circle enters a plastic state; it is assumed that the radial stress and the radial displacement between the layers of the model are continuous, and the allowable tensile strain limit value of the second lining is set; the radial displacement of the inner wall of the second lining, the outer wall of the second lining, the inner wall of the primary support, the outer wall of the primary support and the inner wall of the loose circle is obtained; the interface pressure is obtained; the circumferential tensile strain of the inner wall of the second lining is calculated, and the implicit relationship between the circumferential tensile strain and the thickness of the second lining is obtained; and the minimum thickness of the second lining is obtained through iterative calculation according to the convergence criterion. The present application realizes the accurate calculation of the minimum thickness of the second lining of the water conveyance tunnel by constructing a three-layer thick-walled cylinder model based on the H-B criterion and coupling the allowable tensile strain constraint of the second lining.

Description

Technical Field

[0001] This invention belongs to the field of water conveyance tunnel technology, specifically relating to a method for calculating the secondary lining thickness of water conveyance tunnels that takes into account the plastic deformation of the surrounding rock. Background Technology

[0002] Water conveyance tunnels are core facilities in major water conservancy projects such as inter-basin water transfer and urban water supply. They bear the combined effects of internal water pressure and surrounding rock loads for extended periods. As the permanent load-bearing structure of water conveyance tunnels, the thickness design of the secondary lining directly affects the safety and economy of the project. During tunnel excavation, the original geostress field is redistributed, and the surrounding rock is prone to forming a certain range of plastic zone (i.e., loose zone) due to unloading. In this area, the rock mass strength deteriorates and deformation characteristics change, significantly reconstructing the load sharing relationship of "secondary lining (i.e., secondary lining) - initial support (i.e., initial support) - surrounding rock". If the mechanical effects in this area are ignored, it will lead to deviations between the structural stress analysis and the actual working conditions.

[0003] Currently, the traditional design method for the secondary lining thickness of water conveyance tunnels has the following drawbacks:

[0004] 1) Most analyses are based on elastic theory, which completely ignores the plastic deformation of the surrounding rock and assumes that the material is always in an elastic state. This often leads to a serious overestimation of the load acting on the lining, resulting in overly conservative designs and material waste. This theory does not match the fact that plastic deformation often occurs in the surrounding rock after being subjected to stress in actual engineering. Because the disturbance of the loosened zone of the surrounding rock to the displacement field and stress field is not considered, the calculation of the pressure at the secondary lining-primary support interface and the pressure at the primary support-surrounding rock interface is biased. This leads to redundant secondary lining thickness, which increases costs, or insufficient thickness, which may cause cracking risks.

[0005] 2) Using only stress intensity as a control index without considering problems such as concrete cracking and water-stopping failure caused by excessive deformation of the secondary lining, or excessive control of thickness leading to waste of resources, makes it difficult to balance safety and economy; although some studies have established stress sharing models that consider the plastic zone of the surrounding rock, they have not established a direct relationship between "nonlinear failure-stress sharing-thickness-deformation", making it difficult to accurately quantify the thickness of the secondary lining, nor can they accurately quantify the stress sharing ratio between the initial support and the secondary lining, thus failing to provide a reliable basis for optimizing the support parameters and controlling the construction timing of water conveyance tunnels;

[0006] 3) Existing design methods for secondary lining thickness of water conveyance tunnels lack universality under different geological conditions and are difficult to apply widely to complex and variable tunnel engineering scenarios.

[0007] In view of this, there is an urgent need to develop a complete and engineering-applicable system for determining the secondary lining thickness of water conveyance tunnels that takes into account the plastic deformation of the surrounding rock. Summary of the Invention

[0008] In view of the shortcomings of the related technologies, the present invention provides a method for calculating the secondary lining thickness of water conveyance tunnels that takes into account the plastic deformation of the surrounding rock, so as to solve the technical problems mentioned in the background art.

[0009] This invention provides a method for calculating the secondary lining thickness of water conveyance tunnels considering the plastic deformation of surrounding rock. When applied to water conveyance tunnels in jointed rock masses, the method includes the following steps:

[0010] S1. A three-layer thick-walled cylinder model is used to simulate the stress system of the water conveyance tunnel, establishing a stress model for the water conveyance tunnel. The three-layer thick-walled cylinder model consists of the secondary lining, the primary support, and the loosened zone of the surrounding rock from the inside out. It is assumed that the secondary lining and the primary support are both linear elastic materials, the plastic deformation of the surrounding rock follows the Hoek-Brown criterion, and the rock mass within the loosened zone enters a plastic state. It is assumed that the interlayers of the secondary lining, the primary support, and the loosened zone of the surrounding rock are in complete contact, and that the radial stress and radial displacement are continuous. The allowable tensile strain limit of the secondary lining is set to be... ;

[0011] S2. Based on the continuity of interlayer radial stress in the secondary lining, primary support, and surrounding rock loosening zone, the radial displacement of the inner wall of the secondary lining is obtained. Radial displacement of the outer wall of the secondary lining Radial displacement of the inner wall of the initial support Radial displacement of the outer wall of the initial support Radial displacement of the inner wall of the loosened zone of surrounding rock ;

[0012] S3. Based on the continuity of interlayer radial displacement between the secondary lining, primary support, and surrounding rock loosened zone, the interfacial pressure between the secondary lining and primary support is obtained. interfacial pressure between the primary support and the surrounding rock ;

[0013] S4. Calculate the circumferential tensile strain of the inner wall of the secondary lining according to equation (1). Combine it with the thickness of the secondary lining Combine, obtain and The implicit relation is expressed as equation (2); where, Let be the radius of the inner wall of the secondary lining. The elastic modulus of the secondary lining is given by [value]. For the Poisson's ratio of the secondary lining, The internal water pressure borne by the inner wall of the secondary lining;

[0014] (1);

[0015] (2);

[0016] S5, according to The convergence criterion is used for iterative calculation to obtain the secondary lining thickness. The solution; among which, This represents the allowable tensile strain error value for the project.

[0017] This invention also provides a method for calculating the secondary lining thickness of a water conveyance tunnel considering the plastic deformation of the surrounding rock. When applied to soft rock water conveyance tunnels or deeply buried water conveyance tunnels, the method includes the following steps:

[0018] D1. A three-layer thick-walled cylinder model is used to simulate the stress system of the water conveyance tunnel, establishing a stress model for the water conveyance tunnel. The three-layer thick-walled cylinder model consists of, from the inside out, the secondary lining, the initial support, and the loosened zone of the surrounding rock. It is assumed that the secondary lining and the initial support are both linearly 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. It is also assumed that the interlayers of the secondary lining, the initial support, and the loosened zone of the surrounding rock are in complete contact, and that radial stress and radial displacement are continuous. The allowable deformation of the inner wall of the secondary lining is given by... ;

[0019] D2. Based on the continuity of interlayer radial stress in the secondary lining, primary support, and surrounding rock loosening zone, the radial displacement of the inner wall of the secondary lining is obtained. Radial displacement of the outer wall of the secondary lining Radial displacement of the inner wall of the initial support Radial displacement of the outer wall of the initial support Radial displacement of the inner wall of the loosened zone of surrounding rock ;

[0020] D3. Based on the continuity of interlayer radial displacement between the secondary lining, primary support, and surrounding rock loosened zone, the interfacial pressure between the secondary lining and primary support is obtained. interfacial pressure between the primary support and the surrounding rock ;

[0021] D4. Radial displacement of the inner wall of the secondary lining With secondary lining thickness Combine, obtain and The implicit relation is expressed as equation (3); where, Let be the radius of the inner wall of the secondary lining. The elastic modulus of the secondary lining is given by [value]. For the Poisson's ratio of the secondary lining, The internal water pressure borne by the inner wall of the secondary lining;

[0022] (3);

[0023] D5, according to The convergence criterion is used for iterative calculation to obtain the secondary lining thickness. The solution; among which, This represents the allowable displacement error value for the project.

[0024] In some embodiments, in steps S1 and D1, the stress model of the water conveyance tunnel is also based on the following assumptions: axisymmetric plane strain condition, specifically, the axial dimension of the water conveyance tunnel is much larger than the radial dimension, the stress and displacement only change radially, and the influence of axial stress is ignored.

[0025] In some embodiments, the radial displacement of the inner wall of the secondary lining is obtained in steps S2 and D2. Radial displacement of the outer wall of the secondary lining Radial displacement of the inner wall of the initial support Radial displacement of the outer wall of the initial support Radial displacement of the inner wall of the loosened zone of surrounding rock , respectively represented by equations (4) to (8); where, The stress borne by the original rock on the outer wall of the loosened zone of the surrounding rock. , These are the elastic moduli of the initial support and the loosened zone of the surrounding rock, respectively. , Poisson's ratio for the initial support and the loosened zone of the surrounding rock, respectively. 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 initial support and the outer wall of the secondary lining. The radius of the inner wall of the loosened zone and the outer wall of the initial support;

[0026] (4);

[0027] (5);

[0028] (6);

[0029] (7);

[0030] (8).

[0031] In some embodiments, in step S1, when the method for calculating the secondary lining thickness of a water conveyance tunnel considering the plastic deformation of the surrounding rock is applied to a jointed rock mass water conveyance tunnel, it is assumed that the plastic deformation of the surrounding rock follows the Hoek-Brown criterion, and the radius of the outer wall of the loosened zone of the surrounding rock is calculated according to equation (9). The elastic modulus of the loosened zone of the surrounding rock is calculated according to equation (10). ;in, The uniaxial compressive strength of the rock mass; , , The rock mass quality correction factor is calculated according to equations (11) to (13); For the Hoek-Brown parameters of the intact rock mass, As a geological strength index of the rock mass, For the disturbance parameters, The elastic modulus of the surrounding rock. Damage coefficient;

[0032] (9);

[0033] (10);

[0034] (11);

[0035] (12);

[0036] (13);

[0037] When the method for calculating the secondary lining thickness of water conveyance tunnels that considers the plastic deformation of the surrounding rock is applied to soft rock water conveyance tunnels or deeply buried water conveyance tunnels, it is assumed that the plastic deformation of the surrounding rock follows the Mohr-Coulomb criterion, and the radius of the outer wall of the loosened zone of the surrounding rock is calculated according to equation (14). The elastic modulus of the loosened zone of the surrounding rock is calculated according to equation (15). ;in, The cohesion of the rock mass, The internal friction angle of the rock mass. This is the initial support reaction force; The elastic modulus of the surrounding rock;

[0038] (14);

[0039] (15).

[0040] In some embodiments, in steps S3 and D3, the interfacial pressure between the secondary lining and the primary support... interfacial pressure between the primary support and the surrounding rock They are represented by equations (16) and (17) respectively; where, , , These are the secondary lining displacement contribution coefficient, the initial support displacement contribution coefficient, and the surrounding rock displacement contribution coefficient, respectively, calculated according to formula (11);

[0041] (16);

[0042] (17);

[0043] (18).

[0044] In some embodiments, a stress sharing ratio calculation step is also included, specifically, using the secondary lining thickness obtained after iterative calculation. ,according to calculate Then calculate according to equations (16) to (17). , Then, the stress sharing ratio of the secondary lining is calculated according to equation (19). Stress sharing ratio of initial support Stress sharing ratio of surrounding rock ;

[0045] (19).

[0046] In some embodiments, when the method for calculating the secondary lining thickness of a water conveyance tunnel that considers the plastic deformation of the surrounding rock is applied to a water conveyance tunnel in jointed rock mass, it also includes... Impact analysis steps and parameters Sensitivity analysis steps; The specific steps of the impact analysis are as follows: referring to typical parameters of jointed rock mass water conveyance tunnel projects, calculate different... Lower lining thickness interfacial pressure between the secondary lining and the primary support interfacial pressure between the primary support and the surrounding rock The stress distribution ratio of each layer, in order to conduct Influence analysis and verification of mechanical laws; parameter effects The specific steps of the sensitivity analysis are as follows: using the controlled variable method, analyze the impact of key parameters on the secondary lining thickness. Sensitivity; key parameters include in-situ stress. The elastic modulus of the secondary lining , initial support elastic modulus Uniaxial compressive strength of rock mass Rock mass geological strength index .

[0047] In some embodiments, when the method for calculating the secondary lining thickness of a water conveyance tunnel, which takes into account the plastic deformation of the surrounding rock, is applied to soft rock water conveyance tunnels or deeply buried water conveyance tunnels, it also includes... Impact analysis steps and parameters Sensitivity analysis steps; The specific steps of the impact analysis are as follows: referring to typical parameters of soft rock water conveyance tunnels or deep-buried water conveyance tunnels, calculate different... Lower lining thickness interfacial pressure between the secondary lining and the primary support interfacial pressure between the primary support and the surrounding rock The stress distribution ratio of each layer, in order to conduct Influence analysis and verification of mechanical laws; parameter effects The specific steps of the sensitivity analysis are as follows: using the controlled variable method, analyze the impact of key parameters on the secondary lining thickness. Sensitivity; key parameters include in-situ stress. Internal water pressure internal friction angle of rock mass The elastic modulus of the secondary lining , initial support elastic modulus .

[0048] Based on the above technical solution, the method for calculating the secondary lining thickness of water conveyance tunnels considering the plastic deformation of surrounding rock in this embodiment of the invention introduces the effect of the loosened ring of surrounding rock by constructing a three-layer thick-walled cylinder coupled analytical model of "secondary lining-initial support-loosened ring of surrounding rock" based on the Hoek-Brown criterion or the Mohr-Coulomb criterion. This method can more accurately reveal the mechanical behavior of water conveyance tunnel structures with different rock masses under complex stress conditions, overcome the shortcomings of traditional elastic theory that ignores the plastic deformation of surrounding rock and is difficult to describe the nonlinear strength evolution of rock mass, fill the gap in nonlinear rock mechanics analysis in deep excavation engineering, and theoretically realize the leap from ideal elastic state to elastic-plastic synergistic stress theory and from empirical design to vectorized design. This improves the mechanical analysis system of tunnel structures and makes theoretical research more consistent with the actual stress state of surrounding rock. On this basis, the nonlinear failure characteristics of rock mass are coupled with the allowable tensile strain limit of secondary lining or the allowable deformation of the inner wall of secondary lining to derive the optimal value of the secondary lining thickness of water conveyance tunnels. This invention establishes an implicit analytical relationship for the minimum thickness of the secondary lining, and then uses an iterative solution method to accurately calculate the minimum thickness of the secondary lining. It establishes a direct correlation between "nonlinear failure, stress sharing, thickness, and deformation," meeting the engineering requirements for quantified secondary lining thickness. This solves the problem that traditional methods neglect the influence of the surrounding rock's plastic zone or secondary lining deformation constraints, leading to overly conservative or unsafe secondary lining thickness designs for water conveyance tunnels. It provides a precise, efficient, and reliable theoretical tool for the optimized design of secondary linings in water conveyance tunnels, thus providing reliable guidance for support parameter optimization and construction timing control, avoiding overly conservative or unsafe support designs, and achieving a balance between engineering safety and economy. Therefore, this invention provides a complete and engineeringable computational framework for secondary lining thickness design and stress sharing analysis in jointed rock masses, soft rock, and deeply buried water conveyance tunnel support systems. It provides theoretical support for the design and optimization of secondary lining thickness in water conveyance tunnels under different geological conditions, and has significant theoretical and practical implications for promoting the mechanical analysis and design optimization of underground engineering. Attached Figure Description

[0049] 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:

[0050] Figure 1 This is a flowchart of an embodiment of the method for calculating the secondary lining thickness of a water conveyance tunnel considering the plastic deformation of surrounding rock according to the present invention;

[0051] Figure 2 This is a flowchart of Example 2 of the method for calculating the secondary lining thickness of a water conveyance tunnel considering the plastic deformation of surrounding rock according to the present invention;

[0052] Figure 3 This is a schematic diagram of the three-layer thick-walled cylinder model in this invention. Detailed Implementation

[0053] 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.

[0054] 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.

[0055] 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.

[0056] 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.

[0057] Example 1:

[0058] refer to Figure 1 , Figure 3 As shown, the present invention provides a method for calculating the secondary lining thickness of a water conveyance tunnel considering the plastic deformation of the surrounding rock. When applied to a water conveyance tunnel in jointed rock mass, it includes the following steps S1 to S5.

[0059] Step S1: A three-layer thick-walled cylinder model is used to simulate the stress system of the water conveyance tunnel, establishing a stress model for the jointed rock mass water conveyance tunnel. The water conveyance tunnel is theoretically designed as 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 radius of the inner wall of the secondary lining is denoted as... Let the outer wall radius of the secondary lining and the inner wall radius of the initial support be denoted as... The radius of the outer wall of the initial support and the radius of the inner wall of the loosened zone of the surrounding rock are denoted as... The radius of the outer wall of the loosened zone of the surrounding rock is denoted as . ,in, That is, the excavation radius of the water conveyance tunnel.

[0060] Assuming both the secondary lining and the primary support are linearly elastic materials, and the plastic deformation of the surrounding rock follows the Hoek-Brown criterion (abbreviated as HB criterion), with the rock mass within the loosened zone entering a plastic state. Assuming complete interlayer contact between the secondary lining, the primary support, and the loosened zone of the surrounding rock, and that radial stress and radial displacement are continuous; and assuming the allowable tensile strain limit for the secondary lining is [value missing]. .

[0061] Furthermore, the stress model of the water conveyance tunnel is based on the following assumptions: axisymmetric plane strain condition, specifically, the axial dimension of the water conveyance tunnel is much larger than the radial dimension, and the stress and displacement only change radially, ignoring the influence of axial stress; 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. .

[0062] To further explain, based on the fact that the plastic deformation of the surrounding rock follows the Hoek-Brown criterion, the radius of the outer wall of the loosened zone of the surrounding rock is calculated according to equation (9). ,in, The uniaxial compressive strength of the rock mass. , , This is the rock mass quality correction factor; it should be noted that the Hoek-Brown criterion can describe the post-peak softening and nonlinear strength evolution of jointed rock masses, reflecting the nonlinear mechanical behavior of jointed rock masses;

[0063] (9).

[0064] Furthermore, the rock mass quality correction coefficients are calculated according to equations (11) to (13). , , ,in, The Hoek-Brown parameters for intact rock masses range from 5 to 10. This is a geological strength index for rock mass, with a value range of 0 to 100. This is a disturbance parameter, with a value range of 0 to 1;

[0065] (11);

[0066] (12);

[0067] (13).

[0068] Step S2: Based on the continuity of interlayer radial stress in the secondary lining, primary support, and surrounding rock loosening zone, the radial displacement of the inner wall of the secondary lining is obtained according to the thick-walled cylinder theory and Hooke's law. Radial displacement of the outer wall of the secondary lining Radial displacement of the inner wall of the initial support Radial displacement of the outer wall of the initial support Radial displacement of the inner wall of the loosened zone of surrounding rock .

[0069] 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, ;

[0070] (twenty one);

[0071] 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);

[0072] (twenty two);

[0073] 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 inner wall of the secondary lining ( Radial displacement and the outer wall of the secondary lining ( Radial displacement , respectively expressed as equation (4) and equation (5);

[0074] (twenty three);

[0075] (4);

[0076] (5).

[0077] 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, ;

[0078] (31);

[0079] 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, Let be 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);

[0080] (32);

[0081] 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 and the outer wall of the initial support ( Radial displacement , respectively expressed as equation (6) and equation (7);

[0082] (33);

[0083] (6);

[0084] (7).

[0085] Similarly, the radial stress of the loosened zone of the surrounding rock The expression for is given by equation (41), where , The integral constant is determined by the boundary conditions. Radial coordinates, ;

[0086] (41);

[0087] Based on boundary conditions, when At this time, the inner wall of the loosened zone of the surrounding rock is in contact with the outer wall of the initial support. Because the radial stress between the two is continuous, the radial stress of the loosened zone of the surrounding rock is... ;when At this time, the loosened zone of the surrounding rock bears the original rock stress, and the radial stress of the loosened zone of the surrounding rock is... Substituting the boundary condition into equation (41), the integral constant can be solved simultaneously. , , expressed as equation (42);

[0088] (42);

[0089] Radial displacement of the loosened zone of the surrounding rock Represented as equation (43), where, Let be the elastic modulus of the loosened zone of the surrounding rock. Let be the Poisson's ratio of the loosened zone of the surrounding rock; substituting equation (42) into equation (43) and simplifying, we obtain the inner wall of the loosened zone of the surrounding rock ( Radial displacement , expressed as equation (8);

[0090] (43);

[0091] (8).

[0092] Furthermore, in Example 1, which is applied to a water conveyance tunnel in a jointed rock mass, considering the plastic damage of the loosened zone of the surrounding rock, the elastic modulus is corrected using the damage factor method; the elastic modulus of the loosened zone of the surrounding rock is calculated according to Equation (10). ,in, The elastic modulus of the surrounding rock. This is the damage coefficient; based on experience, it is usually... ;

[0093] (10).

[0094] Step S3: Based on the continuity of interlayer radial displacement of the secondary lining, initial support, and surrounding rock loosening zone, i.e. , Substituting equations (5) and (6) into In the middle, substitute equations (7) and (8) into In the middle, the interfacial pressure between the secondary lining and the primary support is obtained by simplification. interfacial pressure between the primary support and the surrounding rock , respectively expressed as equation (16) and equation (17); where, , , The displacement contribution coefficients are the secondary lining displacement contribution coefficient, the initial support displacement contribution coefficient, and the surrounding rock displacement contribution coefficient, respectively, and are calculated according to formula (18). The displacement contribution coefficient can quantify the displacement response capability of each layer under unit pressure. The larger the displacement contribution coefficient, the greater the displacement will be under the same pressure.

[0095] (16);

[0096] (17);

[0097] (18).

[0098] Step S4, Circumferential tensile strain of the secondary lining Caused by radial displacement difference, the circumferential tensile strain of the inner wall of the secondary lining is calculated according to equation (1). ,

[0099] (1);

[0100] Equation (16) represents the interfacial pressure between the secondary lining and the primary support. Substituting into equations (4) and (5), and then into equation (1), and considering the thickness of the secondary lining... ,get and The implicit relation is expressed as equation (2); it should be noted that, due to Displacement contribution coefficient in the expression , All with Related, and Value Dependency Therefore, the equation shown in equation (5) cannot be simplified to an explicit form and needs to be solved by iterative method.

[0101] (2).

[0102] Step S5, to achieve The precise calculation and iterative process ensure that "the circumferential tensile strain error of the secondary lining is less than the allowable tensile strain error value of the project". "The convergence criterion is based on..." The convergence criterion is used for iterative calculation to obtain the secondary lining thickness. The solution. The specific iterative process is explained below:

[0103] 1) Initial setting of secondary lining thickness value Calculate the corresponding outer wall radius of the secondary lining. ;

[0104] 2) Calculation of displacement contribution coefficient parameters: Substitute into equation (1) and calculate , , ;

[0105] 3) Interface pressure calculation: , , Substituting into equation (2), the initial interfacial pressure between the secondary lining and the primary support is calculated. ;

[0106] 4) Circumferential tensile strain calculation: , Substituting into equations (11) and (12), and then into equation (4), the actual circumferential tensile strain of the secondary lining is calculated. ;

[0107] 5) Convergence judgment: If Iterative calculation converges. If the circumferential tensile strain of the secondary lining is too large, that is... Then increase , can make If the radial displacement of the inner wall of the secondary lining is too small, that is... Then decrease , can make ;in, The step thickness value can be set to 0.01 or 0.02, but is not limited to this; then, the aforementioned iterative steps are repeated until final convergence.

[0108] The above illustrative embodiment, by constructing a three-layer thick-walled cylinder model of "secondary lining-initial support-loosening ring of surrounding rock" based on the Hoek-Brown criterion, introduces the effect of the loosening ring of surrounding rock, which can accurately describe the nonlinear strength characteristics and damage accumulation effect of jointed rock mass, and achieve precise connection between the nonlinear mechanical behavior of jointed rock mass and the design of support structure. It constructs a mechanical analysis framework for calculating the secondary lining thickness of water conveyance tunnels in jointed rock mass considering the plastic deformation of surrounding rock. Simultaneously, it designs allowable tensile strain limit constraints for the secondary lining, based on the three-layer thick-walled cylinder model, coupling the mechanical properties of the loosening ring of surrounding rock with the allowable tensile strain limit constraints of the secondary lining, and derives... This study investigates the evolution of the plastic zone (loosening zone) in jointed rock masses and the stress-displacement relationship between the support and surrounding rock. By introducing the displacement contribution coefficient and the iterative logic of interfacial pressure, an implicit analytical formula for the minimum thickness of the secondary lining of water conveyance tunnels in jointed rock masses is obtained. This directly correlates the allowable tensile strain of the secondary lining with its thickness, and then achieves accurate calculation of the minimum thickness of the secondary lining through an iterative solution method. This solves the problem that traditional methods ignore the influence of the plastic zone of the surrounding rock or the deformation constraints of the secondary lining, leading to overly conservative design of the secondary lining thickness of water conveyance tunnels in jointed rock masses or potential safety hazards. This provides a precise, efficient, and reliable theoretical tool for the optimized design of the secondary lining of water conveyance tunnels in jointed rock masses.

[0109] In some embodiments, the method for calculating the secondary lining thickness of a water conveyance tunnel considering the plastic deformation of the surrounding rock, when applied to a jointed rock mass water conveyance tunnel, further includes a stress sharing ratio calculation step. Specifically, this involves using the secondary lining thickness obtained after iterative calculation... ,according to calculate Then, the displacement contribution coefficient is calculated according to equation (18). , , The interfacial pressure between the secondary lining and the primary support is calculated according to equations (16) and (17). interfacial pressure between the primary support and the surrounding rock Then, the stress sharing ratio of the secondary lining is calculated according to equation (19). Stress sharing ratio of initial support Stress sharing ratio of surrounding rock This allows us to understand the load-bearing capacity of the water conveyance tunnel's support structure; understandably... ;

[0110] (19).

[0111] In some embodiments, when the method for calculating the secondary lining thickness of a water conveyance tunnel that considers the plastic deformation of the surrounding rock is applied to a water conveyance tunnel in jointed rock mass, it also includes... Impact analysis steps and parameters The sensitivity analysis steps.

[0112] The specific steps of the impact analysis are as follows: referring to typical parameters of jointed rock mass water conveyance tunnel projects, calculate different... Lower lining thickness interfacial pressure between the secondary lining and the primary support interfacial pressure between the primary support and the surrounding rock The stress distribution ratio of each layer, in order to conduct The impact analysis and verification of mechanical laws.

[0113] To further illustrate, typical parameters for jointed rock mass water conveyance tunnel engineering are shown in Table 1. Substituting the parameters from Table 1 into the aforementioned formula, the allowable tensile strain limit of the secondary lining can be calculated. Secondary lining thickness The iterative calculation process is shown in Table 2. After convergence, the thickness of the secondary lining is... m, interfacial pressure between the secondary lining and the primary support Pa, the interfacial pressure between the initial support and the surrounding rock. Pa, and then the stress sharing ratio of the secondary lining is calculated according to equation (16). Stress sharing ratio of the initial support Stress sharing ratio of surrounding rock A negative initial support ratio indicates that it primarily bears "reverse loads," and its core function is to control the deformation of the surrounding rock during construction, rather than long-term load bearing; calculations based on this... Lower lining thickness 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 3.

[0114] Table 1: Typical parameters of jointed rock mass water conveyance tunnel engineering

[0115]

[0116] Table 2: Iterative Calculation Process

[0117]

[0118] Table 3: Differences Lower lining thickness Calculation results

[0119]

[0120] Table 3 shows the allowable tensile strain limit for the secondary lining. When the value increases from 0.0012 to 0.0018, the secondary lining thickness... The stress distribution ratio of the secondary lining decreased from 0.45m to 0.21m, a reduction of 34.4%; Simultaneous reduction, surrounding rock stress sharing ratio The increase aligns with the mechanical principle that "the larger the allowable tensile strain limit of the secondary lining, the more the load borne by the support structure is transferred to the surrounding rock." (Allowable tensile strain limit of the secondary lining) The thickness of the secondary lining is a key control indicator in the design. In engineering design, it is necessary to combine the crack resistance performance of concrete and the requirements for water sealing to determine a reasonable allowable tensile strain limit for the lining (it is recommended to take 0.0013 to 0.0016 for Class V surrounding rock). In addition, as shown in Table 3, the secondary lining bears 82% to 94% of the long-term load, while the surrounding rock bears 23% to 28% of the load. The initial support mainly plays a role in controlling deformation during the construction period. The design should pay attention to the permanent bearing function of the secondary lining and limit the expansion of the loosening zone by timely construction of the initial support to achieve the coordinated stress of "support-surrounding rock".

[0121] Parameter pair The specific steps of the sensitivity analysis are as follows: using the controlled variable method, analyze the impact of key parameters on the secondary lining thickness. Sensitivity to determine the impact of key parameters on secondary lining thickness The degree of influence; key parameters include original rock stress. The elastic modulus of the secondary lining , initial support elastic modulus Uniaxial compressive strength of rock mass Rock mass geological strength index 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. The results of the calculation of the change rate are shown in Table 4.

[0122] Table 4: Results of parameter sensitivity analysis

[0123]

[0124] Table 4 shows the geological strength indicators of the rock mass. and the elastic modulus of the secondary lining Highly sensitive parameters; rock mass geological strength index When the thickness is increased by 20%, the integrity of the rock mass is significantly improved. According to formula (6), the range of the loosened zone decreases from 5.75m to 5.12m, and the secondary lining thickness... Reduced by approximately 15.6%; elastic modulus of the secondary lining With a 20% increase, the stiffness of the secondary lining is enhanced, and the required thickness of the secondary lining is correspondingly reduced. This also reduces the strength by approximately 15.6%; during construction, it is necessary to accurately obtain the geological strength indicators of the rock mass through geological surveys. High-elasticity modulus concrete should be preferred. Original rock stress. Uniaxial compressive strength of rock mass For medium sensitivity parameters; original rock stress When the thickness is increased by 20%, the secondary lining thickness is adjusted to control structural strain. Approximately 12.5% ​​increase is needed in the uniaxial compressive strength of the rock mass. After increasing the thickness by 20%, the rock mass's resistance to plastic deformation is enhanced, the support requirements are reduced, and the secondary lining thickness is increased. Decreased by approximately 6.2%. Initial support elastic modulus. Low-sensitivity parameter; initial support elastic modulus A 20% increase only affects the thickness of the secondary lining. The thickness of the primary support is reduced by approximately 3.1%. This is mainly because the primary support bears the temporary load during the construction period and has a relatively limited impact on the long-term stress and deformation of the secondary lining. Therefore, the thickness of the primary support can be optimized while ensuring construction safety.

[0125] The above illustrative embodiments, through calculation examples and sensitivity analysis, clarify the influence of key parameters such as the allowable tensile strain limit of the secondary lining, the geological strength index of the rock mass, and the elastic modulus of the secondary lining on the thickness of the secondary lining of the jointed rock mass water conveyance tunnel, as well as the direction of engineering design optimization. They are more suitable for practical engineering design applications, providing accurate, efficient, and reliable theoretical tools for the optimized design of the secondary lining of the jointed rock mass water conveyance tunnel, avoiding redundant or under-design of the secondary lining, and effectively balancing structural safety and economy.

[0126] In summary, the method for calculating the secondary lining thickness of water conveyance tunnels considering the plastic deformation of surrounding rock in this invention constructs a three-layer thick-walled cylinder model of "secondary lining-initial support-loosening ring of surrounding rock" based on the Hoek-Brown criterion, and couples the nonlinear failure characteristics of jointed rock mass with the allowable tensile strain limit constraint of the secondary lining. An implicit analytical formula for the minimum secondary lining thickness of water conveyance tunnels in jointed rock mass is derived, and then an iterative solution method is used to accurately calculate the minimum secondary lining thickness. The stress sharing ratio is quantified, solving the problem that traditional methods neglect the nonlinear failure characteristics of rock mass or the deformation constraint of the secondary lining, leading to overly conservative secondary lining thickness design or safety hazards in water conveyance tunnels in jointed rock mass. This reduces engineering risks and costs, and provides a quantitative tool for optimizing support parameters and controlling construction timing in water conveyance tunnels in jointed rock mass. It can be directly applied to the secondary lining design of water conveyance tunnels in jointed rock mass, which is beneficial to improving the design efficiency and accuracy of water conveyance tunnels in jointed rock mass.

[0127] Example 2:

[0128] refer to Figure 1 , Figure 3 As shown, the present invention also provides a method for calculating the secondary lining thickness of a water conveyance tunnel considering the plastic deformation of the surrounding rock. When applied to soft rock water conveyance tunnels or deeply buried water conveyance tunnels, the method includes the following steps D1 to D5.

[0129] Step D1: Simulate the stress system of the water conveyance tunnel using a three-layer thick-walled cylinder model to establish a stress model for a soft rock water conveyance tunnel or a deeply buried water conveyance tunnel. The water conveyance tunnel is theoretically designed as a circle. The three-layer thick-walled cylinder model consists of, from the inside out, 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 radius of the inner wall of the secondary lining is denoted as... Let the outer wall radius of the secondary lining and the inner wall radius of the initial support be denoted as... The radius of the outer wall of the initial support and the radius of the inner wall of the loosened zone of the surrounding rock are denoted as... The radius of the outer wall of the loosened zone of the surrounding rock is denoted as . ,in, That is, the excavation radius of the water conveyance tunnel.

[0130] Assuming both the secondary lining and the primary support are linearly elastic materials, and the plastic deformation of the surrounding rock follows the Mohr-Coulomb criterion (MC criterion for short), the rock mass within the loosened zone enters a plastic state; assuming complete interlayer contact between the secondary lining, the primary support, and the loosened zone of the surrounding rock, and that radial stress and radial displacement are continuous, and assuming the allowable deformation of the inner wall of the secondary lining is... Furthermore, the stress model of the water conveyance tunnel is based on the following assumptions: axisymmetric plane strain condition, specifically, the axial dimension of the water conveyance tunnel is much larger than the radial dimension, and the stress and displacement only change radially, ignoring the influence of axial stress; 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. .

[0131] To further explain, based on the fact that the plastic deformation of the surrounding rock follows the Mohr-Coulomb criterion, the radius of the outer wall of the loosened zone of the surrounding rock is calculated according to equation (14). ,in, The cohesion of the rock mass, The internal friction angle of the rock mass. The initial support reaction force is set to 0. It should be noted that the Mohr-Coulomb criterion can accurately describe the shear slip and tensile fracture propagation process of soft rock or deeply buried rock mass, reflecting the nonlinear mechanical behavior of soft rock or deeply buried rock mass.

[0132] (14).

[0133] Step D2: Based on the continuity of interlayer radial stress in the secondary lining, initial support, and surrounding rock loosening zone, the radial displacement of the inner wall of the secondary lining is obtained according to the thick-walled cylinder theory and Hooke's law. Radial displacement of the outer wall of the secondary lining Radial displacement of the inner wall of the initial support Radial displacement of the outer wall of the initial support Radial displacement of the inner wall of the loosened zone of surrounding rock The solution method and expression are the same as in Example 1, and will not be repeated here.

[0134] Step D3: Based on the continuity of interlayer radial displacement of the secondary lining, initial support, and surrounding rock loosening zone, i.e. , To obtain the interfacial pressure between the secondary lining and the primary support. interfacial pressure between the primary support and the surrounding rock The solution method and expression are the same as in Example 1, and will not be repeated here. It should be noted that, for Example 2 applied to soft rock or deeply buried water conveyance tunnels, the elastic modulus of the loosened zone of the surrounding rock... Equal to the elastic modulus of the surrounding rock .

[0135] Step D4: The interfacial pressure between the secondary lining and the primary support, expressed by equation (16) Substituting into equation (4), the radial displacement of the inner wall of the secondary lining In, and in combination with the thickness of the secondary lining ,get and The implicit relation is expressed as equation (3); it should be noted that, due to Displacement contribution coefficient in the expression , All with Related, and Value Dependency Therefore, the equation shown in equation (4) cannot be simplified to an explicit form and needs to be solved by iterative method.

[0136] (3);

[0137] Step D5, to achieve The precise calculation and iterative process ensure that "the radial displacement error of the inner wall of the secondary lining is less than the allowable displacement error value in the project". "The convergence criterion is based on..." The convergence criterion is used for iterative calculation to obtain the secondary lining thickness. The solution. The specific iterative process is explained below:

[0138] 1) Initial setting of secondary lining thickness value Calculate the corresponding outer wall radius of the secondary lining. ;

[0139] 2) Calculation of displacement contribution coefficient: Substitute into equation (1) and calculate , , ;

[0140] 3) Interface pressure calculation: , , Substituting into equation (2), the initial interfacial pressure between the secondary lining and the primary support is calculated. ;

[0141] 4) Radial displacement calculation: , Substituting into equation (10), the actual radial displacement of the inner wall of the secondary lining is calculated. ;

[0142] 5) Convergence judgment: If Iterative calculation converges. If the radial displacement of the inner wall of the secondary lining is too large, that is... Then increase , can make If the radial displacement of the inner wall of the secondary lining is too small, that is... Then decrease , can make ;in, The step thickness value can be set to 0.01 or 0.02, but is not limited to this; then, the aforementioned iterative steps are repeated until final convergence.

[0143] The above illustrative embodiment, by constructing a three-layer thick-walled cylinder model of "secondary lining-initial support-surrounding rock loosening zone" based on the Mohr-Coulomb criterion, introduces the surrounding rock loosening zone effect, which can accurately reveal the mechanical behavior of soft rock or deeply buried water conveyance tunnel structures under complex stress conditions. It constructs a mechanical analysis framework for calculating the secondary lining thickness of soft rock or deeply buried water conveyance tunnels considering the plastic deformation of the surrounding rock. Simultaneously, it designs allowable deformation constraints on the inner wall of the secondary lining, based on the three-layer thick-walled cylinder model, coupling the mechanical properties of the surrounding rock loosening zone with the allowable deformation constraints on the inner wall of the secondary lining, and deriving the stress-displacement relationship of the secondary lining. By introducing the displacement contribution coefficient and the interface pressure iteration logic, an implicit analytical relationship for the minimum thickness of the secondary lining of soft rock or deeply buried water conveyance tunnels is obtained. The allowable deformation of the secondary lining is directly related to the thickness of the secondary lining. Then, the minimum thickness of the secondary lining can be accurately calculated through iterative solution method, which can meet the precise deformation control requirements of engineering projects. This solves the problem that the traditional method ignores the influence of the plastic zone of the surrounding rock or does not clearly define the deformation constraints, resulting in the secondary lining thickness design of soft rock or deeply buried water conveyance tunnels being too conservative or having safety hazards. It provides an accurate, efficient and reliable theoretical tool for the optimized design of the secondary lining of soft rock or deeply buried water conveyance tunnels.

[0144] In some embodiments, the method for calculating the secondary lining thickness of a water conveyance tunnel considering the plastic deformation of the surrounding rock, when applied to soft rock water conveyance tunnels or deeply buried rock mass water conveyance tunnels, also includes a stress sharing ratio calculation step. The solution method and expression are the same as in Embodiment 1, and will not be repeated here.

[0145] In some embodiments, when the method for calculating the secondary lining thickness of a water conveyance tunnel that considers the plastic deformation of the surrounding rock is applied to soft rock water conveyance tunnels or deeply buried water conveyance tunnels, it also includes... Impact analysis steps and parameters The sensitivity analysis steps.

[0146] The specific steps of the impact analysis are as follows: referring to typical parameters of soft rock water conveyance tunnels or deep-buried water conveyance tunnels, calculate different... Lower lining thickness interfacial pressure between the secondary lining and the primary support interfacial pressure between the primary support and the surrounding rock The stress distribution ratio of each layer, in order to conduct The impact analysis and verification of mechanical laws.

[0147] To further explain, typical parameters for soft rock water conveyance tunnels or deep-buried water conveyance tunnels are shown in Table 5. Substituting the parameters in Table 5 into the aforementioned formula, the allowable deformation of the inner wall of the secondary lining can be calculated. The secondary lining thickness at mm The iterative calculation process is shown in Table 6. After convergence, the thickness of the secondary lining is... m, interfacial pressure between the secondary lining and the primary support Pa, the interfacial pressure between the initial support and the surrounding rock. Pa; different according to this calculation Lower lining thickness 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 7.

[0148] Table 5: Typical parameters for soft rock water conveyance tunnels or deep-buried water conveyance tunnels

[0149]

[0150] Table 6: Iterative Calculation Process

[0151]

[0152] Table 7: Differences Lower lining thickness Calculation results

[0153]

[0154] As can be seen from Table 7, the allowable deformation of the inner wall of the secondary lining When the thickness of the secondary lining increases from 0.5 mm to 2.0 mm, The depth decreased from 0.44m to 0.29m, a drop of 34.1%; Increase the secondary lining's load-bearing ratio The initial expenditure sharing ratio decreased from 36.1% to 31.2%. The percentage of surrounding rock increased from 53.1% to 61.9%. The percentage decrease from 10.8% to 6.9% aligns with the mechanical principle that "the greater the allowable deformation of the secondary lining's inner wall, the more the load shifts from the support structure to the primary support." In engineering design, a reasonable allowable deformation threshold needs to be determined by considering the performance of the water-stop structure and the crack resistance requirements of the concrete. Furthermore, as shown in Table 7, the primary support bears 53%–62% of the load, the secondary lining bears 31%–36% of the load, and the surrounding rock bears 7%–11% of the load. The design must emphasize the permanent bearing capacity of the primary support, and timely installation of the primary support after excavation should limit the expansion of the loosened zone to achieve coordinated stress distribution between the support and the surrounding rock.

[0155] Parameter pair The specific steps of the sensitivity analysis are as follows: using the controlled variable method, analyze the impact of key parameters on the secondary lining thickness. Sensitivity to determine the impact of key parameters on secondary lining thickness The degree of influence; key parameters include original rock stress. Internal water pressure internal friction angle of rock mass The elastic modulus of the secondary lining , initial support elastic modulus 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. The results of the calculation of the rate of change are shown in Table 8.

[0156] Table 8: Results of parameter sensitivity analysis

[0157]

[0158] As can be seen from Table 8, the internal water pressure and the elastic modulus of the secondary lining Highly sensitive parameter; internal water pressure Increasing the thickness by 20% results in a thicker secondary lining. The increase of 20.5% is due to internal water pressure. The stress acts directly on the inner wall of the secondary lining, requiring an increase in the lining thickness to offset the additional stress; strict control of internal water pressure fluctuations is necessary during construction, and high-elasticity modulus concrete should be prioritized; the elastic modulus of the secondary lining... Increase the thickness of the secondary lining by 20% The 15.9% reduction is due to the fact that materials with high elastic modulus have greater stiffness, requiring less thickness for the same deformation. (Internal friction angle of the rock mass) and original rock stress For medium sensitivity parameters; friction angle within the rock mass. Increase the thickness of the secondary lining by 20% The reduction of 6.8% is due to the friction angle within the rock mass. Increasing the shear strength of the surrounding rock can improve its strength and reduce the loosened zone; the original rock stress... Increasing the thickness by 20% results in a thicker secondary lining. The increase of 9.1% is due to the stress in the original rock. Increasing the load on the surrounding rock shifts to the support structure, necessitating an increase in the secondary lining thickness to balance the stress; these two parameters must be accurately obtained through geological surveys during construction. The elastic modulus of the initial support... Low-sensitivity parameter; elastic modulus of the initial support Increasing by 20% only affects the thickness of the secondary lining. The reduction of 2.1% is because the initial support mainly bears the temporary load during the construction period, while the surrounding rock and secondary lining are the main load-bearing structures under permanent loads. The stiffness of the initial support has a relatively small impact, and the design of the initial support can be optimized while ensuring construction safety.

[0159] The above illustrative embodiments, through numerical verification and sensitivity analysis, clarify the influence of key parameters such as allowable deformation of the inner wall of the secondary lining and internal water pressure on the thickness of the secondary lining of soft rock or deeply buried water conveyance tunnels, as well as the direction of engineering design optimization. They are more suitable for practical engineering design applications, providing accurate, efficient and reliable theoretical tools for the optimized design of the secondary lining of soft rock or deeply buried water conveyance tunnels, avoiding redundant or under-design of the secondary lining, and effectively balancing structural safety and economy.

[0160] In summary, the method for calculating the secondary lining thickness of water conveyance tunnels considering the plastic deformation of surrounding rock in this invention constructs a three-layer thick-walled cylinder model of "secondary lining-initial support-loosening zone of surrounding rock" based on the Mohr-Coulomb criterion, and couples the mechanical properties of the loosening zone of surrounding rock with the allowable deformation constraint of the inner wall of the secondary lining. This derives an implicit analytical formula for the minimum secondary lining thickness of soft rock or deeply buried water conveyance tunnels. Furthermore, an iterative solution method is used to accurately calculate the minimum secondary lining thickness and quantifies the stress sharing ratio. This solves the problem that traditional methods neglect the influence of the plastic zone of surrounding rock or fail to clearly define deformation constraints, leading to overly conservative or unsafe secondary lining thickness designs for soft rock or deeply buried water conveyance tunnels. It reduces engineering risks and costs, and provides a quantitative tool for optimizing support parameters and controlling construction timing for soft rock or deeply buried water conveyance tunnels. This method can be directly applied to the secondary lining design of soft rock or deeply buried water conveyance tunnels, improving the design efficiency and accuracy of such tunnels.

[0161] 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.

[0162] 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 the secondary lining thickness of a water conveyance tunnel considering the plastic deformation of the surrounding rock, characterized in that, When applied to water conveyance tunnels in jointed rock masses, the following steps are included: S1. A three-layer thick-walled cylinder model is used to simulate the stress system of the water conveyance tunnel, establishing a stress model for the water conveyance tunnel. The three-layer thick-walled cylinder model consists of the secondary lining, the primary support, and the loosened zone of the surrounding rock, from the inside out. It is assumed that the secondary lining and the primary support are both linear elastic materials, the plastic deformation of the surrounding rock follows the Hoek-Brown criterion, and the rock mass within the loosened zone enters a plastic state. It is assumed that the interlayers of the secondary lining, the primary support, and the loosened zone of the surrounding rock are in complete contact, and that the radial stress and radial displacement are continuous. The allowable tensile strain limit of the secondary lining is set to... ; S2. Based on the continuity of interlayer radial stress in the secondary lining, primary support, and surrounding rock loosening zone, the radial displacement of the inner wall of the secondary lining is obtained. Radial displacement of the outer wall of the secondary lining Radial displacement of the inner wall of the initial support Radial displacement of the outer wall of the initial support Radial displacement of the inner wall of the loosened zone of surrounding rock ; S3. Based on the continuity of interlayer radial displacement between the secondary lining, primary support, and surrounding rock loosened zone, the interfacial pressure between the secondary lining and primary support is obtained. interfacial pressure between the primary support and the surrounding rock ; S4. Calculate the circumferential tensile strain of the inner wall of the secondary lining according to equation (1). Combine it with the thickness of the secondary lining Combine, obtain and The implicit relation is expressed as equation (2); where, Let be the radius of the inner wall of the secondary lining. The elastic modulus of the secondary lining is given by [value]. For the Poisson's ratio of the secondary lining, The internal water pressure borne by the inner wall of the secondary lining; (1)； (2)； S5, according to The convergence criterion is used for iterative calculation to obtain the secondary lining thickness. The solution; among which, This represents the allowable tensile strain error value for the project.

2. A method for calculating the secondary lining thickness of a water conveyance tunnel considering the plastic deformation of the surrounding rock, characterized in that, When applied to soft rock water conveyance tunnels or deeply buried water conveyance tunnels, the following steps are included: D1. A three-layer thick-walled cylinder model is used to simulate the stress system of the water conveyance tunnel, establishing a stress model for the water conveyance tunnel. The three-layer thick-walled cylinder model consists of the secondary lining, the primary support, and the loosened zone of the surrounding rock, from the inside out. It is assumed that the secondary lining and the primary support are both linear 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. It is assumed that the interlayers of the secondary lining, the primary support, and the loosened zone of the surrounding rock are in complete contact, and that the radial stress and radial displacement are continuous. The allowable deformation of the inner wall of the secondary lining is set as follows: ; D2. Based on the continuity of interlayer radial stress in the secondary lining, primary support, and surrounding rock loosening zone, the radial displacement of the inner wall of the secondary lining is obtained. Radial displacement of the outer wall of the secondary lining Radial displacement of the inner wall of the initial support Radial displacement of the outer wall of the initial support Radial displacement of the inner wall of the loosened zone of surrounding rock ; D3. Based on the continuity of interlayer radial displacement between the secondary lining, primary support, and surrounding rock loosened zone, the interfacial pressure between the secondary lining and primary support is obtained. interfacial pressure between the primary support and the surrounding rock ; D4. Radial displacement of the inner wall of the secondary lining With secondary lining thickness Combine, obtain and The implicit relation is expressed as equation (3); where, Let be the radius of the inner wall of the secondary lining. The elastic modulus of the secondary lining is given by [value]. For the Poisson's ratio of the secondary lining, The internal water pressure borne by the inner wall of the secondary lining; (3)； D5, according to The convergence criterion is used for iterative calculation to obtain the secondary lining thickness. The solution; among which, This represents the allowable displacement error value for the project.

3. The method for calculating the secondary lining thickness of a water conveyance tunnel considering the plastic deformation of the surrounding rock according to claim 1 or 2, characterized in that, In steps S1 and D1, the stress model of the water conveyance tunnel is also based on the following assumptions: axisymmetric plane strain condition, specifically, the axial dimension of the water conveyance tunnel is much larger than the radial dimension, the stress and displacement only change along the radial direction, and the influence of axial stress is ignored.

4. The method for calculating the secondary lining thickness of a water conveyance tunnel considering the plastic deformation of the surrounding rock according to claim 3, characterized in that, In steps S2 and D2, the obtained radial displacement of the inner wall of the secondary lining Radial displacement of the outer wall of the secondary lining Radial displacement of the inner wall of the initial support Radial displacement of the outer wall of the initial support Radial displacement of the inner wall of the loosened zone of surrounding rock , respectively represented by equations (4) to (8); where, The stress borne by the original rock on the outer wall of the loosened zone of the surrounding rock. , These are the elastic moduli of the initial support and the loosened zone of the surrounding rock, respectively. , Poisson's ratio for the initial support and the loosened zone of the surrounding rock, respectively. 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 initial support and the outer wall of the secondary lining. The radius of the inner wall of the loosened zone and the outer wall of the initial support; (4)； (5)； (6)； (7)； (8)。 5. The method for calculating the secondary lining thickness of a water conveyance tunnel considering the plastic deformation of the surrounding rock according to claim 4, characterized in that, When the method for calculating the secondary lining thickness of a water conveyance tunnel considering the plastic deformation of the surrounding rock is applied to a jointed rock mass water conveyance tunnel, the plastic deformation of the surrounding rock follows the Hoek-Brown criterion. The radius of the outer wall of the loosened zone of the surrounding rock is calculated according to equation (9). The elastic modulus of the loosened zone of the surrounding rock is calculated according to equation (10). ;in, The uniaxial compressive strength of the rock mass; , , The rock mass quality correction factor is calculated according to equations (11) to (13); For the Hoek-Brown parameters of the intact rock mass, As a geological strength index of the rock mass, For the disturbance parameters, The elastic modulus of the surrounding rock. Damage coefficient; (9)； (10)； (11)； (12)； (13)； When the method for calculating the secondary lining thickness of water conveyance tunnels that considers the plastic deformation of the surrounding rock is applied to soft rock water conveyance tunnels or deeply buried water conveyance tunnels, the plastic deformation of the surrounding rock follows the Mohr-Coulomb criterion, and the radius of the outer wall of the loosened zone of the surrounding rock is calculated according to equation (14). The elastic modulus of the loosened zone of the surrounding rock is calculated according to equation (15). ;in, The cohesion of the rock mass, The internal friction angle of the rock mass. This is the initial support reaction force; The elastic modulus of the surrounding rock; (14)； (15)。 6. The method for calculating the secondary lining thickness of a water conveyance tunnel considering the plastic deformation of the surrounding rock according to claim 5, characterized in that, In steps S3 and D3, the interfacial pressure between the secondary lining and the primary support... interfacial pressure between the primary support and the surrounding rock They are represented by equations (16) and (17) respectively; where, , , These are the secondary lining displacement contribution coefficient, the initial support displacement contribution coefficient, and the surrounding rock displacement contribution coefficient, respectively, calculated according to formula (18); (16)； (17)； (18)。 7. The method for calculating the secondary lining thickness of a water conveyance tunnel considering the plastic deformation of surrounding rock according to claim 6, characterized in that, It also includes a stress sharing ratio calculation step, specifically, using the secondary lining thickness obtained after iterative calculation. ,according to calculate Then calculate according to equations (16) to (17). , Then, the stress sharing ratio of the secondary lining is calculated according to equation (19). Stress sharing ratio of initial support Stress sharing ratio of surrounding rock ; (19)。

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