Design method for flexible joint parameters of section lining of fault-crossing tunnel structure

Abstract

The invention discloses a fault-crossing tunnel structure segment lining flexible joint parameter design method, which comprises the steps of S1, constructing a surrounding rock-tunnel structure theoretical model based on theoretical conditions; s2, relevant parameters of surrounding rock and tunnel structures are obtained; s3, calculating the longitudinal response of the tunnel structure under the fault action based on the related parameters in the S2; and S4, according to the longitudinal response in the S3, judging whether the parameters of the flexible joint meet the anti-dislocation design requirements of the active fault crossing tunnel, if so, completing the design, and if not, adjusting the related parameters and recalculating until the design requirements are met. According to the method, the effectiveness of the provided theoretical model is proved through numerical simulation and model tests, reference is provided for the anti-dislocation design of the section type lining flexible joint of the fault-crossing tunnel structure, and the method has wide applicability.

Description

Technical Field

[0001] The invention relates to the technical field of tunnel engineering, in particular to a method for designing parameters of flexible joints of a lining of a fault-crossing tunnel structure segment. Background Art

[0002] With the rapid development of transportation tunnels and oil and gas pipeline tunnel construction, tunnel site selection inevitably involves crossing active fault zones. Mountainous areas are particularly prone to frequent plate movement, intense tectonic activity, and complex geological conditions. Fault slip generally causes far more severe damage to tunnel structures than seismic wave effects. Furthermore, under fault strike-slip motion, tunnel structures are highly susceptible to severe shear failure. Research has shown that the use of segmental linings and flexible joints can improve tunnel structures' resistance to slippage.

[0003] Currently, the mechanical properties and deformation characteristics of tunnel structures under fault dislocation are primarily studied using theoretical analysis, numerical simulation, and model testing. Tunnel structure deformation is closely related to the displacement of the surrounding rock and the stiffness matching relationship between the surrounding rock, tunnel lining, and flexible joints. However, existing research methods primarily use geometric principles to hypothesize the displacement distribution of the tunnel structure after fault dislocation and derive flexible joint design methods based on this assumption. These methods ignore the stiffness matching relationship between the surrounding rock, tunnel lining, and joints, resulting in a limited scope of application. Summary of the Invention

[0004] The present invention provides a design method for parameters of flexible joints of segmental linings of a tunnel structure crossing a fault, which is aimed at effectively studying the anti-fault performance of the tunnel structure and can solve at least one of the above-mentioned technical problems.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0006] A method for designing parameters of flexible joints of a tunnel segment lining across a fault, comprising the following steps:

[0007] S1: Based on theoretical conditions, a theoretical model of surrounding rock-tunnel structure is constructed;

[0008] S2: Obtain relevant parameters of the surrounding rock and tunnel structure, including the mechanical parameters of the soil, the geometric parameters of the fault, the parameters of the segmental lining, and the parameters of the flexible joint;

[0009] S3: Based on the relevant parameters of S2, the longitudinal response of the tunnel structure under the action of fault dislocation is calculated, mainly including the bending moment, shear force and displacement of the segmental lining, and the shear deformation and opening deformation of the flexible joints;

[0010] S4: Based on the longitudinal response of S3, determine whether the parameters of the flexible joint meet the anti-fault design requirements of the tunnel crossing the active fault. If so, complete the design; if not, adjust the relevant parameters and recalculate until the design requirements are met.

[0011] Furthermore, in said S1, the tunnel structure includes multiple segmental linings and multiple flexible joints, the multiple segmental linings are represented by a series of short Timoshenko beams located on the Winkler foundation, and the multiple flexible joints are represented by a series of shear springs and torsion springs. The flexible joints are connected between two adjacent segmental linings and include at least one shear spring and one torsion spring. The shear spring is used to resist the shear force between adjacent segmental linings, and the torsion spring is used to maintain the bending moment between adjacent segmental linings. The shear deformation and torsional deformation generated at the flexible joints, as well as the deformation generated by the segmental linings, jointly determine the final deformation of the tunnel structure.

[0012] Furthermore, the theoretical conditions in S1 at least include:

[0013] Assume that the soil is an isotropic, homogeneous, continuous semi-infinite elastic material, and the tunnel structure is always connected to the ground without separation;

[0014] In tunnel structures, flexible joints between adjacent segmental linings are able to withstand shear and torsional deformations.

[0015] Furthermore, the S3 further includes:

[0016] S31. Assuming free-field displacement, determine the external load acting on the tunnel structure based on the fault displacement based on the elastic foundation beam model;

[0017] S32. Based on the finite difference method, solve the free boundary conditions of the tunnel structure and the continuity conditions of the segmental lining;

[0018] S33. Based on the bending moment and shear continuity conditions, the virtual node method is used to solve the continuity conditions at the flexible joint;

[0019] S34. Combine the free boundary conditions of the tunnel structure, the continuity conditions at the segmental lining, and the continuity conditions at the flexible joints to solve the longitudinal displacement of the tunnel structure using MATLAB.

[0020] S35. Determine the internal force of the tunnel structure and the deformation of the flexible joints through the longitudinal displacement of the tunnel structure;

[0021] S36. Study the longitudinal response of the tunnel structure under fault dislocation based on numerical simulation and surrounding rock-tunnel structure theoretical model;

[0022] S37. Conduct a model test of a tunnel crossing a strike-slip fault to verify whether the deformation response determined by the theoretical model is consistent with the deformation response obtained from the actual model test under the action of fault slip.

[0023] Furthermore, the S31 further includes:

[0024] S311. Taking the intersection of the tunnel structure axis and the fault center as the origin, the displacement form of the free field is:

[0025]

[0026] Among them, u f1 、u f2 and u f3 are the displacements of the free field in the fixed disk, fault zone, and moving disk, respectively; L is the width of the fault zone; and Δf is the maximum displacement of the fault zone.

[0027] S312. Simplify the tunnel structure into a Timoshenko beam. The outer radius of the circular section of the Timoshenko beam is R, and the inner radius is r. Simplify the Winkler foundation into a series of normal foundation springs. The Timoshenko beam and the normal foundation springs form an elastic foundation beam model. The modulus of the normal foundation spring can be expressed as:

[0028]

[0029] Where v is the Poisson's ratio of the ground, K is the elastic modulus of the ground, and D t is the width of the Timoshenko beam, which can be expressed as 2R;

[0030] S313. The equilibrium differential equation of the Timoshenko beam considering the shear deformation of the segmental lining is as follows:

[0031]

[0032] Where G is the shear modulus of the segmental lining and the cross section of the Timoshenko beam has a constant bending stiffness E b I, E b is the elastic modulus of the segmental lining, and I is the rotational inertia of the segmental lining.

[0033] Furthermore, the S32 further includes:

[0034] S321. Discretize the tunnel structure into a series of nodes. The tunnel structure consists of n2 segments, each segment consists of n1 nodes, the distance between adjacent nodes is 1, the connection between adjacent segments consists of 2 nodes, and both ends of the tunnel structure each contain 2 virtual nodes. Therefore, the tunnel structure is discretized into a total of n1xn2+4 nodes.

[0035] S322. According to the principle of finite difference method, convert equation (3) into the differential form of equation (4) to obtain the following free boundary conditions of the tunnel structure:

[0036]

[0037] Assuming that no bending moment or shear force is generated at both ends of the tunnel structure and that equation (4) is satisfied, the following segmental lining continuity conditions are obtained:

[0038] Q0=Q n =0,M0=M n =0 (5).

[0039] Furthermore, the S33 further includes:

[0040] S331. According to the principle of finite difference method, the displacement expressions of the four virtual nodes located at the starting point and end point of the tunnel structure are:

[0041]

[0042] S332. The segmental lining is connected by flexible joints. Therefore, the longitudinal displacement function W(x) of the segmental lining is not a continuous function. The deformation at the flexible joints is discontinuous. The bending moment and shear force at the flexible joints satisfy formula (7):

[0043]

[0044] Among them, K θ and K S are the shear stiffness and torsional stiffness of the flexible joint, respectively;

[0045] S333, the bending moment at the flexible joint is represented by a virtual node as follows:

[0046]

[0047] The shear forces at the flexible joints are represented by virtual nodes as follows:

[0048]

[0049] S334, combined with equations (8) and (9), we get the transformed expression of the virtual node:

[0050]

[0051] in, and are coefficient matrices;

[0052] S335, combined with equations (4) and (10), we get the continuity condition at the flexible joint:

[0053]

[0054] Among them, K j-1 、 and K j+1 are coefficient matrices.

[0055] Furthermore, in S34, by combining equations (4), (5) and (11), the differential expressions of all real nodes of the tunnel structure are obtained, which are expressed in the following matrix-vector form:

[0056] K·w=q (12)

[0057] in:

[0058] K is the stiffness matrix of the tunnel structure, which consists of free boundary conditions, continuity conditions at the segmental lining, and continuity conditions at the flexible joints;

[0059] w is the deflection vector of the tunnel structure, expressed as:

[0060]

[0061] q is the external load generated by fault dislocation, expressed as:

[0062]

[0063] u i is the displacement of the fault, which is obtained from formula (1).

[0064] Furthermore, the S4 further includes:

[0065] S41. According to material mechanics, the normal stress at any point on the cross section of a straight beam is:

[0066]

[0067] Where M is the bending moment on the cross section, I z is the moment of inertia of the cross section about the neutral axis z, y max is the point farthest from the neutral axis D / 2, where D is the outer ring diameter of the tunnel structure;

[0068] The moment of inertia of the tunnel structure cross section I z for:

[0069]

[0070] Where d is the inner ring diameter of the tunnel structure;

[0071] The maximum shear stress on the circular ring of the tunnel structure cross section is:

[0072]

[0073] Among them, F S is the shear force on the cross section, S z * is the static moment of the semicircular ring area about the neutral axis, b is the cross-sectional width of the ring, which is equal to 2δ, δ is the ring wall thickness, and r0 is the average radius of the ring;

[0074] S42, combined with equations (15), (16) and (10), determines whether the stress on the tunnel structure falls within the stress index range;

[0075] If S43 falls within the stress index range, then the parameters of the flexible joint of the tunnel structure in the current surrounding rock-tunnel structure theoretical model meet the anti-fault design requirements for tunnels crossing active faults;

[0076] S44. If it falls within the stress index range, adjust the mechanical parameters of the surrounding rock soil and the geometric parameters of the fault in the current surrounding rock-tunnel structure theoretical model, as well as the parameters of the segmental lining and the flexible joints of the tunnel structure until the anti-fault design requirements of the tunnel crossing the active fault are met.

[0077] The beneficial effects of the present invention are embodied in:

[0078] This paper proposes a simplified anti-fault method for evaluating the longitudinal response of segmental lining flexible joints in tunnel structures caused by fault dislocation. This method is used to study adaptive design parameters for tunnel linings. This application demonstrates the effectiveness of the proposed theoretical model through numerical simulations and model tests. This method provides a reference for the anti-fault design of segmental lining flexible joints in tunnel structures crossing faults, and has broad applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] The drawings described herein are used to provide further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute improper limitations on the present application.

[0080] Figure 1 It is a flow chart of a method for designing parameters of flexible joints of a lining of a fault-crossing tunnel structure segment according to an embodiment of the present invention.

[0081] Figure 2 Schematic diagram of a tunnel structure with flexible joints crossing a strike-slip fault according to an embodiment of the present invention.

[0082] Figure 3 It is the free field displacement under fault creep in the embodiment of the present invention.

[0083] Figure 4Schematic diagram of an elastic foundation beam model according to an embodiment of the present invention.

[0084] Figure 5 Schematic diagram of shear deformation at a flexible joint in a Timoshenko beam according to an embodiment of the present invention.

[0085] Figure 6 Schematic diagram of torsional deformation at a flexible joint in a Timoshenko beam according to an embodiment of the present invention.

[0086] Figure 7 Schematic diagram of the comprehensive deformation of two adjacent segmental linings in a Timoshenko beam according to an embodiment of the present invention.

[0087] Figure 8 Schematic diagram of the discretization of the tunnel structure according to an embodiment of the present invention.

[0088] Figure 9 It is a schematic diagram of actual nodes and added virtual nodes at the joints between tunnel structure segments according to an embodiment of the present invention.

[0089] Figure 10 This is a displacement simulation diagram of the longitudinal dynamic response of the tunnel structure passing through a fault according to an embodiment of the present invention.

[0090] Figure 11 The embodiment of the present invention is Figure 10 A detailed enlarged view of the displacement simulation of the longitudinal dynamic response of the middle tunnel structure crossing a fault.

[0091] Figure 12 This is a bending moment simulation diagram of the longitudinal dynamic response of the tunnel structure passing through a fault according to an embodiment of the present invention.

[0092] Figure 13 This is a shear force simulation diagram of the longitudinal dynamic response of the tunnel structure passing through a fault according to an embodiment of the present invention.

[0093] Figure 14 This is a simulation diagram of the longitudinal displacement response of a tunnel structure passing through a fault according to an embodiment of the present invention.

[0094] Figure 15 The embodiment of the present invention is Figure 14 A detailed enlarged view of the longitudinal displacement response simulation of the middle tunnel structure crossing a fault.

[0095] Figure 16 It is a schematic diagram of the overall structure of a test equipment model box for a real tunnel crossing a strike-slip fault model test according to an embodiment of the present invention.

[0096] Figure 17 The embodiment of the present invention is Figure 16 Enlarged schematic diagram of the Π-shaped fixture in the middle A section.

[0097] Figure 18 The embodiment of the present invention is Figure 16 Enlarged schematic diagram of the sliding device in part B.

[0098] Figure 19 It is a simulation diagram comparing the measured and calculated displacement values of the tunnel structure in the absence of flexible joints according to an embodiment of the present invention.

[0099] Figure 20 It is a simulation diagram comparing the measured and calculated displacement values of the tunnel structure in the presence of flexible joints according to an embodiment of the present invention. DETAILED DESCRIPTION

[0100] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. In the absence of conflict, the embodiments in this application and the features in the embodiments can be combined with each other. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0101] It should be noted that if the embodiments of the present invention involve directional indications (such as up, down, left, right, front, back, etc.), the directional indications are only used to explain the relative position relationship, movement, etc. between the components under a specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indications will also change accordingly. In addition, the meaning of "and / or" appearing throughout the text includes three parallel solutions. Taking "A and / or B" as an example, it includes solution A, solution B, or solutions that meet both A and B. In addition, "multiple" refers to more than two.

[0102] See also Figure 1 The embodiment of the present invention provides a method for designing parameters of flexible joints of a lining of a fault-crossing tunnel structure segment, comprising the following steps:

[0103] S1: Based on theoretical conditions, a theoretical model of surrounding rock-tunnel structure is constructed;

[0104] S2: Obtain relevant parameters of the surrounding rock and tunnel structure, including the mechanical parameters of the soil, the geometric parameters of the fault, the parameters of the segmental lining, and the parameters of the flexible joint;

[0105] S3: Based on the relevant parameters of S2, the longitudinal response of the tunnel structure under the action of fault dislocation is calculated, mainly including the bending moment, shear force and displacement of the segmental lining, and the shear deformation and opening deformation of the flexible joints;

[0106] S4: Based on the longitudinal response of S3, determine whether the parameters of the flexible joint meet the anti-fault design requirements of the tunnel crossing the active fault. If so, complete the design; if not, adjust the relevant parameters and recalculate until the design requirements are met.

[0107] This application proves the effectiveness of the proposed theoretical model through numerical simulation and model tests, provides a reference and reference for the anti-fracture design of segmental lining flexible joints in tunnel structures crossing faults, and has relatively wide applicability.

[0108] See also Figure 2-Figure 7 In this embodiment, in S1, the tunnel structure includes multiple segmental linings and multiple flexible joints. The multiple segmental linings are represented by a series of short Timoshenko beams located on the Winkler foundation. The multiple flexible joints are represented by a series of shear springs and torsion springs. The flexible joints are connected between two adjacent segmental linings and include at least one shear spring and one torsion spring. The shear spring is used to resist the shear force between adjacent segmental linings, and the torsion spring is used to maintain the bending moment between adjacent segmental linings. The shear deformation and torsional deformation generated at the flexible joints, as well as the deformation generated by the segmental linings, jointly determine the final deformation of the tunnel structure.

[0109] See also Figure 2-Figure 4 In this embodiment, the theoretical conditions in S1 at least include:

[0110] Assume that the soil is an isotropic, homogeneous, continuous semi-infinite elastic material, and the tunnel structure is always connected to the ground without separation;

[0111] In tunnel structures, flexible joints between adjacent segmental linings are able to withstand shear and torsional deformations.

[0112] See also Figures 8-18 In this embodiment, S3 further includes:

[0113] S31. Assuming free-field displacement, determine the external load acting on the tunnel structure based on the fault displacement based on the elastic foundation beam model;

[0114] S32. Based on the finite difference method, solve the free boundary conditions of the tunnel structure and the continuity conditions of the segmental lining;

[0115] S33. Based on the bending moment and shear continuity conditions, the virtual node method is used to solve the continuity conditions at the flexible joint;

[0116] S34. Combine the free boundary conditions of the tunnel structure, the continuity conditions at the segmental lining, and the continuity conditions at the flexible joints to solve the longitudinal displacement of the tunnel structure using MATLAB.

[0117] S35. Determine the internal force of the tunnel structure and the deformation of the flexible joints through the longitudinal displacement of the tunnel structure;

[0118] S36. Study the longitudinal response of the tunnel structure under fault dislocation based on numerical simulation and surrounding rock-tunnel structure theoretical model;

[0119] S37. Conduct a model test of a tunnel crossing a strike-slip fault to verify whether the deformation response determined by the theoretical model is consistent with the deformation response obtained from the actual model test under the action of fault slip.

[0120] See also Figure 2-Figure 7 In this embodiment, the S31 further includes:

[0121] S311. Taking the intersection of the tunnel structure axis and the fault center as the origin, the displacement form of the free field is:

[0122]

[0123] Among them, u f1 、u f2 and u f3 are the displacements of the free field in the fixed disk, fault zone, and moving disk, respectively; L is the width of the fault zone; and Δf is the maximum displacement of the fault zone.

[0124] S312. Simplify the tunnel structure into a Timoshenko beam. The outer radius of the circular section of the Timoshenko beam is R, and the inner radius is r. Simplify the Winkler foundation into a series of normal foundation springs. The Timoshenko beam and the normal foundation springs form an elastic foundation beam model. The modulus of the normal foundation spring can be expressed as:

[0125]

[0126] Where v is the Poisson's ratio of the ground, K is the elastic modulus of the ground, and D t is the width of the Timoshenko beam, which can be expressed as 2R;

[0127] S313. The equilibrium differential equation of the Timoshenko beam considering the shear deformation of the segmental lining is as follows:

[0128]

[0129] Where G is the shear modulus of the segmental lining and the cross section of the Timoshenko beam has a constant bending stiffness E b I, E b is the elastic modulus of the segmental lining, and I is the rotational inertia of the segmental lining.

[0130] The longitudinal response of a tunnel structure with flexible joints under fault motion is shown in the following example: Figure 1 As shown in Figure 1, the segmental lining undergoes shear and torsional deformation at the flexible joints to accommodate the displacement of the fault. Based on post-earthquake observations, tunnels crossing the fault zone are likely to suffer severe damage due to the forced displacement of the fault. Therefore, the free-field displacement has a crucial influence on the longitudinal response of the tunnel. Figure 2 Shown are the free-field displacements under fault creep.

[0131] See also Figure 8-Figure 9 In this embodiment, the S32 further includes:

[0132] S321. Discretize the tunnel structure into a series of nodes. The tunnel structure consists of n2 segments, each segment consists of n1 nodes, the distance between adjacent nodes is 1, the connection between adjacent segments consists of 2 nodes, and both ends of the tunnel structure each contain 2 virtual nodes. Therefore, the tunnel structure is discretized into a total of n1xn2+4 nodes.

[0133] S322. According to the principle of finite difference method, convert equation (3) into the differential form of equation (4) to obtain the following free boundary conditions of the tunnel structure:

[0134]

[0135] Assuming that no bending moment or shear force is generated at both ends of the tunnel structure and that equation (4) is satisfied, i.e., the free boundary condition is satisfied, the following segmental lining continuity condition is obtained:

[0136] Q0=Q n =0,M0=M n =0 (5).

[0137] See also Figure 8-Figure 9 In this embodiment, the S33 further includes:

[0138] S331. According to the principle of finite difference method, the displacement expressions of the four virtual nodes located at the starting point and end point of the tunnel structure are:

[0139]

[0140] S332. The segmental lining is connected by flexible joints. Therefore, the longitudinal displacement function W(x) of the segmental lining is not a continuous function. The deformation at the flexible joints is discontinuous. The bending moment and shear force at the flexible joints satisfy formula (7):

[0141]

[0142] Among them, K θ and K Sare the shear stiffness and torsional stiffness of the flexible joint, respectively;

[0143] S333, the bending moment at the flexible joint is represented by a virtual node as follows:

[0144]

[0145] The shear forces at the flexible joints are represented by virtual nodes as follows:

[0146]

[0147] S334, combined with equations (8) and (9), we get the transformed expression of the virtual node:

[0148]

[0149] in, and They are all coefficient matrices, including the conversion relationship between virtual nodes and real nodes and the conversion relationship results, as shown below:

[0150]

[0151] S335, combined with equations (4) and (10), we get the continuity condition at the flexible joint:

[0152]

[0153] Among them, K j-1 、 and K j+1 They are all coefficient matrices, including the conversion relationship between the external force at the flexible joint and the structural deformation, as well as the conversion relationship results, as shown below:

[0154]

[0155]

[0156] The longitudinal displacement function W(x) of the segmental lining is not a continuous function. The internal force at the flexible joint is continuous, but the deformation at the flexible joint is discontinuous and immutable. Adding virtual nodes is used to obtain the continuity condition of the flexible connection. Figure 9 A schematic diagram showing the actual nodes and added virtual nodes at the tunnel structure segments and flexible joints, where the virtual nodes represent the deformed positions of the tunnel structure when the flexible joints do not exist.

[0157] See also Figure 10-15In this embodiment, in S34, equations (4), (5) and (11) are combined to obtain the differential expressions of all real nodes of the tunnel structure, which are expressed in the following matrix-vector form:

[0158] K·w=q (12)

[0159] in:

[0160] K is the stiffness matrix of the tunnel structure, which consists of free boundary conditions, continuity conditions at the segmental lining, and continuity conditions at the flexible joints;

[0161] w is the deflection vector of the tunnel structure, expressed as:

[0162]

[0163] q is the external load generated by fault dislocation, expressed as:

[0164]

[0165] u i is the displacement of the fault, which is obtained from formula (1).

[0166] Figure 10-13 The displacement, bending moment and shear force along the tunnel axis when the flexible joint is used and when the flexible joint is not used are shown in sequence.

[0167] Figure 14-15 The adaptability of the tunnel structure to fault movement under different flexible joint stiffnesses was calculated in turn.

[0168] See also Figures 1-4 as well as Figure 19-20 In this embodiment, the S4 further includes:

[0169] S41. According to material mechanics, the normal stress at any point on the cross section of a straight beam is:

[0170]

[0171] Where M is the bending moment on the cross section, I z is the moment of inertia of the cross section about the neutral axis z, y max is the point farthest from the neutral axis D / 2, where D is the outer ring diameter of the tunnel structure;

[0172] The moment of inertia of the tunnel structure cross section I z for:

[0173]

[0174] Where d is the inner ring diameter of the tunnel structure;

[0175] The maximum shear stress on the circular ring of the tunnel structure cross section is:

[0176]

[0177] Among them, F S is the shear force on the cross section, S z * is the static moment of the semicircular ring area about the neutral axis, b is the cross-sectional width of the ring, which is equal to 2δ, δ is the ring wall thickness, and r0 is the average radius of the ring;

[0178] S42, combined with equations (15), (16) and (10), determines whether the stress on the tunnel structure falls within the stress index range;

[0179] If S43 falls within the stress index range, then the parameters of the flexible joint of the tunnel structure in the current surrounding rock-tunnel structure theoretical model meet the anti-fault design requirements for tunnels crossing active faults;

[0180] S44. If it falls within the stress index range, adjust the mechanical parameters of the surrounding rock soil and the geometric parameters of the fault in the current surrounding rock-tunnel structure theoretical model, as well as the parameters of the segmental lining and the flexible joints of the tunnel structure until the anti-fault design requirements of the tunnel crossing the active fault are met.

[0181] The damage of tunnel structure under fault dislocation is mainly caused by shear force and bending moment. This application uses the stress strength condition of the beam as the evaluation index to study whether the tunnel structure performance meets the structural anti-dislocation requirements. Figure 16-Figure 18 As shown, the present application also provides a set of test equipment model box suitable for this method, which at least includes a Π-shaped clamp and a sliding device. Figure 19-20 As can be seen from the simulation diagram, under the action of fault dislocation, the deformation response determined by the analytical solution is highly consistent with the deformation response obtained by the model test.

[0182] According to the standard (Ministry of Housing and Urban-Rural Development of the People's Republic of China. Code for Design of Concrete Structures: GB55008-2021[S]. Beijing: China Architecture Publishing and Media Co., Ltd., 2021.), the design strength value and allowable stress of C40 concrete used in this study are shown in Table 1 below:

[0183] Table 1: C40 concrete strength design value and allowable stress table (unit: MPa)

[0184]

[0185] When the concrete strength design value and the allowable shear stress are exceeded, the tunnel structure will be damaged or even collapse. Therefore, the stress on the tunnel structure should fall within the strength and allowable value range. Combining Table 1 with the above formulas (1), (2), and (3), it can be determined whether the current tunnel structure meets the design requirements.

[0186] In summary, the present invention proposes a simplified anti-dislocation method for evaluating the longitudinal response of a tunnel structure with flexible joints of a segmented lining caused by fault dislocation, which is used for the study of adaptive design parameters of tunnel linings. First, a theoretical model is proposed, which can capture the torsional deformation and shear deformation of the flexible joints between adjacent segmental linings, so that the mechanical behavior and longitudinal response of the tunnel can be described and predicted more accurately. Secondly, it is judged whether the segmented lining parameters and flexible joint parameters meet the requirements based on the longitudinal response of the tunnel structure. Finally, if they do not meet the requirements, the parameters can be adjusted and recalculated until the design requirements are met. This application proves the effectiveness of the proposed theoretical model through numerical simulation and model tests, and provides a reference and reference for the anti-dislocation design of flexible joints of segmented linings in tunnel structures crossing faults, and has a relatively wide applicability.

[0187] It should be understood that the examples and implementation methods described herein are for illustrative purposes only and are not intended to limit the present invention. Those skilled in the art may make various modifications or changes based on them. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for designing parameters of flexible joints in lining segments of a tunnel structure crossing a fault, characterized in that: The following steps are involved: S1: Based on theoretical conditions, a theoretical model of surrounding rock-tunnel structure is constructed; S2: Obtain relevant parameters of the surrounding rock and tunnel structure, including the mechanical parameters of the soil, the geometric parameters of the fault, the parameters of the segmental lining, and the parameters of the flexible joint; S3: Based on the relevant parameters of S2, the longitudinal response of the tunnel structure under the action of fault dislocation is calculated, mainly including the bending moment, shear force and displacement of the segmental lining, and the shear deformation and opening deformation of the flexible joints; S4: Based on the longitudinal response of S3, determine whether the parameters of the flexible joint meet the anti-fault design requirements of the tunnel crossing the active fault. If so, complete the design; if not, adjust the relevant parameters and recalculate until the design requirements are met.

2. The method for designing parameters of flexible joints in lining of a fault-crossing tunnel structure segment according to claim 1, characterized in that: In S1, the tunnel structure includes multiple segmental linings and multiple flexible joints. The multiple segmental linings are represented by a series of short Timoshenko beams located on the Winkler foundation. The multiple flexible joints are represented by a series of shear springs and torsion springs. The flexible joints are connected between two adjacent segmental linings and include at least one shear spring and one torsion spring. The shear spring is used to resist the shear force between adjacent segmental linings, and the torsion spring is used to maintain the bending moment between adjacent segmental linings. The shear deformation and torsional deformation generated at the flexible joints, as well as the deformation generated by the segmental linings, jointly determine the final deformation of the tunnel structure.

3. The method for designing parameters of flexible joints in lining of a fault-crossing tunnel structure segment according to claim 1, characterized in that: The theoretical conditions in S1 include at least: Assume that the soil is an isotropic, homogeneous, continuous semi-infinite elastic material, and the tunnel structure is always connected to the ground without separation; In tunnel structures, flexible joints between adjacent segmental linings are able to withstand shear and torsional deformations.

4. The method for designing parameters of flexible joints in lining of a fault-crossing tunnel structure segment according to claim 1, characterized in that: Said S3 further comprises: S31. Assuming free-field displacement, determine the external load acting on the tunnel structure based on the fault displacement based on the elastic foundation beam model; S32. Based on the finite difference method, solve the free boundary conditions of the tunnel structure and the continuity conditions of the segmental lining; S33. Based on the bending moment and shear continuity conditions, the virtual node method is used to solve the continuity conditions at the flexible joint; S34. Combine the free boundary conditions of the tunnel structure, the continuity conditions at the segmental lining, and the continuity conditions at the flexible joints to solve the longitudinal displacement of the tunnel structure using MATLAB. S35. Determine the internal force of the tunnel structure and the deformation of the flexible joints through the longitudinal displacement of the tunnel structure; S36. Study the longitudinal response of the tunnel structure under fault dislocation based on numerical simulation and surrounding rock-tunnel structure theoretical model; S37. Conduct a model test of a tunnel crossing a strike-slip fault to verify whether the deformation response determined by the theoretical model is consistent with the deformation response obtained from the actual model test under the action of fault slip.

5. The method for designing parameters of flexible joints in lining of a fault-crossing tunnel structure segment according to claim 4, characterized in that: The S31 further includes: S311. Taking the intersection of the tunnel structure axis and the fault center as the origin, the displacement form of the free field is: Among them, u f1 、u f2 and u f3 are the displacements of the free field in the fixed disk, fault zone, and moving disk, respectively; L is the width of the fault zone; and Δf is the maximum displacement of the fault zone. S312. Simplify the tunnel structure into a Timoshenko beam. The outer radius of the circular section of the Timoshenko beam is R, and the inner radius is r. Simplify the Winkler foundation into a series of normal foundation springs. The Timoshenko beam and the normal foundation springs form an elastic foundation beam model. The modulus of the normal foundation spring can be expressed as: Where v is the Poisson's ratio of the ground, K is the elastic modulus of the ground, and D t is the width of the Timoshenko beam, which can be expressed as 2R; S313. The equilibrium differential equation of the Timoshenko beam considering the shear deformation of the segmental lining is as follows: Where G is the shear modulus of the segmental lining and the cross section of the Timoshenko beam has a constant bending stiffness E b I, E b is the elastic modulus of the segmental lining, and I is the rotational inertia of the segmental lining.

6. The method for designing parameters of flexible joints in lining of a fault-crossing tunnel structure segment according to claim 5, characterized in that: The S32 further includes: S321. Discretize the tunnel structure into a series of nodes. The tunnel structure consists of n2 segments, each segment consists of n1 nodes, the distance between adjacent nodes is 1, the connection between adjacent segments consists of 2 nodes, and both ends of the tunnel structure each contain 2 virtual nodes. Therefore, the tunnel structure is discretized into a total of n1xn2+4 nodes. S322. According to the principle of finite difference method, convert equation (3) into the differential form of equation (4) to obtain: The above formula (4) is the free boundary condition of the tunnel structure; Assuming that no bending moment or shear force is generated at both ends of the tunnel structure and that equation (4) is satisfied, we can obtain: Q0=Q n =0,M0=M n =0 (5) The above formula (5) is the continuity condition of segmental lining.

7. The method for designing parameters of flexible joints in lining of a fault-crossing tunnel structure segment according to claim 6, characterized in that: The S33 further includes: S331. According to the principle of finite difference method, the displacement expressions of the four virtual nodes located at the starting point and end point of the tunnel structure are: S332. The segmental lining is connected by flexible joints. Therefore, the longitudinal displacement function W(x) of the segmental lining is not a continuous function. The deformation at the flexible joints is discontinuous. The bending moment and shear force at the flexible joints satisfy formula (7): Among them, K θ and K S are the shear stiffness and torsional stiffness of the flexible joint, respectively; S333, the bending moment at the flexible joint is represented by a virtual node as follows: The shear forces at the flexible joints are represented by virtual nodes as follows: S334, combined with equations (8) and (9), we get the transformed expression of the virtual node: in, and are coefficient matrices; S335, combined with equations (4) and (10), we get the continuity condition at the flexible joint: Among them, K j-1 、 and K j+1 are coefficient matrices.

8. The method for designing parameters of flexible joints in lining of a fault-crossing tunnel structure segment according to claim 7, characterized in that: In S34, by combining equations (4), (5) and (11), the differential expressions of all real nodes of the tunnel structure are obtained, which are expressed in the following matrix-vector form: K·w=q (12) in: K is the stiffness matrix of the tunnel structure, which consists of free boundary conditions, continuity conditions at the segmental lining, and continuity conditions at the flexible joints; w is the deflection vector of the tunnel structure, expressed as: q is the external load generated by fault dislocation, expressed as: u i is the displacement of the fault, which is obtained from formula (1).

9. The method for designing parameters of flexible joints in a fault-crossing tunnel segment lining according to claim 1, characterized in that: Said S4 further comprises: S41. According to material mechanics, the normal stress at any point on the cross section of a straight beam is: Where M is the bending moment on the cross section, I z is the moment of inertia of the cross section about the neutral axis z, y max is the point farthest from the neutral axis D / 2, where D is the outer ring diameter of the tunnel structure; The moment of inertia of the tunnel structure cross section I z for: Where d is the inner ring diameter of the tunnel structure; The maximum shear stress on the circular ring of the tunnel structure cross section is: Among them, F S is the shear force on the cross section, S z * is the static moment of the semicircular ring area about the neutral axis, b is the cross-sectional width of the ring, which is equal to 2δ, δ is the ring wall thickness, and r0 is the average radius of the ring; S42, combined with equations (15), (16) and (10), determines whether the stress on the tunnel structure falls within the stress index range; If S43 falls within the stress index range, then the parameters of the flexible joint of the tunnel structure in the current surrounding rock-tunnel structure theoretical model meet the anti-fault design requirements for tunnels crossing active faults; S44. If it falls within the stress index range, adjust the mechanical parameters of the surrounding rock soil and the geometric parameters of the fault in the current surrounding rock-tunnel structure theoretical model, as well as the parameters of the segmental lining and the flexible joints of the tunnel structure until the anti-fault design requirements of the tunnel crossing the active fault are met.

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