A scaled test design and calculation method for the annular joint of shield segments

Abstract

The present invention discloses a scaled test design and calculation method for the circumferential joint of a shield segment. The method decomposes the function of the bolted joint of the prototype shield segment into tensile resistance, shear resistance, and bending resistance, and accordingly designs a combined joint model of "external spring connection component and internal sleeve bolt". Then, based on the equivalent stiffness hypothesis theory and similarity theory, the equivalent condition expressions required for each component of the combined model joint are calculated, and then the specific physical and mechanical parameters of each component are determined according to the specific situation and construction requirements. The scaled model of the circumferential joint designed and calculated by this method can accurately and effectively simulate the shear resistance, tensile resistance, and bending resistance of the bolted circumferential joint of the prototype segment at the same time, and can restore the mechanical properties of the shield segment joint with discontinuity under actual conditions to a large extent, thereby providing a reference and basis for various shield tunnel model tests.

Description

Technical Field

[0001] The invention relates to the technical field of underground space engineering, and in particular to a design and calculation method for a scaled-down test of annular joints of shield segments. Background Art

[0002] Most subways are assembled from shield tunnel lining rings. Each lining ring is an assembled structure composed of several arc-shaped segments, and the segments are mostly connected by circumferential bolt joints. With the long-term operation of subway shield tunnels in cities across the country, various problems with shield tunnels have also emerged, and scholars and experts have gradually deepened their research on related aspects. At present, scholars have conducted in-depth explorations on the mechanical properties, waterproof properties and structural properties of shield tunnels, and have achieved considerable results. In the research on shield tunnels, the research on circumferential joints of segments has always been in an extremely important position.

[0003] In view of the problem of shield tunnel segment joints, domestic and foreign scholars have conducted a lot of research using numerical simulation, theoretical analysis, scaled model test, prototype test and other methods. The scaled model test is widely used by scholars because it can simulate the stress conditions and response laws of the segments in different environments more realistically and accurately. However, there are many factors affecting the scaled model segment joints, such as the segment material, the bending, compression and shear stiffness of the joint bolts, the preload of the bolts, etc., which will have a great impact on the stiffness of the segment joints. Moreover, a large number of experiments have proved that when a small-sized model test (such as 1:10) is used, the simulation effect is extremely poor, especially in the circumferential bolt joint part. The scale of the segment material and the bolt makes the model unable to match the original concrete-steel bolt contact force. In addition, the small-sized model segments are often configured with relatively low-strength gypsum as aggregate, which is brittle and easy to break. This causes the gypsum segment itself to crack before the bolts are fully tensile. At the same time, because the contact is difficult to match the prototype segment, the bolts and gypsum segments at the joint will also slip and wear. Therefore, for scaled model experiments, it is impossible to accurately simulate the circumferential joints of shield segments by simply using bolt joints of similar sizes, and the experimental error is often orders of magnitude.

[0004] To this end, model tests have been conducted at home and abroad on the stress characteristics of shield tunnel segments using circumferential joints of different functions and types. The most common and widely used type of joint is the slotted model joint, which achieves the purpose of weakening the joint stiffness by cutting the segment at the joint position. However, although the slotting method can make the bending stiffness of the circumferential joint equivalent to that of the bolted joint, the segment material is still continuous at the circumferential joint, and the interaction between the segments at the joint and the influence of the discontinuity of the circumferential joint are not considered. In fact, each ring of shield segments has more or less several joints, which makes the segments complex and discontinuous in the circumferential direction. The model segments using the slotting method cannot accurately simulate the actual stress and deformation of the prototype shield segments.

[0005] Therefore, if a method can be designed to accurately and quantitatively simulate the circumferential joints of shield segments, so that the scaled test model of the shield segment can achieve a set ratio with the prototype segment in terms of joint performance and joint stiffness, and accurately simulate the similarity theorem and equivalent stiffness assumption, then it can effectively and accurately simulate the mechanical properties of the shield segment joints under actual conditions, and is expected to provide a reference and basis for various shield tunnel model tests. Summary of the invention

[0006] The purpose of the present invention is to propose a scaled model design and calculation method for the circumferential joint of shield segments based on the similarity theory of model tests and the equivalent stiffness hypothesis theory according to the deficiencies of the above-mentioned existing methods and technologies. The circumferential joint of shield segments designed and calculated by this method is a combined joint model of "external springs and internal bolts" to accurately and effectively simulate the shear resistance, preload, tensile strength and bending resistance of the prototype segment bolt joints, and to a large extent restore the mechanical properties of the discontinuous shield segment joints under actual conditions, thereby providing a reference and basis for various shield tunnel model tests.

[0007] The purpose of the present invention is achieved by the following steps:

[0008] (1) Determine the prototype size, assembly form and circumferential joint type of the shield tunnel segment, set reasonable similarity constants based on the specific situation and similarity criteria and theorems, and then further determine the required strength of the main aggregate of the model segment. Then, select appropriate materials as the main aggregate of the model segment according to the requirements.

[0009] (2) Based on the similarity ratio and model segment material described in step (1), the segment body can be manufactured. On this basis, the performance of the segment circumferential bolt joint is orderly decomposed, and the bolt joint function is decomposed into: bolt shear resistance, bolt preload and tensile resistance, bolt bending resistance. Then, through different functional categories, corresponding components that meet the functional and usage requirements are designed, thereby obtaining a specific model segment circumferential joint.

[0010] (3) Make reasonable assumptions about the model segment annular joint designed in step (2) to obtain a simplified physical and mechanical model. Then, based on the equivalent stiffness assumption theory and similarity theory, calculate the equivalent condition expressions required for each component of the model joint. Then, by combining the equivalent condition expressions and similarity relationships, calculate the required physical and mechanical parameters of each component.

[0011] (4) According to the required physical and mechanical parameters of the model joint components, based on the structural requirements and specifications of the shield tunnel segment, the specific materials, forms, and sizes of each component are selected, and then the specific parameter values ​​selected for each component are substituted into the equivalent condition expression for verification;

[0012] If not, reselect the material, form and size of each component of the model segment joint, i.e. repeat step (4);

[0013] If satisfied, the final style and parameters of the circumferential joint of the model segment can be determined and the next step can be entered;

[0014] (5) Based on the joint style and parameters finally determined in step (4), a shield tunnel segment joint test model is designed that can accurately and quantitatively consider the influence of the circumferential joint, thereby effectively and accurately simulating the mechanical properties of the shield segment joint under actual conditions.

[0015] In step (1), the similarity constant is selected according to the specific situation, similarity criterion and similarity theorem.

[0016] First, the size similarity constant is preliminarily selected based on the similarity criterion and specific conditions. The similarity criterion believes that the similarity constant set for the model test should not be too small or too large. If it is too large, the model size and strength will be reduced, making the error amplification of the model more obvious during the test; while if it is too small, the test data obtained will be more accurate, but its size, test equipment and site, manpower and material resources will also be greatly increased. Combining the above similarity judgment criteria, the judgment of the feasibility of the test, the layout principles of the monitoring components and other specific conditions, the size similarity constant of the scaled model is determined to be C 0 , the bulk density similarity constant is C γ :

[0017] According to the first and second similarity theorems, the geometric similarity constant C 0 and the heavy similarity constant C γ As the basic quantity, the similarity relationship formula of various physical parameters is obtained through dimensional analysis, as shown in Table 1. The specific similarity constant values ​​of various physical quantities can be obtained through calculation.

[0018] Table 1 Similarity relations and similarity constants

[0019]

[0020]

[0021] The design components of the model segment annular joint in step (2) are: sleeve bolts preset inside the segment, and spring connection components arranged on the inner and outer sides of the segment splicing longitudinal seam. The design principle of the model joint is to decompose the original bolt function, simulate the tensile strength of the original bolt with the external spring connection component, simulate the shear strength of the original bolt with the internal pre-buried sleeve bolt, and the bending strength is shared by the two.

[0022] The spring connection component consists of two identical hook springs and their fixing parts. The two parts are connected by symmetrical spring hooks, and the contact surface between the parts is a smooth arc surface. This design allows the spring connection component to only bear the tensile force along the direction of the bolt. When subjected to the shear force perpendicular to the bolt direction, it can rotate so that the component is not affected by shear, thereby achieving the purpose of only simulating the tensile strength of the original bolt.

[0023] The sleeve bolt component is assembled from two sleeves and two smooth steel bars. The spacing, length, and installation position of the sleeves and steel bars are designed similarly to the prototype segment. The setting of the smooth steel bar and sleeve allows the steel bar to slide relatively along the tension direction when the component is subjected to tension in the direction of the bolt, so that it is not subjected to tension and only bears shearing in the direction perpendicular to the bolt.

[0024] The bending resistance of the bolt is jointly borne by the spring connection component and the sleeve bolt component. The force causing the bolt bending deformation can be decomposed into the tension F along the bolt direction, the shear force T perpendicular to the bolt direction, and the pure bending moment M acting on the joint. From the above analysis, it can be seen that the tension F can be borne by the spring connection component, the shear force T can be borne by the sleeve bolt component, and the pure bending moment M can be borne by the steel rod in the sleeve bolt.

[0025] In step (3), reasonable assumptions and simplifications are made on the prototype segment bolt joint and the model segment circumferential joint, as follows:

[0026] 1) There is no waterproof gasket between the longitudinal seams of the prototype segments, and only bolts are used for connection; 2) The longitudinal seam sections of the model segments and the prototype segments are both flat and smooth rectangular sections; 3) The model segments and the prototype segments have the same cross-sectional central axis; 4) The model segments and the prototype segments are always within the linear elastic range, and both satisfy the continuity assumption, uniformity assumption, and plane section assumption.

[0027] Based on the above assumptions, in order to briefly explain the design and calculation method of the model joint, the prototype segment and the model segment are kept consistent in terms of material, bolt length and segment size. The equivalent theoretical assumption calculation of the prototype segment bolt joint and the model segment joint is performed as follows:

[0028] ① Equivalent analysis of tensile stiffness of model segment joints Since the spring connection component and the prototype segment bolts have different tensile stiffness manifestations, it is impossible to directly make the tensile stiffness of the two equivalent, but the tensile characteristics of the bolts within the linear elastic deformation range are very similar to those of the spring. Both satisfy Hooke's law, and the bolt can be regarded as a uniform tensile spring. Therefore, the tensile stiffness equivalence problem is transformed into the tensile spring equivalence problem. It is only necessary to make the spring of the spring connection component and the "bolt spring" equal in stiffness coefficient. The stiffness coefficient expression of the special spring component in the model segment is:

[0029]

[0030] Note: In formula (1)

[0031] K 1 is the stiffness coefficient of the combined spring component;

[0032] K 0 is the stiffness coefficient of a single spring component;

[0033] G is the rigidity modulus of the spring wire;

[0034] D.D M is the spring wire diameter and coil median diameter;

[0035] N C is the effective number of coils of the spring.

[0036] Assume that the mechanical equation of the "bolt spring" in the prototype segment is:

[0037] F T =K 2 (ΔL+L 0 ) (2)

[0038] Note: In formula (2)

[0039] The variable ΔL is the bolt elongation;

[0040] Dependent variable F T is the tension on the bolt;

[0041] Unknown quantity L 0 is the initial tensor of the bolt;

[0042] Unknown quantity K 2 is the stiffness coefficient of Eq.

[0043] Let the initial tension of the "bolt spring" in equation (2) (ΔL = 0) be equal to the initial preload force F of the prototype segment bolt. N , that is, let F N =K 2 L 0 , the unknown quantity L of "bolt spring" can be calculated0 With K 2 At the same time, let the tension of the "bolt spring" in formula (2) (ΔL=L 1 ) is equal to the ultimate tensile bearing capacity of the prototype segment bolt F σ , that is, let F σ =K 2 (L 1 +L 0 ), the stiffness coefficient K of the "bolt spring" can be obtained from the above 2 The expression is:

[0044]

[0045] Combine equations (1) to (3), let K 1 =K 2 The equivalent condition expression of the tensile stiffness of the model joint and the prototype segment bolt joint can be solved as follows:

[0046]

[0047] In summary, by setting appropriate spring material, spring wire diameter D, and median diameter D for the design model joint M 、Effective number of turns N C , we can get a spring stiffness coefficient K that satisfies formula (4) 0 At this time, it can be considered that the design model joint and the prototype segment bolt joint are equivalent in tensile stiffness.

[0048] ② Equivalent analysis of shear stiffness of model segment joints

[0049] The shear stiffness of bolted joints is mainly divided into the shear stiffness of the segment itself and the shear stiffness of the bolts. The shear stiffness of the segment itself and the shear stiffness of the bolts of the bolted joint segment are:

[0050] K Qg =G g A g =G g bh(5)

[0051]

[0052] In formula (5) and (6), K Qg , K Ql is the shear stiffness of the segment itself and the shear stiffness of the bolts;

[0053] G g , G l It is the shear modulus of the segment material and the bolt material.

[0054] The shear stiffness of the design model joint is mainly composed of the shear stiffness of the segment itself and the shear stiffness of the sleeve bolt component. The shear stiffness of the segment itself and the shear stiffness of the special sleeve bolt component of the design model joint are:

[0055] K QG =G G A G =G G bh (7)

[0056]

[0057] In formula (7) and (8), K QG , K QL G is the shear stiffness of the model segment itself and the shear stiffness of the special sleeve bolt; G , GL is the shear modulus of the segment material, the shear modulus of the special sleeve bolt, d 1 For special sleeve bolt diameter.

[0058] Assuming the tensile stiffness of the two segments is equal, even if equation (5) is equal to equation (7), we can get G g =G G , Since the Poisson's ratio u of gypsum and concrete is about 0.2, it can be approximately considered that u G =u g The shear modulus calculation formula is:

[0059]

[0060] It can be seen that to make the shear modulus of the two equal, it is only necessary to make the elastic modulus of the segment material the same. After multiplying by the similarity constant, the elastic modulus of the model segment material is almost the same as that of the prototype segment, so the tensile stiffness of the two segments themselves can be made equal.

[0061] Similarly, if the shear stiffness of the bolt is equal to the shear stiffness of the special sleeve bolt, the combined equations (6), (8), and (9) can be obtained:

[0062]

[0063] In summary, when the sleeve bolt satisfies formula (10), the shear stiffness of the sleeve bolt can be equal to the shear stiffness of the segment bolt. At this time, it can be considered that the design model joint and the prototype segment bolt joint are equivalent in shear stiffness.

[0064] ③Equivalent analysis of bending stiffness of model segment joints

[0065] Assuming that the same pure bending moment M acts on both ends of the prototype bolt joint segment and the model joint segment, the lengths of the three types of bending beams (hereinafter referred to as bolt joint curved beam, slotted joint curved beam, and design model joint curved beam) are calculated based on the arc length of their neutral axis when bending, which are L, L 1 , L 2 , the angles of rotation of the three are all α.

[0066]

[0067] In formula (11), D 1 , D 2 are the inner diameter and outer diameter of the segment respectively.

[0068] Here, the relative rotation angles of the sections at both ends of the curved beams of the three types of joints under the action of pure bending moment M are equal as the equivalent theoretical assumption of the stiffness of the segment joints.

[0069] The relative rotation angle of the bolted joint curved beam under the action of pure bending moment M is mainly caused by the bending deformation of the segment curved beam itself and the opening deformation at the bolted joint. Assume that the rotation stiffness of the prototype segment bolted joint is K. The relative rotation angle of the joint opening at the bolted joint and the relative rotation angle of the segment curved beam itself can be expressed as:

[0070]

[0071]

[0072] In formula (2) and (3), θ 0 Open the relative rotation angle of the joint at the bolt joint;

[0073] θ′ is the relative rotation angle of the segment curved beam itself;

[0074] K 0 is the rotational stiffness of the prototype segment bolt joint;

[0075] E is the elastic modulus of the prototype segment;

[0076] I is the moment of inertia of the prototype segment joint section;

[0077] b is the width of the longitudinal seam section of the prototype segment;

[0078] h is the height of the longitudinal seam section of the prototype segment.

[0079] The curved beam of the design model joint is similar to the prototype bolt joint segment under the action of pure bending moment M. The relative rotation angle is caused by the joint opening at the sleeve bolt and the bending deformation of the curved beam of the segment itself, which can be expressed as:

[0080]

[0081]

[0082] In formula (14) and (15), θ 1 is the relative rotation angle caused by the opening of the joint at the bolt joint, θ 2 The relative rotation angle of the curved beam of the design model joint, I 2 is the moment of inertia of the bolt cross section of the model joint, E 1 is the elastic modulus of the sleeve bolt.

[0083] Therefore, the equivalent theoretical assumption of the stiffness of the prototype bolted segment and the design model segment joint can be expressed as:

[0084] θ′+θ 0 =θ 2 +θ 3 (16)

[0085] Taking equations (1) to (3) as the basic known quantities and substituting equations (4) to (6) into equation (7), the equivalent condition expression of the prototype segment joint and the design model joint can be obtained as follows:

[0086]

[0087] In summary, when the sleeve bolt diameter d of the design model joint segment is 1 When formula (17) is satisfied, the above-mentioned design model joint and the prototype segment bolt joint can be considered equivalent in joint bending stiffness.

[0088] The specific parameter values ​​selected for each component in step (4) include: the elastic modulus E of the sleeve bolt 1 , steel bar shear modulus G 1 , Steel rod diameter d 1 , Spring rigidity modulus G 0 , spring wire diameter D, spring middle diameter D M 、N effective number of spring turns C , initial extension of the spring L 0 .

[0089] The beneficial effects of the present invention are as follows:

[0090] ① It provides a design calculation method that can simulate the shear, tensile and bending effects of prototype segment bolt joints. Compared with the traditional slotting or slicing simulation method, this method is more accurate and comprehensive, and can restore the mechanical properties of the discontinuous shield segment joints in actual situations to a greater extent;

[0091] ② Based on the design calculation method, a novel and convenient combined joint model of "external spring and internal bolt" is proposed. This joint model can make the shield segment scale test model reach the set proportion with the prototype segment in terms of joint performance and joint stiffness, and accurately simulate the similarity theorem and equivalent stiffness assumption;

[0092] ③ Each component of the designed model joint was subjected to equivalent theoretical assumptions and verification calculations corresponding to the actual prototype segment joints, decomposing the complex problem of the original joint stiffness into several simplified indicators, thereby accurately and quantitatively summarizing the various strengths and stiffnesses of the circumferential joints of the shield tunnel segments, which can provide new ideas for shield tunnel joint model tests and related research. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] Figure 1 It is a flow chart of the design and calculation method of the scaled model of the shield segment annular joint in the present invention;

[0094] Figure 2 It is a typical cross-sectional schematic diagram of a shield segment in the present invention;

[0095] Figure 3 It is a schematic diagram of the main body of the model segment in the present invention;

[0096] Figure 4 It is a combined joint model of the model segment "externally connected with springs and internally provided with bolts" in the present invention;

[0097] Figure 5 It is a schematic diagram of the sleeve bolt in the present invention;

[0098] Figure 6 It is a schematic diagram of a spring connection component in the present invention;

[0099] Figure 7 for Figure 6 Enlarged view of point A in the middle;

[0100] Figure 8 It is a schematic diagram of a simplified calculation model of a prototype segment bolt joint in the present invention;

[0101] Fig. 9 It is a schematic diagram of a simplified model for calculating the model segment joint in the present invention;

[0102] Fig.10 It is a schematic diagram of calculating the rotational stiffness of the prototype segment bolt joint in the present invention;

[0103] Fig.11 It is a schematic diagram of calculating the rotational stiffness of the model segment joint in the present invention;

[0104] Fig.12 It is a schematic diagram of a shield tunnel model segment with a designed annular joint in the present invention. DETAILED DESCRIPTION

[0105] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0106] As shown in the attached picture, Figure 3 Mark 10 in the middle is the main structure of the segment; Figure 4 The reference numeral 20 is a sleeve bolt member, and the reference numeral 30 is a spring connection member; Figure 5 The mark 21 is a smooth steel rod, and 22 is a bolt sleeve; Figure 6 and Figure 7 In the middle, reference numeral 31 is a fixing member, and reference numeral 32 is a hook spring.

[0107] This embodiment specifically involves the design and calculation method of the scaled model of the shield segment annular joint. Based on the model test similarity theory and the equivalent stiffness hypothesis theory, this method designs and calculates a combined shield segment joint model of "external spring, internal bolt", which can accurately and effectively simulate the shear resistance, preload, tensile strength and bending resistance of the prototype segment bolt joint, thereby largely restoring the mechanical properties of the shield tunnel segment joint with discontinuity in actual situations. The specific steps of the design and calculation method are as follows (see the flowchart Figure 1 ):

[0108] Step 1

[0109] like Figure 2 As shown, in this embodiment, the cross section of the prototype shield segment is determined as a circular structural section of 3A+2B+C. The segment is divided into three standard blocks with a central angle of 67.5°, located at the bottom; a capping block with a central angle of 22.5°, located at the top; and two adjacent blocks with a central angle of 67.5°, adjacent to the capping block. The inner diameter of the prototype segment is 5400mm, the radial width is 1200mm, and the thickness is 300mm. The main material of the segment is C50 concrete, and the circumferential direction is connected with 6.8-grade M30 bent bolts.

[0110] The size similarity constant is initially selected based on the similarity criteria and specific conditions. The similarity criteria believe that the similarity constant set for the model test should not be too small or too large. If it is too large, the model size and strength will be reduced, making the error amplification of the model more obvious during the test; while if it is too small, the test data obtained will be more accurate, but its size, test equipment and site, manpower and material resources will also be greatly increased. Combining the above similarity judgment criteria, the judgment of the feasibility of the test, the layout principles of the monitoring components and other specific conditions, the size similarity constant of the scaled model is determined to be C0 =10, the bulk density similarity constant is C γ =1.

[0111] According to the first and second similarity theorems, the geometric similarity constant 10 and the weight similarity constant 1 are used as the basic quantities, and the similarity relationship formulas of various physical parameters are obtained through dimensional analysis. The specific similarity constant values ​​of various physical quantities can be obtained through calculation, as shown in Table 2:

[0112] Table 2 Similarity relations and similarity constants

[0113]

[0114] Step 2: Based on the similarity ratio and model segment material described in step (1), the segment body 10 can be manufactured. On this basis, the performance of the segment circumferential bolt joint is orderly decomposed, and the bolt joint function is decomposed into: the bolt's shear resistance, bolt preload and tensile resistance, and bolt's bending resistance. Then, through different functional categories, the corresponding components that meet the functional and usage requirements are designed, thereby obtaining a specific model segment circumferential joint. Figure 4 As shown in the figure, the design components of the model segment annular joint are: sleeve bolts 20 preset inside the segment, and spring connection components 30 set on the inner and outer sides of the segment splicing longitudinal seam. The design principle of the model joint is to decompose the original bolt function, use the external spring connection component 30 to simulate the tensile resistance of the original bolt, and use the internal pre-buried sleeve bolts 20 to simulate the shear resistance of the original bolt, while the bending resistance is shared by the two.

[0115] The spring connection component 30 is composed of two identical hook springs 32 and a fixing component 31. The two components are connected by a symmetrical spring hook A. The contact surface between the components is a smooth arc surface. This design allows the spring connection component 30 to only withstand the tensile force along the bolt direction. When subjected to the shear force perpendicular to the bolt direction, it can rotate so that the component is not subjected to shearing, thereby achieving the purpose of only simulating the tensile strength of the original bolt.

[0116] The sleeve bolt 20 component is assembled from two sleeves 22 and two smooth steel rods 21. The spacing, length, and installation position of the sleeves 22 and the steel rods 21 are designed similarly to the prototype segment. The arrangement of the smooth steel rods 21 and the sleeves 22 allows the steel rods 21 to slide relatively along the tension direction when the component is subjected to tension in the bolt direction, so that it is not subjected to tension and only bears shearing in the direction perpendicular to the bolt.

[0117] The bending resistance of the bolt is jointly borne by the spring connection component 30 and the sleeve bolt component 20. The force causing the bolt bending deformation can be decomposed into the tension F along the bolt direction, the shear force T perpendicular to the bolt direction, and the pure bending moment M acting on the joint. From the above analysis, it can be seen that the tension F can be borne by the spring connection component 30, the shear force T can be borne by the sleeve bolt 20 component, and the pure bending moment M can be borne by the steel rod 21 in the sleeve bolt.

[0118] Step 3

[0119] Reasonable assumptions and simplifications are made for the prototype segment bolt joint and the model segment circumferential joint, as follows:

[0120] 1) There are no waterproof gaskets between the longitudinal seams of the prototype segments, and only bolts are used for connection; 2) The longitudinal seam sections of the model segments and the prototype segments are both flat and smooth rectangular sections; 3) The model segments and the prototype segments have the same cross-sectional central axis; 4) The model segments and the prototype segments are always within the linear elastic range and both satisfy the continuity assumption, uniformity assumption, and plane section assumption.

[0121] At the same time, based on the above assumptions, in order to briefly explain the design and calculation method of the model joint, the prototype segment and the model segment are kept consistent in material, bolt length and segment size. The simplified calculation model is as follows Figures 8 to 11 As shown in the figure, the simplified model is used to calculate the equivalent theoretical assumptions of tensile, shear and bending stiffness of the prototype segment bolt joint model and the model segment joint model, as follows:

[0122] ① Equivalent analysis of tensile stiffness of model segment joints

[0123] Based on the assumption that the simplified prototype bolt joint and model joint are Figure 8 , 9 As shown in the figure, since the spring connection component and the prototype segment bolt have different tensile stiffness manifestations, the tensile stiffness of the two cannot be directly made equivalent. However, the tensile characteristics of the bolt within the linear elastic deformation range are very similar to those of the spring. Both satisfy Hooke's law, and the bolt can be regarded as a uniform tensile spring. Therefore, the tensile stiffness equivalence problem is transformed into the tensile spring equivalence problem. It is only necessary to make the spring of the spring connection component and the "bolt spring" equal in stiffness coefficient. The stiffness coefficient expression of the spring component in the model segment is:

[0124]

[0125] Note: In formula (1)

[0126] K 1 is the stiffness coefficient of the combined spring component;

[0127] K 0 is the stiffness coefficient of a single spring component;

[0128] G is the rigidity modulus of the spring wire;

[0129] D.D M is the spring wire diameter and coil median diameter;

[0130] N C is the effective number of coils of the spring.

[0131] Assume that the mechanical equation of the "bolt spring" in the prototype segment is:

[0132] F T =K 2 (ΔL+L 0 ) (2)

[0133] Note: In formula (2)

[0134] The variable ΔL is the bolt elongation;

[0135] Dependent variable F T is the tension on the bolt;

[0136] Unknown quantity L 0 is the initial tensor of the bolt;

[0137] Unknown quantity K 2 is the stiffness coefficient of Eq.

[0138] Let the initial tension of the "bolt spring" in equation (2) (ΔL = 0) be equal to the initial preload force F of the prototype segment bolt. N , that is, let F N =K 2 L 0 , the unknown quantity L of "bolt spring" can be calculated 0 With K 2 quantitative relationship; at the same time, let the tension of the "bolt spring" in formula (2) (ΔL = L 1 ) is equal to the ultimate tensile bearing capacity of the prototype segment bolt F σ , that is, let F σ =K 2 (L 1 +L 0 ), the stiffness coefficient K of the "bolt spring" can be obtained from the above 2 The expression is:

[0139]

[0140] Combine equations (1) to (3), let K 1 =K 2 The equivalent condition expression of the tensile stiffness of the model joint and the prototype segment bolt joint can be solved as follows:

[0141]

[0142] In summary, by setting appropriate spring material, spring wire diameter D, and median diameter D for the design model joint M 、Effective number of turns N C , we can get a spring stiffness coefficient K that satisfies formula (4) 0 At this time, it can be considered that the design model joint and the prototype segment bolt joint are equivalent in tensile stiffness.

[0143] ② Equivalent analysis of shear stiffness of model segment joints

[0144] The shear stiffness of bolted joints is mainly divided into the shear stiffness of the segment itself and the shear stiffness of the bolts. The shear stiffness of the segment itself and the shear stiffness of the bolts of the bolted joint segment are:

[0145] K Qg =G g A g =G g bh (5)

[0146]

[0147] In formula (5) and (6), K Qg , K Ql is the shear stiffness of the segment itself and the shear stiffness of the bolts;

[0148] G g , G l It is the shear modulus of the segment material and the bolt material.

[0149] The shear stiffness of the design model joint is mainly composed of the shear stiffness of the segment itself and the shear stiffness of the sleeve bolt component. The shear stiffness of the segment itself and the shear stiffness of the special sleeve bolt component of the design model joint are:

[0150] K QG =G G A G =G G bh (7)

[0151]

[0152] In formula (7) and (8), K QG , K QL G is the shear stiffness of the model segment itself and the shear stiffness of the special sleeve bolt; G , GL is the shear modulus of the segment material, the shear modulus of the special sleeve bolt, d 1 For special sleeve bolt diameter.

[0153] Assuming the tensile stiffness of the two segments is equal, even if equation (5) is equal to equation (7), we can get G g =GG , Since the Poisson's ratio u of gypsum and concrete is about 0.2, it can be approximately considered that u G =u g The shear modulus calculation formula is:

[0154]

[0155] It can be seen that to make the shear modulus of the two equal, it is only necessary to make the elastic modulus of the segment material the same. After multiplying by the similarity constant, the elastic modulus of the model segment material is almost the same as that of the prototype segment, so the tensile stiffness of the two segments themselves can be made equal.

[0156] Similarly, if the shear stiffness of the bolt is equal to the shear stiffness of the special sleeve bolt, the combined equations (6), (8), and (9) can be obtained:

[0157]

[0158] In summary, when the sleeve bolt satisfies formula (10), the shear stiffness of the sleeve bolt can be equal to the shear stiffness of the segment bolt. At this time, it can be considered that the design model joint and the prototype segment bolt joint are equivalent in shear stiffness.

[0159] ③Equivalent analysis of bending stiffness of model segment joints

[0160] Assuming that the same pure bending moment M acts on both ends of the prototype bolt joint segment and the model joint segment, the lengths of the three types of bending beams (hereinafter referred to as bolt joint curved beam, slotted joint curved beam, and design model joint curved beam) are calculated based on the arc length of their neutral axis when bending, which are L, L 1 , L 2 The three are rotated at an angle of α. The simplified prototype bolt joint and model joint are as follows Fig.10 , 11 shown.

[0161]

[0162] In formula (11), D 1 , D 2 are the inner diameter and outer diameter of the segment respectively.

[0163] Here, the relative rotation angles of the sections at both ends of the curved beams of the three types of joints under the action of pure bending moment M are equal as the equivalent theoretical assumption of the stiffness of the segment joints.

[0164] The relative rotation angle of the bolted joint curved beam under the action of pure bending moment M is mainly caused by the bending deformation of the segment curved beam itself and the opening deformation at the bolted joint. Assume that the rotation stiffness of the prototype segment bolted joint is K. The relative rotation angle of the joint opening at the bolted joint and the relative rotation angle of the segment curved beam itself can be expressed as:

[0165]

[0166]

[0167] In formula (2) and (3), θ 0 Open the relative rotation angle of the joint at the bolt joint;

[0168] θ′ is the relative rotation angle of the segment curved beam itself;

[0169] K 0 is the rotational stiffness of the prototype segment bolt joint;

[0170] E is the elastic modulus of the prototype segment;

[0171] I is the moment of inertia of the prototype segment joint section;

[0172] b is the width of the longitudinal seam section of the prototype segment;

[0173] h is the height of the longitudinal seam section of the prototype segment.

[0174] The curved beam of the design model joint is similar to the prototype bolt joint segment under the action of pure bending moment M. The relative rotation angle is caused by the joint opening at the sleeve bolt and the bending deformation of the curved beam of the segment itself, which can be expressed as:

[0175]

[0176]

[0177] In formula (14) and (15), θ 1 is the relative rotation angle caused by the opening of the joint at the bolt joint, θ 2 The relative rotation angle of the curved beam of the design model joint, I 2 is the moment of inertia of the bolt cross section of the model joint, E 1 is the elastic modulus of the sleeve bolt.

[0178] Therefore, the equivalent theoretical assumption of the stiffness of the prototype bolted segment and the design model segment joint can be expressed as:

[0179] θ′+θ 0 =θ 2 +θ 3 (16)

[0180] Taking equations (1) to (3) as the basic known quantities and substituting equations (4) to (6) into equation (7), the equivalent condition expression of the prototype segment joint and the design model joint can be obtained as follows:

[0181]

[0182] In summary, when the sleeve bolt diameter d of the design model joint segment is1 When formula (17) is satisfied, the above-mentioned design model joint and the prototype segment bolt joint can be considered equivalent in joint bending stiffness.

[0183] By combining equivalent conditional expressions (4), (10), and (17) and similarity relation table 2, the required physical and mechanical parameters of each component can be calculated.

[0184] Step 4

[0185] According to the required physical and mechanical parameters of the model joint components, based on the structural requirements and specifications of the shield tunnel segment, the specific materials, forms and sizes of each component are selected, and then the specific parameter values ​​selected for each component are calculated: the elastic modulus E of the sleeve bolt 1 , steel bar shear modulus G 1 , Steel rod diameter d 1 , Spring rigidity modulus G 0 , spring wire diameter D, spring middle diameter D M 、N effective number of spring turns C , initial extension of the spring L 0 Substitute into equivalent conditional expressions (4), (10), and (17) for verification;

[0186] When the calculation results meet the requirements of the segment structure and the specification use requirements, the materials and parameters of each component can be determined. One of the parameter materials that meets the requirements is shown in Table 3.

[0187] Table 3 Parameters of model segments and joint components

[0188]

[0189]

[0190] Step 5

[0191] According to the joint style and parameters finally determined in step (4), a shield tunnel segment joint test model that can accurately and quantitatively consider the influence of the circumferential joint is designed, such as Fig.12 As shown, it is assembled from a segment body 10, a sleeve bolt component 20, and a spring connection component 30, and can effectively and accurately simulate the mechanical properties of a shield segment joint under actual conditions.

[0192] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0193] Although the embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the claims and their equivalents.

Claims

1. A shield segment annular joint scale test design and calculation method, characterized in that: The designed scaled model of the annular joint is a combined joint model with an external spring connection component and an internal sleeve bolt. The method comprises the following steps: (1) Determine the prototype size, assembly form, and circumferential joint type of the shield tunnel segment, set a reasonable similarity constant, and then select the appropriate model segment main aggregate; (2) The performance of the bolted joints in the circumferential direction of the segment is decomposed into shear resistance, tensile resistance, and bending resistance, and then the corresponding components that meet the functional and usage requirements are designed according to different functional categories; (3) The equivalent condition expressions required by each component of the designed model segment annular joint are calculated by using the equivalent stiffness hypothesis theory and similarity theory, and then the required physical and mechanical parameters of each component are calculated by combining the equivalent condition expressions and similarity relationships; (4) Based on the structural requirements and specifications of shield tunnel segments, the materials, forms, and dimensions of each component are selected and then substituted into the equivalent condition expressions for verification to determine the final style and parameters of the circumferential joints of the model segments; The similarity constant is selected according to the specific situation, similarity criterion and similarity theorem. Through similarity criterion, experimental feasibility and monitoring element arrangement principle, the similarity constant of scale model size is determined as C0 and the similarity constant of bulk density is determined as C. γ Then, according to the first and second similarity theorems, the geometric similarity constant C0 and the weight similarity constant C γ As the basic quantity, the similarity relationship formula of various physical parameters is obtained through dimensional analysis; The design components of the model segment annular joint are: sleeve bolts preset inside the segment and spring connection components arranged on the inner and outer sides of the segment longitudinal joints. The design principle is to decompose the original bolt function, use the external spring connection component to simulate the tensile strength of the original bolt, and use the internal embedded sleeve bolt to simulate the shear resistance of the original bolt, while the bending resistance is borne by both.

2. The shield segment annular joint scale test design and calculation method according to claim 1 is characterized in that: The spring connection component consists of two identical hook springs and their fixing parts. The two parts are connected by a symmetrical spring hook. The contact surface between the parts is a smooth arc surface, so that the spring connection component only bears the tensile force along the bolt direction. When subjected to the shear force perpendicular to the bolt direction, it can rotate so that the component is not affected by shear, thereby achieving the purpose of only simulating the tensile strength of the original bolt.

3. The shield segment annular joint scale test design and calculation method according to claim 1 is characterized in that: The sleeve bolt component is assembled from two sleeves and two smooth steel rods. The spacing, length, and installation position of the sleeves and steel rods are designed similarly to the prototype segment. The setting of the smooth steel rod and sleeve allows the steel rod to slide relatively along the direction of tension when the component is subjected to tension in the direction of the bolt, so that it is not subjected to tension and only bears shearing action in the direction perpendicular to the bolt.

4. The shield segment annular joint scale test design and calculation method according to claim 1 is characterized in that: The bending resistance of the bolt is jointly borne by the spring connection component and the sleeve bolt component. The force causing the bolt bending deformation can be decomposed into the tensile force F along the bolt direction, the shear force T perpendicular to the bolt direction, and the pure bending moment M acting on the joint. The tensile force F is borne by the spring connection component, the shear force T is borne by the sleeve bolt component, and the pure bending moment M is borne by the steel rod inside the sleeve bolt.

5. The shield segment annular joint scale test design and calculation method according to claim 1 is characterized in that: Reasonable assumptions and simplifications are made for the prototype segment bolt joints and the model segment circumferential joints, as follows: 1) There is no waterproof gasket between the longitudinal seams of the prototype segments, and only bolts are used for connection; 2) The longitudinal seam sections of the model segment and the prototype segment are both flat and smooth rectangular sections; 3) The model segment and the prototype segment have the same cross-sectional central axis; 4) The model segment and the prototype segment are always within the linear elastic range, and both satisfy the continuity assumption, uniformity assumption, and plane section assumption. The prototype segment and the model segment are consistent in material, bolt length, and segment size.

6. The shield segment annular joint scale test design and calculation method according to claim 1 is characterized in that: Based on simplified assumptions, equivalent theoretical assumptions are calculated for the prototype segment bolt joint and the model segment joint, including: equivalent analysis of the tensile stiffness of the model segment joint, equivalent analysis of the shear stiffness of the model segment joint, and equivalent analysis of the bending stiffness of the model segment joint. The equivalent condition expressions are as follows: When designing the parameters of the model joint segment: sleeve bolt elastic modulus E1, steel rod shear modulus G1, steel rod diameter d1, spring rigidity modulus G0, spring wire diameter D, spring middle diameter D M 、N effective number of spring turns C When the initial elongation L0 of the spring satisfies the above formula, it is deemed that the design model joint and the prototype segment bolt joint are equivalent in joint bending stiffness.

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