Internal force calculation method of symmetrical shield tunnel structure based on physical model driving

Abstract

The invention discloses an internal force calculation method of a symmetric shield tunnel structure based on physical model driving. The internal force calculation method comprises the following steps: S1, obtaining design parameters of a segment ring; s2, calculating a structural deformation value detected on site; s3, assuming that the initial rigidity of the joint is equal to the rigidity of the duct piece; s4, establishing an expression of tunnel structure deformation; s5, calculating a correlation coefficient between the deformation of the tunnel structure and a structure deformation value detected on site; s6, the internal force of the tunnel structure is calculated in response to the situation that the load around the tunnel is 0 or above and the correlation coefficient is larger than 0.6; s7, calculating the bending moment rigidity of the new joint, and judging whether the relative error between the bending moment rigidity of the new joint and the bending moment rigidity of the current joint is greater than 5% or not; if yes, taking the bending moment rigidity of the new joint as the bending moment rigidity of the current joint, and returning to S4; if not, entering S8; and S8, according to the internal force of the tunnel structure, calculating the stress of the segment reinforcing steel bar and the concrete, and calculating the stress of the joint bolt and the concrete.

Description

Technical Field

[0001] The present invention belongs to the technical field of tunnel structure deformation, and in particular relates to an internal force calculation method of a symmetrical shield tunnel structure driven by a physical model. Background Art

[0002] Currently, 3D lidar can be used to measure the internal dimensions of tunnel structures. By comparing these dimensions with the tunnel's initial design, tunnel deformation can be calculated. However, when using standards to determine the structural safety status, the tunnel's design dimensions, the detailed construction of joints, and the surrounding rock conditions are all ignored. Clearly, there can be significant discrepancies between the conclusions given by the standards and the actual stress state of the structure. Combining this data with physical models is an important approach to improving the reliability of tunnel mechanical conditions.

[0003] In terms of physical model research, it mainly includes the study of segment joints and full-ring tunnels. In the study of segment joints, Li et al. proposed an analytical model of segment joints considering four-stage stress by considering the detailed structure of the segment joints. Kou proposed a theoretical calculation model for the bending stiffness of segment joints under high water pressure and studied the influence of axial force, bolt strength and concrete strength on the bending stiffness of the joints. Huang et al. established an algorithm for calculating the effective ratio of bending stiffness based on the bending stiffness of segment joints. In the study of full-ring tunnels, Naggar and Hinchberger established analytical equations for structural bending moments and axial forces considering elastic strata and homogeneous circular ring tunnels based on the stratum-structure model. Liu et al. proposed a method for calculating the internal forces of the tunnel lining during the segment assembly process based on the principle of minimum potential energy. Huang et al. established a calculation model for the internal forces of full-ring tunnels considering the effective stiffness of joints based on the load-structure model and explored the influence of structural stiffness on the internal forces of the tunnel. Chen et al. equated the segment rings to Timoshenko beams and the inter-ring joints to ideal springs, and derived analytical solutions for the longitudinal dynamic response of shield tunnel linings based on the state-space method and d'Alembert's principle. In summary, a wide range of physical models have been proposed for studying the mechanical behavior of segment joints and full-ring tunnels. These models consider the detailed structure of the joints, the synergistic effects between the joints and the segments, and the soil-tunnel interaction. The mechanical behavior of segment joints under loads has been clearly understood. However, these models all calculate the internal forces and deformations of the segments and joints based on known external loads, and cannot directly analyze the mechanical behavior of tunnel structures when the external loads are unknown.

[0004] Some researchers have also studied data-driven approaches that combine physics and data. Distributed optical fibers were randomly placed circumferentially on the upper and lower surfaces of the steel cage within the segments. Using a proposed inversion analysis method, the displacement, internal forces, and external load distribution of the segments during the monitoring period were calculated. Zhang et al. proposed an inversion model for the internal forces of longitudinal joints based on field measurements of vertical convergence deformation in shield tunnels. Lin et al. and Wang et al. used physics and data-driven methods to predict the deformation of strata and adjacent buildings during tunnel construction. Zhao et al. evaluated the long-term safety performance of soft rock tunnel structures using a knowledge-driven decision-making model based on the analytic hierarchy process. In summary, data-driven models for tunnel engineering are primarily used for structural internal forces, lining deformation, deformation of adjacent structures, and tunnel performance evaluation. However, due to the influence of the operating environment of active tunnels, the internal forces of tunnel structures cannot be inferred from monitoring data. Although Zhao et al. evaluated the safety status of tunnel structures, the weightings used were still highly subjective. Therefore, the rationality and reliability of shield tunnel structural safety analysis models still need to be improved. Summary of the Invention

[0005] In response to the above-mentioned deficiencies in the prior art, the internal force calculation method of a symmetrical shield tunnel structure driven by a physical model provided by the present invention solves the problem that the rationality and reliability of the internal force calculation of the shield tunnel structure still need to be improved.

[0006] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: a method for calculating the internal forces of a symmetrical shield tunnel structure driven by a physical model, comprising the following steps: S1. Obtain the design parameters of the segment ring according to the shield tunnel design documents, including the size and position of the segments and joints; S2. Based on the shield tunnel inner profile dimension data detected on site and the tunnel design parameters, a fitting value of the 3D laser scanning data is obtained by curve fitting, and then the structural deformation value detected on site is calculated; S3. Assume that the initial stiffness of the joint is equal to the stiffness of the segment; S4. Calculate the internal force of the tunnel structure based on the current bending moment stiffness of the joint and the load around the tunnel, calculate the displacement coefficient matrix of the tunnel structure, and establish an expression for the deformation of the tunnel structure; S5. Substitute the structural deformation value detected on site into the expression for tunnel structural deformation to inversely calculate the load around the tunnel; calculate the deformation of the tunnel structure based on the expression for tunnel structural deformation, and then calculate the correlation coefficient between the deformation of the tunnel structure and the structural deformation value detected on site; S6, in response to the load around the tunnel being greater than 0 and the correlation coefficient being greater than 0.6, calculating the internal force of the tunnel structure based on the inversely calculated load around the tunnel; S7. Calculate the bending moment stiffness of the new joint based on the internal force of the joint, and determine whether the relative error between the bending moment stiffness of the new joint and the bending moment stiffness of the current joint is greater than 5%. If so, use the bending moment stiffness of the new joint as the bending moment stiffness of the current joint and return to S4. If not, proceed to S8. S8. Based on the internal forces of the tunnel structure, calculate the stresses of the segment reinforcement and concrete, and calculate the stresses of the joint bolts and concrete.

[0007] Further: In S2, the structural deformation value detected on site is calculated The specific expression is: Where, and are the horizontal and vertical coordinates of the tunnel structure, and are the horizontal and vertical coordinates of the tunnel structure after deformation, R is the radius at the center of the segment thickness; Where, is the deflection angle of the ellipse, and is the fitting value of 3D laser scanning data.

[0008] Furthermore: in S4, the loads around the tunnel include the earth pressure above the tunnel, the reaction of the soil below the tunnel, the lateral earth pressure, the deadweight load of the segments, and the ground reaction caused by the squeezing of the tunnel structure; Ground reaction caused by tunnel structure compression The specific expression is: Where, P h is the formation resistance, The angle between the specified position of the tunnel and the vertical axis; Where, K s is the formation resistance coefficient, is the horizontal displacement of the tunnel haunch; Segment deadweight load P The specific expression of 5 is: . . Where, is the deadweight of concrete, B is the width of the segment, h is the thickness of the joint contact surface; The reaction force of the soil under the tunnel P The specific expression of 2 is: Where, P 1 is the earth pressure above the tunnel; Lateral earth pressure includes the first lateral pressure P 3 and second lateral pressure P 4; Where, is the lateral pressure coefficient of soil; Where, is the dead weight of the soil, R is the radius at the center of the segment thickness.

[0009] Further: In S4, the internal forces of the tunnel structure include the total bending moment M , total axial force N and total shear force Q ; Where, is the bending moment at the tunnel vault, is the axial force at the tunnel vault, 、 and They are The virtual bending moment, virtual axial force and virtual shear force of the tunnel structure under the unit virtual load in the direction, 、 and They are The virtual bending moment, virtual axial force and virtual shear force of the tunnel structure under the unit virtual load in the direction; is the structural bending moment caused by the load around the tunnel, and its specific expression is: is the structural axial force caused by the load around the tunnel, and its specific expression is: is the structural shear force caused by the load around the tunnel, and its specific expression is: .

[0010] Further: In S4, the tunnel structure is Deformation at The specific expression is: Where, is the load around the tunnel, , is the displacement coefficient matrix of the tunnel structure, .

[0011] Furthermore: In S7, the method for calculating the bending moment stiffness of the new joint is specifically as follows: (1) Bending moment stiffness of joint under positive bending moment: 1) Under the stress state of the joint being closed, the expression for calculating the bending moment stiffness of the joint is: Where, For the i The total bending moment at each joint, and are the compression displacements of the inner and outer edges of the joint, respectively; Where, and is the compressive strain on the outer and inner arc sides of the joint, A coefficient between 0.55 and 0.7; 2) When the joint is open but the bolt is still under compression, the expression for calculating the bending moment stiffness of the joint is: Where, y is the height of the compression zone of the joint concrete, is the compression displacement of the outer edge when the seam opens, , is the compressive strain of concrete; 3) When the joint is open and the bolt is under tension, the expression for calculating the bending moment stiffness of the joint is: Where, is the elongation of the bolt, is the compression displacement of the outer edge when the seam opens, is the distance between the bolt and the outer edge of the joint; When the bending moment at the joint increases to the preset maximum value, the concrete at the outer edge of the joint will enter the plastic state. The expression for calculating the bending moment stiffness of the joint is: Where, is the height of the concrete plastic zone, is the bolt length, is the tensile strain of the bolt, is the distance between the bolt and the outer edge of the joint; (8) Bending moment stiffness of joint under negative bending moment: The distance between the bolt and the outer edge of the joint is , replace the joint moment stiffness expression with Replace with , Take the absolute value to obtain the calculation formula of the bending moment stiffness of the joint under negative bending moment.

[0012] The beneficial effects of the present invention are: (1) The present invention provides a method for calculating the internal forces of a symmetrical shield tunnel structure driven by a physical model. In the physical model, first, based on the classical load-structure model and the force equation, an analytical equation between tunnel deformation and external load is derived, and a physical-data dual-driven model is constructed to calculate the internal forces of the tunnel structure. At the same time, the physical model for calculating the internal forces of the tunnel structure takes into account the coordinated deformation of the segments and joints, and the matching of the nonlinear joint stiffness and the internal forces of the structure. Secondly, in the detection data, the internal contour dimensions of the tunnel are obtained by three-dimensional laser radar scanning. On this basis, a method for calculating the deformation of the tunnel structure that matches the physical model is proposed. Finally, the physical model and the detection data are fused and driven to realize the calculation of the internal forces and stresses of the tunnel structure, thereby improving the rationality and reliability of the internal force calculation of the shield tunnel structure.

[0013] (8) The present invention constructs a physical-data dual-driven model to calculate the internal forces of tunnel structures. The reliability of the physical-data dual-driven model is evaluated by using the correlation coefficient between the detected displacement and the calculated displacement. It is worth noting that the present invention reveals the influence of physical constraints and geological information on the calculated internal forces of tunnel structures. The proposed method for calculating the internal forces of tunnel structures, combined with the currently popular three-dimensional laser detection technology, will help promote the quantitative assessment of tunnel safety status analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 This is a flow chart of the internal force calculation method of a symmetrical shield tunnel structure driven by a physical model according to the present invention.

[0015] Figure 2 is the load structure model of the circular shield tunnel. Figure 2 (a) is load-structure symmetry, Figure 2 (b) is the simplified model.

[0016] Figure 3 This is the deformation diagram of the tunnel structure.

[0017] Figure 4 This is the model diagram for unit load.

[0018] Figure 5 is the stress model when the joint is not opened, Figure 5 (a) is the mechanical model, Figure 5 (b) is the mechanical model after deformation.

[0019] Figure 6 is the stress model when the joint is open and the bolt is closed, Figure 6 (a) is the mechanical model, Figure 6 (b) is the mechanical model after deformation.

[0020] Figure 7 The stress model when the joint is open and the bolt is under tension, Figure 7 (a) is the mechanical model, Figure 7 (b) is the mechanical model after deformation.

[0021] Figure 8 is the stress model after the outer edge of the joint yields, Figure 8 (a) is the mechanical model, Figure 8 (b) is the mechanical model after deformation.

[0022] Figure 9 Schematic diagram of the fitted ellipse of the 376th segment ring in the lateral convergence deformation statistics of the 1440m shield tunnel. DETAILED DESCRIPTION

[0023] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0024] like Figure 1 As shown, in one embodiment of the present invention, a method for calculating the internal force of a symmetrical shield tunnel structure driven by a physical model includes the following steps: S1. Obtain the design parameters of the segment ring according to the shield tunnel design documents, including the size and position of the segments and joints; S2. Based on the shield tunnel inner profile dimension data detected on site and the tunnel design parameters, a fitting value of the 3D laser scanning data is obtained by curve fitting, and then the structural deformation value detected on site is calculated; S3. Assume that the initial stiffness of the joint is equal to the stiffness of the segment; S4. Calculate the internal force of the tunnel structure based on the current bending moment stiffness of the joint and the load around the tunnel, calculate the displacement coefficient matrix of the tunnel structure, and establish an expression for the deformation of the tunnel structure; S5. Substitute the structural deformation value detected on site into the expression for tunnel structural deformation to inversely calculate the load around the tunnel; calculate the deformation of the tunnel structure based on the expression for tunnel structural deformation, and then calculate the correlation coefficient between the deformation of the tunnel structure and the structural deformation value detected on site; S6, in response to the load around the tunnel being greater than 0 and the correlation coefficient being greater than 0.6, calculating the internal force of the tunnel structure based on the inversely calculated load around the tunnel; S7. Calculate the bending moment stiffness of the new joint based on the internal force of the joint, and determine whether the relative error between the bending moment stiffness of the new joint and the bending moment stiffness of the current joint is greater than 5%. If so, use the bending moment stiffness of the new joint as the bending moment stiffness of the current joint and return to S4. If not, proceed to S8. S8. Based on the internal forces of the tunnel structure, calculate the stresses of the segment reinforcement and concrete, and calculate the stresses of the joint bolts and concrete.

[0025] In S2, the structural deformation value detected on site can be calculated through the detection data of the tunnel structure, according to Figure 2 In the tunnel model of (b), the tunnel arch is constrained. Therefore, the relative deformation of the tunnel arch should be zero. A rectangular coordinate system can be established at the tunnel arch, such as Figure 3 The equation for the initial position of the tunnel is: (1) Where, and are the horizontal and vertical coordinates of the tunnel structure respectively. The equation of the contour line of the lining structure after the tunnel is subjected to stress is: (2) Where, and are the horizontal and vertical coordinates of the tunnel structure after deformation, respectively. and is the fitting value of 3D laser scanning data.

[0026] according to Figure 4 , the direction of tunnel structure deformation points to the center of the circle. Therefore, the tunnel structure deformation calculated by the detection data should be consistent. 、 and the center of the circle Should be in a straight line, satisfying: (3) When equations (1) and (2) are expressed in polar coordinates, they are as follows: (5) (6) Where, is the deflection angle of the ellipse. Substituting equations (5) and (6) into equation (3), we can calculate Then, according to formula (6) and , calculate the structural deformation value of the on-site inspection The specific expression is: (7) Where, and are the horizontal and vertical coordinates of the tunnel structure, and are the horizontal and vertical coordinates of the tunnel structure after deformation, R is the radius at the center of the segment thickness; In S4, the loads around the tunnel include the earth pressure above the tunnel, the reaction of the soil below the tunnel, the lateral earth pressure, the deadweight load of the segments, and the ground reaction caused by the squeezing of the tunnel structure; In this embodiment, the derivation steps for calculating the load around the tunnel are specifically as follows: This example studies a circular shield tunnel with symmetrical structure. The rock layer where the tunnel is located is homogeneous and the load is symmetrically distributed []. Figure 2 (a), where ( , ,…, ) is the load around the tunnel, and the tunnel structure takes into account the segments and joints. Since the load and structure are symmetrically distributed, the tunnel load-structure model is simplified to Figure 2 (b). Among them, x 1 and x 2 is the bending moment and axial force at the tunnel vault.

[0027] P 1 is the earth pressure above the tunnel, and its action range is . P 2 is the reaction force of the soil under the tunnel, and its action range is . P 3 and P 4 is the lateral earth pressure, and its action range is . P 5 is the self-weight load of the segment, and its action range is . P 6 is the ground reaction force caused by the tunnel structure extrusion, which follows a quadratic function distribution, namely: Ground reaction caused by tunnel structure compression The specific expression is: (8) Where, P h is the formation resistance, The angle between the specified position of the tunnel and the vertical axis; (9) Where, K s is the formation resistance coefficient, is the horizontal displacement of the tunnel haunch; The self-weight load of the segment can be directly obtained from the design parameters of the segment. P The specific expression of 5 is: (10) Where, is the deadweight of concrete, B is the width of the segment, h is the thickness of the joint contact surface; according to Figure 2 The vertical load balance relationship, the reaction force of the soil under the tunnel P The specific expression of 2 is: (11) Where, P 1 is the earth pressure above the tunnel; Lateral earth pressure includes the first lateral pressure P 3 and second lateral pressure P 4; (12) Where, is the lateral pressure coefficient of soil; (13) Where, is the dead weight of the soil, R is the radius at the center of the segment thickness.

[0028] In S4, the internal forces of the tunnel structure include the total bending moment M , total axial force N and total shear force Q ; (14) Where, is the bending moment at the tunnel vault, is the axial force at the tunnel vault, 、 and They are The virtual bending moment, virtual axial force and virtual shear force of the tunnel structure under the unit virtual load in the direction, 、 and They are The virtual bending moment, virtual axial force and virtual shear force of the tunnel structure under the unit virtual load in the direction; In this embodiment, the derivation steps of the internal force of the tunnel structure are specifically as follows: According to the force method equation, the equilibrium equation at the dome is: (15) Where, and is the displacement in its own direction caused by the unit virtual load in the direction of the bending moment, and is the displacement in the bending moment direction caused by the unit virtual load in the axial direction, ; (or ) is the displacement in the direction of the bending moment (or axial force) caused by the external load. and The loads around the tunnel [P] cause the structure to and Displacement in direction.

[0029] Compared with bending moment, the influence of axial force and shear force on structural deformation is very small in thin-walled structures. Therefore, only the influence of bending moment is considered when calculating tunnel structure deformation. The deformation of the tunnel is caused by both the segments and the joints, that is: (16) Wherein, the subscripts s and j represent the segment deformation and joint deformation caused by load, respectively. and for The deformation of the segments and joints caused by the load, and for The deformation of the segments and joints caused by the load, and for The deformation of the pipe segments and joints caused by the load.

[0030] 、 and Through the calculation of the virtual internal force of the tunnel structure. x The internal force of the tunnel structure under the unit virtual load in direction 1 is: (17) in, 、 、 They are x Virtual bending moment, virtual axial force and virtual shear force of the tunnel structure under the action of unit virtual load in the 1 direction.

[0031] exist The internal force of the tunnel structure under the unit virtual load in the direction is: (18) in, 、 、 They are x The virtual bending moment, virtual axial force and virtual shear force of the tunnel structure under the unit virtual load in the 1st direction, R is the radius at the center of the segment thickness. Thus: (19) (20) Where, E is the elastic modulus of the segment, I is the section moment of inertia of the segment, , n 1 representative The number of joints between is the angle between the joint and the vertical axis, n 2 representatives The number of joints between n 3 represents The number of joints between n 4 represents The number of joints between For the iThe bending moment stiffness of the joint, For the i The angle between each joint and the vertical axis; In formula (16), and By external loads [ P ] Calculation of structural internal forces caused by loads around the tunnel. Structural bending moments caused by loads around the tunnel for: (twenty one) Structural axial forces caused by loads around the tunnel for: (twenty two) Structural shear caused by loads around the tunnel for: (twenty three) So, we can get: (twenty four) (25) (26) (27) Substitute equations (16), (19), (20), (24), (25), (26), and (27) into equation (15) to obtain x 1 and x 2. That is: (28) (29) In the formula, the coefficient 、 、 、 arrive 、 arrive The specific expression is: Finally, the expression of the internal force of the tunnel structure is obtained.

[0032] In S4, the derivation steps of the expression for calculating the deformation of the tunnel structure are as follows: like Figure 4 As shown, the angle is calculated as The displacement at A unit load is applied towards the center of the circle T ; At unit load T Under the action of the tunnel, the bending moment is: (30) Where, Unit load T Under the effect Bending moment at β The structural displacement at is: (31) Where, 、 and They are The total displacement of the tunnel structure, the displacement caused by segment deformation, and the displacement caused by joint deformation.

[0033] The calculation formula is: (32) Where, for x 1 caused by the segment displacement, for x 2. The segment displacement caused by for M pi caused by segment displacement.

[0034] (33) (34) (35) (36) When range, then: (37) When range, then: (38) (39) (40) (41) When range, then: (42) When range, then: (43) When range, then: (44) The calculation formula is: (45) Where, Unit load T Under the action of i The bending moment at the joint, For the i The total bending moment at each joint. The function consists of three parts, and the above formula can be simplified to: (46) in, for x 1 caused by the joint displacement, for x 2 caused by the joint displacement, for M p The joint displacement caused by and ( k =1, 2, ..., n) are closest and satisfy: (47) So we can get the following formula: (48) (49) because P 1 to P h The function interval is different. It can be written as: (50) in, The items in are: (51) (52) (53) (54) by P 2 The influence of load, Within the range, i < n 1+ n 2, we can get the following formula: (55) exist Within the range, n 1+ n 2≤ i < n , we can get the following formula: (56) by P h The influence of load on Within the range, i < n 1, then we can get the following formula: (57) exist Within the range, n 1≤ i < n – n 4, we can get the following formula: (58) exist Within the range, n – n 4≤ i < n , we can get the following formula: (59) Substituting equations (32) to (59) into equation (31), the displacement at any position in the tunnel can be calculated. The deformation at can be expressed as ; (60) Where, is the load around the tunnel, , , is the displacement coefficient matrix of the tunnel structure, which is related to the design parameters of the tunnel and is a known quantity, and It is composed of the coefficients of equations (32) to (59) and can be calculated by programming.

[0035] In S6, if the load around the tunnel is above 0 and the correlation coefficient is greater than 0.6, it means that this method is suitable; if the load around the tunnel is not above 0 and the correlation coefficient is greater than 0.6, it means that this method is not suitable.

[0036] In S7, the bending moment stiffness of the joint The deformation of the tunnel is significantly affected. It is closely related to the composition of the joint (design of the segments and bolts) and the stress state (including bending moment and axial force). Therefore, in the physical model The value of must be reasonable. Regarding joint forces, positive bending moments may cause the inner surface of the joint to open, while negative bending moments may cause the outer surface to open. Furthermore, whether a joint opens significantly affects its stiffness. Therefore, the calculation of the bending moment stiffness of a new joint is divided into the following cases.

[0037] (1) Bending moment stiffness of joint under positive bending moment: 1) When the joint is closed: When the joint is closed, its simplified force model is as follows Figure 5 As shown, y is the height of the compression zone of the joint concrete, is the resultant force of the joint pressure, For the i Axial force at a joint.

[0038] The concrete stress is calculated using the constitutive equation of concrete in the Code for Design of Concrete Structures, namely: (61) in, and are the compressive stress and compressive strain of concrete, respectively. is the compressive strength of concrete, For concrete The corresponding compressive strain.

[0039] According to the force balance of the joint: (62) in, For the i Axial force at a joint. and are the compressive stresses on the outer and inner arc sides of the joint,b and h are the width and thickness of the joint contact surface respectively. Substituting Equation (62) into Equation (61), the outer arc side of the joint can be obtained. and the compressive strain on the inner arc side .

[0040] The compressive displacement of the inner and outer edges of the joint can be approximately calculated according to the following formula: (63) in, and are the compressive displacements of the inner and outer edges of the joint, respectively. It is a coefficient between 0.55 and 0.7, and is 0.6 in this embodiment.

[0041] Under the stress state of the joint being closed, the expression for calculating the bending moment stiffness of the joint is: (64) Substituting equations (61) to (63) into equation (64), the bending stiffness of the joint when closed can be obtained. It is worth noting that It is impossible to be greater than the bending stiffness of the segment. Need to meet: (65) 2) The joint is open, but the bolts are still under pressure: When the joint is gradually opened, but the bolt is still under pressure, the stress model of the joint will be as follows: Figure 6 As shown, at this time, the force on the bolt is not considered. Figure 6 middle, h b is the distance between the bolt and the outer edge of the joint.

[0042] According to the flat section assumption, the stress in the compression zone of the joint is: (66) in, For height x The displacement at y is the height of the compression zone of the joint concrete.

[0043] According to the balance of forces: (67) (68) In the formula For the i The axial force at each joint can be obtained from equations (66) to (68): and y The compressive displacement of the outer edge of the joint is then: (69) in, is the compression displacement of the outer edge when the seam is opened; When the joint is open but the bolt is still under compression, the expression for calculating the bending moment stiffness of the joint is: (70) Similarly, Equation (70) needs to satisfy Equation (65).

[0044] 3) The joint is open and the bolt is under tension: When the joint is opened and the bolt is under tension, the force model of the joint is as follows: Figure 7 As shown, according to mechanical equilibrium: (71) (72) Where, is the distance between the bolt and the outer edge of the joint, is the number of bolts at the joint, is the tension of the bolt. The bolt adopts a bilinear structure, then The calculation formula is: (73) Where, is the cross-sectional area of ​​the bolt, is the tensile strain of the bolt, is the elastic modulus of the bolt, is the tensile yield stress of the bolt.

[0045] According to deformation coordination: (74) Combining equations (66), (71) to (74), we can obtain 、 and y .

[0046] The formula for calculating the elongation of the bolt is: (75) Where, is the elongation of the bolt, is the bolt length, Calculated by formula (69).

[0047] When the joint is open and the bolt is under tension, the expression for calculating the bending moment stiffness of the joint is: (76) When the bending moment at the joint increases to a certain value, the concrete at the outer edge of the joint will enter the plastic state. At this time, the stress model of the joint will be as follows: Figure 8 shown.

[0048] at this time The stress calculation formula of concrete at height is: (77) Where, After the concrete at the outer edge of the joint enters the plastic state x Stress at height.

[0049] According to mechanical balance: (78) (79) Where, y 0 is the height of the plastic zone of concrete.

[0050] According to deformation coordination: (80) Combining equations (66), (77) to (80), we can find 、 y 0 and y ; When the bending moment at the joint increases to the preset maximum value, the concrete at the outer edge of the joint will enter the plastic state. The expression for calculating the bending moment stiffness of the joint is: (81) (8) Bending moment stiffness of joint under negative bending moment: Under the action of negative bending moment, the outer arc surface of the joint opens, which is just opposite to the effect of positive bending moment. The distance between the bolt and the outer edge of the joint is .at this time, Take the absolute value and replace the equations (61) to (81) with h b Replace with , which will become the calculation formula for the bending moment stiffness of the joint under negative bending moment.

[0051] In this embodiment, the present invention also provides experimental data to verify the effect of the technical solution, which is as follows: Determine the tunnel structure parameters as shown in Table 1.

[0052] Table 1 Tunnel structural parameters In the test data, Figure 9 The 376th segment ring was demonstrated, ea and e b They are 6.036m and 5.968m respectively. To simplify the calculation, the deflection angle (-2°) of the fitting ellipse is ignored. The deformation [D] of the tunnel pointing to the center of the circle is calculated using equations (1) to (7). The coefficient matrix [K] of [P] is calculated using equations (8) to (60). Transforming equation (60) yields: (82) Substitution and , the load [P] is: [166.1, 194.6, 68.1, 47.9, 8.75, 0] kN / m (83) Equation (83) has horizontal loads and vertical loads. Its flaw is 0 means that the calculated result does not take into account the formation resistance. Therefore, the load in formula (83) is relatively reasonable.

[0053] Substituting Equation (83) into Equation (28) and Equation (29), we can calculate x 1 and x 2. Then calculate according to formula (14) M , N and Q. Further, according to equations (60) to (80), the bending stiffness of the joint is: [2.43×10 7 , 9.97×10 6 , 3.11×10 7 ] N·m 2 (84) According to equations (60) to (80), the stress states of the concrete and bolts in the joints are shown in Table 2. It can be seen that the bolt stress at joint 1 is the largest (450.6 MPa), reaching 70.4% of the bolt yield stress. The concrete stress at joint 2 is the largest (19.7 MPa), reaching 81.0% of the concrete compressive strength (23.1 MPa). Therefore, the stress at the joint of ring 376 is within the safe range.

[0054] Table 2 Stress state of the joint The stresses of the steel and concrete in the segments can be calculated according to the Code for Design of Concrete Structures (GB 50010-2010, 2015). The maximum internal forces in the tunnel occur at the crown or base of the arch. The calculated stresses of the concrete and steel are shown in Table 3. It can be seen that the maximum stress of the steel in the segments is 250.2 MPa, reaching 62.6% of the yield stress of HRB400 steel (400 MPa) (GB50010-2010, 2015). The maximum stress of the concrete is 11.6 MPa, reaching 50.2% of its compressive strength.

[0055] Table 3 Maximum internal forces and stresses of tunnel structures In summary, for the most deformed segment ring (segment ring 376) in this shield tunnel section, the maximum stresses in the bolts and concrete at the joints reached 70.4% and 81.0% of their yield stress, respectively. The maximum stresses in the steel bars and concrete in the segments reached 62.6% and 50.2% of their yield stress, respectively. The calculated results have a reliability of 95.4%.

[0056] In the description of the present invention, it should be understood that the terms "center", "thickness", "upper", "lower", "horizontal", "top", "bottom", "inner", "outer", "radial", etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and "third" are used for descriptive purposes only and cannot be understood as indicating or implying the relative importance or the number of technical features implicitly specified. Therefore, the features defined by "first", "second", and "third" may explicitly or implicitly include one or more of such features.

Claims

1. A method for calculating the internal forces of a symmetrical shield tunnel structure driven by a physical model, characterized in that: The following steps are involved: S1. Obtain the design parameters of the segment ring according to the shield tunnel design documents, including the size and position of the segments and joints; S2. Based on the shield tunnel inner profile dimension data detected on site and the tunnel design parameters, a fitting value of the 3D laser scanning data is obtained by curve fitting, and then the structural deformation value detected on site is calculated; S3. Assume that the initial stiffness of the joint is equal to the stiffness of the segment; S4. Calculate the internal force of the tunnel structure based on the current bending moment stiffness of the joint and the load around the tunnel, calculate the displacement coefficient matrix of the tunnel structure, and establish an expression for the deformation of the tunnel structure; S5. Substitute the structural deformation value detected on site into the tunnel structural deformation expression to inversely calculate the load around the tunnel; The deformation of the tunnel structure is calculated according to the expression of the tunnel structure deformation, and then the correlation coefficient between the deformation of the tunnel structure and the structural deformation value detected on site is calculated; S6, in response to the load around the tunnel being greater than 0 and the correlation coefficient being greater than 0.6, calculating the internal force of the tunnel structure based on the inversely calculated load around the tunnel; S7. Calculate the bending moment stiffness of the new joint based on the internal force of the joint, and determine whether the relative error between the bending moment stiffness of the new joint and the bending moment stiffness of the current joint is greater than 5%. If so, use the bending moment stiffness of the new joint as the bending moment stiffness of the current joint and return to S4. If not, proceed to S8. S8. Based on the internal forces of the tunnel structure, calculate the stresses of the segment reinforcement and concrete, and calculate the stresses of the joint bolts and concrete.

2. The internal force calculation method of a symmetrical shield tunnel structure based on physical model driving according to claim 1 is characterized in that: In S2, calculate the structural deformation value of the on-site detection The specific expression is: . Where, and are the horizontal and vertical coordinates of the tunnel structure, and are the horizontal and vertical coordinates of the tunnel structure after deformation, R is the radius at the center of the segment thickness; Where, is the deflection angle of the ellipse, and is the fitting value of 3D laser scanning data.

3. The internal force calculation method of a symmetrical shield tunnel structure based on physical model driving according to claim 2 is characterized in that: In S4, the loads around the tunnel include the earth pressure above the tunnel, the reaction of the soil below the tunnel, the lateral earth pressure, the deadweight load of the segments, and the ground reaction caused by the squeezing of the tunnel structure; Ground reaction caused by tunnel structure compression The specific expression is: Where, P h is the formation resistance, The angle between the specified position of the tunnel and the vertical axis; Where, K s is the formation resistance coefficient, is the horizontal displacement of the tunnel haunch; Segment deadweight load P The specific expression of 5 is: Where, is the deadweight of concrete, B is the width of the segment, h is the thickness of the joint contact surface; The reaction force of the soil under the tunnel P The specific expression of 2 is: Where, P 1 is the earth pressure above the tunnel; Lateral earth pressure includes the first lateral pressure P 3 and second lateral pressure P 4; Where, is the lateral pressure coefficient of soil; Where, is the dead weight of the soil, R is the radius at the center of the segment thickness.

4. The internal force calculation method of a symmetrical shield tunnel structure based on physical model driving according to claim 3 is characterized in that: In S4, the internal forces of the tunnel structure include the total bending moment M , total axial force N and total shear force Q ; Where, is the bending moment at the tunnel vault, is the axial force at the tunnel vault, 、 and They are The virtual bending moment, virtual axial force and virtual shear force of the tunnel structure under the unit virtual load in the direction, 、 and They are The virtual bending moment, virtual axial force and virtual shear force of the tunnel structure under the unit virtual load in the direction; is the structural bending moment caused by the load around the tunnel, and its specific expression is: is the structural axial force caused by the load around the tunnel, and its specific expression is: is the structural shear force caused by the load around the tunnel, and its specific expression is: 。 5. The internal force calculation method of a symmetrical shield tunnel structure based on physical model driving according to claim 4 is characterized in that: In S4, the tunnel structure is Deformation at The specific expression is: Where, is the load around the tunnel, , is the displacement coefficient matrix of the tunnel structure, .

6. The internal force calculation method of a symmetrical shield tunnel structure based on physical model driving according to claim 5 is characterized in that: In S7, the method for calculating the bending moment stiffness of the new joint is as follows: (1) Bending moment stiffness of joint under positive bending moment: 1) Under the stress state of the joint being closed, the expression for calculating the bending moment stiffness of the joint is: Where, For the i The total bending moment at each joint, and are the compression displacements of the inner and outer edges of the joint, respectively; Where, and is the compressive strain on the outer and inner arc sides of the joint, A coefficient between 0.55 and 0.7; 2) When the joint is open but the bolt is still under compression, the expression for calculating the bending moment stiffness of the joint is: Where, y is the height of the compression zone of the joint concrete, is the compression displacement of the outer edge when the seam opens, , is the compressive strain of concrete; 3) When the joint is open and the bolt is under tension, the expression for calculating the bending moment stiffness of the joint is: Where, is the elongation of the bolt, is the compression displacement of the outer edge when the seam opens, is the distance between the bolt and the outer edge of the joint; When the bending moment at the joint increases to the preset maximum value, the concrete at the outer edge of the joint will enter the plastic state. The expression for calculating the bending moment stiffness of the joint is: Where, is the height of the concrete plastic zone, is the bolt length, is the tensile strain of the bolt, is the distance between the bolt and the outer edge of the joint; (8) Bending moment stiffness of joint under negative bending moment: The distance between the bolt and the outer edge of the joint is , replace the joint moment stiffness expression with Replace with , Take the absolute value to obtain the calculation formula of the bending moment stiffness of the joint under negative bending moment.

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