Method for calculating internal force of symmetrical shield tunnel structure based on physical model driving

Abstract

The application discloses a method for calculating internal force of a symmetrical shield tunnel structure based on a physical model, comprising the following steps: S1, obtaining design parameters of a segment ring; S2, calculating a structural deformation value detected on site; S3, assuming that initial stiffness of a joint is equal to stiffness of a segment; S4, establishing an expression of deformation of the tunnel structure; S5, calculating a correlation coefficient of the deformation of the tunnel structure and the structural deformation value detected on site; S6, in response to a load around the tunnel being greater than 0 and the correlation coefficient being greater than 0.6, calculating internal force of the tunnel structure; S7, calculating bending moment stiffness of a new joint, and judging whether a relative error between the bending moment stiffness of the new joint and bending moment stiffness of a current joint is greater than 5%; if yes, the bending moment stiffness of the new joint is taken as the bending moment stiffness of the current joint, and the step S4 is returned to; if no, the step S8 is entered; S8, according to the internal force of the tunnel structure, calculating stress of segment reinforcement and concrete, and calculating stress of a joint bolt and concrete.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of tunnel structure deformation, and particularly relates to a method for calculating internal force of a symmetric shield tunnel structure based on a physical model. BACKGROUND

[0002] Currently, three-dimensional laser radar can be used to measure the internal contour size of a tunnel structure, and the deformation of the tunnel can be calculated by comparing with the initial design size of the tunnel. However, when judging the safety state of the structure by using the specification, the design size of the tunnel, the detailed structure of the joint, and the surrounding rock condition of the tunnel are all ignored. Obviously, there may be a large difference between the conclusion given by the specification and the actual stress state of the structure. Combining data with a physical model is an important way to improve the reliability of the mechanical state of the tunnel.

[0003] In the aspect of physical model research, mainly includes the research of segment joint and whole ring tunnel. In the research of segment joint, Li et al. proposed an analytical model of segment joint considering four-stage stress by considering the detailed structure of segment joint. Kou proposed a theoretical calculation model of bending stiffness of segment joint under high water pressure, and studied the influence of axial force, bolt strength and concrete strength on the bending stiffness of joint. Huang et al. established an algorithm for calculating the effective ratio of bending stiffness based on the bending stiffness of segment joint. In the research of whole ring tunnel, Naggar and Hinchberger established the analytical equations of bending moment and axial force of structure considering elastic stratum and homogeneous circular tunnel based on stratum-structure model. Liu et al. proposed a calculation method of internal force of tunnel lining during segment assembly according to the principle of minimum potential energy. Huang et al. established a whole ring tunnel internal force calculation model considering the effective stiffness of joint based on load-structure model, and discussed the influence of structure stiffness on tunnel internal force. Chen et al. equivalent segment ring as Timoshenko beam and inter-ring joint as ideal spring, and based on state space method and D'Alembert principle, deduced the analytical solution of longitudinal dynamic response of shield tunnel lining. The above shows that in the research of mechanical behavior of segment joint and whole ring tunnel, a large number of scholars have proposed rich physical models, which not only consider the detailed structure of joint, but also consider the cooperation of joint and segment, and also consider the interaction of soil-tunnel. The mechanical behavior of segment joint under load has been clearly understood. However, these models are all based on known external load to calculate the internal force and deformation of segment and joint, and cannot directly analyze the mechanical behavior of tunnel structure when the external load is unknown.

[0004] Some scholars also studied the combined method of data and physics. The distributed optical fiber is randomly laid along the circumferential direction on the upper and lower surfaces of the reinforcement cage inside the segment, and the displacement, internal force and external load distribution of the segment during the monitoring period are calculated by using the inverse analysis method. Zhang et al. proposed a longitudinal joint internal force inversion model based on the vertical convergence deformation of the shield tunnel. Lin et al. and Wang et al. used the physics and data-driven method to predict the deformation of the stratum and adjacent buildings during tunnel construction. Zhao et al. evaluated the long-term safety performance of soft rock tunnel structure based on the knowledge decision-data driven model of analytic hierarchy process. In summary, the data-driven model of tunnel engineering is mainly used in the aspects of internal force of structure, deformation of lining, deformation of adjacent structure, performance evaluation of tunnel, etc. However, due to the influence of the service environment of the tunnel, the internal force of the tunnel structure cannot be obtained by monitoring data inversion. Although Zhao et al. evaluated the safety state of the tunnel structure, the weight used still has strong subjectivity. Therefore, the rationality and reliability of the safety analysis model of the shield tunnel structure still need to be improved. SUMMARY

[0005] In view of the above problems in the prior art, the internal force calculation method for the symmetric shield tunnel structure based on the physical model driving provided by the present application 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 purpose of the application, the technical scheme adopted by the present application is as follows: the internal force calculation method for the symmetric shield tunnel structure based on the physical model driving, comprising the following steps:

[0007] S1, obtaining the design parameters of the segment ring according to the design file of the shield tunnel, including the size and position of the segment and the joint;

[0008] S2, obtaining the fitting value of the three-dimensional laser scanning data by curve fitting according to the detected internal contour size data of the shield tunnel and the tunnel design parameters, and then calculating the structure deformation value detected on site;

[0009] S3, assuming that the initial stiffness of the joint is equal to the stiffness of the segment;

[0010] S4, calculating the internal force of the tunnel structure according to the bending moment stiffness of the current joint and the load around the tunnel, calculating the displacement coefficient matrix of the tunnel structure, and establishing the expression of the tunnel structure deformation;

[0011] S5, bringing the structure deformation value detected on site into the expression of the tunnel structure deformation to inversely calculate the load around the tunnel; calculating the deformation of the tunnel structure according to the expression of the tunnel structure deformation, and then calculating the correlation coefficient of the deformation of the tunnel structure and the structure deformation value detected on site;

[0012] S6, in response to the load around the tunnel being above 0 and the correlation coefficient being greater than 0.6, calculating the internal force of the tunnel structure according to the inverse calculated load around the tunnel;

[0013] S7, calculating the bending moment stiffness of the new joint according to the internal force of the joint, and judging whether the relative error of the bending moment stiffness of the new joint and the bending moment stiffness of the current joint is greater than 5%; if yes, taking the bending moment stiffness of the new joint as the bending moment stiffness of the current joint, and returning to S4; if no, entering S8;

[0014] S8, calculating the stress of the segment reinforcement and the concrete according to the internal force of the tunnel structure, and calculating the stress of the joint bolt and the concrete.

[0015] Further, in S2, the structural deformation value detected on site is calculated The expression is specifically:

[0016]

[0017] In the formula, and are the horizontal coordinate and the vertical coordinate of the tunnel structure respectively, and are the horizontal coordinate and the vertical coordinate of the structure after tunnel deformation respectively, R is the radius at the center of the segment thickness;

[0018]

[0019]

[0020] In the formula, is the eccentric angle of the ellipse, and are the fitting values of the three-dimensional laser scanning data.

[0021] Further, in S4, the load around the tunnel includes the tunnel upper soil pressure, the reaction force of the soil under the tunnel, the lateral soil pressure, the segment self-weight load and the ground reaction force caused by the extrusion of the tunnel structure;

[0022] The ground reaction force caused by the extrusion of the tunnel structure The expression is specifically:

[0023]

[0024] In the formula, P h is the ground resistance, is the included angle between the specified position of the tunnel and the vertical axis;

[0025]

[0026] wherein, K s is the ground resistance coefficient, is the horizontal displacement of the tunnel haunch;

[0027] the self-weight load of the segment P The expression of 5 is specifically:

[0028] . .

[0029] wherein, is the self-weight of the concrete, B is the width of the segment, h is the thickness of the joint contact surface;

[0030] the reaction force of the soil under the tunnel P The expression of 2 is specifically:

[0031]

[0032] wherein, P 1 is the soil pressure on the upper part of the tunnel;

[0033] the lateral soil pressure includes a first lateral pressure P 3 and a second lateral pressure P 4;

[0034]

[0035] wherein, is the lateral pressure coefficient of the soil;

[0036]

[0037] wherein, is the self-weight of the soil, R is the radius at the center of the segment thickness.

[0038] Further: in S4, the internal force of the tunnel structure includes the total bending moment M , the total axial force N and the total shear force Q ;

[0039]

[0040]

[0041]

[0042] wherein, is the bending moment at the tunnel crown, is the axial force at the tunnel crown, , and are respectively the virtual bending moment, virtual axial force and virtual shear force of the tunnel structure under the action of the unit virtual load in the direction are respectively the virtual bending moment, virtual axial force and virtual shear force of the tunnel structure under the action of the unit virtual load in the direction , and are respectively the virtual bending moment, virtual axial force and virtual shear force of the tunnel structure under the action of the unit virtual load in the direction are respectively the virtual bending moment, virtual axial force and virtual shear force of the tunnel structure under the action of the unit virtual load in the direction

[0043] is the structural bending moment caused by the load around the tunnel, and its expression is specifically:

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050] is the structural axial force caused by the load around the tunnel, and its expression is specifically:

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057] is the structural shear force caused by the load around the tunnel, and its expression is specifically:

[0058]

[0059]

[0060]

[0061]

[0062] .

[0063] Further, in S4, the deformation of the tunnel structure at is expressed as

[0064]

[0065] wherein, is the load around the tunnel, , is the displacement coefficient matrix of the tunnel structure, .

[0066] Further, in S7, the method for calculating the bending moment stiffness of the new joint is specifically:

[0067] (1) The bending moment stiffness of the joint under the action of positive bending moment is:

[0068] 1) In the force state of joint closure, the expression for calculating the bending moment stiffness of the joint is specifically:

[0069]

[0070] wherein, is the total bending moment at the i th joint, and are the compression displacement amounts of the inner and outer edges of the joint, respectively;

[0071]

[0072]

[0073] wherein, and are the compression strains of the outer arc side and the inner arc side of the joint, is a coefficient between 0.55 and 0.7;

[0074] 2) In the force state of joint opening, but the bolt is still under compression, the expression for calculating the bending moment stiffness of the joint is specifically:

[0075]

[0076] wherein, y is the compression zone height of the joint concrete, is the compression displacement amount of the outer edge when the joint is opened, , is the compression strain of the concrete;

[0077] 3) In the force state of joint opening, and the bolt is under tension, the expression for calculating the bending moment stiffness of the joint is specifically: ​

[0078]

[0079] In the formula, is the elongation of the bolt, is the compression displacement of the outer edge when the joint is opened, is the distance between the bolt and the outer edge of the joint;

[0080] When the bending moment at the joint increases to the preset maximum value, the concrete of the outer edge of the joint will enter the plastic state, and the expression for calculating the bending moment stiffness of the joint is specifically:

[0081]

[0082] In the formula, is the height of the plastic zone of the concrete, is the length of the bolt, is the tensile strain of the bolt, is the distance between the bolt and the outer edge of the joint;

[0083] (8) Bending moment stiffness of the joint under negative bending moment:

[0084] Let the distance between the bolt and the outer edge of the joint be , replace in the expression of the bending moment stiffness of the joint with , Take the absolute value to obtain the calculation formula of the bending moment stiffness of the joint under the negative bending moment.

[0085] The beneficial effects of the present application are:

[0086] (1) The present application provides a symmetric shield tunnel structure internal force calculation method based on a physical model drive. In the physical model, first, based on the classic load-structure model and the force method equation, the analytical equation between the tunnel deformation and the external load is derived, and the physical-data double drive model is constructed to calculate the internal force of the tunnel structure. At the same time, the coordinated deformation of the segment and the joint, the matching of the nonlinear joint stiffness and the structure internal force are considered in the physical model for calculating the internal force of the tunnel structure. Secondly, in the detection data, the tunnel inner contour size is obtained by using three-dimensional laser radar scanning. On this basis, a tunnel structure deformation calculation method matched with the physical model is proposed. Finally, the physical model and the detection data are fused and driven to realize the calculation of the internal force and stress of the tunnel structure, and the rationality and reliability of the internal force calculation of the shield tunnel structure are improved.

[0087] (8) The physical-data double driving model is constructed to calculate the internal force of the tunnel structure, and the correlation coefficient between the detected displacement and the calculated displacement is used to evaluate the reliability of the physical-data double driving model. It is worth noting that the influence of physical constraints and geological information on the calculation of the internal force of the tunnel structure is disclosed. The method for calculating the internal force of the tunnel structure is combined with the current popular three-dimensional laser detection technology, which helps to promote the quantitative evaluation of the safety state analysis of the tunnel. BRIEF DESCRIPTION OF DRAWINGS

[0088] Figure 1 The flow chart of the internal force calculation method of the symmetric shield tunnel structure based on the physical model driving of the present application.

[0089] Figure 2 The load structure model of the circular shield tunnel, Figure 2 (a) is the load-structure symmetry, Figure 2 (b) is the model simplification.

[0090] Figure 3 The deformation diagram of the tunnel structure.

[0091] Figure 4 The model diagram under the action of unit load.

[0092] Figure 5 The force model when the joint is not expanded, Figure 5 (a) is the mechanical model, Figure 5 (b) is the deformed mechanical model.

[0093] Figure 6 The force model when the joint is expanded and the bolt is closed, Figure 6 (a) is the mechanical model, Figure 6 (b) is the deformed mechanical model.

[0094] Figure 7 The force model when the joint is expanded and the bolt is in tension, Figure 7 (a) is the mechanical model, Figure 7 (b) is the deformed mechanical model.

[0095] Figure 8 The force model after the outer edge of the joint yields, Figure 8 (a) is the mechanical model, Figure 8 (b) is the deformed mechanical model.

[0096] Figure 9 The schematic diagram of the fitting ellipse of the 376th ring segment ring in the transverse convergence deformation statistics of the 1440m shield tunnel. DETAILED DESCRIPTION

[0097] The specific embodiments of the present application are described below to enable those skilled in the art to understand the present application, but it should be clear that the present application is not limited to the scope of the specific embodiments, and for those skilled in the art, any changes that are obvious within the spirit and scope of the present application defined and determined by the appended claims are included in the protection of the present application.

[0098] As shown in the figure, in one embodiment of the present application, the internal force calculation method of the symmetric shield tunnel structure based on the physical model driven, comprising the following steps: Figure 1

[0099] S1, obtaining the design parameters of the segment ring according to the design file of the shield tunnel, including the size and position of the segment and the joint;

[0100] S2, obtaining the fitting value of the three-dimensional laser scanning data by curve fitting according to the internal contour size data of the shield tunnel detected on site and the tunnel design parameters, and then calculating the structural deformation value detected on site;

[0101] S3, assuming that the initial stiffness of the joint is equal to the stiffness of the segment;

[0102] S4, calculating the internal force of the tunnel structure according to the bending moment stiffness of the current joint and the load around the tunnel, calculating the displacement coefficient matrix of the tunnel structure, and establishing the expression of the tunnel structure deformation;

[0103] S5, bringing the structural deformation value detected on site into the expression of the tunnel structure deformation to back-calculate the load around the tunnel; calculating the deformation of the tunnel structure according to the expression of the tunnel structure deformation, and then calculating the correlation coefficient of the deformation of the tunnel structure and the structural deformation value detected on site;

[0104] 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 according to the back-calculated load around the tunnel;

[0105] S7, calculating the bending moment stiffness of the new joint according to the internal force of the joint, and judging 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 yes, taking the bending moment stiffness of the new joint as the bending moment stiffness of the current joint, and returning to S4; if no, entering S8;

[0106] S8, calculating the stress of the segment reinforcement and the concrete, and calculating the stress of the joint bolt and the concrete according to the internal force of the tunnel structure.

[0107] In S2, the structural deformation value detected on site can be calculated by the detection data of the tunnel structure, according to the formula: 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 As shown. The equation for the initial position of the tunnel is:

[0108] (1)

[0109] In the formula, and Here, x and y are the abscissa and ordinate of the tunnel structure, respectively. The equation of the contour line of the tunnel lining structure after being subjected to stress is:

[0110] (2)

[0111] In the formula, and These are the abscissa and ordinate of the tunnel structure after deformation, respectively. and These are the fitted values ​​for the three-dimensional laser scanning data.

[0112] according to Figure 4 The direction of tunnel structural deformation points towards the center of the circle. Therefore, the tunnel structural deformation calculated from the detection data should remain consistent. Thus, , and the center They should be on a straight line, satisfying:

[0113] (3)

[0114] When equations (1) and (2) are expressed in polar coordinates, they are as follows:

[0115] (5)

[0116] (6)

[0117] In the formula, Let be the angle of inclination of the ellipse. Substituting equations (5) and (6) into equation (3), we can calculate... Then, calculate according to equation (6). and Calculate the structural deformation values ​​detected on site. The specific expression is:

[0118] (7)

[0119] In the formula, and These are the x-coordinate and y-coordinate of the tunnel structure, respectively. and These are the x-coordinate and y-coordinate of the tunnel structure after deformation, respectively.R is the radius at the center of the segment thickness;

[0120] In S4, the loads around the tunnel include the earth pressure above the tunnel, the reaction force of the soil below the tunnel, the lateral earth pressure, the self-weight load of the segment, and the ground reaction force caused by the extrusion of the tunnel structure;

[0121] In the present embodiment, the derivation step of calculating the loads around the tunnel is specifically as follows:

[0122] The present embodiment studies a circular shield tunnel with symmetrical structure. The rock stratum where the tunnel is located is homogeneous, and the load is symmetrically distributed, as shown in (a) of Figure 2 , wherein ( , ,…, ) are the loads around the tunnel, and the tunnel structure considers the segment and the joint. Since the load and the structure are symmetrically distributed, the tunnel load-structure model is simplified as (b). Wherein Figure 2 1 and x 2 are the bending moment and the axial force at the crown of the tunnel. x

[0123] P 1 is the earth pressure above the tunnel, and the action range is . P 2 is the reaction force of the soil below the tunnel, and the action range is . P 3 and P 4 are the lateral earth pressure, and the action range is . P 5 is the self-weight load of the segment, and the action range is . P 6 is the ground reaction force caused by the extrusion of the tunnel structure, which follows a quadratic function distribution, that is:

[0124] The expression of the ground reaction force caused by the extrusion of the tunnel structure is specifically as follows:

[0125] (8)

[0126] In the formula, P h is the ground resistance, is the angle between the specified position of the tunnel and the vertical axis;

[0127] (9)

[0128] In the formula, K s is the ground resistance coefficient, is the horizontal displacement of the haunch of the tunnel; ​

[0129] The self-weight load of the segment can be directly obtained by the design parameters of the segment, and the self-weight load of the segment is P The expression of the self-weight load of the segment 5 is specifically as follows:

[0130] (10)

[0131] In the formula, is the self-weight of the concrete, B is the width of the segment, h is the thickness of the joint contact surface;

[0132] According to the load balance relationship in the vertical direction of the tunnel structure, Figure 2 the reaction force of the soil under the tunnel is P The expression of the reaction force of the soil under the tunnel 2 is specifically as follows:

[0133] (11)

[0134] In the formula, P 1 is the soil pressure on the upper part of the tunnel;

[0135] The lateral soil pressure includes the first lateral pressure P 3 and the second lateral pressure P 4;

[0136] (12)

[0137] In the formula, is the lateral pressure coefficient of the soil;

[0138] (13)

[0139] In the formula, is the self-weight of the soil, R is the radius at the center of the segment thickness.

[0140] In S4, the internal force of the tunnel structure includes the total bending moment M , the total axial force N , and the total shear force Q ;

[0141] (14)

[0142] In the formula, is the bending moment at the crown of the tunnel, is the axial force at the crown of the tunnel, , and are the virtual bending moment, the virtual axial force and the virtual shear force of the tunnel structure under the action of the unit virtual load in the direction respectively, , and are respectively virtual bending moment, virtual axial force and virtual shear force of the tunnel structure under the action of unit virtual load in the direction of

[0143] In the embodiment, the derivation steps of the internal force of the tunnel structure are specifically:

[0144] According to the force method equation, the balance equation at the arch top is:

[0145] (15)

[0146] In the formula, and are the displacements in the self direction caused by unit virtual load in the bending moment direction and the axial force direction respectively, and are the displacements in the bending moment direction caused by unit virtual load in the axial force direction, ; (or ) is the displacement in the bending moment (or axial force) direction caused by external load. and are the displacements of the structure in the and directions caused by the load [P] around the tunnel.

[0147] Compared with the bending moment, the influence of the axial force and the shear force on the deformation of the structure is very small in the thin-walled structure. Therefore, only the influence of the bending moment is considered when calculating the deformation of the tunnel structure. The deformation of the tunnel is jointly generated by the segment and the joint, that is:

[0148] (16)

[0149] wherein the subscripts s and j respectively represent the segment deformation and the joint deformation caused by the load, and are the segment deformation and the joint deformation caused by the load of , and are the segment deformation and the joint deformation caused by the load of , and are the segment deformation and the joint deformation caused by the load of .

[0150] , and are calculated by the virtual internal force of the tunnel structure. The internal force of the tunnel structure under the action of unit virtual load in the x 1 direction is:

[0151] (17)

[0152] wherein , , They are respectively x Virtual bending moment, virtual axial force, and virtual shear force of tunnel structure under unit virtual load in direction 1.

[0153] exist The internal forces of the tunnel structure under a unit virtual load in the direction are:

[0154] (18)

[0155] in, , , They are respectively x Virtual bending moment, virtual axial force, and virtual shear force of the tunnel structure under a unit virtual load in one direction. R Let be the radius at the center of the segment thickness. Therefore:

[0156] (19)

[0157] (20)

[0158] In the formula, E The elastic modulus of the tunnel segment. I Let be the moment of inertia of the tunnel segment. , n 1 represents The number of joints between them The angle between the joint and the vertical axis. n 2 represents The number of joints between them n 3 represents The number of joints between them n 4 represents The number of joints between them For the first i The bending moment stiffness of each joint. For the first i The angle between the connector and the vertical axis;

[0159] In equation (16), and Through external loads respectively P Calculation of internal forces caused by loads around the tunnel. Structural bending moment caused by loads around the tunnel. for:

[0160] (twenty one)

[0161] Structural axial forces caused by loads around the tunnel for:

[0162] (22)

[0163] Structural shear force caused by load around tunnel is:

[0164] (23)

[0165] Thus, we have:

[0166] (24)

[0167] (25)

[0168] (26)

[0169] (27)

[0170] Substitute equations (16), (19), (20), (24), (25), (26), (27) into equation (15), we have x 1 and x 2. That is:

[0171] (28)

[0172] (29)

[0173] In the equation, the expressions of coefficients , , , to , to are as follows:

[0174]

[0175]

[0176]

[0177]

[0178]

[0179]

[0180]

[0181]

[0182]

[0183]

[0184]

[0185]

[0186]

[0187]

[0188]

[0189] Finally, the expression for the internal forces of the tunnel structure was obtained.

[0190] In S4, the derivation steps of the expression for calculating the deformation of the tunnel structure are as follows:

[0191] like Figure 4 As shown, the angle is calculated as... Displacement at point, Apply a unit load pointing towards the center of the circle. T ;

[0192] Under unit load T Under the action of the force, the bending moment of the tunnel is:

[0193] (30)

[0194] In the formula, unit load T Under the action Bending moment at the point;

[0195] β The structural displacement at point is:

[0196] (31)

[0197] In the formula, , and They are respectively The total displacement of the tunnel structure, the displacement caused by segment deformation, and the displacement caused by joint deformation.

[0198] The formula for calculation is:

[0199] (32)

[0200] In the formula, for x The segment displacement caused by 1 for x2 induced segment displacement, For M pi induced segment displacement.

[0201] (33)

[0202] (34)

[0203] (35)

[0204] (36)

[0205] When in the range then:

[0206] (37)

[0207] When in the range then:

[0208] (38)

[0209] (39)

[0210] (40)

[0211] (41)

[0212] When in the range then:

[0213] (42)

[0214] When in the range then:

[0215] (43)

[0216] When in the range then:

[0217] (44)

[0218] The calculation formula is:

[0219] (45)

[0220] where, is the bending moment at the T first joint under the action of a unit load i is the bending moment at the second joint under the action of a unit loadi the total bending moment at the joint. The function is composed of 3 parts, and the above equation can be simplified as:

[0221] (46)

[0222] where, is x the joint displacement caused by is x the joint displacement caused by is M p the joint displacement caused by and ( k =1, 2, …, n) are the closest, and satisfy:

[0223] (47)

[0224] Thus, the following equation can be obtained:

[0225] (48)

[0226] (49)

[0227] Since P 1 to P h are different in the function interval, can be written as:

[0228] (50)

[0229] where, each term in

[0230] (51)

[0231] (52)

[0232] (53)

[0233] (54)

[0234] Under the influence of P 2 load, in the range of i < n 1+ n 2, the following equation can be obtained:

[0235] (55)

[0236] In range, n 1+ n 2≤ i n Then the following equation can be obtained:

[0237] (56)

[0238] Affected by P h load, in range, i n 1, then the following equation can be obtained:

[0239] (57)

[0240] In range, n 1≤ i n - n 4, then the following equation can be obtained:

[0241] (58)

[0242] In range, n - n 4≤ i n Then the following equation can be obtained:

[0243] (59)

[0244] Substitute equations (32) to (59) into equation (31), and the displacement of the tunnel at any position can be obtained. That is, the deformation of the tunnel structure at can be expressed as ;

[0245] (60)

[0246] In the equation, 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, is a known quantity, and is composed of the coefficients of equations (32) to (59) and can be calculated by programming.

[0247] ​​​​In S6, if the load around the tunnel is above 0 and the correlation coefficient is greater than 0.6, then the method is suitable; if the load around the tunnel is not above 0 and the correlation coefficient is not greater than 0.6, then the method is not suitable.

[0248] In S7, the bending moment stiffness of the joint It has a significant impact on tunnel deformation, and It is closely related to the composition of the joint (design of 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 the stress on the joint, the inner surface of the joint may open under a positive bending moment, while the outer surface may open under a negative bending moment. Furthermore, whether the joint opens or not significantly affects its stiffness. Therefore, the calculation of the bending moment stiffness of a new joint is divided into the following cases.

[0249] (1) Bending moment stiffness of the joint under positive bending moment:

[0250] 1) When the joint is closed:

[0251] When the joint is closed, its simplified force model is as follows: Figure 5 As shown, where, y The height of the compression zone of the joint concrete. The resultant force of the joint pressure, For the first i Axial force at the joint.

[0252] The stress in concrete is calculated using the constitutive equation of concrete in the "Code for Design of Concrete Structures", namely:

[0253] (61)

[0254] in, and These represent the compressive stress and compressive strain of concrete, respectively. This refers to the compressive strength of concrete. For concrete The corresponding compressive strain.

[0255] Based on the force balance of the joint:

[0256] (62)

[0257] in, For the first i Axial force at the joint. and These are the compressive stresses on the outer and inner arc sides of the joint, respectively. b and hrespectively, the width and thickness of the joint contact surface. Substituting equation (62) into equation (61), the compressive strain of the outer arc side and the inner arc side of the joint .

[0258] The compression displacement amount of the inner and outer edges of the joint can be approximately calculated according to the following equation:

[0259] (63)

[0260] wherein, and are the compression displacement amounts of the inner and outer edges of the joint, respectively. is a coefficient between 0.55 and 0.7, and is taken as 0.6 in the present embodiment.

[0261] The expression for calculating the bending stiffness of the joint in the force state of the closed joint is specifically:

[0262] (64)

[0263] Substituting equations (61) to (63) into equation (64), the bending stiffness of the closed joint can be calculated. It is worth noting that, cannot be greater than the bending stiffness of the segment. Therefore needs to satisfy:

[0264] (65)

[0265] 2) The joint is opened, but the bolt is still under compression:

[0266] When the joint is gradually opened, but the bolt is still under compression, the force model of the joint will be as shown in Figure 6 At this time, without considering the force of the bolt, Figure 6 wherein, h b is the distance between the bolt and the outer edge of the joint.

[0267] According to the plane section assumption, the stress of the compression zone of the joint is:

[0268] (66)

[0269] wherein, is the displacement at a height of x is the compression zone height of the joint concrete. y According to the balance of the resultant force:

[0270]

[0271] (67)

[0272] ​​(68)

[0273] where is the axial force at the i th joint. According to equations (66) to (68), one can solve and y . Then the compression displacement of the outer edge of the joint is:

[0274] (69)

[0275] where is the compression displacement of the outer edge of the joint when the joint is opened;

[0276] When the joint is opened but the bolt is still under compression, the expression for calculating the bending stiffness of the joint is:

[0277] (70)

[0278] Similarly, equation (70) needs to satisfy equation (65).

[0279] 3) The joint is opened and the bolt is under tension:

[0280] When the joint is opened and the bolt is under tension, the force model of the joint is shown in Figure 7 According to the mechanical equilibrium:

[0281] (71)

[0282] (72)

[0283] 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. If the bolt adopts a bilinear structure, then The calculation formula of

[0284] (73)

[0285] 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.

[0286] According to the deformation compatibility:

[0287] (74)

[0288] Solving equations (66), (71) to (74) together, one can solve 、 and y .

[0289] The formula for calculating the elongation of the bolt is:

[0290] (75)

[0291] In the formula, is the elongation of the bolt, is the length of the bolt, calculated by formula (69).

[0292] The expression for calculating the bending stiffness of the joint is specifically:

[0293] (76)

[0294] When the bending moment at the joint increases to a certain value, the concrete at the outer edge of the joint will enter a plastic state, at which time the stress model of the joint will be as shown in Figure 8 .

[0295] At this time the stress calculation formula for the concrete at the height of the joint is:

[0296] (77)

[0297] In the formula, is the stress at the height of the joint after the outer edge concrete of the joint enters plasticity. x

[0298] According to the mechanical equilibrium:

[0299] (78)

[0300] (79)

[0301] In the formula, y 0 is the height of the plastic zone of the concrete.

[0302] According to the deformation compatibility:

[0303] (80)

[0304] Solving formulas (66), (77) to (80) can obtain , y 0 and y .

[0305] When the bending moment at the joint increases to a preset maximum value, the concrete at the outer edge of the joint will enter a plastic state, and the expression for calculating the bending stiffness of the joint is specifically: ​

[0306] (81)

[0307] (8) Bending moment stiffness of the joint under negative bending moment:

[0308] Under negative bending moment, the outer arc surface of the joint opens up, exactly opposite to the effect of positive bending moment. Let the distance between the bolt and the outer edge of the joint be denoted as... .at this time, Take the absolute value and convert the values ​​in equations (61) to (81) to the absolute value. h b Replace with This will become the formula for calculating the moment stiffness of the joint under negative bending moment.

[0309] In this embodiment, the present invention also provides experimental data to verify the effectiveness of the technical solution, as follows:

[0310] The tunnel structural parameters are determined as shown in Table 1.

[0311] Table 1 Tunnel structural parameters

[0312]

[0313] In the detection data, with Figure 9 The 376th ring segment was demonstrated, among which e a and e b The lengths are 6.036m and 5.968m respectively. To simplify the calculation, the deflection angle (-2°) of the fitted ellipse is ignored. Equations (1) to (7) are used to calculate the deformation [D] of the tunnel pointing towards the center of the circle. The coefficient matrix [K] of [P] is calculated using equations (8) to (60). Transforming equation (60), we get:

[0314] (82)

[0315] Substitution and The load [P] is:

[0316] [166.1, 194.6, 68.1, 47.9, 8.75, 0] kN / m (83)

[0317] Equation (83) has both horizontal and vertical loads. Its drawback is... A value of 0 indicates that the calculation results did not consider formation resistance. This is a common occurrence in some studies. Due to the influence of the load, the load in equation (83) is relatively reasonable.

[0318] Substituting equation (83) into equation (28) and equation (29), the maximum stresses of the bolts and the concrete at the joint can be calculated as x 1 and x 2. Then, the stresses of the bolts, the concrete, N and Q can be calculated according to equation (14). M

[0319] [2.43 x 10 7 , 9.97 x 10 6 , 3.11 x 10 7 ] N-m 2 (84)

[0320] According to equation (60) to (80), the stresses of the concrete and the bolts at the joint are shown in Table 2. It can be seen that the maximum stress of the bolt at joint 1 is 450.6 MPa, which reaches 70.4% of the yield stress of the bolt. The maximum stress of the concrete at joint 2 is 19.7 MPa, which reaches 81.0% of the compressive strength of the concrete (23.1 MPa). Therefore, the stresses of the joint at the 376th segment are within the safety range.

[0321] Table 2 Stresses of the joint

[0322]

[0323] The stresses of the steel and the concrete in the segment can be calculated according to the Code for Design of Concrete Structures (GB 50010-2010, 2015). The maximum internal forces of the tunnel are located at the crown or the invert. The calculated stresses of the steel and the concrete are shown in Table 3. It can be seen that the maximum stress of the steel in the segment is 250.2 MPa, which reaches 62.6% of the yield stress of the HRB400 steel (400 MPa) (GB 50010-2010, 2015). The maximum stress of the concrete is 11.6 MPa, which reaches 50.2% of the compressive strength of the concrete.

[0324] Table 3 Maximum internal forces and stresses of the tunnel structure

[0325]

[0326] Based on the above analysis, for the maximum deformation segment (the 376th segment) of the shield tunnel, the maximum stresses of the bolts and the concrete at the joint reach 70.4% and 81.0% of the yield stress, respectively. The maximum stresses of the steel and the concrete in the segment reach 62.6% and 50.2% of the yield stress, respectively. The reliability of the calculation results is 95.4%.

[0327] ​In the description of the application, it needs to be understood that the terms "center", "thickness", "upper", "lower", "horizontal", "top", "bottom", "inner", "outer", "radial" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the application and simplifying the description, and do not indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the application. In addition, the terms "first", "second", "third" are only for the purpose of description, and cannot be understood as indicating or implying relative importance or implying the number of technical features indicated. Therefore, the features defined by "first", "second", "third" can explicitly or implicitly include one or more of the features.

Claims

1. A method for calculating the internal forces of a symmetrical shield tunnel structure based on a physical model, characterized in that, Includes the following steps: S1. Obtain the design parameters of the segment ring based on the shield tunnel design documents, including the size and location of the segments and joints; S2. Based on the shield tunnel's internal contour dimensions and tunnel design parameters obtained from on-site inspection, the fitting values ​​of the three-dimensional laser scanning data are obtained through curve fitting, and then the structural deformation values ​​obtained from on-site inspection are calculated. S3. Assume that the initial stiffness of the joint is equal to the stiffness of the segment. S4. Calculate the internal forces 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 the expression for the deformation of the tunnel structure. S5. Substitute the structural deformation values ​​detected on-site into the expression for tunnel structural deformation to calculate the load around the tunnel. The deformation of the tunnel structure is calculated based on the expression for tunnel structure deformation, and then the correlation coefficient between the tunnel structure deformation and the structural deformation value detected on site is calculated. S6. Calculate the internal forces of the tunnel structure based on the back-calculated loads around the tunnel, provided that the loads around the tunnel are above 0 and the correlation coefficient is greater than 0.

6. 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 yes, use the bending moment stiffness of the new joint as the bending moment stiffness of the current joint and return to S4. If no, proceed to S8. S8. Based on the internal forces of the tunnel structure, calculate the stress of the segment reinforcement and concrete, and calculate the stress of the joint bolts and concrete. In S4, the internal forces of the tunnel structure include the total bending moment. M Total axial force N and total shear force Q ; In the formula, This represents the bending moment at the tunnel arch. This refers to the axial force at the tunnel arch. , and They are respectively The virtual bending moment, virtual axial force, and virtual shear force of the tunnel structure under a unit virtual load in the direction of rotation. , and They are respectively Virtual bending moment, virtual axial force, and virtual shear force of tunnel structure under unit virtual load in the direction; The structural bending moment caused by the loads around the tunnel is expressed as follows: In the formula, P 1 represents the earth pressure above the tunnel. P 2 represents the reaction force of the soil beneath the tunnel. P 3 represents the first lateral pressure. P 4 represents the second lateral pressure. P 5 represents the self-weight load of the tunnel segments. R The radius at the center of the segment thickness is [missing information]. Specify the angle between the tunnel's location and the vertical axis. P h For formation resistance; The structural axial force caused by the loads around the tunnel is expressed as follows: The structural shear force caused by the loads around the tunnel is expressed as follows: 。 2. The method for calculating the internal forces of a symmetrical shield tunnel structure based on a physical model as described in claim 1, characterized in that, In S2, the structural deformation values ​​detected in the field are calculated. The specific expression is: . In the formula, and These are the x-coordinate and y-coordinate of the tunnel structure, respectively. and These are the abscissa and ordinate of the tunnel structure after deformation, respectively; In the formula, The angle of inclination of the ellipse. and These are the fitted values ​​for the three-dimensional laser scanning data.

3. The method for calculating the internal forces of a symmetrical shield tunnel structure based on a physical model as described in claim 2, characterized in that, In S4, the loads around the tunnel include the earth pressure above the tunnel, the reaction force of the soil below the tunnel, the lateral earth pressure, the self-weight load of the tunnel segments, and the ground reaction force caused by the compression of the tunnel structure. Ground reaction force caused by tunnel structure compression The specific expression is: In the formula, K s This is the formation resistance coefficient. This refers to the horizontal displacement of the tunnel arch. Segment self-weight load P The expression for 5 is as follows: In the formula, The weight of the concrete. B For the width of the tunnel segments, h The thickness of the joint contact surface; reaction force of the soil beneath the tunnel P The expression for 2 is as follows: Lateral earth pressure includes the first lateral pressure. P 3 and second lateral pressure P 4; In the formula, The lateral pressure coefficient of the soil; In the formula, The weight of the soil.

4. The method for calculating the internal forces of a symmetrical shield tunnel structure based on a physical model as described in claim 3, characterized in that, In S4, the tunnel structure is Deformation at the location The specific expression is: In the formula, For the load around the tunnel, , The displacement coefficient matrix of the tunnel structure. .

5. The method for calculating the internal forces of a symmetrical shield tunnel structure based on a physical model as described in claim 4, characterized in that, In S7, the specific method for calculating the bending moment stiffness of the new joint is as follows: (1) Bending moment stiffness of the joint under positive bending moment: 1) Under the stress state of joint closure, the specific expression for calculating the bending moment stiffness of the joint is as follows: In the formula, For the first i Total bending moment at each joint and These are the compression displacements of the inner and outer edges of the joint, respectively. In the formula, and The compressive strain is measured on the outer and inner arc sides of the joint. A coefficient between 0.55 and 0.7; 2) Under the stress state of joint opening but bolts still being compressed, the specific expression for calculating the bending moment stiffness of the joint is as follows: In the formula, y The height of the compression zone of the joint concrete. This refers to the compression displacement of the outer edge when the seam opens. , This represents the compressive strain of the concrete. 3) Under the condition of joint opening and bolts under tension, the specific expression for calculating the bending moment stiffness of the joint is as follows: In the formula, This represents the elongation of the bolt. This refers to the compression displacement of the outer edge when the seam opens. This 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 a plastic state. The specific expression for calculating the bending moment stiffness of the joint is as follows: In the formula, The height of the plastic zone of concrete. For bolt length, For the tensile strain of the bolt, This is the distance between the bolt and the outer edge of the joint; (8) Bending moment stiffness of the joint under negative bending moment: Let the distance between the bolt and the outer edge of the joint be . The expression for the bending moment stiffness of the joint Replace with , Taking the absolute value, we obtain the formula for calculating the moment stiffness of the joint under negative bending moment.

Images