A simplified calculation method and system for shear force and opening of immersed tube tunnel segment joints

Abstract

The present invention discloses a simplified calculation method and system for the shear force and opening of segment joints in immersed tube tunnels. The method comprises: determining basic assumptions; then setting the relative axial and vertical deformations and relative rotation angles at the neutral axis of the joint, and clarifying the calculation method for the deformation of the concrete end spring, Ω waterstop, and shear key; then performing force analysis on the concrete per unit area of ​​the end face, the shear key, etc., deriving force formulas, and clarifying the expressions and force mechanisms for the axial force, shear force, and bending moment; considering the extreme conditions of overall heating and cooling, deriving the heating using an elastic foundation beam model and treating the cooling as an articulated joint, and simulating using three-dimensional finite element software; finally, determining the influencing factors and assumptions based on longitudinal three-dimensional model parameter analysis, establishing and deriving a simplified theoretical calculation model, and verifying the formula by comparing the results of the three-dimensional calculation model. This method achieves efficient and accurate calculation of the shear force and opening of segment joints.

Description

Technical Field

[0001] The present invention relates to the technical field of immersed tube tunnel engineering, and in particular to a simplified calculation method and system for shear force and opening amount of segment joints in an immersed tube tunnel. Background Art

[0002] In the current technical system of immersed tube tunnel engineering, there are two major categories: longitudinal integral pipe segment structures and longitudinal segmental pipe segment structures. The stress and deformation of the segment joints of the segmental pipe segment are complex. The main focus in engineering is the shear force and opening of the segment joints. The relevant calculations in the design work mainly rely on traditional mechanical models and numerical simulation methods. Although traditional mechanical models have a certain theoretical basis, when faced with complex actual working conditions, they are often difficult to accurately reflect the actual stress state of the segment joints due to over-simplification. Numerical simulation methods, such as finite element analysis, can accurately simulate structural behavior to a certain extent, but they require a large amount of computing resources, tedious model construction, parameter setting and long-term calculations. For example, constructing a detailed finite element model of the segment joints of a medium-sized immersed tube tunnel often takes hours or even days to complete a complete calculation, and the performance requirements of the computing equipment are extremely high.

[0003] At present, the core problems faced by the calculation of segment joints in immersed tube tunnels are prominent. On the one hand, the complex factors in actual engineering are difficult to be fully considered in the existing calculation methods. The unevenness of foundation conditions leads to significant differences in foundation stiffness in different areas, making the distribution of reaction forces acting on segment joints extremely complex and difficult to accurately grasp. At the same time, the inevitable errors in the construction process, as well as the dynamic changes in traffic loads and large fluctuations in ambient temperature during operation, all have a superimposed impact on the stress state of the segment joints, further increasing the difficulty and uncertainty of the calculation. On the other hand, the high complexity and low efficiency of existing calculation methods cannot meet the needs of engineering practice for fast and accurate acquisition of the mechanical parameters of segment joints. The cumbersome calculation process not only consumes a lot of time and manpower costs, but also easily introduces human errors in the calculation process, affecting the reliability of the calculation results.

[0004] In summary, there is an urgent need to develop a new system for calculating the shear force and opening of immersed tube tunnel segment joints. This system must comprehensively account for all influencing factors, from complex geological conditions to changing environmental factors. Furthermore, by leveraging innovative theoretical derivations and rational assumptions, it can eliminate the complexity and redundancy of traditional methods and achieve efficient and accurate calculations. This will provide solid, powerful, and practical technical support for immersed tube tunnel projects, lay a solid foundation for tunnel design and construction, and help improve the overall construction quality and safety of immersed tube tunnel projects. Summary of the Invention

[0005] Based on this, the present invention aims to provide a simplified calculation method and system for the shear force and opening of segment joints in immersed tube tunnels. Through innovative theoretical derivation and reasonable assumptions, it fully considers the complex factors in actual engineering, abandons the excessive complexity of traditional methods, and achieves efficient and accurate calculation of the internal forces and related parameters of segment joints. The present invention is expected to significantly shorten calculation time and reduce calculation costs, provide reliable and convenient technical support for the design and construction of immersed tube tunnels, and effectively improve the construction quality and safety of immersed tube tunnel projects.

[0006] In response to the above-mentioned deficiencies or improvement needs of the prior art, as a first aspect of the present invention, the present invention provides a simplified calculation method for shear force and opening of immersed tube tunnel segment joints, comprising:

[0007] S1. Determine the basic assumptions;

[0008] S2. Set the relative axial and vertical deformations and relative rotation angles at the neutral axis of the joint to determine the deformation of the concrete end springs, Ω waterstops, and shear keys on the joint;

[0009] S3. Conduct stress analysis on the concrete per unit area of ​​the end face, the shear key, the Ω waterstop, and the entire joint, derive the corresponding stress formulas, and clarify the expressions and stress mechanisms of the joint axial force, shear force, and bending moment.

[0010] S4. Consider two extreme operating conditions: overall heating and overall cooling, and analyze their stress patterns. When heating, treat the joint as a submerged tube cross-section using an elastic foundation beam model. When cooling, treat it as an articulated joint. Use 3D finite element software to simulate the stress behavior of the joint.

[0011] S5. Determine the main influencing factors corresponding to shear force and opening through the results of the relevant parameter analysis of the longitudinal three-dimensional model, and determine their corresponding assumptions. Then, establish a simplified theoretical calculation model for shear force and a simplified theoretical calculation model for opening and complete the derivation. Finally, verify the theoretical formula by comparing the results of the three-dimensional calculation model.

[0012] Furthermore, the basic assumptions in S1 are:

[0013] Assuming that the relative displacement and relative rotation of the joint are small, the concrete at the joint end surface conforms to the plane section assumption;

[0014] The structural design between the shear key tenon and the groove can ensure that the vertical shear key is always in a single-sided contact state when subjected to vertical force. When subjected to axial force, the vertical shear key does not transmit axial force;

[0015] It is assumed that the thickness variation of the asphalt cushion layer set between the upper and lower end faces of the shear key tenon and the groove is only caused by uneven foundation stiffness or load variation;

[0016] It is assumed that after hydraulic compression, the concrete end faces except the shear key area are in close contact and can transmit the axial force;

[0017] It is assumed that the axial force between the end concrete surfaces can cause a certain shear force due to the friction coefficient. When this shear force serves as a safety reserve, the friction coefficient is taken as 0.

[0018] Furthermore, the deformation of the concrete end spring, Ω waterstop and shear key on the joint in S2 is calculated as follows:

[0019] Assume that the relative axial deformation of the two end faces at the neutral axis of the joint is , the relative vertical deformation is , the relative rotation angle of the joint is , then the deformation of the concrete end spring, Ω water stop and shear key on the joint can be written as:

[0020]

[0021] Where, Indicates the axial deformation of the concrete end spring; Indicates the axial deformation of the Ω waterstop; represents the axial deformation of the shear key; Indicates the vertical deformation of the concrete end spring; Indicates the vertical deformation of the Ω waterstop; represents the vertical deformation of the shear key; It represents the distance from the neutral axis of the joint to the spring action point on the concrete end face; Indicates the distance from the neutral axis of the joint to the action point of the Ω waterstop; Represents the distance from the neutral axis of the joint to the shear key application point.

[0022] Furthermore, when the temperature rises in S4, the joint is regarded as a submerged tube cross section and the elastic foundation beam model is used for derivation. The specific process is as follows:

[0023] Under the overall temperature rising condition, the entire section of the joint is subjected to axial pressure. :

[0024]

[0025] Where, It represents the axial force of the joint, which is the internal force borne by the entire joint in the axial direction; It represents the axial force per unit area on the concrete end surface; Indicates that the joint is subjected to vertical shear force. Indicates that the joint is subjected to bending moment; Indicates the joint height; Indicates the width of the joint; represents the number of shear keys; It represents the force corresponding to the unit relative compression per unit area on the shear key concrete contact surface; Indicates the calculated transverse width of the shear key; represents the vertical deformation of the i-th shear key; Indicates the maximum longitudinal length of the shear key, which is a specific value; It represents the longitudinal length variable of shear key calculation; Indicates the compression of the asphalt layer; Indicates the effective height of the bending section of the joint;

[0026] In this load mode, the axial force It consists of two parts. One part is the axial force formed by the axial stress caused by hydraulic pressure connection and overall temperature rise. The other part is the axial force caused by the bending stress caused by uneven load and uneven foundation stiffness changes. ;

[0027] Shear force of joint It is also caused by two parts, one of which is The shear force caused by Shear force caused by

[0028] Under this stress mode, the joint can transmit axial force, shear force, and bending moment. The vertical displacement and rotation angle of the joint position are approximately continuous. The segment joint can be approximately regarded as a submerged tube section. In the process of multi-segment analysis, the elastic foundation beam model can be used for deduction to obtain the shear force and bending moment at the joint position, and the stiffness influence line can be used to derive the differential settlement control standard.

[0029] Furthermore, when cooling in S4, it is treated as an articulated joint, and the specific process is as follows:

[0030] Under overall cooling conditions, the entire joint section is disengaged and the axial force is zero:

[0031]

[0032] In this load mode, the bending moment of the joint is caused by the shear force multiplied by the length of the shear key. The bending moment value is very small and is too simple to be ignored.

[0033] In this way, the joint forms a force mode that only transmits shear force but not bending moment, with approximately continuous displacement but discontinuous rotation, and is treated as a hinged joint.

[0034] Furthermore, the specific derivation process of the simplified theoretical calculation model of shear force in S5 is as follows:

[0035] Based on theoretical analysis and combined with the research results of shear sensitivity analysis of segment joints in the longitudinal three-dimensional model, the main influencing factors are determined. The main influencing factors include: pipe top load P, segment length L, foundation stiffness ki, and elastic cushion stiffness k;

[0036] Establish basic assumptions for simplified shear forces at segmental joints;

[0037] Based on basic assumptions, the following equation is established:

[0038]

[0039] Solving the equation yields:

[0040]

[0041] If there is no cushion between the shear keys, , substituting it into the formula, we can get

[0042]

[0043] Where, Indicates the longitudinal distribution of load; represents the segment joint shear force; Indicates segment length; 、 Indicates foundation stiffness; Indicates the elastic cushion stiffness; 、 Indicates the vertical displacement of the segment.

[0044] Furthermore, the basic assumptions for the simplified shear force of the segment joints are as follows:

[0045] Without considering the load difference between adjacent segments, the longitudinal non-uniform load on the pipe top is uniformly distributed. The pipe top load is uniformly distributed, and the pipe top load is calculated as P and the segment length is L.

[0046] The longitudinal non-uniform foundation stiffness of the segment pipe bottom is processed by integral equivalent homogenization. Each segment has longitudinal uniform foundation stiffness, and the foundation stiffness of adjacent segments is calculated as follows: 、 Alternate appearance;

[0047] Since the foundation stiffness of adjacent segments is 、 They appear alternately, so the shear force transmitted by each joint shear key is equal, which is assumed to be Q;

[0048] Since the load and stiffness of a single segment are uniform, and the shear force transmitted by the shear key is also symmetrical, the settlement of the segment is also uniform; Settlement corresponding to stiffness , Settlement corresponding to stiffness ;

[0049] The stiffness of the flexible pad set by the shear key is , under the action of shear force Q of shear key, the displacement is ;

[0050] Since the model is only subjected to vertical loads and the influence of geometric nonlinearity is not considered, the axial force of the pipe section is zero.

[0051] Furthermore, the specific derivation process of the simplified theoretical calculation model of the opening amount in S5 is as follows:

[0052] Combined with the results of the sensitivity analysis of the longitudinal three-dimensional model segment joint opening, the main influencing factors are determined. The main influencing factors include: pipe top load P, segment length L, foundation stiffness k i , the friction coefficient f between the formation and the structure, and the temperature rise and fall ΔT of the system;

[0053] Establish basic assumptions:

[0054] Considering the difference in load at both ends of the segment in the longitudinal direction, it is assumed that the load changes linearly along the longitudinal direction;

[0055] Considering the difference in foundation stiffness at both ends of the segment longitudinally, it is assumed to change linearly along the longitudinal direction;

[0056] Under the cooling condition, the segment joints have a tendency to come apart. It is assumed that the longitudinal axial force is zero under this condition.

[0057] According to the analysis, the segment joint opening is mainly affected by uneven load, uneven foundation stiffness, system temperature change and ground friction. The segment joint opening caused by uneven load and uneven foundation stiffness is obtained through theoretical deduction. The influence of system temperature change and ground friction on the segment joint opening is determined based on the calculation results of the longitudinal three-dimensional model.

[0058]

[0059] Where: δ represents the total opening of the segment joint;

[0060] δ1 represents the opening of segment joints caused by uneven load and uneven foundation stiffness;

[0061] δ2 represents the opening of segment joints caused by system temperature change and formation friction effect;

[0062] The force diagram of the segment joint calculated by δ1 theory is established, and the calculation equation is obtained according to the force diagram:

[0063]

[0064] Calculated:

[0065]

[0066] According to the research results of sensitivity analysis of segment joint opening of longitudinal three-dimensional model, we can get:

[0067]

[0068] ΔT=ΔT1+ΔT2

[0069] Further, we get:

[0070]

[0071] Where, , represents the equivalent distributed load at the ends of the two segments, assuming that the load varies linearly along the longitudinal direction of the pipe segment; ΔT represents the system temperature drop; ΔT1 represents the equivalent temperature drop due to concrete shrinkage and creep; ΔT2 represents the maximum temperature difference between the operation period and the precast period.

[0072] As a second aspect of the present invention, a simplified calculation system for shear force and opening of immersed tunnel segment joints is provided, comprising:

[0073] A basic assumption determination unit, used for determining basic assumptions;

[0074] The deformation calculation unit is used to set the relative axial and vertical deformations and relative rotation angles at the neutral axis of the joint, and to determine the calculation method for the deformations of the concrete end springs, Ω waterstops, and shear keys on the joint;

[0075] The force mode analysis unit is used to analyze the force of the end surface unit area concrete, shear key, Ω water stop, and joint as a whole, derive the corresponding force formula, and clarify the expressions and force mechanism of the joint axial force, shear force and bending moment;

[0076] The extreme working condition analysis unit is used to consider two extreme working conditions: overall heating and overall cooling, and analyze their stress modes respectively. When heating, the joint is treated as a submerged tube cross-section and derived using the elastic foundation beam model. When cooling, it is treated as an articulated joint. 3D finite element software is used to simulate the stress characteristics of the joint.

[0077] The parameter simplification calculation and verification unit is used to determine the main influencing factors corresponding to shear force and opening through the analysis results of relevant parameters of the longitudinal three-dimensional model, and determine their corresponding assumptions. It then establishes a simplified theoretical calculation model for shear force and a simplified theoretical calculation model for opening and completes the derivation. Finally, it verifies the theoretical formula by comparing the results of the three-dimensional calculation model.

[0078] As a third aspect of the present invention, a computer-readable storage medium is further provided, on which a computer program is stored, and the computer program is used by a processor to execute any step of the simplified calculation method for shear force and opening amount of immersed tube tunnel segment joints.

[0079] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0080] 1. The simplified calculation method for shear force and opening of immersed tunnel segment joints proposed in this invention effectively simplifies complex actual engineering situations by establishing scientifically sound basic assumptions, providing a clear theoretical framework for subsequent calculations. Simultaneously, the relative axial and vertical deformations and relative rotational angles at the joint's neutral axis are precisely set, accurately determining the deformation calculation method for the concrete end springs, Ω waterstops, and shear keys at the joint. Furthermore, force analysis is performed on the concrete per unit area of ​​the end face, the shear keys, and other components, resulting in precise force formulas. This clearly defines the expressions and force mechanisms for the joint's axial force, shear force, and bending moment, laying a solid foundation for accurate calculations.

[0081] 2. The present invention provides a simplified calculation method for the shear force and opening of immersed tunnel segment joints. By considering two extreme operating conditions: overall heating and overall cooling, targeted force mode analysis is employed. During heating, the joint is treated as an immersed tunnel cross-section, and the elastic foundation beam model is used for derivation. During cooling, the joint is treated as an articulated joint, and three-dimensional finite element software is used to simulate the joint's force behavior. This comprehensive and scientific analysis method fully considers a variety of practical scenarios, enabling the calculation results to more realistically reflect the joint's mechanical properties under different environments.

[0082] 3. This simplified calculation method for shear force and opening at immersed tube tunnel segment joints uses a longitudinal three-dimensional model to analyze relevant parameters, accurately identifying the primary influencing factors for different parameters and determining corresponding assumptions. Based on this, a simplified theoretical calculation model is established and deduced, and the theoretical formula is finally verified by comparing it with the results of the three-dimensional calculation model. This method greatly simplifies the calculation process and significantly improves efficiency while ensuring accuracy, providing efficient and reliable technical support for the design and construction of immersed tube tunnel projects. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 This is a flow chart of a simplified calculation method for shear force and opening amount of immersed tube tunnel segment joints according to an embodiment of the present invention;

[0084] Figure 2 Schematic diagram of load and foundation support of a segmental immersed tube tunnel according to an embodiment of the present invention;

[0085] Figure 3A simplified diagram of the force mode of a joint according to an embodiment of the present invention;

[0086] Figure 4 Schematic diagram of the relative displacement and relative rotation angle on the neutral axis of the joint according to an embodiment of the present invention;

[0087] Figure 5 Schematic diagram of the force and deformation of the shear key contact surface according to an embodiment of the present invention;

[0088] Figure 6 This is a simplified diagram of the joint model of the embodiment of the present invention with overall temperature rise and without considering the end surface friction coefficient (intended to be simplified as a rigidly connected elastic foundation beam);

[0089] Figure 7 A simplified diagram of a joint model for overall cooling without considering the end surface friction coefficient in an embodiment of the present invention (intended to be simplified as a hinged elastic foundation beam);

[0090] Figure 8 This is a force diagram of a simplified calculation model without considering the joint opening according to an embodiment of the present invention;

[0091] Figure 9 This is a schematic diagram of the structure of two adjacent segments separated according to an embodiment of the present invention;

[0092] Figure 10 A schematic diagram comparing the simplified calculation method for segmental joint shear force according to an embodiment of the present invention and the calculation results of the longitudinal three-dimensional model;

[0093] Figure 11 This is a schematic diagram of verifying the simplified calculation formula using indoor model test data according to an embodiment of the present invention;

[0094] Figure 12 Schematic diagram of calculating the segment joint opening amount according to an embodiment of the present invention;

[0095] Figure 13 A schematic diagram comparing the simplified calculation method of an embodiment of the present invention and the calculation of segment joint opening using a longitudinal three-dimensional model;

[0096] Figure 14 This is a unit diagram of a simplified calculation system for shear force and opening of immersed tube tunnel segment joints according to an embodiment of the present invention. DETAILED DESCRIPTION

[0097] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only intended to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0098] Example 1

[0099] Please refer to Figure 1 This embodiment 1 provides a simplified calculation method for shear force and opening of immersed tube tunnel segment joints, comprising the following steps:

[0100] S1. Determine the basic assumptions;

[0101] S2. Set the relative axial and vertical deformations and relative rotation angles at the neutral axis of the joint to determine the calculation method for the deformation of the concrete end springs, Ω waterstops, and shear keys on the joint;

[0102] S3. Conduct stress analysis on the concrete per unit area of ​​the end face, the shear key, the Ω waterstop, and the entire joint, derive the corresponding stress formulas, and clarify the expressions and stress mechanisms of the joint axial force, shear force, and bending moment.

[0103] S4. Consider two extreme operating conditions: overall heating and overall cooling, and analyze their stress patterns. When heating, treat the joint as a submerged tube cross-section using an elastic foundation beam model. When cooling, treat it as an articulated joint. Use 3D finite element software to simulate the stress behavior of the joint.

[0104] S5. Determine the main influencing factors corresponding to shear force and opening through the results of the relevant parameter analysis of the longitudinal three-dimensional model, and determine their corresponding assumptions. Then, establish a simplified theoretical calculation model for shear force and a simplified theoretical calculation model for opening and complete the derivation. Finally, verify the theoretical formula by comparing the results of the three-dimensional calculation model.

[0105] The following embodiment 1 specifically describes the steps of the present invention.

[0106] (1) Derivation of calculation formula of internal force of joint based on segment joint rotation stiffness

[0107] 1.1 Basic Assumptions

[0108] Assuming that the relative displacement and relative rotation of the joint are small, the concrete at the joint end surface conforms to the plane section assumption;

[0109] The structural design between the shear key tenon and the groove can ensure that the vertical shear key is always in a single-sided contact state when subjected to vertical force. When subjected to axial force, the vertical shear key does not transmit axial force;

[0110] It is assumed that the thickness variation of the asphalt cushion layer set between the upper and lower end faces of the shear key tenon and the groove is only caused by uneven foundation stiffness or load variation;

[0111] It is assumed that after hydraulic compression, the concrete end faces except the shear key area are in close contact and can transmit the axial force;

[0112] It is assumed that the axial force between the end concrete surfaces can cause a certain shear force due to the friction coefficient. When this shear force serves as a safety reserve, the friction coefficient is taken as 0.

[0113] 1.2 Derivation process of segment joint stress mode

[0114] Please refer to Figure 2-Figure 4 , assuming that the relative axial deformation of the two end faces at the neutral axis of the joint is (relative compression is positive), and the relative vertical deformation is (positive when relatively close), the relative rotation angle of the joint is (Counterclockwise rotation is positive), then Figure 3 The deformation of the concrete end spring, Ω waterstop and shear key at the joint shown can be expressed as:

[0115] ,

[0116] Where, Indicates the axial deformation of the concrete end spring; Indicates the axial deformation of the Ω waterstop; represents the axial deformation of the shear key; Indicates the vertical deformation of the concrete end spring; Indicates the vertical deformation of the Ω waterstop; represents the vertical deformation of the shear key; It represents the distance from the neutral axis of the joint to the spring action point on the concrete end face; Indicates the distance from the neutral axis of the joint to the action point of the Ω waterstop; Represents the distance from the neutral axis of the joint to the shear key application point.

[0117] 1.3 Force analysis of the concrete contact surface per unit area of ​​the end face

[0118] A compression-only spring that can only be compressed but not stretched is used for simulation. The formula for calculating the axial force of concrete per unit area on the end face is:

[0119]

[0120] Where, is the compressive stiffness per unit area of ​​the concrete end surface, The compression per unit area of ​​the concrete end surface, unit: m; It is the axial force per unit area of ​​the concrete end surface caused by the initial hydraulic pressure connection and the overall temperature drop;

[0121]

[0122] It is the value of overall temperature reduction, unit: °C, the value is positive if the temperature drops, and negative if the temperature rises; is the length of the immersed tube tunnel segment.

[0123]

[0124] when hour, .

[0125] 1.4 Force analysis of a joint shear key

[0126] Please refer to Figure 5 The concrete shear key is simulated as a spring that does not bear axial force in the axial direction and is supported vertically by a spring. Relative vertical displacement threshold The system composed of. The unit is kN / m, is the compression of the asphalt layer, , In fact, it is also composed of many small springs composition, The force corresponding to the unit relative compression per unit area on the shear key concrete contact surface, in kN / m 3 .

[0127] when When , the stress on the shear key is:

[0128]

[0129] when When , the stress on the shear key is:

[0130]

[0131] 1.5 Stress analysis of Ω waterstop

[0132] If the stiffness contribution of the Ω waterstop is considered, the corresponding calculation formula can also be derived. However, since the contribution of the Ω waterstop to the joint stiffness is limited, the beneficial effect of the Ω waterstop is not considered in the simplified calculation, and the derivation process is on the safe side.

[0133] 1.6 Stress analysis of the joint as a whole

[0134] Combining the forces on the concrete end face and shear key within the range of joint width (-B / 2 to B / 2) and joint height (-H / 2 to H / 2) yields:

[0135] when When , the stress condition of the joint is:

[0136]

[0137] when When , the stress condition of the joint is:

[0138]

[0139] The above two formulas are expressions of the joint axial force, shear force and bending moment, reflecting the force mechanism of the joint.

[0140] The axial force N of the joint is mainly composed of the initial hydraulic pressure force and the axial force caused by the overall temperature rise or fall of the structure. The distribution of the axial force on the end face is affected by the relative rotation angle of the joint. The impact of the corner When the angle is small, the entire end face bears axial pressure. As the force gradually increases, one end of the joint section will be disengaged while the other end will be further compressed, resulting in an asymmetric axial force distribution. When the overall cooling condition occurs, the axial force of the entire section becomes zero.

[0141] In addition, the friction coefficient of the joint end faces significantly affects the distribution pattern of joint shear forces. When considering the shear force caused by the axial force, the shear force caused by the end face axial force is also large due to the large axial force, while the shear force of the shear key is small. In this derivation, the joint shear force caused by the axial force is not considered for the time being, and the influence of the friction coefficient is not considered, and it is used as a safety reserve.

[0142] 1.7 Simplification and application of segment joint stress mode

[0143] Consider two extreme load cases:

[0144] Under the overall temperature rising condition, the entire section of the joint is subjected to axial pressure. :

[0145]

[0146] Where, It represents the axial force of the joint, which is the internal force borne by the entire joint in the axial direction; It represents the axial force per unit area on the concrete end surface; Indicates that the joint is subjected to vertical shear force. Indicates that the joint is subjected to bending moment; Indicates the joint height; Indicates the width of the joint; represents the number of shear keys; It represents the force corresponding to the unit relative compression per unit area on the shear key concrete contact surface; Indicates the calculated transverse width of the shear key; represents the vertical deformation of the i-th shear key; Indicates the maximum longitudinal length of the shear key, which is a specific value; It represents the longitudinal length variable of shear key calculation; Indicates the compression of the asphalt layer; Indicates the effective height of the bending section of the joint;

[0147] In this load mode, the axial force It can be considered to be composed of two parts. One part is the axial force formed by the axial stress caused by hydraulic pressure connection and overall temperature rise. The other part is the axial force caused by the bending stress caused by uneven load and uneven foundation stiffness changes. . Shear force of the joint It is also caused by two parts, one of which is Part of the shear force caused by the vertical relative displacement of the joint due to direct shear is (Vertical relative displacement caused by bending) caused by shear force.

[0148] Please refer to Figure 6 Under this load mode, the joint can transmit axial force, shear force, and bending moment. The vertical displacement at the joint is approximately continuous, and the angular displacement is continuous (because it is not open). The segmental joint can be approximately considered as a submerged tube section. During multi-segment analysis, the elastic foundation beam model can be used to derive the shear force and bending moment at the joint location, and the stiffness influence line can be used to derive the differential settlement control standard. Unlike rigid joints, the allowable displacement difference between the shear key tenon and the slot can be superimposed on the analysis of the rigidly connected elastic foundation beam as an approximate consideration.

[0149] Under overall cooling conditions, the entire joint section is disengaged and the axial force is zero:

[0150]

[0151] In this load mode, the bending moment of the joint is caused by the shear force multiplied by the length of the shear key. The value of this bending moment is very small and can be approximately ignored for simple considerations.

[0152] Please refer to Figure 7 This joint forms a load pattern that transmits only shear forces but not bending moments, with approximately continuous displacement but discontinuous rotation, and can be treated as a hinged joint. Unlike a hinged joint, the allowable displacement difference between the shear key tenon and slot can be added to the analysis of the hinged elastic foundation beam as an approximation.

[0153] From a precision perspective, it is advisable to place the above-mentioned joint stress mode into three-dimensional finite element software, so that the stress characteristics of the joint can be fully simulated.

[0154] (2) Simplified calculation method of segmental joint shear force

[0155] 2.1 Research ideas

[0156] Based on theoretical analysis and combined with the research results of shear sensitivity analysis of segmental joints in longitudinal three-dimensional models, the main influencing factors were determined;

[0157] Reasonably determine the assumed conditions and perform mathematical processing on some influencing factors to simplify the calculation;

[0158] Establish theoretical calculation models and complete theoretical derivation;

[0159] The theoretical formula is compared and verified using the results of a three-dimensional calculation model;

[0160] 2.2 Theoretical derivation

[0161] Determination of the main influencing factors: pipe top load P, segment length L, foundation stiffness k i , elastic cushion stiffness k. Please refer to Figure 8 , the basic assumptions are as follows:

[0162] Without considering the load difference between adjacent segments, the longitudinal non-uniform load on the pipe top is uniformly distributed. The pipe top load is uniformly distributed, and the pipe top load is calculated as P and the segment length is L.

[0163] The longitudinal non-uniform foundation stiffness of the segment pipe bottom is processed by integral equivalent homogenization. Each segment has longitudinal uniform foundation stiffness, and the foundation stiffness of adjacent segments is calculated as follows: 、 Alternate appearance;

[0164] Since the foundation stiffness of adjacent segments is 、 They appear alternately, so the shear force transmitted by each joint shear key is equal, which is assumed to be Q;

[0165] Since the load and stiffness of a single segment are uniform, and the shear force transmitted by the shear key is also symmetrical, the settlement of the segment is also uniform; Settlement corresponding to stiffness , Settlement corresponding to stiffness ;

[0166] The stiffness of the flexible pad set by the shear key is , under the action of shear force Q of shear key, the displacement is ;

[0167] Since the model is only subjected to vertical loads and the influence of geometric nonlinearity is not considered, the axial force of the pipe section is zero.

[0168] Please refer to Figure 9 Separate two adjacent segment structures;

[0169] Therefore, the following equation can be established:

[0170]

[0171] Solving the equation yields:

[0172]

[0173] If there is no cushion between the shear keys, , substituting it into the formula, we can get

[0174]

[0175] Where, Indicates the longitudinal distribution of load; represents the segment joint shear force; Indicates segment length; 、 Indicates foundation stiffness; Indicates the elastic cushion stiffness; 、 Indicates the vertical displacement of the segment.

[0176] 2.3 Simplified calculation formula verification

[0177] Please refer to Figure 10 According to the longitudinal load distribution of the entire section of the immersed tube tunnel of the Hong Kong-Zhuhai-Macao Bridge and the foundation stiffness distribution, the shear force of the segment joints was compared using a three-dimensional full longitudinal model and a simplified calculation formula. The comparative calculation results are shown in Figure 10 ;

[0178] By comparison, it can be seen that the simplified calculation method is in good agreement with the three-dimensional calculation. This working condition can take into account the differences in foundation stiffness of adjacent segments and can reflect the areas with sharp changes in longitudinal foundation stiffness to a relatively large extent, thus ensuring the engineering practicality of the simplified calculation results.

[0179] Please refer to Figure 11 At the same time, the simplified calculation formula was verified using indoor test data, and the results are as follows. It can be seen from the figure that the shear force of the segment joint and the differential settlement basically show a positive correlation. The indoor model test results are in good agreement with the simplified calculation formula and three-dimensional calculation results. It should be noted that the differential settlement of the indoor test is the forced displacement differential settlement value at the segment joint, and the differential settlement of the simplified formula and three-dimensional calculation results is the differential settlement value calculated by vertical load and the corresponding foundation stiffness of the segment. The comparative data is limited, and the conclusion is not universal, but the overall trend is in good agreement.

[0180] (3) Simplified calculation method of segmental joint shear force

[0181] 3.1 Research ideas

[0182] Based on theoretical analysis and combined with the results of sensitivity analysis of segmental joint opening of longitudinal three-dimensional model, the main influencing factors were determined;

[0183] Reasonably determine the assumptions and mathematically simplify some influencing factors;

[0184] The combined effects of formation friction and temperature on segment joint opening are determined based on the results of longitudinal model sensitivity analysis.

[0185] Establish theoretical calculation models and complete theoretical derivation;

[0186] The theoretical formula is compared and verified using the results of a three-dimensional calculation model;

[0187] 3.2 Theoretical derivation

[0188] Determination of the main influencing factors: pipe top load P, segment length L, foundation stiffness k i , formation and structure friction coefficient f, system temperature rise and fall ΔT.

[0189] The basic assumptions are as follows:

[0190] The difference in load at both ends of the segment in the longitudinal direction is considered, but it is assumed to vary linearly along the longitudinal direction;

[0191] The difference in foundation stiffness at both ends of the segment is considered, but it is assumed to vary linearly along the longitudinal direction;

[0192] The segment joint opening is more unfavorable under the cooling condition. Assuming that the segment joint has a tendency to disengage under this condition, the longitudinal axial force is zero;

[0193] 3.3 Analysis process

[0194] According to the analysis, the segment joint opening is mainly affected by uneven load, uneven foundation stiffness, system temperature change and formation friction effect. The segment joint opening caused by uneven load and uneven foundation stiffness is obtained through theoretical deduction, and the influence of system temperature change and formation friction on the segment joint opening is determined based on the calculation results of the longitudinal three-dimensional model.

[0195]

[0196] Where: δ represents the total opening of the segment joint;

[0197] δ1 represents the opening of segment joints caused by uneven load and uneven foundation stiffness;

[0198] δ2 represents the opening of segment joints caused by system temperature change and formation friction effect;

[0199] Please refer to Figure 12 , establish the segment joint force diagram of δ1 theoretical calculation, and obtain the calculation equation according to the force diagram:

[0200]

[0201] Calculated:

[0202]

[0203] According to the research results of sensitivity analysis of segment joint opening of longitudinal three-dimensional model, we can get:

[0204]

[0205] ΔT=ΔT1+ΔT2

[0206] Further, we get:

[0207]

[0208] Where, , represents the equivalent distributed load at the ends of the two segments, assuming that the load varies linearly along the longitudinal direction of the pipe segment; ΔT represents the system temperature drop; ΔT1 represents the equivalent temperature drop due to concrete shrinkage and creep; ΔT2 represents the maximum temperature difference between the operation period and the precast period.

[0209] 3.4 Simplified calculation formula verification

[0210] According to the longitudinal load distribution and foundation stiffness distribution of the entire immersed tube tunnel of the Hong Kong-Zhuhai-Macao Bridge, and considering the cooling condition, a three-dimensional full longitudinal model and a simplified calculation formula were used to compare the segment joint opening.

[0211] Where: ΔT1=4.65℃, ΔT2=15℃ (cooling), the calculation results refer to Figure 13 .

[0212] Taking the pipe segments of the natural foundation section, excluding the segment joints with zero opening calculated by the longitudinal three-dimensional model, the simplified calculation formula for the segment joint opening was compared with the numerical calculation results of the longitudinal model. According to the comparative calculation, it can be seen that the simplified calculation method has basically the same trend as the calculation results of the longitudinal three-dimensional model, has good adaptability in the natural foundation section (E7~E25), and can be used for engineering estimation.

[0213] Example 2

[0214] Referring to FIG. 14 , this embodiment 2 provides a simplified calculation system for shear force and opening of immersed tunnel segment joints, including:

[0215] A basic assumption determination unit, used for determining basic assumptions;

[0216] The deformation calculation unit is used to set the relative axial and vertical deformations and relative rotation angles at the neutral axis of the joint, and to determine the calculation method for the deformations of the concrete end springs, Ω waterstops, and shear keys on the joint;

[0217] The force mode analysis unit is used to analyze the force of the end surface unit area concrete, shear key, Ω water stop, and joint as a whole, derive the corresponding force formula, and clarify the expressions and force mechanism of the joint axial force, shear force and bending moment;

[0218] The extreme working condition analysis unit is used to consider two extreme working conditions: overall heating and overall cooling, and analyze their stress modes respectively. When heating, the joint is treated as a submerged tube cross-section and derived using the elastic foundation beam model. When cooling, it is treated as an articulated joint. 3D finite element software is used to simulate the stress characteristics of the joint.

[0219] The parameter simplification calculation and verification unit is used to determine the main influencing factors corresponding to shear force and opening through the analysis results of relevant parameters of the longitudinal three-dimensional model, and determine their corresponding assumptions. It then establishes a simplified theoretical calculation model for shear force and a simplified theoretical calculation model for opening and completes the derivation. Finally, it verifies the theoretical formula by comparing the results of the three-dimensional calculation model.

[0220] Example 3

[0221] This embodiment 3 further provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, any step of the simplified calculation method for shear force and opening of immersed tunnel segment joints can be implemented.

[0222] The computer-readable storage medium may include: a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, etc., which can store program codes.

[0223] For an introduction to the computer-readable storage medium provided in this application, please refer to the above method embodiment, and this application will not go into details here.

[0224] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A simplified calculation method for shear force and opening of immersed tunnel segment joints, characterized in that: The following steps are involved: S1. Determine the basic assumptions; S2. Set the relative axial and vertical deformations and relative rotation angles at the neutral axis of the joint to determine the calculation method for the deformation of the concrete end springs, Ω waterstops, and shear keys on the joint; S3. Conduct stress analysis on the concrete per unit area of ​​the end face, the shear key, the Ω waterstop, and the entire joint, derive the corresponding stress formulas, and clarify the expressions and stress mechanisms of the joint axial force, shear force, and bending moment. S4. Consider two extreme operating conditions: overall heating and overall cooling, and analyze their stress patterns. When heating, treat the joint as a submerged tube cross-section using an elastic foundation beam model. When cooling, treat it as an articulated joint. Use 3D finite element software to simulate the stress behavior of the joint. S5. Determine the primary influencing factors of shear force and opening through the results of the longitudinal 3D model's relevant parameter analysis, and determine the corresponding assumptions. Then, establish and derive simplified theoretical calculation models for shear force and opening. Finally, verify the theoretical formulas by comparing the results of the 3D calculation models. The basic assumptions in S1 are: Assuming that the relative displacement and relative rotation deformation of the joint are small, the concrete at the joint end surface conforms to the plane section assumption; The structural design between the shear key tenon and the groove can ensure that the vertical shear key is always in a single-sided contact state when subjected to vertical force. When subjected to axial force, the vertical shear key does not transmit axial force; It is assumed that the thickness variation of the asphalt cushion layer set between the upper and lower end faces of the shear key tenon and the groove is only caused by uneven foundation stiffness or load variation; It is assumed that after hydraulic compression, the concrete end faces except the shear key area are in close contact and can transmit the axial force; It is assumed that the axial force between the end concrete surfaces can cause a certain shear force due to the friction coefficient. When this shear force serves as a safety reserve, the friction coefficient is taken as 0.

2. A simplified calculation method for shear force and opening of immersed tunnel segment joints according to claim 1, characterized in that: The calculation method for the deformation of the concrete end spring, Ω waterstop and shear key on the joint in S2 is as follows: Assume that the relative axial deformation of the two end faces at the neutral axis of the joint is , the relative vertical deformation is , the relative rotation angle of the joint is , then the deformation of the concrete end spring, Ω water stop and shear key on the joint can be written as: ， Where, Indicates the axial deformation of the concrete end spring; Indicates the axial deformation of the Ω waterstop; represents the axial deformation of the shear key; Indicates the vertical deformation of the concrete end spring; Indicates the vertical deformation of the Ω waterstop; represents the vertical deformation of the shear key; It represents the distance from the neutral axis of the joint to the spring action point on the concrete end face; Indicates the distance from the neutral axis of the joint to the action point of the Ω waterstop; Represents the distance from the neutral axis of the joint to the shear key application point.

3. The simplified calculation method for shear force and opening of immersed tunnel segment joints according to claim 1 is characterized in that: In the above S4, when the temperature rises, the joint is regarded as the sunken tube cross section and the elastic foundation beam model is used for derivation. The specific process is as follows: Under the overall temperature rising condition, the entire section of the joint is subjected to axial pressure. : ， Where, It represents the axial force of the joint, which is the internal force borne by the entire joint in the axial direction; It represents the axial force per unit area on the concrete end surface; Indicates that the joint is subjected to vertical shear force. Indicates that the joint is subjected to bending moment; Indicates the joint height; Indicates the width of the joint; represents the number of shear keys; It represents the force corresponding to the unit relative compression per unit area on the shear key concrete contact surface; Indicates the calculated transverse width of the shear key; represents the vertical deformation of the i-th shear key; Indicates the maximum longitudinal length of the shear key, which is a specific value; It represents the longitudinal length variable of shear key calculation; Indicates the compression of the asphalt layer; Indicates the effective height of the bending section of the joint; Indicates the relative rotation angle of the joint; In this load mode, the axial force It consists of two parts. One part is the axial force formed by the axial stress caused by hydraulic pressure connection and overall temperature rise. The other part is the axial force caused by the bending stress caused by uneven load and uneven foundation stiffness changes. ; Shear force of joint It is also caused by two parts, one of which is The shear force caused by Shear force caused by Under this stress mode, the joint can transmit axial force, shear force, and bending moment. The vertical displacement and rotation angle of the joint position are approximately continuous. The segment joint can be approximately regarded as a submerged tube section. In the process of multi-segment analysis, the elastic foundation beam model can be used for deduction to obtain the shear force and bending moment at the joint position, and the stiffness influence line can be used to derive the differential settlement control standard.

4. The simplified calculation method for shear force and opening of immersed tunnel segment joints according to claim 1 is characterized in that: When cooling in S4, it is treated as an articulated joint, and the specific process is as follows: Under overall cooling conditions, the entire joint section is disengaged and the axial force is zero: ， Where, It represents the axial force of the joint, which is the internal force borne by the entire joint in the axial direction; Indicates that the joint is subjected to vertical shear force. represents the number of shear keys; Indicates that the joint is subjected to bending moment; It represents the force corresponding to the unit relative compression per unit area on the shear key concrete contact surface; Indicates the calculated transverse width of the shear key; represents the vertical deformation of the i-th shear key; Indicates the maximum longitudinal length of the shear key, which is a specific value; It represents the longitudinal length variable of shear key calculation; Indicates the compression of the asphalt layer; Indicates the relative rotation angle of the joint; In this load mode, the bending moment of the joint is caused by the shear force multiplied by the length of the shear key. The bending moment value is very small and is too simple to be ignored. In this way, the joint forms a force mode that only transmits shear force but not bending moment, with approximately continuous displacement but discontinuous rotation, and is treated as a hinged joint.

5. The simplified calculation method for shear force and opening of immersed tunnel segment joints according to claim 1 is characterized in that: The specific derivation process of the simplified theoretical calculation model of shear force in S5 is as follows: Based on theoretical analysis and combined with the research results of shear sensitivity analysis of segment joints in the longitudinal three-dimensional model, the main influencing factors are determined. The main influencing factors include: pipe top load P, segment length L, foundation stiffness ki, and elastic cushion stiffness k; Establish basic assumptions for simplified shear forces at segmental joints; Based on basic assumptions, the following equation is established: ， Solving the equation yields: ， If there is no cushion between the shear keys, , substituting it into the formula, we can get ， Where, Indicates the longitudinal distribution of load; represents the segment joint shear force; Indicates segment length; 、 Indicates foundation stiffness; Indicates the elastic cushion stiffness; 、 Indicates the vertical displacement of the segment.

6. A simplified calculation method for shear force and opening of immersed tunnel segment joints according to claim 5, characterized in that: The basic assumptions for the simplified shear force of segmental joints are as follows: Without considering the load difference between adjacent segments, the longitudinal non-uniform load on the pipe top is uniformly distributed. The pipe top load is uniformly distributed, and the pipe top load is calculated as P and the segment length is L. The longitudinal non-uniform foundation stiffness of the segment pipe bottom is processed by integral equivalent homogenization. Each segment has longitudinal uniform foundation stiffness, and the foundation stiffness of adjacent segments is calculated as follows: 、 Alternate appearance; Since the foundation stiffness of adjacent segments is 、 They appear alternately, so the shear force transmitted by each joint shear key is equal, which is assumed to be Q; Since the load and stiffness of a single segment are uniform, and the shear force transmitted by the shear key is also symmetrical, the settlement of the segment is also uniform; Settlement corresponding to stiffness , Settlement corresponding to stiffness ; The stiffness of the flexible pad set by the shear key is , under the action of shear force Q of shear key, the displacement is ; Since the model is only subjected to vertical loads and the influence of geometric nonlinearity is not considered, the axial force of the pipe section is zero.

7. The simplified calculation method for shear force and opening of immersed tunnel segment joints according to claim 1 is characterized in that: The specific derivation process of the simplified theoretical calculation model of the opening amount in S5 is as follows: Combined with the results of the sensitivity analysis of the longitudinal three-dimensional model segment joint opening, the main influencing factors are determined. The main influencing factors include: pipe top load P, segment length L, foundation stiffness k i , the friction coefficient f between the formation and the structure, and the temperature rise and fall ΔT of the system; Establish basic assumptions: Considering the difference in load at both ends of the segment in the longitudinal direction, it is assumed that the load changes linearly along the longitudinal direction; Considering the difference in foundation stiffness at both ends of the segment longitudinally, it is assumed to change linearly along the longitudinal direction; Under the cooling condition, the segment joints have a tendency to come apart. It is assumed that the longitudinal axial force is zero under this condition. According to the analysis, the segment joint opening is mainly affected by uneven load, uneven foundation stiffness, system temperature change and ground friction. The segment joint opening caused by uneven load and uneven foundation stiffness is obtained through theoretical deduction. The influence of system temperature change and ground friction on the segment joint opening is determined based on the calculation results of the longitudinal three-dimensional model. ， Where: δ represents the total opening of the segment joint; δ1 represents the opening of segment joints caused by uneven load and uneven foundation stiffness; δ2 represents the opening of segment joints caused by system temperature change and formation friction effect; The force diagram of the segment joint calculated by δ1 theory is established, and the calculation equation is obtained according to the force diagram: ， Where, k represents the elastic cushion stiffness; s represents the settlement value of the adjacent ends of two segments; Indicates the settlement value of the left end of the left segment; Indicates the settlement value of the right end of the right segment; Indicates segment length; H indicates tube segment height; , represents the equivalent distributed load concentration at the non-adjacent ends of two segments; P represents the equivalent distributed load concentration at the adjacent ends of two segments; Calculated: ， According to the research results of sensitivity analysis of segment joint opening of longitudinal three-dimensional model, we can get: ， ΔT=ΔT1+ΔT2 Further, we get: ， Where, , represents the equivalent distributed load at the ends of the two segments, assuming that the load varies linearly along the longitudinal direction of the pipe segment; ΔT represents the system temperature drop; ΔT1 represents the equivalent temperature drop due to concrete shrinkage and creep; ΔT2 represents the maximum temperature difference between the operation period and the precast period.

8. A simplified calculation system for shear force and opening of immersed tunnel segment joints, characterized by: include: A basic assumption determination unit, used for determining basic assumptions; The deformation calculation unit is used to set the relative axial and vertical deformations and relative rotation angles at the neutral axis of the joint, and to determine the calculation method for the deformations of the concrete end springs, Ω waterstops, and shear keys on the joint; The force mode analysis unit is used to analyze the force of the end surface unit area concrete, shear key, Ω water stop, and joint as a whole, derive the corresponding force formula, and clarify the expressions and force mechanism of the joint axial force, shear force and bending moment; The extreme working condition analysis unit is used to consider two extreme working conditions: overall heating and overall cooling, and analyze their stress modes respectively. When heating, the joint is treated as a submerged tube cross-section and derived using the elastic foundation beam model. When cooling, it is treated as an articulated joint. 3D finite element software is used to simulate the stress characteristics of the joint. The parameter simplification calculation and verification unit is used to determine the main influencing factors corresponding to shear force and opening through the analysis results of relevant parameters of the longitudinal three-dimensional model, and determine their corresponding assumptions. It then establishes and deduces a simplified theoretical calculation model for shear force and a simplified theoretical calculation model for opening, and finally verifies the theoretical formula by comparing the results of the three-dimensional calculation model; The basic assumptions are: Assuming that the relative displacement and relative rotation deformation of the joint are small, the concrete at the joint end surface conforms to the plane section assumption; The structural design between the shear key tenon and the groove can ensure that the vertical shear key is always in a single-sided contact state when subjected to vertical force. When subjected to axial force, the vertical shear key does not transmit axial force; It is assumed that the thickness variation of the asphalt cushion layer set between the upper and lower end faces of the shear key tenon and the groove is only caused by uneven foundation stiffness or load variation; It is assumed that after hydraulic compression, the concrete end faces except the shear key area are in close contact and can transmit the axial force; It is assumed that the axial force between the end concrete surfaces can cause a certain shear force due to the friction coefficient. When this shear force serves as a safety reserve, the friction coefficient is taken as 0.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: The computer program is executed by a processor to implement the simplified calculation method for shear force and opening amount of immersed tube tunnel segment joints as described in any one of claims 1 to 7.

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