Simplified calculation method and system for shearing force and opening amount of immersed tunnel segment joint

Abstract

The invention discloses a simplified calculation method and system for shearing force and opening amount of immersed tunnel segment joints. The method comprises the steps that basic assumed conditions are determined; setting relative axial and vertical deformation and relative rotation angles of a neutral axis of the joint, and determining a calculation method of deformation of a concrete end surface spring, an omega water stop belt and a shear key; then, stress analysis is conducted on concrete, shear keys and the like of the unit area of the end face, a stress formula is obtained, and axial force, shear force and bending moment expressions and a stress mechanism are clarified; overall heating and cooling extreme working conditions are considered, heating is deduced through an elastic foundation beam model, cooling is processed according to a hinged joint, and three-dimensional finite element software is used for simulation; finally, influence factors and assumed conditions are determined according to longitudinal three-dimensional model parameter analysis, a simplified theoretical calculation model is established and deduced, and a verification formula is compared through a three-dimensional calculation model result. The shearing force and the opening amount of the section joint are efficiently and accurately calculated.

Description

Technical Field

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

[0002] In the current technical system of immersed tunnel engineering, there are two major categories: longitudinal integral pipe segment structures and longitudinal segmental pipe segment structures. For segmental pipe segments, the forces and deformations at the segment joints are complex. In engineering, the shear force and opening amount of the segment joints are mainly concerned. In the design work, the relevant calculations mainly rely on traditional mechanical models and numerical simulation methods. Although the traditional mechanical models have a certain theoretical basis, when facing complex actual working conditions, they are often difficult to accurately reflect the true stress state of the segment joints due to excessive simplification. Numerical simulation means, such as finite element analysis, although can finely simulate the structural behavior to a certain extent, but require a large amount of computing resources, and need to carry out cumbersome model building, parameter setting and long-time operation. For example, constructing a fine finite element model of a segment joint of a medium-sized immersed tunnel often takes several hours or even several days to complete a full calculation, and has extremely high requirements for the performance of the computing equipment. At present, the core problems faced by the calculation of segment joints of immersed 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 non-uniformity of the foundation conditions leads to significant differences in the foundation stiffness in different regions, making the distribution of the reaction forces acting on the 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 of traffic loads and the large fluctuations of environmental temperatures during the operation period, all have a superimposed impact on the stress state of the segment joints, further increasing the calculation difficulty and uncertainty. On the other hand, the high complexity and low efficiency of the existing calculation methods cannot meet the needs of engineering practice for quickly and accurately obtaining the mechanical parameters of segment joints. The cumbersome calculation process not only consumes a large amount of time and labor costs, but also easily introduces human errors in the calculation process, affecting the reliability of the calculation results. In summary, there is an urgent need to construct a new calculation system for the shear force and opening amount of segment joints of immersed tunnels. This system should be able to comprehensively cover various influencing factors, whether it is complex geological conditions or variable environmental factors, and can accurately consider them. At the same time, by means of innovative theoretical derivation and reasonable assumption setting, the complexity and redundancy of traditional methods are abandoned, and efficient and accurate calculation is realized. In this way, it provides strong and practical technical support for the immersed tunnel engineering, lays a solid foundation for the design and construction of the tunnel, and helps to improve the overall construction quality and safety of the immersed tunnel project. Summary of the Invention

[0003] Based on this, the present invention aims to provide a simplified calculation method and system for the shear force and opening amount of segment joints in immersed tube tunnels. Through innovative theoretical derivation and reasonable assumption settings, fully considering the complex factors in actual engineering, the excessive complexity of traditional methods is abandoned, and the internal forces and related parameters of segment joints can be calculated efficiently and accurately. The present invention expects to significantly shorten the calculation time, reduce the calculation cost, 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.

[0004] In view of the above defects or improvement requirements of the prior art, as the first aspect of the present invention, the present invention provides a simplified calculation method for the shear force and opening amount of segment joints in immersed tube tunnels, including: S1. Determine the basic assumption conditions; S2. Set the relative axial, vertical deformations and relative rotation angles at the neutral axis of the joint, and determine the calculation methods for the deformations of the concrete end face springs, Ω waterstops and shear keys on the joint; S3. Conduct force analyses on the concrete per unit area of the end face, shear keys, Ω waterstops and the joint as a whole respectively, obtain the corresponding force formulas, clarify the expressions and force mechanisms of the axial force, shear force and bending moment of the joint; S4. Consider two extreme working conditions of overall temperature rise and overall temperature drop, analyze their force modes respectively. When the temperature rises, the joint is regarded as an elastic foundation beam model of the immersed tube section for derivation, and when the temperature drops, it is treated as a hinged joint; use three-dimensional finite element software to simulate the force behavior of the joint; S5. Determine the main influencing factors corresponding to the shear force and opening amount through the analysis results of relevant parameters of the longitudinal three-dimensional model, and correspondingly determine their assumption conditions. Then establish a simplified theoretical calculation model for shear force and a simplified theoretical calculation model for opening amount and complete the derivation. Finally, verify the theoretical formulas through the comparison of the results of the three-dimensional calculation model.

[0005] Further, the basic assumption conditions in S1 are: Assume that the relative displacements, relative rotation angles and other deformations of the joint are relatively small, and the concrete on the joint end face 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 vertically loaded, and when axially loaded, the vertical shear key does not transfer axial force; Assume that the change in the thickness of the asphalt cushion layer between the upper and lower end faces of the shear key tenon and the groove is only caused by uneven foundation stiffness or load changes; Assume that after hydraulic pressing, the concrete end faces except in the shear key area are closely attached and can transfer axial force; Assume that the axial force between the end face concretes can cause a certain shear force due to the friction coefficient. When this shear force is used as a safety reserve, the friction coefficient is taken as 0.

[0006] Furthermore, the calculation methods for the deformations of the concrete end-face springs, Ω waterstops, and shear keys on the joints in S2 are as follows: Let the relative axial deformation of the two end faces at the neutral axis of the joint be , the relative vertical deformation be , and the relative rotation angle of the joint be . Then, the deformations of the concrete end-face springs, Ω waterstops, and shear keys on the joint are written as:

[0007] In the formula, represents the axial deformation of the concrete end-face spring; represents the axial deformation of the Ω waterstop; represents the axial deformation of the shear key; represents the vertical deformation of the concrete end-face spring; represents the vertical deformation of the Ω waterstop; represents the vertical deformation of the shear key; represents the distance from the neutral axis of the joint to the action point of the concrete end-face spring; represents 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 action point of the shear key.

[0008] Furthermore, when the temperature rises in S4, the joint is regarded as an immersed tube section and is derived using the elastic foundation beam model. The specific process is as follows: Under the overall temperature rise condition, the entire cross-section of the joint is subjected to axial pressure, :

[0009] In the formula, represents the axial force of the joint, which is the internal force borne by the entire joint in the axial direction; represents the axial force per unit area of the concrete end face; represents the vertical shear force received by the joint, represents the bending moment borne by the joint; represents the height of the joint; represents the width of the joint; represents the number of shear keys; represents the force corresponding to a unit relative compression amount per unit area on the concrete contact surface of the shear key; represents the calculated transverse width of the shear key; represents the vertical deformation of the i-th shear key; represents the maximum calculated longitudinal length of the shear key, which is a specific value; represents the calculated longitudinal length variable of the shear key; represents the compression amount of the asphalt layer. Denote the effective height of the joint's flexural section; In this stress mode, the axial force consists of two parts. One part is the axial force formed by the axial stress caused by hydraulic caulking and overall temperature rise , and the other part is the axial force caused by the bending stress caused by uneven load and uneven foundation stiffness change ; The shear force of the joint is also caused by two parts. One part is the shear force caused, and one part is the shear force caused; In this stress mode, the joint can transfer axial force, shear force, and bending moment. The vertical displacement and rotation angle at the joint position are approximately continuous. The segment joint can be approximately regarded as a immersed tube section for consideration. During the analysis of multiple segments, the elastic foundation beam model can be used for derivation to obtain the shear force and bending moment at the joint position, and the stiffness influence line can be used for the derivation of the differential settlement control standard.

[0010] Furthermore, during the temperature drop in S4, it is treated as a hinged joint, and the specific process is as follows: Under the overall temperature drop condition, the entire cross-section of the joint is disengaged, and the axial force is zero:

[0011] In this stress mode, the bending moment of the joint is caused by the shear force multiplied by the length of the shear key. This bending moment value is very small and is simply ignored for simplicity; In this way, the joint forms a stress mode that only transfers shear force, does not transfer bending moment, has approximately continuous displacement but discontinuous rotation angle, and is treated as a hinged joint.

[0012] Furthermore, the specific derivation process of the theoretical calculation model for shear force simplification in S5 is as follows: According to theoretical analysis and combined with the research results of the shear force sensitivity analysis of the longitudinal three-dimensional model segment joint, the main influencing factors are determined. The main influencing factors include: the top load P of the pipe, the segment length L, the foundation stiffness ki, and the elastic cushion stiffness k; Establish the basic assumption conditions for the shear force simplification of the segment joint; Based on the basic assumption conditions, establish the following equations:

[0013] Solve the equations to obtain:

[0014] If there is no cushion between the shear keys, then , substitute it into the formula, and we can get

[0015] In the formula, represents the longitudinal distribution of the load; represents the shear force of the segment joint; represents the segment length; 、 represents the foundation stiffness; represents the stiffness of the elastic cushion layer; 、 represents the vertical displacement of the segment.

[0016] Furthermore, the basic assumptions for the simplification of the shear force of the segment joint are as follows: The difference in loads between adjacent segments is not considered. At the same time, the longitudinally non-uniform load on the top of the pipe is evenly distributed, and a uniform load acts on the top of the pipe. The load on the top of the pipe is denoted as P, and the segment length is L; The longitudinally non-uniform foundation stiffness at the bottom of the segment is integrally equivalent and homogenized. Each segment has a longitudinally uniform foundation stiffness, and the foundation stiffness of adjacent segments alternates according to 、 alternately; Since the foundation stiffness of adjacent segments alternates according to 、 alternately, the shear force transmitted by each joint shear key is equal, assumed to be Q; Since the force and stiffness of a single segment are both uniform, and the shear force transmitted by the shear key is also symmetric, the settlement of the segment is also uniform; The settlement corresponding to the stiffness , The settlement corresponding to the stiffness ; The stiffness of the flexible cushion layer set by the shear key is ,and under the action of the shear force Q of the 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.

[0017] Furthermore, the specific derivation process of the theoretical calculation model for the simplification of the opening amount in S5 is as follows: Combining the research results of the sensitivity analysis of the segment joint opening amount in the longitudinal three-dimensional model to determine the main influencing factors, which mainly include: the load P on the top of the pipe, the segment length L, the foundation stiffness k i 、the friction coefficient f between the stratum and the structure, and the temperature rise and fall ΔT of the system; Establish the basic assumptions: Consider the difference in loads at both longitudinal ends of the segment, and assume a linear variation along the longitudinal direction; Consider the difference in foundation stiffness at both longitudinal ends of the segment, and assume a linear variation along the longitudinal direction; Under the cooling condition, there is a tendency for the segment joints to separate. It is assumed that the longitudinal axial force is zero under this condition; According to the analysis, the opening of the segment joints is mainly affected by uneven loads, uneven foundation stiffness, system temperature changes, and formation friction effects. The opening of the segment joints caused by uneven loads and uneven foundation stiffness is obtained through theoretical derivation, and the effects of system temperature changes and formation friction on the opening of the segment joints are determined based on the calculation results of the longitudinal three-dimensional model;

[0018] In the formula: δ represents the total opening of the segment joints; δ 1 represents the opening of the segment joints caused by uneven loads and uneven foundation stiffness; δ 2 represents the opening of the segment joints caused by system temperature changes and formation friction effects; Establish the force diagram of the segment joints calculated by δ 1 and obtain the calculation equation according to the force diagram:

[0019] The calculation results are:

[0020] According to the research results of the sensitivity analysis of the opening of the segment joints in the longitudinal three-dimensional model, it is obtained that:

[0021] ΔT = ΔT 1 +ΔT 2 Furthermore, it is obtained that:

[0022] In the formula, , represents the equivalent distributed load at the end positions of two segments, assuming that the load varies linearly along the longitudinal direction of the pipe section; ΔT represents the value of the system temperature drop; ΔT 1 represents the equivalent temperature drop due to concrete shrinkage and creep; ΔT 2 represents considering the maximum temperature difference during the operation period and prefabrication.

[0023] As the second aspect of the present invention, a simplified calculation system for the shear force and opening of the segment joints of a immersed tunnel is provided, including: A basic assumption condition determination unit for determining basic assumption conditions; A deformation calculation unit for setting the relative axial, vertical deformations and relative rotation angles at the neutral axis of the joint, and determining the calculation methods for the deformations of the concrete end face springs, Ω waterstops and shear keys on the joint; A force mode analysis unit is used to respectively conduct force analysis on the concrete per unit area of the end face, shear keys, Ω waterstops, and the joint as a whole, obtain corresponding force formulas, and clarify the expressions and force mechanisms of the axial force, shear force, and bending moment of the joint. An extreme condition analysis unit is used to consider two extreme conditions of overall temperature rise and overall temperature drop, respectively analyze their force modes. When the temperature rises, the joint is regarded as a immersed tube section and the elastic foundation beam model is used for derivation. When the temperature drops, it is treated as a hinged joint. The three-dimensional finite element software is used to simulate the force behavior of the joint. A parameter simplification calculation and verification unit is used to determine the main influencing factors corresponding to the shear force and the opening amount through the analysis results of relevant parameters of the longitudinal three-dimensional model, and correspondingly determine its assumed conditions. Then, a simplified theoretical calculation model for shear force and a simplified theoretical calculation model for the opening amount are established and the derivation is completed. Finally, the theoretical formula is verified by comparing with the results of the three-dimensional calculation model.

[0024] As the 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 executes any step of the simplified calculation method for the shear force and opening amount of the immersed tube tunnel segment joint.

[0025] Generally speaking, compared with the prior art by the above technical solutions conceived by the present invention, the following beneficial effects can be achieved: 1. For the simplified calculation method for the shear force and opening amount of the immersed tube tunnel segment joint of the present invention, by determining scientific and reasonable basic assumed conditions, the complex actual engineering situation is effectively simplified, providing a clear theoretical framework for subsequent calculations. At the same time, the relative axial, vertical deformations and relative rotation angles at the neutral axis of the joint are accurately set, and the deformation calculation methods of the concrete end face spring, Ω waterstop and shear keys on the joint are accurately determined. Moreover, the force analysis is respectively carried out on the concrete per unit area of the end face, shear keys, etc., and accurate force formulas are obtained, clearly clarifying the expressions and force mechanisms of the axial force, shear force, and bending moment of the joint, laying a solid foundation for accurate calculation.

[0026] 2. For the simplified calculation method for the shear force and opening amount of the immersed tube tunnel segment joint of the present invention, by considering two extreme conditions of overall temperature rise and overall temperature drop, targeted force mode analyses are respectively adopted. When the temperature rises, the joint is regarded as an immersed tube section and the elastic foundation beam model is used for derivation. When the temperature drops, the joint is treated as a hinged joint, and the three-dimensional finite element software is also used to simulate the force behavior of the joint. This comprehensive and scientific analysis method fully considers various actual possible situations, enabling the calculation results to more truly reflect the mechanical properties of the joint under different environments.

[0027] 3. A simplified calculation method for the shear force and opening amount of segment joints in a immersed tube tunnel of the present invention analyzes relevant parameters through a longitudinal three-dimensional model, accurately determines the main influencing factors corresponding to different parameters, and accordingly determines the assumed conditions. On this basis, a theoretical calculation model with simplified parameters is established and the derivation is completed. Finally, the theoretical formula is verified by comparing with the results of the three-dimensional calculation model. This method greatly simplifies the calculation process and significantly improves the calculation efficiency on the premise of ensuring the calculation accuracy, providing efficient and reliable technical support for the design and construction of immersed tube tunnel projects. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a flow chart of a simplified calculation method for the shear force and opening amount of segment joints in an immersed tube tunnel according to an embodiment of the present invention; Figure 2 It is a schematic diagram of the load and foundation support of a segment pipe joint immersed tube tunnel according to an embodiment of the present invention; Figure 3 It is a simplified diagram of the force-bearing mode of a joint according to an embodiment of the present invention; Figure 4 It is a schematic diagram of the meanings of relative displacement and relative rotation angle on the neutral axis of a joint according to an embodiment of the present invention; Figure 5 It is a schematic diagram of the force and deformation of the shear key contact surface according to an embodiment of the present invention; Figure 6 It is a simplified diagram of a joint model with overall temperature rise and without considering the end face friction coefficient according to an embodiment of the present invention (to be simplified as a rigidly connected elastic foundation beam); Figure 7 It is a simplified diagram of a joint model with overall temperature drop and without considering the end face friction coefficient according to an embodiment of the present invention (to be simplified as a hinged elastic foundation beam); Figure 8 It is a schematic diagram of the force-bearing of a simplified calculation model without considering joint opening according to an embodiment of the present invention; Figure 9 It is a schematic diagram of the separation of adjacent two segment structures according to an embodiment of the present invention; Figure 10 It is a schematic diagram of the comparison between the simplified calculation method of segment joint shear force and the calculation result of the longitudinal three-dimensional model according to an embodiment of the present invention; Figure 11 It is a schematic diagram of verifying the simplified calculation formula by using indoor model test data according to an embodiment of the present invention; Figure 12 It is a schematic diagram of the calculation of the opening amount of segment joints according to an embodiment of the present invention; Figure 13 It is a schematic diagram of the comparison of the opening amount of segment joints calculated by the simplified calculation method and the longitudinal three-dimensional model according to an embodiment of the present invention; Figure 14It is a unit diagram of a simplified calculation system for shear force and opening amount of segment joints in a immersed tube tunnel according to an embodiment of the present invention. Detailed implementation manners

[0029] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be 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 used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0030] Embodiment 1 Please refer to Figure 1 , Embodiment 1 of the present invention provides a simplified calculation method for shear force and opening amount of segment joints in an immersed tube tunnel, including the following steps: S1. Determine the basic assumption conditions; S2. Set the relative axial, vertical deformations and relative rotation angles at the neutral axis of the joint, and determine the calculation methods for the deformations of the concrete end face spring, Ω water stop and shear keys on the joint; S3. Conduct force analyses on the concrete per unit area of the end face, shear keys, Ω water stop and the whole joint respectively, obtain the corresponding force formulas, clarify the expressions and force mechanisms of the axial force, shear force and bending moment of the joint; S4. Consider two extreme working conditions of overall temperature rise and overall temperature drop, analyze their force modes respectively. When the temperature rises, the joint is regarded as an elastic foundation beam model for the immersed tube section for derivation, and when the temperature drops, it is treated as a hinged joint; use three-dimensional finite element software to simulate the force behavior of the joint; S5. Determine the main influencing factors corresponding to the shear force and opening amount through the analysis results of relevant parameters of the longitudinal three-dimensional model, and correspondingly determine their assumption conditions, then establish a simplified theoretical calculation model for shear force and a simplified theoretical calculation model for opening amount and complete the derivation, and finally verify the theoretical formula through the comparison of the results of the three-dimensional calculation model.

[0031] Next, Embodiment 1 of the present invention will specifically expand and explain the steps of the present invention.

[0032] (1) Derivation of the internal force calculation formula of the joint based on the rotational stiffness of the segment joint 1.1 Basic assumptions Assume that the relative displacements and relative rotation angles and other deformations of the joint are relatively small, and the concrete at the joint end face conforms to the plane section assumption; For the structural design between the shear key tenon and the groove, it can ensure that the vertical shear key is always in a single-sided contact state when vertically stressed, and when axially stressed, the vertical shear key does not transmit axial force; Assume that the change in the thickness of the asphalt cushion layer provided between the upper and lower end faces of the shear key tenon and the groove is only caused by uneven foundation stiffness or load change; Assume that after hydraulic press-fitting, the concrete end faces except for the shear key area are in close contact and can transfer axial force; Assume that the axial force between the end face concretes can cause a certain shear force due to the friction coefficient. When this shear force is used as a safety reserve, the friction coefficient is taken as 0.

[0033] 1.2 Derivation process of the force mode of the segment joint Please refer to Figures 2 - 4 , let the relative axial deformation of the two end faces at the neutral axis of the joint be (relative compression is positive), the relative vertical deformation be (relative approach is positive), and the relative rotation angle of the joint be (counterclockwise rotation is positive). Then, for the Figure 3 shown deformation of the concrete end face spring, Ω waterstop and shear key on the joint can be written as: ,

[0034] In the formula, represents the axial deformation of the concrete end face spring; represents the axial deformation of the Ω waterstop; represents the axial deformation of the shear key; represents the vertical deformation of the concrete end face spring; represents the vertical deformation of the Ω waterstop; represents the vertical deformation of the shear key; represents the distance from the neutral axis of the joint to the action point of the concrete end face spring; represents 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 action point of the shear key.

[0035] 1.3 Force analysis of the concrete contact surface per unit area of the end face It is simulated by using a compression-only spring that can only be compressed and not stretched. The calculation formula for the axial force of the concrete per unit area of the end face is:

[0036] In the formula, is the compressive stiffness per unit area of the concrete end face, is the compression amount per unit area of the concrete end face, unit: m; is the axial force caused by the initial hydraulic press-fitting and the overall temperature drop change per unit area of the concrete end face;

[0037] is the value of the overall temperature drop, unit: °C, temperature drop is positive, such as negative for temperature rise; is the length of the immersed tube tunnel segment.

[0038]

[0039] When is the case, .

[0040] 1.4 Force analysis of a certain joint shear key Please refer to Figure 5 and simulate the concrete shear key as a system that does not bear axial force axially and consists of a spring and the vertical relative displacement threshold . The unit of is kN / m, , and it is actually composed of many small springs . is the force corresponding to a unit relative compression amount per unit area on the concrete contact surface of the shear key, and the unit is kN / m 3 .

[0041] When is the case, the force condition of the shear key is:

[0042] When is the case, the force condition of the shear key is:

[0043] 1.5 Force analysis of the Ω waterstop 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, in the simplified calculation, the beneficial effect of the Ω waterstop is not considered, and the derivation process is on the safe side.

[0044] 1.6 Force analysis of the overall joint Combining the forces on the concrete end faces and shear keys within the joint width (-B / 2~B / 2) and joint height (-H / 2~H / 2) ranges, we can obtain: When is the case, the force condition of the joint is:

[0045] When is the case, the force condition of the joint is:

[0046] The above two formulas are the expressions of the axial force, shear force and bending moment of the joint, reflecting the force mechanism of the joint.

[0047] 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 mode of the axial force on the end face is affected by the relative rotation angle of the joint When the rotation angle is small, the entire end face bears axial pressure. When the rotation angle gradually becomes larger, one end of the joint section will become disengaged, while the other end will be further compressed with an asymmetric axial force distribution. When the overall temperature drop condition occurs, the axial force of the entire section becomes 0.

[0048] In addition, the friction coefficient of the joint end face has a great influence on the distribution mode of the joint shear force. When considering the shear force caused by the axial force, due to the large axial force, the shear force caused by the axial force on the end face is also large, and the shear force of the shear key is small. In this derivation, the shear force of the joint caused by the axial force is not considered temporarily, and the influence of this friction coefficient is not considered, which is regarded as a safety reserve.

[0049] 1.7 Simplification and Application of the Force Mode of Segment Joints Consider two extreme force conditions: Under the overall temperature rise condition, the entire section of the joint is subjected to axial pressure, :

[0050] In the formula, represents the axial force of the joint, which is the internal force borne by the entire joint in the axial direction; represents the axial force per unit area of the concrete end face; represents the vertical shear force received by the joint, represents the bending moment borne by the joint; represents the height of the joint; represents the width of the joint; represents the number of shear keys; represents the force corresponding to a unit relative compression amount per unit area on the concrete contact surface of the shear key; represents the calculated transverse width of the shear key; represents the vertical deformation of the i-th shear key; represents the maximum calculated longitudinal length of the shear key, which is a specific value; represents the calculated longitudinal length variable of the shear key; represents the compression amount of the asphalt layer; represents the effective height of the joint cross-section under bending; In this force mode, the axial force can be considered to be composed of two parts. One part is the axial force formed by the axial stress caused by hydraulic pressure and overall temperature rise Another part is the axial force caused by the bending stress induced by uneven loads and the change in the stiffness of the uneven foundation. The shear force of the joint is also caused by two parts. One part is the shear force caused by (the vertical relative displacement generated by the direct shear of the joint), and one part is the shear force caused by (the vertical relative displacement generated by the bending).

[0051] Please refer to Figure 6 . In this stress mode, the joint can transfer axial force, shear force, and bending moment. The vertical displacement at the joint position is approximately continuous, and the rotation angle is continuous (because there is no opening). The segment joint can be approximately regarded as a caisson section for consideration. During the analysis of multiple segments, the elastic foundation beam model can be used for derivation to obtain the shear force and bending moment at the joint position, and the stiffness influence line can be used for the derivation of the differential settlement control standard. The difference from the rigid joint is that the allowable displacement difference between the shear key tenon and the groove can be superimposed on the basis of the analysis of the rigid connection elastic foundation beam as an approximate consideration.

[0052] Under the overall temperature drop condition, the entire cross-section of the joint is disengaged, and the axial force is zero:

[0053] In this stress mode, the bending moment of the joint is caused by the shear force multiplied by the length of the shear key. This bending moment value is very small and can be approximately ignored for simplicity.

[0054] Please refer to Figure 7 . In this way, the joint forms a stress mode that only transfers shear force, does not transfer bending moment, has approximately continuous displacement but discontinuous rotation angle, and can be treated as a hinged joint. The difference from the hinged joint is that the allowable displacement difference between the shear key tenon and the groove can be superimposed on the basis of the analysis of the hinged elastic foundation beam as an approximate consideration.

[0055] From an accurate perspective, it is advisable to place the above joint stress mode into a three-dimensional finite element software, so as to comprehensively simulate the stress behavior of the joint.

[0056] (2) Simplified calculation method for the shear force of the segment joint 2.1 Research idea According to the theoretical analysis and combined with the research results of the shear force sensitivity analysis of the segment joint in the longitudinal three-dimensional model, determine the main influencing factors; Reasonably determine the assumed conditions, and perform mathematical processing on some influencing factors to facilitate simplified calculation; Establish a theoretical calculation model and complete the theoretical derivation; Compare and verify the theoretical formula with the results of the three-dimensional calculation model; 2.2 Theoretical derivation Determination of main influencing factors: the load P on the pipe top, the segment length L, and the foundation stiffness k i , and the stiffness k of the elastic cushion. Please refer to Figure 8 for the following basic assumptions: The difference in loads between adjacent segments is not considered. At the same time, the non-uniform longitudinal load on the pipe top is evenly distributed. A uniform load acts on the pipe top, with the load on the pipe top being P and the segment length being L; The non-uniform longitudinal foundation stiffness at the bottom of the segment is integrated and homogenized. Each segment has a uniform longitudinal foundation stiffness, and the foundation stiffness of adjacent segments alternates according to and ; Since the foundation stiffness of adjacent segments alternates according to and , the shear force transmitted by each joint shear key is equal, assumed to be Q; Since the force and stiffness of a single segment are both uniform, and the shear force transmitted by the shear key is also symmetric, the settlement of the segment is also uniform; The settlement corresponding to the stiffness , The settlement corresponding to the stiffness ; The stiffness of the flexible cushion set for the shear key is , and under the action of the shear force Q of the 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.

[0057] Please refer to Figure 9 to separate the structures of two adjacent segments; Therefore, the following equations can be established:

[0058] Solving the equations gives:

[0059] If there is no cushion between the shear keys, then , substituting it into the formula, we can get

[0060] In the formula, represents the longitudinal distribution of the load; represents the shear force at the segment joint; represents the segment length; , represent the foundation stiffness; represents the stiffness of the elastic cushion; , Indicates the vertical displacement of the segment.

[0061] 2.3 Verification of Simplified Calculation Formula Please refer to Figure 10 , according to the longitudinal distribution of segment loads and the foundation stiffness distribution along the whole line of the immersed tube tunnel of the Hong Kong-Zhuhai-Macao Bridge, the shear force of segment joints is calculated by using the three-dimensional full-longitudinal model and the simplified calculation formula respectively. The comparison calculation results are shown in Figure 10 ; It can be seen from the comparison that the simplified calculation method has a good agreement with the three-dimensional calculation. This working condition can consider the difference in foundation stiffness of adjacent segments, and can relatively reflect the area where the longitudinal foundation stiffness changes sharply to a large extent, ensuring the engineering practicability of the simplified calculation results.

[0062] Please refer to Figure 11 , and at the same time, the indoor test data is used to verify the simplified calculation formula. 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 results of the indoor model test have a good agreement with the simplified calculation formula and the three-dimensional calculation results. It should be particularly noted that the differential settlement in the indoor test is the differential settlement value of the forced displacement at the segment joint, and the differential settlement of the simplified formula and the three-dimensional calculation results is the differential settlement value calculated through the vertical load and the corresponding foundation stiffness of the segment. The comparison data is limited and the conclusion is not universal, but the overall trend is in good agreement.

[0063] (3) Simplified Calculation Method for Shear Force of Segment Joints 3.1 Research Ideas According to the theoretical analysis, combined with the research results of the sensitivity analysis of the segment joint opening amount in the longitudinal three-dimensional model, the main influencing factors are determined; Reasonably determine the assumed conditions and make mathematical simplification for some influencing factors; The comprehensive influence of the two factors of formation friction and temperature on the segment joint opening amount is determined according to the research results of the longitudinal model sensitivity analysis; Establish a theoretical calculation model and complete the theoretical derivation; Compare and verify the theoretical formula with the results of the three-dimensional calculation model; 3.2 Theoretical Derivation Determination of main influencing factors: top load P of the pipe, segment length L, foundation stiffness k i , friction coefficient f between the formation and the structure, temperature rise and fall ΔT of the system.

[0064] The basic assumptions are as follows: Consider the difference in loads at both ends of the segment in the longitudinal direction, but assume a linear change along the longitudinal direction; Consider the difference in foundation stiffness at both ends of the segment in the longitudinal direction, but assume a linear change along the longitudinal direction; The segment joint opening is more unfavorable under the condition of temperature drop. Assuming that there is a tendency for the segment joint to disengage under this condition, the longitudinal axial force is zero; 3.3 Analysis process 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 derivation, and the influence of system temperature change and formation friction on the segment joint opening is determined according to the calculation results of the longitudinal three-dimensional model.

[0065]

[0066] In the formula: δ represents the total opening of the segment joint; δ 1 represents the segment joint opening caused by uneven load and uneven foundation stiffness; δ 2 represents the segment joint opening caused by system temperature change and formation friction effect; Please refer to Figure 12 , establish the force diagram of the segment joint for theoretical calculation of δ 1 , and obtain the calculation equation according to the force diagram:

[0067] Calculated:

[0068] According to the research results of the sensitivity analysis of the segment joint opening of the longitudinal three-dimensional model, it is obtained that:

[0069] ΔT = ΔT 1 +ΔT 2 Furthermore, it is obtained that:

[0070] In the formula, , represents the equivalent distributed load at the end positions of two segments, assuming that the load varies linearly along the longitudinal direction of the pipe section; ΔT represents the system temperature drop value; ΔT 1 represents the equivalent temperature drop due to concrete shrinkage and creep; ΔT 2 represents considering the maximum temperature difference during the operation period and prefabrication.

[0071] 3.4 Verification of simplified calculation formula According to the longitudinal distribution of the pipe section load and the foundation stiffness distribution of the entire line of the immersed tube tunnel of the Hong Kong-Zhuhai-Macao Bridge, considering the temperature drop condition, the segment joint opening is calculated and compared respectively by using the three-dimensional full-longitudinal model and the simplified calculation formula.

[0072] Where: ΔT 1 =4.65℃, ΔT 2 =15℃ (cooling), calculation results refer to Figure 13 .

[0073] Take the natural foundation section pipe segments, eliminate the segment joints with zero opening calculated by the longitudinal three-dimensional model, and compare the simplified calculation formula of the segment joint opening 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, and has good adaptability in the natural foundation section (E7~E25), and can be used for engineering estimation.

[0074] Example 2 Referring to FIG. 14 , this embodiment 2 provides a simplified calculation system for shear force and opening amount of segment joints of immersed tube tunnels, including: A basic assumption condition determination unit, used for determining basic assumption conditions; 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 determine the calculation method for the deformations of the concrete end springs, Ω water stop strips 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 the temperature rises, the joint is regarded as the immersed tube section and the elastic foundation beam model is used for derivation. When the temperature drops, it is treated as an articulated joint. The three-dimensional 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 the shear force and the opening amount through the relevant parameter analysis results of the longitudinal three-dimensional model, and determine their assumptions accordingly, and then establish a simplified theoretical calculation model for shear force and a simplified theoretical calculation model for opening amount and complete the derivation, and finally verify the theoretical formula by comparing the results of the three-dimensional calculation model.

[0075] Example 3 This embodiment 3 also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, any step of the simplified calculation method for shear force and opening amount of immersed tube tunnel segment joints can be implemented.

[0076] The computer-readable storage medium may include: various media that can store program codes, such as USB flash drives, external hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical discs.

[0077] For the introduction of the computer-readable storage medium provided in this application, please refer to the above method embodiments, and details are not described herein again.

[0078] Those skilled in the art can easily understand that the above are only preferred embodiments of the present invention and are not used to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A simplified calculation method for shear force and opening of segment joints of immersed tunnel, 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, and determine the calculation method for the deformations of the concrete end springs, Ω waterstops and shear keys on the joint; S3. Analyze the stress of the end surface unit area concrete, shear key, Ω water stop and joint as a whole, obtain the corresponding stress formula, and clarify the expressions and stress mechanism of the joint axial force, shear force and bending moment; S4. Considering two extreme conditions of overall heating and overall cooling, the stress modes are analyzed respectively. When the temperature rises, the joint is regarded as the section of the immersed tube and the elastic foundation beam model is used for derivation. When the temperature drops, it is treated as an articulated joint. The stress characteristics of the joint are simulated using three-dimensional finite element software. S5. Determine the main influencing factors corresponding to shear force and opening amount through the analysis results of relevant parameters of the longitudinal three-dimensional model, and determine their assumptions accordingly. Then establish a simplified theoretical calculation model for shear force and a simplified theoretical calculation model for opening amount and complete the derivation. Finally, verify the theoretical formula by comparing the results of the three-dimensional calculation model.

2. According to claim 1, a simplified calculation method for shear force and opening of immersed tunnel segment joints is characterized in that: The basic assumptions in S1 are: Assuming that the relative displacement and relative rotation of the joint are small, the concrete at the end of the joint 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, and the vertical shear key does not transmit axial force when subjected to 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 can cause a certain shear force due to the friction coefficient. When this shear force is used as a safety reserve, the friction coefficient is taken as 0.

3. According to claim 1, a simplified calculation method for shear force and opening of immersed tunnel segment joints is characterized in that: The calculation method of the deformation of the concrete end spring, Ω water stop 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: ， In the formula, 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; Represents 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 surface; 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.

4. According to claim 1, a simplified calculation method for shear force and opening of immersed tunnel segment joints is characterized in that: In the S4, when the temperature rises, the joint is regarded as the submerged tube cross section and the elastic foundation beam model is used for derivation. The specific process is as follows: Under the condition of overall temperature rise, the entire section of the joint is subjected to axial pressure. : ， In the formula, 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 ith shear key; It indicates the maximum longitudinal length of the shear key calculation, 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; 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 is partly The shear force caused Under this stress mode, the joint can transmit axial force, shear force and bending moment. The vertical displacement and rotation angle of the joint are approximately continuous. The segment joint can be approximately regarded as a immersed tube section. In the process of multi-segment analysis, the elastic foundation beam model can be used for derivation 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.

5. According to claim 1, a simplified calculation method for shear force and opening of immersed tunnel segment joints is characterized in that: When the temperature is lowered in S4, it is treated as an articulated joint, and the specific process is as follows: Under the overall cooling condition, the entire section of the joint is disengaged and the axial force is zero: ， In this stress 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 simple, so it is 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.

6. A simplified calculation method for shear force and opening of immersed tunnel segment joints according to claim 1, characterized in that: The specific derivation process of the simplified theoretical calculation model of shear force in S5 is as follows: According to theoretical analysis, 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, 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 ， In the formula, Indicates the longitudinal distribution of load; represents the segment joint shear force; Indicates segment length; , Indicates foundation stiffness; Indicates the stiffness of the elastic cushion; , Indicates the vertical displacement of the segment.

7. A simplified calculation method for shear force and opening of immersed tunnel segment joints according to claim 6, characterized in that: The basic assumptions for the simplification of the segment joint shear force are as follows: Without considering the load difference between adjacent segments, the longitudinal non-uniform load on the pipe top is uniformly distributed, and the pipe top load is uniformly distributed. The pipe top load is 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 according to , 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, assumed to be Q; Since the force 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 shear force Q of the shear key, the displacement is ; Since the model is only subject to vertical loads and the influence of geometric nonlinearity is not considered, the axial force of the pipe section is zero.

8. A simplified calculation method for shear force and opening of immersed tunnel segment joints according to claim 1, 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 segment joint opening of 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 k i , the friction coefficient between the formation and the structure f, and the temperature rise and fall of the system ΔT; Establish basic assumptions: Consider the difference in load at both ends of the segment in the longitudinal direction, assuming a linear change along the longitudinal direction; Considering the difference in foundation stiffness at both ends of the segment in the longitudinal direction, it is assumed to change linearly along the longitudinal direction; Under the cooling condition, the segment joints have a tendency to come apart, and 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 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 according to 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 amount 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: ， Calculated: ， According to the research results of the sensitivity analysis of the segment joint opening of the longitudinal three-dimensional model, it is obtained that: ， ΔT=ΔT1+ΔT2 Further, we get: ， In the formula, , It 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 reduction value; ΔT1 represents the equivalent temperature reduction due to concrete shrinkage and creep; ΔT2 represents the maximum temperature difference between the operation period and the prefabrication period.

9. A simplified calculation system for shear force and opening of segment joints of immersed tunnel, characterized in that: include: A basic assumption condition determination unit, used for determining basic assumption conditions; 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 determine the calculation method for the deformations of the concrete end springs, Ω water stop strips 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 the temperature rises, the joint is regarded as the immersed tube section and the elastic foundation beam model is used for derivation. When the temperature drops, it is treated as an articulated joint. The three-dimensional 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 the shear force and the opening amount through the relevant parameter analysis results of the longitudinal three-dimensional model, and determine their assumptions accordingly, and then establish a simplified theoretical calculation model for shear force and a simplified theoretical calculation model for opening amount and complete the derivation, and finally verify the theoretical formula by comparing the results of the three-dimensional calculation model.

10. 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 1-8.

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