A nonlinear analysis method for bending capacity of prefabricated comprehensive pipe gallery cross joint

Abstract

The application provides a precast comprehensive pipe gallery transverse joint bending capacity nonlinear analysis method, wherein the method comprises the following steps: obtaining target data; based on the target data, performing stress analysis of the precast comprehensive pipe gallery transverse joint in consideration of the nonlinear constitutive relation of concrete in the depressurization stage, the initial opening stage and the fully open stage respectively, and obtaining stress analysis results; based on the stress analysis results, determining the stress-deformation whole process and the failure stage information of the precast comprehensive pipe gallery transverse joint; based on the stress analysis results, drawing a result curve; and based on the stress analysis results, assisting the user in joint design. The application realizes that, in the precast pipe gallery design stage, the internal force-deformation relationship of the joint is calculated by the nonlinear analysis method to replace the finite element simulation analysis of the joint in the case that there is no joint test data, precious time and resources are saved, the design work efficiency is improved, remarkable economic benefits are generated, and the application is suitable for popularization and use.

Description

Technical Field

[0001] This invention relates to the field of prefabricated underground utility tunnel application technology, and in particular to a nonlinear analysis method for the bending capacity of transverse joints in prefabricated utility tunnels. Background Technology

[0002] Prefabricated integrated utility tunnels, as an industrialized construction method, produce tunnel components in prefabrication plants and use mechanized hoisting and assembly technologies to achieve efficient and precise on-site construction. Their significant advantages include ensuring project quality, saving construction time, reducing environmental impact, reducing the use of formwork and supports, and saving labor costs, thus having broad application prospects.

[0003] The trough-type prefabricated utility tunnel is divided into horizontal and vertical sections connected by prestressed tendons. The stress performance and structural calculation methods of its horizontal joints directly affect the overall safety of the tunnel structure. Currently, domestic and international scholars have conducted theoretical research and engineering experiments on the stress performance of joints in prefabricated integrated utility tunnels. Hu Xiang et al. conducted full-scale experimental research on integrated utility tunnel joints connected by prestressed tendons, analyzing the failure mechanism of the overall tunnel model and the bending stiffness and deformation capacity of the joints. They optimized the depth of the pre-reserved groove for the elastic sealing gasket to meet the interface stress requirements of the elastic sealing gasket, while simultaneously achieving complete closure of the prefabricated utility tunnel joints under prestress. Hu Mingliang et al., based on the classification of joint stiffness, concluded that the optimal location for the horizontal joint of a single-compartment rectangular integrated utility tunnel structure is the elastic hinge region of the tunnel structure. Zhou Jing et al., through bending test research and finite element nonlinear numerical analysis of the socket joints of prefabricated integrated utility tunnels, concluded that increasing the prestress of the joint can effectively enhance the joint's deformation resistance and increase the joint's stress-relieving bending moment, while maintaining the joint's bending bearing capacity unchanged. Wang Qinghua et al. proposed a beam-line model and a stiffness reduction coefficient method through joint bending tests to improve the calculation model of the closed frame with local stiffness reduction in prefabricated pipe gallery. Wang Pengyu et al. proposed a theoretical calculation model for transverse joints with high-strength bolts arranged on the inner side based on indoor model tests.

[0004] According to the "Technical Specification for Urban Integrated Utility Tunnel Engineering" GB 50838-2015, the design of transverse joints in precast utility tunnels should involve engineering tests to determine parameters such as the rotational stiffness of the joints. However, in actual engineering design, the rotational stiffness of the joints varies due to differences in the cross-sectional dimensions of the utility tunnel, soil cover conditions, joint construction, and prestress magnitude. Conducting model tests or full-scale tests for each type of joint before design is constrained by practical limitations. Another approach to address these issues is finite element simulation analysis of the joints. However, this often requires designers to possess corresponding simulation analysis capabilities, and adjusting finite element parameters requires experienced designers and is often difficult to standardize and promote. Furthermore, simulation analysis needs to consider the nonlinear constitutive relationship of the concrete material at the joint to accurately reflect its deformation performance; currently, no relevant research results have been found.

[0005] In summary, in the design of transverse joints in precast pipe gallery projects, an analytical method that can consider the nonlinear constitutive relationship of the joint concrete material is needed to replace the cumbersome finite element simulation analysis, so as to improve work efficiency and engineering benefits. Summary of the Invention

[0006] The purpose of this invention is to provide a nonlinear analysis method for the stress balance and deformation coordination of transverse joints in precast utility tunnels during the design phase, when joint test data is unavailable. This method utilizes material mechanics calculations that consider the nonlinear constitutive relationship of the concrete material at the joints, providing a design basis for calculating the internal forces and joint deformations of the utility tunnel, thus replacing finite element simulation analysis of the joints. Specifically addressing the bending performance of transverse joints in segmented precast utility tunnels, this nonlinear analysis method describes the entire bending capacity process of the transverse joints. It establishes nonlinear mathematical expressions for the entire load-internal force-deformation process from joint decompression, initial opening, full opening, to failure. This yields concrete stress-deformation curves, prestressed tendon stress-deformation curves, bending moment-deformation curves, and rotational stiffness-deformation curves, similar to those obtained in finite element simulation analysis, thus solving the design problems of transverse joints in precast utility tunnels during the design phase.

[0007] This invention provides a nonlinear analysis method for the bending capacity of transverse joints in prefabricated integrated utility tunnels, comprising:

[0008] Obtain the target data;

[0009] Based on the target data, stress analysis considering the nonlinear constitutive relationship of concrete was carried out on the depressurization stage, initial opening stage and fully opening stage of the transverse joint of the prefabricated integrated pipe gallery, and the stress analysis results were obtained.

[0010] Based on the stress analysis results, the entire process of stress-deformation and failure stage of the transverse joints of the prefabricated integrated utility tunnel are determined.

[0011] Based on the force analysis results, plot the result curve;

[0012] Based on the stress analysis results, we assist users in joint design.

[0013] Optionally, the target data may include at least: the cross-sectional dimensions of the transverse joints of the precast pipe gallery, concrete material parameters, prestressing tendon material parameters, prestressing tendon area, tension control stress coefficient, and prestress loss.

[0014] Optionally, based on the target data, the steps for performing stress analysis on the depressurization stage of the transverse joints of the prefabricated integrated utility tunnel include:

[0015] Based on the target data, the effective compressive stress, the critical bending moment under full-section compression, and the corresponding maximum compressive stress at the edge of the concrete in the compression zone of the prefabricated integrated utility tunnel transverse joint are calculated using the following formulas:

[0016]

[0017] σ c1 =2σ ce

[0018]

[0019] In the formula, σ ce : Effective compressive stress of the joint concrete under uniform compression; N k0 : Standard value of axial force on the joint; σ pe : Initial effective stress of prestressing tendons; A p b: area of ​​prestressing tendon; h: longitudinal length of joint; σ: height of joint section; c1 : with M k1 The maximum compressive stress at the edge of the concrete in the corresponding joint compression zone;

[0020] M k1 Critical bending moment under full-section compression.

[0021] Optionally, based on the target data, the steps for performing a stress analysis considering the nonlinear constitutive relationship of concrete material during the initial opening stage of the transverse joints of the prefabricated integrated utility tunnel include:

[0022] Based on the target data, the stress distribution of the joint concrete, the effective total stress of the prestressed tendons, the external bending moment, the joint opening amount, the joint rotation angle, and the joint rotational stiffness of the precast integrated utility tunnel transverse joint during the initial opening stage are calculated using the following formulas:

[0023]

[0024]

[0025] In the formula, σc : Maximum compressive stress at the edge of the concrete in the joint compression zone during this stage; N k0 : Standard value of axial force on the joint; σ pe : Initial effective stress of prestressing tendons; α E The ratio of the elastic modulus of prestressed tendons to the elastic modulus of concrete; A p b: area of ​​prestressing tendon; h: longitudinal length of joint; y: height of joint section; σ: length of zero-stress zone of joint; p σ: Effective total stress of prestressed tendons ce M: Effective compressive stress in the joint concrete under uniform compression; k External bending moment; Δ y θ: Opening amount of the outer edge of the joint; y : Joint angle; η: Height coefficient influenced by concrete compression deformation in the compression zone, ranging from 0 to 1.0; H0: Total calculated height of the upper and lower pipe gallery sections; n: Coefficient, see Clause 6.2.1 of GB / T 50010-2010 "Standard for Design of Concrete Structures"; f c ε0: Design value of axial compressive strength of concrete; ε0: Concrete compressive stress reaching f c Concrete compressive strain at time; K Ry : Joint rotational stiffness.

[0026] Optionally, based on the target data, the steps for performing a stress analysis considering the nonlinear constitutive relationship of concrete material during the fully open stage of the transverse joints of the precast integrated utility tunnel include:

[0027] Based on the target data, the stress distribution of the joint concrete, the effective total stress of the prestressed tendons, the external bending moment, the joint opening amount, the joint rotation angle, and the joint rotational stiffness of the precast integrated utility tunnel transverse joint during the fully open stage are calculated using the following formulas:

[0028]

[0029] In the formula, σ c : Maximum compressive stress at the edge of the concrete in the joint compression zone during this stage; N k0 : Standard value of axial force on the joint; σ pe : Initial effective stress of prestressing tendons; α E The ratio of the elastic modulus of prestressed tendons to the elastic modulus of concrete; A p b: area of ​​prestressing tendon; h: longitudinal length of joint; y: height of joint section; σ: length of zero-stress zone of joint; p σ: Effective total stress of prestressed tendons ce M: Effective compressive stress in the joint concrete under uniform compression; k External bending moment; Δ y θ: Opening amount of the outer edge of the joint; y: Joint angle; η: Height coefficient influenced by concrete compression deformation in the compression zone, ranging from 0 to 1.0; H0: Total calculated height of the upper and lower pipe gallery sections; n: Coefficient, see Clause 6.2.1 of GB / T 50010-2010 "Standard for Design of Concrete Structures"; f c ε0: Design value of axial compressive strength of concrete; ε0: Concrete compressive stress reaching f c Concrete compressive strain at time; K Ry : Joint rotational stiffness.

[0030] Optionally, the steps for determining the failure stage of the transverse joints of the prefabricated integrated utility tunnel based on the stress analysis results include:

[0031] When the compressive stress of the concrete at the compression edge of the joint in the stress analysis results exceeds the design value of the concrete compressive strength, or the stress of the prestressed tendon in the stress analysis results exceeds its design strength value, or the joint deformation is too large, the transverse joint of the precast integrated utility tunnel is judged to be damaged, and the corresponding bending moment is taken as the ultimate bending moment value of the joint.

[0032] Optionally, the resulting curves may include at least: concrete stress-deformation curve, prestressed tendon stress-deformation curve, bending moment-deformation curve, and rotational stiffness-deformation curve.

[0033] Optionally, the steps to assist designers in connector design include:

[0034] Output the stress analysis results and result curves that take into account the nonlinear constitutive relationship of concrete material to the designers.

[0035] The present invention has achieved the following beneficial effects:

[0036] For transverse joints of pipe racks of different sizes and prestress levels, in the design stage where joint test data is unavailable, this nonlinear analysis method can calculate the concrete stress-deformation curve, prestressed tendon stress-deformation curve, bending moment-deformation curve, and rotational stiffness-deformation curve of the joint, replacing the finite element simulation analysis of the joint. This saves valuable time and resources, improves design efficiency, and generates significant economic benefits, making it suitable for widespread use.

[0037] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings.

[0038] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0039] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0040] Figure 1 This is a flowchart of the nonlinear analysis method for the bending capacity of the transverse joints of the prefabricated integrated utility tunnel according to the present invention;

[0041] Figure 2 This is a three-dimensional schematic diagram of the transverse joint of the prefabricated integrated pipe gallery in an embodiment of the present invention;

[0042] Figure 3 This is the stress-deformation curve of the concrete at the transverse joint of the prefabricated integrated utility tunnel in this embodiment of the invention (I).

[0043] Schematic diagram;

[0044] Figure 4 This is the stress-deformation curve of the concrete at the transverse joint of the prefabricated integrated utility tunnel in this embodiment of the invention (II).

[0045] Schematic diagram;

[0046] Figure 5 This is the stress-deformation curve of the prestressed tendon at the transverse joint of the prefabricated integrated utility tunnel in this embodiment of the invention (I).

[0047] Schematic diagram;

[0048] Figure 6 This is the stress-deformation curve (II) of the prestressed tendon of the transverse joint of the prefabricated integrated utility tunnel in this embodiment of the invention.

[0049] Schematic diagram;

[0050] Figure 7 This is a schematic diagram of the bending moment-deformation curve (I) of the transverse joint of the prefabricated integrated pipe gallery in an embodiment of the present invention;

[0051] Figure 8 This is a schematic diagram of the bending moment-deformation curve (II) of the transverse joint of the prefabricated integrated pipe gallery in an embodiment of the present invention;

[0052] Figure 9 This is the rotational stiffness-deformation curve (I) of the transverse joint of the prefabricated integrated utility tunnel in this embodiment of the invention.

[0053] Schematic diagram;

[0054] Figure 10 This is the rotational stiffness-deformation curve (II) of the transverse joint of the prefabricated integrated utility tunnel in this embodiment of the invention.

[0055] Schematic diagram. Detailed Implementation

[0056] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0057] This invention provides a nonlinear analysis method for the bending capacity of transverse joints in prefabricated integrated utility tunnels, such as... Figures 1 to 2 As shown, it includes:

[0058] Obtain the target data;

[0059] Based on the target data, stress analysis considering the nonlinear constitutive relationship of concrete was carried out on the depressurization stage, initial opening stage and fully opening stage of the transverse joint of the prefabricated integrated pipe gallery, and the stress analysis results were obtained.

[0060] Based on the stress analysis results, the entire process of stress-deformation and failure stage of the transverse joints of the prefabricated integrated utility tunnel are determined.

[0061] Based on the stress analysis results, the resulting curves are plotted; based on the stress analysis results, the user is assisted in joint design.

[0062] The target data should include at least: the cross-sectional dimensions of the transverse joints of the precast pipe gallery, concrete material parameters, prestressing tendon material parameters, prestressing tendon area, tension control stress coefficient, and prestress loss.

[0063] Based on the target data, the steps for stress analysis of the transverse joints of prefabricated integrated utility tunnels during the depressurization stage include:

[0064] Based on the target data, the effective compressive stress, the critical bending moment under full-section compression, and the corresponding maximum compressive stress at the edge of the concrete in the compression zone of the prefabricated integrated utility tunnel transverse joint are calculated using the following formulas:

[0065]

[0066] σ c1 =2σ ce

[0067]

[0068] In the formula, σ ce : Effective compressive stress of the joint concrete under uniform compression; N k0 : Standard value of axial force on the joint; σ pe : Initial effective stress of prestressing tendons; A p b: area of ​​prestressing tendon; h: longitudinal length of joint; σ: height of joint section; c1 : with M k1 The maximum compressive stress at the edge of the concrete in the corresponding joint compression zone;

[0069] M k1 Critical bending moment under full-section compression.

[0070] Based on the target data, the steps for performing a stress analysis considering the nonlinear constitutive relationship of concrete material during the initial opening stage of the transverse joints of prefabricated integrated utility tunnels include:

[0071] Based on the target data, the stress distribution of the joint concrete, the effective total stress of the prestressed tendons, the external bending moment, the joint opening amount, the joint rotation angle, and the joint rotational stiffness of the precast integrated utility tunnel transverse joint during the initial opening stage are calculated using the following formulas:

[0072]

[0073]

[0074] In the formula, σ c : Maximum compressive stress at the edge of the concrete in the joint compression zone during this stage; N k0 : Standard value of axial force on the joint; σ pe : Initial effective stress of prestressing tendons; α E The ratio of the elastic modulus of prestressed tendons to the elastic modulus of concrete; A p b: area of ​​prestressing tendon; h: longitudinal length of joint; y: height of joint section; σ: length of zero-stress zone of joint; p σ: Effective total stress of prestressed tendons ce M: Effective compressive stress in the joint concrete under uniform compression; k External bending moment; Δ y θ: Opening amount of the outer edge of the joint; y : Joint angle; η: Height coefficient influenced by concrete compression deformation in the compression zone, ranging from 0 to 1.0; H0: Total calculated height of the upper and lower pipe gallery sections; n: Coefficient, see Clause 6.2.1 of GB / T 50010-2010 "Standard for Design of Concrete Structures"; f c ε0: Design value of axial compressive strength of concrete; ε0: Concrete compressive stress reaching f c Concrete compressive strain at time; K Ry : Joint rotational stiffness.

[0075] Based on the target data, the steps for performing a stress analysis considering the nonlinear constitutive relationship of concrete material during the fully open stage of the transverse joints of the precast integrated utility tunnel include:

[0076] Based on the target data, the stress distribution of the joint concrete, the effective total stress of the prestressed tendons, the external bending moment, the joint opening amount, the joint rotation angle, and the joint rotational stiffness of the precast integrated utility tunnel transverse joint during the fully open stage are calculated using the following formulas:

[0077]

[0078]

[0079] In the formula, σ c : Maximum compressive stress at the edge of the concrete in the joint compression zone during this stage; N k0 : Standard value of axial force on the joint; σ pe : Initial effective stress of prestressing tendons; α E The ratio of the elastic modulus of prestressed tendons to the elastic modulus of concrete; A p b: area of ​​prestressing tendon; h: longitudinal length of joint; y: height of joint section; σ: length of zero-stress zone of joint; p σ: Effective total stress of prestressed tendons ce M: Effective compressive stress in the joint concrete under uniform compression; k External bending moment; Δ y θ: Opening amount of the outer edge of the joint; y : Joint angle; η: Height coefficient influenced by concrete compression deformation in the compression zone, ranging from 0 to 1.0; H0: Total calculated height of the upper and lower pipe gallery sections; n: Coefficient, see Clause 6.2.1 of GB / T 50010-2010 "Standard for Design of Concrete Structures"; f c ε0: Design value of axial compressive strength of concrete; ε0: Concrete compressive stress reaching f c Concrete compressive strain at time; K Ry : Joint rotational stiffness.

[0080] Based on the stress analysis results, the steps to determine the failure stage of the transverse joints in the prefabricated integrated utility tunnel include:

[0081] When the compressive stress of the concrete at the compression edge of the joint in the stress analysis results exceeds the design value of the concrete compressive strength, or the stress of the prestressed tendon in the stress analysis results exceeds its design strength value, or the joint deformation is too large, the transverse joint of the precast integrated utility tunnel is judged to be damaged, and the corresponding bending moment is taken as the ultimate bending moment value of the joint.

[0082] The results curves should include at least: concrete stress-deformation curve, prestressed tendon stress-deformation curve, bending moment-deformation curve, and rotational stiffness-deformation curve.

[0083] The steps to assist designers in connector design include:

[0084] Output the stress analysis results and result curves that take into account the nonlinear constitutive relationship of concrete material to the designers.

[0085] Example 1

[0086] Please see Figure 1A nonlinear analysis method for the bending capacity of transverse joints in prefabricated integrated utility tunnels includes the following steps:

[0087] Step A: Parameter values ​​for the target data. The parameters of the target data include: cross-sectional dimensions of the transverse joint of the precast pipe gallery, concrete material parameters, prestressing tendon material parameters, prestressing tendon area, tension control stress coefficient, prestress loss, etc.

[0088] Step B: Stress calculation for the decompression stage of the transverse joint of the precast pipe gallery. This stage is characterized by the gradual increase in external bending moment load on the joint from 0, transitioning from a uniformly compressed full-section state to an eccentrically compressed full-section state, with no zero-stress zone appearing. Substituting the parameters determined in Step A into the mathematical formula for joint stress calculation during the decompression stage, the effective compressive stress (also known as effective interface stress) of the joint concrete under uniform compression, the critical bending moment under full-section compression, and the corresponding maximum compressive stress at the edge of the joint's compression zone concrete are calculated. The joint opening is zero during this stage.

[0089] Step C involves the stress calculation of the precast pipe gallery transverse joint during the initial opening stage, considering the nonlinear constitutive relationship of the concrete. This stage is characterized by the emergence of a zero-stress zone and opening amount at the joint as the external bending moment continues to increase, but the length of the zero-stress zone does not cross the position of the prestressing tendons. Based on the mathematical formulas used in this step, the stress distribution of the joint concrete, the effective total stress of the prestressing tendons, the external bending moment, the joint opening amount, the joint rotation angle, and the joint rotational stiffness are calculated for this stage.

[0090] Step D involves calculating the stress of the precast pipe gallery transverse joint during its fully open stage, considering the nonlinear constitutive relationship of the concrete. This stage is characterized by the joint's zero-stress zone extending beyond the prestressing tendon location as the external bending moment continues to increase. Based on the mathematical formulas used in this step, the stress distribution of the joint concrete, the effective total stress of the prestressing tendons, the external bending moment, the joint opening, the joint rotation angle, and the joint rotational stiffness are calculated for this stage.

[0091] Step E: Determination of the failure stage of the transverse joint of the precast pipe gallery. The characteristic of this stage is that, as the external bending moment continues to increase, the compressive stress of the concrete at the compression edge of the joint calculated according to Step C or Step D exceeds the design value of the concrete compressive strength, or the stress of the prestressing tendon exceeds its design strength value, or the joint deformation is too large. At this time, the joint is determined to be in failure, and the corresponding bending moment is the ultimate bending moment value of the joint.

[0092] Step F involves using a computer program to perform the calculations from the above steps and simultaneously plotting the resulting curves: concrete stress-deformation curve, prestressed tendon stress-deformation curve, bending moment-deformation curve, rotational stiffness-deformation curve, etc.

[0093] In this embodiment of the invention, in step B, the effective compressive stress of the joint concrete under uniform compression, the critical bending moment of the full-section compression state, and the corresponding maximum compressive stress at the edge of the joint compression zone concrete can be calculated using the following formula:

[0094]

[0095] σ c1 =2σ ce

[0096]

[0097] In the formula, σ ce : Effective compressive stress of the joint concrete under uniform compression; N k0 : Standard value of axial force on the joint; σ pe : Initial effective stress of prestressing tendons; A p b: area of ​​prestressing tendon; h: longitudinal length of joint; σ: height of joint section; c1 : with M k1 The maximum compressive stress at the edge of the concrete in the corresponding joint compression zone;

[0098] M k1 Critical bending moment under full-section compression.

[0099] In this embodiment of the invention, in step C, the stress distribution of the joint concrete, the effective total stress of the prestressing tendons, the external bending moment, the joint opening, the joint rotation angle, and the joint rotational stiffness can be calculated according to the formula:

[0100]

[0101]

[0102] In the formula, σ c : Maximum compressive stress at the edge of the concrete in the joint compression zone during this stage; N k0 : Standard value of axial force on the joint; σ pe : Initial effective stress of prestressing tendons; α E The ratio of the elastic modulus of prestressed tendons to the elastic modulus of concrete; A p b: area of ​​prestressing tendon; h: longitudinal length of joint; y: height of joint section; σ: length of zero-stress zone of joint; p σ: Effective total stress of prestressed tendons ce M: Effective compressive stress in the joint concrete under uniform compression; k External bending moment; Δ y θ: Opening amount of the outer edge of the joint; y: Joint angle; η: Height coefficient influenced by concrete compression deformation in the compression zone, ranging from 0 to 1.0; H0: Total calculated height of the upper and lower pipe gallery sections; n: Coefficient, see Clause 6.2.1 of GB / T 50010-2010 "Standard for Design of Concrete Structures"; f c ε0: Design value of axial compressive strength of concrete; ε0: Concrete compressive stress reaching f c Concrete compressive strain at time; K Ry : Joint rotational stiffness.

[0103] In this embodiment of the invention, in step D, the stress distribution of the joint concrete, the effective total stress of the prestressing tendons, the external bending moment, the joint opening, the joint rotation angle, and the joint rotational stiffness can be calculated according to the formula:

[0104]

[0105]

[0106] In the formula, σ c : Maximum compressive stress at the edge of the concrete in the joint compression zone during this stage; N k0 : Standard value of axial force on the joint; σ pe : Initial effective stress of prestressing tendons; α E The ratio of the elastic modulus of prestressed tendons to the elastic modulus of concrete; A p b: area of ​​prestressing tendon; h: longitudinal length of joint; y: height of joint section; σ: length of zero-stress zone of joint; p σ: Effective total stress of prestressed tendons ce M: Effective compressive stress in the joint concrete under uniform compression; k External bending moment; Δ y θ: Opening amount of the outer edge of the joint; y : Joint angle; η: Height coefficient influenced by concrete compression deformation in the compression zone, ranging from 0 to 1.0; H0: Total calculated height of the upper and lower pipe gallery sections; n: Coefficient, see Clause 6.2.1 of GB / T 50010-2010 "Standard for Design of Concrete Structures"; f c ε0: Design value of axial compressive strength of concrete; ε0: Concrete compressive stress reaching f c Concrete compressive strain at time; K Ry : Joint rotational stiffness.

[0107] Example 2

[0108] Please participate Figures 3-10 A nonlinear analysis method for the bending capacity of transverse joints in prefabricated integrated utility tunnels includes the following steps:

[0109] Step A: Parameter values ​​for the target data. The parameters of the target data include: cross-sectional dimensions of the transverse joint of the precast pipe gallery, concrete material parameters, prestressing tendon material parameters, prestressing tendon area, tension control stress, and prestress loss.

[0110] This embodiment describes a precast, segmented, trough-shaped pipe gallery with centrally located prestressed steel reinforcement. The total calculated height H0 = 4.2m, the transverse joint section height h = 400mm, the longitudinal length of a single component b = 2.4m, the concrete used is C40, the prestressing tendons are four φ26PC steel bars, the standard value of the ultimate strength of the prestressing tendons is 1230MPa, the design strength value of the prestressing tendons is 1080MPa, the tension control stress coefficient is 0.70, the prestress loss is 80MPa, and the standard value of the axial force on the joint is N. k0 =280.8kN, initial effective stress σ of prestressed tendon pe =0.70×1230-80=781MPa.

[0111] Step B: Stress calculation for the decompression stage of the transverse joint of the precast pipe gallery. The effective compressive stress of the joint concrete under uniform compression, the critical bending moment of the full-section compression state, and the corresponding maximum compressive stress at the edge of the joint compression zone concrete are obtained according to the following formulas.

[0112]

[0113] σ c1 =2σ ce =4.04MPa

[0114]

[0115] In the formula, σ ce : Effective compressive stress of the joint concrete under uniform compression; N k0 : Standard value of axial force on the joint; σ pe : Initial effective stress of prestressing tendons; A p b: area of ​​prestressing tendon; h: longitudinal length of joint; σ: height of joint section; c1 : with M k1 The maximum compressive stress at the edge of the concrete in the corresponding joint compression zone;

[0116] M k1 Critical bending moment under full-section compression.

[0117] Step C: Stress calculation of the initial opening stage of the transverse joint of the precast pipe gallery. Based on the calculation parameters and results of steps A to B, further calculate the stress distribution of the joint concrete, the effective total stress of the prestressing tendons, the external bending moment, the joint opening amount, the joint rotation angle, and the joint rotational stiffness during the initial opening stage. This can be calculated using the following formulas:

[0118]

[0119] In the formula, σ c : Maximum compressive stress at the edge of the concrete in the joint compression zone during this stage; N k0 : Standard value of axial force on the joint; σ pe : Initial effective stress of prestressing tendons; α E The ratio of the elastic modulus of prestressed tendons to the elastic modulus of concrete; A p b: area of ​​prestressing tendon; h: longitudinal length of joint; y: height of joint section; σ: length of zero-stress zone of joint; p σ: Effective total stress of prestressed tendons ce M: Effective compressive stress in the joint concrete under uniform compression; k External bending moment; Δ y θ: Opening amount of the outer edge of the joint; y : Joint angle; η: Height coefficient influenced by concrete compression deformation in the compression zone, in this embodiment 2, η is taken as 0.75; H0: Total calculated height of the upper and lower pipe gallery sections; n: Coefficient, see Clause 6.2.1 of "Standard for Design of Concrete Structures" GB / T 50010-2010 for details; f c ε0: Design value of axial compressive strength of concrete; ε0: Concrete compressive stress reaching f c Concrete compressive strain at time; K Ry : Joint rotational stiffness.

[0120] In this second embodiment, the load-internal force-deformation nonlinear analysis results (partial results) of the joint in the initial opening stage are shown in the table below:

[0121]

[0122] Step D: Stress calculation of the transverse joint of the precast pipe gallery during the fully open stage. Based on the calculation parameters and results of steps A to C, further calculate the stress distribution of the joint concrete, the effective total stress of the prestressing tendons, the external bending moment, the joint opening amount, the joint rotation angle, and the joint rotational stiffness during the fully open stage. This can be calculated using the following formulas:

[0123]

[0124] In the formula, σ c : Maximum compressive stress at the edge of the concrete in the joint compression zone during this stage; N k0 : Standard value of axial force on the joint; σ pe : Initial effective stress of prestressing tendons; α E The ratio of the elastic modulus of prestressed tendons to the elastic modulus of concrete; A p b: area of ​​prestressing tendon; h: longitudinal length of joint; y: height of joint section; σ: length of zero-stress zone of joint;p σ: Effective total stress of prestressed tendons ce M: Effective compressive stress in the joint concrete under uniform compression; k External bending moment; Δ y θ: Opening amount of the outer edge of the joint; y : Joint angle; η: Height coefficient influenced by concrete compression deformation in the compression zone, in this embodiment 2, η is taken as 0.75; H0: Total calculated height of the upper and lower pipe gallery sections; n: Coefficient, see Clause 6.2.1 of "Standard for Design of Concrete Structures" GB / T 50010-2010 for details; f c ε0: Design value of axial compressive strength of concrete; ε0: Concrete compressive stress reaching f c Concrete compressive strain at time; K Ry : Joint rotational stiffness.

[0125] In this second embodiment, the load-internal force-deformation nonlinear analysis results (partial results) of the joint in the fully opened stage are shown in the following table:

[0126]

[0127] Step E: Determining the failure stage of the transverse joint of the precast pipe gallery. In step D of this embodiment, the nonlinear analysis results of the entire joint process show that the maximum compressive stress at the edge of the concrete in the compression zone and the effective total stress of the prestressing tendons do not exceed their design strength values. However, due to excessive joint deformation, the bending moment reaches its maximum value at y = 290 mm, thus determining joint failure. The corresponding ultimate bending moment value of the joint is M. k = 384.2 kN·m.

[0128] Step F: The computer program completes the calculations from the above steps and simultaneously plots the resulting curves: concrete stress-deformation curve, prestressed tendon stress-deformation curve, bending moment-deformation curve, and rotational stiffness-deformation curve, such as... Figures 3 to 10 .

[0129] The calculation results, as shown in the tables and curves, clearly indicate that as the external bending moment on the transverse joints of the prefabricated pipe gallery increases, the joint opening and rotation angle gradually increase, while the joint rotational stiffness gradually decreases. The changes reflected by the curves are consistent with actual engineering conditions. Furthermore, as the bending capacity of the joint reaches yield and failure, the joint rotational stiffness remains relatively low. Moreover, according to the "Technical Specification for Urban Integrated Pipe Gallery Engineering" GB 50838-2015, the joint opening limit is 2mm. From the results curves, the corresponding bending moment value at this point is 274.7 kN·m, and the corresponding joint rotational stiffness is... It is evident that the method of this invention more realistically and effectively reflects the intrinsic relationship between the internal forces and deformations of the pipe gallery joints. The concept is clear, the calculation is convenient, and the effect is very significant.

[0130] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for nonlinear analysis of the bending capacity of a prefabricated utility tunnel cross-joint, characterized in that, The method comprises the following steps: acquiring target data; the target data comprises: cross joint section size of prefabricated pipe gallery, concrete material parameters, prestressed reinforcement material parameters, prestressed reinforcement area, tension control stress coefficient, and prestressed loss amount; based on the target data, force analysis of the decompression stage, initial opening stage, and complete opening stage of the prefabricated comprehensive pipe gallery cross joint is carried out by considering the nonlinear constitutive relation of concrete, and force analysis results are obtained; effective compressive stress in the decompression stage, critical bending moment of full section compression state, and corresponding maximum compressive stress of joint compression zone concrete edge are calculated by the following formula: stress distribution of joint concrete, effective total stress of prestressed reinforcement, external bending moment, joint opening amount, joint rotation angle, and joint rotation stiffness in the initial opening stage are calculated by the following formula: stress distribution of joint concrete, effective total stress of prestressed reinforcement, external bending moment, joint opening amount, joint rotation angle, and joint rotation stiffness in the complete opening stage are calculated by the following formula: In the formula, σ ce : Effective compressive stress of the joint concrete under uniform compression; N k0 : Standard value of axial force on the joint; σ pe : Initial effective stress of prestressing tendons; A p b: area of ​​prestressing tendon; h: longitudinal length of joint; σ: height of joint section; c1 : with M k1 The corresponding maximum compressive stress at the edge of the concrete in the compression zone of the joint; M k1 : Critical bending moment under full-section compression; σ c α: Maximum compressive stress at the edge of the concrete in the compression zone of the joint; E : Ratio of the elastic modulus of the prestressing tendon to the elastic modulus of the concrete; y: Length of the zero-stress zone at the joint; σ p M: Effective total stress of prestressed tendons k External bending moment; Δy: Opening of the outer edge of the joint; n: Coefficient, see section 6.2.1 of the "Code for Design of Concrete Structures" GB50010-2010; f c ε0: Design value of axial compressive strength of concrete; ε0: Concrete compressive stress reaching f c The concrete compressive strain at time; η: the height coefficient of the concrete compression deformation in the compression zone, with a value range of 0 to 1.0; H0: the total calculated height of the upper and lower sections of the pipe gallery; θ y : Connector corner; K Ry : Joint rotational stiffness; based on the force analysis results, the force-deformation whole process and failure stage information of the prefabricated comprehensive pipe gallery cross joint are determined; based on the force analysis results, a result curve is drawn; based on the force analysis results, the user is assisted in joint design.

2. The method for nonlinear analysis of the bending capacity of a prefabricated utility tunnel cross joint according to claim 1, characterized in that, The step of determining the failure stage information of the prefabricated comprehensive pipe gallery cross joint based on the force analysis results comprises: when the compressive stress of the joint compression edge concrete in the force analysis results exceeds the compressive strength design value of the concrete or the stress of the prestressed reinforcement in the force analysis results exceeds its strength design value or the joint deformation is too large, it is determined that the prefabricated comprehensive pipe gallery cross joint is damaged, and the corresponding bending moment is taken as the joint ultimate bending moment value.

3. The method for nonlinear analysis of the bending capacity of a prefabricated utility tunnel cross joint according to claim 1, characterized in that, The result curve at least comprises: concrete stress-deformation curve, prestressed reinforcement stress-deformation curve, bending moment-deformation curve, and rotation stiffness-deformation curve.

4. The method for nonlinear analysis of the bending capacity of a prefabricated utility tunnel cross joint according to claim 1, characterized in that, The step of assisting the designer in joint design comprises: outputting the force analysis results considering the nonlinear constitutive relation of concrete material and the result curve to the designer.

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