An analytical method, apparatus, computer-readable storage medium, and computer program product for calculating the opening amount of quick-connect pipe segments.

Abstract

This invention belongs to the field of service performance calculation for tunnel boring machine (TBM) segment structures, and discloses an analytical method, apparatus, computer-readable storage medium, and computer program product for calculating the opening amount and bending stiffness of quick-joint TBM segments. The method includes the following steps: inputting an axial force N; calculating M based on the applied N. co With M bo Input the bending moment M step by step, and then input M... ca With M co M bo By comparison, the stress stage corresponding to the tunnel segment is determined; the stress of the tunnel segment is calculated to determine whether it has reached the ultimate stress. If it has not reached the ultimate stress, the value of M is increased and the calculation continues; if it has reached the ultimate stress, the bending moment M corresponding to the ultimate state is obtained. ca Calculate the corresponding segment rotation angle θ and segment bending stiffness k. m This invention can quickly calculate the ultimate bearing bending moment of the tunnel segment under specified working conditions and the opening amount and bending stiffness of the quick-joint tunnel segment under a given stress state, thereby providing a mechanical performance evaluation of the joint during the design stage and improving the design efficiency of the structure.

Description

Technical Field

[0001] This invention belongs to the field of service performance calculation of tunnel segment structures, and more specifically, relates to an analytical method, apparatus, computer-readable storage medium, and computer program product for calculating the opening amount of quick-joint tunnel segments. Background Technology

[0002] Over the past three decades, China has constructed thousands of shield tunnels, most of which were designed based on the assumptions of uniform strata and plane strain. The segments are typically connected by bolts. It is evident that the use of bolts inevitably involves the installation of handholes, which weaken the local bearing capacity of the composite soil components, easily leading to localized cracking during construction and use, resulting in leakage. Furthermore, bolt tightening is largely manual, consuming significant time and manpower, and the quality of construction cannot be guaranteed.

[0003] To avoid these problems, several new types of shield tunnel segment joints have been proposed. The most widely used is a one-pass joint, which eliminates the need for manual tightening. It is directly aligned and assembled using an assembly machine, and the internal slope of the joint creates a tightening force during assembly. Chinese Invention Patent Publication No. CN110761414A discloses an I-type standard block composite mortise and tenon joint structure for prefabricated construction components. This invention requires only one I-type standard steel plate of the same size, shape, and material, made by stamping or laser cutting, along with a bolt of the same material. In two components, one component uses one I-type standard steel plate as a male clamping connector on its side, while the other component uses two I-type standard steel plates as C-type female clamping connectors on its side. After welding to achieve integration, the connection between the sides of adjacent components is achieved through the matching male and female clamping connectors for quick snap-fit. The wedge (mortise and tenon) effect is achieved by setting an inclination (slop) that creates a tensioning bonding force between the segments. The inclination (slop) is formed by welding a steel wedge (steel crucible) into a steel mold, joining the mortise and tenon joint of the present invention with the steel wedge, and inserting the male and female clamps at an inclination into the end face between the segments.

[0004] The bending resistance of tunnel segments is one of the most important evaluation indicators for longitudinal joints. Currently, there are generally three methods for evaluating this performance: testing, numerical simulation, and analytical solutions. Among them, testing requires sophisticated experimental equipment and is costly; numerical simulation often has high computational costs if accurate results are obtained, while analytical solutions have the lowest computational cost and wide applicability. However, most current analytical solutions are for bolted joints, and there are no analytical methods for quick-connect joints. Summary of the Invention

[0005] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides an analytical method for calculating the opening amount of quick-connect joint segments, the purpose of which is to solve the technical problem of ensuring analytical accuracy while reasonably simplifying the joint.

[0006] To achieve the above objectives, according to one aspect of the present invention, an analytical method for calculating the opening amount of quick-connect joint segments is provided, comprising the following steps:

[0007] Input the axial force N into the quick-connect segment model to obtain the bending moment M at the neutral axis at the concrete edge. co The bending moment M at the joint of the neutral shaft bo ;

[0008] When a bending moment M is input into the quick-joint segment model, the model experiences three stress stages under the action of axial force N and bending moment M. The first stage is a full-section compression state, where 0 ≤ M ≤ M. co The second stage involves the neutral axis being located between the lower edge of the concrete and the joint axis, M. co ≤M≤M bo The third stage is when the neutral axis is located between the joint axis and the upper edge of the concrete, M bo <M;

[0009] The bending moment M input at this time and M co M bo By comparison, the stress stage corresponding to M is determined. The stress of the segments in this stress stage is calculated to see if it reaches the ultimate stress. If not, the value of the bending moment M is increased, and the quick-joint segment model is re-entered to recalculate whether the stress of the segments in the corresponding stress stage reaches the ultimate stress, until the ultimate stress is reached. If the ultimate stress is reached, the value of M at this point is the bending moment M corresponding to the ultimate state. ca At this point, the corresponding opening amount is the limit opening amount of the quick-connect joint segment under axial force N.

[0010] Furthermore, the calculation process for the three stress stages needs to satisfy the following assumptions:

[0011] (1) The opening amount and deformation of the segments are negligible in relation to the size of the segments;

[0012] (2) When calculating the segment opening angle, the contact surface is a plane before and after contact;

[0013] (3) The concrete strain is linearly distributed along the contact surface;

[0014] (4) The joint is only subjected to tensile force, while the concrete is only subjected to compressive force.

[0015] Furthermore, the quick-connect joint segment model in step (1) includes the following constitutive relationship between the concrete and the joint:

[0016] Concrete constitutive model:

[0017] (4)

[0018] Where k1 is the calculation parameter, For the stress in concrete; For the strain of concrete; f cd The allowable compressive strength of concrete, This represents the ultimate compressive strength of concrete.

[0019] Joint constitutive model:

[0020] The formulas for calculating the overall spring coefficient and tensile force of the joint are as follows:

[0021] (5)

[0022] (6)

[0023] in, k a It is the spring constant of the anchor bar; k c It is the spring coefficient of the connector body; k j It is the equivalent spring constant of the entire joint; T is the overall tensile length of the joint, and T is the overall tensile force of the joint.

[0024] Furthermore, a rectangular distributed stress model was used in the calculation of the three stress stages, where the equivalent stress F c The expression is as follows:

[0025] (9)

[0026] in, α and β For the fitting parameters, f c For concrete compressive strength, y c This is the equivalent compressive height of the concrete. y This is the actual compressive height of the concrete. b For segment thickness;

[0027] and Calculate according to the following formula:

[0028] (15)

[0029] (16)

[0030] in, s ( e ) is the strain of concrete e The corresponding stress at that time;

[0031] Alternatively, by performing polynomial fitting on equations (15) and (16), and Simplify to the following two polynomials:

[0032] (17)

[0033] (18)

[0034] in, A , B , D The coefficients of the fitted polynomial, C , E The constant term obtained from the fitting is denoted as .

[0035] Furthermore, in the three stress stages, the bending stiffness is calculated according to the following formula:

[0036] Stress stage 1: 0≤M≤M co At this stage, the neutral axis is located below the lower edge of the concrete, and M is the bending moment experienced by the concrete at this time. Since the segment opening is 0 at this stage, the bending stiffness k m1 = ;

[0037] Stress Stage 2: M co ≤M≤M bo At this stage, the neutral axis is located between the lower edge of the concrete and the joint axis, and M is the bending moment that the concrete experiences at this time.

[0038] (25)

[0039] (26)

[0040] Where, k m2 θ represents the first-stage flexural stiffness, and θ represents the amount of concrete opening when subjected to a bending moment M.

[0041] Solve the system of equations as follows:

[0042] (27)

[0043] (28)

[0044] (29)

[0045] in,h For the height of the tunnel segments, l It refers to the depth of concrete affected by compression. x The compression height of the tunnel segment when the concrete reaches its ultimate state;

[0046] Stress Stage 3: M bo <M ca At this stage, the neutral axis is located between the joint axis and the upper edge of the concrete, and M is the bending moment that the concrete experiences at this time.

[0047] (30)

[0048] (31)

[0049] (32)

[0050] Where, k m3 This refers to the third stage of bending stiffness;

[0051] Solve i The system of equations is as follows:

[0052] (33)

[0053] (34)

[0054] (35)

[0055] in, β bo Therefore, the fitting parameters under the stress state T For the tensile force of the joint, d PT is the distance between the joint and the outer edge of the concrete, and PT is the preload of the joint.

[0056] Furthermore, in step (3), M co M is the bending moment at the edge of the concrete along the neutral axis. bo M is the bending moment of the neutral shaft at the joint. co and M bo The solution is as follows:

[0057] M co Solving for:

[0058] (20)

[0059] in, h For the height of the tunnel segments, β co Therefore, the fitting parameters under stress conditions;

[0060] M boSolving for:

[0061] (twenty three)

[0062] in, β bo These are the fitting parameters under the stress state.

[0063] Furthermore, after determining the stress stage corresponding to M, the segment rotation angle θ and segmental bending stiffness corresponding to the limit state are calculated based on the model of the corresponding stress stage.

[0064] According to another aspect of the present invention, an analytical apparatus for calculating the opening amount of quick-connect joint segments is provided, comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the analytical method as described in any of the preceding claims.

[0065] According to another aspect of the invention, a computer-readable storage medium is provided having a computer program stored thereon that, when executed by a processor, implements the steps of the parsing method as described in any of the preceding claims.

[0066] According to another aspect of the invention, a computer program product is provided, comprising a computer program that, when executed by a processor, implements the steps of the parsing method as described in any of the preceding claims.

[0067] In summary, the technical solutions conceived in this invention, compared with the prior art, can achieve the following beneficial effects:

[0068] 1. This invention divides the quick-connect joint segment model into three stress stages and performs staged ultimate stress analytical matching by progressively increasing M to match the stress stages.

[0069] 2. By establishing a constitutive model of the quick-connect joint and combining it with the constitutive empirical formulas of the rest, it is possible to quickly and accurately calculate the opening amount and bending stiffness of the quick-connect joint segments under different stress states.

[0070] 3. By calculating the critical bending moment values ​​for each stage before the formal calculation, it is easier to quickly determine the stress stage corresponding to the target bending moment in the later stage, thus achieving the effect of quickly calculating the segmental bending stiffness of the tunnel segment. Attached Figure Description

[0071] Figure 1 This is a concrete stress-strain curve in a preferred embodiment of the present invention;

[0072] Figure 2 This is the parallel constitutive model of the quick-connect joint in a preferred embodiment of the present invention;

[0073] Figure 3This refers to the stress distribution along the concrete contact surface and the equivalent rectangular stress distribution in a preferred embodiment of the present invention.

[0074] Figure 4 This is a schematic diagram of deformation and stress distribution in the first stage of stress under positive bending moment in a preferred embodiment of the present invention.

[0075] Figure 5 This is a schematic diagram of deformation and stress distribution in the second stage of stress under positive bending moment in a preferred embodiment of the present invention;

[0076] Figure 6 This is a schematic diagram of deformation and stress distribution in stress stage three under positive bending moment in a preferred embodiment of the present invention.

[0077] Figure 7 This is a schematic diagram of the moment-rotation angle during the first stress stage under positive bending moment in a preferred embodiment of the present invention.

[0078] Figure 8 This is a schematic diagram of the bending moment-rotation angle in the second stress stage under positive bending moment in a preferred embodiment of the present invention;

[0079] Figure 9 This is a schematic diagram of the bending moment-rotation angle in the third stress stage under positive bending moment in a preferred embodiment of the present invention;

[0080] Figure 10 This is a flowchart illustrating a preferred embodiment of the present invention. Detailed Implementation

[0081] To make the objectives, technical solutions, and advantages of this invention clearer, the 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 merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0082] The preferred analytical method for calculating the opening amount of the quick-connect joint segments in this invention is as follows:

[0083] (1) Prepare the basic calculation data for the structure;

[0084] (2) Input axial force N and bending moment M;

[0085] (3) Calculate M based on the N applied in step (2). co With M bo ;

[0086] (4) Input the bending moment M step by step; combine the bending moment M input in step (2) with M ca、 M co Mbo By comparison, the stress stage corresponding to M can be determined;

[0087] (5) Substitute the axial force N and bending moment M into the corresponding stress stage calculation to determine whether the segment stress has reached the ultimate stress. If it has not reached the ultimate stress, return to step 4. If it has reached the ultimate stress, obtain the bending moment M corresponding to the ultimate state. ca ;

[0088] (6) Calculate the segment rotation angle θ and segment bending stiffness corresponding to the limit state. The segment rotation angle θ corresponding to the limit state is the limit opening amount of the quick-joint segment under axial force N.

[0089] Based on the above calculation steps, the characteristic is that the following assumptions need to be satisfied:

[0090] (1) The opening and deformation of the segments are very small relative to the size of the segments;

[0091] (2) When calculating the segment opening angle, the contact surface is a plane before and after contact;

[0092] (3) The concrete strain is linearly distributed along the contact surface;

[0093] (4) The joint is only subjected to tensile force, while the concrete is only subjected to compressive force;

[0094] Preferably, the basic calculation data in step (1) includes a constitutive relationship model of concrete and joint, and the calculation model is as follows:

[0095] Concrete constitutive model:

[0096] (1)

[0097] (2)

[0098] (3)

[0099] (4)

[0100] Where k1 is the calculation parameter, For the stress in concrete; For the strain of concrete; f ck This refers to the standard compressive strength of concrete. f cd The allowable compressive strength of concrete, This represents the ultimate compressive strength of concrete.

[0101] Joint constitutive model:

[0102] The spring coefficient of the joint can be considered as a parallel connection of anchor bar-body-anchor bar. In this embodiment, the anchor bar spring coefficient is calculated using a length equal to 6 times the diameter (other empirical values ​​may be used in different embodiments). The final formulas for calculating the overall spring coefficient and tensile force of the joint are:

[0103] (5)

[0104] (6)

[0105] in, k a It is the spring constant of the anchor bar; k c It is the spring coefficient of the connector body; k j It is the equivalent spring constant of the entire joint; T is the overall tensile length of the joint, and T is the overall tensile force of the joint.

[0106] Preferably, in other embodiments, the above-described constitutive relation model can also be replaced by other empirical models, traditional numerical models, intelligent models trained by conventional deep learning networks, etc.

[0107] Preferably, in this embodiment, a rectangular distributed stress model is used instead of the original force mode, wherein the equivalent stress F c The expression is as follows:

[0108] (7)

[0109] (8)

[0110] (9)

[0111] in, a and b For the fitting parameters, f c For concrete compressive strength, y c This is the equivalent compressive height of the concrete. y This is the actual compressive height of the concrete. b For segment thickness;

[0112] From the linear strain distribution of concrete, we can obtain:

[0113] (10)

[0114] in, e For concrete strain, e c Strain at the end of the compressive stress of the concrete ，y'This is the distance between the equivalent compression point of the concrete and the starting point of the concrete compression.

[0115] Differentiating both sides, we get:

[0116] (11)

[0117] Substituting into the theoretical model, we get:

[0118] (12)

[0119] (13)

[0120] (14)

[0121] in, s ( e The concrete strain is... e The corresponding stress at that time;

[0122] so and It can be calculated using the following formula:

[0123] (15)

[0124] (16)

[0125] By performing polynomial fitting on equations (14) and (15), and Simplify to the following two polynomials:

[0126] (17)

[0127] (18)

[0128] in, A , B , D The coefficients of the fitted polynomial, C , E The constant term obtained from the fitting is denoted as .

[0129] Preferably, for the M co and M bo M co M is the bending moment at the edge of the concrete along the neutral axis. bo M is the bending moment of the neutral shaft at the joint. co and M bo The solution is as follows:

[0130] M co Solving for:

[0131] (19)

[0132] (20)

[0133] (twenty one)

[0134] Where, θ co The axial force N and bending moment M of the tunnel segments co The opening angle below, l This is the depth of the concrete under compressive stress, which is an empirical value. In this embodiment, we take... l =0.55 h , h For the height of the tunnel segments, β co Therefore, the fitting parameters under the stress state e co Therefore, the stress state is determined by the final strain of the concrete under compression.

[0135] M bo Solving for:

[0136] (twenty two)

[0137] (twenty three)

[0138] (twenty four)

[0139] Where, θ bo The axial force N and bending moment M of the tunnel segments bo The opening angle below, β bo Therefore, the fitting parameters under the stress state e bo Therefore, the stress state is determined by the final strain of the concrete under compression.

[0140] Preferably, the stress stages consist of three stages: the first stage is a full-section compression state; the second stage is when the neutral axis is located between the lower edge of the concrete and the joint axis; and the third stage is when the neutral axis is located between the joint axis and the upper edge of the concrete.

[0141] Preferably, in the three stress stages, the bending stiffness is calculated according to the following formula.

[0142] Stress stage 1: 0≤M≤M co At this stage, the neutral axis is located below the lower edge of the concrete, M ca This is the bending moment when the concrete reaches its ultimate limit state. Since the segment opening is zero at this stage, the bending stiffness k... m1 = .

[0143] Stress Stage 2: M co ≤M ca ≤M bo At this stage, the neutral axis is located between the lower edge of the concrete and the joint axis, M ca It is the bending moment when the concrete reaches its ultimate state.

[0144] (25)

[0145] (26)

[0146] Where, k m2 For the first stage bending stiffness, θ ca This refers to the amount of segment opening when the concrete reaches its ultimate limit state.

[0147] Solve The system of equations is as follows:

[0148] (27)

[0149] (28)

[0150] (29)

[0151] in, x The compression height of the tunnel segment when the concrete reaches its ultimate state;

[0152] Stress Stage 3: M bo <M ca At this stage, the neutral axis is located between the joint axis and the upper edge of the concrete, M ca It is the bending moment when the concrete reaches its ultimate state.

[0153] (30)

[0154] (31)

[0155] (32)

[0156] Where, k m3 This refers to the third stage of bending stiffness;

[0157] Solve The system of equations is as follows:

[0158] (33)

[0159] (34)

[0160] (35)

[0161] in, T For the tensile force of the joint, d PT is the distance between the joint and the outer edge of the concrete, and PT is the preload of the joint.

[0162] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An analytical method for calculating the opening amount of quick-connect joint segments, characterized in that, Includes the following steps: Input the axial force N into the quick-connect segment model to obtain the bending moment M at the neutral axis at the concrete edge. co The bending moment M at the joint of the neutral shaft bo ; When a bending moment M is input into the quick-joint segment model, the model experiences three stress stages under the action of axial force N and bending moment M. The first stage is a full-section compression state, where 0 ≤ M ≤ M. co The second stage involves the neutral axis being located between the lower edge of the concrete and the joint axis, M. co ≤M≤M bo The third stage is when the neutral axis is located between the joint axis and the upper edge of the concrete, M bo <M; The bending moment M input at this time and M co M bo By comparison, determine the stress stage corresponding to M, calculate whether the segment stress in this stress stage has reached the ultimate stress. If it has not reached the ultimate stress, increase the value of bending moment M and re-enter the quick-connect joint segment model to recalculate whether the segment stress in the corresponding stress stage has reached the ultimate stress, until the ultimate stress is reached. If the ultimate stress is reached, then the value of M at this point is the bending moment M corresponding to the ultimate state. ca At this point, the corresponding opening amount is the limit opening amount of the quick-joint segment under axial force N; The calculation process for the three stress stages needs to satisfy the following assumptions: (1) The opening amount and deformation of the segments are negligible in relation to the size of the segments; (2) When calculating the segment opening angle, the contact surface is a plane before and after contact; (3) The concrete strain is linearly distributed along the contact surface; (4) The joint is only subjected to tensile force, while the concrete is only subjected to compressive force.

2. The analytical method for calculating the opening amount of quick-connect joint segments according to claim 1, characterized in that, The quick-connect joint segment model in step (1) includes the following constitutive relationship between the concrete and the joint: Concrete constitutive model: （4） Where k1 is the calculation parameter, For the stress in concrete; For the strain of concrete; f cd The allowable compressive strength of concrete, This refers to the ultimate compressive strength of concrete. Joint constitutive model: The formulas for calculating the overall spring coefficient and tensile force of the joint are as follows: （5） （6） in, k a It is the spring constant of the anchor bar; k c It is the spring coefficient of the connector body; k j It is the equivalent spring constant of the entire joint; T is the overall tensile length of the joint, and T is the overall tensile force of the joint.

3. The analytical method for calculating the opening amount of quick-connect joint segments according to claim 2, characterized in that, In the calculation of the three stress stages, a rectangular distributed stress model was used, where the equivalent stress F c The expression is as follows: （9） in, α and β For the fitting parameters, f c For concrete compressive strength, y c This is the equivalent compressive height of the concrete. y This is the actual compressive height of the concrete. b For segment thickness; and Calculate according to the following formula: （15） （16） in, σ ( ε ) is the strain of concrete ε The corresponding stress at that time; Alternatively, by performing polynomial fitting on equations (15) and (16), and Simplify to the following two polynomials: （17） （18） in, A , B , D The coefficients of the fitted polynomial, C , E The constant term obtained from the fitting is denoted as .

4. The analytical method for calculating the opening amount of quick-connect joint segments according to claim 3, characterized in that, In the three stress stages mentioned above, the bending stiffness is calculated as follows: Stress stage 1: 0≤M≤M co At this stage, the neutral axis is located below the lower edge of the concrete, and M is the bending moment experienced by the concrete at this time. Since the segment opening is 0 at this stage, the bending stiffness k m1 = ; Stress Stage 2: M co ≤M≤M bo At this stage, the neutral axis is located between the lower edge of the concrete and the joint axis, and M is the bending moment that the concrete experiences at this time. （25） （26） Where, k m2 Let θ be the first-stage flexural stiffness, and θ be the amount of concrete opening when subjected to a bending moment M. co The axial force N and bending moment M of the tunnel segments co The opening angle below; Solve the system of equations as follows: （27） （28） （29） in, h For the height of the tunnel segments, l It refers to the depth of concrete affected by compression. x The compression height of the tunnel segment when the concrete reaches its ultimate state; Stress Stage 3: M bo <M ca At this stage, the neutral axis is located between the joint axis and the upper edge of the concrete, and M is the bending moment that the concrete experiences at this time. （30） （31） （32） Where, k m3 For the third stage bending stiffness, θ bo The axial force N and bending moment M of the tunnel segments bo The opening angle below; Solve θ The system of equations is as follows: （33） （34） （35） in, β bo Therefore, the fitting parameters under the stress state T For the tensile force of the joint, d PT is the distance between the joint and the outer edge of the concrete, and PT is the preload of the joint.

5. The analytical method for calculating the opening amount of quick-connect joint segments according to claim 1, characterized in that, In step (3), M co M is the bending moment at the edge of the concrete along the neutral axis. bo M is the bending moment of the neutral shaft at the joint. co and M bo The solution is as follows: M co Solving for: （20） in, h For the height of the tunnel segments, β co This is the fitting parameter under the stress state, where N is the axial force; M bo Solving for: （23） in, β bo These are the fitting parameters under the stress state.

6. The analytical method for calculating the opening amount of quick-connect joint segments according to claim 1, characterized in that, After determining the stress stage corresponding to M, the segment rotation angle θ and segmental bending stiffness corresponding to the limit state are calculated based on the model of the corresponding stress stage.

7. An analytical device for calculating the opening amount of quick-connect joint segments, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the parsing method according to any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the parsing method according to any one of claims 1 to 6.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the parsing method according to any one of claims 1 to 6.

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