Analytic method and device for calculating opening amount of novel fast splicing joint segment, computer readable storage medium and computer program product

Abstract

The invention belongs to the field of shield segment structure service performance calculation, and discloses a novel analysis method and device for calculation of the opening amount and the flexural rigidity of a fast joint segment, a computer readable storage medium and a computer program product. The method comprises the following steps: inputting an axial force N; calculating Mco and Mbo according to the applied N; inputting a bending moment M step by step, comparing Mca with Mco and Mbo, and determining a stress stage corresponding to the duct piece; calculating and judging whether the stress of the duct piece reaches limit stress, if not, increasing the value of M, and continuing calculation; if yes, the bending moment Mca corresponding to the limit state is obtained; and calculating a corresponding duct piece rotation angle theta and a corresponding segment bending rigidity km. According to the method, the ultimate bearing bending moment of the duct piece under the specified working condition and the opening amount and flexural rigidity of the duct piece of the novel quick joint under the given stress state can be quickly calculated, so that the mechanical property evaluation of the joint is given in the design stage, and the design efficiency of the structure is improved.

Description

Technical Field

[0001] The present invention belongs to the field of shield segment structure service performance calculation, and more specifically, relates to an analytical method, device, computer-readable storage medium and computer program product for calculating the opening amount of a new type of quick-joint segment. Background Art

[0002] In the past three decades, China has built thousands of shield tunnels, most of which were designed based on the assumption of uniform strata and plane strain. The segments are usually connected by bolts. Obviously, when using bolts, the setting of hand holes is inevitable, which will weaken the local bearing capacity of the mixed soil pipe fittings and easily cause local cracking of the tunnel during construction and use, resulting in water leakage. On the other hand, the tightening of bolts is basically manual work, which not only consumes a lot of time and manpower, but also the construction quality cannot be guaranteed.

[0003] In order to avoid these problems, some new shield tunnel segment joints have been proposed. Among them, the most widely used is a one-pass joint, which does not require manual tightening of the joint. It is directly aligned and assembled by an assembly machine. At the same time, the internal slope of the joint is set to form a tightening force during assembly. Chinese invention patent publication number CN110761414A provides an I-type standard block combined mortise and tenon joint structure of an assembled construction component. The mortise and tenon joint of the invention only requires a piece of I-type standard steel plate of the same size, shape, and material, which is stamped or laser cut, plus a screw of the same material. In the two components, one I-type standard steel plate is used on the side of one component as a male clamp joint, and two I-type standard steel plates are used on the side of the other component as a C-type female clamp joint. After integration is achieved through welding, the connection of the sides of the two adjacent components is achieved by the matching male clamp joint and the female clamp joint to achieve quick clamping. The wedge (mortise and tenon) effect is achieved by setting a slope between blocks to tighten the bonding force of the pipe segments. The slope is formed by welding a steel wedge (steel crucible) into a steel mold, combining the mortise and tenon joint of the present invention with the steel wedge, and obliquely inserting the male and female clips at the end faces between the pipe segment blocks.

[0004] The bending resistance of pipe segments is the most important evaluation index of longitudinal joints. There are three evaluation methods for this performance: test, numerical simulation, and analytical solution. Among them, the test has high requirements for experimental equipment and high cost; if numerical simulation is to obtain accurate results, the calculation cost is often very high, while the analytical solution has the lowest calculation cost and strong applicability. However, most of the current analytical solutions are for bolt joints, and there is no analytical method for new quick-joint joints. Summary of the invention

[0005] In view of the above defects or improvement needs of the prior art, the present invention provides an analytical method for calculating the opening amount of a new quick-joint pipe segment, the purpose of which is to solve the technical problem of ensuring analytical accuracy while reasonably simplifying the new joint.

[0006] To achieve the above object, according to one aspect of the present invention, an analytical method for calculating the opening amount of a new quick-joint pipe segment is provided, comprising the following steps:

[0007] Input the axial force N into the new quick-joint segment model and obtain the bending moment M when the neutral axis is at the edge of the concrete. co Bending moment M when the neutral axis is at the joint bo ;

[0008] Input the bending moment M into the new quick-joint segment model. Under the action of axial force N and bending moment M, the new quick-joint segment model has three stress stages. The first stage is the full-section compression state 0≤M≤M co ; The second stage is when the neutral axis is 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 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, determine the stress stage corresponding to M, calculate whether the segment stress at this stress stage reaches the ultimate stress. If not, increase the value of the bending moment M and re-enter the new quick-joint segment model to calculate again whether the segment stress at the corresponding stress stage reaches the ultimate stress until the ultimate stress is reached. If the ultimate stress is reached, the M value at this time is the bending moment M corresponding to the limit state. ca At this time, the corresponding opening amount is the limit opening amount of the new quick-joint segment under the axial force N.

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

[0011] (1) The segment opening and deformation are negligible for the size of the segment;

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

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

[0014] (4) The joint is only subjected to tension and the concrete is only subjected to compression.

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

[0016] Concrete constitutive structure:

[0017]

[0018] Among them, k1 is the calculation parameter, σ c is the stress of concrete; ε c is the strain of concrete; f cd is the allowable compressive strength of concrete, ε cu is the ultimate compressive strength of concrete.

[0019] Joint constitutive structure:

[0020] The calculation formula for the spring coefficient and tension of the joint as a whole is:

[0021]

[0022] T=Δx·k j (6)

[0023] Among them, k a is the spring coefficient of the anchor bar; k c is the spring constant of the joint body; k j is the equivalent spring coefficient of the joint as a whole; Δx is the tensile length of the joint as a whole, and T is the tensile force of the joint as a whole.

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

[0025]

[0026] Among them, α and β are fitting parameters, f c is the compressive strength of concrete, y c is the equivalent compressive height of concrete, y is the actual compressive height of concrete, and b is the thickness of the segment;

[0027] α and β are calculated as follows:

[0028]

[0029] Among them, σ(ε) is the stress corresponding to the concrete strain of ε;

[0030] Alternatively, by performing polynomial fitting on equations (15) and (16), α and β can be simplified into the following two polynomials:

[0031] α=Aε c 2 +Bε c +C (17)

[0032] β=Dε c +E (18)

[0033] Among them, A, B, and D are the polynomial coefficients obtained by fitting, and C and E are the constant terms obtained by fitting.

[0034] Furthermore, in the three stress stages, the bending stiffness is calculated according to the following formula:

[0035] Stress stage 1: 0≤M≤M co ; At this stage, the neutral axis is below the lower edge of the concrete, and M is the bending moment of the concrete at this time; since the segment opening is 0 at this stage, the bending stiffness k m1 =∞;

[0036] Stress Stage 2: M co ≤M≤M bo ; At this stage, the neutral axis is between the lower edge of the concrete and the axis of the joint, and M is the bending moment to which the concrete is subjected;

[0037] k m1 =∞(25)

[0038]

[0039] Among them, k m2 is the bending stiffness of the first stage, θ is the opening of the concrete when it receives the bending moment M;

[0040] Solve the following system of equations:

[0041] N=F c (27)

[0042] M=0.5N(h-βx) (28)

[0043]

[0044] Where h is the segment height, l is the depth of concrete compression, and x is the segment compression height when the concrete reaches the limit state;

[0045] Stress Stage 3: M bo <M ca ; At this stage, the neutral axis is between the joint axis and the upper edge of the concrete, and M is the bending moment to which the concrete is subjected;

[0046] k m1 =∞ (30)

[0047]

[0048] Among them, k m3 is the bending stiffness of the third stage;

[0049] The system of equations to solve for θ is as follows:

[0050] N=F c -(T+PT) (33)

[0051]

[0052] Among them, β bo As the fitting parameters under this stress state, T is the joint tension, d is the distance between the joint and the outer edge of the concrete, and PT is the preload of the joint.

[0053] Furthermore, in step (3), M co is the bending moment when the neutral axis is at the edge of the concrete, M bo is the bending moment when the neutral axis is at the joint, M co and M bo The solution is as follows:

[0054] M co The solution:

[0055] M co =0.5N(h-β co h) (20)

[0056] Where h is the segment height, β co The fitting parameters under this stress state are:

[0057] M bo The solution:

[0058]

[0059] Among them, β bo is the fitting parameter under this stress state.

[0060] Furthermore, after determining the stress stage corresponding to M, the segment rotation angle θ and the segment bending stiffness corresponding to the limit state are calculated based on the model corresponding to the stress stage.

[0061] According to another aspect of the present invention, there is provided an analytical device for calculating the opening amount of a new quick-joint pipe segment, 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 items.

[0062] According to another aspect of the present invention, there is provided a computer-readable storage medium on which a computer program is stored, and when the computer program is executed by a processor, the steps of the parsing method as described in any of the preceding items are implemented.

[0063] According to another aspect of the present invention, a computer program product is provided, comprising a computer program, which implements the steps of the parsing method as described in any of the preceding items when executed by a processor.

[0064] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0065] 1. The present invention divides the new quick-joint segment model into three stress stages, and performs stage-by-stage limit stress analytical matching by gradually increasing M to match the stress stages.

[0066] 2. By establishing the constitutive model of the new quick-joint and combining it with the constitutive empirical formulas of the rest of the parts, it is possible to quickly and accurately calculate the opening amount and bending stiffness of the new quick-joint segment under different stress states.

[0067] 3. By calculating the critical bending moment value of each stage before the formal calculation, it is convenient to quickly determine the stress stage corresponding to the target bending moment in the later stage, so as to achieve the effect of quickly calculating the bending stiffness of the segment in different stages. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 is a concrete stress-strain curve in a preferred embodiment of the present invention;

[0069] Figure 2 It is the parallel constitutive model of the quick-joint in the preferred embodiment of the present invention;

[0070] Figure 3 The stress distribution along the concrete contact surface and the equivalent rectangular stress distribution in the preferred embodiment of the present invention;

[0071] Figure 4 Schematic diagram of deformation and stress distribution in stress stage 1 under positive bending moment in a preferred embodiment of the present invention;

[0072] Figure 5 It is a deformation schematic diagram and a stress distribution schematic diagram of the stress stage 2 under the action of positive bending moment in a preferred embodiment of the present invention;

[0073] Figure 6 It is a deformation schematic diagram and a stress distribution schematic diagram of stress stage three under the action of positive bending moment in a preferred embodiment of the present invention;

[0074] Figure 7 It is a schematic diagram of bending moment-rotation angle in stress stage 1 under positive bending moment in a preferred embodiment of the present invention;

[0075] Figure 8 It is a schematic diagram of bending moment-rotation angle in stress stage 2 under positive bending moment in a preferred embodiment of the present invention;

[0076] Fig. 9 Schematic diagram of bending moment-rotation angle in stress stage three under positive bending moment in a preferred embodiment of the present invention;

[0077] Fig.10 It is a flow chart of a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0078] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with 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 intended 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.

[0079] The analytical method for calculating the opening amount of the new quick-joint pipe segment preferred in the present invention is as follows:

[0080] (1) Prepare basic calculation data of the structure;

[0081] (2) Input axial force N and bending moment M;

[0082] (3) Calculate M based on the N applied in step (2) co With M bo ;

[0083] (4) Input the bending moment M step by step; compare the bending moment M input in step (2) with M ca、 M co 、M bo By comparison, determine the stress stage corresponding to M;

[0084] (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 not, return to step 4. If it has, obtain the bending moment M corresponding to the ultimate state. ca ;

[0085] (6) The segment rotation angle θ and segment bending stiffness corresponding to the limit state are calculated. The segment rotation angle θ corresponding to the limit state is the limit opening amount of the new quick-joint segment under the axial force N.

[0086] According to the above calculation steps, it is characterized in that the following assumptions need to be met:

[0087] (1) The segment opening and deformation are very small for the segment size;

[0088] (2) When calculating the segment opening angle, the contact surface is flat before and after contact;

[0089] (3) Concrete strain is distributed linearly along the contact surface;

[0090] (4) The joint is only subjected to tension and the concrete is only subjected to compression;

[0091] Preferably, the basic calculation data of step (1) includes a constitutive relationship model of concrete and joints, and the calculation model is as follows:

[0092] Concrete constitutive structure:

[0093] k1=1-0.003f ck ≤0.85 (1)

[0094]

[0095] 0.0025≤ε cu ≤0.0035 (3)

[0096]

[0097] Among them, k1 is the calculation parameter, σ c is the stress of concrete; ε c is the strain of concrete; f ck is the standard compressive strength of concrete; f cd is the allowable compressive strength of concrete, ε cu is the ultimate compressive strength of concrete.

[0098] Joint constitutive structure:

[0099] The spring coefficient of the new joint can be regarded as the parallel connection of anchor bar-body-anchor bar. When calculating the spring coefficient of the anchor bar, this embodiment uses a length equal to 6 times the diameter for calculation (other empirical values ​​may also be used in different embodiments). The final spring coefficient calculation formula and tension calculation formula of the entire joint are:

[0100]

[0101] T=Δx·k j (6)

[0102] Among them, k a is the spring coefficient of the anchor bar; k c is the spring constant of the joint body; k j is the equivalent spring coefficient of the joint as a whole; Δx is the tensile length of the joint as a whole, and T is the tensile force of the joint as a whole.

[0103] Preferably, in other embodiments, the above-mentioned constitutive relationship model may also be replaced by other empirical models or traditional numerical models, intelligent models trained by conventional deep learning networks, etc.

[0104] Preferably, in this embodiment, a rectangular distribution stress model is used to replace the original stress mode, wherein the equivalent stress Fc The expression is as follows:

[0105] σ c =αf c (7)

[0106] y c =βy (8)

[0107]

[0108] Among them, α and β are fitting parameters, f c is the compressive strength of concrete, y c is the equivalent compressive height of concrete, y is the actual compressive height of concrete, and b is the thickness of the segment;

[0109] From the linear distribution of concrete strain, we can get:

[0110]

[0111] Where ε is the concrete strain, ε c is the strain at the end point of concrete compression, y' is the distance between the equivalent compression point of concrete and the starting point of concrete compression;

[0112] Taking the derivative of both sides, we get:

[0113]

[0114] Substituting into the theoretical model, we can get:

[0115]

[0116] Among them, σ(ε) is the stress corresponding to the concrete strain of ε;

[0117] So α and β can be calculated as follows:

[0118]

[0119] By performing polynomial fitting on equations (14) and (15), α and β are simplified into the following two polynomials:

[0120] α=Aε c 2 +Bε c +C (17)

[0121] β=Dε c +E (18)

[0122] Among them, A, B, and D are the polynomial coefficients obtained by fitting, and C and E are the constant terms obtained by fitting.

[0123] Preferably, for the Mco and M bo , where M co is the bending moment when the neutral axis is at the edge of the concrete, M bo is the bending moment when the neutral axis is at the joint, M co and M bo The solution is as follows:

[0124] M co The solution:

[0125] N=F c (19)

[0126] M co =0.5N(h-β co h) (20)

[0127]

[0128] Among them, θ co is the axial force N and bending moment M of the segment co The opening angle under the condition of l is the depth of concrete under pressure, which is an empirical value. In this embodiment, l=0.55h is taken, h is the height of the pipe segment, and β co For this force state, the fitting parameter, ε co For this stress state, the concrete compression end strain is proposed;

[0129] M bo The solution:

[0130] N=F c (twenty two)

[0131]

[0132] Among them, θ bo is the axial force N and bending moment M of the segment bo The opening angle under bo For this force state, the fitting parameter, ε bo For this stress state, the concrete compression end strain is proposed;

[0133] Preferably, there are three stress stages in the stress stage. The first stage is the full cross-section compression state. The second stage is the neutral axis between the lower edge of the concrete and the joint axis. The third stage is the neutral axis between the joint axis and the upper edge of the concrete.

[0134] Preferably, in the three stress stages, the bending stiffness is calculated according to the following formula:

[0135] Stress stage 1: 0≤M≤M co At this stage, the neutral axis is below the lower edge of the concrete, Mca is the bending moment when the concrete reaches the ultimate state. Since the segment opening is 0 at this stage, the bending stiffness k m1 =∞.

[0136] Stress Stage 2: M co ≤M ca ≤M bo At this stage, the neutral axis is between the lower edge of the concrete and the joint axis, M ca is the bending moment when the concrete reaches the ultimate limit state.

[0137] k m1 =∞ (25)

[0138]

[0139] Among them, k m2 is the bending stiffness of the first stage, θ ca It is the opening amount of the segment when the concrete reaches the ultimate state;

[0140] Solving for θ ca The system of equations is as follows:

[0141] N=F c (27)

[0142] M=0.5N(h-βx) (28)

[0143]

[0144] Where x is the compressive height of the segment when the concrete reaches the ultimate limit state;

[0145] Stress Stage 3: M bo <M ca ; At this stage, the neutral axis is between the joint axis and the upper edge of the concrete, M ca is the bending moment when the concrete reaches the ultimate limit state;

[0146] k m1 =∞ (30)

[0147]

[0148] Among them, k m3 is the bending stiffness of the third stage;

[0149] Solving for θ ca The system of equations is as follows:

[0150] N=F c -(T+PT) (33)

[0151]

[0152] Among them, T is the joint tension, d is the distance between the joint and the outer edge of the concrete, and PT is the preload of the joint.

[0153] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. An analytical method for calculating the opening amount of a new type of quick-joint pipe segment, characterized in that: The steps include: Input the axial force N into the new quick-joint segment model and obtain the bending moment M when the neutral axis is at the edge of the concrete. co Bending moment M when the neutral axis is at the joint bo ; Input the bending moment M into the new quick-joint segment model. Under the action of axial force N and bending moment M, the new quick-joint segment model has three stress stages. The first stage is the full-section compression state 0≤M≤M co ; The second stage is when the neutral axis is 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 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 at this stress stage reaches the ultimate stress. If not, increase the value of the bending moment M and re-enter the new quick-joint segment model to calculate again whether the segment stress at the corresponding stress stage reaches the ultimate stress, until the ultimate stress is reached; If the ultimate stress is reached, the M value at this time is the bending moment M corresponding to the ultimate state. ca At this time, the corresponding opening amount is the limit opening amount of the new quick-joint segment under the axial force N.

2. The analytical method for calculating the opening amount of a new quick-joint pipe segment according to claim 1 is characterized in that: The calculation process of the three stress stages needs to meet the following assumptions: (1) The segment opening and deformation are negligible for the size of the segment; (2) When calculating the segment opening angle, the contact surface is flat before and after contact; (3) Concrete strain is distributed linearly along the contact surface; (4) The joint is only subjected to tension and the concrete is only subjected to compression.

3. The analytical method for calculating the opening amount of a new quick-joint pipe segment according to claim 1 is characterized in that: The new quick-joint segment model in step (1) includes the following constitutive relationship between concrete and the joint: Concrete constitutive structure: Among them, k1 is the calculation parameter, σ c is the stress of concrete; ε c is the strain of concrete; f cd is the allowable compressive strength of concrete, ε cu is the ultimate compressive strength of concrete. Joint constitutive structure: The calculation formula for the spring coefficient and tension of the joint as a whole is: T=Δx·k j (6) Among them, k a is the spring coefficient of the anchor bar; k c is the spring constant of the joint body; k j is the equivalent spring coefficient of the joint as a whole; Δx is the tensile length of the joint as a whole, and T is the tensile force of the joint as a whole.

4. The analytical method for calculating the opening amount of a new quick-joint pipe segment according to claim 3 is characterized in that: In the calculation process of the three stress stages, a rectangular distribution stress model was used, in which the equivalent stress F c The expression is as follows: Among them, α and β are fitting parameters, f c is the compressive strength of concrete, y c is the equivalent compressive height of concrete, y is the actual compressive height of concrete, and b is the thickness of the segment; α and β are calculated as follows: Among them, σ(ε) is the stress corresponding to the concrete strain of ε; Alternatively, by performing polynomial fitting on equations (15) and (16), α and β can be simplified into the following two polynomials: a=Aε c 2 +Be c +C (17) β=Dε c +E (18) Among them, A, B, and D are the polynomial coefficients obtained by fitting, and C and E are the constant terms obtained by fitting.

5. The analytical method for calculating the opening amount of a new quick-joint pipe segment according to claim 4 is characterized in that: In the three stress stages, the bending stiffness is calculated according to the following formula: Stress stage 1: 0≤M≤M co ; At this stage, the neutral axis is below the lower edge of the concrete, and M is the bending moment of 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 between the lower edge of the concrete and the axis of the joint, and M is the bending moment to which the concrete is subjected; k m1 ＝∞ (25) Among them, k m2 is the bending stiffness of the first stage, θ is the opening of the concrete when it receives the bending moment M; Solve the following system of equations: N=F c (27) M=0.5N(h-βx) (28) Where h is the segment height, l is the depth of concrete compression, and x is the segment compression height when the concrete reaches the limit state; Stress Stage 3: M bo <M ca ; At this stage, the neutral axis is between the joint axis and the upper edge of the concrete, and M is the bending moment to which the concrete is subjected; k m1 ＝∞ (30) Among them, k m3 is the bending stiffness of the third stage; The system of equations to solve for θ is as follows: N=F c -(T+PT) (33) Among them, β bo As the fitting parameters under this stress state, T is the joint tension, d is the distance between the joint and the outer edge of the concrete, and PT is the preload of the joint.

6. The analytical method for calculating the opening amount of a new quick-joint pipe segment according to claim 1 is characterized in that: In step (3), M co is the bending moment when the neutral axis is at the edge of the concrete, M bo is the bending moment when the neutral axis is at the joint, M co and M bo The solution is as follows: M co The solution: M co =0.5N(h-β co h) (20) Where h is the segment height, β co The fitting parameters under this stress state are: M bo The solution: Among them, β bo is the fitting parameter under this stress state.

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

8. A novel analytical device for calculating the opening amount of a quick-joint pipe segment, 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 analysis method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the analysis method according to any one of claims 1 to 7 are implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the analysis method according to any one of claims 1 to 7 are implemented.

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