Buried pipeline base reaction force calculation model and structure calculation method thereof

Abstract

The invention discloses a buried pipeline base reaction force calculation model and a structural calculation method thereof, and relates to the technical field of trench-buried structure base reaction force calculation, the reaction force calculation model is a trapezoidal model, and the trapezoidal model is constructed by the following steps: establishing an x-q'coordinate system, taking a coordinate origin o as a pipeline vertex position in the x-q 'coordinate system, and calculating the pipeline base reaction force in the x-q' coordinate system; and constructing a trapezoidal model by taking the horizontal rightward direction of the pipeline as the positive direction of an abscissa axis x and the vertical downward direction of the pipeline as the positive direction of a ordinate axis q '. According to the buried pipeline base reaction force calculation model and the structural calculation method thereof, the base reaction force calculation model is provided, a pipeline deformation and stress calculation formula under the model is obtained, base reaction force distribution is in a trapezoidal distribution form, and compared with a traditional method, the structural calculation method has the advantages that the structure is simple, and the calculation efficiency is high. The coincidence degree of a substrate reaction calculation model, a finite element and a test result is better, and errors are reduced.

Description

Technical Field

[0001] The invention relates to the technical field of trench-buried structure base reaction force calculation, and in particular to a buried pipeline base reaction force calculation model and a structural calculation method thereof. Background Art

[0002] As one of the most commonly used water conveyance structures in water diversion and regulation projects, buried pipelines are the "lifeline" of water diversion projects. Among them, buried steel pipes have the advantages of light weight, simple structure, convenient and fast construction, high water conveyance efficiency, long service life, low maintenance cost, and the ability to restore vegetation. They are particularly suitable for major water diversion and regulation projects with long distances, large diameters, high internal pressures, and complex external environments.

[0003] The basis of buried pipeline stress analysis is to determine the distribution and size of soil pressure around the pipe. Therefore, domestic and foreign scholars have carried out a lot of research work to accurately characterize the soil pressure around the pipe. At present, the mainstream pipeline stress model is the Spangler model, which assumes that the base reaction force is uniformly distributed along the cushion angle. In view of the fact that the assumption of soil pressure around the pipe in the Spangler model is greatly simplified, Fujita Hiroai conducted an experimental study on buried steel pipes with a diameter of 2.4m. He assumed that the base reaction force is divided into a point foundation (2α = 20°), a 90° foundation (manually dug) and a 90° foundation (the pipe wall is pressed into the foundation soil), all of which are assumed to be parabolic distribution. In addition, the calculation models of buried flexible pipelines used in my country's power, water supply and drainage industries in the past all refer to the Ye-style model proposed by Л.Μ.Емельянов (Yemelyanov), which basically assumes that the base reaction force is uniformly distributed along the pipe diameter.

[0004] In summary, the current assumptions of the distribution of the base reaction force of buried pipelines are mainly uniform distribution or parabolic distribution, and these assumptions have large errors. Therefore, a buried pipeline base reaction force calculation model and its structural calculation method are proposed. Summary of the invention

[0005] The purpose of the present invention is to provide a buried pipeline base reaction force calculation model and a structural calculation method thereof, so as to solve the problem of large errors existing in the prior art.

[0006] To achieve the above-mentioned purpose, the present invention provides a buried pipeline base reaction force calculation model, the reaction force calculation model is a trapezoidal model, and the construction process of the trapezoidal model is as follows: establish an xq′ coordinate system, in which the coordinate origin o is the vertex position of the pipeline, the horizontal rightward direction of the pipeline is the positive direction of the horizontal coordinate axis x, and the vertical downward direction of the pipeline is the positive direction of the vertical coordinate axis q′ to construct the trapezoidal model;

[0007] In the trapezoidal model, the dividing point of the change in the distribution of the base reaction force is at the intersection of the sand cushion layer and the original soil. Specifically, when the central angle of the soil arc foundation is 2α, the dividing point is Dsinα / 2, and the base reaction force is uniformly distributed in the range of [0, Dsinα / 2], and [Dsinα / 2, D / 2] is a linear distribution, where D is the pipe diameter.

[0008] Preferably, the expression of the trapezoidal model is:

[0009]

[0010] In the formula, q′ v is the maximum value of the base reaction force, a is Dsinα / 2, D is the pipe diameter, and x is the horizontal coordinate variable;

[0011] or,

[0012]

[0013] Where α is half of the central angle of the soil arc foundation;

[0014] Substituting D = 2r, x = rsin(π-θ) = rsinθ into the above formula, we get the trapezoidal model expression related to θ:

[0015]

[0016] Where θ is the angle from the top of the tube to the bottom of the tube in the clockwise direction.

[0017] A method for calculating a buried pipeline structure comprises the following steps:

[0018] Step S1, combining the trapezoidal model of base reaction force with the Spangler model of soil pressure around pipes, and obtaining a model of soil pressure around pipes based on the trapezoidal model by changing only the base reaction force on the basis of the Spangler model;

[0019] Step S2: Under the soil pressure model around the pipe, calculate the sum of the base reaction forces, and then calculate the internal force of the pipe wall under the base reaction force according to different θ ranges. By calculating the generalized displacement, the unknown bending moment x is obtained. 21 and the unknown axial force x 22 , and superimpose it with the internal force of the pipe wall caused by the external load q′ to obtain the internal force of the pipe ring;

[0020] Step S3, adding a horizontal outward unit force at the pipe waist, calculating the internal bending moment of the pipe, and then calculating the horizontal radial displacement caused by the base reaction force at the pipe waist through the internal bending moment of the pipe, and then obtaining the horizontal deformation of the pipe caused by the soil pressure on the pipe top and its base reaction force;

[0021] Step S4: According to K under different soil arc foundation center angles 1TFinally, we get the calculation formula for pipeline deformation, as well as the calculation formula for the bending moment and bending stress at the top, waist and bottom of the pipe ring.

[0022] Preferably, the total base reaction force in step S2 is expressed as follows:

[0023]

[0024] Where r is the pipe radius.

[0025] Preferably, the expressions of the internal forces of the pipe wall in different θ ranges in step S2 are as follows:

[0026] When 0≤θ≤π / 2,

[0027]

[0028] Where M q′ is the bending moment caused by the external load q′ only, N q′ is the axial force caused by the external load q′ only, Q q′ is the shear force caused by the external load q′ only;

[0029] When π / 2≤θ≤π-α,

[0030]

[0031] When π-α≤θ≤π,

[0032]

[0033] In the formula, A is a constant related to α, B is a constant related to α, and C is a constant related to α. The calculation formula is as follows:

[0034]

[0035] Preferably, the unknown bending moment x in step S2 21 Unknown axial force x 22 The expression is as follows:

[0036]

[0037] In the formula, δ 21 For x 21 = 1, the unknown bending moment x 21 The generalized displacement in the direction; δ 22 For x 22 =1, the unknown axial force x 22 The generalized displacement in the direction; δ 1q′ is the unknown bending moment x under the external load q′ 21 The generalized displacement in the direction; δ2q′ is the unknown axial force x under the external load q′ 22 The generalized displacement in the direction, E is the elastic modulus of the pipeline, I is the moment of inertia of the pipeline section, D1 is a constant related to α, E1 is a constant related to α, F is a constant related to α, and G is a constant related to α. The calculation formula is as follows:

[0038]

[0039]

[0040] Preferably, in step S2, the expression of the internal force of the pipe ring is as follows:

[0041]

[0042] Where M2 represents the unknown bending moment x 21 , unknown axial force x 22 The bending moment under the combined action of the external load q′, N2 represents the unknown bending moment x 21 , unknown axial force x 22 The axial force under the combined action of the external load q′, Q2 represents the unknown bending moment x 21 , unknown axial force x 22 The shear force under the combined action of the external load q′, M 21 represents only the unknown bending moment x 21 Bending moment under action, N 21 represents only the unknown bending moment x 21 The axial force under action, Q 21 represents only the unknown bending moment x 21 The shear force under action, M 22 Indicates that only the unknown axial force x 22 Bending moment under action, N 22 Indicates that only the unknown axial force x 22 The axial force under action, Q 22 Indicates that only the unknown axial force x 22 Shear force under action.

[0043] Preferably, the horizontal deformation of the pipeline 2Δ' caused by the soil pressure on the top of the pipe and the reaction force at the base in step S3 1h The expression is as follows:

[0044]

[0045] In the formula, 2Δ 1h is the horizontal deformation under the soil pressure on the top of the pipe, 2Δ 2h is the horizontal deformation caused by the base reaction force at the tube waist;

[0046] Among them, the vertical deformation coefficient of earth pressure K 1TThe expression is as follows:

[0047]

[0048] In the formula, H is a constant related to α, and I1 is a constant related to α. The calculation formula is as follows:

[0049]

[0050] Preferably, the pipeline deformation calculation formula in step S4 is as follows:

[0051]

[0052] The calculation formula for the bending moment of the pipe ring at the top, waist and bottom is:

[0053]

[0054] The bending stress calculation formula is:

[0055]

[0056] Where, Δ is the vertical / horizontal deformation of the pipeline; D L is the deformation hysteresis coefficient; K 1T is the vertical deformation coefficient of soil pressure, which is related to the value of the central angle 2α of the soil arc foundation; K3 is the pipe deformation coefficient under the action of the horizontal resistance on the pipe side, which is determined by the central angle 2β of the horizontal resistance on the pipe side; r is the pipe radius; E is the elastic modulus of the pipe; E′ is the soil reaction modulus; I is the moment of inertia of the pipe section; W is the resultant force of the soil pressure on the top of the pipe; and t is the pipe wall thickness.

[0057] Therefore, the present invention adopts the above-mentioned buried pipeline base reaction force calculation model and its structural calculation method, proposes a base reaction force calculation model, and obtains the pipeline deformation and stress calculation formula under the model. The base reaction force distribution adopts a trapezoidal distribution form. Compared with the traditional method, the base reaction force calculation model has a better consistency with the finite element and test results, and reduces the error.

[0058] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a schematic diagram of a trapezoidal model of an embodiment of a buried pipeline base reaction force calculation model and a structural calculation method thereof according to the present invention;

[0060] Figure 2 It is a schematic diagram of a pipe surrounding soil pressure model of an embodiment of a buried pipeline base reaction force calculation model and a structural calculation method thereof according to the present invention;

[0061] Figure 3It is a schematic diagram of the force decomposition of a semicircular ring of base reaction force of an embodiment of a base reaction force calculation model and a structural calculation method of a buried pipeline of the present invention. DETAILED DESCRIPTION

[0062] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0063] Unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0064] Example

[0065] See also Figure 1-3 The present invention provides a buried pipeline base reaction force calculation model, and the proposed trapezoidal model is as follows Figure 1 As shown. Where D represents the pipe diameter; in the xq′ coordinate system, the origin o is the position of the pipe vertex, the positive direction of the horizontal axis x is horizontally to the right along the pipe, and the positive direction of the vertical axis q′ is vertically downward along the pipe. In the trapezoidal model, the dividing point of the change in the distribution of the base reaction force is at the intersection of the sand cushion layer and the original soil, that is, at the central angle of the soil arc foundation of 2α, the dividing point is Dsinα / 2, and it is uniformly distributed in the range of [0, Dsinα / 2], that is, the soil pressure q′=q′ v is a constant value, and [Dsinα / 2,D / 2] is a linear distribution.

[0066] Since the base reaction force is symmetrical about the axis, Figure 3 The derivation is carried out by taking the right half of as an example. The process is as follows.

[0067] When 0≤x≤a,

[0068] q'(x)=q' v (1)

[0069] When a≤x≤D / 2, in the x1-q′1 coordinate system, the linear equation is assumed to be:

[0070] q′1=kx1 (2)

[0071] Let a = Dsinα / 2 and substitute the boundary conditions: x1 = D / 2-a, q′1 = -q′ v So k = q′ v / (aD / 2). Therefore, in the x1-q′1 coordinate system, the linear equation is:

[0072]

[0073] After coordinate transformation,

[0074]

[0075] In the xq′ coordinate system, the linear equation becomes:

[0076]

[0077] Therefore, the formula of the trapezoidal model is expressed as:

[0078]

[0079] In the formula, q′ v is the maximum value of the base reaction force, a is Dsinα / 2, D is the pipe diameter, and x is the horizontal coordinate variable;

[0080] or,

[0081]

[0082] Where α is half of the central angle of the soil arc foundation;

[0083] Substituting D = 2r, x = rsin(π-θ) = rsinθ into equation (7), the trapezoidal model can be transformed into a formula related to θ:

[0084]

[0085] Where θ is the angle from the top of the tube to the bottom of the tube in the clockwise direction.

[0086] A method for calculating a buried pipeline structure comprises the following steps:

[0087] Step S1, combining the trapezoidal model of base reaction force with the Spangler model of soil pressure around pipes, and obtaining a model of soil pressure around pipes based on the trapezoidal model by changing only the base reaction force on the basis of the Spangler model;

[0088] Step S2: Under the soil pressure model around the pipe, calculate the sum of the base reaction forces, and then calculate the internal force of the pipe wall under the base reaction force according to different θ ranges. By calculating the generalized displacement, the unknown bending moment x is obtained. 21 and the unknown axial force x 22, and superimpose it with the internal force of the pipe wall caused by the external load q′ to obtain the internal force of the pipe ring;

[0089] Step S3, adding a horizontal outward unit force at the pipe waist, calculating the internal bending moment of the pipe, and then calculating the horizontal radial displacement caused by the base reaction force at the pipe waist through the internal bending moment of the pipe, and then obtaining the horizontal deformation of the pipe caused by the soil pressure on the pipe top and its base reaction force;

[0090] Step S4: According to K under different soil arc foundation center angles 1T Finally, we get the calculation formula for pipeline deformation, as well as the calculation formula for the bending moment and bending stress at the top, waist and bottom of the pipe ring.

[0091] The specific steps of the above method are as follows:

[0092] Combining the trapezoidal model of base reaction force with the Spangler pipe surrounding earth pressure model, the calculation method of buried pipeline structure can be derived, such as Figure 2 The figure shows the soil pressure model around the pipe. In the figure, Δx is the horizontal deformation of the pipe; 2α is the central angle of the soil arc foundation; 2β is the central angle of the horizontal resistance of the pipe side; q is the soil pressure on the top of the pipe; q′ v is the maximum value of the base reaction force; q H is the maximum horizontal resistance of the pipe side; E′ is the soil reaction modulus; W is the resultant soil pressure on the pipe top.

[0093] This model only changes the base reaction force based on the Spangler model, and the horizontal resistance and distribution form of the pipe side remain unchanged. Therefore, the calculation formula of pipeline deformation and internal force under this model is only the pipeline deformation coefficient K under the soil pressure on the top of the pipe and its base reaction force. 1T (α) changes, and the formula derivation process is as follows.

[0094] The force decomposition of the semicircular ring of base reaction is as follows Figure 3 The sum of the base reaction forces is:

[0095]

[0096] but,

[0097]

[0098] When the base reaction force is a trapezoidal model, the internal force of the pipe wall under the action of this load is:

[0099] When 0≤θ≤π / 2,

[0100]

[0101] Where M q′ represents the bending moment caused by the external load q′ only; N q′represents the axial force caused by the external load q′ only; Q q′ represents the shear force caused by external load q′ only.

[0102] When π / 2≤θ≤π-α,

[0103]

[0104] When π-α≤θ≤π,

[0105]

[0106] In the formula, A is a constant related to α, B is a constant related to α, and C is a constant related to α. The calculation formula is as follows:

[0107]

[0108] When x 21 and x 22 When is unit force,

[0109]

[0110] At this time, the generalized displacement is:

[0111]

[0112] In the formula, D1 is a constant related to α, E1 is a constant related to α, F is a constant related to α, and G is a constant related to α. The calculation formula is as follows:

[0113]

[0114] In the formula, δ 21 For x 21 = 1, the unknown bending moment x 21 The generalized displacement in the direction; δ 22 For x 22 =1, the unknown axial force x 22 The generalized displacement in the direction; δ 1q′ is the unknown bending moment x under the external load q′ 21 The generalized displacement in the direction; δ 2q′ is the unknown axial force x under the external load q′ 22 The generalized displacement in the direction, E is the elastic modulus of the pipeline, and I is the moment of inertia of the pipeline section.

[0115] Then, the unknown force x 21 、x 22 for:

[0116]

[0117] x21 、x 22 The internal force of the pipe ring can be obtained by superimposing the internal force caused by the external load q′:

[0118]

[0119] Where M2 represents the unknown bending moment x 21 , unknown axial force x 22 The bending moment under the combined action of the external load q′, N2 represents the unknown bending moment x 21 , unknown axial force x 22 The axial force under the combined action of the external load q′, Q2 represents the unknown bending moment x 21 , unknown axial force x 22 The shear force under the combined action of the external load q′, M 21 represents only the unknown bending moment x 21 Bending moment under action, N 21 represents only the unknown bending moment x 21 The axial force under action, Q 21 represents only the unknown bending moment x 21 The shear force under action, M 22 Indicates that only the unknown axial force x 22 Bending moment under action, N 22 Indicates that only the unknown axial force x 22 The axial force under action, Q 22 Indicates that only the unknown axial force x 22 Shear force under action.

[0120] When 0≤θ≤π / 2

[0121]

[0122] When π / 2≤θ≤π-α

[0123]

[0124] When π-α≤θ≤π,

[0125]

[0126] So far, the internal force of the pipe ring under the action of the base reaction force has been obtained. The following will calculate the deformation of the pipe under the action of the base reaction force. Add a horizontal outward unit force F at the waist of the pipe, and the bending moment inside the pipe is:

[0127]

[0128] The horizontal radial displacement △ caused by the base reaction force at the tube waist 2h for:

[0129]

[0130] In the formula, H is a constant related to α, and I1 is a constant related to α. The calculation formula is as follows:

[0131]

[0132] The horizontal deformation of the pipeline caused by the soil pressure on the top of the pipe and the reaction force at the base is 2△′ 1h for:

[0133]

[0134] In the formula, 2Δ 1h is the horizontal deformation under the soil pressure on the top of the pipe, 2Δ 2h is the horizontal deformation caused by the base reaction force at the tube waist, Δ 2h is the horizontal radial displacement caused by the base reaction force at the tube waist.

[0135] Among them, the vertical deformation coefficient of earth pressure K 1T The expression is as follows:

[0136]

[0137] In order to facilitate engineering applications, the K 1T The (α) values ​​are listed in Table 1.

[0138] Table 1 K under different soil arc foundation center angles in the trapezoidal distribution model of base reaction 1T (α) value

[0139]

[0140] Therefore, the final calculation formula for pipeline deformation (the change in the vertical or horizontal diameter of the pipeline) is:

[0141]

[0142] The calculation formula for the bending moment of the pipe ring at the top, waist and bottom is:

[0143]

[0144] The bending stress calculation formula is:

[0145]

[0146] Where, Δ is the vertical / horizontal deformation of the pipeline; D L is the deformation hysteresis coefficient; K 1Tis the vertical deformation coefficient of soil pressure, which is related to the value of the central angle 2α of the soil arc foundation; K3(β) is the pipe deformation coefficient under the action of the horizontal resistance on the pipe side, which is determined by the central angle 2β of the horizontal resistance on the pipe side; r is the pipe radius; E is the elastic modulus of the pipe; E′ is the soil reaction modulus; I is the moment of inertia of the pipe section; W is the resultant force of the soil pressure on the top of the pipe, and t is the pipe wall thickness.

[0147] Therefore, the present invention adopts the above-mentioned buried pipeline base reaction force calculation model and its structural calculation method, proposes a base reaction force calculation model, and obtains the pipeline deformation and stress calculation formula under the model. The base reaction force distribution adopts a trapezoidal distribution form. Compared with the traditional method, the base reaction force calculation model has a better consistency with the finite element and test results, and reduces the error.

[0148] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A buried pipeline base reaction force calculation model, characterized in that: The reaction force calculation model is a trapezoidal model. The construction process of the trapezoidal model is as follows: establish an xq′ coordinate system, in which the coordinate origin o is the vertex position of the pipeline, the horizontal rightward direction of the pipeline is the positive direction of the horizontal coordinate axis x, and the vertical downward direction of the pipeline is the positive direction of the vertical coordinate axis q′ to construct the trapezoidal model; In the trapezoidal model, the dividing point of the change in the distribution of the base reaction force is at the intersection of the sand cushion layer and the original soil. Specifically, when the central angle of the soil arc foundation is 2α, the dividing point is Dsinα / 2, and the base reaction force is uniformly distributed in the range of [0, Dsinα / 2], and [Dsinα / 2, D / 2] is a linear distribution, where D is the pipe diameter.

2. A buried pipeline base reaction force calculation model according to claim 1, characterized in that: The expression of the trapezoidal model is: In the formula, q′ v is the maximum value of the base reaction force, a is Dsinα / 2, D is the pipe diameter, and x is the horizontal coordinate variable; or, Where α is half of the central angle of the soil arc foundation; Substituting D = 2r, x = rsin(π-θ) = rsinθ into the above formula, we get the trapezoidal model expression related to θ: Where θ is the angle from the top of the tube to the bottom of the tube in the clockwise direction.

3. A method for calculating buried pipeline structure, characterized in that: The following steps are involved: Step S1, combining the trapezoidal model of base reaction force with the Spangler model of soil pressure around pipes, and obtaining a model of soil pressure around pipes based on the trapezoidal model by changing only the base reaction force on the basis of the Spangler model; Step S2: Under the soil pressure model around the pipe, calculate the sum of the base reaction forces, and then calculate the internal force of the pipe wall under the base reaction forces according to different θ ranges. By calculating the generalized displacement, the unknown bending moment x is obtained. 21 and the unknown axial force x 22 , and superimpose it with the internal force of the pipe wall caused by the external load q′ to obtain the internal force of the pipe ring; Step S3, adding a horizontal outward unit force at the pipe waist, calculating the internal bending moment of the pipe, and then calculating the horizontal radial displacement caused by the base reaction force at the pipe waist through the internal bending moment of the pipe, and then obtaining the horizontal deformation of the pipe caused by the soil pressure on the pipe top and its base reaction force; Step S4: According to K under different soil arc foundation center angles 1T Finally, we get the calculation formula for pipeline deformation, as well as the calculation formula for the bending moment and bending stress at the top, waist and bottom of the pipe ring.

4. A buried pipeline structure calculation method according to claim 3, characterized in that: The total base reaction force in step S2 is expressed as follows: Where r is the pipe radius.

5. A buried pipeline structure calculation method according to claim 3, characterized in that: The expressions of the internal forces of the pipe wall in different θ ranges in step S2 are as follows: When 0≤θ≤π / 2, Where M q′ is the bending moment caused by the external load q′ only, N q′ is the axial force caused by the external load q′ only, Q q′ is the shear force caused by the external load q′ only; When π / 2≤θ≤π-α, When π-α≤θ≤π, In the formula, A is a constant related to α, B is a constant related to α, and C is a constant related to α. The calculation formula is as follows:

6. A buried pipeline structure calculation method according to claim 3, characterized in that: The unknown bending moment x in step S2 21 Unknown axial force x 22 The expression is as follows: In the formula, δ 21 For x 21 = 1, the unknown bending moment x 21 The generalized displacement in the direction; δ 22 For x 22 = 1, the unknown axial force x 22 The generalized displacement in the direction; δ 1q′ is the unknown bending moment x under the external load q′ 21 The generalized displacement in the direction; δ 2q′ is the unknown axial force x under the external load q′ 22 The generalized displacement in the direction, E is the elastic modulus of the pipeline, I is the moment of inertia of the pipeline section, D1 is a constant related to α, E1 is a constant related to α, F is a constant related to α, and G is a constant related to α. The calculation formula is as follows:

7. A buried pipeline structure calculation method according to claim 3, characterized in that: In step S2, the expression of the internal force of the pipe ring is as follows: Where M2 represents the unknown bending moment x 21 , unknown axial force x 22 The bending moment under the combined action of the external load q′, N2 represents the unknown bending moment x 21 , unknown axial force x 22 The axial force under the combined action of the external load q′, Q2 represents the unknown bending moment x 21 , unknown axial force x 22 The shear force under the combined action of the external load q′, M 21 represents only the unknown bending moment x 21 Bending moment under action, N 21 represents only the unknown bending moment x 21 The axial force under action, Q 21 represents only the unknown bending moment x 21 The shear force under action, M 22 Indicates that only the unknown axial force x 22 Bending moment under action, N 22 Indicates that only the unknown axial force x 22 The axial force under action, Q 22 Indicates that only the unknown axial force x 22 Shear force under action.

8. A buried pipeline structure calculation method according to claim 3, characterized in that: The horizontal deformation of the pipeline 2Δ' caused by the soil pressure on the top of the pipe and the reaction force at the base in step S3 1h The expression is as follows: In the formula, 2Δ 1h is the horizontal deformation under the soil pressure on the top of the pipe, 2Δ 2h is the horizontal deformation caused by the base reaction force at the tube waist; Among them, the vertical deformation coefficient of earth pressure K 1T The expression is as follows: In the formula, H is a constant related to α, and I1 is a constant related to α. The calculation formula is as follows:

9. A buried pipeline structure calculation method according to claim 3, characterized in that: The pipeline deformation calculation formula in step S4 is as follows: The calculation formula for the bending moment of the pipe ring at the top, waist and bottom is: The bending stress calculation formula is: Where, Δ is the vertical / horizontal deformation of the pipeline; D L is the deformation hysteresis coefficient; K 1T is the vertical deformation coefficient of soil pressure, which is related to the value of the central angle 2α of the soil arc foundation; K3 is the pipe deformation coefficient under the action of the horizontal resistance on the pipe side, which is determined by the central angle 2β of the horizontal resistance on the pipe side; r is the pipe radius; E is the elastic modulus of the pipe; E′ is the soil reaction modulus; I is the moment of inertia of the pipe section; W is the resultant force of the soil pressure on the top of the pipe; and t is the pipe wall thickness.

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