A method for longitudinal deformation and stress analysis of rectangular jacking pipes passing under existing pressure pipelines

Abstract

This invention relates to the field of underground engineering structural safety assessment methods, providing a method for analyzing the longitudinal deformation and stress of rectangular pipe jacking under existing pressure pipelines. The method includes: establishing a simplified mechanical model of the pressure pipeline; establishing a prediction model for ground settlement caused by the rectangular pipe jacking by modifying the Peck empirical formula, and establishing an analytical relationship between the vertical displacement of the pipeline and the free displacement of the soil; solving the longitudinal displacement field of the pipeline caused by the new rectangular pipe jacking under the pipeline based on the displacement compatibility equation; and applying the Mises stress criterion to calculate the composite stress state of the pipeline, thereby achieving a pipeline stress safety assessment. This invention proposes a calculation method considering the coupling of internal pressure, pipeline, and soil, and theoretically establishes a quantitative relationship between displacement and stress of municipal pipelines caused by the new rectangular pipe jacking under the pipeline. This method can consider the influence of internal forces in municipal pipelines, providing a reliable theoretical method for the safety assessment of rectangular pipe jacking under municipal pressure pipelines.

Description

Technical Field

[0001] This invention belongs to the field of underground engineering structural safety assessment methods, and particularly relates to a method for longitudinal deformation and stress analysis of rectangular jacking pipes passing under existing pressure pipelines. Background Technology

[0002] With the rapid development of urban underground space, it is becoming increasingly common for new connecting passages and integrated utility tunnels to pass close to existing municipal pressure pipelines. As an important component of urban lifeline engineering, the structural safety of pressure pipelines such as gas pipelines, heating pipelines, and industrial pipelines is directly related to the safety of urban operations and the stability of residents' lives.

[0003] However, under the disturbance of rectangular pipe jacking construction, existing pressure pipelines are prone to longitudinal deformation and stress concentration due to factors such as soil stress release, stratum settlement and construction load, which may lead to risks such as pipeline cracking, joint leakage or even breakage.

[0004] Therefore, it is of great practical significance to reasonably assess the stress and deformation of existing pressure pipelines caused by rectangular pipe jacking.

[0005] Currently, the methods for predicting settlement of existing pipelines under tunnels are basically the same. The main methods are generally based on the elastic foundation beam theory framework, that is, the existing pipeline is usually simplified into an Euler-Bernouli beam or Timoshenko beam model, and the pipe-soil interaction mechanism is simulated by the Winkler foundation model or Pasternak two-parameter foundation model.

[0006] The above methods are mostly designed for circular tunnels. Although these methods can reflect the deformation characteristics of pipeline structures under external loads, their mechanical assumptions completely ignore the prestress field of the pipeline structure caused by the pressure and temperature changes of the medium inside the pressure pipeline. Therefore, they are only applicable to unpressurized pipelines.

[0007] In fact, for municipal pressure pipelines, changes in the pressure and temperature of the transmitted medium can cause internal stress in the pipeline in both the circumferential and axial directions.

[0008] When the construction of rectangular pipe jacking causes uneven settlement due to ground disturbance, the superposition effect of the initial prestress field inside the pipe and the additional stress field caused by external deformation will significantly change the mechanical response mechanism of the pipe structure. Summary of the Invention

[0009] This invention provides a method for analyzing the longitudinal deformation and stress of a rectangular jacking pipe passing under an existing pressure pipeline. The aim is to solve the problem of how to calculate the quantitative relationship between the displacement and stress of a municipal pipeline caused by the rectangular jacking pipe passing under it, under the influence of internal forces in the municipal pipeline.

[0010] This invention provides a method for analyzing the longitudinal deformation and stress of a rectangular jacking pipe passing under an existing pressure pipeline, comprising the following steps:

[0011] S1: Establish a simplified mechanical model of the pressure pipeline, simplifying the municipal pressure pipeline longitudinally into a coupled Euler-Bernoulli beam-Pasternak foundation model containing internal pressure effects;

[0012] S2: By modifying Peck's empirical formula, a prediction model for ground settlement caused by rectangular pipe jacking is established. The dynamic coupling effect of soil and pipe is introduced into the mechanical model in S1 to establish the analytical relationship between the vertical displacement of the pipe and the free displacement of the soil.

[0013] S3: Solving the longitudinal displacement field of the pipeline caused by the underpass of a newly built rectangular jacking pipe based on the displacement equation;

[0014] S4: Apply the Mises stress criterion to calculate the composite stress state of the pipeline, and conduct a safety assessment of the pipeline stress based on the calculation results.

[0015] Preferably, in S1:

[0016] Analysis using the Pasternak foundation model: Pipe-soil interaction, internal pressure generates axial compressive strain on the pipe. The existing pressure pipe is considered as a continuous Euler-Bernoulli beam with longitudinal axial force to calculate the longitudinal axial force T.

[0017] The formula for calculating the longitudinal axial force T is as follows:

[0018] ;

[0019] In the formula, T is the axial force in the pipe caused by internal pressure; A s υ is the cross-sectional area of ​​the pipe; σ is the Poisson's ratio of the pipe material; L ρ is the circumferential stress caused by changes in internal pressure and temperature; P is the pressure of the medium transported in the pipeline; D is the outer diameter of the pipeline; t is the pipe wall thickness; E is the elastic modulus of the pipeline material; α is the linear thermal expansion coefficient of the pipeline material; ∆T is the difference between the pipeline's operating temperature and its burial temperature.

[0020] Preferably, in S2: the free settlement s(x) of the strata is calculated using the modified Peck formula;

[0021] The formula for calculating the free settlement s(x) of the strata is as follows:

[0022] ;

[0023] In the formula: S represents surface settlement; B and H are the width and height of the rectangular jacking pipe section, respectively; α is the correction factor; x is the horizontal distance from the jacking pipe axis; V sThe ground loss rate caused by rectangular pipe jacking construction;

[0024] i is the width coefficient of the stratum settlement trough, and its value is determined by: i=K(Z0-Z), where K is the settlement trough width parameter;

[0025] Z represents the vertical distance from the calculated location to the ground surface; Z0 represents the burial depth of the newly constructed pipe jacking axis.

[0026] Preferably, in S2:

[0027] Assuming that the deformation of the pipeline and the soil are coordinated, the differential control equation of displacement of the pressure pipeline is determined through mechanical analysis of the soil-pipeline coupling effect.

[0028] The formula for calculating the differential control equation of displacement in a pressure pipeline is as follows:

[0029] ;

[0030] In the formula: EI is the longitudinal bending stiffness of the pipeline; k is the subgrade coefficient; G c is the shear layer coefficient; w(x) is the displacement of the pipe.

[0031] Preferably, in S2 and S3:

[0032] In the differential control equation of the displacement of the pressure pipeline, the boundary condition of the differential control equation of the displacement of the pressure pipeline is that both ends are free. Then the boundary condition is that the bending moment and shear force at both ends are zero. From this, the displacement of the four virtual nodes at both ends can be obtained. The functional relationship between the displacement of the pressure pipeline and the vertical free displacement of the soil can be derived using the finite difference method.

[0033] The functional relationship is expressed as follows:

[0034] ;

[0035] In the formula, {w} is the vertical displacement vector of the pipeline; {s} is the free displacement vector of the strata caused by the construction of the new pipe jacking project; [K p [K] represents the existing pipe stiffness matrix; s [G] represents the foundation reaction stiffness matrix; s [T] represents the foundation shear stiffness matrix; p [ ] represents the axial force matrix of the pipeline.

[0036] Preferably, in S4:

[0037] Based on the Mises stress criterion, the composite stress state of the pipeline is calculated as follows: After the rectangular jacking pipe is installed, the three principal stresses corresponding to any point on the pipeline are: axial stress σ z Circumferential stress σ h and radial stress σj ;

[0038] The Mises stress criterion formula is:

[0039] ;

[0040] In the formula, σ m [σ] represents the Mises equivalent stress at a point on the pipeline; [σ] represents the allowable stress of the pipeline; f represents the pipeline safety design factor; σ s The yield stress of the pipe material;

[0041] Wherein, axial stress σ z Mainly caused by internal pressure, temperature, and pipe bending, axial stress σ z The calculation formula is:

[0042] ;

[0043] In the formula, M is the pipe bending moment; I is the pipe moment of inertia;

[0044] Among them, the circumferential stress σ h Mainly caused by internal pressure;

[0045] Circumferential stress σ h The calculation formula is:

[0046] ;

[0047] Wherein, radial stress σ j Radial stress σ is caused by internal pressure and soil pressure. j Treat it as 0, that is:

[0048] σ j =0.

[0049] Preferably, the existing continuous municipal pipeline is discretized into finite node elements with an element length of l, totaling n+5 elements, including two virtual elements at each end;

[0050] Based on the central standard finite difference formula, calculate the difference form of the displacement control equation for the pressure pipeline;

[0051] The displacement difference equation for a pressure pipeline is expressed as follows:

[0052] .

[0053] Preferably, the expressions for the vector matrices are as follows:

[0054] ;

[0055]

[0056] ;

[0057] ;

[0058] ;

[0059] .

[0060] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0061] 1. In this invention, a calculation method considering the coupling of internal pressure, pipeline and soil is proposed, which can more accurately reflect the deformation characteristics of existing municipal pressure pipelines under the action of rectangular pipe jacking.

[0062] 2. In this invention, by introducing a temperature gradient effect equation, the invention is applicable to media conditions with large temperature variations, such as heating and gas supply.

[0063] 3. In this invention, by modifying the Peck formula, the method of this invention is made applicable to rectangular pipe jacking tunnels.

[0064] 4. In this invention, by introducing the von Mises yield criterion, a multi-field collaborative safety judgment criterion is proposed, which integrates the internal stress of the pipeline and the strain of external disturbances, thus avoiding the misjudgment problem caused by the traditional method relying solely on external loads.

[0065] In summary, this invention proposes a calculation method that considers the coupling of internal pressure, pipeline, and soil. By theoretically establishing a quantitative relationship between displacement and stress caused by the underpass of a newly constructed rectangular jacking pipe for municipal pipelines, it can take into account the influence of medium pressure and temperature inside the municipal pipeline, providing a reliable theoretical method for the safety assessment of rectangular jacking pipes under municipal pressure pipelines. Attached Figure Description

[0066] Figure 1 This is a schematic cross-sectional view of the computational model in this invention.

[0067] Figure 2 This is a force analysis diagram of the infinitesimal element in this invention.

[0068] Figure 3 This is a schematic diagram of the discrete model of the pressure pipeline in this invention.

[0069] Figure 4 This is a schematic diagram of the force on the pipeline and the stress state of the unit in this invention.

[0070] Figure 5 This is a schematic diagram of the ground settlement caused by the construction of rectangular pipe jacking in this invention.

[0071] Figure 6This is a schematic diagram comparing the pressure pipeline settlement monitoring data and the calculation results of different evaluation methods in this invention.

[0072] Figure 7 This is a schematic diagram of the Mises stress calculation results of the pressure pipeline caused by the construction of rectangular jacking pipe in this invention.

[0073] Figure 8 This is a schematic diagram showing the changes in maximum displacement and equivalent stress of an existing pipeline under different internal pressures in this invention. Detailed Implementation

[0074] 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.

[0075] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.

[0076] like Figure 1-8 As shown, this invention provides a method for analyzing the longitudinal deformation and stress of a rectangular jacking pipe passing under an existing pressure pipeline, comprising the following steps:

[0077] S1: Establish a simplified mechanical model of the pressure pipeline, simplifying the municipal pressure pipeline longitudinally into a coupled Euler-Bernoulli beam-Pasternak foundation model containing internal pressure effects;

[0078] S2: By modifying Peck's empirical formula, a prediction model for ground settlement caused by rectangular pipe jacking is established. The dynamic coupling effect of soil and pipe is introduced into the mechanical model in S1 to establish the analytical relationship between the vertical displacement of the pipe and the free displacement of the soil.

[0079] S3: Solving the longitudinal displacement field of the pipeline caused by the underpass of a newly built rectangular jacking pipe based on the displacement equation;

[0080] S4: Apply the Mises stress criterion to calculate the composite stress state of the pipeline, and conduct a safety assessment of the pipeline stress based on the calculation results.

[0081] This invention proposes a calculation method that considers the coupling of internal pressure, pipeline, and soil. By theoretically establishing a quantitative relationship between displacement and stress caused by the underpass of a newly constructed rectangular jacking pipe to a municipal pipeline, it can take into account the influence of medium pressure and temperature inside the municipal pipeline, providing a reliable theoretical method for the safety assessment of rectangular jacking pipes under municipal pressure pipelines.

[0082] Example 1: Establishing a mechanical calculation model for a rectangular jacking pipe passing under a pressure pipeline.

[0083] like Figure 1 As shown:

[0084] In S1: Analysis using the Pasternak foundation model: Pipe-soil interaction, internal pressure generates axial compressive strain on the pipe, the existing pressure pipe is regarded as a continuous Euler-Bernoulli beam with longitudinal axial force to calculate the longitudinal axial force T (i.e., the axial stress generated in the pipe due to internal pressure and temperature, etc.).

[0085] The formula A for calculating the longitudinal axial force T is as follows:

[0086] ;

[0087] In formula A, T is the axial force in the pipe caused by internal pressure; A s υ is the cross-sectional area of ​​the pipe; σ is the Poisson's ratio of the pipe material; L ρ is the circumferential stress caused by changes in internal pressure and temperature; P is the pressure of the medium transported in the pipeline; D is the outer diameter of the pipeline; t is the pipe wall thickness; E is the elastic modulus of the pipeline material; α is the linear thermal expansion coefficient of the pipeline material; ∆T is the difference between the pipeline's operating temperature and its burial temperature.

[0088] In this invention:

[0089] The existing pipeline is simplified as an Euler-Bernoulli beam resting on the Pasternak foundation. Assuming the existing pipeline does not detach from the surrounding soil (i.e., the pipeline and soil deformation are coordinated), the relationship between the free soil displacement s(x) caused by pipeline excavation, the pipeline displacement u(x) resisting soil deformation, and the final pipeline displacement w(x) is as follows:

[0090] ;

[0091] In the formula, w(x), s(x) and u(x) are all displacements of the existing pipeline axis position.

[0092] like Figure 2 As shown:

[0093] Consider a small element at any point in a continuous pipe for force analysis. Shear force is positive upwards, and bending moment is positive clockwise. Through force equilibrium analysis, we can obtain the following:

[0094] ;

[0095] Where Q is the shear force; M is the bending moment; q(x) is the force exerted by the surrounding strata on the pressure pipeline; D is the diameter of the existing pressure pipeline; and T is the axial stress generated in the pipeline due to internal pressure and temperature, etc.

[0096] Based on the above formula, the formula for calculating the axial stress T generated in the pipeline due to internal pressure and temperature is as follows:

[0097] .

[0098] Example 2: Calculate the vertical free displacement at the pipeline axis caused by the construction of rectangular pipe jacking.

[0099] In S2: the surface settlement curve caused by rectangular pipe jacking excavation is approximately a Gaussian curve; the prediction formula for stratum settlement is calculated using the modified Peck empirical formula;

[0100] Therefore, the formula for calculating the free settlement s(x) of the stratum caused by rectangular pipe jacking construction is as follows:

[0101] ;

[0102] In the formula: S represents surface settlement; B and H are the width and height of the rectangular jacking pipe section, respectively; α is the correction factor; x is the horizontal distance from the jacking pipe axis; V s The ground loss rate caused by rectangular pipe jacking construction;

[0103] i is the width coefficient of the stratum settlement trough, and its value is determined by: i=K(Z0-Z), where K is the settlement trough width parameter;

[0104] Z represents the vertical distance from the calculated location to the ground surface; Z0 represents the burial depth of the newly constructed pipe jacking axis.

[0105] Example 3: Determining the differential control equation for the displacement of a pressure pipeline.

[0106] In S2: it is assumed that the deformation of the pipeline and the soil are coordinated, and the displacement differential control equation of the pressure pipeline is determined through mechanical analysis of the soil-pipeline coupling effect;

[0107] The formula for calculating the differential control equation of displacement in a pressure pipeline is as follows:

[0108] ;

[0109] In the formula: EI is the longitudinal bending stiffness of the pipeline; k is the subgrade coefficient; G c is the shear layer coefficient; w(x) is the displacement of the pipe.

[0110] In this invention:

[0111] The force p(x) that causes the displacement u(x) in the strata due to the pipeline is opposite to the force q(x) exerted on the pipeline by the strata, that is:

[0112] ;

[0113] Combining Examples 1 and 2, and incorporating materials mechanics, the displacement differential governing equation for a rectangular jacking pipe passing under a pressure pipeline is obtained:

[0114] .

[0115] like Figure 3 As shown:

[0116] By combining the finite difference method to solve the above equation, the existing continuous municipal pipeline is discretized into finite node elements with an element length of l, totaling n+5 elements, including two virtual elements at each end.

[0117] Based on the central standard finite difference formula, calculate the difference form of the displacement control equation for the pressure pipeline:

[0118] ;

[0119] In the formula, w i Let s be the pipe displacement at the i-th node; i Let be the free displacement of the soil at the i-th node.

[0120] Example 4: Determine the functional relationship between the displacement of the pressure pipeline and the vertical free displacement of the soil.

[0121] In S2 and S3:

[0122] In the differential control equation of the displacement of the pressure pipeline, the boundary condition of the differential control equation of the displacement of the pressure pipeline is that both ends are free. Then the boundary condition is that the bending moment and shear force at both ends are zero. From this, the displacement of the four virtual nodes at both ends can be obtained. The functional relationship between the displacement of the pressure pipeline and the vertical free displacement of the soil can be derived using the finite difference method.

[0123] The functional relationship is expressed as follows:

[0124] ;

[0125] In the formula, {w} is the vertical displacement vector of the pipeline; {s} is the free displacement vector of the strata caused by the construction of the new pipe jacking project; [K p [K] represents the existing pipe stiffness matrix; s [G] represents the foundation reaction stiffness matrix; s [T] represents the foundation shear stiffness matrix; p [ ] represents the axial force matrix of the pipeline.

[0126] In this invention:

[0127] Assuming the pipe is free at both ends, the boundary conditions are that the bending moment and shear force at both ends are zero. From this, the displacement expressions for the four virtual nodes at both ends can be obtained as follows:

[0128] ;

[0129] Substituting the virtual nodes into the difference form of the displacement control equation for the pressure pipeline in Example 3, we obtain the difference equation for the displacements of the existing pipeline's n+1 nodes, and the matrix algebraic expression for the displacement vector is obtained as follows:

[0130] ;

[0131] Right now,

[0132] .

[0133] The expressions for each vector matrix are as follows:

[0134] ;

[0135]

[0136] ;

[0137] ;

[0138] ;

[0139] .

[0140] Example 5: Determining the longitudinal displacement field of the pipeline.

[0141] The formulas in Examples 1-4 are solved algebraically to obtain the vertical displacement of the existing pressure pipeline under the action of rectangular pipe jacking construction.

[0142] Example 6: Stress analysis of pressure pipeline.

[0143] In S4:

[0144] Based on the Mises stress criterion, the composite stress state of the pipeline is calculated as follows: After the rectangular jacking pipe is installed, the three principal stresses corresponding to any point on the pipeline are: axial stress σ z Circumferential stress σ h and radial stress σ j ;

[0145] The Mises stress criterion formula is:

[0146] ;

[0147] In the formula, σ m [σ] represents the Mises equivalent stress at a point on the pipeline; [σ] represents the allowable stress of the pipeline; f represents the pipeline safety design factor; σ s The yield stress of the pipe material;

[0148] Wherein, axial stress σ z Mainly caused by internal pressure, temperature, and pipe bending, axial stress σ z The calculation formula is:

[0149] ;

[0150] In the formula, M is the pipe bending moment; I is the pipe moment of inertia;

[0151] Among them, the circumferential stress σ h Mainly caused by internal pressure;

[0152] Circumferential stress σ h The calculation formula is:

[0153] ;

[0154] Wherein, radial stress σ j Radial stress σ is caused by internal pressure and soil pressure. j Treat it as 0, that is:

[0155] σ j =0.

[0156] In this invention:

[0157] Ignoring the dynamic effects of the medium transported inside the pipeline, a simplified static analysis is performed on the pipeline. When the pressure of the medium transported inside is P, the force and stress state of the pipeline is as follows: Figure 4 As shown;

[0158] P s The external soil pressure is negligible because municipal pipelines are generally buried at shallow depths, and the soil pressure is much smaller than the working pressure of the internal medium.

[0159] The pipe wall generates forces in three directions under internal pressure, namely:

[0160] Axial stress σ l Circumferential stress σ θ and radial stress σ j .

[0161] The triaxial stress in the upper element of the pipe caused by internal pressure can be derived using Lamé's formula:

[0162] Axial stress σ l , means as follows:

[0163] ;

[0164] Circumferential stress σ θ , means as follows:

[0165] ;

[0166] Radial stress σ j , means as follows:

[0167] ;

[0168] Where r is the inner diameter of the pipe, R is the outer diameter of the pipe, and x is the distance from a point inside the pipe wall to the center of the circle.

[0169] For thin-walled pipes, since the wall thickness is much smaller than the radius, a simplified formula for triaxial stress can be obtained:

[0170] , , , ;

[0171] According to the fourth strength theory (Mises stress criterion), the main cause of yielding is the maximum deformation energy density. It provides a comprehensive stress metric by comprehensively considering the stress components of the material in different directions, which is used to represent the material strength under complex stress states.

[0172] They believe that the material will yield when the distortion energy density under complex stress conditions reaches a certain limit.

[0173] The criterion (i.e., the Mises stress criterion formula) is established based on Mises stress theory and is expressed as follows:

[0174] ;

[0175] In the formula, σ m [σ] represents the Mises equivalent stress at a point on the pipeline; [σ] represents the allowable stress of the pipeline; f represents the pipeline safety design factor; σ s The yield stress of the pipe material;

[0176] The heat and pressure of the medium inside the pipe work together to cause the pipe to expand axially.

[0177] During the expansion process, due to the constraints at the ends and the friction of the soil, axial compressive stress T will be generated inside the steel pipe.

[0178] The ground subsidence caused by pipe jacking construction will result in the existing pipeline being subjected to additional vertical stress q(x).

[0179] Under the combined action of these two loads, the pipeline experienced uneven settlement and deformation.

[0180] Therefore, pipeline stress is mainly caused by pipeline bending, internal pressure, and temperature changes, at which point the axial stress σz Circumferential stress σ θ and radial stress σ j They are respectively:

[0181] Axial stress is mainly caused by internal pressure, temperature changes, and pipe bending, as follows:

[0182] ;

[0183] ;

[0184] ;

[0185] Where, σ l The axial stress caused by internal pressure; σ t σ is the axial stress caused by temperature change. w The axial stress is caused by bending deformation (assuming the neutral axis is at the center).

[0186] Circumferential stress σ θ Mainly caused by internal pressure, as follows:

[0187] ;

[0188] Radial stress σ j It is mainly caused by internal pressure and soil pressure, but its value is much smaller than the other two stresses, therefore, it can be regarded as 0, that is:

[0189] σ j =0.

[0190] Ignoring pipe torsion and given that the shear force is relatively small compared to the axial stress, we can consider the axial stress, circumferential stress, and radial stress as the three principal stresses, with the radial stress being zero. Therefore, the Mises stress criterion is:

[0191] ;

[0192] Since the Mises stress value is necessarily greater than the individual stresses, it is no longer necessary to calculate the axial stress and circumferential stress separately.

[0193] Example 7: Practical application of the present invention.

[0194] The following demonstrates the applicability and rationality of the present invention's method in analyzing the deformation and stress of rectangular jacking pipes passing under existing pressure pipelines, and verifies the settlement prediction method for rectangular jacking pipes passing under pressure pipelines provided by the present invention through engineering examples.

[0195] For example, monitoring data from the subway entrance pipe jacking project shows that the tunnel uses a 7.7×4.3m cross-section pipe jacking machine to vertically pass under a 500mm diameter Class A secondary high-pressure gas pipeline. The jacking depth is about 5.7m. The gas pipeline is made of steel with an elastic modulus of 210GPa, a wall thickness of 7.9mm, a burial depth of 1.75m, and a working pressure of 1.6MPa.

[0196] like Figure 5 As shown:

[0197] Based on surface settlement monitoring data, the settlement trough width parameter is taken as 0.55, the formation loss is taken as 0.5%, the pipeline is mainly located in silty clay formation, and the formation elastic modulus is taken as 20MPa.

[0198] like Figure 6 The results show a comparison between engineering monitoring data and the existing elastic foundation beam method (without considering internal pressure) and the pipeline settlement curve calculated by the method of this invention.

[0199] It can be seen that the method of the present invention is basically consistent with the existing methods for calculating pipeline settlement trends, but the method of the present invention is closer to the actual monitoring data.

[0200] Compared with this method, the calculation results of existing methods that do not consider internal pressure are smaller. This is because the presence of internal pressure in the pipeline will enhance the impact of pipe jacking and cause the pipeline deflection to increase.

[0201] like Figure 7 As shown: Mises stress calculation results for pressure pipelines;

[0202] It can be seen that the maximum equivalent stress calculated by the method of the present invention is about 1.35 times that of the method without considering internal pressure, that is, ignoring internal pressure will seriously underestimate the stress state of the pipeline.

[0203] In addition, this case is located in a high-traffic area, so the strength design factor is recommended to be 0.4, and the allowable stress is 138MPa;

[0204] It can be seen that the maximum equivalent stress of the pipeline is less than the allowable stress, and the structural stress is still in a safe state.

[0205] like Figure 8 The diagram shows the variation of maximum displacement and equivalent stress of an existing pipeline under different internal pressures.

[0206] It can be seen that as the internal pressure of the pipeline increases, the maximum displacement of the pipeline caused by pipe jacking construction and the maximum Mises stress in the pipeline both increase exponentially. This is because, after the pipeline is constrained by friction between the ends and the soil, the increase in internal pressure leads to a greater axial compressive stress in the pipeline.

[0207] When a pipeline experiences localized uneven settlement under the action of pipe jacking construction, the axial stress will increase the pipeline's deflection. Therefore, the greater the internal pressure, the greater the increase in pipeline displacement caused by the increase in internal pressure.

[0208] Therefore, the greater the working pressure of the pipeline, the greater the error when using existing methods that do not consider internal forces.

[0209] In summary, the present invention has the following advantages:

[0210] 1. In this invention, a calculation method considering the coupling of internal pressure, pipeline and soil is proposed, which can more accurately reflect the deformation characteristics of existing municipal pressure pipelines under the action of rectangular pipe jacking.

[0211] 2. In this invention, a temperature gradient effect equation is introduced to be applicable to media conditions with large temperature variations, such as heating and gas supply.

[0212] 3. In this invention, a modified Peck formula is used to make it applicable to rectangular pipe jacking tunnels.

[0213] 4. In this invention, the von Mises yield criterion is introduced, and a multi-field collaborative safety judgment criterion is proposed. By integrating the internal stress of the pipeline and the strain of external disturbances, the misjudgment problem caused by the traditional method relying solely on external loads can be avoided.

[0214] 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 within the protection scope of the present invention.

Claims

1. A method for analyzing the longitudinal deformation and stress of a rectangular jacking pipe passing under an existing pressure pipeline, characterized in that, Includes the following steps: S1: Establish a simplified mechanical model of the pressure pipeline, simplifying the municipal pressure pipeline longitudinally into a coupled Euler-Bernoulli beam-Pasternak foundation model containing internal pressure effects; S2: By modifying Peck's empirical formula, a prediction model for ground settlement caused by rectangular pipe jacking is established. The dynamic coupling effect of soil and pipe is introduced into the mechanical model in S1 to establish the analytical relationship between the vertical displacement of the pipe and the free displacement of the soil. S3: Solving the longitudinal displacement field of the pipeline caused by the underpass of a newly built rectangular jacking pipe based on the displacement equation; S4: Apply the Mises stress criterion to calculate the composite stress state of the pipeline, and conduct a safety assessment of the pipeline stress based on the calculation results.

2. The method for longitudinal deformation and stress analysis of rectangular jacking pipes passing under existing pressure pipelines according to claim 1, characterized in that, In S1: Analysis using the Pasternak foundation model: Pipe-soil interaction, internal pressure generates axial compressive strain on the pipe. The existing pressure pipe is considered as a continuous Euler-Bernoulli beam with longitudinal axial force to calculate the longitudinal axial force T. The formula for calculating the longitudinal axial force T is as follows: ； In the formula, T is the axial force in the pipe caused by internal pressure; A s υ is the cross-sectional area of ​​the pipe; σ is the Poisson's ratio of the pipe material; L ρ is the circumferential stress caused by changes in internal pressure and temperature; P is the pressure of the medium transported in the pipeline; D is the outer diameter of the pipeline; t is the pipe wall thickness; E is the elastic modulus of the pipeline material; α is the linear thermal expansion coefficient of the pipeline material; ∆T is the difference between the pipeline's operating temperature and its burial temperature.

3. The method for longitudinal deformation and stress analysis of rectangular jacking pipes passing under existing pressure pipelines according to claim 1, characterized in that, In S2: the free settlement s(x) of the strata is calculated using the modified Peck formula; The formula for calculating the free settlement s(x) of the strata is as follows: ； In the formula: S represents surface settlement; B and H are the width and height of the rectangular jacking pipe section, respectively; α is the correction factor; x is the horizontal distance from the jacking pipe axis; V s The ground loss rate caused by rectangular pipe jacking construction; i is the width coefficient of the stratum settlement trough, and its value is determined by: i=K(Z0-Z), where K is the settlement trough width parameter; Z represents the vertical distance from the calculated location to the ground surface; Z0 represents the burial depth of the newly constructed pipe jacking axis.

4. The method for longitudinal deformation and stress analysis of rectangular jacking pipes passing under existing pressure pipelines according to claim 1, characterized in that, In S2: Assuming that the deformation of the pipeline and the soil are coordinated, the differential control equation of displacement of the pressure pipeline is determined through mechanical analysis of the soil-pipeline coupling effect. The formula for calculating the differential control equation of displacement in a pressure pipeline is as follows: ； In the formula: EI is the longitudinal bending stiffness of the pipeline; k is the subgrade coefficient; G c is the shear layer coefficient; w(x) is the displacement of the pipe.

5. The method for longitudinal deformation and stress analysis of rectangular jacking pipes passing under existing pressure pipelines according to claim 4, characterized in that, In S2 and S3: In the differential control equation of the displacement of the pressure pipeline, the boundary condition of the differential control equation of the displacement of the pressure pipeline is that both ends are free. Then the boundary condition is that the bending moment and shear force at both ends are zero. From this, the displacement of the four virtual nodes at both ends can be obtained. The functional relationship between the displacement of the pressure pipeline and the vertical free displacement of the soil can be derived using the finite difference method. The functional relationship is expressed as follows: ； In the formula, {w} is the vertical displacement vector of the pipeline; {s} is the free displacement vector of the strata caused by the construction of the new pipe jacking project; [K p [K] represents the existing pipe stiffness matrix; s [G] represents the foundation reaction stiffness matrix; s [T] represents the foundation shear stiffness matrix; p [ ] represents the axial force matrix of the pipeline.

6. The method for longitudinal deformation and stress analysis of rectangular jacking pipes passing under existing pressure pipelines according to claim 1, characterized in that, In S4: Based on the Mises stress criterion, the composite stress state of the pipeline is calculated as follows: After the rectangular jacking pipe is installed, the three principal stresses corresponding to any point on the pipeline are: axial stress σ z Circumferential stress σ h and radial stress σ j ; The Mises stress criterion formula is: ； In the formula, σ m [σ] represents the Mises equivalent stress at a point on the pipeline; [σ] represents the allowable stress of the pipeline; f represents the pipeline safety design factor; σ s The yield stress of the pipe material; Wherein, axial stress σ z Mainly caused by internal pressure, temperature, and pipe bending, axial stress σ z The calculation formula is: ； In the formula, M is the pipe bending moment; I is the pipe moment of inertia; Among them, the circumferential stress σ h Mainly caused by internal pressure; Circumferential stress σ h The calculation formula is: ； Wherein, radial stress σ j Radial stress σ is caused by internal pressure and soil pressure. j Treat it as 0, that is: s j =0.

7. The method for longitudinal deformation and stress analysis of rectangular jacking pipes passing under existing pressure pipelines according to claim 4, characterized in that, The existing continuous municipal pipeline is discretized into finite node elements with an element length of l, totaling n+5 elements, including two virtual elements at each end; Based on the central standard finite difference formula, calculate the difference form of the displacement control equation for the pressure pipeline; The displacement difference equation for a pressure pipeline is expressed as follows: 。 8. The method for longitudinal deformation and stress analysis of rectangular jacking pipes passing under existing pressure pipelines according to claim 5, characterized in that, The expressions for the vector matrix are as follows: ； ； ； ； 。

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