Analysis method of pipe-soil interaction mechanism under thermal shock action

Abstract

The invention belongs to the technical field of pipe-soil interaction research methods, and discloses a method for analyzing a pipe-soil interaction mechanism under a thermal shock action, and the method comprises the following steps: S1, obtaining parameters; s2, establishing a mathematical model; s3, combining initial conditions, boundary conditions and interface conditions, and solving the equation by utilizing Laplace transformation and inverse transformation thereof to obtain pipeline-surrounding soil system thermodynamic response data; and S4, analyzing the influence rule of the impact load, the interface thermal resistance, the local contact coefficient, the thermal conductivity, the pipeline density and the pipeline specific heat capacity on the thermal response of the pipe-soil system. According to the analysis method, the influence rule of the thermal shock load, the interface condition and the material attribute on the thermal response of the pipeline-surrounding soil system is analyzed, the method has important guiding significance on the actual engineering design and construction process, the design scheme can be optimized, the reliability and durability of the pipeline can be improved, and the surrounding soil can be kept stable.

Description

Technical Field

[0001] The invention relates to the technical field of pipe-soil interaction research methods, and in particular to an analysis method for the pipe-soil interaction mechanism under thermal shock. Background Art

[0002] Long-distance oil and gas pipelines are pipeline systems specifically used for large-scale transportation of crude oil, refined oil, natural gas, liquefied natural gas and petroleum products. This type of pipeline system is built to achieve long-distance transportation and is used to connect production sites, oil storage bases, refineries, and consumption or transportation sites in different regions. In short, long-distance oil and gas pipelines play an important role in the energy industry and are important infrastructure supporting the operation of the global economy. Proper planning and management of pipeline construction and operation can help improve the security and efficiency of energy supply.

[0003] However, due to the complex terrain and landforms along the long-distance oil and gas pipelines, various types of pipeline geological disasters frequently occur. Therefore, in the actual engineering design and construction process, a theoretical guidance or calculation method is urgently needed to reduce geological disasters and increase the service life of the pipeline. Summary of the invention

[0004] The present invention aims to provide an analysis method for the pipe-soil interaction mechanism under thermal shock, and analyze the influence of thermal shock load, interface conditions and material properties on the thermal response of the pipeline-surrounding soil system. It has important guiding significance for the actual engineering design and construction process, helps to optimize the design scheme, improve the reliability and durability of the pipeline, and is conducive to maintaining the stability of the surrounding soil.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] A method for analyzing the pipe-soil interaction mechanism under thermal shock, comprising the following steps:

[0007] S1. Obtain parameters, including impact load, initial temperature, inner and outer diameters of the pipeline, density of the pipeline and surrounding soil, pipeline thickness, interface thermal resistance, local thermal contact coefficient, thermal conductivity and specific heat capacity under constant strain;

[0008] S2. Establishing a mathematical model, the mathematical model includes a displacement control equation and a temperature control equation;

[0009] S3. Combining the initial conditions, boundary conditions and interface conditions, the displacement control equation and the temperature control equation are solved by using Laplace transform and its inverse transform to obtain the thermal response data of the pipeline-surrounding soil system, namely, temperature, displacement and radial stress;

[0010] S4. Analyze the influence of impact load, interface thermal resistance, local contact coefficient, thermal conductivity, pipeline density, and pipeline specific heat capacity on the thermal response of the pipeline-surrounding soil system.

[0011] Furthermore, in S2, the displacement control equation and the temperature control equation are:

[0012]

[0013] Where j = 1, 2, 1 represents the pipe, 2 represents the soil, λ j and μ j is the Lamé constant, j =2υ j μ j / (1-2υ j ), μ j =G j , j is Poisson's ratio, G j is the shear modulus, e j is the body strain, u rj is the radial displacement, the thermoelastic modulus β j =(3λ j +2μ j )α j , α j is the linear thermal expansion coefficient, θ j is the temperature increment, θ j =T j -T0,T j , T0 are absolute temperature and initial temperature respectively, ρ j is the density, c Ej is the specific heat capacity under constant strain, k j is the thermal conductivity coefficient.

[0014] Furthermore, in S3, the boundary conditions and interface conditions are:

[0015]

[0016] Where R is the interface thermal resistance and η is the local thermal contact coefficient.

[0017] The beneficial effects of the technical solution are:

[0018] The present invention discloses an analysis method for the pipe-soil interaction mechanism under thermal shock, which analyzes the influence of different forms of thermal shock loads, interface conditions, local thermal contact coefficients, density of pipelines, thermal conductivity and specific heat capacity on the thermal response of the pipeline-surrounding soil system. In the actual engineering design and construction process, it can help designers select more suitable load forms, interface conditions, and material properties of pipelines, which has important guiding significance for engineering practice, helps to optimize the design scheme, improve the reliability and durability of pipelines, and is beneficial to maintaining the stability of surrounding soil, thereby reducing the occurrence of geological disasters. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is a schematic diagram of a circular pipe deeply buried in infinite homogeneous elastic soil of the present invention;

[0020] Figure 2 A schematic diagram of thermal shock load coordinates in step S4 of a method for analyzing the pipe-soil interaction mechanism under thermal shock of the present invention;

[0021] In the figure, (a) is a schematic diagram of sudden load coordinates, (b) is a schematic diagram of step load coordinates, and (c) is a schematic diagram of trigonometric function load coordinates;

[0022] Figure 3 A curve diagram showing the influence of different thermal shock loads on the thermal response of the pipeline-surrounding soil system in step S4 of the method for analyzing the pipe-soil interaction mechanism under thermal shock of the present invention;

[0023] In the figure, (a) is a curve diagram of the influence law of the temperature increment of the surrounding soil, (b) is a curve diagram of the influence law of the radial displacement of the surrounding soil, (c) is a curve diagram of the influence law of the radial stress of the surrounding soil; (d) is a curve diagram of the influence law of the circumferential stress of the surrounding soil;

[0024] Figure 4 A curve diagram showing the influence of interface conditions on the thermal response of a pipeline-surrounding soil system in step S4 of a method for analyzing the pipe-soil interaction mechanism under thermal shock of the present invention;

[0025] In the figure, (a) is a curve diagram of the influence law of the temperature increment of the surrounding soil, (b) is a curve diagram of the influence law of the radial displacement of the surrounding soil, (c) is a curve diagram of the influence law of the radial stress of the surrounding soil; (d) is a curve diagram of the influence law of the circumferential stress of the surrounding soil;

[0026] Figure 5 A curve diagram showing the influence of the local thermal contact coefficient on the thermal response of the pipeline-surrounding soil system in step S4 of the method for analyzing the pipe-soil interaction mechanism under thermal shock of the present invention;

[0027] In the figure, (a) is a curve diagram of the influence law of the temperature increment of the surrounding soil, (b) is a curve diagram of the influence law of the radial displacement of the surrounding soil, (c) is a curve diagram of the influence law of the radial stress of the surrounding soil; (d) is a curve diagram of the influence law of the circumferential stress of the surrounding soil;

[0028] Figure 6 A curve diagram showing the influence of the density of the pipeline on the thermal response of the pipeline-surrounding soil system in step S4 of the method for analyzing the mechanism of the pipe-soil interaction under thermal shock of the present invention;

[0029] In the figure, (a) is a curve diagram of the influence law of the temperature increment of the surrounding soil, (b) is a curve diagram of the influence law of the radial displacement of the surrounding soil, (c) is a curve diagram of the influence law of the radial stress of the surrounding soil; (d) is a curve diagram of the influence law of the circumferential stress of the surrounding soil;

[0030] Figure 7 A curve diagram showing the influence of the thermal conductivity of the pipeline on the thermal response of the pipeline-surrounding soil system in step S4 of the method for analyzing the mechanism of pipe-soil interaction under thermal shock of the present invention;

[0031] In the figure, (a) is a curve diagram of the influence law of the temperature increment of the surrounding soil, (b) is a curve diagram of the influence law of the radial displacement of the surrounding soil, (c) is a curve diagram of the influence law of the radial stress of the surrounding soil; (d) is a curve diagram of the influence law of the circumferential stress of the surrounding soil;

[0032] Figure 8 A curve diagram showing the influence of the specific heat capacity of the pipeline on the thermal response of the pipeline-surrounding soil system in step S4 of the method for analyzing the mechanism of pipe-soil interaction under thermal shock of the present invention;

[0033] In the figure, (a) is a curve diagram of the influence law of the temperature increment of the surrounding soil, (b) is a curve diagram of the influence law of the radial displacement of the surrounding soil, (c) is a curve diagram of the influence law of the radial stress of the surrounding soil; (d) is a curve diagram of the influence law of the circumferential stress of the surrounding soil;

[0034] The names of the corresponding marks in the accompanying drawings are:

[0035] Pipeline 1, surrounding soil 2, interface 3. DETAILED DESCRIPTION

[0036] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments:

[0037] A method for analyzing the pipe-soil interaction mechanism under thermal shock, comprising the following steps:

[0038] S1. Obtain the density, thermal conductivity k, and specific heat capacity C of the pipeline 1 and surrounding soil 2 under constant strain E, initial temperature T0, inner and outer diameters of pipe 1, r1 and r2 respectively, thickness of pipe 1 h = r2-r1, interface thermal resistance R, local thermal contact coefficient η. Figure 1 As shown, a circular pipe 1 is buried deep in infinite homogeneous elastic soil, and its inner and outer radii are r1 and r2 respectively. The thickness of pipe 1 is h = r2-r1. Assuming that the circular pipe 1 is infinitely long, the plane strain model can be used for analysis. Assuming that the inner surface of pipe 1 is subjected to transient thermal shock load;

[0039] S2. Establishing a mathematical model, the mathematical model includes a displacement control equation and a temperature control equation;

[0040] Among them, the displacement control equation and temperature control equation are:

[0041]

[0042] Where j = 1, 2, 1 represents the pipe, 2 represents the surrounding soil, λ j and μ j is the Lamé constant, j =2υ j μ j / (1-2υ j ), μ j =G j , j is Poisson's ratio, G j is the shear modulus, e j is the body strain, u rj is the radial displacement, the thermoelastic modulus β j =(3λ j +2μ j )α j , α j is the linear thermal expansion coefficient, θ j is the temperature increment, θ j =T j -T0,T j , T0 are absolute temperature and initial temperature respectively, ρ j is the density, c Ej is the specific heat capacity under constant strain, k j is the thermal conductivity coefficient.

[0043] For the convenience of calculation, the following dimensionless quantity is introduced, namely:

[0044]

[0045] Substitute equation (3) into (1) and (2), make it dimensionless, and then perform Laplace transform to obtain the control mathematical models of pipeline 1 and surrounding soil 2 respectively (* omitted):

[0046]

[0047] Where s is the Laplace transform parameter,

[0048]

[0049] S3. Combining the initial conditions, boundary conditions and interface conditions, the displacement control equation and the temperature control equation are solved by using Laplace transform and its inverse transform to obtain the thermal response data of the pipeline 1-surrounding soil 2 system, namely, temperature, displacement and radial stress;

[0050] Combining equations (4) and (5), (6) and (7) yields:

[0051]

[0052] where f1=ξ2ξ3s 3 ,f2=sξ3+sξ1ξ4+s 2 ξ2,d1=s(ε+1)+s 2 ,d2=s 3 .

[0053] Using the Cayley-Hamilton rule, (23) and (24) can be further decomposed into:

[0054]

[0055] in and are the characteristic roots of (23) and (24) respectively.

[0056] when Therefore, the solutions of equations (10) and (11) are respectively set to:

[0057]

[0058] The boundary conditions and interface conditions are:

[0059]

[0060] Where R is the interface thermal resistance, η is the local thermal contact coefficient;

[0061] Using the above conditions, the expressions of the six unknowns in the Laplace domain can be determined. Then, the fast inverse Laplace transform proposed by Brancik is used. This algorithm is based on the fast Fourier transform and uses the quotient difference method to accelerate the convergence of the infinitely complex Fourier series. Finally, the time domain expression of the thermal-mechanical coupled dynamic response of the pipeline 1-surrounding soil 2 system under the action of thermal shock load is obtained, and the thermal response data of the pipeline 1-surrounding soil 2 system, namely temperature, displacement and radial stress, are obtained.

[0062] S4. Analyze the influence of impact load, interface conditions (interface thermal resistance, local contact coefficient), and material properties (thermal conductivity of pipeline 1, density of pipeline 1, specific heat capacity of pipeline 1) on the thermal-mechanical coupling response of pipeline 1-surrounding soil 2 system.

[0063] The dimensionless inner diameter of pipeline 1 is r1=1, the dimensionless outer diameter is r2=1.5, the material parameter values ​​of pipeline 1 are shown in Table 1, and the material parameter values ​​of the surrounding soil are shown in Table 2;

[0064] Table 1 Pipe material parameters

[0065] <![CDATA[G1(Mpa)]]> <![CDATA[υ1]]> <![CDATA[α1(K -1 )]]> <![CDATA[ρ1(kg / m 3 )]]> <![CDATA[c E1 (m 2 ·s -2 ·℃ -1 )]]> <![CDATA[k1(W)]]> 350 0.55 <![CDATA[1.78x10 -5 ]]> 2440 2710 5.6

[0066] Table 2 Material parameters of surrounding soil

[0067] <![CDATA[G2(Mpa)]]> <![CDATA[υ2]]> <![CDATA[α2(K -1 )]]> <![CDATA[ρ2(kg / m 3 )]]> <![CDATA[c E2 (m 2 ·s -2 ·℃ -1 )]]> <![CDATA[k2(W)]]> 3.86 0.3 <![CDATA[4x10 -6 ]]> 1800 2000 3.8

[0068] (1) The influence of thermal shock load on the thermal response of the pipeline 1-surrounding soil 2 system

[0069] Assume that the inner boundary of pipeline 1 is subjected to a radial thermal shock load f(t) that varies with time. The shock loads are sudden load, step load, and trigonometric function load, and the amplitude is f0, such as Figure 2 shown.

[0070] The influence of different thermal shock loads on the thermal response of the pipeline 1-surrounding soil 2 system is as follows: Figure 3 As shown in the figure, when the load form suddenly changes, that is, the sudden load is applied, it will have a significant impact on the stability of the pipeline 1-surrounding soil 2 system. This impact is manifested as large deformation and thermal stress in the system, thus affecting the overall safety of the system. On the contrary, when the load form changes linearly, that is, step load, the deformation and thermal stress of the system are significantly reduced. Therefore, in the actual engineering design and construction process, sudden changes in the load form should be avoided as much as possible, and a relatively gentle load application method should be adopted to ensure the long-term stability and safety of the pipeline 1-surrounding soil 2 system. The results have important guiding significance for engineering practice, which helps to optimize the design scheme and improve the reliability and durability of pipeline 1.

[0071] (2) The influence of interface conditions on the thermal response of the pipeline 1-surrounding soil 2 system

[0072] For the interface between the pipeline 1 and the surrounding soil 2 (r = r2), four different thermal contact conditions are considered:

[0073] Perfect thermal contact: Step thermal contact:

[0074] Local thermal contact: Generalized thermal contact:

[0075] The influence of interface thermal resistance R on the thermal response of pipeline 1-surrounding soil 2 system is as follows: Figure 4 As shown in the figure, it can be seen that when the interface thermal resistance is 0, there is no temperature difference at the interface, and most of the energy passes through the interface into the surrounding soil 2, causing large displacement and stress in the surrounding soil 2. The interface thermal resistance is 10 10 When , there is a large temperature difference at the interface, and almost no energy passes through the interface to enter the surrounding soil 2, resulting in the displacement and stress of the surrounding soil 2 being almost zero. In other words, as the thermal resistance of the interface increases, the temperature difference of the interface increases, and the energy passing through the interface to enter the surrounding soil 2 decreases, which in turn leads to a decrease in the displacement, radial stress, and hoop stress of the surrounding soil 2, which is conducive to maintaining the stability of the surrounding soil 2.

[0076] The influence of interface thermal resistance on the thermal response of the pipeline 1-surrounding soil 2 system is as follows: Figure 5 As shown in the figure, the existence of the local thermal contact coefficient η causes a temperature difference at the interface. As the local thermal contact coefficient increases, the interface temperature difference increases, and the amount of heat entering the surrounding soil 2 decreases, which in turn leads to a decrease in the deformation and stress of the surrounding soil 2. The increase in the local thermal contact coefficient means that the heat loss rate inside the pipeline 1 increases, which helps to reduce the deformation and stress concentration of the pipeline 1-surrounding soil 2 system, and is of great significance to improving the stability of the system. Figure 4 and Figure 5 It can be seen that the interface thermal resistance and local thermal contact coefficient have similar influences on the thermal response of the system, and both play a role in hindering heat flow transfer.

[0077] (3) The influence of material properties on the thermal response of the pipeline 1-surrounding soil 2 system

[0078] Using the controlled variable method and assuming that the material properties of the surrounding soil 2 remain unchanged, the influence of changes in the material properties of pipeline 1 (including density, thermal conductivity, specific heat capacity, etc. of pipeline 1) on the thermal-mechanical coupling response of the system is studied.

[0079] The influence of pipeline 1 density on the thermal response of pipeline 1-surrounding soil 2 system is as follows: Figure 6As shown in the figure, it can be seen that the greater the density of the pipeline 1, the less heat will pass through the interface and enter the surrounding soil 2, which is less conducive to the rapid release of energy and more likely to cause damage to the pipeline 1 itself. However, the greater the density of the pipeline 1, the smaller the deformation and stress change of the surrounding soil 2, that is, the pipeline 1 material with a higher density will cause less harm to the surrounding soil 2 under transient thermal shock loads.

[0080] The influence of the thermal conductivity of pipeline 1 on the thermal response of the pipeline 1-surrounding soil 2 system is as follows: Figure 7 As shown in the figure, it can be seen that the greater the thermal conductivity of the pipeline 1, the more heat passes through the interface and enters the surrounding soil 2, resulting in greater deformation and stress in the surrounding soil 2, and greater damage to the surrounding soil 2.

[0081] The influence of the specific heat capacity of pipeline 1 on the thermal response of the pipeline 1-surrounding soil 2 system is as follows: Figure 8 As shown in the figure, it can be seen that the larger the specific heat capacity of the pipeline 1, the less heat will pass through the interface and enter the surrounding soil 2, which is less conducive to the rapid release of energy and more likely to cause damage to the pipeline 1 itself. At the same time, the larger the specific heat capacity of the pipeline 1, the smaller the deformation and stress change of the surrounding soil 2, that is, the pipeline 1 material with a larger specific heat capacity will cause less harm to the surrounding soil 2 under transient thermal shock loads. Figure 6 and Figure 8 It can be found that the influence of pipeline 1 density and specific heat capacity on the thermal response of the system is similar. Therefore, in terms of the harm to the surrounding soil 2, it is more beneficial to choose a larger pipeline 1 density / specific heat capacity and a smaller pipeline 1 thermal conductivity for actual engineering.

[0082] The analysis shows that a gentle load application method can better ensure the long-term stability and safety of the pipeline 1-surrounding soil 2 system. When the interface thermal resistance R and the local thermal contact coefficient η exist, the interface temperature difference increases, and the interface thermal resistance and the local thermal contact coefficient have similar effects on the thermal response of the system, both of which play a role in hindering heat flow transfer. In terms of the hazard of the surrounding soil, choosing a larger pipeline 1 density / specific heat capacity and a smaller pipeline 1 thermal conductivity is more beneficial to actual engineering.

[0083] In summary, the present invention provides an analysis method for the pipe-soil interaction mechanism under thermal shock, analyzes the influence of different forms of thermal shock loads, interface conditions, local thermal contact coefficient, density, thermal conductivity and specific heat capacity of pipeline 1 on the thermal response of the pipeline 1-surrounding soil 2 system, and can help designers select more suitable load forms, interface conditions, and material properties of pipeline 1 during engineering design and construction. It has important guiding significance for engineering practice, helps to optimize the design scheme, improve the reliability and durability of pipeline 1, and is beneficial to maintaining the stability of surrounding soil 2, thereby reducing the occurrence of geological disasters.

[0084] The above is only an embodiment of the present invention, and the common knowledge such as the known specific technical solutions or characteristics in the solution is not described in detail here. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the technical solution of the present invention, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. A method for analyzing the pipe-soil interaction mechanism under thermal shock, characterized in that: The following steps are involved: S1. Obtain parameters, including impact load, initial temperature, inner and outer diameters of the pipeline, density of the pipeline and surrounding soil, pipeline thickness, interface thermal resistance, local thermal contact coefficient, thermal conductivity and specific heat capacity under constant strain; S2. Establishing a mathematical model, the mathematical model includes a displacement control equation and a temperature control equation; S3. Combining the initial conditions, boundary conditions and interface conditions, the displacement control equation and the temperature control equation are solved by using Laplace transform and its inverse transform to obtain the thermal response data of the pipeline-surrounding soil system, namely, temperature, displacement and radial stress; S4. Analyze the influence of impact load, interface thermal resistance, local contact coefficient, thermal conductivity, pipeline density, and pipeline specific heat capacity on the thermal response of the pipeline-surrounding soil system.

2. The method for analyzing the pipe-soil interaction mechanism under thermal shock according to claim 1, characterized in that: In S2, the displacement control equation and temperature control equation are: Where j = 1, 2, 1 represents the pipe, 2 represents the surrounding soil, λ j and μ j is the Lamé constant, j =2υ j μ j / (1-2υ j ), μ j =G j , j is Poisson's ratio, G j is the shear modulus, e j is the body strain, u rj is the radial displacement, the thermoelastic modulus β j =(3λ j +2μ j )α j , α j is the linear thermal expansion coefficient, θ j is the temperature increment, θ j =T j -T0,T j , T0 are absolute temperature and initial temperature respectively, ρ j is the density, c Ej is the specific heat capacity under constant strain, k j is the thermal conductivity coefficient.

3. The method for analyzing the pipe-soil interaction mechanism under thermal shock according to claim 1, characterized in that: In S3, the boundary conditions and interface conditions are: Where R is the interface thermal resistance and η is the local thermal contact coefficient.

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