Research on Strain of Unequal Wall Thickness Pipeline of the X80 Pipeline under Lateral Load

X80 steel is a material with high strength and good toughness, which is widely used in long-distance natural gas pipelines. Pipelines will have different wall thicknesses, depending on the safety level requirements of different regions. Two sections of pipes with different wall thickness form unequal wall thickness of pipeline (UWTP) that is joined together by welding. UWTP pass through some geohazard areas, such as landslides. The frequency of landslides is extremely high in mountainous areas, which can seriously affect the safe operation of UWTP. In this paper, a model of a 12.8 mm wall pipe section and a 15.6 mm wall pipe section are linked by girth welds. The strain between the pipe section and the weld was quantitatively analyzed. The results show that the strain at the girth weld in the 3 o’clock direction of the pipe increases sharply. The strain in the 9 o’clock direction of the pipe is generally lower than the strain in the 3 o’clock direction. The strain value of the 12.8mm wall thickness pipe section is generally greater than the strain value of the 15.6mm wall thickness pipe section.


Introduction
Long-distance oil and gas pipelines span multiple regions, which means passing through a variety of topographical areas.Due to the different population densities and rare resources in the topographic areas, this will lead to different safety levels of pipelines.This results in two sections of pipe with different wall thicknesses being welded together.Geological disasters along the pipeline may occur frequently and in many types, such as neotectonic movements and earthquakes.The steel grade of the pipeline continues to increase with development.Pipelines of high-grade steel (PHGS) have become the mainstream of pipeline steel.As a typical representative PHGS, X80 is widely used in China, such as China-Myanmar natural gas pipelines.Therefore, it is necessary to carry out the strain analysis at the girth weld of UWTP of high-grade steel under lateral load.This can provide a basis for the subsequent establishment of pipeline failure evaluation index under landslide.
Many scholars have studied pipelines under landslide loads through experiments, theoretical analysis and numerical simulations.Rajani [1] simplified the landslide model and analyzed the mechanical response of the buried pipeline under the action of lateral load.Rourke [2] proposed an elastoplastic model of the force-deformation of the pipe-soil contact surface, and obtained the relationship between the maximum stress of the buried pipeline and the depth of the buried pipeline and the properties of the soil, when the relative displacement of the pipe-soil is small.Mohareb [3] compared the numerical simulation results with the experimental results to prove the accuracy of numerical simulation in predicting pipeline buckling failure, and determined the location of pipeline buckling under landslide disasters.Yatabe and Evans analyzed the pipeline deviation in the case of changes in key factors such as the amount of landslides, and developed a series of preventive measures from the perspective of pipeline safety [4][5].Kunert simulated a landslide by applying a displacement load to the pipeline, and studied the effects of burial depth and soil parameters on the buckling performance of the pipeline [6].Zhang used the finite element method to analyze the influence of pipeline-soil interaction on the mechanical behavior of buried steel pipes [7].Mehmet solved the impact of landslides on solid soil elements through numerical simulation [8].Zhang studied the distribution of the maximum axial stress and strain of the pipeline, and determined the location of the maximum stress and strain of the pipeline under landslide conditions [9].Gu studied the effects of lateral landslides on X80 PHGS with corrosion defects, and identified landslide displacement as the most sensitive factor [10].Wu used large-scale model tests to analyze the interaction and synergistic deformation mechanism of landslides, micropiles, and pipelines under the action of external forces [11].Zhu et al. analyzed the effects of pipeline corrosion size, operating internal pressure, and corrosion location on the ultimate bearing capacity of buried pipelines with corrosion defects, and derived the ultimate load prediction formula [12].Ning established a multi-factor comprehensive evaluation scheme for pipeline landslide disasters [13].Li obtained the pipeline deformation parameters, landslide and pipeline parameters affected by landslides in different directions through numerical simulation [14].
In summary, the current study does not consider the dynamic process of landslides.Most studies apply displacements to soil to simulate actual landslides, which is not in line with reality.Most of the current research is on single-walled pipes, and there is a lack of research on UWTP.In this paper, the SPH smooth particle model is used to study the landslide process as a dynamic process.And the X80 pipeline is taken as a specific object to study the variation of pipeline strain.

Establishment of geometry model
The model is established by means of pipe-soil contact, with the soil as a solid and the pipes placed in the soil.The pipe is constrained by face-to-face contact.Figure 1 shows the model, which can be divided into a pipe model and a soil model.The soil model size is 48×50×30 m.

Figure 1. Schematic diagram of the pipe-soil model
A pipe with a wall thickness of 12.8 mm and a pipe with a wall thickness of 15.6 mm are connected by welds to form UWTP. Figure 2 shows the structure of the pipe and weld.Figure 2 shows the pipe model.

Material properties
The assignment of material properties is mainly based on the constitutive model selection of pipes and soils.

1) Selection of the pipe constitutive model
The elastoplastic model is used as the mechanical model for pipeline steel.Table 1 shows the parameters of X80 steel.
where τ is Shear strength, Pa; c is cohesion, Pa; σn is Normal stress, Pa; φ is angle of friction, o .Table 2 shows the specific parameters in the Morh-Coulomb model.

Solver, load, and boundary condition settings
The model is solved in a dynamic way.The total computing duration is 8 seconds and the time step is 0.00001 seconds.Logarithmic strain value (Abbreviated as strain) is output at 0.08s intervals in the Field Output Request Manager. Figure 4 shows the binding connection between the pipe and the weld, which ensures that no small displacements occur.Figure 5 shows the boundary conditions and load settings for the model.The forces on the pipeline include internal pressure and gravity, and the soil model is subjected to gravity.

Meshing
The model generates C3D8R reduced integral mesh elements by sweeping, and the mesh type is hexahedral mesh elements.The following parameters are used in mesh independence validation.The diameter of the pipe is 1016mm, and the internal pressure is 3MPa.The volume of the landslide is 2340m 3 .The sliding section adopts a smooth particle fluid unit, which can ensure that the sliding section slides smoothly.In this study, multi-factor orthogonal simulation was used to verify the mesh independence of each part in order to reduce the influence of the mesh on the simulation.Table 3 shows the specific dimensions of the individual parts of the simulation.The Mises stress at 3 o'clock at the pipe weld position was selected as the mesh independence verification indicator.The following conclusions are obtained through the grid independence verification.The increase of the size of the soil model leads to a significant increase in the calculation time, while the improvement of the accuracy is relatively weak.Therefore, it was determined that the grid size of the foundationslide was 1800-720mm.The change of the size of the pipe mesh has a weak impact on the calculation time, but has a serious impact on the accuracy of the calculation results.Therefore, the mesh size of the piping model is set to 100 mm. Figure 6 shows the meshing results.

Simulation analysis of strain in landslide pipeline
This research simulates the effects of different pipe diameters, operating pressures, buried depths, landslide volumes, and landslide widths on pipeline strains on the basis of existing models and parameters.This study determined the influence of different factors on pipeline strain through the control variable method.Table 4 shows the specific simulation scenarios for each factor, According to GB 50251-2015 requirements for long-distance natural gas pipelines and the current situation of X80 pipelines in service.The control variable method changes only one parameter on the basis of the parameters in row 3 in table 4.

Effect of pipe diameter on pipe strain
Pipe strain is related to pipe stress.The principal stress of the pipe is related to the normal stress and shear stress of the two components of XY, which can be seen from the relationship between stress and strain.The external force of the pipeline increases with the increase of the pipe diameter due to the increase of the force area.Therefore, the variation of normal stress and shear stress is controlled by two factors, and does not show a simple linear relationship.Figure 7 shows the strain at 813 mm, 916 mm, 1016 mm, 1219 mm, and 1422 mm pipe diameters at 3 o'clock and 9 o'clock.Table 5 shows the maximum strain of the five pipe diameters at 3 o'clock and 9 o'clock.Compared with the 813 mm pipe diameter, the strain change rates of other pipe diameters at 3 o'clock were -17.88 %, -42.22 %, -68.89 % and -80 %.For the 9 o'clock direction, the strain change rates of the other four pipe diameters were -8.33 %, -12.12 %, -20.45 % and -21.97 %.The pipe strain gradually decreases with the increase of the pipe diameter, when the pipe diameter is greater than 813mm.

Effect of internal pressure on pipe strain
Figure 8 shows the pipe strain at 3 o'clock and 9 o'clock at internal pressures of 3 MPa, 5 MPa, 8 MPa, 10 MPa, and 12 MPa.Table 6 shows the maximum strain at 3 o'clock and 9 o'clock under five internal pressure conditions.Compared with the working condition with an internal pressure of 3MPa, the maximum strain change rates in the direction of 3 o'clock under other internal pressure conditions are -4.07%,-42.15%, -57.63% and -77.59%.The maximum strain change rates at 9 o'clock are 2.82%, 7.66%, 258.87% and 500.81%.This phenomenon is due to the fact that the principal stress of the pipeline is related to τxy, σx, and σy.The axial tensile stress and hoop stress of the pipeline increase with the increase of pipeline operating pressure, and the axial compressive stress decreases.Therefore, the strain in the 3 o'clock direction of the pipeline decreases with the increase of the operating pressure of the pipeline, while the strain in the 9 o'clock direction of the pipeline changes in the opposite law.

Effect of buried depth on pipeline strain
The burial depth will affect the change of the soil pressure on the pipeline and the relative displacement of the pipeline and the soil.The earth pressure acting on the pipeline increases with the increase of burial depth, and the rate of relative displacement between the pipeline and the soil decreases.Figure 9 shows the pipe strain at 3 o'clock and 9 o'clock at 1m, 2m, 3m, 4m and 5m depths.
Table 7 shows the maximum strain at 3 o'clock and 9 o'clock for five burial depths.Compared with the pipeline with a buried depth of 1m, the maximum strain change rates of other buried pipelines at 3 o'clock were -26.82%, -47.92%, -71.35% and -85.16%.For the 9 o'clock direction, the maximum strain change rates of other buried pipelines are 39.94%, 89.94%, 132.14% and 133.77%.This is because the main controlling factors of the strain in the direction of the pipeline at 3 o'clock and 9 o'clock are the relative displacement rate of the pipeline and the soil mass and the earth pressure on the pipeline, respectively.Therefore, the strain of the pipeline in the direction of 3 o'clock decreases with the increase of the buried depth, and the strain change law of the pipeline in the direction of 9 o'clock is reversed.

Conclusion
This paper studied the effects of pipe diameter, internal pressure, buried depth and landslide volume on the strain of UWTP of the X80 pipeline.Analyzing the strains of the 3 o'clock and 9 o'clock directions of the pipeline, the conclusions are as follows: 1) The transverse landslide will cause a sharp increase in the strain at the girth weld at 3 o'clock.The strain of the pipeline at 3 o'clock will decrease within the simulation range, with the increase of pipe diameter, internal pressure and buried depth of the pipeline.However, the strain of the pipeline at 3 o'clock will increase first and then decrease，with the increase of the volume of the landslide.
2) The transverse landslide will cause a wavy change in the strain at 9 o'clock in the axial direction of the pipeline, but the strain value of the girth weld is still at the maximum.The overall condition of the pipe strain at 9 o'clock is significantly lower than the strain at 3 o'clock.The strain of the pipe will decrease at 9 o'clock in the simulation range with the increase of pipe diameter.The strain of the pipeline increases at 9 o'clock, with the increase of internal pressure and buried depth.The influence of the landslide volume on the strain of the pipeline in the direction of 9 o'clock is consistent with that in the direction of 3 o'clock.
3) The strain value of the pipe section with a wall thickness of 12.8mm is greater than that of the pipe section with a wall thickness of 15.6mm, according to the strain of the overall variable wall thickness pipe.

Figure 4 .Figure 5 .
Figure 4. Binding connection of the pipe to the weld

Table 1 .
Pipeline parameters (1)Selection of the soil constitutive modelThe Morh-Coulomb model is used in the study of pipe-soil interaction in the soil parameter model.Equation(1)shows the linear relationship between the Mohr equation and the Coulomb equation.c tan n

Table 3 .
Grid-independent verification scheme

Table 4 .
Parameters for the simulation

Table 5 .
Maximum strain for 5 pipe diameters

Table 6 .
Maximum strain for 5 types of internal pressure

Table 7 .
Maximum strains for 5 buried depths the five landslide volumes.Compared with the landslide volume of 2340m 3 , the maximum strain change rates of other landslide volumes in the 3 o'clock direction are 87.18%,68.27%, 48.72% and 37.50%.For the pipeline at 9 o'clock, the maximum strain change rates of other landslide volume pipelines are 2.46%, 4.10%, -5.74% and -8.20%.

Table 8 .
Maximum strains for the 5 types of landslide volumes