Prediction Model of Pipeline Push Resistance in Tunnels

Abstract

The installation of pipes in tunnel construction using the external welding method requires the assistance of a pipe pusher and roller support to push the welded pipe into the tunnel. Accurate determination of pipeline push resistance and the selection of an appropriate pipe pusher model are crucial factors for successful construction. Currently, there is no effective method available for predicting push resistance, which may result in inaccurate estimation and inadequate thrust provided by the selected pipe pusher. Therefore, this study aims to establish a reliable formula for calculating push resistance through theoretical analysis and numerical simulation. Additionally, we investigate the rolling resistance coefficient between the pipe and roller wheel to develop a corresponding prediction formula. Finally, a test platform is set up to validate our proposed formula for estimating push resistance. The results demonstrate that there is approximately a 5% error between the calculated values and the test values, confirming that this method effectively predicts pipeline push resistance.

1. Introduction

Due to the limitations of topography, the lines of oil and gas pipelines will overlap when they pass through the same area. To save construction costs, new pipelines need to be installed in existing tunnels [1,2]. The traditional welding method in the tunnel requires the pipe to be transported to the tunnel first, and then welding and other work is carried out in the tunnel. However, the space available in the tunnel does not meet the construction requirements. In order to solve the problem, the method of welding outside the tunnel is used for construction. Because the work such as pipe welding is carried out outside the tunnel, it is not restricted by the space inside the tunnel. The installation diagram of welding outside the tunnel is shown in Figure 1.

Before construction, it is necessary to install roller supports in the tunnel, a pipe pusher, and a pipeline prefabrication delivery platform outside the tunnel. During the construction process, a portion of the pipeline will be welded on the prefabricated delivery platform. To ensure welding joint quality, this work will be conducted within a dedicated welding shed. After welding, the pipe is pushed into the tunnel using a pipe pusher. Pipe welding continues after each section has been inserted. These steps are repeated until all tube segments have been fed into the tunnel. Finally, concrete support piers and pipe hoops are used to fix the pipeline.

In order to prevent damage during pipeline movement on the roller wheel, an arc structure is adopted for the roller wheel, which is coated with a layer of polyurethane on its surface. The roller wheel is connected to the support using a bearing, as illustrated in Figure 2. Therefore, in the process of transmission, the pipe pusher not only needs to overcome the gravity component of the pipe acting down the inclined plane, but also needs to overcome the rotating resistance of the bearing and the rolling resistance between the pipe and the roller wheel. However, current calculations of push resistance are primarily based on general experience and do not consider how the structure of the roller wheel affects the coefficient of rolling resistance. Consequently, inadequate thrust selection for the pipe pusher hinders successful completion of pipeline transportation tasks during construction [2,3].

In addition, Coulomb proposed the first formula for calculating rolling resistance (F = Nd/R) by studying the rolling of a wooden wheel on a wooden plane in his research on rolling resistance. In this formula, N represents the normal reaction force exerted by the plane on the wheel, R represents the radius of the wheel, and d represents the force arm of the normal reaction force at the center of the wheel, also known as the rolling resistance coefficient. Despite being able to explain certain phenomena, Coulomb’s formula remains a subject of controversy [4]. Currently, researchers have put forward various mechanisms to explain rolling friction including micro-sliding friction on contact surfaces [5], nonlinear deformation of contact solids [6,7], viscous hysteresis [8,9,10,11,12,13], and surface adhesion [14]. The viscous hysteresis mechanism is widely employed to elucidate energy dissipation in rolling contact. For instance, Rudolphi [15,16,17] utilized a standard linear solid model to describe viscoelastic material characteristics and presented an approach for calculating rolling resistance when a rigid cylinder rolls on viscoelastic materials based on asymmetric stress distribution. Qiu [18,19] used a two-dimensional semi-analytic method to study the rolling problem and further simplified the formula needed to calculate the rolling resistance. Munzenberger [20,21,22] used the finite element method to study the rolling resistance produced by the compression collapse of a rigid cylinder on a rubber belt, used the three-parameter Maxwell model to describe the viscoelastic characteristics of the rubber material, and discussed the influence of temperature, structure, and other factors on the rolling resistance coefficient produced by the compression collapse. Bonhomme [23,24] proposed a new measuring device to measure and study the correlation and influence degree between surface roughness and temperature on production. Larsen [25] investigated belt tensioning and testing problems in industrial feeders and designed a special device to calibrate the testing system.

However, these studies primarily focus on the problem of cylindrical rolling on a flat surface and fail to address the rolling resistance of pipelines on circular-arc roller wheels. Therefore, this paper initially examines the pipeline, roller support, and roller wheel during construction and investigates their interactions. Subsequently, the finite element method is employed to study the rolling resistance between complex pipelines and roller wheels in order to identify its main source. Furthermore, this research constructs calculation and prediction models for push resistance during pipeline installation in tunnels by considering factors such as the friction coefficient between the pipe and roller wheel surfaces, the arc angle of the roller wheel, polyurethane thickness, and the diameter of both the pipeline and the roller wheel. Finally, relevant experiments are conducted for verification purposes.

2. Stress Analysis in the Process of Pipeline Push

In order to derive the resistance calculation formula for pipeline transmission, an analysis of the force state of the pipeline is conducted. As depicted in Figure 1, when employing welding methods for pipe installation outside tunnels, the resistance encountered during pipe pushing increases proportionally with length. Eventually, as the pipeline nears completion, it reaches its maximum resistance generation. To meet construction requirements, the selected pipe pusher must exert a thrust equal to or greater than this maximum value. Therefore, a force analysis of the pipeline at this stage is performed to calculate and determine an appropriate pipe pusher.

The force condition of the pipeline is illustrated in Figure 3. The figure depicts n roller supports, where P represents the thrust force exerted in opposition to the total resistance F during pipeline transmission. N denotes the supporting reaction force exerted by the support on the pipeline, while f signifies the resistance offered by roller supports during pipeline transmission. The equilibrium equation of forces can be derived from the following expression:

$$P=F$$

(1)

$$F=F_{f1}+F_{f2}+\dots +F_{fn}+mg\sin \theta$$

(2)

$$mg\cos \theta =(F_{N1}+F_{N2}+\dots +F_{Nn})$$

(3)

In the formula: P—thrust [N]; F—total resistance [N]; $F_f$—the resistance of the roller support to the pipeline [N]; $F_N$—the support force of the roller support on the pipeline [N]; m—pipe mass [kg]; g—the acceleration of gravity [m/s²]; θ—tunnel inclination [°]; n—the number of roller supports.

Generally, a mountain-crossing tunnel is long, and the number of roller wheels that needs to be laid is large. Therefore, it can be assumed that the force condition of each roller support is the same:

$$F_{f1}=F_{f2}=\dots =F_{fn}=F_f$$

(4)

$$F_{N1}=F_{N2}=\dots =F_{Nn}=F_N$$

(5)

Equations (2) and (3) can be rewritten as:

$$F=mg\sin \theta +{nF}_f$$

(6)

$$mg\cos \theta =n{F}_N$$

(7)

Further force analysis is conducted on the roller support, as depicted in Figure 4. To ensure the pipeline remains aligned with the roller support during transmission, a V-shaped arrangement of roller wheels with a deflection angle φ is employed. In order to meet the requirements of construction, the roller wheels will be arranged side by side in the horizontal direction. Suppose that the number of roller wheels on a roller support is “a”, the support reaction $F_N$ and resistance $F_f$ exerted by each roller wheel on the pipeline can be determined through force analysis, as shown in Figure 5.

In the figure: φ—roller deflection angle [°]; β—roller arc angle [°]; ϕ—outside diameter of the pipe [m]; d—roller wheel diameter [m]; h—polyurethane layer thickness [m].

$$F_{Nc}=\frac{F_N}{a\cos \phi }$$

(8)

$$F_{fc}=\frac{F_f}{a}$$

(9)

In the formula: $F_{Nc}$—the reaction force of a single roller to the pipe [N]; $F_{fc}$—the resistance of a single roller to the pipe [N]; a—the number of roller wheels on the roller support.

Finally, the interaction between a single roller wheel and the pipeline is analyzed. Firstly, as the pipe moves across the roller wheel, it induces rotational motion in the roller wheel due to the frictional forces acting upon it. The roller wheel is connected to a shaft through a bearing. In the process of rotation, the bearing will produce a certain rotational resistance moment, which indirectly acts on the pipeline through the roller wheel. Moreover, energy loss occurs in the rubber material on the surface of the roller wheel during its deformation process. Additionally, since the roller wheel has an arc structure with a smaller radius at its middle part and larger radii at both sides, when the roller wheel rotates at a certain angle, the displacement of both sides of the roller wheel and the middle part is different, and the displacement of any position of the pipe surface is the same, so the roller wheel and the pipe surface will produce friction loss (Figure 6).

The resistance of the roller wheel to the pipeline can be divided into two components: one component is the rotational resistance ($F_{fb}$) of the bearing, while the other component is the rolling resistance ($F_{fr}$) between the pipe and the roller wheel, as expressed in Formula (10). The rolling resistance includes both viscoelastic losses in rubber material and surface friction losses.

$$F_{fc}=F_{fr}+F_{fb}$$

(10)

The rotation of the bearing generates a moment of resistance, denoted as M, which can be calculated using Equation (11) [26]. Such a moment on the roller wheel is equivalent to that of a tangential force on the pipeline ($F_{fb}$) applied at a radius of no sliding as indicated by Equation (12). Since d < d_x (Figure 7), in order to make the calculation of the formula more conservative, Equation (12) is replaced by Equation (13).

$$M={\mu }_b{d}_m{F}_{Nc}/2$$

(11)

$$F_{fb}=\frac{2M}{d_x}$$

(12)

$$F_{fb}=\frac{2M}{d}$$

(13)

where μ_b—the bearing friction coefficient of the tapered roller bearing: 0.0017~0.0025 [26]; d_m—the nominal diameter of the bearing [m].

There is the rolling resistance $F_{fr}$ between the pipe and the roller wheel, which encompasses both the viscoelastic loss of rubber material and the surface friction loss. Previous studies [8,9,10,11,12,13] have shown that Formula (14) can be used to calculate rolling resistance.

$$F_{fr}={\mu }_r{F}_{Nc}$$

(14)

where μ_r—the rolling resistance coefficient.

According to the aforementioned analysis, the resistance encountered during pipeline transmission primarily consists of three components: the gravitational force acting along the inclined plane of the pipeline, the rotational resistance of bearings, and the rolling resistance between the pipeline and roller wheels. By organizing Formulas (1)–(14) systematically, we can determine the push resistance experienced in the process of pipeline transmission.

$$F=mg\sin (\theta )+\frac{mg\cos (\theta )}{\cos (\phi )}\left({\mu }_r+{\mu }_b\frac{d_m}{d}\right)$$

(15)

At present, due to the complex interaction between the pipe and the roller, the rolling resistance coefficient r is not clear, so further analysis is needed.

3. Research on Rolling Resistance Between Pipe and Roller

By using the Abaqus finite element method, the rolling resistance between pipeline and a single roller wheel was studied, and the contact model between the pipeline and the roller wheel was established, as shown in Figure 8. First of all, due to the large stiffness of the hub, the hub will not undergo significant deformation when the pipeline moves across the roller wheel, so only the geometric structure of the polyurethane outer layer of the roller wheel is considered. The unit type adopts the C3D8RH reduced integration unit. At the same time, the inner surface of the polyurethane is coupled to the center point of roller wheel ROLL-RP to simulate the restraint effect of the wheel hub on the polyurethane. The center point of the roller wheel is constrained so that it can only rotate in the axial direction. Secondly, the pipeline model is established, and the element type is a C3D8R linear hexahedron element. To facilitate the application of load and boundary conditions to the pipe, the surfaces at both ends of the pipe are coupled to PIPE-RP at the center point of the pipe. Constraints are applied to this point so that the pipe can only move along the axial direction. Finally, contact action is added to the surface of the pipe and the roller wheel, and the boundary conditions are shown in Figure 9. The surface friction coefficient of the pipe and roller wheel is 0.5 [27]. The model size is shown in

Table 1. Structural parameters.

Pipe Diameter mm	Wall Thickness mm	Minimum Diameter of Roller mm	Roller Arc Angle °	Polyurethane Layer Thickness mm
1016	22	200	45	30

, and the material parameters are shown in

Table 2. Material parameters.

Material	Density kg/m3	Young’s Modulus MPa	Poisson Ratio
Polyurethane	1000	44	0.49
Pipe	7810	2.1 × 105	0.3

. The viscoelastic behavior of the polyurethane materials is characterized by the Prony series, as shown in

Table 3. Prony series.

Number	Normalized Elastic Modulus	Relaxation Time s
1	0.1925	0.06281
2	0.05624	0.8681
3	0.0285	11.683

. In order to take into account the simulation time and the accuracy of the model, the mesh size was 0.01 m and the analysis step time was 0.01 s.

The initial parameters of the model are determined according to the case in the actual project. The pipe size is 1016 × 22 mm. The distance of the roller support is 20 m. The roller wheel deflection angle is 35°. The number of roller wheels on the roller support is 4. It can be calculated that the supporting reaction force of each roller wheel on the pipeline is 30 kN. In order to prevent the speed of pipe pusher from being too fast, the pipeline pushing process will be considered dangerous. The selected push machine has a rated speed of 0.02 m/s.

Therefore, a downward concentration force is applied to the center point of the pipe, with a size of 30 kN. Then, a force along the axial direction of the pipe is applied to this point, so that the pipe moves uniformly at a speed of 0.02 m/s. In the process of pipeline movement, the resistance is equal to the thrust, so the resistance can be obtained by measuring the thrust. The simulation results are shown in Figure 10.

In order to visually describe the force condition of the roller wheel, a cylindrical coordinate system was created along the roller wheel axis, and the circumferential stress cloud diagram of the roller wheel was extracted, as shown in Figure 11. Before the push operation begins, the pipe is in contact with the roller wheel under the action of concentrated force, as shown in Figure 11a. When the pipe is moving on the roller wheel, the surface friction between the pipe rollers will drive the roller wheel to rotate. Because the radius of the roller wheel gradually increases from the middle to both ends, the displacement of both ends is greater than the displacement of the middle position when the roller wheel rotates at a certain angle. At the same time, the displacement of any position of the pipe surface is the same, which leads to the relative sliding of the roller wheel part of the surface and the pipe surface, resulting in friction loss. In addition, there must be a position on the roller wheel where the roller wheel surface displacement is the same as the pipe displacement. In the inner part of the position, the displacement of the pipe is greater than the displacement of the roller wheel surface, the pipe moves forward relative to the roller wheel surface, and the front end of the surface of the roller wheel in contact with the pipe is compressed. Outside this position, the pipe displacement is greater than the displacement of the roller wheel surface, and the pipe moves backward relative to the roller wheel surface, resulting in the compression of the back end of the surface where the pipe meets the roller table, as shown in Figure 11b.

At the initial stage of movement, the distribution of roller wheel circumferential stress is relatively uniform. Although there will be a certain relative displacement between the pipe and the roller wheel surface, under the action of friction, it will not directly cause the pipe and the roller wheel surface to slide relative to one another, but will make the roller wheel undergo a certain deformation. With the continuous movement of the pipeline, the deformation of the roller wheel increases gradually, and the tangential force on the pipeline also increases gradually. When the tangential force between the roller wheel and the pipe surface reaches the sliding condition, the rolling resistance of the pipe reaches its maximum. Within 0~1 s, with the increase in pipeline movement time, the rolling resistance of the pipeline gradually increases, and after 1 s, the rolling resistance tends to stabilize.

In addition, the work done by external forces (ALLWK) during pipeline movement is equal to the sum of viscoelastic loss (ALLCD), recoverable elastic strain energy (ALLSE), kinetic energy (ALLKE), and frictional loss (ALLFD), as shown in Figure 12. At the initial stage of pipeline movement, the friction loss between the pipe and the roller wheel surface is small, and the external work is mainly converted into the elastic strain energy of the system. When the tangential force of the contact surface between the pipe and the roller wheel reaches the sliding condition, friction loss occurs between them, and the elastic strain energy reaches its maximum and tends to be stable. At this timepoint, the work of the external force is mainly converted into the friction loss of the system. In addition, since polyurethane is a viscoelastic material, there is viscoelastic loss during deformation, but it only accounts for 20% of the total energy loss, and the friction loss on the surface of the pipe and roller wheel is the main source of rolling resistance.

The change in rolling resistance with supporting reaction was studied by changing the concentrated force applied at the center point of the pipeline, as shown in Figure 13. There is a linear relationship between the rolling resistance and the supporting reaction between the pipe and the roller wheel, which can be described by $F_{fr}={\mu }_r{F}_{Nc}$.

4. A Study on the Factors Influencing the Rolling Resistance Coefficient

The rolling resistance coefficient between the pipe and roller wheel is related to the pipe’s diameter, the minimum diameter of the roller wheel, the arc angle of the roller wheel, the thickness of the polyurethane layer, and the friction coefficient between the pipe and the roller wheel surfaces. In order to obtain an accurate prediction formula for the rolling resistance coefficient, it is necessary to study the influence of various factors on the rolling resistance coefficient.

4.1. Influence of Friction Coefficient of Pipe and Roller Wheel Surface

In general, the friction coefficient between polyurethane material and metal is between 0.4 and 0.8 [27]. The friction coefficients between pipe and the roller wheel surface are set at 0.4, 0.5, 0.6, 0.7, and 0.8 for simulation analysis. The changes in the rolling resistance coefficient between the pipe and roller wheel under different friction coefficients are studied, and the simulation results are shown in Figure 14. According to previous studies, rolling resistance mainly comes from the friction between the pipe and the roller wheel surface. Therefore, with the gradual increase in friction coefficient, more friction loss will be caused, resulting in an increase in the rolling resistance coefficient.

4.2. Effect of Polyurethane Thickness on Push Resistance

The friction coefficient of the pipe and roller wheel surfaces was set to 0.5, and the polyurethane thickness of the roller wheel was changed to 10 mm, 20 mm, 30 mm, 40 mm, 50 mm, respectively, to study the influence of polyurethane thickness on the rolling resistance coefficient, as shown in Figure 15. With the increase in PU thickness, the rolling resistance between the pipe and roller wheel first increases and then decreases, and reaches its maximum and minimum values at thicknesses of 30 mm and 50 mm, respectively, with a difference of 0.0014, accounting for 3.7% of the average rolling resistance coefficient. With the increase in polyurethane thickness, the viscoelastic loss (ALLCD) of the material increases, but the friction loss (ALLFD) between the pipe and roller wheel decreases, so that the energy loss of the whole system does not change greatly, as shown in Figure 16.

4.3. The Influence of Roller Arc Angle

The radius angle of the arc of the roller wheel on the rolling resistance coefficient was studied, as shown in Figure 17. The surface of the roller wheel has an arc structure. When the pipe and the roller wheel contact, the roller wheel not only generates a vertical supporting force on the pipe, but also exerts an axial force along the roller wheel. With the gradual increase in the arc angle, the total contact force between the pipe and the roller wheel increases, resulting in more friction loss, and the rolling resistance coefficient between the two increases accordingly.

4.4. The Influence of the Minimum Diameter of the Roller

The simulation models were established by using minimum diameters of the roller of 100 mm, 150 mm, 200 mm, 250 mm, and 300 mm, respectively, to study the influence of the minimum diameter of the roller on the rolling resistance coefficient, as shown in Figure 18.

The diameter of the pipe is ϕ, the arc angle of the roller is φ, the minimum diameter of the roller is d, and the displacement of the pipe is l. The displacement difference Δx between the center and periphery of the roller wheel can be calculated, as in Equation (16).

$$\Delta x=l\cos \frac{\phi }{2}\frac{\varphi }{d}$$

(16)

Under the condition that the arc angle of the roller, the diameter of the pipe, and the displacement of the pipe are constant, as the minimum diameter of the roller gradually increases, the displacement difference between the middle position of the roller and the two ends of the roller decreases, so that the relative displacement of the roller and the surface of the pipe decreases, and the work done by the friction force will also decrease. The rolling resistance coefficient and the diameter of the roller are in a negative exponential distribution.

4.5. The Influence of Pipe Diameter on Push Resistance

At present, the diameters of commonly used oil and gas pipelines are 559 mm, 711 mm, 813 mm, 1016 mm, 1219 mm, and 1422 mm. These six pipeline diameters are used to establish simulation models to study the influence of different pipeline diameter on the rolling resistance coefficient, as shown in Figure 19. It can be seen from Equation (15) that, as the diameter of the pipe increases, the displacement difference between the middle position of the roller and the two ends of the roller increases, resulting in more friction loss. Therefore, the rolling resistance coefficient between the pipe and the roller will also increase.

5. Rolling Resistance Coefficient Prediction Formula Fitting

Design-Expert 13 software was applied to fit and combine the response analysis on the friction coefficient, the arc angle of roller wheel, the pipe diameter, the minimum roller wheel diameter, the rolling resistance coefficient, and the polyurethane thickness to obtain the linear polynomial regression equation (Equation (17)). The regression variance is shown in

Table 4. Analysis of variance of regression model.

Source	Sum of Squares	df	Mean Squares	F-Value	p-Value
Mode	0.1046	5	0.0209	292.99	0.0001
Pipe diameter [m]	0.07	1	0.0792	1109.45	0.0001
Arc angle of roller wheel [°]	0.0131	1	0.0131	183.34	0.0001
Roller wheel diameter [m]	0.0220	1	0.0220	308.34	0.0001
Polyurethane thickness [m]	1 × 10−6	1	1 × 10−6	0.0142	0.9055
Surface friction coefficient	0.0097	1	0.0097	136.26	0.0001

. The R² of this equation is 0.91, which has good fitting accuracy. The predicted R² is 0.89, the adjusted R² is 0.90, and the difference between the two is less than 0.2, indicating that the fitting is valid.

$${\mu }_r=0.045\varphi +0.0021\beta +0.0936\mu -0.27d-0.014h-0.0923$$

(17)

The model’s F-value of 292.99 implies that the model is significant. There is only a 0.01% chance that an F-value this large could occur due to noise. p-values less than 0.0500 indicate model terms are significant. In this case, the pipe diameter, arc angle of the roller wheel, roller wheel diameter, and surface friction coefficient are significant model terms.

The calculation formula for push resistance can be derived by incorporating Formula (17) into Formula (15).

6. Field Test

In order to verify the accuracy of the formula, field tests were carried out, as shown in Figure 20. A 1219 × 27 mm pipeline was used at the test site, the material of the pipeline was X80, the length of the pipeline was 36 m, and the total weight of the pipeline was 29.400 kg. The pipe is placed on the roller support and it was ensured that it is level. Powered by a trailer, the trailer and the pipe are connected by a tension meter in the middle for measuring the tension, as in Figure 21. The tension gauge model is Cap-500 kg. The structure of the roller wheel is shown in Figure 4, and its parameters are shown in

Table 5. Structure parameters of roller wheel.

Pipe Diameter m	Roller Wheel Deflection Angle °	Roller Wheel Diameter m	Nominal Diameter of Bearing m	Arc Angle of Roller Wheel °	Polyurethane Layer Thickness mm
1.219	35	0.2	0.12	45	30

.

Start the trailer and drag the pipeline at a speed of 0.02 m/s to move it about a 1 m distance to ensure that the pipeline will not separate from the roller support. After the test, read the data collected by the tension meter, as shown in Figure 22. The average tension of the tension gauge is 19.29 kN. The parameters of the roller support are introduced into Equation (17), and the rolling resistance coefficient is calculated as μ_r = 0.0496. In addition, take the bearing friction coefficient μ_b = 0.0025 and put it into Equation (15) to obtain the pushing resistance of 18.17 kN. The experimental value is 5.8% higher than the calculated value. This proves that the formula can accurately calculate the pushing resistance.

7. Conclusions

In this paper, the stress state of a pipeline during the pipeline transmission process is analyzed, and the calculation formula of the pipeline push resistance is preliminarily obtained. Then, the rolling resistance with complex stress is analyzed by the finite element method, and the following conclusions are obtained:

(1)

The rolling resistance between the pipe and the roller is derived from the friction loss between the two and the viscoelastic loss of the polyurethane material. The friction loss between the pipe and the roller accounts for a large proportion of the total energy loss, about 80%.

(2)

The rolling resistance coefficient between the pipe and the roller is positively correlated with the friction coefficient between the pipe and the roller, the pipe diameter, and the arc angle of the roller, and negatively correlated with the minimum diameter of the roller. In addition, it is less affected by the thickness of the polyurethane and has nothing to do with the support reaction of the roller to the pipe.

(3)

Finally, a field test is carried out, and the error between the test results and the calculation results is about 5%, which means the model can achieve the prediction of push resistance.

In this paper, the rolling resistance of a pipe and a roller wheel under ideal conditions is studied. In practical applications, due to construction errors and other special reasons, the contact state of the roller wheel and the pipeline may change, and affect the push resistance. Therefore, it is necessary to conduct a great deal of research on the field application, and analyze the resistance of the pipeline when using it in practical applications.