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Article

A Study of the Global Buckling Response and Control Measures for Snake-Laid Pipelines Under Uneven Soil Resistances

by
Runnan Miao
1,
Xiang Sun
2,
Chengfeng Li
1,2,*,
Run Liu
1,*,
Xiangning Du
1 and
Yinuo Liu
1
1
State Key Laboratory of Hydraulic Engineering Intelligent Construction and Operation, Tianjin University, Tianjin 300072, China
2
State Key Laboratory of Geomechanics and Geotechnical Engineering Safety, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China
*
Authors to whom correspondence should be addressed.
J. Mar. Sci. Eng. 2025, 13(7), 1258; https://doi.org/10.3390/jmse13071258
Submission received: 16 May 2025 / Revised: 17 June 2025 / Accepted: 26 June 2025 / Published: 28 June 2025
(This article belongs to the Special Issue Safety Evaluation and Protection in Deep-Sea Resource Exploitation)
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Abstract

The snake-laying method is widely employed as an effective strategy for global buckling mitigation in submarine pipelines. The uneven distribution of soil resistance along pipeline routes significantly amplifies the complexity of global buckling responses in snake-laid pipelines and challenges their control mechanisms. This study establishes a finite element computational model to investigate the effects of soil resistance distribution gradients and patterns along pipeline routes, alongside their coupling with critical snake-laying parameters (spacing, offset, curvature). The research revealed that an uneven distribution of soil resistance can induce the global buckling submersion phenomenon in snake-laid pipelines. Among the critical snake-laying parameters, curvature enhancement proves to be the most effective mitigation strategy against the global buckling submersion phenomenon. Additionally, an improvement in the conventional uniform-laying scheme is proposed for uneven soil resistance distribution: the originally planned snake-laid section can be replaced by a straight pipeline section in the high-resistance zone. This study provides enhanced technical solutions for global buckling prevention in pipelines traversing uneven seabeds.

1. Introduction

Submarine pipelines operating in deep-sea HP/HT (high-pressure/high-temperature) environments are susceptible to global buckling phenomena. For the problem of global buckling protection of deep-sea pipelines, the design of actively induced global buckling in submarine pipelines is often used in practical engineering [1,2]. Industry practice employs three primary mitigation strategies, the buoyancy method, the sleeper method, and the snake-laying method, while a combination of these methods also exists in practical engineering [3]. Among these protective measures, the snake-laying method is widely used because of its simplicity of execution and its advantages of not requiring expensive submarine equipment and installation costs [4].
The snake-laying method, involving controlled geometric reconfiguration during subsea installation, strategically induces global buckling under thermal loading through predefined lateral offsets. Early foundational work established critical design principles: Saevik’s prebent pipeline concept (1995) demonstrated lateral buckling control via imposed curvature [5], while Preston’s parametric analysis (1999) quantified geometric influences under idealized uniform seabed conditions [6]. Subsequent industrial applications revealed methodological adaptability—Hooper’s PIP system implementation in the North Sea Penguins project (2004) validated offshore scalability [7]. Rundsag et al. (2008) enhanced the installation methodology of the snake-laying technique under uniform seabed conditions [8]. Liu et al. (2013) incorporated sleeper supports along a pipeline routing using the snake-laying method to enhance global buckling control [9]. Wang (2015) combined genetic algorithm and finite element analysis to optimize the pipeline routing of the snake-laying method [10]. Liu et al. (2018) analyzed the influence of snake-laid pipeline parameters on global buckling deformation by comparing numerical simulation results between snake-laid and straight pipeline configurations [11]. Cao et al. (2019) used numerical simulation to study the key parameters of snake-laid pipelines and found that the snake-laying method can improve the excitation effect of global buckling by optimizing the key parameters [12]. Seyfipour I. et al. (2019) proposed a “continuous snake-laying method”, and, comparing it with the straight pipeline, proved that the snake-laying method can effectively reduce the axial force of the pipeline [13]. Yasaman et al. (2022) employed a spring-based pipe–soil interaction model to simulate seabed resistance on snake-laid pipelines and analyzed fracture failure modes post-global buckling deformation [14]. Li Tao (2023) analyzed the global buckling characteristics, the optimization of virtual anchor spacing, and the finite element simulation verification of the snake-laying method, which provided important technical guidance for the engineering application of this technology [15].
The complex seabed distribution in practical engineering makes the soil resistance along the pipeline routing show uneven variation [16,17,18], and this variation affects the location of excitation and the degree of global buckling of the pipeline [19,20]. However, a notable limitation of the established studies is that the simplifying assumption of a uniform distribution of soil resistances along the route is commonly followed for the global buckling analysis of pipelines [21], while relatively few studies have been conducted on the case of uneven variations in soil resistance along the course of pipelines [16,21,22]. Therefore, this paper establishes a finite element computational model for the global buckling of snake-laid pipeline routing under uneven soil resistance, and investigates the effects of the distribution gradient and distribution pattern of uneven soil resistance along the pipeline routing, as well as its coupling with the snake-laid parameter, on the global buckling of the snake-laid pipeline. For actual engineering, this study fills the theoretical gap regarding the corresponding global buckling of snake-laid pipelines under uneven soil resistance conditions, and provides the key parameter relationship and design basis for assessing the risk of global buckling of pipelines under complex actual working conditions.

2. Finite Element Modeling

2.1. Numerical Analysis Models

In order to study the global buckling response of a snake-laid pipeline along the pipeline routing under uneven soil resistance, reference is made to the snake-laid pipeline in the Penguins project, which employed the snake-laying method with a spacing of 2 km, a radius of 1500 m, and an arc length of 300 m [23]. Figure 1 shows a diagram of the snake-laid pipeline for the Penguins project. Based on the pipeline’s axial forces, the axial force release is known to be consistent for each snake-laid section in the middle, whereas the axial force release at the both ends varies due to the difference in boundary conditions; therefore, the snaked laying at both ends is not taken into account during the analysis of this study.
The finite element model was established based on the 3D-Explicit algorithm in ABAQUS 6.14-4 numerical simulation software [24], and the pipeline was simulated using a beam cell with cell type pipe31, length 16 km, pipeline radius 0.16195 m, and wall thickness 0.0127 m, and the mesh used had a 1 m spread. The seabed was constructed using a 3D solid cell and cell type C3D8R; it was 16 km long, 20 m wide, and 1 m thick, with a 2 m grid. The boundary conditions are free at the ends of the pipeline, fully constrained at the bottom of the soil body, and constrained at the sides of the soil body for degrees of freedom in the x and y directions. The interaction between the pipeline and the seabed was simulated using the Moore–Cullen model, where the contact type was surface-to-surface, the normal contact was “hard”, and the tangential contact was “penalty”. The model was calculated in two steps: (1) applying gravity to achieve full pipe–soil contact; (2) loading a linear temperature field to excite buckling. An example of the constructed model is shown in Figure 2, with only a single snake-laid pipeline shown due to space constraints. The detailed material parameters of the pipeline and seabed are shown in Table 1.
The soil resistance of the pipeline was simplified by friction, and the uneven soil resistance was simulated by setting differentiated friction coefficients along the pipeline route. In the modeling process, the pipeline was cut into segmented areas and different friction coefficients μ were applied to each segment to achieve a non-uneven soil resistance of the pipeline routing. In order to control the variables, the soil friction coefficients of the pipeline start and end segments were taken as 0.5. After considering the calculation cost and the accuracy of the results, eight snake-laid pipeline segments were selected for the whole pipeline model, including the start and end segments. The specific operation was to cut the 2–14 km pipe section of the 16 km pipeline, of which 0–2 km and 14–16 km are the start and end segments, into 12 regions, i.e., 6 snake-laid segments (S-L Ⅰ–Ⅵ). The uneven soil resistance along the pipeline routing is shown in Figure 3.

2.2. Model Validation

In order to verify the reliability of the above calculation model, the pipeline model is established based on the pipeline parameters in Section 2.1, and the results of the global buckling and the practical engineering phenomena are compared and analyzed. Figure 4 shows the comparison between the results of the monitoring data of the snaked laying of the “Penguins” project pipeline and the results of the numerical model.
As shown in Figure 4, the buckling modes of the snake-laid pipeline monitored in the Penguins project are consistent with the numerical simulation results [25,26], with buckling amplitudes of 3.97 m and 3.96 m, respectively, which are in high agreement, thus verifying the reliability of the numerical model.

3. Global Buckling Response of Snake-Laid Pipeline Under Uneven Soil Resistances

3.1. Global Buckling Response of Pipeline Under Different Distribution Gradients of Soil Resistances

In order to study the effect of different distribution gradients of uneven soil resistance on the global buckling of pipeline routing, based on the computational model established in Section 2.1, different distribution gradients of soil resistance are realized by changing the difference in adjacent friction coefficients or by changing the spacing of pipeline segments corresponding to the friction coefficients, and detailed numerical simulation working conditions are shown in Table 2.
Figure 5 shows the gradients of different soil resistance distributions along the pipeline routing for the snake-laid pipeline and the lateral displacements corresponding to global buckling.
From Figure 5, compared to the uniform distribution of buckling in the uniform condition, the buckling of the snake-laid pipeline in the uneven condition produces a higher buckling amplitude in the region of lower soil resistance. Condition B2 buckles only at the snake-laid segments where the soil resistance is low, while little buckling is excited at S-L Ⅱ and S-L Ⅳ. It can be seen that the uneven distribution of the soil resistance will result in the pipe buckling being borne more by the snake-laid pipeline in the region of lower soil resistance. When the gradient of soil resistance distribution is large, i.e., the soil resistance in one snake-laid segment is high while the soil resistance in the adjacent snake-laid segments is relatively low, it may result in the snake-laid pipelines in the area of high soil resistance not undergoing global buckling, which is called the “buckling submerged” phenomenon, which increases the pipeline’s safety hazards.
In order to further analyze the global buckling submerged phenomenon of the snake-laid pipeline, the development of axial force under condition B2 is comparatively analyzed, as shown in Figure 6.
According to Figure 6a,b, when temperature load increases to 4.65 °C in condition B2, axial release occurs at S-L Ⅲ and S-L Ⅴ, and the critical load is about 0.13 MN. The axial force at S-L Ⅳ reaches the maximum value of 0.75 MN when the temperature load increases by 27.9 °C, indicating that the critical axial force at the S-L Ⅳ is greater than 0.75 MN under condition B2. But due to the release of the axial force of the adjacent snake-laid segments, the axial force at S-L Ⅳ is always less than the critical axial force in the process of warming up, and the release of the axial force cannot occur. Combined with the final stress state of the snake-laid pipeline in Figure 6c, it can be seen that the stress magnitudes at S-L Ⅱ and S-L Ⅳ are low and fluctuate gently compared to the other snake-laid segments, indicating that the pipelines at S-L Ⅱ and S-L Ⅳ hardly deform.
Combined with Table 2 comparing the gradients of different soil resistance distributions, the soil resistance along the snake-laid pipeline routing shows significant volatility along the pipeline, which may lead to the global buckling submersion of a particular snake-laid pipeline section when the magnitude of change is large, resulting in wasted costs and increased safety hazards of the pipeline in the actual operation process. In summary, the distribution of soil resistance is an important factor affecting the global buckling submerged pipelines, and the satisfaction of the quantitative relationship between the spacing and the magnitude of the soil resistance is what ensures that the global buckling of adjacent snake-laid pipelines will not be submerged.

3.2. Global Buckling Response of Pipeline with Different Distribution Patterns of Soil Resistance

In order to study the influence of different distribution patterns of soil resistance on global buckling in pipeline routing, based on the computational model established in Section 2.1, different distribution patterns of soil resistance are realized by assigning different friction coefficients to the pipeline–soil contact in each segmented area, and the detailed numerical simulation conditions are arranged as shown in Table 3.
Figure 7 shows the lateral displacement of the snake-laid pipeline along the pipeline routing due to global buckling according to different soil resistance distribution patterns.
As can be seen from Figure 6, the global buckling modes of the pipeline, in conditions D1 and D2 with uneven symmetric soil resistances, are symmetrically distributed, and the location of buckling and the lateral displacements at the symmetric location are exactly the same. In conditions B1 and B2 with randomly distributed soil resistances, the global buckling modes of the pipeline are also randomly distributed, indicating that the distribution of soil resistances along the pipeline routing affects the global buckling modes of the pipeline.
Further analysis of each of the snake-laid pipe segments shows that for S-L Ⅱ and S-L Ⅴ in condition D2 and S-L Ⅴ in condition B2, the soil resistances on both sides of the center of their snake-laid segments are the same, with two major occurrences of buckling occurring. In other conditions where the soil resistance is different on both sides of the snake-laid segments, the pipeline buckles only on the one with the lower soil resistance, and does not buckle significantly on the side with higher resistance. In summary, it can be seen that for a single snake-laid pipeline section spanning areas of varying soil resistance, the pipeline will buckle at one point where the soil resistance is lower and not buckle significantly on the side with higher resistance.
The axial force development pattern of each pipeline along the routing for different soil resistance distribution patterns is shown in Figure 8.
Figure 8 shows that the axial force along the pipeline in the two conditions D1 and D2 is symmetrically distributed, and with the increase in temperature load, the development of axial force also always maintains a symmetrical distribution form; the two conditions E1 and E2 are randomly distributed, but in the region of the same soil resistance (S-L Ⅱ and S-L Ⅵ in condition E1), the axial force development law is also basically the same. It can be seen that the distribution form of soil resistance is an important factor for the development law of the axial force of the pipeline.
In order to further analyze the effect of soil resistance on the development of the axial force of the pipeline, the relationship curves of axial force–temperature load at the center of buckling occurring in each snake-laid segments are compared and analyzed by taking condition E1 as an example, as shown in Figure 9.
According to Figure 9, when the temperature load is increased to 4.65 °C, the pipeline firstly undergoes axial release at S-L Ⅳ, with a critical axial force of 0.11 MN. As the temperature load is further increased, the pipeline undergoes axial release at snake-laid segments in the order of soil resistance from smallest to largest, and the maximum critical axial force (S-L Ⅰ and Ⅴ) reaches about 0.39 MN, which is approximately 3.5 times the minimum critical axial force (S-L Ⅳ). Combined with the distribution of friction coefficients for E1 in Table 3, it can be seen that for every 0.1 increase in the friction coefficient corresponding to the local minimum soil resistance, the critical axial force is increased by about 0.09 MN on average. It is shown that under uneven soil resistance conditions, the snake-laid pipeline will preferentially buckle in the region with less resistance in the local soil at each snake-laid section as the temperature load increases.

4. Study of Snake-Laid Pipeline Scheme Under the Coupling of Uneven Soil Resistance and Snake-Laid Pipeline Parameters

4.1. Global Buckling Response of Snake-Laid Pipelines Under Coupling of Routing Soil Resistance and Snake-Laying Parameters

From Section 3.1, the buckling submerged phenomenon at some snake-laid segments of the pipeline and thus leading to increased pipeline safety hazards can be seen for the soil resistance distribution for condition B2. Pipeline parameters are important factors affecting the global buckling of the pipeline. The coupling effect of the soil resistance and snake-laid pipeline parameters was used to analyze the global buckling response law of the pipeline through the change in the snake-laid pipeline parameters at S-LⅢ-Ⅴ under condition B2; the specific conditions are shown in Table 4.
Figure 10 shows the global buckling response of the pipeline at S-L Ⅲ–Ⅴ for different snake-laid pipeline parameters.
As shown in Figure 10, when decreasing the spacing of the snake-laid pipelines (F1), the pipelines are able to buckle in areas with less soil resistance, but the complete snake-laid segments in areas with more soil resistance may still not buckle. When increasing the spacing of the snake-laid segments (F2), although the pipeline is able to undergo axial release at each snake-laid segment, the value of the axial force increases significantly after release. Under the condition of changing the offset, the buckling behavior of the pipeline remains almost unchanged compared to the original B2 condition, and buckling submersion still occurs. When increasing the snake-laid segments’ curvature (H1), significant axial release of the pipeline occurred at S-LⅣ, indicating that increasing the snake-laid segments’ curvature is an effective measure to address buckling submersion under uneven soil resistance conditions. In order to further analyze the effect of snake-laid pipeline curvature on the development of axial forces, a plot of the development of axial forces in the snake-laid pipeline for H1’s snake-laying parameters is given in Figure 11.
As shown in Figure 11, after increasing the curvature of the snake-laid pipeline, axial release occurs at S-L Ⅲ and S-L Ⅴ when the temperature load is increased to 4.65 °C and the critical axial force is reduced from about 0.13 MN (1/R = 1500 m) to 0.07 MN (1/R = 1000 m), which is a reduction of about 46%. The axial force release occurs at S-L Ⅳ with a critical axial force of about 0.65 MN when the temperature load is increased by 23.25 °C. This indicates that the critical axial force of the pipeline in the regions of higher soil resistance could be significantly reduced by increasing the snake-laid segments’ curvature under the condition of uneven soil resistance, with the critical axial force being reduced by about 46% in the low-soil-resistance region, and the high-soil-resistance region being changed from having an inability to axially release to achieving a successful release of axial force. In summary, when the soil resistance along the snake-laid pipeline routing shows significant volatility along the pipeline, with a large variation in its magnitude, the curvature of the snake-laid pipeline in the adjacent areas with higher soil resistance can be appropriately increased to ensure that these areas can effectively release the axial force and avoid the occurrence of the buckling submerged phenomenon.

4.2. Determination of Snake-Laying Position Under Random Soil Resistance

The snake-laid pipelines in existing projects are usually evenly arranged with a fixed spacing of 2000 m, but for the consideration of pipeline routing under conditions of uneven distribution of soil resistance, the buckling axial force release effect is poor in continuous snake-laid pipelines in regions of higher soil resistance, and even the buckling submerged phenomenon occurs, resulting in a waste of costs and other issues. To solve this problem, the randomly distributed soil resistance shown in Figure 12 is used as an example to analyze the determination of the pipeline routing based on the location of snake laying under uneven soil resistance.
Combined with the global buckling response law of snake-laid pipelines under random soil resistance described in Section 3.2, the snake-laid pipeline scheme based on uniform soil resistance can be improved by considering prioritizing the installation of snake-laid pipelines in areas of lower soil resistance, and replacing them with straight pipes in areas of higher soil resistance. According to Figure 11, the areas of higher random soil resistance for this condition are mainly concentrated at S-L Ⅱ and S-L Ⅳ. Therefore, two different snake-laid pipeline routing schemes are designed as shown in Table 5: Pipeline I2 replaces the snake-laid segments at S-L Ⅱ and S-L Ⅳ with straight-line pipeline segments, whereas Pipeline I3 replaces the straight-line pipeline segments at S-L Ⅱ only.
Figure 13 shows a comparison of axial forces for Pipelines I1–3 under random soil resistance conditions.
As can be seen in Figure 13, Pipeline I1 shows a significant buckling submerged phenomenon at S-L Ⅱ. In contrast, Pipeline I3, after replacing the snake-laid pipeline segments there with straight pipeline segments, ends up with almost the same axial force as Pipeline I1, even with a slight reduction at S-L Ⅱ. Pipeline I1 originally excited a smaller amount of buckling at S-L Ⅳ, and Pipeline I2 did not excite buckling at S-L Ⅳ after being replaced with a straight pipe segment. The final axial forces at S-L Ⅳ are not much different between the two. It can be seen that, for random soil resistance conditions, the laying of continuous snake-laid pipelines should be prioritized in areas of lower soil resistance, while in adjacent areas of higher soil resistance, the snake-laid pipeline sections should be replaced with straight-line pipeline sections to effectively avoid the poor buckling axial force release effect and the buckling submerged phenomenon in part of the snake-laid pipeline section, and also in the whole pipeline to ensure safety on the premise of construction cost savings.
Combining the studies in Section 4, it is clear that there are two ways to increase the curvature or replace the snake-laid pipeline section with a straight section in cases of the buckling submerged phenomenon in the snake-laid pipeline. Therefore, the following decision tree is given, as shown in Figure 14.

5. Discussion

This paper establishes a finite element computational model for the global buckling of snake-laid pipeline routing under uneven soil resistance. The influence of the distribution gradient and distribution pattern of uneven soil resistance along the pipeline routing and its coupling with snake-laid pipeline parameters (laying spacing, offset, curvature) on the global buckling of pipelines is investigated. The snake-laid pipeline scheme under uneven soil resistance is improved. The following main conclusions are obtained:
(1) Compared with the uniform distribution of soil resistance, the uneven distribution of soil resistance along the pipeline routing will result in the pipeline buckling being borne more by the snake-laid pipeline in the area of lower soil resistance, making the maximum buckling amplitude of the pipeline increase significantly. Uneven soil resistance spacing and gradient are important factors affecting the global buckling of the pipeline; when the soil resistance shows significant volatility along the pipeline route, it may even lead to the global buckling submerged phenomenon in some pipeline segments, so the pipeline axial release can only be borne by less global buckling than in the design stage.
(2) The soil resistance distribution pattern significantly affects the buckling response of the pipeline. Under uneven symmetric soil resistance conditions, the global buckling excitation location, the buckling amplitude, and the mode shape of the pipeline will show a symmetric distribution according to the soil resistance distribution pattern, while there is a random distribution under random soil resistance. For a single snake-laid pipeline section spanning across different soil resistance zones, the pipeline will buckle on the side where the soil resistance is lower, while the side with higher resistance does not produce significant buckling. Different local friction coefficients due to uneven soil resistance affect the critical axial force of the pipeline at the corresponding positions, and the maximum critical axial force can reach 3.5 times that of the minimum critical axial force under the calculation conditions in this paper.
(3) Increasing the spacing and curvature of the snake-laid segments can improve the buckling submerged problem in the pipeline at higher soil resistances, while changing the snake-laid offset has no effect. When the curvature was increased from 1/1500 m−1 to 1/1000 m−1, the critical axial force in the low-resistance region was reduced by about 46%, and the high-soil-resistance region changed from an inability to axially release the force to a successful release of the force. Therefore, increasing the curvature of the snake-laid segments is recommended as an effective measure to solve the buckling submerged problem under the comprehensive consideration of the safe and controllable engineering requirements for the release of the axial force.
(4) For the random soil resistance condition, some snake-laid segments may have poor buckling axial force release and experience the buckling submerged phenomenon because of the higher soil resistance compared with the adjacent area. Continuous snake-laid pipelines can be considered to prioritize the use of snake-laid pipelines in areas of lower soil resistance, and in adjacent areas of larger soil resistance, the snake-laid segment sections can be replaced by straight pipeline segments to ensure the safety of the pipeline with the aim of saving construction costs.
It should be noted that the soil resistance in practical engineering inevitably presents an uneven distribution along the pipeline routing, but according to the random field theory, the adjacent soils have variability and correlation at the same time. This makes the soil resistance show continuous gradual change characteristics along the axial direction, instead of the discrete random distribution pattern set in this paper. Therefore, there are some limitations in this study in analyzing the buckling response of snake-laid pipelines by using artificially set uneven soil resistance conditions, and the results are somewhat different from real engineering scenarios. However, mechanistically speaking, the discrete random distribution mode set up in this paper can initially reflect the global buckling response law of snake-laid pipelines under the uneven distribution of soil resistance along the routing, the simplified method is reasonable in the initial exploration stage of the project, and its conclusions can provide theoretical anchors and calibration benchmarks for the refinement of the modeling of the real gradient scenario.

Author Contributions

Conceptualization, R.M. and C.L.; methodology, R.M. and X.S.; software, R.M. and C.L.; validation, R.L., X.D. and Y.L.; writing—original draft preparation, C.L.; writing—review and editing, X.S., X.D. and Y.L.; supervision, X.S. and R.L. All authors have read and agreed to the published version of the manuscript.

Funding

The study is supported by the National Natural Science Foundation of China (Grant no. 42207183), and Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering Safety, Grant No. SKLGME022033.

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Diagram of the snake-laid pipeline for the Penguins project.
Figure 1. Diagram of the snake-laid pipeline for the Penguins project.
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Figure 2. Snake-laid pipeline modeling.
Figure 2. Snake-laid pipeline modeling.
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Figure 3. Uneven soil resistance along pipeline routing.
Figure 3. Uneven soil resistance along pipeline routing.
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Figure 4. Numerical buckling modes and Penguins project pipeline buckling modes.
Figure 4. Numerical buckling modes and Penguins project pipeline buckling modes.
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Figure 5. Lateral displacement of global buckling of snake-laid pipeline with different gradients of soil resistance distribution. (a) A; (b) B1; (c) B2; (d) B3; (e) C1; (f) C2.
Figure 5. Lateral displacement of global buckling of snake-laid pipeline with different gradients of soil resistance distribution. (a) A; (b) B1; (c) B2; (d) B3; (e) C1; (f) C2.
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Jmse 13 01258 g006
Figure 6. Axial force development of the snake-laid pipeline for condition B2. (a) Development of axial force; (b) axial force–temperature load curve; (c) pipeline stress.
Figure 6. Axial force development of the snake-laid pipeline for condition B2. (a) Development of axial force; (b) axial force–temperature load curve; (c) pipeline stress.
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Figure 7. The lateral displacement of the snake-laid pipeline due to global buckling in different soil resistance distribution patterns. (a) D1; (b) D; (c) E1; (d) E2.
Figure 7. The lateral displacement of the snake-laid pipeline due to global buckling in different soil resistance distribution patterns. (a) D1; (b) D; (c) E1; (d) E2.
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Figure 8. The axial force development pattern of each pipeline for different soil resistance distribution patterns. (a) D1; (b) D; (c) E1; (d) E2.
Figure 8. The axial force development pattern of each pipeline for different soil resistance distribution patterns. (a) D1; (b) D; (c) E1; (d) E2.
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Figure 9. Relationship curve of axial force–temperature loading.
Figure 9. Relationship curve of axial force–temperature loading.
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Figure 10. Global buckling response of snake-laid pipeline with different snake-laid pipeline parameters. (a) Lateral displacement under different spacing. (b) Axial forces under different spacing; (c) Lateral displacement under different offsets. (d) Axial forces under different offsets. (e) Lateral displacement under different curvatures. (f) Axial forces under different curvatures.
Figure 10. Global buckling response of snake-laid pipeline with different snake-laid pipeline parameters. (a) Lateral displacement under different spacing. (b) Axial forces under different spacing; (c) Lateral displacement under different offsets. (d) Axial forces under different offsets. (e) Lateral displacement under different curvatures. (f) Axial forces under different curvatures.
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Figure 11. Axial force development of snake-laid pipeline under H1’s snake-laying parameters. (a) Axial force development. (b) Axial force–temperature load curve.
Figure 11. Axial force development of snake-laid pipeline under H1’s snake-laying parameters. (a) Axial force development. (b) Axial force–temperature load curve.
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Figure 12. Distribution of random soil resistance conditions.
Figure 12. Distribution of random soil resistance conditions.
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Figure 13. Comparison of axial forces for Pipelines I1–3.
Figure 13. Comparison of axial forces for Pipelines I1–3.
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Figure 14. The decision tree.
Figure 14. The decision tree.
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Table 1. Pipeline- and seabed-specific parameters.
Table 1. Pipeline- and seabed-specific parameters.
Density
ρ (kg/m3)		Young’s Modulus
E (Pa)		Poisson’s Ratio vCohesion
C (Pa)		Friction Angle
φ (°)		Expansion Coefficient
α (°C)
Pipeline6007.932.06 × 10110.3——1.1 × 10−5
Seabed7803 × 1060.3180018—
Table 2. Numerical simulation conditions under different distribution gradients of soil resistances.
Table 2. Numerical simulation conditions under different distribution gradients of soil resistances.
Condition NumberType of Soil Resistance Along Pipeline RoutingDistribution of Friction Coefficients Along Pipeline Routing
Auniform soil resistanceJmse 13 01258 i001
B1different spacing; the same friction coefficient differenceJmse 13 01258 i002
B2different spacing; the same friction coefficient differenceJmse 13 01258 i003
B3different spacing; the same friction coefficient differenceJmse 13 01258 i004
C1the same spacing; different friction coefficient differencesJmse 13 01258 i005
C2the same spacing; different friction coefficient differencesJmse 13 01258 i006
Table 3. Numerical simulation conditions with different distribution patterns of soil resistance.
Table 3. Numerical simulation conditions with different distribution patterns of soil resistance.
Condition NumberType of Soil Resistance Along Pipeline RoutingDistribution of Friction Coefficients Along Pipeline Routing
D1uneven symmetric distributionJmse 13 01258 i007
D2uneven symmetric distributionJmse 13 01258 i008
E1uneven randomness distributionJmse 13 01258 i009
E2uneven randomness distributionJmse 13 01258 i010
Table 4. Parameters of snake-laid pipeline.
Table 4. Parameters of snake-laid pipeline.
No.Spacing L (km)Curvature 1/R (m−1)Offset w (m)
B221/150092.8
F11.21/150092.8
F231/150092.8
G121/150062.8
G221/1500122.8
H121/100092.8
H221/200092.8
Table 5. Snake-laid pipeline scheme.
Table 5. Snake-laid pipeline scheme.
NO.Pipeline Routing by Laying
I1Jmse 13 01258 i011
I2Jmse 13 01258 i012
I3Jmse 13 01258 i013
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MDPI and ACS Style

Miao, R.; Sun, X.; Li, C.; Liu, R.; Du, X.; Liu, Y. A Study of the Global Buckling Response and Control Measures for Snake-Laid Pipelines Under Uneven Soil Resistances. J. Mar. Sci. Eng. 2025, 13, 1258. https://doi.org/10.3390/jmse13071258

AMA Style

Miao R, Sun X, Li C, Liu R, Du X, Liu Y. A Study of the Global Buckling Response and Control Measures for Snake-Laid Pipelines Under Uneven Soil Resistances. Journal of Marine Science and Engineering. 2025; 13(7):1258. https://doi.org/10.3390/jmse13071258

Chicago/Turabian Style

Miao, Runnan, Xiang Sun, Chengfeng Li, Run Liu, Xiangning Du, and Yinuo Liu. 2025. "A Study of the Global Buckling Response and Control Measures for Snake-Laid Pipelines Under Uneven Soil Resistances" Journal of Marine Science and Engineering 13, no. 7: 1258. https://doi.org/10.3390/jmse13071258

APA Style

Miao, R., Sun, X., Li, C., Liu, R., Du, X., & Liu, Y. (2025). A Study of the Global Buckling Response and Control Measures for Snake-Laid Pipelines Under Uneven Soil Resistances. Journal of Marine Science and Engineering, 13(7), 1258. https://doi.org/10.3390/jmse13071258

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