Open AccessArticle

A Decoupled Buckling Failure Analysis of Buried Steel Pipeline Subjected to the Strike-Slip Fault

Mozhgan Asgarihajifirouz

Xiaoyu Dong

and

Hodjat Shiri

Department of Civil Engineering, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, Canada

Author to whom correspondence should be addressed.

J. Mar. Sci. Eng. 2024, 12(8), 1243; https://doi.org/10.3390/jmse12081243

Submission received: 15 May 2024 / Revised: 15 July 2024 / Accepted: 17 July 2024 / Published: 23 July 2024

(This article belongs to the Special Issue Advanced Studies in Marine Geomechanics and Geotechnics)

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Abstract

Over the past few years, there has been an increased focus on offshore pipeline safety due to the development of offshore oil and gas resources. Both onshore and offshore pipelines may face significant geological hazards resulting from active faults. Pre-excavated soil can be used as backfill for trenches to prevent major pipeline deformations. Since these backfill materials have been heavily remolded, they are softer than the native soil. Therefore, the difference in shear strength between the backfill and native ground may have an effect on the interaction between the pipeline and the backfill. In this paper, the pipeline–backfill–trench interaction is investigated using a hybrid beam–spring model. The P-Y curves obtained from CEL analysis are incorporated into a 3D beam–spring model to analyze the pipeline’s response to lateral strike-slip faults. Additionally, the nonlinearity of pipeline materials is considered to study pipeline failure modes under strike-slip fault movements. A series of parametric studies were conducted to explore the effects of fault intersection angle, pipe diameter, buried depth of the pipe, and soil conditions on the failure modes of buckling pipelines. The developed method can be used to analyze and assess pipeline–backfill–trench interaction when subjected to strike-slip fault displacements.

Keywords:

pipeline–backfill–trench interaction; force–displacement curves; beam–spring model; coupled Eulerian–Lagrangian (CEL) method; strain softening; strike-slip fault

1. Introduction

Buried pipelines play an essential role in the worldwide economy and society by facilitating the transmission of oil, gas, and other fluids over long distances. However, these pipelines are often at risk of significant damage due to various sources of permanent ground displacement (PGD), such as surface faulting, landslides, seismic settlement, and soil liquefaction caused by lateral movement.

Throughout history, earthquakes such as the 1906 San Francisco, 1976 Tang-shan, 1983 Nihonkai-Chubu, 1989 Loma Prieta, 1995 Kobe, and 1999 Kocaeli earthquakes have caused significant damage to pipeline systems, including water pipelines [1,2,3,4,5,6].

Detecting faults in subsea pipelines is challenging primarily due to the system’s inaccessibility. A leak in hydrocarbon-carrying pipeline systems leads to significant incidents. In the case of a gas line leak, the economic impact on the company would be substantial due to the high cost associated with lost or deferred gas production. Recently, methods utilizing transient tests have been introduced [7,8] These techniques were applied in transient field tests for fault detection in the Trieste subsea, with discussions focusing on the numerical and analytical models employed to analyze the pressure signals recorded during these tests [9,10].

The fault displacement resulting from these earthquakes exposes the pipeline to substantial axial and bending stresses, which can lead to pipeline buckling or rupture. Newmark and Hall (1975) and Kennedy (1977) made significant contributions to the mechanical analysis of pipelines subjected to fault displacement [10,11]. Following their pioneering work, researchers such as Wang and Yeh (1985), Takada et al. (2001), Karamitros et al. (2007), and Trifonov (2010) proposed improved analytical techniques for strain analysis [12,13,14,15]. However, it is important to note that these analytical methods are based on several assumptions and can only calculate tensile strains.

Advanced numerical simulation tools have become the most effective approach for analyzing pipelines under compression. In recent years, researchers have used these tools to investigate how steel pipelines behave when crossing active faults and how they respond to the fault movement. Takada et al. (2001) developed a beam–shell hybrid finite element model to study the correlation between maximum strain and bending angle [11]. Karamitros et al. (2011) further enhanced the model proposed by Takada et al. (2001) by simulating pipeline–soil interactions with a series of springs [16]. Vazouras et al. (2010), Shokouhi et al. (2013), Uckan et al. (2015), and Melissianos et al. (2017) investigated the mechanical behavior of onshore steel pipelines subjected to fault movement [17,18,19,20]. Furthermore, Ha et al. (2008), Xie et al. (2011), and Jalali et al. (2012,2015) performed numerical studies on buried polyethylene (PE) pipelines under normal, strike-slip, and reverse fault movement, respectively [21,22,23,24]. Recently, Qin et al. (2019) conducted numerical simulations to examine the behavior of rigid pipelines buried in granular soil under downward movement [25]. The authors discovered that the existing code expressions tend to overestimate the bearing capacity. As an alternative, they proposed a new force–displacement relationship based on the local shear failure theory, which is different from the general shear failure theory used in existing codes.

Buried pipelines are often placed in excavated trenches with pre-existing soil to protect pipelines against environmental forces. Previous studies and current design codes, such as ALA (2001) and PRCI (2009), assume pipelines are designed within a uniform seabed, neglecting the geometry and material properties altered by trenching [26,27]. However, the pre-excavated backfill material is often extensively remolded and exhibits lower stiffness compared to the surrounding native soil. The significance of trenching and pre-excavated backfilling on pipe–backfill–trench interactions has been acknowledged by previous studies. However, modeling a 3D trenched pipeline under fault crossing using LDFE analysis involves several challenges. These include significant computational work, difficulties in simulating fault movement, and complexities in modeling the contact between the pipeline, backfill, and trench wall. This study aimed to fill this gap in the literature by conducting a systematic examination of the buckling failure modes of steel pipelines under strike-slip faults. To achieve this, a hybrid FE model utilizing a highly efficient algorithm was employed to investigate the buckling behavior of buried pipelines under various conditions.

2. Numerical Model and Material Properties

This paper investigates the pipeline–backfill–trench interaction by employing a hybrid method using the commercial FE software ABAQUS 2019 [28]. The investigation begins by developing a coupled Eulerian–Lagrangian (CEL) method to determine the mobilized soil resistance (P-Y curves) against the significant lateral displacement of the trenched/backfilled pipeline. Subsequently, the P-Y curves obtained from the CEL dynamic analysis are incorporated into a 3D beam–spring model to evaluate the pipeline’s response to lateral strike-slip faults.

Two parameters are used to assess the influence of fault movement on pipelines: fault displacement (δ) and the crossing angle (β) between the pipeline and the fault. The schematic shape of the developed beam–spring model is illustrated in Figure 1.

The assumed length of the pipeline is 1200 m. It is necessary for the pipe length on both sides of the fault line to be significantly longer than the unanchored length (

L

). The unanchored length is calculated using the following formula [29]:

L = \frac{σ_{u} π D t}{T_{u}}

(1)

where

D

and

t

represent the diameter and thickness of pipeline in meters,

σ_{u}

is the ultimate strength

(P a)

, and

T_{u}

denotes the maximum axial soil friction force

(N)

. Considering the native soil friction force and the dimensions and material properties of an X80 pipeline, the maximum unanchored length is determined to be 1008 m.

In ABAQUS, the nonlinear soil springs that describe pipe–soil interactions are represented by pipe–soil interaction elements (PSI 34) [28]. The PSI element consists of four nodes: two nodes connect to the soil, and the other two connect to the pipeline. To ensure the accuracy of results near the fault line areas, a fine mesh of PIPE31 elements with a size of 0.1 m was used for the two pipeline sections adjacent to the fault line, each extending 100 m on either side. Conversely, for the 500 m sections near the two pipeline ends, a coarser mesh with a size of 1.0 m was used. A set of 3001 soil nodes, representing the pipeline nodes, were established and connected using 3000 pipe–soil interaction elements (PSI 34) to simulate the nonlinear soil constraints on the pipeline.

The nonlinear buckling analysis of pipelines subjected to strike-slip fault movement involves both geometric and material nonlinearities. Therefore, a nonlinear stabilization algorithm was deemed appropriate for this study. In the beam–spring analysis, two nonlinear steps were considered to simulate the effects of fault displacement on the pipeline. The first step involved applying internal pressure to the entire pipeline. In the second step, the soil nodes on the left side of the fault line are fixed, while fault displacements are applied to the soil nodes on the right side. The fault displacement consists of two components: one in the axial direction and the other in the transverse direction (

δ_{x} = δ c o s β a n d δ_{y} = δ s i n β

, respectively).

The required P-Y curves for the nonlinear beam–spring model were obtained through a 2D CEL analysis. The schematic configuration of the CEL model is presented in Figure 2. In Figure 2a, the entire domain in the CEL analysis consists of soil as the Eulerian material, void space, and a buried Lagrangian pipeline.

The simulation process involved three steps. It began with a geostatic step. The second step was to push the pipeline downwards, with a velocity of 0.05 m/s, until it reached the specified embedment depth. In the third step, the pipeline was subjected to a constant lateral velocity of 0.046 m/s. The boundary condition properties are illustrated in Figure 2b.

2.1. Steel Pipeline Model

In this study, the steel pipeline stress–strain relationship is described by the Ramberg–Osgood model. Equation (2) represents the Ramberg–Osgood model [30]:

ε = \frac{σ}{E} [1 + \frac{α}{1 + r} {(\frac{σ}{σ_{y}})}^{r}]

(2)

In this Equation,

E

is the initial elastic modulus

(M P a)

ε

denotes strain, and

σ

and

σ_{y}

represent stress and yield stress

(M P a)

, respectively. Additionally,

α

and

r

are the parameters of the Ramberg–Osgood model.

2.2. Pipe–Soil Interaction

According to the requirements of the Canadian Standard Association for oil and gas pipeline systems, CSA (2007), the analysis of pipe–soil interactions is required by the guidelines for seismic design and assessment of natural gas and liquid hydrocarbon pipelines established by the Pipeline Research Council International (PRCI) as outlined in Honegger and Nyman (2004) [27,31]. Therefore, the soil spring characteristics were derived following the guidelines provided by both PRCI (Honegger and Nyman, 2004) and the American Lifeline Alliance (ALA, 2001).

ALA-ASCE guidelines define the force–displacement relationship for soil springs as elastic and perfectly plastic, characterized by two parameters (the maximum soil resistance per unit length and the soil yield displacement) [26]. Figure 3 shows a schematic representation of a pipe–soil interaction.

-: Longitudinal soil spring

According to the ALA guideline [26], the maximum transferable axial force per unit length (

T_{u}

) can be calculated as

T_{u} = π D α c + π D H \bar{γ} \frac{1 + K_{0}}{2} t a n δ

(3)

where

D

represents the pipeline diameter,

H

is the burial depth (measured from the ground surface to the pipeline center),

\bar{γ}

is the unit weight of the pipeline,

K_{0}

is the lateral soil pressure coefficient at rest, and

δ

represents the friction interface angle between the pipeline and soil.

The corresponding displacement at

T_{u}

, depending on the soil type, is 3–5 mm for dense to loose sand and 8–10 mm for stiff to soft clay.

-: Transverse horizontal soil spring

The maximum transverse horizontal force per unit length along the pipeline can be calculated as follows:

P_{u} = N_{c h} c D + N_{q h} \bar{γ} H D

(4)

The expressions of

N_{c h}

and

N_{q h}

can be found in the ALA code [26].

∆_{p}

, the displacement at

P_{u}

, can be obtained as

∆_{p} = 0.04 (H + \frac{D}{2}) \leq 0.1 D o r 0.15 D

(5)

-: Vertical uplift and bearing soil springs

ALA-ASCE describes the maximum uplift and bearing soil spring forces per unit length, as well as their corresponding yield displacement for sand, as follows [26]:

Q_{u} = N_{c v} c D + N_{q v} \bar{γ} H D

(6)

Δ_{q u} = (0.01 H - 0.02 H) < 0.1 D

(7)

Q_{d} = N_{c} c D + N_{q} \bar{γ} H D + N_{γ} γ \frac{D^{2}}{2}

(8)

Δ_{q u} = 0.1 D

(9)

The expressions of

N_{c v}

N_{q v}

N_{c}

N_{q},

and

N_{γ}

are specified in the ALA-ASCE code [26]. In this study, the P-Y curves obtained from the CEL analysis were used as the transverse soil springs, and the ALA-ASCE soil spring equations were used to calculate the vertical and axial soil spring properties.

2.3. Pipeline Internal Pressure and Failure Criteria

The pipeline internal pressure,

p

, can be obtained by the following equation considering the safety factor of 0.72 according to ASME [32]:

p = 0.72 \frac{2 t σ_{s}}{D}

(10)

There have been several studies to determine the critical compressive strain,

ε_{c r}

, that leads to wrinkles and decreased load carrying capacity in pipelines. The proposed

ε_{c r}

by Gresnigt A. M. (1987) (Equation (11)) has been adopted by CSA Z662 and is widely used in the industry due to its reasonable and conservative value [31,33]. In this study, using this criteria the local buckling failure of trenched pipelines is investigated. It should be noted that the concrete coating on the pipeline was not considered in this study. A review of the research works conducted on the strain concentration factor at field joints for offshore concrete-coated pipelines can be found in Gresnigt (1987) [33].

ε_{c r} = 0.5 (\frac{t}{D}) - 0.0025 + 3000 {(\frac{σ_{h}}{E})}^{2}

(11)

In this equation,

σ_{h}

is the hoop stress, which can be calculated as follows:

σ_{h} = \{\begin{matrix} \frac{p D}{2 t}, \frac{p D}{2 t σ_{s}} \leq 0.4 \\ 0.4 σ_{s}, \frac{p D}{2 t σ_{s}} > 0.4 \end{matrix}

(12)

2.4. Verification Basis

To verify the accuracy of the proposed FE model, the experimental and FE studies conducted by Rofooei et al. (2015) were used. In this study, the proposed beam–spring model was validated by obtaining soil spring parameters based on the sand properties used in the experiment [23]. Figure 4 illustrates the properties of the soil springs.

The true stress–strain curve (See Figure 5) of the API-5L Grade B material used in the experiment was also considered. The steel pipeline diameter, thickness, and length are 114.3 mm, 8.6 mm, and 8.0 m, respectively. An internal pressure of 413 kPa

(60 p s i)

was applied to the model. Regarding the given fault, displacement components in the axial, vertical, and transverse directions are −0.08 m, 0.35 m, and −0.18 m, respectively.

The numerical results obtained by the proposed model were compared with the experiment and simplified FE model results obtained by Rofooei et al. (2015). Figure 6 represents the steel pipeline displacement in three directions (

δ_{a}

δ_{v}

, and

δ_{t}

correspond to the axial, vertical, and transverse displacements, respectively). Axial displacement generates compressive strains along the pipeline, whereas vertical and transverse displacements lead to bending, which induces both compressive and tensile strains. Due to the three-dimensional loading on the pipeline, the maximum strains may not occur at the top or bottom of the pipeline cross-section. Comparing the results in Figure 6 shows that the proposed FE model exhibits a closer match with the FE results reported by Rofooei et al. (2015).

Figure 7 illustrates the distribution of invert and crown strains along the pipeline in the region of large deformation. In the proposed model, the oval deformation of the pipeline was ignored due to the limitations of the PIPE31 elements in simulating the local buckling. However, the results obtained from the proposed model closely match the FE and experimental findings reported by Rofooei et al. (2015).

As shown in this figure, the longitudinal strain distribution for the experimental data, the FE models used by Rofooei et al. (2015), and the proposed FE model reveal that the maximum compressive and tensile strains occur at the locations where local buckling is observed. The distance between these buckling points is approximately 1.20 m, 0.9 m, and 1.25 m in the detailed FE model, simple FE model, and the proposed FE model, respectively. This discrepancy may be caused by the inability of the proposed FE model to capture the pipeline’s local buckling accurately.

In the experimental results and the proposed FE model, there is a 0.50 m separation between the local buckling points. This discrepancy may be due to the complex behavior of soil under fault movement, such as the formation of cracks and the softening of soil at high plastic strains.

As a result, the calculated strains in the proposed FE model provide results that are reasonable from an engineering perspective, and this model was therefore selected for comprehensive parametric studies.

3. Results and Discussion

A series of numerical studies were conducted in this study to investigate the influence of factors such as fault intersection angle, pipeline diameter, burial depth, initial embedding, and properties of backfilling soils on the buckling behavior of X80 steel pipelines under strike-slip faults.

The stress–strain curve for the X80 pipeline material is presented in Figure 8. The Young’s modulus and yielding stress of X80 are 2.07 × 10⁵

M P a

and 530

M P a

, respectively. The Ramberg–Osgood parameters α and r are determined to be 15.94 and 15.95, respectively. For a pipeline with a diameter of 0.9144 m and a thickness of 0.027 m, the internal pressure is calculated as 22.5

M P a

according to Equation (10). Additionally, the critical compressive strain is 2.24% (Equation (11)).

The soil was modeled as an isotropic continuum material with the Tresca yield criterion, which is equivalent to the Mohr–Coulomb yield criterion with a friction angle of zero. The soil’s elastic behavior was defined by the Young’s modulus-to-shear strength ratio of

E / s_{u} = 500

and Poison’s ratio of v = 0.495 to ensure zero volume change. To account for strain-softening effects, the empirical equation proposed by Zhang et al. (2015; 2019) [34,35] was incorporated as follows:

s = s_{u} + (s_{u, r} - s_{u}) \frac{γ^{p}}{γ_{r}^{p}}

(13)

where

s_{u}

is the peak undrained shear strength,

s_{u, r}

is the residual undrained shear strength,

γ^{p}

is the accumulated plastic shear strain, and

γ_{r}^{p}

is the value of

γ^{p}

that reduces the shear strength from peak to residual. In this study, the effect of the soil strength gradient on the strain softening was considered to model pipe–soil interactions. This was implemented using a VUSDFLD subroutine for the explicit analysis in the CEL model. It should be noted that the pipe–soil interface strength was limited to half of the soil undrained shear strength at the pipe spring line, considering a total stress friction coefficient of 0.50. Additionally, the parameter

γ^{p}

was calculated by the VUSDFLD subroutine, and the assumed values of

γ_{r}^{p}

and

s_{u, r}

were 10.0 and 6.65 kPa, respectively. The trench configurations and soil properties are presented in Table 1, while Table 2 presents the parametric study properties.

The submerged unit weight (γ′) of native seabed soil and backfill soil used was 9.3 kN/m³ and 7.5 kN/m³, respectively. Based on these properties, a series of CEL analyses were conducted to extract the required P-Y curves.

3.1. Effect Influence of Strain Softening and Soil Strength on the Soil and Pipeline Failure Mechanisms

In this section, the effects of soil strain softening and shear strength pattern effects on the soil and pipeline failure mechanisms are studied through four different case studies: CS-1, CS-5, CS-12, and CS-13.

The lateral load–displacement (P-Y) responses and pipeline trajectories for the investigations are shown in Figure 9. Figure 9a shows that as the pipeline moves laterally in the soil, uplift is observed along the displacement trajectory. A comparison of the pipeline trajectories in different case studies shows a higher uplift in the soil when the strain-softening effect and linear soil strength are considered. It causes the localization of soil strain along shear bands, as depicted in Figure 10a. Consequently, the linear soil strength case studies exhibit lower lateral soil resistance due to the higher uplift (see Figure 9b).

The plastic strain contours for case studies CS-1 and CS-5 are presented in Figure 10. By comparing these contours with the displacement vectors shown in Figure 11, the significant influence of considering the linear strength of the native soil on the failure mechanism can be observed. In the case studies where the soil strength is constant (CS-5), the plastic strain and shear bands are localized behind the pipeline in the backfilling soil. However, in CS-1, the shear bands reach the top surface of the backfilling soil as the pipeline moves through it due to the linear distribution of shear strength. Therefore, the upper surface of the trench remains almost planar until the pipeline reaches the trench wall (y/D = 1.07 and y/D = 1.20). After the pipeline touches the trench wall (y/D = 1.20), shear bands appear in the seabed soil. A comparison of plastic strain reveals that CS-1 exhibits larger plastic strains in the induced shear bands in the seabed soil at y/D = 1.57 and y/D = 1.97. The linear soil strength variation in CS-1 causes a larger uplift due to the localized strain in the backfilling and seabed soils compared to the other cases.

The soil spring characteristics to study the pipeline failure are presented in Figure 12. Figure 13 shows the FE analysis results for the four case studies.

A comparison of pipeline deflection curves in Figure 13a,b reveals that the length of the large deformation area in soil with the strain-softening effect and linear soil strength is greater compared to the other cases. The strain-softening effect with a linear shear strength pattern induces a higher uplift due to the localized shear bands. Consequently, the pipeline can move easily in the fault direction, and the axial strain on the pipeline decreases (see the invert and crown strain curves in Figure 13). Figure 13 illustrates the increase in the distance between the two wrinkles due to the linear shear strength distribution. For a fault angle of 55°, this distance is 18.10 m for CS-1 and 16.50 m for CS-5. When the fault angle is 90°, the distances are 32.80 m for CS-1 and 27.12 m for CS-5. Furthermore, Figure 13 shows that the maximum axial strain in CS-1 is lower than in the other cases. Therefore, CS-1 and CS-5 exhibit a greater distance between two wrinkles due to the strain-softening effect. Additionally, when strain softening is considered, and the fault angle is 55°, the wrinkle distances for CS-1 and CS-13 are 18.1 m and 14.7 m, respectively. For a fault angle of 90° with strain softening, the distances are 27.12 m for CS-1 and 23.78 m for CS-13. A comparison of invert and axial strains considering two different intersection angles (55° and 90°) reveals that linear shear strength patterns reduce axial strain by approximately 5%.

3.2. The Influence of the Pipeline Burial Depth Ratio

In this section, the influence of the burial depth ratio on the pipeline behavior is investigated. Three different burial depth ratios (H/D), 1.92, 2.92, and 3.92, were investigated in this study.

The initial embedment, which represents the penetration depth of the pipeline bottom into the trench bed, was 4 mm. The undrained shear strengths of the native soil and the backfill are equal to those shown in Table 1. The results of the conducted analyses are presented in Figure 14 and Figure 15. As shown in Figure 14a, a shallow-depth buried pipeline trajectory exhibits a larger uplift compared to a deep-depth buried pipeline trajectory as the pipeline moves through the seabed soil. However, the uplift of the pipelines is almost the same before reaching the trench wall. Figure 14b demonstrates that the induced lateral load in the buried pipeline increases with depth. This can be attributed to the increase in soil weight on the buried pipelines, as the height of soil above the pipeline increases as the burial depth ratio rises.

Figure 15 illustrates the soil failure mechanism in the three case studies corresponding to different burial depth ratios. It can be observed that the burial depth ratio of the pipeline affects the shape of shear bands around the pipeline. In shallow depths, the shear bands reach the top surface of backfilling soil. The failure mechanism in the deep depth (H/D = 3.92) is predominantly confined to the rear of the pipeline. However, the surrounding soil tends to move upwards (Figure 15c).

Figure 16 presents the corresponding soil spring properties used in this analysis. According to the analytical study conducted by Asgarihajifirouz et al. (2023) [36], the axial strain of the pipeline decreases significantly in the presence of backfilling soil, and the maximum axial strain does not vary significantly with the increasing burial depth ratio.

Figure 17 clearly demonstrates the effect of the burial depth ratio on the deflection and axial strain curves. In Figure 17a,b, it is evident that bending deformations decrease with increasing burial depth ratios. This is because the burial depth ratio of the pipeline affects the shape of shear bands around the pipeline (see Figure 15). At shallow depths, shear bands reach the top surface of backfilling soil. Comparing Figure 17b,c highlights the influence of the intersection angle on invert and crown strain. The invert strain remains relatively constant as the fault angle increases, while the crown strain experiences a 50% increase. Figure 17b shows that increasing the fault crossing angle and burial depth ratios has a minor impact on bending deformation.

Comparing the invert and crown strain in Figure 17 reveals that as the burial depth increases, the axial strain also varies, and the location of the wrinkles is not constant. It is crucial to use an appropriate burial depth. The results for a fault crossing angle of 55° indicate that the distance between two wrinkles is 14.70 m, 33.4 m, and 25.08 m for H/D ratios of 1.92, 2.92, and 3.92, respectively. The position of maximum axial strain at shallow depths is near the fault line because the pipeline can easily fold up. Buried pipelines at shallow depths experience smaller forces compared to those at greater depths due to the thickness of the overlying soil. The parametric studies indicate that the induced axial strain in trenched pipelines is 10 times less than the critical strain (2.24%). Consequently, the buried pipeline does not experience local buckling if it is buried within the trench.

3.3. The Influence of Initial Embedment

In this section, the nonlinear response of the pipeline is studied by considering three different initial embedment depths: 4 mm, 154 mm, and 254 mm.

The conducted analyses (CS-1, CS-10, and CS-11) reveal that the uplift of the buried pipeline inside the trench decreases as the initial embedment increases (See Figure 18a). Figure 18a shows that a smaller embedment height results in faster upward movement than the other embedment values. To better understand the reason behind this behavior, the failure mechanisms of the soil in these three case studies were compared. Figure 19 illustrates that a smaller embedment depth induces a larger volume of berm formation in front of the pipeline. Additionally, the localized soil plastic strain value increases. Therefore, the pipeline lateral load inside the trench increases as the embedment depth increases.

Figure 20 illustrates the soil spring properties for these case studies. Figure 21 presents the FE analysis results. The deflection curves in Figure 21a demonstrate that as the embedment height decreases, the pipeline is more prone to moving towards the seabed, resulting in the formation of wrinkles in the region near the fault.

The axial strain curves in Figure 21 show that the location of the maximum axial strain shifts with the increasing initial embedment height, allowing the pipeline to fold more easily. As a result, the magnitude of the maximum axial strain rises with higher initial embedment heights. The results for a fault crossing angle of 55° indicate that the distance between two wrinkles is 14.70 m, 36.30 m, and 45.32 m for initial embedments of 4 mm, 154 mm, and 254 mm, respectively. Furthermore, this figure indicates that while the invert strain does not significantly change with increasing fault crossing angles, the crown strain increases by about 50%. These results indicate that selecting an appropriate initial embedment is crucial for maintaining pipeline integrity when designing pipelines within trenches.

3.4. The Influence of Backfilling Material Strength

This section provides an analysis of the pipeline deformation under three different undrained shear strengths of the backfill soil. Three different backfilling materials were used to evaluate the soil failure mechanism and pipeline displacement trajectory. The results are presented in Figure 22 and Figure 23. A comparison of the results reveals that the weaker backfilling material leads to smaller uplift compared to the stronger backfilling material. This is attributed to the larger lateral soil resistance inside the trench, resulting in a greater uplift for the pipeline (see Figure 22). In Figure 23, it can be observed that the maximum plastic strain in the trench with weaker backfilling material is concentrated on the surface of the trench because of the larger berm height in this case study. However, the pipeline lateral load inside the trench with weaker material is smaller than that with the other backfilling materials. Additionally, this figure indicates that the backfilling soil strength influences the formation of shear bands in the seabed soil. The occurrence of shear bands in the seabed soil indicates that as the backfilling strength increases, the number of shear bands produced in the seabed soil also increases.

The soil spring properties are presented in Figure 24. Figure 25 illustrates the FE results for pipeline deformation under three different undrained shear strengths of the backfill soil. It shows that as the friction force between the pipeline and the soil increases, the axial force also increases.

In Figure 25b,c, it can be observed that when the backfill soil shear strength changes from soft to stiff, the length of the large deformation area decreases. Consequently, the maximum axial strain, including invert and crown strains, increases. The results for a fault crossing angle of 55° indicate that the distance between two wrinkles is 14.70 m, 13.25 m, and 18.23 m for CS-1, CS-6, and CS-7, respectively. Therefore, as the strength of the backfilling soil increases, the distance between the wrinkles also increases.

3.5. The Influence of Pipeline Diameter

The capacity and deformability of a pipeline are directly influenced by its diameter. This section aims to investigate the impact of pipeline diameter on the interaction between the pipeline, backfill, and trench soil. Two pipelines with outer diameters of 0.9144 m and 0.95 m were considered, corresponding to D/t ratios of 33.87 and 35.18, respectively. Both pipelines have the same thickness (t = 0.027 m). The pipeline with a diameter of 0.9144 m can withstand a maximum internal pressure of 22.5 MPa and has a critical compressive strain of 2.24%. The pipeline with a diameter of 0.95 m, on the other hand, can withstand a maximum internal pressure of 22.5 MPa and has a critical compressive strain of 2.19%.

Figure 26a shows that a larger diameter results in a greater uplift in the pipeline trajectory; however, the lateral resistance of the pipeline inside the trench decreases (Figure 26b). The failure mechanism of the soil is presented in Figure 27. As shown in this figure, a larger pipeline diameter produces a larger berm volume. Consequently, the plastic strain value rises as the berm volume increases.

The soil spring properties for these two case studies are presented in Figure 28.

Figure 29a depicts the deflection curve of the buried pipeline under different diameter–thickness ratios and fault intersection angles. The Y-axis denotes the vertical displacement of the fault, and the X-axis represents the distance from the fault. It is worth noting that the deflection curve remains constant at point C regardless of the diameter value. However, Figure 29a shows that point C is located at a higher vertical position (1.5 m) when the fault intersection angle is 90 degrees.

Figure 29b,c illustrate the maximum axial strain at the invert and crown points, indicating that the most vulnerable section of the pipeline is the one with a larger diameter (D = 0.95 m). However, the distance between two wrinkles is shorter for the pipeline with a smaller diameter compared to the one with a larger diameter. For instance, for a fault crossing angle of 55°, the distance between two wrinkles is 14.70 m and 23.41 m for CS-1 and CS-2, respectively. The results also indicate that the maximum compressive strain experienced by the buried pipeline is below the critical strain value. Additionally, as the fault intersection angle increases, the axial strain decreases, even though the vertical displacement is greater compared to that of the fault with a 55° intersection.

3.6. Pipeline Surface Roughness

The impact of pipeline surfaces was considered in three P-Y curves obtained from the CEL analysis. The surface roughness of the pipeline significantly affects the pipe–soil interaction, failure mechanisms, and resultant lateral soil resistance. Figure 30 presents the finite element results considering rough, penalty, and smooth surface contacts. As shown in this figure, as the surface roughness increases, the lateral soil resistance also increases in both small and large deformation areas (for small displacements inside the trench and large displacements while penetrating the trench wall). Figure 30 demonstrates that a rotational flow occurs as the pipe moves inside the trench and interacts solely with the backfilling material. As the pipe interacts with the trench wall, the upper part of the trench wall starts to gradually slide towards the trench. Therefore, the model with smooth surface contact produces a smaller lateral load (Figure 31b) and a larger uplift (Figure 31a).

It should be noted that the axial and vertical soil springs are determined using force–displacement equations in ALA, which already account for the effect of surface roughness. Consequently, there are no changes in these curves for the three case studies mentioned above. The force–displacement curves presented in Figure 32 were utilized to derive the deflection and axial strain curves derived for the pipeline under a strike-slip fault.

Figure 33 presents the FE analysis results. In Figure 33a, it can be observed that the deflection curves remain unchanged when the fault crossing angle is 90 degrees. However, a small reduction in the deflection and axial strain curves can be seen when the surface roughness is smooth. The axial strain curves in Figure 33 show that near the fault line, the use of rough contacts results in higher axial invert and crown strains compared to the penalty and smooth contacts. For a fault crossing angle of 55°, the distance between two wrinkles is 14.70 m, 15.20 m, and 12.80 m for CS-1, CS-8, and CS-9, respectively. Conversely, for a fault crossing angle of 90°, the distance remains almost the same at 14.7 m. The results for a fault crossing angle of 55° show that in cases of smooth contact, the interaction between the pipe and soil lacks sufficient strength to secure the pipe within the soil, making it prone to folding.

4. Conclusions

The pipeline–backfill–trench interaction under strike-slip faulting was investigated through parametrical study using a decoupled beam–spring FE model. Both material and geometry nonlinearity were considered in this study. The parameters that were considered in this study were strain softening and soil shear strength, burial depth, initial embedment, backfilling material strength, pipe diameter, and pipeline surface roughness. Based on these parametric studies, the following conclusions are made:

Incorporating strain-softening behavior for seabed soil leads to an increase in the mobilized soil volume while reducing lateral soil resistance. This highlights the importance of considering strain-softening characteristics for accurate soil–pipeline interaction modeling.
When comparing a linear variation in soil strength to a constant soil strength profile, the linear variation results in a lower lateral force–displacement response and a greater tendency for the pipeline to move upward. This indicates that linear soil strength profiles may underestimate the resistance provided by the soil against lateral pipeline displacement.
The backfilling strength has a significant impact on the lateral soil resistance. A higher backfilling strength (1) increases the intensity of pipeline–trench bed interaction intensity; (2) increases the soil resistance when the pipe moves inside the trench; and (3) generates higher ultimate lateral soil resistance, producing passive pressure against trench wall collapse and mobilizing a larger soil volume in front of the moving pipeline.
The initial embedment depth of the pipeline within the trench significantly affects its lateral load–displacement behavior. An increased embedment depth results in greater pipeline–trench bed resistance and earlier propagation of shear bands beyond the trench wall to the soil surface.
The surface roughness of the pipeline is a critical factor in determining lateral soil resistance. A rough pipeline surface fosters stronger interaction with the surrounding soil, leading to increased resistance. For pipelines with rough surfaces, the trench wall failure mechanism is characterized by global shear failure, whereas smooth pipelines tend to exhibit local flow failure mechanisms.
Utilizing backfilling soil reduces the likelihood of local buckling in the pipeline. This suggests that appropriate backfilling materials can enhance the structural stability of buried pipelines.
Considering strain softening and linear shear strength in soil models results in lower induced axial strains in the pipeline. This underscores the importance of accurately modeling soil behavior to predict pipeline strains.
Using stiffer backfilling materials does not significantly alter the location of maximum axial strain along the pipeline, suggesting that stiffness primarily affects lateral resistance rather than strain localization.
Higher initial embedment depths lead to increased axial strain in the pipeline. This finding emphasizes the need to optimize embedment depth to manage axial strain levels effectively.
An increased burial depth results in higher axial strains within the pipeline, indicating that deeper burial may impose greater demands on pipeline integrity.

These conclusions provide comprehensive insights into the critical factors influencing pipeline behavior under strike-slip faulting. This study emphasizes the need for detailed consideration of soil properties, backfilling materials, and pipeline surface characteristics in the design and construction of buried pipelines in fault-prone areas to ensure their structural integrity and safety.

Author Contributions

Conceptualization, H.S.; Methodology, X.D. and H.S.; Software, X.D. and H.S.; Validation, M.A.; Formal analysis, M.A.; Investigation, M.A.; Data curation, M.A.; Writing—original draft, M.A.; Writing—review & editing, X.D. and H.S.; Visualization, M.A.; Supervision, X.D. and H.S.; Project administration, H.S.; Funding acquisition, H.S. All authors have read and agreed to the published version of the manuscript.

Funding

The authors gratefully acknowledge the financial support of “Wood” through establishing the Research Chair program in Arctic and Harsh Environment Engineering at the Memorial University of Newfoundland, the “Natural Science and Engineering Research Council of Canada (NSERC)”, and the “Newfoundland Research and Development Corporation (RDC) (now InnovateNL) through “Collaborative Research and Developments Grants (CRD)”. Special thanks are extended to Memorial University for providing excellent resources for conducting this research program.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Schematic shape of a buried pipeline subjected to a strike-slip fault. (a coarser mesh of PIPE31 elements with a size of 1.0 m for the 500 m section (A) and a fine mesh with a size of 0.1 m extending over the 100 m section (B)).

Figure 2. Schematic representation of the CEL model. (a) CEL domain dimensions; (b) boundary condition properties.

Figure 3. Schematic representation of pipe–soil interaction in ALA-ASCE [26]. (a) Nonlinear soil springs; (b) force–displacement relationships: (A) lateral, (B) axsial, (C) vertical.

Figure 4. Soil spring characteristics from Rofooei et al. (2015): (a) axial, (b) horizontal, and (c) vertical soil springs [23].

Figure 5. Steel pipeline stress–strain curve (Rofooei et al. (2015)) [23].

Figure 6. Pipeline displacement in three orthogonal directions. (a) The FE model used by Rofooei et al. (2015) [23]; (b) the verified FE model.

Figure 7. (a) Invert and (b) crown strains of FE and experimental models [23].

Figure 8. X80 steel pipeline stress–strain curve.

Figure 9. Comparison of pipeline lateral response considering the effect of strain softening and with constant and linear soil strength: (a) pipeline trajectory; (b) load–displacement curve.

Figure 10. Volume fraction average of plastic strain with strain softening: (a) CS-1 and (b) CS-5.

Figure 11. Displacement vectors (a) CS-1 and (b) CS-5.

Figure 12. Soil spring characteristics for investigating strain softening and soil strength: (a) axial, (b) horizontal, and (c) vertical soil springs.

Figure 13. Strain-softening and soil strength pattern effect on the deformation and axial strain of the pipeline: (a) distribution of vertical displacement, (b) invert axial strain, (c) crown axial strain.

Figure 14. Comparison of pipeline lateral response considering different burial depth ratios: (a) pipeline trajectory; (b) load–displacement.

Figure 15. Volume fraction average of plastic strain with strain softening and displacement vectors for different burial depth ratios: (a) CS-1 (H/D = 1.92), (b) CS-3 (H/D = 2.92), (c) CS-4 (H/D = 3.92).

Figure 16. Soil spring characteristics for different burial depth ratios: (a) axial, (b) horizontal, and (c) vertical soil springs.

Figure 17. Burial depth effect on the deformation and axial strain of the pipeline: (a) distribution of vertical displacement, (b) invert axial strain, (c) crown axial strain.

Figure 18. Comparison of pipeline lateral response considering different initial embedment heights: (a) pipeline trajectory; (b) load–displacement.

Figure 19. Volume fraction average of plastic strain with strain softening and displacement vectors for different initial embedment values: (a) CS-1 (4 mm), (b) CS-10 (154 mm), (c) CS-11 (254 mm).

Figure 20. Soil spring characteristics of case studies with different initial embedment (a) axial, (b) horizontal, and (c) vertical soil springs.

Figure 21. The initial embedment effect on the deformation and axial strain of the pipeline: (a) distribution of vertical displacement, (b) invert axial strain, (c) crown axial strain.

Figure 22. Comparison of pipeline lateral response considering different backfilling soil strengths: (a) pipeline trajectory; (b) load–displacement.

Figure 23. Volume fraction average of plastic strain with strain softening and displacement vectors for different backfilling material: (a) CS-1 (1.6 kPa), (b) CS-6 (0.1 kPa), (c) CS-7 (5.0 kPa).

Figure 24. Soil spring characteristics for different backfilling soil strengths: (a) axial, (b) horizontal, and (c) vertical soil springs.

Figure 25. Backfilling soil strength effect on the deformation and axial strain of the pipeline: (a) distribution of vertical displacement, (b) invert axial strain, (c) crown axial.

Figure 26. Comparison of pipeline lateral response considering different pipeline diameters: (a) pipeline trajectory; (b) load–displacement.

Figure 27. Volume fraction average of plastic strain with strain softening and displacement vectors for different pipeline diameters: (a) CS-1 (0.9144 m), (b) CS-2 (0.95 m).

Figure 28. Soil spring characteristics of case studies with different pipeline diameters: (a) axial, (b) horizontal, and (c) vertical soil springs.

Figure 29. Pipeline diameter effect on the deformation and axial strain of the pipeline: (a) distribution of vertical displacement, (b) invert axial strain, (c) crown axial strain.

Figure 30. Comparison of pipe lateral response considering different surface roughness values: (a) pipe trajectory; (b) load–displacement.

Figure 31. Volume fraction average of plastic strain with strain softening for different surface toughness values: (a) CS-1 (rough), (b) CS-8 (penalty), (c) CS-9 (smooth).

Figure 32. Soil spring characteristics of case studies with different pipeline surface roughness: (a) axial, (b) horizontal, and (c) vertical soil springs.

Figure 33. Surface roughness effects on the deformation and axial strain of the pipeline: (a) distribution of vertical displacement, (b) invert axial strain, (c) crown axial strain.

Table 1. Trench geometry and soil properties adopted from the centrifuge tests.

Property		Value
Geometry	Burial depth to pipeline center (m)	1.92
	Trench width (m)	2.5
	Initial embedment of pipeline (mm)	4
Native seabed soil	Undrained shear strength at pipeline centerline (kPa)	33.1
Native seabed soil	Linear variation in undrained shear strength with depth (kPa)	24.43 + 6.8 z
Backfill soil	Undrained shear strength at pipeline centerline (kPa)	1.6
Backfill soil	Linear variation in undrained shear strength with depth (kPa)	1.26 z

Table 2. Case studies’ properties.

Case Name	Pipe Diameter (m)	Burial Depth Ratio	Soil Strength Pattern	Backfill s_u (kPa)	Pipe Roughness	Initial Embedment (mm)	Strain Softening
CS-1	0.9144	1.92	Linear	1.6	Rough	4	Yes
CS-2	0.95	1.92	Linear	1.6	Rough	4	Yes
CS-3	0.9144	2.92	Linear	1.6	Rough	4	Yes
CS-4	0.9144	3.92	Linear	1.6	Rough	4	Yes
CS-5	0.9144	1.92	Constant	1.6	Rough	4	Yes
CS-6	0.9144	1.92	Linear	0.1	Rough	4	Yes
CS-7	0.9144	1.92	Linear	5.0	Rough	4	Yes
CS-8	0.9144	1.92	Linear	1.6	Penalty	4	Yes
CS-9	0.9144	1.92	Linear	1.6	Smooth	4	Yes
CS-10	0.9144	1.92	Linear	1.6	Rough	154	Yes
CS-11	0.9144	1.92	Linear	1.6	Rough	254	Yes
CS-12	0.9144	1.92	Linear	1.6	Rough	4	No
CS-13	0.9144	1.92	Constant	1.6	Rough	4	No

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Asgarihajifirouz, M.; Dong, X.; Shiri, H. A Decoupled Buckling Failure Analysis of Buried Steel Pipeline Subjected to the Strike-Slip Fault. J. Mar. Sci. Eng. 2024, 12, 1243. https://doi.org/10.3390/jmse12081243

AMA Style

Asgarihajifirouz M, Dong X, Shiri H. A Decoupled Buckling Failure Analysis of Buried Steel Pipeline Subjected to the Strike-Slip Fault. Journal of Marine Science and Engineering. 2024; 12(8):1243. https://doi.org/10.3390/jmse12081243

Chicago/Turabian Style

Asgarihajifirouz, Mozhgan, Xiaoyu Dong, and Hodjat Shiri. 2024. "A Decoupled Buckling Failure Analysis of Buried Steel Pipeline Subjected to the Strike-Slip Fault" Journal of Marine Science and Engineering 12, no. 8: 1243. https://doi.org/10.3390/jmse12081243

APA Style

Asgarihajifirouz, M., Dong, X., & Shiri, H. (2024). A Decoupled Buckling Failure Analysis of Buried Steel Pipeline Subjected to the Strike-Slip Fault. Journal of Marine Science and Engineering, 12(8), 1243. https://doi.org/10.3390/jmse12081243

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A Decoupled Buckling Failure Analysis of Buried Steel Pipeline Subjected to the Strike-Slip Fault

Abstract

1. Introduction

2. Numerical Model and Material Properties

2.1. Steel Pipeline Model

2.2. Pipe–Soil Interaction

2.3. Pipeline Internal Pressure and Failure Criteria

2.4. Verification Basis

3. Results and Discussion

3.1. Effect Influence of Strain Softening and Soil Strength on the Soil and Pipeline Failure Mechanisms

3.2. The Influence of the Pipeline Burial Depth Ratio

3.3. The Influence of Initial Embedment

3.4. The Influence of Backfilling Material Strength

3.5. The Influence of Pipeline Diameter

3.6. Pipeline Surface Roughness

4. Conclusions

Author Contributions

Funding

Institutional Review Board Statement

Informed Consent Statement

Data Availability Statement

Conflicts of Interest

References

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