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Deformation capacity of buried hybrid-segmented pipelines under longitudinal permanent ground deformation

Publication: Canadian Geotechnical Journal
3 September 2020

Abstract

Innovative hybrid-segmented pipeline systems are being used more frequently in practice to improve the performance of water distribution pipelines subjected to permanent ground deformation (PGD), such as seismic-induced landslides, soil lateral spreading, and fault rupture. These systems employ joints equipped with anti-pull-out restraints, providing the ability to displace axially before locking up and behaving as a continuous pipeline. To assess the seismic response of hazard-resistant pipeline systems equipped with enlarged joint restraints to longitudinal PGD, this study develops numerical and semi-analytical models considering the nonlinear properties of the system, calibrated from large-scale test data. The deformation capacities of two hybrid-segmented pipelines are investigated: (i) hazard-resilient ductile iron (DI) pipe and (ii) oriented polyvinylchloride (PVCO) pipe with joint restraints capable of axial deformation. The numerical analysis demonstrates that, for the conditions investigated, the maximum elongation capacity of the analyzed DI pipe system is greater than that of the PVCO pipeline. The implemented semi-analytical approach revealed that the pipeline performance improves strongly by increasing the allowable joint displacement. Comparison of the numerical results with analytical solutions reported in recent research publications showed excellent agreement between the two approaches, highlighting the importance of assigning appropriate axial friction parameters for these systems.

Résumé

Les systèmes de canalisations hybrides innovants sont de plus en plus utilisés dans la pratique pour améliorer les performances des canalisations de distribution d’eau soumises à une déformation permanente du sol (DDP), comme les glissements de terrain provoqués par les séismes, l’épandage latéral du sol et la rupture de failles. Ces systèmes utilisent des joints équipés de dispositifs de retenue anti-extraction, offrant la possibilité de se déplacer axialement, avant de se verrouiller et de se comporter comme un pipeline continu. Afin d’évaluer la réponse sismique des systèmes de pipelines résistants aux risques équipés de joints de retenue élargis au DPI longitudinal, cette étude développe des modèles numériques et semi-analytiques, en tenant compte des propriétés non linéaires du système, calibrés à partir de données d’essai à grande échelle. Les capacités de déformation de deux pipelines à segments hybrides sont étudiées : (i) un tuyau en fonte ductile (DI) résistant aux risques et (ii) un tuyau en polychlorure de vinyle (PVCO) orienté avec des joints de retenue capables de se déformer axialement. L’analyse numérique démontre que, pour les conditions étudiées, la capacité d’allongement maximale du système de tuyauterie DI analysé est supérieure à celle du pipeline PVCO. L’approche semi-analytique mise en œuvre a révélé que la performance du pipeline s’améliore fortement en augmentant le déplacement admissible des joints. La comparaison des résultats numériques avec les solutions analytiques présentées dans de récentes publications de recherche a montré un excellent accord entre les deux approches, soulignant l’importance d’attribuer des paramètres de frottement axial appropriés pour ces systèmes. [Traduit par la Rédaction]

1. Introduction

Buried pipelines installed in seismic regions are susceptible to the effects of transient ground deformation (TGD) due to seismic wave propagation and permanent ground deformation (PGD) resulting from earthquake-induced soil liquefaction, landslides, and surface faulting. According to post-earthquake investigations, damage rates for buried pipelines subjected to seismic-induced PGD were significantly higher than those due to TGD (Barbas and Weir 2007; Liang and Sun 2000; O’Rourke and Liu 2012). Herein, the seismic performance of segmented pipelines is typically inferior to continuous pipelines, because the strength of the joints is typically less than the strength of the pipe segment they connect. Specifically, longitudinal PGDs induce larger damage rates in non-seismically designed buried pipes than transversal PGD (ALA 2005; O’Rourke and Nordberg 1992b) due to lower flexibility in the axial direction.
One potential mitigation measure involves the use of hybrid-segmented pipes equipped with anti-pull-out joint restraints, providing the ability to displace axially to an amount Δ before locking up and behaving like a continuous system. Examples of hybrid-segmented pipeline joint connections emerging in the industry are earthquake-resistant ductile iron (DI) pipe (ERDIP) (Pariya-Ekkasut 2018) and molecularly oriented polyvinylchloride (PVCO) pipe fitted with extendable joint restraints (Wham et al. 2019b), as shown in Fig. 1. The joint type and geometry significantly influence the pipeline performance when subjected to ground displacement.
Fig. 1.
Fig. 1. Examples of pipeline joints including (a) photograph of normal DI push-on (top) and enlarged hybrid-segmented joint (bottom), (b) drawing of typical hybrid-segmented expansion joint, (c) photograph of PVCO joint with restraint harness capable of expansion, and (d) drawing of plastic pipe with restraint harness. [Colour online.]
Moreover, the enlarged joint restraining mechanisms of these new pipe systems behave like vertical anchors, increasing the soil reaction to the relative soil–pipeline movement as a combined effect of the passive bearing pressure, friction, as well as soil yielding and flow (Wham et al. 2019a). While procedures exist for estimating the axial resistance along straight buried pipes (i.e., ASCE Committee on Gas and Liquid Fuel Lifelines 1984; Rajani and Tesfamariam 2004; Wijewickreme et al. 2009; Wijewickreme and Weerasekara 2015; Vazouras et al. 2015; Banushi and Squeglia 2018), recent full-scale experimental studies have demonstrated the significant contribution of enlarged joints and external restraints to the axial system response (Price et al. 2018; Wham et al. 2017b, 2018). Additionally, the connection force capacity (CFC) of the pipeline joints is an important system limit state and contributes to evaluation of the response to earthquake-induced ground movement (Wham et al. 2019c).
The performance of buried pipelines subjected to longitudinal PGD depends on the length Lb, magnitude δ, and pattern of ground deformation. The block pattern, where all soil within the PGD zone undergoes the same ground movement δ, has been widely used in engineering research and design to assess pipeline performance under longitudinal PGD (ALA 2005; O’Rourke et al. 1995; O’Rourke and Nordberg 1992a; Wham and Davis 2019). This abrupt ground deformation pattern induces localized relative soil–pipeline movement at the margins of the PGD zone, resulting in worst-case axial pipe strains compared to other commonly assumed deformation patterns that distribute movement along a greater portion of the system (O’Rourke and Nordberg 1992b). Expanding on work by O’Rourke and Nordberg (1992a), Wham and Davis (2019) developed a simplified analytical approach for calculating pipe strain due to various magnitudes of ground movement for pipelines of any material stiffness and mechanical joint characteristics. This approach uses soil–pipeline axial resistance per unit length of pipe, fr, and other pipe system characteristics to approximate the axial force demand on a pipeline for a given soil block movement, defined by length Lb and magnitude δ. Two conditions are established for which the pipeline force demand is evaluated, depending on whether the soil block length Lb is short (condition II) or long (condition I) enough to fully mobilize friction along the pipeline in response to the imposed ground displacement. The proposed analytical model permits calculation of the CFC required to accommodate a specific quantity of ground movement δ, providing a first-order estimate of pipeline performance for engineering assessment of continuous and segmented pipelines in hazard-prone regions.
While the Wham and Davis analytical approach has demonstrated the ability to predict hybrid-pipeline response for well-documented case studies in Japan (Davis et al. 2019), more advanced numerical analysis, calibrated with experimental data, is needed to confirm its capacity to accurately evaluate the effect of complex system nonlinearities, including the response of the enlarged joint restraints, for various burial conditions and pipeline system characteristics. Moreover, this analytical model requires investigation of the soil–pipeline axial friction resistance, fr, appropriate for estimating axial demand on a segmented pipeline system, necessitating a numerical study that captures nonlinearities measured during full-scale experimentation.
Three primary finite element modelling approaches are commonly used to assess the response of soil–pipeline systems subjected to ground deformation: the simplistic beam on Winkler foundation (Argyrou et al. 2019; Erami et al. 2015; Melissianos et al. 2016; Liu et al. 2017; Ivanov and Takada 2003; Klar et al. 2005); the shell-spring formulation (Oda et al. 2015, 2016; Takada and Higashi 1992) and the more complex continuum models (Balkaya et al. 2012; Becerril García and Moore 2016; Wham and O’Rourke 2016; Hassani and Basirat 2019; Qin and Ni 2019). Although the latter has addressed many of the deficiencies of the Winkler foundation models, allowing the realistic simulation of pipe–soil behaviour for large deformations, it presents disadvantages in terms of elevated computational demands and requires expertise of the engineer to analyze the models for use in routine engineering applications (Qin and Ni 2019; C-CORE et al. 2009).
Because of the complexity associated with the continuum numerical analysis and the accurate representation of the joint mechanical response, more efficient modelling techniques are valuable for capturing global pipeline system response, partially given variability, and uncertainty of fundamental modelling inputs (e.g., soil conditions, ground movement, pipeline system components).
To evaluate the seismic response of hazard-resistant pipeline systems equipped with enlarged, displacement-accommodating joints under longitudinal PGD, this study develops numerical and semi-analytical models considering the nonlinear properties of system components, calibrated from large-scale test data (Wham et al. 2017b, 2018).
First, this paper presents the methodology adopted to evaluate the response of buried segmented pipelines subjected to longitudinal PGD. Second, it discusses the analysis results, examining initially the numerical simulations for evaluating pipeline response within one region of the system behaving like a pull-out test, followed by assessment of the jointed pipelines subjected to two different soil block lengths. Then, pipeline response is evaluated as a function of the allowable joint displacement and the relative position of the edge of the PGD zone along the underlying pipe barrel, using a semi-analytical approach, developed considering the mechanical behaviour of the system components. Subsequently, the obtained numerical results are discussed and compared with the closed-form analytical solution proposed by Wham and Davis (2019), demonstrating its capacity to capture pipeline response. Finally, the conclusion section highlights the contributions of the present paper to the state-of-the-art practice and research of hybrid-segmented pipeline seismic design, suggesting further important perspectives related to the issues addressed.

2. Methodology

This section describes the methodology for evaluating the mechanical response of a PVCO pipeline and DI pipeline subjected to seismic-induced longitudinal PGD. First, system performance is analyzed numerically within beam on Winkler foundation theory, using the finite element software ABAQUS/Standard (Simulia 2019). Then, the influence of key system parameters including allowable joint displacement is evaluated using a semi-analytical approach, developed considering the constitutive relationship and mechanical behaviour of the pipe components. Finally, the obtained analysis results are compared with the closed-form analytical solution proposed by Wham and Davis (2019), demonstrating its capacity to capture pipeline response.
The soil–pipeline system parameters used in this study are summarized in Table 1. Both analyzed pipelines have an outer diameter, D, of 0.175 m and are assumed to be buried in medium-dense sand with the same burial depth H = 0.85 m, measured from the ground surface to the pipe centreline (Fig. 2a). The wall thickness, t, of the PVCO and DI pipelines is 6.22 and 10.2 mm, respectively. As schematically illustrated in Fig. 2, the lay length, h, of each pipe segment is assumed equal to 5.5 m, while the representative length of the enlarged joints, lj, is 0.45 and 0.20 m for the PVCO and DI pipe, respectively. Pipe lay length (h), among other parameters, will vary depending on manufacturer specifications and industry practices and is selected to be equivalent in this study for comparative purposes.
Table 1.
Table 1. Pipe–soil system parameters.
Fig. 2.
Fig. 2. (a) Schematic representation of the buried segmented pipeline displacement subjected to longitudinal soil block movement (condition I) (adapted from Wham and Davis 2019), including finite element model of (b) PVCO and (c) DI pipeline–soil system.
The ground deformation is idealized as rigid-block movement, defined by a downslope movement δ over a block length Lb, resulting in a tension crack of width δ at the upslope end and a compression ridge over a distance δ on the downslope end (Fig. 2a). The present study considers soil block lengths of Lb = 91.4 and 182.9 m. These values are consistent with examples analyzed in Wham and Davis (2019) and represent the approximate average (91.4 m) and the average plus 1.5 standard deviations (182.9 m) of the of the nearly 200 field-measured lateral spread block lengths tabulated by Bartlett and Youd (1992).
Evidently, the region of the soil–pipeline system beyond the soil block behaves like a pull-out test in tension (region I) and in compression (region IV), with the end displacement applied at the pipe points underlying the tension crack and compression bulge, respectively (Fig. 2a). Thus, the maximum pipeline displacement is equal to the total pipeline elongation at each side of the tension crack, i.e., in region 1 (Up1) and region 2 (Up2), behaving like a pull-out test, displaced at the head of the soil block movement (= 0). To gain a better understanding of the system performance, this study first investigates the behaviour of the jointed pipelines subjected to axial pull-out, followed by assessment of the pipeline response under two different soil block lengths.
Within the numerical approach, the pipeline is modeled using the PIPE31 beam element type. The mechanical joints connecting adjacent pipe barrels and the soil–structure interaction at the enlarged joint restraints are modelled using the spring-like connector element CONN3D2, implemented in Abaqus/Standard. The enlarged restraint springs connect the end of the pipe barrel at the restraint to the ground (Fig. 2), simulating their anchor-like behaviour, which increases the soil reaction to the relative soil–pipeline movement as a combined effect of the passive bearing pressure, friction, as well as soil yielding and flow.
Moreover, the soil–pipeline interaction along the pipe barrel is modeled with the spring-like pipe–soil interaction elements PSI34, representing the reaction to the soil movement in the axial, lateral, and vertical directions. One edge of the element shares nodes with the underlying pipe element while the nodes on the other edge are assigned the far-field ground motion through the boundary conditions. The adopted mesh size for the beam pipe and the underlying soil elements is 0.05 m, based on the mesh sensitivity study performed herein, assuring efficiency and accuracy of the numerical solution.
The PVCO and DI material models are defined within the von Mises plasticity theory with nonlinear hardening. At room temperature, PVCO behaves like an elastic–plastic solid, while its viscoelastic behaviour (creep and stress relaxation) is slow and can be neglected for practical purposes (Quesada 2010). The material characteristics of PVCO and DI pipes are derived from tensile coupon and internal pressure tests reported by Wham et al. (2017a) and Stewart et al. (2015), respectively. Figure 3 shows the engineering stress–strain curves derived from uniaxial tensile coupons of the pipe wall, illustrating the difference in barrel stiffness between the two materials. Table 1 tabulates properties for both pipe materials, including the PVCO pipe’s transversely isotropic material properties that exhibit different strength and stiffness characteristics in the axial and circumferential directions of the pipe wall (Wham et al. 2017a).
Fig. 3.
Fig. 3. Engineering stress–strain curve for PVCO and DI pipe materials. [Colour online.]
The mechanical joints are set to allow relative displacement between two adjacent pipe barrels, Δ = 5.5 cm, before locking up and restraining further movement. The PVCO and DI joints are modeled and calibrated considering their specific mechanical response, evaluated from the full-scale axial tension tests reported in Wham et al. (2019b) and Stewart et al. (2015), respectively.
The PVCO joint expansion, after lock-up, is caused by localized deformation of the pipe wall at the connection with the joint restraints, until ultimate failure when the pipe axial force reaches the CFC (91.2 kN). Therefore, each pipe-restraint joint is modeled as a zero-length axial spring, connecting the restraint node to the correspondent pipe barrel end. The two adjacent restraint nodes are connected by a gap-rigid axial spring, permitting relative displacement under negligible axial force until Δ = 5.5 cm, while providing a rigid connection thereafter (Δ > 5.5 cm) (Fig. 2b). The force–displacement relationship is suitably calibrated so that the combined effect in series simulates the aforementioned test response, representing the joint axial force versus displacement between the ends of two adjacent pipe barrels (Fig. 4). In contrast, the DI joint response is suitably modeled as an axial spring connecting the end nodes of two adjacent pipe barrels (Fig. 2c), using a force–displacement relationship calibrated from the full-scale axial tension tests reported in Stewart et al. (2015) (Fig. 4). As shown, the maximum connection-force capacity of the DI pipe joint (358.1 kN) is about four times greater than in the PVCO joint (91.2 kN).
Fig. 4.
Fig. 4. Force–displacement relationship of the joint (Δ = 5.5 cm) for PVCO pipe and DI pipe, as well as joint springs connected in series, representing total PVCO joint behaviour. [Colour online.]
Interestingly, the PVCO joint is more vulnerable to axial extension than compressive deformation, as demonstrated by the axial tension and compression test results reported by Wham et al. (2017a). While the joint reached failure at a maximum axial force of 91.2 kN in tension, in compression it sustained significant compressive deformation without structural or serviceability failure. Full-scale testing of various DI seismic systems shows that the joints are typically capable of sustaining larger axial load in compression than in tension (Pariya-Ekkasut 2018). As elongation capacity has been shown to be the controlling factor for jointed pipeline axial performance, this study focuses on the region of the pipe system undergoing tension, assuming for simplicity the same joint force–displacement relationship in compression as in tension. The proposed methodology can be adopted to simulate the behaviour of many joint types.
The medium-dense sand properties are analogous to those used during the Cornell University large-scale experiments (e.g., Price et al. 2018) and in the calculation example reported in Wham and Davis (2019), as indicated in Table 1. The resultant soil friction reaction per unit pipe length, fp, along the pipe barrel for the PVCO and DI pipeline is 2.15 and 4.29 kN/m, respectively. The force–displacement relationship for the axial soil–pipe interaction along the pipe barrels is considered to be elastic – perfectly plastic, defined by the sliding soil friction force per unit length of the pipeline, fp (Table 1), and the relative soil–pipe displacement at the onset of friction sliding, u0 = 1 mm, for both cases of axial soil–pipe interaction. The resultant friction force along a straight pipe barrel is 10.86 kN for PVCO and 22.74 kN for DI (Fig. 5).
Fig. 5.
Fig. 5. Axial friction force–displacement relationship of enlarged joint restraint for PVCO and DI pipe. [Colour online.]
The force–displacement relationship representing the interaction of the enlarged joint restraint (PVCO) and joint (DI) with the surrounding soil is calibrated from full-scale axial pull-out tests reported by Wham et al. (2018) and Wham et al. (2017b), respectively (Fig. 5).
Due to the symmetric joint restraint configuration of the PVCO pipe, the response of the bell and spigot restraint springs is mutually antisymmetric, with the former following a tension-no-compression behaviour and the latter a compression-no-tension behaviour. Conversely, the bearing response in the neck side of the DI pipe joint bell is slightly lower compared to the response in the face side of the joint, due to the different shape of the joint counteracting passive soil pressure during pipe movement (Wham et al. 2017b). Evidently, the reaction is greater for the PVCO restraint than the DI bell (Fig. 5), because of the greater cross-sectional area of the former, counteracting passive soil pressure.
The pull-out analyses are conducted in one static step, where one end of the of the pipeline is displaced axially to a distance Upull, while the free nodes of the pipe–soil interaction elements are fixed. The lengths of the PVCO and DI pipeline–soil systems are equal to eight pipe barrels (44 m) and 20 pipe barrels (110 m), respectively, so that the system response to the imposed ground displacement is representative of an infinitely long segmented pipeline, unaffected by far-end boundary conditions. Clearly, the required model length to achieve this condition is a function of the characteristics of the soil–pipe system and is greater for the DI pipe, partly due to the higher CFC of the joint (358.1 kN) compared to the PVCO pipe (91.2 kN).
Subsequently, global simulations of the soil–pipeline system subjected to longitudinal soil block movement with lengths of Lb = 91.4 and 182.9 m are performed, considering the pull-out analysis results. The soil block is located at the centre of the soil–pipeline system so that its midpoint lies on the pipeline bisector, as illustrated in Fig. 2a.
The lengths of the PVCO and DI pipeline–soil systems in the global analysis are equal to 55 pipe barrels (302 m) and 73 pipe barrels (401 m), respectively, so that the pipeline response is not affected by boundary conditions at the far ends of the model. The numerical analysis is conducted in one step, where the soil block movement is applied statically with a maximum step increment equal to Δδ = 1 mm. The static analysis is adequate for investigating pipeline response under PGD because the loading rate–dependent behaviour of the system, including the viscoelastic behaviour of the PVCO pipe material (creep and stress relaxation), is relatively slow and can be neglected for practical purposes (Quesada 2010).
Herein, the free nodes of the pipe–soil interaction elements are assigned the ground displacement, δ = 2 m, within the soil block length, while outside of the moving block the soil nodes remain fixed. On each step increment, the nonlinear equilibrium equations are solved iteratively by the Newton–Raphson method, allowing the assessment of system response at any level of applied ground displacement, until joint failure.

3. Analysis results and discussion

This section presents simulation results, based on the proposed methodologies, evaluating jointed pipeline response to longitudinal ground movement. First, the deformation capacities of the PVCO and DI pipelines are analyzed numerically, examining initially the pipeline response within one region of the system behaving like a pull-out test and subsequently the performance of the jointed pipelines subjected to two different soil block lengths. Second, the influence of the allowable joint displacement is assessed using a semi-analytical approach that considers the constitutive relationship and mechanical behaviour of the pipeline components. Finally, the obtained analysis results are compared with the closed-form analytical solution proposed by Wham and Davis (2019), validating the framework’s capacity to capture pipeline performance.

3.1. Jointed pipelines subjected to pull-out displacement

The pull-out analysis evaluates the maximum elongation capacity of the jointed pipelines subjected to an axial displacement that is imposed until the maximum CFC is achieved at the critical joint closest to the pull end. The analysis focuses on the response of jointed pipelines in tension, as elongation represents the controlling mechanism of axial pipeline performance, based on full-scale tension and compression tests (Pariya-Ekkasut 2018; Wham et al. 2019b).

3.1.1. Analysis of jointed PVCO pipeline subjected to pull-out displacement

The PVCO pipeline is subjected to a pull-out displacement at one end, until reaching the joint maximum force CFC (= 91.2 kN) (Wham et al. 2019b). Herein, the first pipe barrel is subjected to the greatest load and deformation demand, while in the remaining pipe barrels the axial force and associated strain do not exceed CFC = 91.2 kN and 0.009, respectively.
Figure 6 illustrates the incremental stages of consecutive joint lock-up, starting from the connection closest to application of axial displacement, as well as the activated axial forces between the various system components. Table 2 presents force and displacement results of the various pipe components at each stage until joint failure, including when each joint restraint displaces Δr1 = 0.1 cm and when the adjacent joint engages (Δr1 = 5.5 cm). Figure 7 presents the analysis results, relative to the distance from the pipe pull-out end, of the pipeline axial force, stress, displacement, and strain, as well as the soil friction reaction, for increasing values of applied pull-out displacement in tension, Upull, at the pipe end (= 0).
Fig. 6.
Fig. 6. Schematic representation of PVCO pipeline pull-out and forces activated during consecutive joint lock-up: (a) first joint expands until lock-up, (b) second joint expands until lock-up, and (c) third joint expands until failure of the first joint. [Colour online.]
Table 2.
Table 2. Numerical results of incremental PVCO pipeline component response during consecutive joint engagement under pull-out displacement (Upull,i).
Fig. 7.
Fig. 7. PVCO pipeline response to pull-out displacement applied at x = 0: (a) pipe axial force, (b) soil friction, (c) pipe axial displacement, and (d) pipe axial strain along the pipe axis. [Colour online.]
As the first pipe barrel is pulled, it elongates due to the reaction of the enlarged restraint and the applied soil friction (Fig. 6a). The latter is fully mobilized along the whole pipe barrel, while the former exceeds the static soil pressure as the adjacent joint restraint displaces an amount equal to the relative soil–pipe displacement at friction sliding (Δr1 = u0 = 0.1 cm). Herein, the mobilized friction force (Ff1 = l0fp = 10.86 kN) and the reaction of the first joint restraint (Fr1 = 9.16 kN) are equilibrated by the pull-out force, Fpull,1 = 20.01 kN (Table 2).
Then, the developed axial forces and associated stresses and strains in the pipe barrel decrease linearly from the pulled end, due to the constant friction reaction of the surrounding soil (fp = 2.15 kN/m). The first joint continues to expand until locking up (Δr1 = 5.5 cm) at a total pull-out displacement Upull,1 = 7.2 cm, where the first pipe barrel elongates ΔL1 = 1.4 cm (Table 2). Herein, the pull-out force (Fpull,1 = 33.56 kN) equilibrates the total reaction of the soil friction (Ff1 = l0fp = 10.86 kN) and the reaction force exerted by the enlarged joint restraint (Fr1 = 22.70 kN).
After full engagement of the first joint, the second pipe segment begins to displace through the soil and the system behaves as a continuous pipeline, opposing the resistance of the two enlarged restraints and of the soil friction (Fig. 6b). As the second joint restraint reaches a displacement of Δr1 = u0 = 0.1 cm, additional resistance is mobilized along the second pipe barrel, corresponding to a pull-out force Fpull,2 = 55.45 kN. Then, the second joint continues to expand until locking up after the restraint displaces Δr1 = 5.5 cm, for a pull-out displacement Upull,2 = 17.3 cm, where the first and the second pipe barrel elongate ΔL2 = 3.4 cm and ΔL1 = 1.4 cm, respectively (Table 2). Herein, the axial force drop between the two pipe barrels (Fr2 = 30.61 kN) is caused by the reaction of the enlarged joint restraint displacing Δr2 = 13.1 cm (). Similarly, the pull-out force (Fpull,2 = 75.02 kN) equilibrates the total reaction of the soil friction in the pipe barrels (Ff2 = 2l0fp = 21.72 kN) and the reaction force exerted by the enlarged joint restraints (ΣFri = 53.31 kN).
After the second joint locks up, the first three pipe segments behave as a continuous pipeline, with the soil reaction mobilized along its length (Fig. 6c), as the third restraint displaces Δr1 = 0.1 cm for a pull-out displacement Upull,3 = 22.1 cm. The corresponding maximum joint and pull-out force are  = 87.14 kN and Fpull,3 = 98.00 kN, respectively (Table 2). Thereafter, the joint expands until the connection of the first pipe barrel with the enlarged restraint fails, for a total pull-out displacement Upull,max = 23.8 cm. The corresponding pull-out force at failure is Fpull,max = 102.16 kN, equilibrating the total reaction of the soil friction in the strained pipe barrels (Ff3 = 3l0fp = 32.76 kN) and the reaction force exerted by the enlarged joint restraints (ΣFri = 69.40 kN). At failure, the expansion of the third joint is negligible (Δ1 < 0.9 cm), so that the maximum length of axially strained PVCO pipeline having friction applied due to relative soil–pipeline movement is equal to three pipe segments, ls3 = 3h = 16.5 m (Fig. 7).
Figure 8 shows the resulting elongation of the deformed pipeline components in tension as a function of the maximum joint force, indicating that only the first two joints lock up. The total joint elongation at failure amounts to 15.2 cm, representing about 64% of the maximum imposed pipeline displacement (Upull,max = 23.8 cm). The maximum elongation at joint failure of the first, second, and third pipe barrels is 5.1, 2.7, and 0.8 cm, respectively.
Fig. 8.
Fig. 8. Axial elongation of PVCO pipe components including joint expansion and axial elongation of the pipe barrels. [Colour online.]
Figure 8 also provides the progression of total pipeline elongation when axial pull is applied along the first pipe barrel at its midpoint (x = l0/2 = 2.525 m) and at the joint connection (x = l0 = 5.05 m), resulting in joint failure at 21.1 and 18.7 cm, respectively (Fig. 8). Consequently, in the global model simulating pipeline response subjected to longitudinal PGD, the pull-out analysis suggests that the joint closest to the tension crack will fail first at a maximum ground displacement δmax = 42.2 cm, with a total joint elongation of 30.3 cm (72% δmax), depending on the point of application of the longitudinal PGD along the pipe barrel.

3.1.2. Analysis of the jointed DI pipeline subjected to pull-out displacement

Pipeline elongation capacity is assessed by subjecting the segmented DI pipeline to pull-out displacement in both axial directions, where the bell face or bell neck resist passive soil pressure, until reaching the maximum DI joint capacity (CFC = 358.1 kN). This level of axial force is associated with relatively low axial strains in the pipe barrel, much less than the DI elastic limit (0.16%).
First, the DI pipeline is oriented such that pull-out displacement mobilizes passive soil pressure at the bell face, representative of region I depicted in Fig. 2a. Figure 9 illustrates the different stages where the joints expand until full engagement in a consecutive pattern, starting from the joint closest to the application of pull, as well as the activated forces between various system components.
Fig. 9.
Fig. 9. Progression of hybrid-segmented DI pipeline response to axial pull-out, mobilizing soil at the bell face: (a) first joint expansion until lock-up, (b) second joint expansion until lock-up, (c) third joint expansion until lock-up, and so on, up to (d) failure of first joint as 10th joint starts displacing. [Colour online.]
Table 3 presents the forces and displacements of the various pipe components at each stage of additional joint expansion, considering the instance when the soil reaction is mobilized in the adjacent pipe barrel (Δ1 = u0 = 0.1 cm), and when the joint engages fully (Δ1 = 5.5 cm). Figure 10 presents analysis results (pipeline axial force, strain, displacement, and soil friction reaction), as a function of distance from the pipe pull-out end, for increasing values of axial pull displacement Upull. In the figure, each curve corresponds to the total axial displacement that initiates engagement of every second joint.
Table 3.
Table 3. Incremental response of DI pipeline components, at consecutive expansion of the ith joint, to axial pull-out displacement (Upull,i) applied in direction of bell face.
Fig. 10.
Fig. 10. Response of DI pipe subjected to pull-out displacement in direction of bell face, as every two consecutive joints lock up, until failure: (a) pipe axial force, (b) soil friction, (c) pipe axial displacement, (d) pipe axial strain. [Colour online.]
As the first pipe is pulled (Fig. 9a), it elongates slightly due to soil friction mobilized along the pipe barrel, as the adjacent joint expands to Δ1, equivalent to the relative soil–pipe displacement at friction sliding (u0 = 0.1 cm). Afterwards, the mobilized friction force (Ff1 = l0fp = 22.74 kN), counteracting the pull-out force (Fpull,1 = Ff1), remains constant as the joint expands until locking up (Δ1 = 5.5 cm), for a pull-out displacement Upull,1 = 5.5 cm. Clearly, the developed axial forces and associated stresses and strains in the pipe barrel decrease linearly from the pull-out end, due to the constant friction reaction of the surrounding soil (fp = 4.29 kN/m).
After full engagement of the first joint, the second pipe segment is engaged and begins pulling through the soil, and the system behaves as a continuous pipeline, resisting the soil reaction in the enlarged bell restraint connected to the second pipe barrel, and the soil friction along the pipeline (Fig. 9b). The latter is fully mobilized along the second pipe barrel, as the second joint displaces Δ1 = u0 = 0.1 cm, for a pull-out force Fpull,2 = 48.95 kN. Subsequently, the second joint expands until locking up (Δ1 = 5.5 cm) at a pull-out displacement Upull,2 = 11.1 cm. Herein, the pull-out force (Fpull,2 = 56.86 kN) equilibrates the total reaction of the soil friction in the first two pipe barrels (Ff2 = 2l0fp = 45.47 kN) and the reaction force exerted by the enlarged bell (Fr2 = 11.38 kN), displacing Δr2 = 5.5 cm (= Upull,1).
After the second joint locks up, the first three pipe segments behave as a continuous pipeline (Fig. 9c), where soil friction is fully mobilized along its length, as the third joint expands Δ1 = u0 = 0.1 cm, for a pull-out displacement Upull,3 = 11.3 cm. The corresponding maximum joint and pull-out force are Fj3 = 60.51 kN and Fpull,3 = 83.25 kN, respectively (Table 3).
Then, the third joint engages fully (Δ1 = 5.5 cm) for a pull-out displacement Upull,3 = 16.7 cm, while the elongation of the pipe barrels remains negligible, (ΔLi < 0.1 cm). The pull-out force (Fpull,3 = 95.81 kN) equilibrates the total reaction of the soil friction in the first three pipe barrels (Ff3 = 3l0fp = 68.21 kN) and the reaction force exerted by the enlarged bell restraints (ΣFri = 27.60 kN). Clearly, the axial force drop between the first two pipe barrels (Fr3 = 16.21 kN) is caused by the reaction of the enlarged bell, displacing Δr3 = 11.1 cm (= Upull,2).
Following progressive pull-out displacement, the joints lock up in a consecutive pattern until, after the ninth joint engages fully, the maximum joint force exceeds the CFC (358.1 kN) at a pull-out displacement Upull,max = 53.3 cm and associated force Fpull,max = 380.8 kN (= CFC + l0fp) (Table 3). This force is not sufficient for the soil friction to fully mobilize along the 10th pipe barrel, while the expansion of the 10th joint is negligible (Δ1 < 0.1 cm). Therefore, at joint failure, the length of the engaged DI pipeline having friction applied due to relative soil–pipeline movement is ls10 = 10h = 55 m.
The cumulative joint elongation at failure is 52.2 cm, representing about 98% of the maximum pipeline displacement at failure (Upull,max = 53.3 cm). Compared to the PVCO pipeline, the maximum elongation of the DI pipe barrels at joint failure is marginal, not exceeding 0.3 cm.
Second, the DI pipeline is subjected to a pull-out displacement in the opposite direction, mobilizing passive soil pressure at the bell neck, representative of region II in Fig. 2a. Herein, the mechanical behaviour of the DI pipeline in this orientation differs from the previous configurations, as failure occurs at the connection of first joint and second pipe barrel.
Table 4 presents the values of the forces and displacements for the various pipe components at each stage of additional joint expansion, considering the instance when the soil reaction is mobilized in the adjacent pipe barrel (Δ1 = u0 = 0.1 cm) and when the joint engages fully (Δ1 = Δ = 5.5 cm).
Table 4.
Table 4. Incremental response of DI pipeline components, at consecutive expansion of the ith joint, to axial pull-out displacement (Upull,i) applied in the direction of the bell neck.
As pull-out displacement increases, the joints lock up in a consecutive pattern until, after the 10th joint engages fully, the maximum joint force exceeds the CFC (358.1 kN) at a total pull-out displacement Upull,max = 59.1 cm and associated force Fpull,max = 401.51 kN (Table 4). This force is not sufficient for the soil friction to fully mobilize along the 11th pipe barrel, while the expansion of the 11th joint is negligible (Δ1 < 0.1 cm). Therefore, at joint failure, the length of strained DI pipeline having friction applied due to relative soil–pipeline movement is ls11 = 11= 60.5 m.
The total joint elongation at failure reaches 57.8 cm, representing about 98% of the maximum pipeline displacement at failure (Upull,max = 59.1 cm). Herein, the DI pipeline maximum elongation and axial force are greater than for the previous bell face orientation (region 1), given the asymmetrical joint response in the two longitudinal directions. Consequently, in the global model simulating pipeline response subjected to longitudinal soil block movement (Fig. 2a), the joint in region 1 closest to the tension crack is expected to be more vulnerable.

3.1.3. Comparison of PVCO and DI pull-out response

The DI pipeline with expansion joints accommodates approximately 2.3 times greater total pull displacement (Upull,max ≈ 56.2 cm) than the PVCO system equipped with displacement accommodating restraints (Upull,max = 23.8 cm), partly due to the higher CFC of the joint (358.1 kN) compared to the PVCO pipe (91.2 kN). Herein, the DI pipe material is more rigid, accommodating a greater amount of imposed ground displacement through axial elongation of the expansion joints (98% Upull,max) than the PVCO system (64% Upull,max).
According to the axial pull-out analysis, the maximum number of fully engaged joints (n) in the PVCO pipeline is two, while in the DI pipeline is nine and 10, for the cases of pipe displaced in the direction of the bell face and bell neck, respectively. Therefore, the maximum length of the system having friction applied due to relative soil–pipeline movement (lsn = (n + 1)h) is 16.5 m for the PVCO pipeline, while reaching 55.0 and 60.5 m in the DI pipelines for the bell face and neck orientations, respectively.
The PVCO and DI (bell face direction) pipelines both fail at the joint connection in the first pipe barrel, where the maximum pull-out force reaches 102.16 and 380.83 kN, respectively. Conversely, the deformation capacity is greater for the DI pipeline subjected to pull-out displacement in the direction of the bell neck, resisting a greater maximum pull-out force, 401.51 kN, due to the additional reaction of the bell neck (Fr11 = 20.68 kN) in the first pipe barrel undergoing pull-out displacement.

3.2. Jointed pipeline response to longitudinal PGD

This section first analyzes the numerical results for assessing the performance of PVCO and DI pipelines subjected to longitudinal PGD (global analysis), considering two soil block lengths, Lb = 91.4 and 182.9 m. Then, the influence of allowable joint displacement, Δ, and position of the critical pipe barrel relative to the soil block tension crack are investigated employing a semi-analytical approach. Finally, the obtained numerical results are further compared with the analytical solutions proposed by Wham and Davis (2019), permitting calibration of the soil–pipeline axial friction resistance, fr, for estimating axial demand on buried pipeline systems.

3.2.1. Numerical analysis results

This study focuses on the response of jointed pipelines under tensile loading, region 1 (x < 0) and region 2 (x < ls2) in Fig. 2a, as tension represents the controlling mechanism of axial pipeline performance, based on full-scale tension and compression tests of the systems under investigation (Wham et al. 2017a, 2019b). In each region, the pipeline behaves like a pull-out test, displaced in tension at the point of application of the soil block movement (x = 0). This point represents the location of maximum axial tensile force and associated axial strain in the critical pipe barrel underlying the tension crack.
Elongation of the pipeline in tension (Upt) can be estimated by summing displacements in region 1 (Up1) and region 2 (Up2). These values may differ from one another, depending on the pipe axial flexibility, the restraint reaction in each longitudinal direction, as well as the relative position of the head of the soil block (x = 0) with respect to the critical pipe barrel underlying the tension crack.
Figure 11 presents the resulting total pipeline elongation, as well as its elongation in each region, as a function of the maximum pipe axial force, until joint failure, for the four cases of analyzed soil–pipeline system. Table 5 presents the analysis results in terms of maximum ground displacement at joint failure, as well as the resulting strength and deformation demand in the PVCO and DI pipelines, for the different conditions of soil block lengths Lb. The following subsections discuss in further detail the obtained numerical results for each type of jointed pipeline.
Fig. 11.
Fig. 11. Total elongation and elongation in regions 1 and 2 of jointed pipelines as a function of maximum pipe axial force for each soil block length: (a) PVCO pipeline, Lb = 91.4 m; (b) PVCO pipeline, Lb = 182.9 m; (c) DI pipeline, Lb = 91.4 m; (d) DI pipeline, Lb = 182.9 m. [Colour online.]
Table 5.
Table 5. Analysis results of PVCO and DI pipelines subjected to longitudinal PGD for varying block lengths Lb.
3.2.1.1. PVCO pipeline subjected to longitudinal PGD
Figures 12 and 13 present the variation of axial force, stress, displacement, strains, and soil friction reaction along the PVCO pipeline for increasing values of the applied ground movement Ug, assuming soil block lengths of Lb = 91.4 and 182.9 m, respectively. For this study, rigid block ground movement is assumed, in which case the applied ground movement, Ug, is equivalent to both the tension crack and compression budge displacement, δ, as illustrated in Fig. 2a. The assumption of rigid block movement is considered a worst-case scenario compared to other distributive geometries considered by O’Rourke and Nordberg (1992a).
Fig. 12.
Fig. 12. PVCO pipeline response to longitudinal PGD with block length Lb = 91.4 m: (a) pipe axial force; (b) pipe axial stress; (c) soil friction; (d) ground displacement; (e) pipe axial displacement; (f) pipe axial strain vs. distance from tension crack. [Colour online.]
Fig. 13.
Fig. 13. PVCO pipe response to longitudinal PGD with block length Lb = 182.9 m: (a) pipe axial force; (b) pipe axial stress; (c) soil friction; (d) ground displacement; (e) pipe axial displacement; (f) pipe axial strain vs. distance from tension crack. [Colour online.]
The overall PVCO pipe elongation in region 1 (Up1) and region 2 (Up2) equals the applied ground displacement Ug for both cases (Figs. 11a and 11b), because the maximum length of pipeline experiencing friction due to relative soil–pipeline movement in region 2 is less than half the soil block lengths (ls2 < 16.5 m < Lb/2) (condition I).
For increasing values of ground displacement Ug, the joints lock up in a consecutive pattern, starting from those closest to the head and toe of the moving soil block, until the joint closest to the tension crack exceeds the CFC (91.2 kN). Herein, the first two joints (n = 2) at each side of the tension crack engage fully, so that the length of pipeline behaving as a continuous pipe undergoing tension is (2n + 1)l0 = 5×5.5 m = 27.5 m. Clearly, the length of the system having friction applied due to relative soil–pipe movement in region 1 (ls1) differs from that in region 2 (ls2), depending on the location of the soil block tension crack along the critical pipe barrel (Table 5).
Joint failure of the PVCO pipe subjected to soil block movement with length Lb = 91.4 m occurs at a ground displacement δmax = 39.9 cm, equivalent to the total pipeline elongation in regions 1 and 2. Specifically, pipe elongation in region 1 (19.4 cm) is less than in region 2 (20.5 cm) because of the shorter length of the critical pipe barrel underlying the tension crack in region 1 (0.80 m) compared to region 2 (4.25 m). Herein, the maximum axial force in the pipe and associated axial stress and strain reach Fmax = 93.0 kN, σmax = 28.46 MPa, and εmax = 0.0096, respectively (Table 5).
While the overall results at failure for the longer soil block length (Lb = 182.9 m) were similar to the former case, the regional distribution of displacements differed. PVCO joint failure for the longer block occurs at a ground displacement δmax = 39.5 cm, corresponding to a maximum axial pipe force and associated axial stress and strain of Fmax = 92.2 kN, σmax = 28.23 MPa, and εmax = 0.0094, respectively (Table 5). Herein, the pipe elongation is greater in region 1 (20.4 cm) than in region 2 (19.1 cm), due to the longer length of the critical pipe barrel underlying the tension crack in region 1 (4.55 m) compared to region 2 (0.50 m).
Axial force along the pipe barrels decreases linearly (Figs. 12a and 13a) due to the mobilized soil–pipe friction (fp = 2.15 kN/m) along each barrel (Figs. 12c and 13c). Axial force drops at the joints between two adjacent pipe barrels is caused by the increased interaction of the enlarged restraints with surrounding soil during relative soil-restraint movement, with larger drops closer to the tension crack due to the greater pipeline displacement.
For both soil block lengths, total elongation of the PVCO joints at failure amount to approximately 29 cm, representing about 73% of the maximum pipeline elongation (Up,max = δmax ≈ 40 cm). Evidently, this response is consistent with the pull-out analysis results.
3.2.1.2. DI Pipeline subjected to longitudinal PGD
Figures 14 and 15 present the variation, relative to distance from the head of the soil block, of the DI pipeline axial force, stress, displacement, and strains, as well as the soil friction reaction, for increasing values of the applied ground movement, Ug, assuming soil block lengths of Lb = 91.4 and 182.9 m, respectively.
Fig. 14.
Fig. 14. DI pipe response to longitudinal PGD with block length Lb = 91.4 m (condition II): (a) pipe axial force; (b) pipe axial stress; (c) soil friction; (d) ground displacement; (e) pipe axial displacement; (f) pipe axial strain. [Colour online.]
Fig. 15.
Fig. 15. DI pipe response to longitudinal PGD with block length Lb = 182.9 m (condition I): (a) pipe axial force; (b) pipe axial stress; (c) soil friction; (d) ground displacement; (e) pipe axial displacement; (f) pipe axial strain. [Colour online.]
For the shorter soil block, the length of DI pipeline having friction applied due to relative soil–pipeline movement (ls2 = 54.0 m) is greater than half of the soil block length (Lb = 91.4 m), resulting in condition II. Therefore, the maximum joint force (340.4 kN) does not exceed the CFC (358.1 kN). Herein, the first eight joints (n = 8) at either side of the tension crack engage fully, so that the length of the pipeline having friction applied due to relative soil–pipe movement in regions 1 and 2 is ls1 = 45.13 m and ls2 = 43.28 m, respectively (Table 5). Joint failure is not predicted for the DI pipeline subjected to the shorter soil block length (Lb = 91.4 m) because insufficient force demand develops along the limited number of engaged joints in region 2 (n2 ≤ int(0.5Lb/h) = 8).
The pipeline elongation (Upt) is equal to the imposed ground displacement until the latter reaches Ug ≈ 90 cm, where transition from condition I to condition II occurs (Fig. 11c). Afterwards, the pipeline elongates less than the ground displacement until the soil reaction mobilizes fully over the entire soil block length, for Ug = 138 cm, remaining constant thereafter (Up,max ≈ 98 cm). The maximum elongation of the DI pipeline joints amounts to about 96 cm, representing almost the totality (98%) of the maximum pipeline elongation, due to the increased stiffness of the DI pipe barrels. Herein, the maximum axial force in the pipe and associated axial stress and strain reach Fmax = 344.4 kN, σmax = 65.24 MPa, and εmax = 0.000 42, respectively (Table 5).
Conversely, joint failure of the DI pipe subjected to soil block movement with length Lb = 182.9 m (condition I) occurs at a ground displacement δmax = 111.1 cm, equal to the total pipeline elongation in region 1 (Up1 = 53.2 cm) and region 2 (Up2 = 57.9 cm) (Fig. 11d).
Herein, the first nine joints (n = 9) at either side of the tension crack engage fully, so that the length of the pipeline having friction applied due to relative soil–pipe movement in regions 1 and 2 is ls1 = 54.25 m and ls2 = 50.25 m, respectively (Table 5). The CFC (358.1 kN) is reached in region 1 at the joint closest to the tension crack because of the lower bell resistance opposing passive soil pressure on the face side (region 1) than on the neck side (region 2) during relative soil–pipeline movement. Again, the cumulative elongation of the joints at failure (approximately 109 cm) accounts for the majority (98%) of the total pipeline elongation (Up,max ≈ 111 cm) due to the elevated stiffness of the DI pipe barrels. The maximum axial force, stress, and strain in the pipe are Fmax = 378.2 kN, σmax = 71.64 MPa, and εmax = 0.00046, respectively (Table 5). They localize at the head of the soil block, decreasing linearly thereupon, due to the sliding soil friction (fp = 4.29 kN/m) along the pipeline segment with locked-up joints, behaving as a continuous pipeline (Fig. 15).

3.2.2. Comparison of PVCO and DI analysis results

In the global analysis, the total pipeline elongation equals the applied ground displacement if the length ls associated with relative soil–pipeline movement does not exceed a specific fraction of the soil block length Lb (condition I). The latter depends on differences in the pipe–joint behaviour under tension and compression loading, as well as on the distribution of the soil reaction along the pipeline. This fraction is approximately equal to 1/2 in the present study, given the assumption of equal joint behaviour in tension and compression. Otherwise, if ls > 0.5Lb, the pipeline elongation in tension (Upt) is equal to the imposed ground movement (Ug) until transition from condition I to condition II occurs (ls = Lb/2). Afterwards, the pipeline rate of elongation decreases (Upt < Ug), until reaching zero, as the soil reaction is fully mobilised over the soil block length.
Specifically, joint failure of the PVCO pipeline subjected to short (Lb = 91.4 m) and long (Lb = 182.9 m) soil blocks occurs at ground displacements of δmax = 39.9 and 39.5 cm, respectively. These δmax values are equal to the cumulative pipeline elongation in region 1 (Up1) and region 2 (Up2), respectively, and differ slightly because of the deformability of the PVCO pipe and the different relative positions of the critical pipe barrel with respect to the soil block head. The joint closest to the tension crack fails first, given the symmetrical response of the PVCO joint restraint in either longitudinal direction. In contrast, the DI pipeline subjected to short soil block movement (Lb = 91.4 m) avoids failure, reaching a maximum elongation Up,max = 97.6 cm, at a ground displacement δmax = 138.2 cm, that remains constant thereafter, as the soil reaction is fully mobilized over the soil block length. Conversely, the DI pipeline subjected to long soil block movement achieves its maximum displacement capacity, Up,max = δmax = 111.1 cm, following failure of the first joint closest to the soil block head in region 1.
The maximum elongation capacity of the DI pipeline (Up,max ≈ 111 cm) is about 2.7 times greater than that of the PVCO pipeline (Up,max ≈ 40 cm), partly due to the higher CFC of the joint (358.1 kN) compared to the PVCO pipe (91.2 kN). Herein, the PVCO pipe material is more deformable, and accommodates a greater amount of imposed ground displacement through axial elongation of the pipe barrels (27%), than the DI system (2%).
The maximum number of fully engaged joints on either side of the soil block head (n) in the PVCO pipeline is two, while in the DI pipeline is nine. Therefore, the maximum length of the system having friction applied due to relative soil–pipeline movement (=(2n + 1)h) is 27.5 m for the PVCO pipeline, while reaching 88.0 and 104.5 m for the DI pipeline in the case of the short and long soil block length, respectively.
The maximum pipe axial force at failure, which occurs at the head of the soil block, is a function of the joint CFC, the distance of the soil block head with respect to the failed joint (x), and the applied soil friction (fp). Hence, the maximum axial force in the PVCO pipeline is Fmax = 93.0 and 92.2 kN for the case of soil block length Lb = 91.4 and 182.9 m, respectively, while reaching Fmax = 378.2 kN in the DI pipeline undergoing long soil block movement. Interestingly, the maximum axial force in the DI pipeline subjected to short soil block displacement (Fmax = 344.4 kN) does not exceed the joint CFC.

3.2.3. Semi-analytical model for pipeline response to longitudinal PGD and comparison with numerical analysis results

In addition to the previously discussed FE analysis, this study proposes a semi-analytical model designed to efficiently evaluate the soil–pipeline system response to long soil block displacement Ug, where ls2 < Lb/2 (condition I), as a function of various system parameters.
First, the pipeline response in regions 1 and 2 (Fig. 2a) is evaluated considering force equilibrium, displacement compatibility, and constitutive relationships of the system components subjected to pull-out displacement at the location of the applied soil block head (x). Herein, x = 0 and x = l0 represent the tension crack positioned at the critical pipe spigot and bell end, respectively, following the layout illustrated in Fig. 2. Then, the total elongation of the pipeline in tension at failure (Up,max) is evaluated by summing its elongation in region 1 (Up1) and region 2 (Up2), as a function of the maximum pipe axial force (Fmax). The proposed semi-analytical methodology is described in detail in Appendix A.
Table 6 indicates the maximum pipeline elongation (Up,max), axial force (Fmax), total joint elongation (Uj,max), and number of fully engaged joints at failure (n), for the PVCO and DI pipelines subjected to long soil block movement (Lb = 182.9 m), evaluated using numerical and semi-analytical methods. The percent difference between the results for the two methods does not exceed 0.2%, demonstrating the validity of the proposed semi-analytical procedure.
Table 6.
Table 6. Maximum axial elongation, Up,max; axial force, Fmax; total joint elongation, Uj,max; and number of engaged joints, n; for the PVCO and DI pipelines subjected to long soil block movement (Lb = 182.9 m), according to the numerical and semi-analytical methods.

3.2.4. Influence of allowable joint displacement, Δ, on pipeline response

Allowable joint displacement will vary for different pipeline products and installation guidelines. Moreover, the location of a pipeline, and its associated components, relative to ground movement geometry is typically unknown. To capture these uncertainties, the previously described semi-analytical method is used to evaluate the influence of allowable joint displacement (Δ) and position (x) of the tension crack along the critical pipe barrel on pipeline performance at failure. The performance of the system subjected to a long soil block displacement Ug, where ls2 < Lb/2 (condition I), is evaluated in terms of total pipeline elongation capacity (Up,max) at joint failure (Fj,max = CFC).
Figure 16 illustrates the response of PVCO and DI pipelines, in terms of maximum elongation capacity, total joint expansion, associated maximum axial force, and effective friction length, for varying values of the joint displacement, Δ (0.1, 2.5, 5.5, 7.5, and 10.0 cm), as a function of the soil block head position (i.e., the tension crack) along the critical pipe barrel. Each data point represents analysis results at the instance a critical joint reaches its maximum axial CFC. In the figure, x = 0 and x = l0 represent the tension crack positioned at the critical pipe spigot and bell ends, respectively, following the layout illustrated in Fig. 2. Table 7 indicates the maximum axial elongation of the pipeline (Up,max = δmax), the fraction of total joint expansion to maximum pipe elongation (Uj,max/Up,max), as well as the associated peak axial force (Fmax) in the PVCO and DI pipelines for various values of joint displacement, Δ, and three positions along the critical pipe barrel (at the barrel’s ends (x = 0 and x = l0) and midspan (x = l0/2)).
Fig. 16.
Fig. 16. Pipeline response to longitudinal PGD for varying soil block locations along critical pipe and allowable joint displacements (Δ): maximum elongation of (a) PVCO and (b) DI; maximum axial force in (c) PVCO and (d) DI; effective friction length for (e) PVCO and (f) DI pipelines. [Colour online.]
Table 7.
Table 7. Maximum axial elongation, Up,max, and axial force, Fmax, in the PVCO and DI pipelines for various values of the joint parameter Δ when ls2 ≤ Lb/2 (condition I).
The PVCO pipeline exhibits symmetrical behaviour with respect to the critical pipe barrel midpoint (Fig. 16), owing to the identical response of the enlarged restraints at the bell and spigot sides of the joint. Herein, for each allowable joint displacement, Δ, the deformation capacity and associated axial force are maximum when the tension crack is coincident with the PVCO pipe barrel midpoint (Table 7) and decreases as either joint is positioned closer to the ground movement head. Conversely, the deformation capacity and axial force of the DI pipeline decreases when the head of the soil block is closer to the spigot end of the critical pipe barrel (x = 0), because of the lower maximum axial force required to reach the CFC of the joint when soil imposes passive pressure in the direction of the bell face (region 1) rather than the bell neck (region 2).
Greater values of allowable joint displacement, Δ, result in increased capacity of the pipeline system to accommodate ground movement (Figs. 16a and 16b). Increased localized joint displacement also results in greater relative soil–pipe movement at the enlarged connections, requiring less engaged pipeline length having friction applied due to relative soil–pipe movement in regions 1 (ls1) and 2 (ls2) (Figs. 16e and 16f). This engaged pipeline length as well as the maximum elongation capacity Up,max and axial force Fmax of the pipeline depend on the position (x) of the head of the soil block along the critical pipe barrel and on the number of fully engaged joints in each region. These are a function of the system properties, including the axial soil–pipeline interaction, pipe axial deformability, and the joint CFC.
As expected, the contribution of the total joint expansion (Uj,max) to the overall pipeline elongation (Up,max) increases for greater Δ in both the DI and PVCO models (Table 7). However, the percent contribution of joint expansion to overall pipe elongation is much greater for the DI pipeline, given its significant material stiffness relative to the thermoplastic pipeline. At Δ = 0.1 cm, joint elongation does contribute measurably to the overall PVCO and DI system response, given the joints’ non-linear force–displacement relationships noted previously (Fig. 4).
While the DI pipeline system can accommodate greater axial displacement than PVCO for larger values of joint displacement, Δ, the PVCO system accommodates greater movement for the Δ = 0.1 cm case due to the deformability of the pipe material. Results attained for Δ = 0.1 cm are representative of pipeline response for a system with fully restrained joints. Increasing the joint displacement capacity from 0.1 to 10 cm results in 2.4 and 15.1 times greater pipe elongation for PVCO and DI pipe systems, respectively, assuming a long soil block length for all cases. Even a modest allowable displacement of 2.5 cm improves system performance by 42% and 369% for PVCO and DI, respectively, compared to the 0.1 cm allowable displacement system.
Evidently, smaller values of allowable joint displacement require greater lengths of engaged pipeline ls. For DI, the Δ = 0.1 cm case requires over 71 m of unobstructed pipe, free of bends, tees, and other typical system components on either side of the tension crack to accommodate its maximum ground movement. Values of required ls reduce for both pipe systems with increased allowable joint opening.

3.2.5. Comparison of numerical and analytical approaches

A primary goal of this study is to use the numerical model, calibrated from full-scale experiments, to assess the ability of a recently developed, closed-form analytical procedure to capture pipeline response to longitudinal ground deformation. The axial pull and global model results confirm the general assumptions of hybrid-segmented pipeline response noted by Wham and Davis (2019), including trends in the pipe strains and displacements along the pipeline due to relative soil–structure interaction. Both condition I and condition II system responses were observed, depending on the length of engaged pipeline, ls, relative to the ground movement parameters, Lb and δ.
Table 8 provides a tabulated comparison between the values obtained from the enclosed numerical analysis (“this study”), presented earlier in Table 5, and results using the analytical approach outlined by Wham and Davis (2019). These are evaluated for various combinations of block length, Lb, and ground movement, δ, that caused a critical joint to experience axial force greater than the CFC determined from physical testing. Three primary outputs are compared: maximum axial pipe force, maximum pipe strain, and the average value of engaged pipeline in each region, which is consistent with the aggregate number of engaged joints in regions 1 and 2. Below each test case shown in Table 8, the percentages that the Wham and Davis analytical approach differ from the FE analysis of this study are provided.
Table 8.
Table 8. Comparison of present study analysis results with Wham and Davis (2019) analytical approach.
Excellent agreement between the analysis approaches is apparent. Results for the PVCO system, in which the maximum ground movements for both block lengths were nearly 40 cm and within condition I limits, are consistent with the analytical approach, exhibiting differences less than 3.2%. This comparison shows that, despite the lack of consideration for non-linear material and soil-interaction modelling, the Wham and Davis (2019) approach captures well the PVCO pipe response.
For the DI system, the longer soil block length (Lb = 182.9 m) also conforms to condition I. For this relatively large ground movement at failure, the axial force and strain differ from the numerical results by about 10%. While this difference is notable, the length of pipeline engaged with soil (ls,avg = 54.2 m) falls within the range reported in Table 7 (ls = 49.5–55.0 m), as the pipe response depends on the location of the critical pipe barrel with respect to the tension crack. Similarly, the number of engaged joints in the numerical model (18 or 19) depends on this configuration.
The DI pipe with shorter block length (Lb = 91.4 m) satisfies condition II, and hence neither the numerical nor analytical models predict failure of the pipeline regardless of the magnitude of block movement. For this case, the analytical procedure compares well with the numerical model, differing by a maximum of 3.4% across all considered metrics (Table 8).
The Wham and Davis (2019) approach is predicated on accurately assigning a representative frictional force, fr, along the pipeline that accounts for both the pipe barrel friction, fp, and the increased localized interaction of the joint restraint, Fjr. Wham et al. (2019a) proposed several methods for estimating a representative fr given soil properties and system geometry. For the approach described and implemented by Wham and Davis (2019), the value of Fjr is estimated as the axial force recorded from full-scale tests at an axial pull-out displacement of approximately 15.2 cm (6 inches), which is equivalent to 27.1 kN (6.1 kips) and 18.7 kN (4.2 kips) for the PVCO restraint and DI joint, respectively. These values are approximately 73% and 84% of the maximum joint resistance force for the PVCO and DI joints, respectively (Fig. 5). Optimization of Fjr for the Wham and Davis approach suggests that 70% of the maximum Fjr for the PVCO system provides the closest correlation to the numerical analysis results for the geometries and conditions investigated. Similarly, for the DI system, assigning a fr calculated using 66% and 80% of the maximum Fjr provides the best correlation to the numerical results for conditions I and II, respectively. Even the lowest Fjr percentage, 66%, more than doubles the effective axial frictional resistance along the pipeline, which would be calculated from traditional estimates of pipe barrel friction (e.g., ASCE Committee on Gas and Liquid Fuel Lifelines 1984).
Taken in aggregate, these results demonstrate that the Wham and Davis (2019) analytical model provides a reasonable first-order approximation of the strains and force that develop in pipelines and their joints, composed of varying material properties and geometric characteristics, for various ground movement parameters.

3.3. Discussion of modelling limitations

Several limitations to the present study are important to identify. The adopted Winkler on foundation model assumes a constant friction reaction along the pipeline barrels, ignoring the effect of operational loads, and the complex soil–pipeline interaction at the edge of the ground movement zone. Circumferential expansion and contraction of the pipe cross section due to different loading conditions may alter the intensity of soil–pipe interaction, in the radial and axial direction, depending on the pipe deformability (Banushi et al. 2018). Furthermore, the axial friction along the pipe barrel increases in proximity of the enlarged restraint due to the greater lateral soil pressure, resisting pipe movement. Realistically simulating this behaviour requires the use of more complex numerical modelling approaches, considering the nonlinear system properties including contact interaction at the soil–pipe interface.
Moreover, thermoplastics, like other common pipeline materials, are rate dependent and have material characteristics that may change over time, which this study does not consider. Likewise, DI, as well as other materials, may degrade over time, resulting in a thinner wall thickness and less overall capacity. The physical state of a pipeline and associated changes with age are important considerations when establishing design requirements and recommendations.
Frictional force along the pipe barrel can change based on internal pressure, deposition time, soil properties, and trench conditions. Different pipe materials, lay length, coating types, and connection geometries may alter the overall system response. Additionally, more distributed deformation patterns of longitudinal PGD may cause a greater number of joints within the PGD zone to experience relative axial displacement, compared to the abrupt deformation pattern (i.e., idealized block) analyzed in this study, requiring further investigation. Further research focused on the soil–pipeline interaction for various connection geometries is needed to expand the modelling efforts herein to other pipeline systems. Moreover, the size of the connection (joint restraint or bell) may vary depending on product specifications, including the diameter, ultimately altering the soil resistance along the system. Additionally, the axial joint force capacity (CFC) was adopted from limited axial tension tests and will differ for various connection–material types, influencing the overall system performance considerably. While the pipeline systems investigated in this study were found to be more vulnerable to axial tension loading, it is possible that a system’s CFC could be limited by its performance under axial compression, highlighting the necessity of considering all potential failure mechanisms before assigning a representative CFC for system evaluation.

4. Conclusions

This study investigates the capacity of buried hazard-resistant pipelines to accommodate longitudinal PGDs during earthquakes, including landsliding, liquefaction-induced lateral spreading, and other forms of ground movement. Two types of hybrid-segmented pipelines are investigated: (i) hazard-resilient ductile iron pipe and (ii) PVCO pipe with joint restraints capable of axial deformation.
The developed numerical models, calibrated from full-scale tests, assess the maximum elongation capacity of the pipelines (Up,max), subjected to longitudinal PGD. The deformation capacity is equal to the total pipeline elongation at each side of the tension crack, i.e., in region 1 (Up1) and region 2 (Up2), behaving like a pull-out test, displaced at the head of the soil block movement (x = 0).
The pull-out numerical analysis, simulating the system response in region 1, showed that the DI pipeline with expansion joints accommodated approximately 2.3 times greater pull displacement (Upull,max ≈ 56.2 cm) than the PVCO equipped with displacement-accommodating restraints (Upull,max = 23.8 cm). While the PVCO pipe responds symmetrically in either longitudinal direction, the DI pipeline exhibits greater deformation capacity when subjected to pull-out displacement that generates passive soil pressure at the bell neck, relative to the bell face.
According to global numerical analysis of system response to longitudinal PGD, the elongation capacity of the DI pipeline (Up,max ≈ 111 cm) is about 2.7 times greater than that of the PVCO pipeline (Up,max ≈ 40 cm), partly due to the higher CFC of the joint (358.1 kN) compared to the PVCO pipe (91.2 kN). Herein, the PVCO pipe material is more deformable, accommodating a greater amount of imposed ground displacement through axial elongation of the pipe barrels (27%), than the DI system (2%). Interestingly, the jointed DI pipeline subjected to longitudinal PGD with a short soil block (condition II) does not reach failure due to the limited length of pipeline within the soil block being able to mobilize sufficient soil reaction due to relative soil–pipeline movement.
The semi-analytical approach, implemented to evaluate the pipeline response as a function of the allowable joint displacement (Δ) and location relative to the soil block, demonstrated that greater values of Δ increase the system performance considerably, while decreasing the length of engaged pipeline. Even a modest allowable displacement of 2.5 cm improves system performance by 42% and 369% for PVCO and DI, respectively, compared to the fully restrained joint system. This fully restrained joint system requires over 21 and 71 m of unobstructed pipe — for the PVCO and DI pipeline, respectively, free of bends, tees, and other anchor-like system components — on either side of the tension crack to accommodate the maximum ground movement.
The axial pull and global model results confirm the general assumptions of hybrid-segmented pipeline response noted by Wham and Davis (2019), including trends in the pipe strains and displacements along the pipeline due to relative soil–structure interaction. The numerical results also demonstrate the capacity of the Wham and Davis (2019) analytical approach to capture the expected system performance for various pipe materials and ground movement parameters, with excellent correlations between the two approaches. The results further illustrate the importance of assigning appropriate axial friction parameters for segmented pipelines with enlarged joints and restraints.
In conclusion, this study provides a useful methodology for evaluating the performance of hybrid-segmented pipelines — subjected to longitudinal PGD — as a function of varying system parameters, highlighting the primary design factors impacting system response.

List of symbols

CFC
axial connection force capacity
D
pipeline outer diameter
Dj
outer diameter of enlarge joint–restraint
Dp
pipe outside diameter
El
pipe elastic modulus in longitudinal direction
Eθ
pipe elastic modulus in circumferential direction
Ff1
mobilized friction force along the first pipe barrel during pull-out
Ffi
mobilized friction force along the pipe barrels as the ith joint expands until lock-up
Fi(x)
axial force along the first pipe barrel at distance x from the pull-out end, as the ith joint expands until lock-up
Fji
maximum axial force in the pipe connection (joint) closest to the pull-out end, as the ith joint expands until lock-up
axial force at the connection with the first PVCO pipe restraint (joint 1) closest to the pull-out end, as the ith joint expands until lock-up
axial force at the connection with the second PVCO pipe restraint (joint 2) closest to the pull-out end, as the ith joint expands until lock-up
Fjr
pipe joint axial resistance force due to relative movement in soil
Fmax
maximum axial force in pipeline
Fpull,i
axial pull force as the ith joint expands until lock-up
Fpull,max
pull force at critical joint failure
Fri
soil reaction force at the joint restraint closest to the pull-out end, as the ith joint expands until lock-up
fp
frictional force per unit length of pipe
fr
axial soil–pipeline resistance force per unit length of pipe
H
burial depth to pipe springline
h
pipe lay length
i
index
K0
Coefficient of lateral soil pressure at rest
Lb
length of rigid soil block
l0
length of pipe barrel
lj
representative joint length
ls
length of hybrid-segmented pipeline having fr applied due to relative soil–pipe movement resulting in an axial pipe strain ε
ls,avg
average length of engaged pipeline regions 1 and 2
lsi
length of hybrid-segmented pipeline having fr applied due to relative soil–pipe movement resulting in axial pipe strain ε within region i (i = 1, 2, 3, 4)
n
number of displaced hybrid-segmented pipe joints over length ls
ni
number of displaced hybrid-segmented pipe joints over length lsi
t
pipe wall thickness
Ug
field of ground displacement
Ui(x)
axial displacement along the first pipe barrel at distance x from the pull-out end, as the ith joint expands until lock-up
Uj,max
maximum total joint elongation at failure
Upi
pipeline elongation within region i (i = 1, 2)
Up,max
maximum pipeline elongation under longitudinal PGD
Upt
total pipeline elongation under longitudinal PGD
Upull
axial pull-out displacement
Upull,i
axial pull-out displacement as the ith joint expands until lock-up
Upull,max
maximum pull-out displacement at joint failure
u0
relative soil-pipe displacement at the onset of friction sliding (assumed equal 1 mm)
x
horizontal distance along the pipeline system
γ
soil density
Δ
distance hybrid-segmented pipe joints can deform in tension and compression
Δ1
displacement of the ith expanding joint until lockup (0 < Δ1 ≤ Δ), during pipe pull-out
Δji
displacement of the joint closest to the pull-out end as the ith joint expands until lock-up
displacement of the DI pipe joint, for a system with full-restraint joints (Δ = 0), as the ith joint expands until lock-up
displacement of the PVCO joint closest to the pull-out end, due to localized pipe deformation at the connection with the first restraint (joint 1), as the ith joint expands until lock-up
displacement of the PVCO joint closest to the pull-out end, due to localized pipe deformation at the connection with the second restraint (joint 2), as the ith joint expands until lock-up
Δri
displacement of the restraint closest to the pull-out end as the ith joint expands until lock-up
ΔL(Fpull)
total elongation of an infinite continuous buried pipeline as a function of the pull-out force at its end (Fpull)
ΔLi
elongation of the pipe barrel closest to the pull-out end as the ith joint expands until lock-up
δ
crack width, rigid-block ground displacement
δi
pipe–soil interface friction angle
δmax
maximum ground displacement at pipe failure
εl
proportionality limit strain in longitudinal direction
εmax
maximum pipe axial strain
νl
Poisson’s ratio of the pipe material in longitudinal direction
νθ
Poisson’s ratio of the pipe material in circumferential direction
σl
proportionality limit stress in longitudinal direction
σmax
maximum pipe axial stress
soil friction angle

Acknowledgements

The authors would like to acknowledge Craig Davis, for constructive input and guidance in developing the models, and Ingo Weidlich for providing helpful input and guidance in revising the paper. Thanks are extended to numerous staff, students, and faculty at Cornell University’s Geotechnical Lifelines Large-scale Testing Facility who contributed to the design and execution of the experiments used to calibrate the analyses, specially Blake Berger, Tim Bond, Tom O’Rourke, and Harry Stewart. Thanks are also extended to the Department of Infrastructural Engineering of HafenCity University in Hamburg for providing the computational resources to perform the numerical analysis presented herein.

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Appendix A. Semi-analytical model for segmented pipeline response to longitudinal PGD

This appendix describes the proposed semi-analytical model for evaluating the maximum deformation capacity of a pipeline subjected to long soil block displacement Ug, where ls2 < Lb/2 (condition I), taking into account the pipeline response to pull-out displacement in regions 1 and 2 (Fig. 2a).
First, the pipeline response to axial pull-out is evaluated semi-analytically, considering the constitutive relationship of the system components, force equilibrium, and displacement compatibility along the first pipe barrel subjected to pull-out displacement, as the ith joint expands until lockup (0 < Δ1 ≤ Δ). Adopting the notation of the main text, the formulations describing PVCO (symmetric joint) and DI (both bell face and neck orientations) pipelines to axial pull-out displacement are indicated in Table A1.
Table A1.
Table A1. Semi-analytical formulation for evaluating response of PVCO and DI pipe components, under pull-out displacement, as ith joint expands until lockup (0 < Δ1Δ).
Herein, Fpull,i–1 and Upull,i–1 are the axial force and displacement, respectively, at the connection of the second pipe barrel and first joint (Figs. 6 and 9), as the ith joint expands until lockup (0 < Δ1 ≤ Δ). For i = 1, the axial force and displacement at the connection of the second pipe barrel with the first joint indicated in Table A1 result in Fpull,i–1 = 0 and Upull,i–1 = 0, respectively. Furthermore, Ff1 is the total reaction of the soil friction along the first pipe barrel, while Fri is the soil reaction at the first joint restraint, as a function of the associated displacement Δri, according to the force–displacement relationship Fri(Δri), represented in Fig. 5. Additionally, Δji is the total joint displacement; and are the displacement of the first and second PVCO joint springs (Fig. 2b) as a function of the associated axial force and , respectively; while is the displacement of the DI pipe joint spring as a function of the associated axial force Fji, in the case of fully restrained joints (Δ = 0; Fig. 4). The elongation of the first pipe barrel within a distance x from the pull-out end, ΔLi(Fpull,i, x), is a function of the distance x (Figs. 6 and 9) and the axial pull-out force, Fpull,i, and is evaluated using the formulation of the equivalent axial spring proposed by Banushi and Squeglia (2018). This formulation permits calculating the total elongation of an infinite continuous buried pipeline ΔL(Fpull) as a function of the pull-out force at its end, Fpull, taking into account the nonlinearities of the pipe–soil system, including the piecewise stress–strain relationship of the pipe material. Therefore, the pipe segment elongation in the first pipe barrel within a distance x from the pull-out end, ΔLi(Fpull,i, x), as the ith joint expands until lockup (0 < Δ1 ≤ Δ) is evaluated as the relative displacement between the pull-out end and a section located a distance x from it. Finally, Ui(x) and axial force Fi(x) are the axial displacement and force along the first pipe barrel, respectively, at a distance x from the pull-out end (Table A1).
By varying the value of the joint expansion parameter, Δ1, between negligible expansion and the allowable joint displacement Δ = 5.5 cm (0 < Δ1 ≤ Δ) for every engaging joint, i, in the expressions indicated in Table A1, it is possible to evaluate the response of the system components under pull-out movement, as consecutive joints lock-up, until failure. Consequently, each system parameter (e.g., the pull-out force Fpull,i and displacement Upull,i, or the maximum joint force Fji and total joint elongation ΣΔji) is a parametric function of the total number of the engaged joints (i) and of the ith joint expansion (Δ1). Given that these relationships are bijective after lockup of the first joint (i > 1), it is possible to determine — for every known system parameter — the value of all other parameters (Table A1) associated with the same number of engaged joints (i) and expansion of the ith joint (Δ1).
This algorithm can be easily implemented within most programming languages, like Python (Van Rossum 2015), for further applications. For example, Fig. A1 compares the results obtained using the semi-analytical procedure and the numerical analysis, in terms of evolution of the pull-out displacement, Upull, as a function of the maximum joint axial force, Fj,max, showing excellent agreement between the numerical and semi-analytical methods.
Fig. A1.
Fig. A1. Comparison of numerical and semi-analytical models, in terms of total pipeline elongation (Upull) vs. maximum joint force, during pull-out of PVCO and DI (bell neck and face orientations) pipelines until joint failure (Fj,max = CFC). [Colour online.]
Next, the response of the soil–pipeline system subjected to long soil block displacement, Ug, where ls2 < Lb/2 (condition I), is evaluated considering the pipeline response to pull-out movement in regions 1 and 2 (Fig. 2a). Thus, the total elongation of the pipeline in tension (Upt) is evaluated by summing its elongation in regions 1 (Up1) and 2 (Up2) as a function of the maximum pipe axial force Fmax. The latter occurs at the location (x) of the soil block head along the underlying pipe barrel, decreasing linearly thereupon, due to the sliding soil friction (fp). Herein, = 0 and x = l0 represent the tension crack positioned at the critical pipe spigot and bell end, respectively, following the layout illustrated in Fig. 2.
Considering the system response during pull-out displacement (Table A1), the methodology for assessing pipeline performance under long soil block movement, in terms of maximum axial force (Fmax), maximum total elongation of the pipeline (Up,max) and joints (Uj,max), and number of engaged joints (n) at failure, consists of four general steps:
1.
Determine the maximum pipe axial force, Fmax(x), at joint failure (Fj,max = CFC), as the minimum of the pipe axial force associated with joint failure under pull-out in region 1 (Fp1,max(l0 − x)) and in region 2 (Fp2,max(x)):
(A1)
2.
Determine the maximum pipeline elongation at joint failure, Up,max(x), as the sum of the pipe axial elongation under pull-out movement in region 1 (Up1(l0 − x)) and region 2 (Up2(x)) associated with the maximum pipe axial force Fmax(x):
(A2)
3.
Determine the maximum joint elongation at failure, Uj,max(x), as the sum of the total joint elongation (ΣΔji) under pull-out movement in region 1 (Uj1(l0 − x)) and region 2 (Uj2(x)) associated with the maximum pipe axial force Fmax(x):
(A3)
4.
Determine the number of engaged joints at failure, n(x), as the sum of the number of engaged joints under pull-out movement in region 1 (n1(l0 − x)) and region 2 (n2(x)) associated with the maximum pipe axial force Fmax(x):
(A4)
The described algorithm can be implemented in most programming languages (e.g., Python) for further parametric analysis. Comparison between the semi-analytical and numerical results for axial pull-out (Fig. A1), as well as global analysis (Table 6), showed excellent agreement between the two approaches, further confirming the validity of the proposed semi-analytical procedure.

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Published In

cover image Canadian Geotechnical Journal
Canadian Geotechnical Journal
Volume 58Number 8August 2021
Pages: 1095 - 1117

History

Received: 20 January 2020
Accepted: 28 August 2020
Accepted manuscript online: 3 September 2020
Version of record online: 3 September 2020

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Key Words

  1. longitudinal ground movement
  2. hybrid-segmented pipeline
  3. seismic performance
  4. soil–pipeline interaction
  5. analytical model
  6. numerical analysis

Mots-clés

  1. analyse numérique
  2. mouvement longitudinal du sol
  3. pipeline hybride segmenté
  4. performance sismique
  5. interaction sol–pipeline
  6. modèle analytique

Authors

Affiliations

Gersena Banushi [email protected]
Department of Infrastructural Engineering, HafenCity University, Henning-Voscherau-Platz 1, Hamburg 20457, Germany.
Brad P. Wham
Center for Infrastructure, Energy, and Space Testing, University of Colorado Boulder, 1111 Engineering Drive, UCB 428 ECOT 428, Boulder, CO 80309, USA.

Notes

Copyright remains with the author(s) or their institution(s). Permission for reuse (free in most cases) can be obtained from copyright.com.
A correction was made to the e-First version of this paper on 6 August 2021 prior to the final issue publication. The current online and print versions are identical and both contain the correction.

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