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.
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.
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.
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 (
x = 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).
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).
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).
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 Δ
δ = 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.
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