Geofoam blocks to protect buried pipelines subjected to strike-slip fault rupture

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Geofoam blocks to protect buried pipelines subjected to strike-slip fault rupture Habib Rasoulia, Behzad Fatahib,∗ a b

School of Civil and Environmental Engineering, University of Technology Sydney, Sydney, Australia School of Civil and Environmental Engineering, University of Technology Sydney (UTS), Sydney, Australia

A R T I C LE I N FO

A B S T R A C T

Keywords: Geosynthetics Geofoam Pipeline Permanent ground deformation Strike-slip fault

This paper proposes using geofoam blocks to improve the safety of buried steel pipelines under permanent ground deformation due to strike-slip fault rupture. Since these geofoam blocks are deformable, they can compress during fault rupture and thus reduce the pressure imposed on the pipeline by the surrounding soil. This means that the pipe can sustain a higher level of tectonic deformations. For the pipeline system adopted in this study, the geofoam blocks consist of two 1 m thick blocks at each side and another on the top of the pipeline. The effectiveness of this configuration is then assessed in comparison to the conventional buried pipeline by three dimensional numerical simulations that consider the interaction between soil and structure and the impact of critical parameters such as the pipeline-fault trace crossing angle, geofoam blocks thickness and the internal pressure of the pipeline. The results indicated that the geofoam blocks reduced the axial tensile strain of nonpressurised pipeline from the unacceptable 4.16% to the safe level of 0.75% when the crossing angle was 135°. In addition, geofoam blocks successfully decreased the maximum ovalisation parameter and compressive strain of the non-pressurised pipeline from 0.237 and −25.8% to 0.065 and −0.47%, respectively when the crossing angle was 65°.

1. Introduction Past earthquake events indicate that large ground deformation due to fault ruptures, landslides, or liquefaction cause significant damage to underground and surface structures (O'Rourke and Palmer, 1996; Tang, 2000; Chen et al., 2002). Of these critical structures, the buried oil and gas pipelines, and tunnels, due to their extended length are more susceptible to structural failure from large ground deformation. Pipelines in the petroleum industry play a crucial role in transferring oil products and natural gas; the CIA World Factbook (2013) reveals there are more than 3.5 million km of pipeline networks in 120 countries around the world, therefore their performance should be addressed and mitigated with regards to their safety and serviceability against fracturing and loss of containment due to large ground deformation. The field studies carried out after past seismic events such as the 1999 Izmit and Chi-Chi earthquakes (Tang, 2000; Tsai et al., 2000) showed that pipeline operations were stopped by large permanent ground deformation due to landslides, lateral spreading and fault rupture incidents (Ha et al., 2008; Vazouras et al., 2012), and not just by ground shaking. The unacceptable performance of buried gas pipelines

may lead to leakage which may have life threatening consequences or may cause an environmental disaster. For instance, during the 1999 Izmit earthquake, a steel pipeline incurred a significant amount of damage due to strike-slip fault ruptures (Tang, 2000). Over the last decades, many researchers have used experimental (Ha et al., 2008; Abdoun et al., 2009; Sim et al., 2012; Saiyar et al., 2016; Hojat Jalali et al., 2018; Ni et al., 2018a, 2018b) and numerical modelling (Vazouras et al., 2010; Tsatsis et al., 2017; Vazouras and Karamanos, 2017; Banushi et al., 2018; Xu et al., 2018) to examine the mechanical behaviour of buried pipelines during large ground deformations. Abdoun et al. (2009) using centrifuge modelling showed that the moisture content and fault slip rate have insignificant effects on the response of buried high-density polyethylene (HDPE) pipes under strike-slip fault in terms of the maximum induced lateral force in the pipe and the position of peak strains, while the burial depth and wall thickness have significant effects on the magnitude of the peak strain. Sim et al. (2012) using an experimental approach also studied the interaction mechanism of the buried pipeline under the combined permanent ground deformation with strong vibration due to faulting and earthquake, respectively. The obtained results indicated that the

∗ Corresponding author. School of Civil and Environmental Engineering, Faculty of Engineering and Information Technology, University of Technology, Sydney (UTS), City Campus PO Box 123 Broadway, NSW, 2007. E-mail address: [email protected] (B. Fatahi).

https://doi.org/10.1016/j.geotexmem.2019.11.011 Received 25 May 2019; Received in revised form 16 October 2019; Accepted 23 November 2019 0266-1144/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Habib Rasouli and Behzad Fatahi, Geotextiles and Geomembranes, https://doi.org/10.1016/j.geotexmem.2019.11.011

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(Tupa and Palmeira, 2007; Palmeira and Andrade, 2010; Pires and Palmeira, 2017), and reinforce them by increasing their resistance to uplift (Selvadurai, 1989; Palmeira and Bernal, 2015), very few studies have attempted to mitigate the detrimental effects that permanent ground deformation has on pipeline performance. Gantes and Melissianos (2016) using numerical modelling reviewed different mitigation techniques in engineering practice and literature to safeguard buried steel fuel pipeline under permanent ground deformation. They categorised the current measures to protect the pipeline against fault rupture in three main categories. The first category includes the measures to reduce the friction between the pipeline and the surrounding soil such as wrapping the pipeline with low friction geosynthetic layer, trench backfilling with loose and low weight material such as tire-derived aggregate, EPS geofoam, and using wider prefabricated concrete culvert. The second mitigation category covers the methods to strengthen the performance of pipelines under larger fault rupture slip such as using thicker wall thickness for the pipe, while the third category includes the methods such as using flexible joints or constructing the pipeline above the ground. They concluded that among the mentioned methods, the most effective method was placing the pipeline with flexible joints in the culvert. EPS geofoam blocks have been extensively used as a lightweight backfill material since 1970 due to the low density (ranging from 10kg/m3 to  30kg/m3 in common engineering practice reported by Horvath (1994). The primary uses of EPS blocks for geotechnical applications are in road construction on low bearing capacity subgrade soil (Mohajerani et al., 2017), retaining wall and bridge abutments as a backfill material (Puppala et al., 2019), slope stabilisation (Akay et al., 2013; Ozer et al., 2014; Akay, 2016), levees (Akay et al., 2014), foundations for lightweight structures (Siabil et al., 2019), protection of underground services (Bartlett et al., 2015; Witthoeft and Kim, 2016; Baziar et al., 2018; AbdelSalam et al., 2019; Abdollahi et al., 2019; Placido and Portelinha, 2019) and vibration damping barriers (Liyanapathirana and Ekanayake, 2016; Baziar et al., 2019b). The efficiency of using EPS geofoam blocks as lightweight backfill material in reducing the vertical and lateral stresses applied to buried pipes was investigated using experimental and numerical pipe pushtests by Yoshizaki and Sakanoue (2003), Choo et al. (2007), Lingwall (2011), Lingwall and Bartlett (2014), and Bartlett et al. (2015). Yoshizaki and Sakanoue (2003) used experimental modelling to show how EPS geofoam blocks reduce the soil-pipe interaction on the pipeline buried with elbows. Choo et al. (2007) used centrifuge modelling to show that using EPS geofoam blocks as backfill will largely reduce the lateral stress on buried non-pressurised HDPE pipes subjected to permanent ground deformation, and EPS blocks will also reduce the peak transverse lateral force at the pipe-soil interface by up to 90%. Tavakoli Mehrjardi et al. (2012) used full-scale experimental modelling to study the effect that geocell-reinforced layers have on unplasticised Polyvinyl Chloride (uPVC) pipelines embedded in a rubber-soil mixture; they also showed that by introducing geocells, the radial strain of the pipeline and ground surface settlement decreased significantly compared to conventional pipelines buried in soil deposits. Bartlett et al. (2015) and Bartlett and Lingwall (2014) summarised the different methods of using EPS to improve the mechanical behaviour of pipeline and culverts under different loading conditions. Hegde and Sitharam (2015) used experimental and numerical simulations to study geocell reinforced sand beds as a mitigation technique to improve the mechanical behaviour of small PVC pipes under vehicle tire loading; they showed that geocell reinforced sand beds reduced vertical pressure and strain at the top of the PVC pipe by 40% and 50%, respectively. Meguid et al. (2017) used numerical simulations to show how effectively EPS geofoam blocks could reduce the contact pressure on the wall of a buried culvert. The existing body of research shows that most researchers have been studying the use of different types of geosynthetic materials as backfill to reduce the vertical or lateral stresses induced by soil settlement or permanent ground deformation, but there has been no

magnitude of bending moment in the buried pipeline did not depend on the earthquake wave propagation, and the intensity of shaking did not impact the results. Vazouras et al. (2012) studied the crossing angle between an underground pipeline and an active strike-slip fault rupture to examine the mechanical performance of the pipeline for various ground parameters such as soil cohesion, the friction angle and stiffness. The study showed that when the crossing angle between the pipeline and the rupture trace is less than 90°, the governing mode of failure in the pipeline is local buckling, but when the crossing angle is more than 90°, the predominant failure mode is axial tensile straining. Vazouras et al. (2010) also showed that pipelines buried in softer cohesive soils or looser non-cohesive soils could tolerate more ground deformation. Banushi et al. (2018) using numerical modelling proposed to increase the deformation capacity of pipelines by choosing a crossing angle in which a pipeline would experience extension rather than compression and thus avoid local buckling. Xu et al. (2018) used numerical simulation to indicate that segments of a pipeline near a fault rupture plane and buried in both foot and hanging blocks are still susceptible to buckling and failure when the fault rupture causes compression along the pipeline. It was also shown that increasing the diameter and thickness of a pipeline, surrounding it with weaker soil and choosing an appropriate depth at which to bury it, could improve the performance of pipelines during a strike-slip fault rupture incident. Tsatsis et al. (2017) carried out a numerical study of the mechanical performance of a buried steel pipeline along the dip of a slope subjected to sliding and showed that the governing failure mode for pipelines is inward local buckling when the pipes are not pressurised. In contrast, the governing mode of failure would be axial tensile straining for pressurised pipelines. Ha et al. (2008) used centrifuge modelling to study the effect that normal and strike-slip fault ruptures have on the mechanical performance of High-Density Polyethylene (HDPE) pipeline for water services and found that the peak axial strain along the HDPE buried pipeline varied linearly with the fault offset; they also found that the axial and bending strains are not symmetric for normal fault rupture, whereas the corresponding values for strike-slip fault rupture were symmetric. Ni et al. (2018a) used full-scale experimental modelling to study the mechanical behaviour of PVC pipes under normal fault rupture. Hojat Jalali et al. (2018) used full-scale laboratory testing of buried pipes to show that the deformation and failure mode of pipes will vary with the burial depth under reverse fault rupture. Moreover, when the D/t ratio increased (D and t being the diameter and wall thickness of the pipe, respectively), the distance between two buckled regions (known as buckling spacing) in hanging and foot blocks decreased. In addition, the results revealed that by reducing the burial depth and the soil friction angle, the buckling spacing and the degree of damage decreased, while increasing the D/t ratio led to an increase in the cross-sectional distortion. Moreover, there was more cross-sectional distortion in the pipeline in the section buried in the hanging wall. Vazouras and Karamanos (2017) used finite element simulation to show that placing elbows in regions prone to strike-slip fault rupture will reduce the detrimental effects of fault rupture on pipelines buried in cohesive soils. Smith et al. (2019) using full-scale normal fault rupture test showed the capabilities of acoustic emission technique on the early detection of pipe deformation under permanent ground deformation. Argyrou et al. (2019) assessed the mechanical performance of pipelines reinforced with cured-in-place linings under strike-slip fault rupture using numerical and experimental approaches. Zhou et al. (2019) using fullscale tests investigated the behaviour of buried lined-corrugated highdensity polyethylene pipes under normal fault rupture and compared the experimental results with three-beam and the Kappa methods. They showed that both the three-beam and Kappa approaches overestimated the bending strains in comparison to the experimental measurements. Compared to the large number of existing research studies investigating the mechanical behaviour of buried pipelines in soil deposits, and techniques to protect pipelines against accidental damage 2

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Fig. 1. Schematic representation of a pipeline interaction with strike-slip fault rupture; (a) axial section, (b) failed area, (c) ovalisation parameter definition.

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pipeline is considerably reduced (Chian and Madabhushi, 2013; Palmeira and Bernal, 2015). For example, several buried pipelines in loose backfilled soils were uplifted due to soil liquefaction during the 1993 Kushiro-Oki, Japan earthquake. In Fig. 3a, a conventional buried pipeline is forced to deform over a relatively short length, and therefore the localised stress and deformation causes the pipeline to fail. In stark contrast, as the EPS blocks on each side of the pipeline compress, the localised stresses and deformations are distributed over a longer length, as shown schematically in Fig. 3b, and therefore prevents pipeline failure as a result strike-slip fault rupture.

investigation into using geofoam blocks to improve the performance of buried pipelines subjected to strike-slip fault rupture in terms of designing criteria such as axial tensile and compressive strains, and crosssectional distortion; which is the subject of this research study. The efficiency of the adopting geofoam surrounding pipelines to reduce the tensile and compressive strains due to fault rupture, and prevent local bulking in the pipeline, is studied through a series of three-dimensional finite element simulations. The performance of EPS blocks on a nonpressurised pipeline is evaluated through three cases by considering the crossing angle between the pipeline and the trace of a strike-slip fault. This is followed by a parametric study to assess the effect of varying the crossing angle from 65° to 135° incrementally and the various operating internal pressures as well as conducting a sensitivity analysis to assess the impacts of the thickness of EPS blocks on the response of the pipeline.

3. Failure criteria for buried pipelines subjected to fault rupture The failure mechanism of pipelines must be identified before their performance under permanent ground deformation can be evaluated. Previous studies attempted to identify the most frequent failure modes of pipelines under seismic and permanent ground deformations through numerical and experimental investigations, and field observations following major earthquake events. According to existing design codes and literature, the design of buried pipelines subjected to large ground deformation should satisfy the following three criteria which cover different modes of deformation:

2. Proposed EPS geofoam blocks configuration Fig. 1 is a schematic diagram of the mechanical response of a conventional pipeline buried in soil that has been subjected to a strike-slip fault rupture. Fig. 1 shows how conventional buried pipeline suffers from local bulking, as well as tensile and compressive strains and crosssectional distortion when subjected to strike-slip fault rupture. To mitigate the detrimental effects of fault rupture on pipelines, the authors propose protecting pipelines with Expanded Polystyrene (EPS) geofoam blocks in configurations that could inhibit the pipe overstressing from permanent ground deformation due to strike-slip fault ruptures. The EPS geofoam blocks used in this study have a unit weight of 0.147 kN/m3 and Young's modulus of 4.2 MPa; these are 110 times and 9.5 times less than the values corresponding to the surrounding soil deposit, respectively. Fig. 2 shows the cross-sectional configuration of the proposed EPS blocks to protect pipelines under permanent ground deformations induced by strike-slip fault rupture. In Fig. 2, the proposed method for the adopted pipeline configuration consists of 1 m thick EPS blocks on the sides and another block above the pipeline. Fig. 3 shows a plan view of the interaction mechanism of a pipeline protected with EPS blocks compared to a conventional pipeline buried in native soil. The conventional buried pipelines usually are installed in trenches and backfilled with loose sand. Besides to minimise the impact of much stiffer native soil, it is recommended that the trench size would be adequately large to reduce the effect of much stiffer native soil (ALA, 2015) which may significantly increase the cost of construction. However, burring the pipeline in loose sand is not favourable, especially in the active seismic areas (O’Rourke and Liu, 1999). The earthquake-induced settlement could cause significant tensile and bending strains along the pipeline due to soil densification of dry sand or liquefaction induced settlement if saturated. In addition, due to potential soil liquefaction of loose sand in seismic areas, the uplift resistance of the

i. Limiting axial tensile strains in the pipeline to avoid tensile yielding: As shown in Fig. 1b, Eurocode 8 (1998) states that for designing buried steel gas pipelines the maximum axial tensile strain in a pipeline under large soil deformation should be limited to 3%. ii. Limiting axial compressive strains to avoid local buckling: As a result of bending moments developed in a pipe, compressive strains may also develop, as shown in Fig. 1b, and due to the considerable compressive strains, local buckling may occur. A buckled pipeline could be torn and the contents leak due to fatigue cracks that develop under loading during the serviceability by internal pressure variations and changes in temperature; therefore local buckling in pipelines should be avoided by limiting the compressive strain to a minimum of [1% and 20 (t/r), where t and r are the wall thickness and radius of the pipe, respectively], as recommended by Eurocode 8 (1998). In this study, the local buckling of a pipeline was considered to begin when the axial compressive strain of the pipeline dramatically increased. iii. Limiting the cross-sectional distortion: The third failure mode is due to a large bending moment on the pipeline which tends to flatten the cross section, as shown in Fig. 1c. Referring to Gresnigt (1986), to avoid pipeline failure due to flattening, the maximum changes in pipe diameter should be kept below (d − d′)/ d = 0.15, where d and d’ are the diameters of the pipe before and after fault rupture, respectively. It should be noted that the submarine pipeline standard (DNV, 2017) limited the ovalisation parameter of the submarine pipeline to 3%. The ovalisation parameter of submarine pipe should be strictly limited since the local oval pipe may collapse due to the high level of external pressure (Alrsai et al., 2018). Indeed, DNV (2017) defined the ovalisation parameter as the ratio of the difference between the maximum and minimum pipe diameter after being deformed to its initial diameter which is applicable to submarine pipelines. 4. Overview of adopted soil-pile–structure system In this study, an X65 steel pipe with an outside diameter of 0.914 m (36 inches) and a thickness of 0.0127 m (0.5 inches) is considered. According to current practice in the pipeline industry (Mohitpour et al., 2007), the pipeline material is X65 steel with tensile yield stress and ultimate strength of 450 MPa and 560 MPa, respectively. In Fig. 2 the pipeline is buried 3 m deep into an 8 m thick deposit of sandy soil with mechanical properties from a real project based on site investigations

Fig. 2. Schematic representation of a pipeline protected with EPS blocks. 4

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Fig. 3. Schematic representation of the interaction of (a) a conventional pipeline buried in soil and (b) pipeline protected with EPS.

strike-slip fault rupture are examined with a series of three dimensional numerical simulation using software package ABAQUS (version - 2018). This study assesses the effects of pipeline - fault crossing angles varying from 65° to 135°, as shown in Fig. 4, which cover a wide range of pipeline deformation patterns and failure modes that include tensile and compressive straining, and local bulking. These numerical simulations took place after installing the pipeline and EPS blocks, in the following three steps: Step 1: define the initial stresses in the soil by imposing a gravity load and the coefficient of lateral earth pressure at rest using Jaky's formula (Jaky, 1948) (i.e. K 0 = 1 − sinϕ ); Step 2: establish the internal pressure of the pipeline in the relevant cases; and Step 3: apply displacements with a fault slip rate of 10 mm/s to the base and side boundaries of the moving block and consequently the fault rupture found its way and propagated through the body of soil and interact with pipe structure. This slow rupture rate grantees the fault slip was applied quasi-statically throughout the numerical analysis (Banushi et al., 2018). In addition, the pipeline - fault crossing angles varied from 65° to 135° with 5° increments, as shown in Fig. 4.

Table 1 Soil properties adopted in the present study. Soil Property

Value

Reference

Young's modulus (MPa) Poisson's ratio (μ) Unit weight (kN/m3) Friction angle (φ ) (degree) Cohesion (kPa)

40 0.3 16.3 30 10

JACE (2015)

and laboratory tests as shown in Table 1 (JACE, 2015). The mechanical properties and axial stress versus strain of the EPS geofoam used in this study came from an experimental study by Lingwall (2011), as shown in Fig. 5. A schematic view of this buried pipeline is also shown in Fig. 4.

4.1. Details of the numerical simulation In the current study, the mechanical response of conventional steel pipelines buried in soil and a pipeline protected with EPS blocks under 5

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Fig. 4. Schematic representation of the adopted buried pipeline buried in soil with a strike-slip fault rupture trace.

(Tsatsis et al., 2017). Moreover, an increasing internal pressure decreases the ovalisation of the buried pipeline under permanent ground deformation (Vazouras et al., 2012; Ozcebe et al., 2017; Tsatsis et al., 2017). This study considers the effect of internal pressure by incrementing the internal pressure while still capped with the maximum permissible internal pressure obtained from ASME B31.8 code (ASME, 2019), as presented below:

t pmax = 0.72 × ⎛2σy ⎞ D⎠ ⎝

(1)

where pmax is the maximum permissible internal pressure in the pipe, and σy , t, and D are the yield stress, thickness, and diameter of steel pipe, respectively. 4.2. Characteristics of the numerical model

Fig. 5. Axial compression test data for EPS 15 geofoam.

The pipeline was modelled using four-node reduced-integration shell elements (S4R), and like existing studies (Banushi et al., 2018; Xu et al., 2018), the mechanical behaviour of a buried steel pipeline was modelled using a large-strain von Mises plasticity model that accounts for isotropic hardening in order to capture its inelastic behaviour under large deformations imposed by strike-slip fault rupture. Young's

One of the key features to consider when designing natural gas (NG) pipelines is the level of internal pressure during operation because it affects the performance of the buried pipeline under permanent ground deformation. The shape of local buckling changes from local inward buckling for a non-pressurised pipeline to local outward buckling

Fig. 6. (a) Representation of adopted penalty method for stiff approximation of hard contact model and (b) adopted Coulomb friction model. 6

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Fig. 7. Finite element model and meshing (a) soil model, EPS geofoam and pipe, (b) the model of pipe.

The soil-pipeline interaction with a fault rupture incident phenomena consists of very complex inertial and kinematic interactions between the pipe content, pipe structure and the surrounding soil. The effect of inertial interaction for buried pipeline usually could be considered negligible since the total weight of piping and its content are very close to the total weight of the replaced soil (O'Rourke and Palmer, 1996; De Normalisation, 1998; Manolis et al., 2020) while the kinematic interaction plays a significant role in the dynamic response of buried pipelines. However, in the space of studying the pipeline response under large permanent ground deformations due to faulting, landslide or liquefaction induced ground deformation, the rupture propagation through the soil layers is generally considered at a very slow rate (i.e. quasi-static fault rupture process). The external surface of a buried pipeline may be detached from or slide against the surrounding soil during a fault rupture, therefore, having an appropriate soil - pipe interface is an integral part of a numerical simulation of soil – structure interaction (Tognon et al., 1999; Brachman et al., 2000; Nguyen et al., 2017). ABAQUS uses general contact, contact pairs, and contact element algorithms to define the interaction between contacting surfaces.

modulus of a steel pipeline was considered to be equal to Es = 210 GPa, with a tensile yield stress of σy = 448.5 MPa, followed by a plastic plateau up to a strain level of 1.48%; this is followed by a strain hardening regime with a reduced stiffness of Es /300 , where Es is Young's modulus of the pipeline (Vazouras et al., 2012). The soil and EPS blocks are modelled using eight-node reduced-integration brick elements (C3D8R), and the mechanical behaviour of EPS was modelled using Mises yield criterion with isotropic hardening and associated flow rule. Meguid and Hussein (2016) and Meguid et al. (2017) by comparing experimental results with numerical simulation showed that this model can capture the behaviour of EPS geofoam subjected to large strains. The mechanical behaviour of soil was modelled using an elastic-perfectly plastic Mohr-Coloumb constitutive model. The ability of the Mohr-Coulomb model for soil surrounding the pipeline to predict the mechanical behaviour of buried pipelines under large ground deformation has been used and validated by many researchers over recent years (Anastasopoulos et al., 2008, 2013; Loukidis et al., 2009; Baziar et al., 2015; Loli et al., 2015; Ni et al., 2018b; Rasouli and Fatahi, 2019).

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Fig. 8. (a) Finite element model of the full-scale experiment of the buried pipeline under strike-slip fault rupture, (b) pipe axial strain response; experimental versus calculated result with FE numerical analysis.

relationships. The hard contact algorithm does not allow any tensile stresses to be transferred between contact pairs while minimising the penetration of the slave surface into the master surface at the constraint locations. As Fig. 6a shows, no contact pressure is transferred between interacting surfaces until the gap is closed and they make contact. The tangential behaviour of the contacting surfaces between the pipe and surrounding soils, the EPS and soil, and EPS and pipe were simulated using the linear elastic-perfectly plastic Mohr-Coulomb model which correlates the critical shear stress (τcr ) (the shear stress at which the interacting surfaces starts sliding relative to each other) and contact pressure (p) by the coefficient of friction (μ), as shown below:

This study used contact pairs to define the corresponding interfaces between various sections, including the outer surface of the pipeline, the EPS, and the soil and also utilises a contact algorithm that allows finite-sliding and adopts surface-to-surface contact formulation. The contact pairs will provide contact between two deformable bodies with a finite-sliding formulation. Defining the contact interaction requires defining the master and slave surfaces between the contacting regions, and like previous studies (Merifield et al., 2008; Chatterjee et al., 2012; Fatahi et al., 2018), the master surfaces were applied onto stiffer material and the slave surfaces were assigned to softer materials; for example, the master and slave surfaces of contact pairs of pipe – soil interfaces were assigned to the outer surface of the pipeline and the contacting surface of soil, respectively. To define the stress transfers between interacting surfaces in a normal direction, a hard contact algorithm was used to define the contact pressure-overclosure

τcr = μp

(2)

In the adopted three-dimensional simulation of interaction in this study, two orthogonal components of shear stress (τ1 and τ1) between the interacting surfaces were combined into an equivalent shear stress as 8

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Fig. 9. Axial strain of the non-pressurised pipeline (a) conventional buried in soil; and (b) protected with EPS blocks under a fault slip of 1.0 m at crossing angle β = 65°.

the contact pairs (τeq) is less than the critical shear stress (τcr ) no slip occurs; however once the equivalent shear stress reaches the critical shear stress (i. e . τeq = τcr ) , the interacting surfaces (i.e. slave and master surfaces) begin to slide relative to each other and dissipate energy plastically through friction. The coefficients of friction (μ) for different interacting surfaces, including steel pipe - soil, steel pipe - EPS geofoam, and soil - EPS geofoam were 0.4, 0.2 and 0.6 respectively (Meguid et al., 2017; Ni et al., 2018b; Baziar et al., 2019a).

4.3. Boundary conditions and fault rupture simulation Since the primary goal is to evaluate the mechanical behaviour of a buried pipeline under strike-slip fault rupture, the bedrock was simulated as a rigid boundary condition. To model a strike-slip fault rupture, the bottom and sides boundaries were divided into two parts; in Fig. 4 the right part represents the fixed block (footwall), and during a fault rupture the left block (hanging wall) moves horizontally along the strike at angles that vary from 65° to 135°. The length of the model (i.e. parallel to the pipeline alignment) was considered to be 65 times greater than the pipe diameter (i.e. 60 m) to minimise the boundary effect on the numerical predictions, as recommended by the existing literature (Vazouras et al., 2012, 2015; Tsatsis et al., 2017; Vazouras and Karamanos, 2017). To capture the soil - pipe interaction accurately

Fig. 10. Evolution of the maximum compressive and tensile strains in the nonpressurised pipeline conventional buried in soil and protected with EPS blocks under different fault slip at the crossing angle β = 65°.

follows:

τeq =

τ12 + τ12

(3)

As shown in Fig. 6b, as long as the equivalent shear stress between 9

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Fig. 7 also shows the typical discretised model of a pipeline protected with EPS geofoam blocks. The model includes the soil deposit, the pipeline, the nonlinear springs to simulate the infinite length of the model, and the EPS blocks; there were 97,186 elements and 105,725 nodes in the entire model. The fast parallel computation facility at the University of Technology Sydney with 2710 cores and 16.3 TB of memory was used to carry out these finite element simulations. 4.4. Validation of the numerical model To validate the developed finite element model in this study, a fullscale experimental result reported by Sarvanis et al. (2018) for a buried steel pipeline under a horizontal ground movement that could simulate a strike-slip fault rupture was chosen. The experimental setup consisted of an X65 steel pipeline with a diameter of 219.6 mm and thickness of 5.56 mm. The pipeline was buried within clean sand in three adjacent boxes with total backfill length of 24.7 m (two fixed blocks at sides with the length of 8.35 m and one moving box at the middle which was 8 m long). The pipeline was buried at a depth corresponding to the depth to pipe diameter ratio (i.e. H/D) of 3.75. The unit weight and friction angle of the soil were 1600 kg/m3 and 45̊, respectively. Fig. 8a shows the finite element model developed in this study to validate the accuracy of the model to predict the response of the pipeline under strike slip fault rupture. Fig. 8b compares the measured pipe axial strain response at two different fault slips of 0.2 m and 0.6 m with the FE numerical predictions conducted in this study. As evident, the obtained results from the numerical model were in good agreement with the experimental measurements capturing the response of the pipeline as reported by Sarvanis et al. (2018). 5. Results and discussion The mechanical performance of conventional pipelines buried in soil and the case protected with EPS geofoam blocks are evaluated under different internal pipe pressures (Pin ), different crossing angles between the pipeline and the strike-slip fault rupture (i.e. β as shown in Fig. 4), and fault slip intensities from 0.2 m to 1 m with a fault slip rate of 10 mm/s. The maximum fault slip depends on many fault features including the type of fault, fault width, fault surface area, fault gouge thickness, the magnitude of stress on the fault plane and the nature of wear process (Scholz, 1987). There are various empirical relations for determining the magnitude of fault slip. However, in this study, the method proposed by Wells and Coppersmith (1994) was used to determine the magnitude of fault slip. They used 29 worldwide earthquakes with moment magnitude ranging from 5.6 to 8.1 to develop an empirical relationship between the average strike-slip fault displacement and moment magnitude as follows:

Fig. 11. Ovalisation parameter along the non-pressurised pipeline; (a) conventional buried in soil and (b) protected with EPS blocks under fault slips of 0.2, 0.4, 0.6, 0.8, 1.0 m at the crossing angle β = 65°.

while optimising the computational time, the transverse dimensions of the soil model was considered to be eight times greater than the pipe diameters, which complies with the recommendations made by Tsatsis et al. (2017), as shown in Fig. 7a. In the vicinity of the fault rupture plane, the mesh size of soil was refined to 0.5 m, while a coarser mesh was used in other regions further away from the fault trace. According to Tsatsis et al. (2017) recommendations, the circumference of the pipe was divided into 48 elements, and the elements in an axial direction of the pipeline was 0.025 m, as shown in Fig. 7b. The large deformation of the pipeline under large ground deformation incidents such as fault rupture usually takes place in a relatively short length (Vazouras et al., 2015; Banushi et al., 2018). In order to optimise the computational costs many researchers tried to simplify the infinite length of soil-pipe interaction beyond the large deformation zone with an equivalent spring element connected to the ends of pipeline (Shokouhi et al., 2013; Tsatsis et al., 2017; Vazouras and Karamanos, 2017; Banushi et al., 2018; Xu et al., 2018) or simulate the system as a beam on Winkler foundation (Liu et al., 2004; Karamitros et al., 2007). Vazouras et al. (2015) using extensive numerical and analytical simulations developed a method that considered the elastic deformation of soil and pipe as well as sliding of pipe within the surrounding soil using a nonlinear force-displacement spring that can successfully mimic the infinite length of the pipeline beyond the large deformation region. In this study, similar to Vazouras et al. (2015), two ends of the pipe were connected to an equivalent-boundary spring by an axial connector element CONN3D2 to simulate the infinite length of the pipeline, as shown in Fig. 7a.

log δf = −6.32 + 0.90M

(4)

where δf and M are the average fault displacement in meter and the moment magnitude of the corresponding earthquake event, respectively. The maximum fault slip of 1 m in this study was selected according to an earthquake with a moment magnitude of 7.0 referring to the relationship proposed by Wells and Coppersmith (1994). Initially, the mechanical performance of the pipeline is compared with three different pipeline - fault crossing angles, where β = 65° (this is associated with a pipeline under compression), β = 90°, and β = 135° which correspond to cases where the pipeline experiences extension due to the strike-slip fault rupture observed by Banushi et al. (2018). 5.1. Case I: Pipeline experiencing compression The first scenario was defined when the crossing angle between the pipeline and the strike-slip fault rupture trace was 65°; in this situation, the fault rupture caused compression in the longitudinal direction of the 10

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Fig. 12. Axial strain of the non-pressurised pipeline (a) conventional buried in soil; and (d) protected with EPS blocks under a fault slip of 1.0 m at the crossing angle β = 90°.

embedded into the moving block and the other into the fixed block. The conventional pipeline suffered from extreme axial tensile and compressive strains which clearly exceeded the allowable values (i.e. 3% for tensile strain and −0.55% (i.e. 20 × (r/t)) for compressive strain) set forth by Eurocode 8 (1998). Indeed, since the maximum tensile and compressive strains induced in the pipe were 14.7% and −25.8% respectively, they well exceeded the allowable strain limits of 3% for tensile and −0.55% for compressive strains. In stark contrast, Fig. 9b shows a buried pipeline protected with EPS blocks survived against local buckling. In addition, the maximum axial strains of this pipeline were 0.17% for tensile and −0.47% for compressive strains, both of which remained below the limits mentioned above and within the operational range required by Eurocode 8 (1998). Fig. 9a also shows that in the case of conventional pipeline buried in soil, the deformation was distributed over a rather short length of about 10.7 m (i.e. more significant stress concentration), while the proposed pipeline protected with EPS blocks has deformed in a longer length of almost 24.5 m (i.e. less pronounced stress concentration). Indeed, since the EPS blocks are very compressible, the stresses and subsequent deformation is distributed over a longer span; this significantly improves the mechanical performance of the pipeline and reduces the detrimental effects due to fault rupture. Fig. 10 shows the evolution of the peak axial tensile and compressive strains in the pipelines for both options, while the fault gradually slipped up to 1 m. The axial compressive strain of the

Fig. 13. Evolution of the maximum compressive and tensile strains in the nonpressurised pipeline conventional buried in soil and protected with EPS blocks under different fault slip at the crossing angle β = 90°.

pipeline. Fig. 9 shows the axial strains of a non-pressurised pipeline ( pin = 0 ) buried in soil and the proposed pipeline protected with EPS blocks under a strike-slip fault rupture with a fault slip of 1 m. In Fig. 9a, a conventional pipeline buried in soil was extensively deformed and buckled in two regions on two sides of the fault rupture line; one is 11

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5.2. Case II: Pipeline perpendicular to the fault trace The second scenario was defined when the strike-slip fault trace was perpendicular to the pipeline. Fig. 12 shows the axial tensile and compressive strains developed in the conventional pipeline and the pipeline protected with EPS blocks after being subjected to a 1 m strikeslip fault rupture. Fig. 12a shows that unlike the previous case (i.e. the pipeline-fault crossing angle of 65° shown in Fig. 9a), the maximum tensile strain generated in the conventional pipeline decreased to 2.4%, which was less than the tensile strain allowed by Eurocode 8 (1998). In Fig. 12a, although the conventional pipeline did not experience local buckling, the axial compressive strain of −1.8% was well above the limit specified in Eurocode 8 (1998). Referring to Fig. 13, the axial tensile strain of the conventional pipeline gradually increased from the onset of the fault slip, unlike in Case I where the axial strain remained almost zero until the onset of local buckling (see Fig. 10). Moreover, the axial compressive strain of the conventional pipeline exceeded the allowable limit when the fault slip reached 0.51 m which was higher than the corresponding value for Case I reported earlier (i.e. 0.38 m, as shown in Fig. 10). It should be noted that similar to Case I, the pipe deflection due to fault rupture in Case II was distributed over a rather short length of 13.6 m for conventional buried pipeline, as shown in Fig. 12a, but when the pipeline was protected with EPS blocks, the fault induced pipe deflection was distributed over a longer length of 33.3 m, as shown in Fig. 12b. Therefore, EPS blocks successfully reduced the localised impact of fault ruptures by distributing the deformation over a larger area in the pipeline. Fig. 12b also shows that the maximum axial tensile and compressive strains in the pipeline protected by EPS were 0.23% and −0.28% for Case II which were less than the corresponding values for Case I and did not exceed the tensile and compressive strains allowed in Eurocode 8 (1998). Furthermore, Fig. 13 shows that the maximum axial compressive and tensile strains of the pipeline protected with EPS gradually increased to −0.28% and 0.23%, while the fault slip reached 1 m. In comparison to Case I where the fault trace crossed the pipeline at an angle of 65°, the cross-sectional distortion of both conventional and EPS protected pipelines in Case II were decreased, as shown in Fig. 14; this Figure also shows that in Case II, the ovalisation was lower than the maximum allowable value (i.e. 0.15 according to Gresnigt (1986)) for both the conventional buried pipeline and EPS protected pipeline (0.122 and 0.039, consecutively); evidently introducing the EPS geofoam blocks significantly reduced the ovalisation by 68%, as shown in Fig. 14. Moreover, Fig. 14 shows that after introducing EPS blocks the cross-sectional distortion of the pipeline was distributed over a longer length.

Fig. 14. Ovalisation parameter along the non-pressurised pipeline; (a) embedded in soil and (b) protected with EPS box under fault slips of 0.2, 0.4, 0.6, 0.8, and 1.0 m at the crossing angle β = 90°.

conventional pipeline buried in soil exceeded the allowable limitation (i.e. −0.55%) when the fault slip exceeded 0.38 m as shown in Fig. 10. In addition, the axial tensile strain of the pipeline remained almost zero until the onset of local buckling which was defined when the axial compressive strain increased dramatically, as shown in Fig. 10. However, beyond the onset of local bucking at a fault slip of 0.62 m, the axial tensile and compressive strains increased quickly because the pipeline only experienced compressive strains when the crossing angle between the fault trace and the pipeline is 65° and the developed tensile strains were due to local buckling. In contrast, the peak compressive and tensile strains of the pipeline protected with EPS blocks gradually increased as the fault ruptured, while the peak tensile and compressive strains remained below the limits allowed by Eurocode 8 (1998) for 1 m fault slips. Fig. 11 shows the evolution of the cross-sectional distortion (represented by the ovalisation parameter) along a non-pressurised pipeline subjected to fault slips ranging from 0.2 m to 1.0 m at 0.2 m increments. Fig. 11a shows that the ovalisation of the conventional pipeline, where the inflection point was embedded into the moving block (i.e. 0.232), exceeded the allowable value of 0.15 reported by Gresnigt (1986). However, the ovalisation of the other local buckling point embedded into the fixed block (i.e. 0.136) was slightly lower than the allowable value. In Fig. 11b, however, the peak ovalisation of the pipeline protected with EPS geofoam blocks (0.062) was well below the allowable ovalisation; in fact, the maximum ovalisation at two points being 9.8 m apart in moving and fixed blocks, were 0.062 and 0.061, as shown in Fig. 11b.

5.3. Case III: Pipeline experiencing extension The third scenario was defined when the crossing angle between the pipeline and the trace of fault rupture was 135°. Fig. 15 shows that the mechanical behaviour of both conventional and EPS protected pipelines significantly differed with Cases I and II (i.e. the pipeline -fault trace crossing angles were 65° and 90°). In fact, the conventional and EPS protected pipelines in Case III only experienced axial tensile strains, as shown in Fig. 15. Fig. 15a indicates that the maximum tensile strain of the conventional buried pipeline was 4.16% which was more than the 3% allowed by Eurocode 8 (1998), while Fig. 16 shows that the axial tensile strain of the conventional buried pipeline exceeded the allowable limit when the fault slipped by 0.97 m. In contrast, the EPS blocks successfully reduced the axial tensile strain in the pipeline to 0.75%, which was much lower than the 3% limit allowed by Eurocode 8 (1998). Furthermore, the pipeline deflection induced by the strike-slip fault rupture was distributed over a longer length of 24.4 m when EPS blocks were introduced (see Fig. 15b), unlike the 13.6 m length of the conventional pipeline buried in soil deposit (see Fig. 15a). Referring to Fig. 17, for Case III, the maximum point of ovalisation 12

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Fig. 15. Axial strain of the non-pressurised pipeline (a) conventional buried in soil; and (d) protected with EPS blocks under a fault slip of 1.0 m at the crossing angle β = 135°.

and another in the stationary/fixed block (refer to Figs. 11 and 14). The conventional pipeline in Case III clearly exceeded the ovalisation limit of 0.15 when 1.0 m fault slip occurred, as shown in Fig. 17a, however as shown in Fig. 17b, the EPS blocks reduced the ovalisation to an acceptable value of 0.035 (i.e. a 77.7% reduction). In Case III, the conventional pipeline buried in soil generally exceeded the allowable ovalisation and axial tensile strain limits when subjected to a fault slip of 1.0 m, whereas the pipeline protected with EPS blocks kept the corresponding values below the allowable limits set out in existing design codes and guidelines. 5.4. Detailed assessment for the impact of the crossing angle This section presents the results of a comprehensive parametric study into non-pressurised pipelines where the axial strains and ovalisation parameter were inspected at crossing angles from 65° to 135° varied at 5° increments. Figs. 18 and 19 show the effect that the crossing angles had on the peak axial strains and ovalisation parameter for a given fault slip of 1.0 m. In Fig. 18, the conventional buried pipeline in soil shows three different failure modes for various crossing angles, as listed below:

Fig. 16. Evolution of the maximum axial tensile strain in the non-pressurised pipeline conventional buried in soil and protected with EPS blocks under different fault slip at crossing angle β = 135°.

for conventional and EPS protected pipelines was close to the point where the pipeline and fault trace intersect, whereas in Cases I and II, there were two maximum points of ovalisation, one in the moving block

a) Failure due to local buckling: Fig. 18a shows that the conventional 13

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Fig. 17. Ovalisation parameter along the non-pressurised pipeline; (a) conventional buried in soil and (b) protected with EPS blocks under fault slips of 0.2, 0.4, 0.6, 0.8, and 1.0 m at the crossing angle β = 135°.

buried pipeline experienced local buckling when the crossing angle between the pipeline and the fault trace was less than 90°; this means it experienced compressive stresses and strains along the axis of the pipe, and the excessive compressive stress caused local buckling at the pipe wall. Moreover, the axial compressive and tensile strains increased dramatically from 2.4% and −1.80% to –14.7% and −25.8% as the crossing angle decreased from 90° to 65°, respectively as shown in Fig. 18a. Moreover, referring to Fig. 19, the ovalisation parameter of the pipeline exceeded the 0.15 limit (set out by Gresnigt (1986)) in the same range of crossing angle (β ) mentioned above. b) Failure as a result of excessive axial compressive strains: According to Fig. 18a, for a given fault rupture of 1 m and when 90° < β < 100°, the failure mode of conventional pipeline buried in soil deposit was exceeding the allowable compressive strain defined in Eurocode 8 (1998), but the ovalisation still remained within the allowable limits defined by Gresnigt (1986) as depicted in Fig. 19. c) Failure due to excessive axial tensile strains: As Fig. 18a shows, by increasing the crossing angle (β ) from 100° to 115°, the axial compressive strain gradually decreased and reached zero at β = 115°, while the axial tensile strain remained unchanged. By increasing the crossing angles beyond 115°, the axial tensile strain increased and crossed the 3% tensile strain limit when β = 125°. The ovalisation had a similar trend, so beyond a crossing angle of 125°, it exceeded the allowable limit shown in Fig. 19.

Fig. 18. Effect of the crossing angle between the fault trace and the pipeline on the maximum compressive and tensile strains in the non-pressurised pipeline (a) conventional buried in soil and (b) protected with EPS under the fault slip of 1 m.

Fig. 19. Effect of the crossing angle between the fault trace and the pipeline on the maximum ovalisation parameter of the non-pressurised pipeline conventional buried in soil and protected with EPS blocks under the fault slip of 1 m.

performance of the pipeline in terms of local buckling, and axial compressive and tensile strains, as well as the ovalisation criteria. Indeed, the EPS blocks shifted the axial compressive and tensile strains within the allowable and operational limits of all the crossing angles from 65°

In contrast to the conventional pipeline cases, Figs. 18b and 19 show that introducing EPS geofoam blocks improved the mechanical 14

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5.5. Effect of internal pipeline pressure The effect of internal pressure on the mechanical behaviour of both pipeline options is investigated by considering the different levels of internal pressures including 0, 25%, 50%, 75%, and 100% of the maximum operating pressure defined by Eq. (1). The reference scenario used to study the effect of internal pressure was when the crossing angle between the pipelines and the trace of the fault rupture (β ) was 135°. Fig. 20 shows the effect of internal pressure on the maximum axial strain of conventional and EPS protected pipelines subjected to fault slips up to 1 m. Here, the effect of internal pressure on the maximum axial strain of conventional buried pipeline in soil was rather negligible for a fault slip up to 0.7 m, but when the fault slip exceeded 0.7 m, the axial tensile strains increased notably. In addition, as illustrated in Fig. 20, the internal pressure amplified the rate at which the axial tensile strain developed with the fault slip; for instance, the non-pressurised conventional buried pipeline exceeded the 3% axial tensile strain limit at a fault slip of 0.97 m, whereas the pressurised pipeline with an internal pressure pin = pmax reached the axial tensile strain limit at a fault slip of 0.86 m, as shown in Fig. 20. A similar trend was captured for the pipeline protected with EPS blocks where the effect of internal pressure on axial tensile strain was insignificant up to fault slip of 0.94 m, while beyond which a slight increase was observed. The increase of axial tensile strain with high levels of internal pressure could be due to additional axial stress imposed by the internal pressure. In addition, in the presence of internal pressure, the hoop stress on the pipe wall causes the pipeline to expand radially, and this leads to a more pronounced pipe - soil interaction (Banushi et al., 2018). However, as expected, the internal pressure helped to reduce the cross-sectional distortion for both conventional and EPS protected pipelines. Referring to Fig. 21a, the maximum ovalisation parameter of the conventional pipeline decreased from 0.157 (exceeding the limit) to 0.086 (satisfying the design criterion; i.e. 44.5% reduction), while the internal pressure increased from zero to maximum allowable internal pressure ( pmax = 9 MPa). Indeed, the impact of internal pressure on the ovalisation parameter was very evident for EPS protected pipeline since the maximum ovalisation parameter significantly decreased from 0.033 to 0.005 (i.e. 85% reduction) as the internal pressure increased from zero to pmax shown in Fig. 21b. Indeed, the initial tensile hoop stress imposed by the internal pressure stabilises the pipe wall and cancels out the external compressive hoop stress induced by soil earth pressure due to permanent ground deformation. Therefore, the ovalisation parameter significantly reduced as a result of internal pipe pressure.

Fig. 20. Effect of the internal pipeline pressure on the maximum axial strain for the conventional buried pipeline in soil and protected with EPS blocks.

5.6. Sensitivity analysis A sensitivity analysis was conducted to show the effect of EPS geofoam blocks configuration on the interaction mechanism of the protected pipeline with strike-slip fault rupture. The protected nonpressurised pipeline at the crossing angle of 90° with fault trace (i.e. β = 90°) was considered as reference scenario to assess the sensitivity of the maximum compressive and tensile strains as well as the ovalisation parameter of the pipeline to the geofoam blocks configuration subjected to the designed fault slip of 1 m. Three different thicknesses of geofoam blocks at the sides of the buried pipeline including 0.5 m, 1.0 m and 1.5 m were considered as shown in Fig. 22a. Referring to Fig. 22a, the maximum compressive strain of the protected pipe with 0.5 m thickness geofoam was −0.54% which is very close to the failure criteria for compressive strain, i.e. −0.55% (20t/r), while by increasing the geofoam thickness to the 1 m, the compressive strain decreased to −0.28% (well below the limit of −0.55%). However, the effect of increasing the geofoam thickness beyond 1 m was negligible as the compressive strain slightly decreased (i.e. compressive strain reduction from −0.28% to −0.24% by increasing geofoam thickness from 1 m to 1.5 m correspondingly) as shown in Fig. 22a. In addition, a similar trend was observed for ovalisation parameter

Fig. 21. Effect of the internal pipeline pressure on the maximum ovalisation parameter for (a) the pipeline embedded in soil and (b) protected with EPS.

to 135°. Fig. 18b shows that the EPS blocks were the most effective in protecting pipelines when the crossing angle between the pipeline and fault trace was higher than 90° (i.e. pipeline experiencing extension). For instance, in the case of EPS protected the pipeline, when β = 80°, the maximum axial compressive strain was −0.42 which was close to the allowable limit of −0.55%, while the maximum compressive strain of the pipeline was −0.19 when β = 100°. Therefore, for the most efficient use of geofoam blocks to protect pipelines, a pipeline should be positioned relative to the fault rupture trace to satisfy β > 90°.

15

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Fig. 22. Effect of geofoam blocks thickness on the (a) axial compressive and tensile strains and (b) ovalisation parameter of the non-pressurised buried pipeline at the crossing angle of 90̊ with fault the trace.

block thickness, and the internal pipe pressures. The adopted numerical model in this study considered the nonlinear behaviour of the steel pipeline and EPS geofoam, as well as the infinite length of the pipeline using an equivalent nonlinear spring. The proposal for EPS blocks to surround the steel pipeline is based on two 1 m thick EPS blocks at each side and one block on top. The results led to the following conclusions:

showing that by increasing the geofoam thickness from 0.5 m to 1.0 m, the ovalisation parameter experienced a considerable reduction from 0.056 to 0.039 (i.e. 30% reduction), while by increasing the geofoam thickness from 1 m to 1.5 m, ovalisation parameter only slightly decreased (i.e. from 0.039 to 0.034). 6. Conclusions

• The conventional pipeline embedded in soil could not escape from local buckling failure due to 1 m strike-slip fault rupture when the crossing angle between the pipeline and the fault trace (β ) was less than 90° (i.e. the pipeline experienced axial compression), while the predominant failure mode of the pipeline was exceeding the allowable axial compressive strain limit when the crossing angle was 90° < β < 100°. The governing mode of failure for the conventional pipeline embedded in the soil where β > 125°, was axial tensile strain failure; for example, the maximum axial tensile strain of 4.16% exceeded the allowable limit when the crossing angle was

This paper investigated the mechanical behaviour of an X65 steel pipeline conventionally buried in soil and proposed a protection technique using EPS geofoam blocks to protect it from strike-slip fault ruptures. Three-dimensional numerical modelling using ABAQUS finite element software was used to examine how effectively EPS blocks could enhance the response of the pipelines under 1 m strike-slip fault rupture; it was also used to assess the pipeline's response to local buckling, axial tensile and compressive strains, cross-sectional distortion for different crossing angles between the pipeline and the fault trace, EPS 16

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•

•

β = 135° . In addition, the cross sectional distortion exceeded the allowable limit when β < 90° or β > 125° . These results also showed that increasing the internal pipeline pressure increased the axial strains in the pipeline and reduced the cross-sectional distortion. EPS blocks surrounding the pipeline safeguarded it from local buckling, excessive axial tensile and compressive strains, and crosssectional distortion over a range of crossing angles from 65° to 135° and with internal pressure from zero (non-pressurised) to a maximum operating pressure pmax . In fact when β = 135° , the EPS blocks shifted the maximum axial tensile strain of the non-pressurised pipeline to a safe zone when subjected a fault slip of 1 m. The highly compressible EPS blocks allowed the pipeline to deform over a much longer span under a strike-slip fault rupture. In other words, the concentrated deformation and stresses due to fault rupture were distributed over a wider length when EPS geofoam blocks were introduced, thus preventing the pipeline from failing.

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