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The damage potential of spatially variable seismic ground motion on buried pipelines has long been confirmed by field evidence, but it is still debatable whether transient seismic loads can be truly detrimental to the pipeline integrity. In the absence of systematic scrutiny of the effects of local site conditions on the seismic behaviour of such structures, this study presents a staged approach to numerically investigate the elastic-plastic buckling response of buried steel natural gas pipelines subject to transient differential ground motions arising from strong lateral site inhomogeneities. The first stage involves the study of 2D linear viscoelastic and equivalent-linear site response for the case of two sites and the resulting seismic demand in terms of longitudinal strains for input motions of various intensities and frequency content. The influence of key problem parameters is examined, and the most unfavourable relative ground deformation cases are identified. In the second stage of analysis, the critical in-plane ground displacement field is imposed monotonically on a near-field trench-like 3D continuum soil model encasing a long cylindrical shell model of the pipeline. Next, the performance of the buried pipeline is assessed under axial compression. The impedance contrast between the laterally inhomogeneous soil profiles is shown to govern the amplitude of induced elastic strains, which are maximized for low-frequency excitations. It is also demonstrated that peak axial strains along the pipeline considering equivalent-linear soil behaviour under strong earthquake motion can be as much as two orders of magnitude larger than their linear counterparts, as a result of the severe, spatially variable moduli degradation. It is finally shown that the seismic vibrations of certain inhomogeneous sites can produce appreciable axial stress concentration in the critically affected pipeline segment near the material discontinuity, enough to trigger coupled buckling modes in the plastic range. This behaviour is found to be controlled by pronounced axial force-bending moment interaction and is not accounted for in code-prescribed limit states.

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... Underground pipelines are widely used nowadays as a mean of conveying natural gas, oil and oil products and other liquid and gas substances. Ensuring their reliability, especially during earthquakes, is an urgent problem [1][2][3][4][5][6][7][8][9][10][11]. According to [1][2][3][4][5][6][7][8][9][10][11], the main factors determining the reliability of underground pipelines during earthquakes are: • external influences and the changes in their parameters [1,2]; • strain characteristics of soil and its interaction with the pipeline [3][4][5]; ...

... Ensuring their reliability, especially during earthquakes, is an urgent problem [1][2][3][4][5][6][7][8][9][10][11]. According to [1][2][3][4][5][6][7][8][9][10][11], the main factors determining the reliability of underground pipelines during earthquakes are: • external influences and the changes in their parameters [1,2]; • strain characteristics of soil and its interaction with the pipeline [3][4][5]; ...

... • design features of underground pipelines [6][7][8][9][10][11]. ...

A one-dimensional statement of unsteady wave problem of a longitudinal monochromatic wave propagation and reflection from a rigid stationary barrier to which an underground pipeline abuts is given. The linear viscoelastic Eyring model, which describes limited creep and limited relaxation, is taken as the pipeline strain law. Eyring model allows us to describe the behavior of underground steel and polymer pipelines under dynamic loading. The problem is solved numerically using the theory of characteristics, followed by the finite difference method in an implicit scheme. Numerical solutions obtained in the form of dependences of plane wave parameters: longitudinal stress, velocity and strain for fixed sections of the pipeline are analyzed in the paper. An analysis of changes in these wave parameters shows that at high frequencies of dynamic load generating the wave, the stress amplitude in the pipeline increases by two or more times compared to the load amplitude. This is due to the superposition of incident and reflected waves in the pipeline and to a high loading rate of the pipeline. At low frequencies of dynamic loading, such an increase is not observed due to the low loading rate. The obtained numerical solutions allow choosing the statement of problems on dynamic stress state of an underground pipeline depending on the frequency of incident wave. It is shown that the greatest longitudinal stress in an underground pipeline arises in points (sections) close to its connection with a rigid stationary solid body.

... ovaling) [5]. Additionally, recent studies have demonstrated that pipelines embedded in heterogeneous sites or subjected to asynchronous seismic motion are more likely to be affected by appreciable strains due to transient ground deformations, which in turn may lead to exceedance of predefined performance limits, reaching even excessive damage on the pipeline [24,25]. Based on the above considerations, the present study focuses on the transient ground deformation effects, as these have not yet been studied in adequate depth. ...

... The study focuses on NG pipelines crossing perpendicularly a vertical geotechnical discontinuity with an abrupt change on the soil properties. In such soil sites, the potential of high compression straining of the pipeline during ground shaking is expected to increase significantly, compared to the case where the pipeline is embedded in a homogeneous soil site [24,25]. A de-coupled numerical framework is developed to fulfil our objective, which includes 1D soil response analyses of selected soil sites and 3D quasi-static analyses of selected soil-pipe configurations. ...

... A 3D full dynamic analysis of the soil-pipe interaction (SPI) phenomena during ground shaking may be seen as computationally prohibitive, when considering the complications in simulating rigorously material or geometrical nonlinearities associated with the problem, as well as the uncertainties in the definition of the characteristics of heterogeneous soil sites and the inherently random varying ground seismic motion [25]. Hence, a simplified, yet efficient, numerical analysis framework should be developed and used, instead. ...

... Indeed, transient ground deformation may trigger diverse damage modes on continuous NG pipelines, including (i) shell-mode or local buckling, (ii) beam-mode buckling, (iii) pure tensile rupture, (iv) flexural bending failure and (v) excessive ovaling deformation of the section (O' Rourke and Liu 1999). Recent studies have demonstrated that pipelines embedded in heterogeneous sites and/or subjected to asynchronous ground seismic motions are likely to be further affected by appreciable deformations and strains due to transient ground deformations, which in turn may lead to buckling damages on the pipeline Psyrras et al. 2019). ...

... The use of the near field 3D continuum trench-pipe model allows for a rigorous simulation of localized buckling modes that might potentially be developed in the pipe under axial compression, as well as for the proper simulation of geometric imperfections of the pipeline walls, which are expected to affect significantly the axial compression response of the buried pipeline (Yun and Kyriakides 1990;Tsinidis et al. 2018;Psyrras et al. 2019). Additionally, it allows for a proper simulation of the operational pressure of the pipeline and contact nonlinear phenomena, i.e. sliding and/or potential detachment in the normal direction, between the pipeline wall and the surrounding ground. ...

... The shallow burial depth of the pipeline in addition to absence of significant inertial SSI effects and the assumption of in-plane ground deformation pattern, allow for the simulation of only the surficial soil-trench, which constitutes a surficial block from the semi-infinite 3D ground domain (Psyrras et al. 2019). Along these lines, the distance between the side boundaries of the trench model and the pipe edges is set equal to one pipe diameter, whereas the distance between the pipe invert and the bottom boundary of the trench model is set equal to 1.0 m. ...

This paper presents an extended set of numerical fragility functions for the structural
assessment of buried steel natural gas (NG) pipelines subjected to axial compression
caused by transient seismic ground deformations. The study focuses on NG pipelines
crossing sites with a vertical geotechnical discontinuity, where high compression straining of a buried pipeline is expected to occur under seismic transient ground deformations. A de-coupled numerical framework is developed for this purpose, which includes a 3D finite element model of the pipe–trench system employed to evaluate rigorously the soil–pipe interaction effects on the pipeline axial response in a quasi-static manner. One-dimensional soil response analyses are used to determine critical ground deformation patterns at the vicinity of the geotechnical discontinuity, caused by the ground shaking. A comprehensive parametric analysis is performed by implementing the proposed analytical framework for an ensemble of 40 recorded earthquake ground motions. Crucial parameters that affect the seismic response and therefore the seismic vulnerability of buried steel NG pipelines namely, the diameter, wall thickness, burial depth and internal pressure of the pipeline, the backfill compaction level, the pipe–soil interface friction characteristics, the soil deposits characteristics, as well as initial geometric imperfections of the walls of the pipeline, are systematically considered. The analytical fragility functions are developed in terms of peak ground velocity at the ground surface, for four performance limit states, considering all the associated uncertainties. The study contributes towards a reliable quantitative risk assessment of buried steel NG pipelines, crossing similar sites, subjected to seismically-induced transient ground deformations.

... The critical review of available 19 fragility relations for the assessment of buried pipelines under seismically-induced transient 20 ground deformations, presented in the first part of this paper, highlighted the need for further 21 investigation of the seismic vulnerability of NG pipeline networks, by employing analytical 22 methodologies, capable of simulating effectively distinct damage modes of this infrastructure. 23 In this part of the paper, alternative methods for the analytical evaluation of the seismic 24 vulnerability of buried steel NG pipelines are presented. The discussion focuses on methods 25 that may appropriately simulate buckling failures of buried steel NG pipelines since these 26 constitute critical damage modes for the structural integrity of this infrastructure, when 27 subjected to seismically-induced transient ground deformations. ...

... ground deformations, is presented in this part of the paper. The discussion focuses on the 23 buckling failures, which constitute critical damage modes for the structural integrity of steel 24 buried pipelines subjected to transient ground deformations. Salient parameters that control the 25 seismic response and vulnerability of buried steel NG pipelines and therefore should be 26 considered by the relevant analytical methods are thoroughly discussed. ...

... was based on relevant specifications from NG pipeline manufactures. ArcelorMittal for 23 example specifies a manufacturing tolerance for the walls of API-5L X65 pipelines in the range 24 of + 15% to -12.5% (ArcelorMittal 2018). As seen in Figure 2, the critical loadings of 25 imperfect segments, as well as the axial shortening levels, where these loadings are observed 26 (i.e. ...

The socio-economic and environmental impact, in case of severe damage on Natural Gas (NG) pipeline networks, highlights the importance of a rational assessment of the structural integrity of this infrastructure against seismic hazards. Up to date, this assessment is mainly performed by employing empirical fragility relations, while a limited number of analytical fragility curves have also been proposed recently. The critical review of available fragility relations for the assessment of buried pipelines under seismically-induced transient ground deformations, presented in the first part of this paper, highlighted the need for further investigation of the seismic vulnerability of NG pipeline networks, by employing analytical methodologies, capable of simulating effectively distinct damage modes of this infrastructure. In this part of the paper, alternative methods for the analytical evaluation of the seismic vulnerability of buried steel NG pipelines are presented. The discussion focuses on methods that may appropriately simulate buckling failures of buried steel NG pipelines since these constitute critical damage modes for the structural integrity of this infrastructure, when subjected to seismically-induced transient ground deformations. Salient parameters that control the seismic response and vulnerability of buried pressurized steel pipelines and therefore should be considered by the relevant analytical methods, such as the operational pressure of the pipeline, the geometric imperfections of the pipeline walls, the trench backfill properties, the site characteristics and the spatial variability of the seismic ground motion along the pipeline axis, are thoroughly discussed. Finally, a new approach for the assessment of buried steel NG pipelines against seismically-induced buckling failures is introduced. Through the discussion, recent advancements in the field are highlighted, whilst acknowledged gaps are identified, providing recommendations for future research.

... The pipeline is simulated by means of inelastic, reduced integration S4R shell elements, having both membrane and bending stiffness. The mesh density of the pipeline at the critical central section of the 3D numerical model, i.e. at the location of the geotechnical discontinuity where the axial strain of the pipeline is expected to maximize, is selected to be fine enough, i.e. around 1.0 -2.0 cm, so as to resolve the inelastic buckling modes of an equivalent axially compressed unconstrained cylindrical steel shell (Psyrras et al, 2019). The mesh density away from the critical central zone is gradually decreased, in an effort to reduce the computation cost of the 3D analyses. ...

... The shear behaviour of the interface model is controlled by the classical Coulomb friction model, through the introduction of a friction coefficient, μ. The plastic behaviour of the steel pipelines is modelled through a classical flow plasticity model combined with a von Mises yield criterion, following Psyrras et al (2019). In particular, Ramberg-Osgood curves, characterized by a yield offset equal to 0.5 %, are fitted to bilinear isotropic curves that describe the tensile uniaxial behaviour of the selected steel grade. ...

... For the latter cases, a stress-free, biased axisymmetric imperfection is considered at the middle of the examined pipe and for a distance equal to 2.0 m. The imperfection is defined as a sinusoid modulated by a second sinusoid, resulting in a peak amplitude at the middle section of the length, where it is applied (Psyrras et al, 2019). The peak amplitude of the imperfection is set equal to 10 % of the pipe lining thickness. ...

The paper presents a numerical methodology for the vulnerability assessment of buried steel natural gas (NG) pipelines, subjected to differential transient ground deformations, stemming from abrupt lateral site inhomogeneities. Idealized systems are considered, consisting of embedded steel NG pipelines crossing sites with vertical geotechnical discontinuity. The proposed analysis framework consists of two steps. A 3D trench-like continuum soil model, encasing a cylindrical shell model of the pipeline, is initially developed in ABAQUS, to compute the axial compressive response of the pipeline under an increasing level of axial relative ground deformation. The ground response under wave propagation is estimated by means of separate 1D nonlinear soil response analyses of the adjacent soil deposits, carried out in DEEPSOIL for an ensemble of selected ground seismic motions. The outcome of the soil response analyses, in terms of relative ground deformation patterns at pipeline's depth and peak ground velocity at the ground surface, is finally correlated with the predicted straining of the pipeline computed from the 3D analyses, in order to develop analytical fragility functions for predefined limit states, considering the associated uncertainties. The proposed approach, which is employed herein for an API-X65 buried gas pipeline with a diameter of 914.4 mm, offers high computational efficiency, whilst accounting for salient parameters that affect the axial response of steel NG pipelines.

... Psyrras et al. [19] numerically investigated the elasticplastic buckling response of buried steel pipelines subjected to transient differential ground motions arising from strong lateral site inhomogeneities and indicted axial stress concentration in the critically affected pipeline segment near the material discontinuity. ...

... No anchors were used at the ends of the pipe on the conservative side and left the pipeline ends free to move horizontally. is decision was driven by the belief that, away from any lateral ground heterogeneities, a pipeline was expected to move with the soil under vertically incident in-plane shear waves [12,19]. Considering the box length of 750 mm, a pipe length of 640 mm was chosen so that 55 mm spaces were left between the pipe ends and the side walls to minimize boundary effects. ...

The deformation and residual strength of the buried pipeline caused by the earthquake in nonuniform sites has an important influence on the safety of the pipeline. Most of the previous research focuses on the permanent ground deformation (PGD) caused by fault or transient ground deformation (TGD) due to seismic wave propagation independently. The mechanical character of buried pipelines crossing nonuniform sites during seismic sequence after ground settlement has not been studied. This article carried out a dynamic centrifuge experiment to simulate the seismic response of buried pipelines of polyvinyl chloride (PVC) and aluminum alloy (AL) horizontally crossing the loose and dense site and study the residual strength of pipelines after an earthquake. Two simulated seismic waves with 0.6 g and 0.3 g of input peak ground accelerations (PGAs) were inputted in sequence to simulate the strong and weak earthquakes. The deformations of ground and pipelines were obtained during and after seismic. The numerical model consistent with the experiment was established and compared with test, and it was found that the strain of pipeline caused by TGD was different between numerical and experimental results, especially in the loose site. The mechanical model of the pipeline by earthquake indicated that the total strain of the pipeline was composed of bending deformation by PGD and axial deformation by TGD. PGD caused by a strong earthquake had great effects on the deformation and residual strength of the pipeline. The strain of pipeline by TGD was compressive-extensional alternating mode between the loose and dense site and the strain amplitude reached peaks near the block interface in the loose site. The residual strain of pipeline in the dense site was a compressive strain, while in the loose site, it was compressive-extensional alternating mode and varied with the stiffness of the pipeline.

... In particular, the soil characteristics of long-distance buried pipelines need to cross significant discontinuities soil. Studies have confirmed that asynchronous ground seismic motion even leads to more serious ground deformation, causing buckling damage of the pipeline [10]. ...

... w nα = w n cos α − w p sin α (10) w pα = w p cos α + w n sin α (11) The selected segment AB is regarded as the beam bearing bending moment M(x) and axial load N(x). Based on the elastoplastic dynamic theory, the illustrated segment is given by ...

Local corrosion poses a big threat to the integrity and safety of steel pipelines. Investigation of the failure pressure of buried pipelines containing multiple corrosion defects subjected to earthquakes is vital for pipeline safety. In-line inspection (ILI) data is introduced to estimate and update the 3D random corrosion growth model, embedded in the development of a nonlinear finite element analysis (FEA) model of the X80 pressure pipeline. The novelty of this work lies in the development of a nonlinear FE dynamic model for the typical spatiotemporal evolution of corroded pipelines considering vertical heterogeneous soil structure, which further implements performance-based reliability assessment. The system reliability is estimated by combining the improved equivalent component approach (IECA) and extreme value theory (EVT). Numerical studies illustrate that the proposed model is feasible for corroded pipelines under an earthquake to execute a multi-failure mode reliability assessment to find the possible failure pressure.

... The problem of ensuring the safe and uninterrupted operation of such underground utilities in the form of underground pipelines in seismic areas is directly related to the reliability and strength of the pipelines [1,2]. The strength and reliability of underground pipelines under various external dynamics, including seismic, impacts depend on the behavior of surrounding soil, i.e. on the force of interaction of the underground pipeline with soil [1][2][3][4][5][6][7][8][9][10][11][12][13]. If we take into account that all external factors are transmitted to underground pipelines through the soil, then the study of the dynamic behavior of soil medium in the vicinity of the underground pipeline is one of the urgent problems of the underground pipeline -soil interaction [4][5][6][7][8][9][10][11]. ...

... The strength and reliability of underground pipelines under various external dynamics, including seismic, impacts depend on the behavior of surrounding soil, i.e. on the force of interaction of the underground pipeline with soil [1][2][3][4][5][6][7][8][9][10][11][12][13]. If we take into account that all external factors are transmitted to underground pipelines through the soil, then the study of the dynamic behavior of soil medium in the vicinity of the underground pipeline is one of the urgent problems of the underground pipeline -soil interaction [4][5][6][7][8][9][10][11]. When considering the problems of the underground pipelines interaction with external medium, usually the latter is replaced by various kinematic or dynamic relationships [4][5] or interaction conditions [14][15]. ...

The results of numerical solutions of an axisymmetric two-dimensional problem of a rigid underground pipeline interaction with elastic-viscous-plastic soil are presented. The pipe-soil interaction begins when the underground pipeline moves in an axial (longitudinal) direction. The changes in velocity, displacement, shear stress, shear strains in the direction of the pipeline axis for fixed points of soil along the radial axis are obtained at a linear change in the given longitudinal velocity of the pipeline from zero to a certain constant value. An analysis of numerical results showed that the changes in the interaction force on the contact soil layer occur according to a two-link law with the manifestation of the peak value of shear stresses. When the pipeline moves at a constant velocity, the values of displacement over time increase, and the shear stress values remain constant. Obviously, at this stage, the Coulomb law is fulfilled. This result agrees with the results of known experiments. The obtained theoretical dependences of shear stresses on soil displacement relative to the underground pipeline reveal the formation mechanisms of the conditions for the underground pipelines - soil interaction. This result could not be obtained within the framework of the one-dimensional problem of the pipe - soil interaction.

... Demirci et al. [23] carried out experimental and numerical study to investigate the response of buried pipelines crossing reverse faults. Psyrras et al. [24] investigated local buckling of a buried pipeline during earthquake ground shaking. However, to the knowledge of the authors, the seismic studies of high pressure/high temperature (HT/HP) pipelines so far has been limited to buried and trenched pipelines [24]. ...

... Psyrras et al. [24] investigated local buckling of a buried pipeline during earthquake ground shaking. However, to the knowledge of the authors, the seismic studies of high pressure/high temperature (HT/HP) pipelines so far has been limited to buried and trenched pipelines [24]. A subsea HT/HP pipeline can undergo large bending stresses and strains due to lateral/upheaval buckling or free-spanning [25][26][27][28]. ...

Vulnerability of subsea high pressure/high temperature (HP/HT) pipelines to seismic actions is studied numerically. Unlike most of the existing researches on buried or trenched pipelines, this study is focused on the response of an unburied pipeline with D/t = 20, laid on the seabed and resting on a sleeper. Two different scenarios: (1) earthquake imposed on a laterally buckled pipeline, and (2) earthquake imposed at temperatures lower than the lateral buckling temperature, are studied. The onset of yield and development of compressive local wrinkles in the wall thickness are calculated as the failure modes. Analytical fragility curves are developed based on probability of exceedance of the failure limits for each scenario. It is understood that the pipeline in scenario 1 is more vulnerable to bending-induced damages.

... The use of underground pipelines as a means of transporting various gas and fluid substances requires ensuring their reliable operation. The researchers pay a great attention to these issues [1][2][3][4][5][6][7][8][9][10]. Earthquake is essentially dangerous for the reliability of underground pipelines. ...

... The safety of underground steel pipelines conveying natural gas was addressed in [4]. The formation of local buckling in gas-conveying pipelines during earthquakes was studied in [5]. Experimental studies in a centrifuge of the effect of an earthquake on buried pipelines were conducted FORM-2020 IOP Conf. ...

The paper presents the results of numerical solution obtained by the modified finite difference method according to the Wilkins scheme, to a two-dimensional unsteady-state problem of the plane shock wave propagation in an underground elastic pipeline, interacting with surrounding soil. Soil is considered to be an undeformable body moving relative to the pipeline at a given velocity. The value of the friction force depends on radial stress in the pipeline, determined by numerical solution to the problem. Changes in longitudinal and radial stresses over time and pipeline length, of velocity and displacements for fixed sections of the pipeline are obtained. Two times increase in values of longitudinal and radial stresses was detected in the case of active Coulomb friction at the pipeline-soil contact. The increase in stress values occurs due to the friction force acting in the direction of wave propagation. At significant values of the friction force on the outer surface of the pipeline, the hypothesis of flat sections is fulfilled for all its sections. This result justifies the consideration of similar problems of underground pipelines earthquake resistance in a one-dimensional statement. The results also make it possible to identify the mechanisms of the stress state formation in an underground pipeline interacting with soil, which can be used in seismic resistance calculation of underground trunk pipelines.

... For example, there is an angle between the loading direction of the seismic wave and the axis of the pipeline. Especially the pipeline crosses the soft soil site and firm soil site [8]. The latter is the unrecoverable ground effect such as fault movements, landslides, soil liquefaction and settlement [8]. ...

... Especially the pipeline crosses the soft soil site and firm soil site [8]. The latter is the unrecoverable ground effect such as fault movements, landslides, soil liquefaction and settlement [8]. Moreover, field pipeline evidence indicates that most of the seismic damage of pipeline is due to PGD. ...

Considering the transient ground deformation(TGD) and permanent ground deformation(PGD), uncertain modeling is proposed by multiple limit states with time-dependent corrosion growth and seismic damage, as well as the rehabilitation. In this work, the developed corrosion growth model implemented the correlated 3D stochastic growth for one-defect. It then embedded in the combination model involved in corroded defect and seismic loading. Further, the Bayesian method and Markov Chain Monte Carlo(MCMC) simulation were used to obtain the updating of failure probability by introducing rehabilitation and in-line inspection (ILI) data. Failure probability was performed to study this difference using Monte Carlo simulation(MCS) to compare with the effect of the different parameters. A numerical example was investigated proposed models, and the influence of assessment rehabilitation was also discussed. The results indicate the potential impact of seismic damage for the corroded pipeline is significant, which can optimize the frame reliability-based anti-seismic for pipe infrastructure.

... However, it is more likely for a pipeline to be subjected to transient ground deformations rather than seismically induced permanent ground deformations. Additionally, studies have demonstrated that pipelines embedded in heterogeneous sites and/or subjected to asynchronous ground seismic motions are likely to be af- fected by appreciable deformations and strains due to transient ground deformations, which in turn may lead to damageon the pipeline ( Psyrras and Sextos, 2018;Psyrras et al., 2019). Along these lines, this study focuses on the transient ground deformation effects. ...

... Local buckling of buried pipelines has been a subject of early and recent stu- dies (e.g. Chen et al., 1980;Lee et al., 1984;Yun and Kyriakides, 1990;Psyrras et al., 2019) and is further examined in the second part of this paper. ...

... Earthquake damage to buried pipelines can be attributed to transient ground deformation (TGD) or to permanent ground deformation (PGD), or both (Psyrras et al., 2019;Toprak et al., 2015). TGD occurs as a result of seismic waves and is often stated as wave propagation or ground shaking effect. ...

The multi-directional, spatially variable earthquake motion is a primary cause of pipeline damage during earthquakes. A comprehensive finite element model considering soil nonlinearity and pipeline-soil interaction nonlinearity was established and validated based on shaking table tests and then employed to investigate the difference in response of buried pipelines subjected to longitudinal unidirectional (UD) and bidirectional (BD) horizontal non-uniform excitations. The responses were evaluated in terms of the acceleration and axial strain time histories along with the peak axial strain, hoop strain, and radial strain in the pipeline cross-section. The results demonstrate that the strain response and axial force of the pipeline under BD excitation are 50%-70% larger than under UD excitation. The large difference is attributed to the increase in maximum frictional force and the delay of the strain growth inflection point under the BD excitation. It was also observed that the pipeline cross-section experienced only lateral ovalization under the UD excitation. For the BD excitation, the cross-section experienced both lateral ovalization and vertical ovalization. Finally, the existence of the Y-direction seismic component in the BD excitation did not significantly change the X-direction acceleration response of the pipeline but increased the peak values.

... The results indicated that the seismic vulnerability curve considering soil uncertainty had a higher failure probability. Psyrras et al. (2019) conducted a study of the seismic response of pipelines passing through two different media and subjected to spatially variable ground motions. The results revealed that pipelines in soft soil may experience higher axial stress under strong seismic excitation. ...

The present study investigates the mechanical behavior of high-pressure pipelines installed through horizontal directional drilling (HDD), a crucial trenchless installation method, under seismic loads. Utilizing the finite element method and artificial viscoelastic boundary conditions, this paper analyzes the stress response of pipelines subjected to seismic loads in two directions. The seismic loads are applied using the response spectrum method, and the pipeline stress is analyzed in time history. A comparison of the stress in pipelines installed through the HDD method and the traditional open-cut method is conducted, and the impact of earthquake magnitude on pipeline stress is evaluated. The results indicate that the pipeline stress is greater when the seismic acceleration acts transversely, with bending deformation being the dominant mode of response. A 9.29% increase in maximum stress is observed for each increment in earthquake magnitude. Furthermore, the stress in pipelines installed through the HDD method is 48% lower than that of pipelines installed using the open-cut method when subjected to transverse seismic loads.

... The present work draws on experimental pipe-soil interface shear strength data and uses Abaqus, a general-purpose finite element software, to study the possibility of improving pipeline design using engineered surface roughness. Abaqus is ideally suited to the problem as it allows for large sized models, contains dedicated pipe elements with appropriate mechanics, can accommodate large displacements and nonlinear behaviour, and has considerable precedent in the literature in this application, e.g., Jukes et al. (2009);Cumming and Rathbone (2010), Liu et al. (2014), Chee et al. (2018), andPsyrras et al. (2018). ...

High-Pressure High-Temperature offshore pipelines laid on the seafloor are subject to large temperature and pressure variations which manifest as axial pipeline loading. Pipes become unstable in this condition and buckles form to relieve the axial stress. Considerable theoretical and experimental energy has been directed at establishing controlling mechanisms and parameters to predict buckling and design pipeline systems to be resilient and serviceable. The pipe-soil interface friction plays a pivotal role in the rate of build-up of axial loads and in controlling the critical buckling threshold. Pipes adopting smooth polymer coatings have very low friction coefficients but experimental work has shown that simple roughening techniques make greater friction coefficients available to a designer. Presented are a series of numerical analyses carried out using Abaqus to model a pipeline resting on the seabed subject to typical HPHT pipeline conditions. Global stability response is assessed with pipe-soil friction coefficients varying from 0.25 to 0.75 and differential friction regimes are adopted. It is shown that targeted application of pipe sections with greater interface friction may be a useful design tool for manipulating global buckling phenomena and could be a useful additional tool for influencing the spacing in Virtual Anchor Spacing analysis.

... Based on the geographic information system (GIS) software platform, by referring to the function and module design of the developed intelligent supervision platform for the safe operation of pipeline networks, combined with the requirements of the operation safety supervision of municipal pipeline network in the park, this study adopts a unified database format and considers the node reliability to carry out the design of GIS background calculation plug-in for pipeline network connectivity. At the same time, for the safety requirements, the water supply pipeline network focuses on the safety risk assessment of the pipeline network operation, the intelligent analysis of the leakage of the pipeline network, the simulation model of the pipeline network operation, and sensing system of pipeline safety monitoring [36][37][38]. ...

Currently, the connectivity calculation of complex pipeline networks is mostly simplified or ignores the influence of nodes such as elbows and tees on the connectivity reliability of the entire network. Historical earthquake damage shows that the seismic performance of municipal buried pipelines depends on the ability of nodes and interfaces to resist deformation. The influence of node reliability on network connectivity under reciprocal loading is a key issue to be addressed. Therefore, based on the general connectivity probabilistic analysis algorithm, this paper embeds the reliability of nodes into the reliability of edges, and derives a more detailed and comprehensive on-intersecting minimum path recursive decomposition algorithm considering elbows, tees, and other nodes; then, based on the reliability calculation theory of various pipeline components, the reliability of various nodes in different soil is calculated using finite element numerical simulation; finally, the reliability of a small simple pipeline network and a large complex pipeline network are used as examples to reveal the importance of considering nodes in the connectivity calculation of pipeline network. The reliability of the network system decreases significantly after considering the nodes such as elbows and tees. The damage of one node usually causes the failure of the whole pipes of the path. The damage probability is greater in the area with dense elbow and tee nodes. In this study, all types of nodes that are more prone to damage are considered in detail in the calculation. As a result, the proposed algorithm has been improved in computational accuracy, which lays the foundation for further accurate calculation of pipeline network connectivity.

... The damage of bending vibration may be more significant than the axial response at the arbitrary propagation direction. Typically, environmental discontinuities can trigger coupled buckling modes of the plastic range, which are failure modes governed by axial force-bending moment interactions in existing codes (Psyrras et al., 2019). An elastic-dynamic waveguide model was used to simulate a finite-length pipeline subjected to spatiotemporal excitation (Kausel, 2017), and further efforts are directed to determine the transverse vibration model as follows: ...

Focusing on reliability-informed and risk-informed pipeline integrity management, this paper proposes a degenerated model for naturally corroded surfaces of pipelines using the random field method and in-line inspection (ILI) data, performing statistical sensitivity analysis of physical parameters. The randomly mechanical properties of the corroded pipelines are subsequently examined via simulation of spatiotemporal vibration. The closed-form solution of the nonlinear vibration model is determined based on the equations of mathematical physics. With the probabilistic framework of Bayes inference and Markov Chain Monte Carlo (MCMC), the ILI data is introduced to update the failure probability of corroded pipelines. The numerical example results demonstrate that the synergic effects of random corrosion and random loads are contributed to degraded mechanical properties of pipelines, including uninspected or shallow corrosion-degraded areas. The proposed method is proven to be an effective and practical representation of naturally corroded surfaces, which can accurately evaluate the structural reliability of the corroded pipeline subjected to spatiotemporal excitation.

... However, it is not so easy to accurately detect the shape and location of the initial geometric imperfections in the pipeline. Hence, a fictitious imperfection shape with the stress-free, biased axisymmetric imperfection [42] is introduced, which follows a standard sinusoid modulated by a second sinusoid. In particular, the radial deflection function is expressed as ...

A comprehensive literature review in seismic analysis of free-spanning offshore pipelines (FSOPs) reveals that two critical aspects, i.e. the offshore earthquake motions and various uncertainty sources, have been normally ignored in numerous previous studies. Specifically, the offshore pipelines are usually modeled by assuming all the structural parameters to be ﬁxed and are excited using the onshore earthquake motions. Such analytical schemes may result in severe misestimates of seismic response predictions of FSOPs. In this paper, a probabilistic approach is developed for numerically investigating the seismic responses and failure mechanisms of FSOPs subjected to the offshore spatial earthquake motions (Off-SEMs). For this purpose, a buried offshore pipeline of API X65 with a free span of 30 m is selected and the corresponding three-dimensional finite element (3D FE) model is established in the ABAQUS software, where the soil-pipe and water-pipe interactions are modeled using the nonlinear soil springs and added mass and damping methods, respectively. Then, the three-dimensional Off-SEMs are stochastically synthesized by explicitly considering the effects of spatial variability and overlying seawater. Next, the general law of dynamic responses and failure modes of FSOPs subjected to the Off-SEMs is analyzed and summarized by the deterministic dynamic analysis. Defining the earthquake motions, structural modeling and soil properties as uncertain sources, the relative sensitivity of seismic behaviors to uncertain parameters involved in these uncertain sources is identified separately by the sensitivity analysis. Finally, uncertainty analysis is performed to examine and discuss the influence of different types of uncertainty sources on the seismic behaviors of FSOPs. Numerical results indicate that the pipeline diameter has the highest influence on the seismic behaviors of FSOPs, while the Poisson's ratio of pipeline material has the smallest effect; uncertainties in earthquake motions, structural modeling and soil properties have significant contributions to the dynamic characteristics and seismic behaviors.

... In the offshore sector, the increasingly important renewables sector also has significant supporting infrastructure such as cables where appropriate soil-surface interface strength is a key parameter. Furthermore, in seismic settings where ground motions impose displacement and loads on a buried pipe, the interface friction determines the amount of force that is imposed on the pipe (Psyrras et al., 2019;Psyrras et al., 2020). ...

Pipelines are an integral part of offshore infrastructure supporting the oil and gas industry and the consequences of their failure have severe economic and environmental ramifications. Changes in pipe internal pressures and temperatures from the as-laid condition to their operational state cause large thermal expansions. When axial strain from thermal expansion is resisted by the pipe-soil friction, the effective axial force in an unburied pipeline is relieved by lateral friction-sliding-buckling. The phenomenon of pipeline buckling is a significant challenge in managing the global stability of high pressure-high temperature offshore on-bottom pipelines. Pipelines are commonly given a protecting coating to aid in protection from damage and to provide thermal insulation. The use of polypropylene in this application is prevalent but relatively recent so correct quantification of the interface shear strength between marine sand soils and polypropylene is key to robust global stability design.
Herein, an extensive campaign of soil and interface shearbox testing has been undertaken to determine and evaluate the shear response of polypropylene surfaces. Parameters such as soil grading, density, surface texture, stress level, and cyclic behaviour have been investigated. The results show that the efficiency of the interface is strongly dependant on the soil grading and the surface texture at the interface. The shear response of soils at the interface with smooth surfaces is bilinear, characterised by an initially linearly elastic response at very small horizontal displacements, that transitions rapidly to a near constant shear stress plateau. Surfaces with greater roughness provoke a dilatant soil shear response more typical of a soil-only behaviour. Greater magnitude of surface texture engenders greater dilation leading to greater peak shear strengths. A relationship has been developed which can aid designers in predicting interface friction for polypropylene surfaces and sandy soils given surface texture, soil grain size, and stress level input parameters.
The application of the experimental results to real-world problems was investigated through numerical modelling in Abaqus of an approximately 5 km long pipe on a rigid seafloor using friction penalty and non-linear springs to model pipe-soil interaction and force-displacement response. The impact on global stability and buckling parameters of changes in pipe-soil friction and of applying a differential friction regime along the pipe was investigated. Numerical analysis results showed that such techniques are able to significantly change the distribution and magnitude of buckles.

... Many other research contributions have been then related to the stability issues of a multitude of loadbearing systems and members can be found in the literature, including plates (Sabouri-Ghomi et al., 2008;Rao and Ra, 2009;Xu et al., 2013;Moradi-Dastjerdi and Malek-Mohammadi, 2017;Riahi et al., 2018;Vu et al., 2019) and nanoplates (Malikan et al., 2018), bracing systems (Rahnavard et al., 2018), tubes (Nouri et al., 2015;Mozafari et al., 2018;Ahmed et al., 2017;Sadath et al., 2017;Sun et al., 2018), frames (Marante et al., 2012;Slimani et al., 2018), pipes (Lolov and Lilkova-Markova, 2005;Melissianos et al., 2017;Moustabchir et al., 2018;Psyrras et al., 2019), or Functionally Graded Material (FGM) structures (Moita et al., 2018;Singh and Harsha, 2019), etc. ...

In this study, a Finite Element Method (FEM) analysis is presented for the loss of stability in elastic states of very slender pinned without friction box-section thin-walled column axially compressed. From the FEM buckling linear stress analyses are determined the compressing critical forces for 36 cases, presented in tables and as the surface functions in dependence on the slenderness ratio and cross-section. Also are presented graphs obtained from the FEM post-buckling linear stress analysis for the elastic central line, slope, deflection and states of the stresses and strains of the box-section column 202812500 mm made of steel, by the assumption that a maximal deflection equals the half of a side dimension. The obtained from the FEM computing function and surface graphs are compared and then discussed with graphs corresponding to Euler's and Technical Stability Theory (TSTh) results. Finally are compared graphs of the stresses and strains of box-section thin-walled column 202812500 obtained from FEM and TSTh, but under compressing critical force determined according to TSTh.

... Difficulties in accurately obtaining displacement metrics from recorded ground motions, due to their sensitivity to filtering and correction processes [16] and the scarcity and spatial sparsity of data in the near-fault region, limit the development of robust ground-displacement models. Recent research has also shown, both numerically and experimentally, that geotechnical and/or geological discontinuities can cause significant differential axial deformation that may buckle buried pipelines, in contrast to the current perception that transient ground displacements does not induce noticeable seismic demands [17]. Along these lines, validated ground displacement models are required for assessing the damage and risk to infrastructure as well as for geohazard analyses such as slope stability. ...

The Sendai Framework for Disaster Risk Reduction 2015-2030 (SFDRR) highlights the importance of scientific research, supporting the ‘availability and application of science and technology to decision making’ in disaster risk reduction (DRR). Science and technology can play a crucial role in the world’s ability to reduce casualties, physical damage, and interruption to critical infrastructure due to natural hazards and their complex interactions. The SFDRR encourages better access to technological innovations combined with increased DRR investments in developing cost-effective approaches and tackling global challenges. To this aim, it is essential to link multi- and interdisciplinary research and technological innovations with policy and engineering/DRR practice. To share knowledge and promote discussion on recent advances, challenges, and future directions on ‘Innovations in Earthquake Risk Reduction for Resilience’, a group of experts from academia and industry met in London, UK, in July 2019. The workshop focused on both cutting-edge ‘soft’ (e.g., novel modelling methods/frameworks, early warning systems, disaster financing and parametric insurance) and ‘hard’ (e.g., novel structural systems/devices for new structures and retrofitting of existing structures, sensors) risk-reduction strategies for the enhancement of structural and infrastructural earthquake safety and resilience. The workshop highlighted emerging trends and lessons from recent earthquake events and pinpointed critical issues for future research and policy interventions. This paper summarises some of the key aspects identified and discussed during the workshop to inform other researchers worldwide and extend the conversation to a broader audience, with the ultimate aim of driving change in how seismic risk is quantified and mitigated.

... Previous studies investigated the seismic behaviour of offshore pipelines [7][8][9]. However, to the knowledge of the authors, the seismic studies of high pressure/high temperature (HP/HT) pipelines so far has been limited to buried and trenched pipelines [10]. A subsea HT/HP pipeline can undergo large bending stresses and strains due to lateral/upheaval buckling or free-spanning [11][12][13][14]. ...

... Single-layer graphene sheets have been examined in (Genoese et al., 2019), while polymer-confined concrete columns have been discussed in (Liang et al., 2012) and hyperelastic tubes are analyzed by (Liu, 2018). Many other research contributions have been then related to the stability issues of a multitude of loadbearing systems and members can be found in the literature, including plates (Sabouri-Ghomi et al., 2008;Rao and Ra, 2009;Xu et al., 2013;Moradi-Dastjerdi and Malek-Mohammadi, 2017;Riahi et al., 2018;Vu et al., 2019) and nanoplates (Malikan et al., 2018), bracing systems (Rahnavard et al., 2018), tubes (Nouri et al., 2015Mozafari et al., 2018;Naveed et al., 2017;Sadath et al., 2017;Sun et al., 2018), frames (Marante et al., 2012;Slimani et al., 2018), pipes (Lolov and Lilkova-Markova, 2005;Melissianos et al., 2017;Moustabchir et al., 2018;Psyrras et al., 2019), or Functionally Graded Material (FGM) structures (Moita et al., 2018;Kiss, 2019;Singh and Harsha, 2019), etc. ...

The stability of load-bearing members, as known, is a challenging issue and several tools are available for designers. Disregarding the material properties in use, the avoidance of possible stability troubles is a mandatory and challenging step of the overall design process. Murawski (2020) presented a theoretical model for the loss of stability in elastic states of very slender rectangular shell elements axially compressed through ball-and-socket joints without friction. According to this theory, as shown, a loss of carrying capacity of very slender columns in elastic states occurred when the line of force left a critical transverse cross-section. The critical transverse cross-section, moreover, progressively moved because of the superposition of bending and pure compression. The theory allowed to determine the governing differential equations of curved central lines and their slopes, as well as the critical stresses of columns, in the form of a surface function in dependence on slenderness ratios and cross-sectional areas. The graphs for the elastic deflected central line y(x), slope dy/dx, dependence yL/2(P), stresses and strains for a rectangular column made of steel and compressed by ball-and-socket joints without friction, as well as the corresponding surface graphs of critical stress, were presented in this study. The obtained surface graphs of critical stresses were then discussed and compared with Euler’s formulation.

... The main cause of failure in BGPs is due to the development of seismic tensile strains [6]. Any minor interruption can cause energy stoppage and effect the daily life [7]. It can also be fatal if the interruption trigger fire or explosions [8]. ...

Research on buried gas pipelines (BGPs) has taken an important consideration due to their failures in recent earthquakes. In permanent ground deformation (PGD) hazards, seismic faults are considered as one of the major causes of BGPs failure due to accumulation of impermissible tensile strains. In current research, four steel pipes such as X-42, X-52, X-60, and X-70 grades crossing through strike-slip, normal and reverse seismic faults have been investigated. Firstly, failure of BGPs due to change in soil-pipe parameters have been analyzed. Later, effects of seismic fault parameters such as change in dip angle and angle between pipe and fault plane are evaluated. Additionally, effects due to changing pipe class levels are also examined. The results of current study reveal that BGPs can resist until earthquake moment magnitude of 7.0 but fails above this limit under the assumed geotechnical properties of current study. In addition, strike-slip fault can trigger early damage in BGPs than normal and reverse faults. In the last stage, an early warning system is proposed based on the current procedure.

... The purpose of this work is to evaluate the mechanism of local buckling of the wall of a hidden pipeline (pipe wall buckling) by applying a new software-digital approach [1] to the analysis of the stress-strain state of the pipe-subsoil system. In contrast to the known solutions [2][3][4][5][6][7][8][9], in this work it is proposed to go from quasi-statics to dynamics, from 2D calculation schemes to 3D schemes, from initial irregularities in shape to technological deviations [10]. The introduction of these factors makes it possible to take into account the effect of shock loads in real time, to consider extended pipeline structures and to abandon the assumption that the initial irregularity of the shape is set arbitrarily. ...

Topical issues of interaction of metal pipes with subsoil in the structures of hidden (underground) main pipelines serving for transporting oil or gas are considered. The shock loading of pipes from the subsoil side, caused by seismic earth movements, was investigated. The loading consists of the total compacting pressure and the force local pressure. The calculations were carried out in order to establish a possibility of local buckling of the pipe (pipe wall buckling). The problem was solved in real time, taking into account the bulk of the pipe– subsoil structure and technological deviations. A 3D finite element model of the structure with unilateral constraint along the surface of the pipe-and-subsoil contact has been developed, which is presented in the form of a thick-walled cylinder. The pipe is considered as an elastoplastic body; the subsoil is considered as linearly elastic. The calculations were performed using the LS-DYNA software package in a nonlinear dynamic formulation. Numerical analysis of the stress-strain state of the steel pipe – subsoil structure showed that there were critical loads at which the pipe wall buckles. It is concluded that it is necessary to carry out dynamic calculations of buried pipelines located in seismically active regions.

... The majority of research efforts on pipeline analysis has been mainly focused on structural responses due to permanent ground deformations (PGD), because PGD can typically induce a higher straining on the steel pipelines [8][9][10][11]. Nevertheless, some studies have revealed that pipelines embedded in heterogeneous sites and/or subjected to asynchronous ground seismic motions are likely to be affected by non-negligible deformations and strains due to earthquake-induced transient ground motions, which can also result damages on the pipeline [12][13][14], such as local buckling, tensile rupture, excessive ovaling deformation, etc. [15]. ...

Natural gas pipelines are subject to a complex set of natural and manmade threats. Earthquakes can generate forces and permanent ground displacements that threaten the integrity of the California gas infrastructure. Earthquakes and landslides have the potential to simultaneously compromise pipelines over a broad region, leading to fires and widespread disruption of gas supply. Current understanding of seismic threats to gas pipelines rely upon models that are too simplistic using limited empirical data resulting in significant uncertainties in predictions. In this study, we will conduct high-fidelity nonlinear soil-structure interaction (SSI) analyses using geohazard characteristics (e.g., displacement magnitude, direction of displacement) and pipeline characteristics (e.g., pipe diameter, thickness), to create models that can predict the seismic response of gas transmission pipelines to the full range of seismic hazards, including ground motion, fault displacement, landslide and liquefaction. This effort is part of a larger project that will examine seismic demands on natural gas infrastructure. The study explores the development of a seismic performance assessment methodology that will complement a broader effort on devising a regional probabilistic seismic risk assessment framework for gas infrastructure in California.

... Similarly, for buried NG pipelines, the impact of out-of-phase oscillation induced by differential earthquake inputs has been highlighted previously. Psyrras et al. (2019Psyrras et al. ( , 2020 numerically and experimentally investigated the seismic risk of buried NG pipelines when subjected to spatially varying transient ground deformations. Results showed that even for straight buried pipelines, the seismic vibrations at the vicinity of laterally inhomogeneous sites can produce differential movements on different locations of a long pipeline due to kinematic soil-pipe interaction. ...

Though often overlooked, the impact of seismic transient ground deformation on natural gas (NG) pipes can be highly adverse. Particularly, pipe elbows may undergo excessive in-plane bending demand and buckling. In this paper, a critical scenario of a pipe coupling two industrial structures typically found in an NG processing plant is studied. High strain and cross-sectional ovalization on the elbows are probable during an earthquake due to the out-of-phase oscillation of the two structures imposing asynchronous displacement demands at the two pipe-ends. A parametric study was first performed to investigate various structure-pipe-structure configurations which increase seismic demands to pipe elbows. Simultaneous mobilisation of divergent oscillation between two supporting structures at the low-frequency range, a lower pipe-structure stiffness ratio, a shorter length of straight pipe segments in the linking pipe element and a higher pipe internal pressure have led to the onset of critical strain demands in pipe elbows.

... The problem of the stability was later searched in many aspects by: [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [ [58], [59], [60], [61], [62], [63], [64], [65], [66], [67], [68], [69], [70], [71], [72], [73], [74], [75], [76], [77], [78], [79], [80], [81], [82], [83], [84], [85], [86], [87], [88], [89], [90], [91], [92], [93], [94], [95], [96], [97], [98], [99], [100], [101], [102], [103], [104], [105], [106], [107], [108], [109], [110], [111], [112], [113], [114], [115], [116], [117], [118], [119], [120], [121], [122], [123], [124], [125], [126], [127], [128], [129], [130], [131], [132], [133], [134], [135], [136], [137], [138], [139], [140], [141], [142], [143], [144], [145], [146], [147], [148], [149], [150], [151], [152], [153], [154], [155], [156], [157], [158], [159], [160], [161], [162], [163], [164], [165], [166], [167], [168], [169], [170], [171], [172], [173], [174], [175], [176], [177], [178], [179], [180], [181], [182], [183], [184], [185], [186], [187], [188], [189], [190], [191], [192], [193], [194], [195], [196], [197], [198], [199], [200], [201], [202], [203], [204], [205], [206], [207], [208], [209], [210], [211], [212], [213], [214], [215], [216], [217], [218], [219], [220], [221], [222], [223], [224], [225], [226], [227], [228], [229], [230], [231], [232], [233], [234], [235], [236], [237], [238], [239], [240], [241], [242], [243], [244], [245], [246], [247], [248], [249], [250], [251], [252], [253], [254], [255], [256], [257], [258], [259], [260], [261], [262], [263], [264], [265], [266], [267], [268], [269], [270], [271], [272], [273], [274], [275], [276], [277], [278], [279], [280], [281], [282], [283], [284], [285], [286], [287], [288], [289], [290], [291], [292], [293], [294], [295], [296], [297], [298], [299], [300], [301], [302], [303], [304], [305], [306], [307], [308], [309], [310], [311], [312], [313], [314], [315], [316], [317], [318], [319], [320], [321], [322], [323], [324], [325], [326], [327], [328], [329] as well as many others. ...

The paper presents the comparison of experimental results obtained from tests on semi-slender columns with pinned ends made of steel R35 to simplifications and hypotheses of loss of stability by lateral buckling in elastic-plastic states of columns axially compressed by force. The Tetmajer-Jasiński's and Johnson-Ostenfeld's simplifications, as well as Engesser-Kármán-Shanley's, Ylinen, Březina, Pearson-Bleich-Vol'mir's and author's approximated hypotheses, are analysed. The graphs of surface functions of critical stress σ cr (A, L*t) depending on a cross-section area and length times thickness product are presented as the theoretical examples of thin-walled cylindrical and square columns made of steel R35. In order to compare the experimental results with other simplifications and hypotheses are shown in adequately ranges for elastic-plastic states as the graphs of the functions σ cr (λ).

... In the study of Psyrras et al. [4], [5], the potential vulnerability of mechanical changes in seismic ground motions on buried pipelines has been investigated. A numerical analysis method was proposed to determine the seismic demand of steel pipelines. ...

In this paper, the numerical study of buried steel pipe in soil is investigated. Buried pipeline under soil weight, after embankment on the pipe leads to ovality of pipe. In this paper also it is considered the percentage of soil compaction, the soil height on the steel pipe and the external load of a mechanical excavator on the steel pipe and finally, the effect of these on the rate of pipe ovality investigated. Furthermore, the effect of the pipes' thickness on ovality has been investigated. The results show that increasing the percentage of soil compaction has more effect on reducing percentage of ovality, and if the percentage of soil compaction increases, we can use the pipe with less thickness. Finally, ovality rate of the pipe and acceptance criteria of pipe diameter up to yield stress is investigated.

... Psyrras and Sextos (2017) present a comprehensive review on 28 multiple aspects of seismic safety of pipelines, including some recent advances in analysis and design 29 methods. More recently, a series of studies reported on the buckling potential of gas pipelines buried in 30 media with sharp stiffness transitions during seismic shaking (Psyrras et al. , 2019aTsinidis et al. 31 2018); in these, non-linear finite element models were developed to analyze the factors that contribute 32 to the development of localized deformation in the pipe walls leading to plastic buckling, and to describe 33 the type of the resulting buckling response. Along the same vein, Yu et al. (2018) This work aims at developing through new experimental data know-how on the mechanisms of axial SPI in laterally inhomogeneous soil and its effects on high-pressure gas pipelines in seismically active 55 areas. ...

This paper reports on results from a series of 1-g, reduced-scale shake table tests of a 216-m-long portion of an onshore steel gas transmission pipeline embedded in horizontally layered soil. A set of first-order dynamic similitude laws was employed to scale system parameters appropriately. Two sands of different mean grain diameter and bulk density were used to assemble a compound symmetrical test soil consisting of three uniform blocks in a dense-loose-dense configuration. The sand-pipe interface friction coefficients were measured as 0.23 and 0.27. Modulated harmonics and recorded ground motions were applied as table excitation. To monitor the detailed longitudinal strain profiles in the model pipe, bare Fiber Bragg Grating (FBG) cables were deployed. In most cases, the pipe response was predominantly axial while bending became significant at stronger excitations. Strain distributions displayed clear peaks at or near the block interfaces, in accord with numerical predictions, with magnitudes increasing at resonant frequencies and with excitation level. By extension to full scale, peak axial strain amounted to 10−3, a demand half the yield strain, but not negligible given the low in situ soil stiffness contrast and soil-pipe friction.

How does an earthquake affect buried pipeline networks? It is well known that the seismic performance of buried pipelines depends on ground failures (GFs) as well as strong ground shaking (SGS), but it is unclear how the various types of earthquake hazards should be collectively combined, as existing methodologies tend to examine each of the earthquake hazards separately. In this article, we develop a probability-based methodology to consistently combine SGS with three types of GF (surface faulting, liquefaction, and landslide) for forecasting seismic damage in buried pipeline networks from a given earthquake rupture scenario. Using a gas transmission pipeline example, we illustrate how the proposed methodology enables others (e.g., researchers, pipeline operators who manage distribution lines, and consultants) to modularly combine various models such as those for estimating probability of GF, permanent ground displacements, and pipeline fragility. Finally, we compare the proposed methodology against the Hazus methodology to explore implications from considering each hazard one at a time.

Citation: Murawski K., 2023. Technical Lateral Buckling, Stress and Strain Analysis of Semi-slender Thin-walled Cylindrical Pinned Column made of Steel St35 Simplified with Aall, Jzall, E= Ec , Epl= Esc. Stability of Structures - Journal of Critical Engineering. https://www.lulu.com/shop/krzysztof-murawski/technical-lateral-buckling-stress-and-strain-analysis-of-semi-slender-thin-walled-cylindrical-pinned-column-made-of-steel-st35-simplified-with-aall-jzall-e-ec-epl-esc/ebook/product-rnwzqn.html?q=&page=1&pageSize=4 ______________________________________________________________________
Summary: Murawski (2023) continued and discussed the next case of the simplified method of the Technical Stability Theory (TSTh) of loss of stability of lateral buckling in elastic-plastic states of semi-slender columns axially compressed by a force. It was again assumed that in the critical elastic-plastic transverse cross-section there were the elastic and plastic parts of the area, keeping strength. Here it was assumed that in the elastic-plastic transverse cross-section, the entire transverse cross-section of the column kept the resistance, i.e. the transverse cross-section area A= Aall, the moment of inertia of a cross-section area Jz= Jzall as well as was assumed that the elastic Young’s modulus E= Ec featured the elastic static moment Szel, and the plastic modulus Epl featured the plastic static moment Szpl. The next assumptions were that the elastic Young’s modulus E was varying with the slenderness ratio Lambda and equalled the compress modulus, i.e. E= Ec(Lambda) taken from the experimental research, and also was varying with the transverse cross-section area A, i.e. E= Ec(Lambda, A). The graphs of the functions of the curved axes, their slopes, deflections, stresses and strains of the thin-walled cylindrical column D45x1x545 mm with slenderness ratio Lambda= 35 as well as the critical compressive stresses depending on the cross-section areas A and slenderness ratios Lambda were presented as the theoretical examples with the new assumptions and compared to results obtained from experiments with thin-walled cylindrical columns made of steel St35.

Onshore high - pressure gas pipelines constitute critical infrastructure that usually cross seismic - prone regions and are vulnerable to Permanent Ground Deformations (PGDs) due to active seismic faults. In design, it may not be feasible to avoid fault rupture areas due to various technical, economical and topographic reasons. Moreover, the presence of soil layers affects the PGDs resulting from a tectonic fault, which in turn may alter the seismic demand on the pipeline. The current study investigates numerically the impact of soft soil layers on the seismic kinematic distress of onshore gas pipelines. For this purpose, a decoupled numerical modeling approach is adopted, consisting of two separate finite - element models for the simulation of soil response and pipeline distress, respectively. Soil non - linearities are taken into account utilizing the Mohr - Coulomb constitutive model with isotropic strain softening. An extensive parametric analysis is performed considering different faulting mechanisms and fault dip angles, as well as soil geometry and mechanical properties. Consequently, the maximum absolute values of both tensile and compressive pipeline strains are correlated with the seismic intensity level (i.e., in terms of bedrock offset which is associated with earthquake magnitude via simple relationships). The paper concludes with a set of design charts and tables for the preliminary seismic design of onshore high - pressure gas pipelines. These charts and tables predict with reasonable accuracy pipeline deformations, in terms of strains, for different magnitude, fault type, dip angle, sand type, and varying overlying soil layer thickness.

Citation:
Murawski K., 2023. Technical Lateral Buckling, Stress and Strain Analysis Simplified with Aall, Jzall, Epl= Ec of Semi-slender Thin-walled Cylindrical Pinned Column made of Steel St35. Stability of Structures - Journal of Critical Engineering. https://www.lulu.com/shop/krzysztof-murawski/technical-lateral-buckling-stress-and-strain-analysis-simplified-with-aall-jzall-epl-ec-of-semi-slender-thin-walled-cylindrical-pinned-column-made-of-steel-st35/ebook/product-9nr5v8.html?q=murawski&page=1&pageSize=4
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Summary:
Murawski (2023) continued and discussed the next case of the simplified method of the Technical Stability Theory (TSTh) of loss of stability of lateral buckling in elastic-plastic states of semi-slender columns axially compressed by a force. It was again assumed that in the critical elastic-plastic transverse cross-section there are the elastic and plastic parts of the area, keeping strength. Here also it was assumed that in the elastic-plastic transverse cross-section, the entire transverse area of the column kept the resistance, i.e. the transverse cross-section area A= Aall, the moment of inertia of a cross-section area Jz= Jzall, as well as it, was assumed that the elastic Young’s modulus E= Ec featured the elastic static moment Szel, and the plastic modulus Epl featured the plastic static moment Szpl. The next assumptions were that the elastic Young’s modulus E varied with the slenderness ratio Lambda and equalled the compress modulus, i.e. E= Ec(Lambda ) taken from the experimental research, and also varied with the transverse cross-section area A, i.e. E= Ec(Lambda,A). The graphs of the functions of the curved axes, their slopes, deflections, stresses and strains of the thin-walled cylindrical column D45x1x545 mm with slenderness ratio Lambda = 35 as well as the critical compressive stresses depending on the cross-section areas A and slenderness ratios Lambda were presented as the theoretical examples with the new assumptions and compared to the results obtained from experiments with thin-walled cylindrical columns made of steel St35.

Gömülü boru hatları su, doğalgaz ve petrol gibi hayati öneme sahip ürünlerin taşınması ve dağıtılması amacıyla kullanılan kritik alt yapı elemanlarıdır. Bu tür enerji nakil sistemleri, güzergahları üzerinde fay hatları ile kesişebilmekte, kesişim açısına bağlı olarak kalıcı zemin deformasyonları etkisinde çekme ve basınç gerilmelerine maruz kalabilmekte ve ciddi hasarlar alabilmektedirler. Tasarım ilkesi açısından çelik borularının çekme göçmesine maruz kalması beklenir. Fakat mecburi güzergâh sebebiyle ters ya da bazı yanal atımlı fayların kesilmesi gerektiği durumlarda net eksenel basınç kuvvetleri altında prematüre göçmeler yaşanabilmektedir. Mevcut yönetmeliğe göre, deprem etkisi altında kalan boru hatları için belirtilen tasarım esasları, kesintisiz kullanım ve kontrollü hasar durumları için tarif edilmiş en büyük eksenel çekme ve basınç birim yer değiştirme değerlerine göre sınırlandırılmıştır. Ancak, boruların özellikle basınç altındaki burkulma sonrası ileri seviye performansları yeteri kadar bilinmemektedir. Bu çalışma kapsamında, özelikle borularda basınç kaybı ve hasar oluşumuna sebebiyet veren eksenel basınç ve eğilme momenti altındaki limit durumları incelenmiştir. Bu amaçla, Türkiye’de bulunan mevcut boru hatlarını karakterize edecek şekilde, su isale (Kullar), doğalgaz (TANAP) ve petrol (BTC) boru hatlarına ait D/t oranları ile malzeme karakteristik özellikleri dikkate alınarak üç boyutlu sonlu elemanlar modeli yardımıyla birleşik yükleme koşulları altındaki davranışları incelenmiştir. Böylelikle, ötelenme miktarlarına ve rotasyon miktarlarına bağlı olarak borularda oluşacak limit durumlar belirlenmiştir. Söz konusu çalışma sonuçlarının ülkemizdeki boru hatlarının performans tabanlı tasarımlarında kullanılması beklenmektedir.

Improving the seismic performance of pipelines is fundamental to achieving resiliency of urban environments against extreme natural events. The vulnerability of pipelines is inevitably associated with their exposure to regional and local geohazards. Seismic hazard assessments of pipelines are uniquely challenged by varying local soil conditions, as evidenced by the concentration of damages in areas prone to ground motion amplification and liquefaction. This paper focuses on the hazard associated with transient seismic waves, which affects the entire pipeline system as opposed to the localized effects imposed by ground failure. Our study provides a review of seismic hazard assessments of pipeline networks and current practices to account for site effects. More specifically, we review available methods to consider the effects of local soil conditions on the seismic demands of pipelines, soil-pipe interaction, spatial variability in soils, and ground motion directionality. First, we summarize relevant observations from past seismic events and then, an evaluation of current practices to account for site effects is provided. Strengths and limitations of simplified approaches are revised and compared to methods that target the quantification of site effects and the network response on a broader regional scale. Areas of future research are identified as potential paths toward improved resiliency of pipelines to seismic hazards.

Reliability analysis of buried pipelines subjected to spatiotemporal seismic involves modeling multiple uncertainties related to loads, soil, and mechanical mechanisms. The present study proposes a probabilistic modeling method that can couple random spatiotemporal seismic vibrations in the axial and transverse directions of the pipeline, enabling probabilistic incorporation of stochastic uncertainty (random variability) into the seismic response analysis of structures. Uncertainties of soil properties are probabilistically modeled to simulate the random pipe-soil interaction effect. Spatiotemporal dynamic response of the pipelines is discretized using extreme value distribution theory, thus making the seismic reliability analysis of the pipeline within a time-invariant framework. The applicability and accuracy of the proposed method are illustrated by numerical studies. The application of the probabilistic modeling method supports reliability- and risk-based inspection and maintenance planning for buried pipelines subjected to spatiotemporal earthquakes.

Estrategias de reducción de riesgos para una adecuada resiliencia. Se presenta una análisis de la evolución de los sistemas estructurales para una adecuada respuesta ante eventos sísmicos como resiliencia sísmica e un portafolio o comodidad, entendiendo que los sistemas estructurales son muy complicados, contienen numerosos tipos de elementos físicos (p. ej., construcción, transporte y sistemas de redes de tuberías), elementos no físicos (p. ej., sociales, económicos y ecosistemas) y varias relaciones complejas entre diferentes subsistemas para ver una ciudad como un sistema de sistemas en un espacio tridimensional (físico, social y cibernético), la connotación y las propiedades de la resiliencia urbana usando varios subsistemas de una ciudad y sus interacciones. Además, las ciudades enfrentan varios tipos de desastres naturales (p. ej., terremotos, inundaciones y huracanes) y desastres no naturales (p. ej., explosiones e impactos). Por lo tanto, la cuantificación de la resiliencia de los sistemas urbanos después de los desastres es compleja. Hasta la fecha, los estudios de cuantificación de la resiliencia generalmente se realizan desde una perspectiva macroscópica o se enfocan en un número limitado de subsistemas bajo un solo desastre.

Understanding soil-pipe interaction during cyclic axial displacement is essential for the design and evaluation of buried pipeline systems. This study introduces an efficient and practical numerical approach using beam-spring-interface elements to simulate soil-pipe interaction behaviour. Numerical predictions of the evolution of shear and normal stress distributions around the pipe are validated against full-scale experimental results for steel and high-density polyethylene pipes buried in sandy soils. Three different backfill cover depths and soil densities ranging between loose and dense were considered to allow a rigorous comparison between the numerical predictions and the experimental results. The results show that the proposed approach provides a high-fidelity representation of the complex soil-pipe interaction behaviour at the interface zones, including stress cyclic degradation, hardening and softening, cyclic accumulative contraction and stabilization. This numerical framework provides accurate predictions for a fraction of the computational cost of a full three-dimensional finite element analysis.

For buried pipelines, the longitudinal strain is the primary seismic design parameter. The strain can be calculated from a three dimensional (3D) time history analysis. However, performing a 3D analysis in practice can be prohibitive. The objective of the study is to provide guidelines for performing a simplified pseudo-static analysis that approximates the output of a 3D nonlinear analysis. A parametric study is performed to evaluate the degree of influence of numerous variables on the calculated longitudinal strain, the results of which are used to sculpture the guidelines. It is recommended to utilize the outputs from a one-dimensional site response analysis and the closed-form equations to calculate the axial and bending strains of pipelines subjected to a harmonic wave propagating at an incident angle to the longitudinal axis of the structure. To represent a transient earthquake motion as an equivalent harmonic motion, a procedure to extract the pulse that induces the maximum strain considering both the amplitude and the duration is presented. Using the proposed procedure, it is revealed that the reliability of the predicted longitudinal strain is acceptable for design purposes.

Oil and gas buried steel pipelines are vulnerable to permanent ground displacements, such as those resulting from tectonic fault activation. The dominant failure mechanism is strongly dependent on the type of faulting. The more complex case is the reverse fault type because the crossing pipeline is significantly compressed and bent and consequently, it may fail due to local buckling, upheaval buckling or tensile weld fracture. Which among those failure modes will be critical, depends on a set of parameters, comprising fault crossing geometry, diameter to thickness ratio (D/t) of the pipeline, pipeline steel grade, and backfill soil properties. An extensive parametric study is carried out, followed by statistical processing of the results in order to formulate simplified statistical models for the prediction of the predominant failure mode according to criteria set by the American Lifelines Alliance and EN 1998-4 standards. The study thus offers the first comprehensive attempt to quantify the qualitative criterion that deeply buried pipes with high D/t ratio tend to buckle locally, while shallowly buried pipes with low D/t ratio tend to buckle globally. Pipe designers may use the provided expressions to predict the predominant failure mode in order to either apply the necessary seismic countermeasures or re-design the pipeline if necessary.

Faulting and permanent ground deformation play a significant rule in evaluating the performance of buried steel pipelines under the devastating effects of earthquake. In this paper, the buried steel pipelines crossing the strikeslip faults are studied in experimental modeling using various full-scale tests to assess the damage during faulting. Ten different burial depths on the diameter of the pipe ratio (H/D) were used to evaluate the effect of burial depth. The linear and nonlinear behavior of the pipe material, the changing strain rate relevant to the H/D alterations, the vertical and horizontal deformation of the soil, and the ovalization of the pipe during faulting were investigated in this paper.

The damaging potential of spatial variability in seismic ground motion on the integrity of buried pipelines is demonstrated in this paper. A numerical analysis methodology is developed first to determine the seismic demand of a typical straight steel natural gas pipeline running through a site composed of two different media with an impedance ratio of 2 and swept by vertically propagating SV-waves. The analysis follows a sub-structured, two-phase approach involving the computation of pipeline input excitation from 2D linear viscoelastic and linear-equivalent seismic site response models and the quasi-static application of the derived critical motion profiles on a near-surface 3D continuum soil model surrounding an extended inelastic shell model of the pipeline. The focus is then placed on identifying the ground and exciting conditions bearing adverse effects on the peak pipeline response. By comparing the pipeline demand in terms of stress and strain to capacity metrics prescribed in present seismic codes, the importance of the local site response is gauged. Results show that low-frequency ground vibrations produce the most unfavorable demand on the pipe for the set of cases examined. More importantly, even though pipeline axial strain demand-to-capacity ratios for elastic local site response under weak excitation imply a large safety margin, pipeline demand can exceed capacity near the site boundary under strong excitations and subsequent nonlinear soil response. Plastic local buckling may also develop in the pipeline under high-intensity input motions, thus highlighting the necessity to account for non-synchronous earthquake ground motion in case of horizontally nonhomogeneous sites.

Evidence from past earthquakes suggests that damage inflicted to buried natural gas (NG) pipelines can cause long service disruptions, leading to unpredictably high socioeconomic losses in unprepared communities. In this review paper, we aim to critically revisit recent progress in the demanding field of seismic analysis, design and resilience assessment of buried steel NG pipelines. For this purpose, the existing literature and code provisions are surveyed and discussed while challenges and gaps are identified from a research, industrial and legislative perspective. It is underscored that, in contrast to common belief, transient ground deformations in non-uniform sites are not necessarily negligible and can induce undesirable deformations in the pipe, overlooked in the present standards of practice. It is further highlighted that the current seismic fragility framework is rich in empirical fragility relations but lacks analytical and experimental foundations that would permit the reliable assessment of the different parameters affecting the expected pipe damage rates. Pipeline network resilience is still in a developing stage, thus only few assessment methodologies are available whereas absent is a holistic approach to support informed decision-making towards the necessary mitigation measures. Nevertheless, there is ground for improvement by adapting existing knowledge from research on other types of lifeline networks, such as transportation networks. All above aspects are discussed and directions for future research are provided.

In the past decades, a number of major earthquakes caused serious damage to natural gas pipeline networks. In most cases, the devastating effects were caused by permanent ground displacement. However, there exist at least two well documented cases (Mexico City and Northridge Earthquakes) where damage were due to seismic wave propagation. Response of buried pipelines is significantly different from that of above-ground structures. However, similarly to bridges or dams, pipelines are also prone to the effects of spatial variability of earthquake ground motion due to their length, which, in some cases, extends beyond national borders. This paper focuses on the effects of asynchronous excitation on the seismic response demand of natural gas pipelines belonging to transmission networks. Parameters examined include time delay due to finite wave propagation velocity and loss of coherency along the pipelines' length, a parameter known to contribute to seismic strains. Impact of local site effects on pipeline response is examined through the use of bedrock-soil surface slope that forms a basin, with impedance ratios varying with depth. Finite element analysis and lumped springs are used to model the interacting soil-pipeline system while excitation input motions are generated through 2D site response analyses. The paper summarizes the effects of various parameters on seismic demand to pipelines. The results indicate that ignoring the wave passage effect, the stress state in the pipeline is roughly symmetric, with the axial strains of the pipeline to be increased over the inclined sides of the basin and to be almost null in the middle. When the wave passage effect is incorporated in the analysis the stress state is no longer symmetric and the location of the maximum strains in the pipeline moves towards the central region of the basin but near to the inclined edge from which the seismic waves are coming. The comparison of the computed axial strains with the respective strains used in conventional design processes showed that in the case of irregular subsurface topographies the conventional may result in unconservative design.

Site effects are one of the most predictable factors of destructive earthquake ground motion but results depend on the type of model chosen. We compare simulations of ground motion for a 3D model of the Mygdonian basin in northern Greece (Euroseistest) using different approximation for this basin. Site effects predicted using simple 1D models at many points inside the basin are compared to site effects predicted using four different 2D cross sections across the basin and with results for a full 3D simulation. Surface topography was neglected but anelastic attenuation was included in the simulations. We show that lateral heterogeneity may increase ground motion amplification by 100 %. Larger amplification is distributed in a wide frequency range, and amplification may occur at frequencies different from the expected resonant frequencies for the soil column. In contrast, on a different cross section, smaller conversion of incident energy into surface waves and larger dispersion leads to similar amplitudes of ground motion for 2D and 1D models. In general, results from 2D simulations are similar to those from a complete 3D model. 2D models may overestimate local surface wave amplitudes, especially when the boundaries of the basin are oblique to the selected cross section. However, the differences between 2D and 3D site effects are small, especially in regard of the difficulties and uncertainties associated to building a reliable 3D model for a large basin.

In an attempt to estimate the intensity of ground motion that the Marina District, San Francisco, California, experienced during the 1989 Loma Prieta earthquake, we investigate the 3D seismic response of a 2D model (referred to in the present article as "2.5D model") of a SW-NE trending cross section of the Marina Basin. As a first step in this endeavor, the simulated elastic response characteristics of the model are compared with recorded aftershock data. The comparison, in terms of peak amplitudes, duration, and frequency content of the time response, is favorable. In simulating the response of the Marina Basin to the Loma Prieta mainshock excitation, we account for the effect of soil nonlinearities by an iterative procedure, referred to as the "equivalent linear approach" according to which the values of soil damping and stiffness are selected to be consistent with the level of strain. Our results show that accelerations and velocities may have reached values as high as 0.23 g and 34 cm/sec, respectively; strains induced by wave propagation were of the order of 10-4, while spectral acceleration Sa for damping ratio 5% reached values as high as 0.8 g for periods in the range of 0.8 ≦ T ≦ 1.2 sec, which contains the fundamental frequencies of the most heavily damaged structures in the Marina District. The simulations confirm the conjecture made by Hanks and Brady (1991) that the motion recorded at Treasure Island is the most likely strong-motion surrogate for the filled areas of the Marina District. Based on the results of the simulations, it may be stated that for strong-motion (i.e., large strain) excitation, 3D focusing and lateral interferences, while still present, are not as prominent as in the weak-motion (i.e., small-strain) excitation case. The above conclusion suggests that, in general, the damping characteristics of soil deposits (particularly of poorly consolidated soft-soil deposits, i.e., mean shear-wave velocity of the upper 30 m of deposits, less than 200 m/sec), selected to be consistent with the level of strain induced by the seismic excitation, are a key factor in controlling the nature of the overall response of a sedimentary basin. Finally, in computing empirical amplification ratios based on recorded motions, selection of an appropriate "free-field" motion, representative of the incident excitation, is very crucial.

Despite the seismic vulnerability of gas systems and the significance of the direct and indirect consequences that loss functionality might have on large communities, the analysis of the earthquake performance and of post-earthquake management for this kind of distribution networks appears under-represented in the international literature, with respect to other lifeline systems. To contribute on this matter, the study presented comprises an investigation of the impact of L’Aquila 2009 earthquake (
$\text{ M }_\mathrm{w}$
M
w
6.3) on the performance of the local medium- and low-pressure gas distribution networks. The assessment of the physical impact of the earthquake to the buried components of network, namely pipes, valves, and demand nodes, was carried out when processing post-earthquake repair activity reports. Repair data, along with geometrical and constructive features, were collected in a geographic information system linked to the digitized maps of the network, and compared with the interpolated map of recorded transient ground motion, measured in terms of peak ground velocity (i.e., a
$Shakemap^\mathrm{TM}$
S
h
a
k
e
m
a
p
TM
). The impact of permanent ground deformation was also investigated and found to be limited in the study area. The resulting observed repair rates (number of repairs per km), presented for different pipeline materials, were compared with repair ratio fragility functions available in literature, showing relatively agreement especially to those for steel pipes, likely also because of the uncertainties in the estimations. Finally, the management of the L’Aquila gas system in the emergency phase and the resilience (functionality recover versus time) of the system was discussed.

Transient ground strains are recognized to govern the response of buried elongated structures, such as pipelines and tunnels,
under seismic wave propagation. Since a direct measure of ground strains is not generally available, simplified formulas relating
peak ground strain to peak ground velocity, and based on 1D wave propagation theory in homogeneous media, are typically used
for seismic design. Although they are adopted by most of the available technical guidelines, the use of these formulas may
be questionable in complex realistic situations as either in the presence of strong lateral discontinuities, or in the epicentral
area of large earthquakes, or in sites where relevant site amplification effects and spatial incoherency of ground motion
are expected. To provide a contribution to overcome the previous limitations, a simplified formula relating peak ground longitudinal
strain to peak ground velocity is proposed in this paper, as a function of the geometrical and dynamic parameters which have
the major influence on strain evaluation. The formula has been obtained under small-strain assumptions, so that it can reasonably
be applied under linear or moderately non-linear soil behaviour. The adequacy of this formula in the most common case of vertically
propagating S-waves has been checked against 2D numerical solutions by Spectral Elements (SE) for representative geological
cross-sections in Parkway Valley (New Zealand) and in the cities of Catania (Italy) and Thessaloniki (Greece). The shear strain
and the longitudinal strain variability with depth is also investigated, through some qualitative examples and comparisons
with analytical formulas.
KeywordsTransient ground strains-Earthquake ground motion-Buried structures-Numerical simulations

This paper describes a full-scale laboratory study of the axial sliding behaviour of a trenched pipeline surrounded by sand backfill. Cyclic axial displacements are applied to a heavy pipe buried in a narrow trench (less than three pipe diameters wide), using various backfill cover depths and two different soils: dry Hostun sand and a damp, silty sand. A novel testing tank is employed, with compressible foam seals to allow the pipe to settle as it moves axially, and a pressure bag system to simulate backfill depths exceeding the height of the tank. The test pipe is instrumented to measure: (a) the axial soil resistance developed on an isolated central section of pipe (thus avoiding tank boundary effects) and (b) the normal and shear contact stresses at a number of points around the pipe circumference. The results indicate that both the axial resistance and the normal stress distribution around the pipe can undergo considerable changes when a pipeline experiences cyclic axial displacements. An extreme case identified here is the potential for a compacted damp sand backfill to 'arch' completely over the pipe as a result of differential settlement, leading to unexpectedly low axial resistance. To address some limitations of the design method currently used in industry, a new approach for estimating axial resistance is suggested and applied to the present test data.

Buried pipelines are often constructed in seismic and other geohazard areas, where severe ground deformations may induce severe strains in the pipeline. Calculation of those strains is essential for assessing pipeline integrity, and therefore, the development of efficient models accounting for soil-pipe interaction is required. The present paper is aiming at developing efficient tools for calculating ground-induced deformation on buried pipelines, often triggered by earthquake action, in the form of fault rupture, liquefaction-induced lateral spreading, soil subsidence, or landslide. Soil-pipe interaction is investigated by using advanced numerical tools, which employ solid elements for the soil, shell elements for the pipe, and account for soil-pipe interaction, supported by large-scale experiments. Soil-pipe interaction in axial and transverse directions is evaluated first, using results from special-purpose experiments and finite element simulations. The comparison between experimental and numerical results offers valuable information on key material parameters, necessary for accurate simulation of soil-pipe interaction. Furthermore, reference is made to relevant provisions of design recommendations. Using the finite element models, calibrated from these experiments, pipeline performance at seismic-fault crossings is analyzed, emphasizing on soil-pipe interaction effects in the axial direction. The second part refers to full-scale experiments, performed on a unique testing device. These experiments are modeled with the finite element tools to verify their efficiency in simulating soil-pipe response under landslide or strike-slip fault movement. The large-scale experimental results compare very well with the numerical predictions, verifying the capability of the finite element models for accurate prediction of pipeline response under permanent earthquake-induced ground deformations.

The Donnell and Flugge forms of the stability equations of cylindrical shells are employed to analyze the axisymmetric, elastic quasi-static buckling of buried pipelines subject to seismic excitations. Using shell dimensions and the stiffness of the soil medium surrounding the pipe as parameters, a series of numerical results are obtained.

The objective of the discussion was to present a procedure for estimating the loading conditions used in design of underground excavations subjected to dynamic loading. In our discussion, a differentiation was made between underground structures that conform to the ground motion and others for which ground/structure interaction is an important consideration. Underground structures of the former type include unlined excavations and lined tunnels in relatively stiff soil or rock. Structures of the latter type include tunnels in soft rock and subaqueous tunnels.

Observations of pipeline behavior during earthquakes have been conducted by using buried pipelines at three different sites. The records indicate that the idea of wave propagation along a pipeline has little significance in explaining the pipeline behavior, and that the model of upwardly incident earthquake motion to the bottom of surface soil layer will be effective.

In this chapter, the main features of plastic buckling under axial compression are first illustrated experimentally. The formulation for predicting the onset of plastic wrinkling is then developed, followed by a study of how wrinkles grow, localize, and lead to collapse. Cylinders thick enough to undergo plastic compression experience a cascade of events eventually leading to failure that usually manifests as localized axisymmetric or nonaxisymmetric folding. At some strain levels in plastic regimes, cylinders develop uniform axisymmetric wrinkling. Under continued compression, the wrinkles grow stably, gradually reducing the axial rigidity of the structure. This reduction in axial rigidity eventually leads to limit-load instability. Beyond the limit load, deformation localizes. The limit load can therefore be designated as the limit state of the structure. Subsequent events can be usually tracked under displacement-controlled loading.

Records and analyses have shown that, apart from soil stratigraphy, the geomorphic conditions (such as those characterising an alluvial valley) tend to modify the amplitude, the frequency content, the duration, and the spatial variability of seismic ground shaking. As most of the related records and studies to date refer to weak motions (and thereby to linear soil response), the question that has been raised is whether and by how much the unavoidably nonlinear soil behaviour during strong shaking may reduce the unavoidable "valley amplification" effects. The paper aims at shedding some light on this important issue by analysing numerically the effects of the sub-surface geomorphic conditions of a valley on its ground surface seismic motion, with emphasis on the influence of soil nonlinearity. Two-dimensional linear and equivalent-linear ground response analyses are performed to study an alluvial valley in Japan, the behaviour of which had been monitored during many earthquakes in the early 1980's. Then, using the geometry of this valley as a basis, a parametric investigation is performed on the effects of potential soil nonlinearity arising from the increased intensity of base excitation and/or decreased "plasticity'" index* of the clayey soil material. It is shown that strong soil nonlinearity may depress the amplitude of the multiply-reflected and, especially of the horizontally propagating Rayleigh waves, leading to substantially lower valley amplification.

As part of various research projects [including the SRS (Savannah River
Site) Project AA891070, EPRI (Electric Power Research Institute)
Project 3302, and ROSRINE (Resolution of Site Response Issues from the
Northridge Earthquake) Project], numerous geotechnical sites were
drilled and sampled. Intact soil samples over a depth range of several
hundred meters were recovered from 20 of these sites. These soil samples
were tested in the laboratory at The University of Texas at Austin (UTA)
to characterize the materials dynamically. The presence of a database
accumulated from testing these intact specimens motivated a
re-evaluation of empirical curves employed in the state of practice. The
weaknesses of empirical curves reported in the literature were
identified and the necessity of developing an improved set of empirical
curves was recognized. This study focused on developing the empirical
framework that can be used to generate normalized modulus reduction and
material damping curves. This framework is composed of simple equations,
which incorporate the key parameters that control nonlinear soil
behavior. The data collected over the past decade at The University of
Texas at Austin are statistically analyzed using First-order,
Second-moment Bayesian Method (FSBM). The effects of various parameters
(such as confining pressure and soil plasticity) on dynamic soil
properties are evaluated and quantified within this framework. One of
the most important aspects of this study is estimating not only the mean
values of the empirical curves but also estimating the uncertainty
associated with these values. This study provides the opportunity to
handle uncertainty in the empirical estimates of dynamic soil properties
within the probabilistic seismic hazard analysis framework. A refinement
in site-specific probabilistic seismic hazard assessment is expected to
materialize in the near future by incorporating the results of this
study into state of practice.

Available experimental data on dynamic shear moduli and damping ratios of various soils including non-plastic sands to highly plastic clays are collected. Those are reanalyzed and brought into simple unified formulas. The unified formulas express the dynamic shear moduli and the damping ratios in terms of maximum dynamic shear modulus, cyclic shear strain amplitude, mean effective confining pressure and soil's plasticity index. Although the availability of experimental data on clay is still limited at this time, the formulas fit those data reasonably well and could be conveniently utilized in dynamic analyses such as seismic ground response and soil-structure interaction problems.

The performance of pipelines subjected to permanent strike–slip fault movement is investigated by combining detailed numerical simulations and closed-form solutions. First a closed-form solution for the force–displacement relationship of a buried pipeline subjected to tension is presented for pipelines of finite and infinite lengths. Subsequently the solution is used in the form of nonlinear springs at the two ends of the pipeline in a refined finite element model, allowing an efficient nonlinear analysis of the pipe–soil system at large strike–slip fault movements. The analysis accounts for large strains, inelastic material behavior of the pipeline and the surrounding soil, as well as contact and friction conditions on the soil–pipe interface. The numerical models consider infinite and finite length of the pipeline corresponding to various angles β between the pipeline axis and the normal to the fault plane. Using the proposed closed-form nonlinear force–displacement relationship for buried pipelines of finite and infinite length, axial strains are in excellent agreement with results obtained from detailed finite element models that employ beam elements and distributed springs along the pipeline length. Appropriate performance criteria of the steel pipeline are adopted and monitored throughout the analysis. It is shown that the end conditions of the pipeline have a significant influence on pipeline performance. For a strike–slip fault normal to the pipeline axis, local buckling occurs at relatively small fault displacements. As the angle between the fault normal and the pipeline axis increases, local buckling can be avoided due to longitudinal stretching, but the pipeline may fail due to excessive axial tensile strains or cross sectional flattening. Finally a simplified analytical model introduced elsewhere, is enhanced to account for end effects and illustrates the formation of local buckling for relative small values of crossing angle.

Some mistakenly believe that wave propagation damage to continuous buried pipe does not occur. Although not common, there have been situations in the past where it has occurred. Two such case histories are presented in the paper with the intension of clarifying the issue. The first case history is local buckling damage to 42 inch diameter welded steel water pipe occasioned by R-wave propagation in Mexico City during the 1985 Michoacan earthquake. In this case, the special circumstances which lead to the damage was the very low propagation velocity of the R-waves in the Lake Zone of Mexico City. The second case history is girth weld failures to a 12 inch diameter gas pipeline occasioned by S-wave propagation in Potrero Canyon during the 1994 Northridge earthquake. In this case, the special circumstances which lead to the damage was very strong ground shaking combined with what turned out to be very poor welds.

A quasi-bifurcation theory of dynamic buckling and a simple flow theory of plasticity are employed to analyze the axisymmetric, elastic-plastic buckling behavior of buried pipelines subject to seismic excitations. Using the seismic records of the 1971 San Fernando earthquake, a series of numerical results have been obtained, which show that, at strain rates prevalent in earthquakes, the dynamic buckling axial stress or strain of a buried pipe is only slightly higher than that of static buckling.

Over 61 years of earthquake performance of steel transmission and distribution supply pipelines operated by the Southern California Gas Company are reviewed The seismic record includes 11 major earthquakes with ML ≥ 5.8 and epicenters within the transmission system An evaluation is made of the most vulnerable types of piping, failure mechanisms, break statistics, threshold seismic intensity to cause failure, and damage induced by permanent ground displacement The database assembled represents one of the most comprehensive and detailed records of seismic response in a large, complex gas transmission system.

A study on the influence of the plasticity index (PI) on the cyclic stress-strain parameters of saturated soils needed for site-response evaluations and seismic microzonation is presented. Ready-to-use charts are included, showing the effect of PI on the location of the modulus reduction curve G/G(max) versus cyclic shear strain-gamma-c, and on the material damping ration gamma-versus-lambda-c curve. The charts are based on experimental data from 16 publications encompassing normally and overconsolidated clays (OCR = 1-15), as well as sands. It is shown that PI is the main factor controlling G/G(max) and lambda for a wide variety of soils; if for a given gamma-c PI increases, G/G(max) rises and lambda is reduced. Similar evidence is presented showing the influence of PI on the rate of modulus degradation with the number of cycles in normally consolidated clays. It is concluded that soils with higher plasticity tend to have a more linear cyclic stress-strain response at small strains and to degrade less at larger gamma-c than soils with a lower PI. Possible reasons for this behavior are discussed. A parametric study is presented showing the influence of the plasticity index on the seismic response of clay sites excited by the accelerations recorded on rock in Mexico City during the 1985 earthquake.

Predictive equations for estimating normalized shear modulus and material damping ratio of Quaternary, Tertiary and older, and residual/saprolite soils are presented in this paper. The equations are based on a modified hyperbolic model and a statistical analysis of existing Resonant Column and Torsional Shear test results for 122 specimens obtained from South Carolina, North Carolina, and Alabama. Variables used in the equations for normalized shear modulus are: shear-strain amplitude, confining stress, and plasticity index (PI). The equations for damping ratio are expressed in terms of a polynomial function of normalized shear modulus plus a minimum damping ratio. It is found that the Quaternary soils exhibit more linearity than soils of the other two groups. Also, it is found that the effect of PI on dynamic soil behavior is not as significant as previously thought. Data from all three groups exhibit significant variations with confining stress, similar to the variations determined by Stokoe et at. The uncertainties associated with the equations for PI of 0 and mean effective confining stress of 100 kPa are quantified using the point estimate method. A case study from Charleston, S.C. is provided to illustrate an application of the equations to seismic response analysis and the importance of considering confining stress and geologic age.

It is often useful in earthquake engineering practice to characterize the frequency content of an earthquake ground motion with a single parameter. Three simplified frequency content parameters are examined: mean period (T-m), predominant period (T-p), and the smoothed spectral predominant period (T-o). These frequency content parameters are calculated for 306 strong motion recordings from 20 earthquakes in active plate-margin regions. These data are used to develop a model that describes the magnitude, distance, and site dependence of these frequency content parameters, Nonlinear regression analyses are performed to evaluate model coefficients and standard error terms. The results indicate that the traditional T-p parameter has the largest uncertainty in its prediction, and that previous relationships proposed to predict T-p are inconsistent with the current data set. Moreover, T-m is judged to be the best simplified frequency content characterization parameter, and it can be reliably estimated.

Lifeline systems have been heavily damaged during past earthquakes; this has often been attributed to the effect of differential ground motion at the supports of these long structures. Based on a stochastic model for the ground excitation the responses of pipelines and bridges of various span lengths subjected to either perfectly or partially correlated random input motions in the axial, lateral (i.e. transverse horizontal) and vertical directions are investigated and the significance of the spatial variation of ground motion is examined.

During the 1999 Athens Earthquake the town of Adàmes, located on the eastern cliff of the Kifissos river canyon, experienced unexpectedly heavy damage. Despite the significant amplification potential of the slope geometry, topography effects cannot alone explain the uneven damage distribution within a 300 m zone behind the crest, characterized by a rather uniform structural quality. This paper illustrates the important role of soil stratigraphy, material heterogeneity, and soil–structure interaction on the characteristics of ground surface motion. For this purpose, we first perform elastic two-dimensional wave propagation analyses utilizing available geotechnical and
seismological data, and validate our results by comparison with aftershock recordings. We then conduct non-linear time-domain simulations that include spatial variability of soil properties and soil–structure interaction effects, to reveal their additive contribution in the topographic motion aggravation.

Remarkable concentration of damages to gas mains and services were observed at the South District of Shiogama Harbor during the 1978 Off Miyagi Earthquake. For the purpose of pointing out the relationship between the strain in buried pipeline and the ground structure, model experiments were carried out using scaled models of the above district -- two dimensional (sectional) model and three dimensional model. Two dimensional models for idealized ground structures were also tested. The influence of non-uniformity, e.g., abrupt change of the thickness of soft surface layer, was observed to be so great as to induce enough strain to cause the failure of pipeline. It was shown that the responses of both ground and pipeline in the case of two dimensional model were very similar to those in the case of three dimensional model. Numerical analyses using two dimensional finite-element models also showed good agreement with the experimental results.

This paper explores the sensitivity of 2D wave effects to crucial problem parameters, such as the frequency content of the base motion, its details, and soil nonlinearity. A numerical study is conducted, utilizing a shallow soft valley as a test case. It is shown that wave focusing effects near valley edges and surface waves generated at valley corners are responsible for substantial aggravation (AG) of the seismic motion. With high-frequency seismic excitation, 1D soil amplification is prevailing at the central part of the valley, while 2D phenomena are localized near the edges. For low-frequency seismic excitation, wave focusing effects are overshadowed by laterally propagating surface waves, leading to a shift in the location of maximum AG toward the valley center. If the response is elastic, the details of the seismic excitation do not seem to play any role on the focusing effects at valley edges, but make a substantial difference at the valley center, where surface waves are dominant. The increase of damping mainly affects the propagation of surface waves, reducing AG at the valley center, but does not appear to have any appreciable effect at the valley edges. Soil nonlinearity may modify the 2D valley response significantly. For idealized single-pulse seismic excitations, AG at the valley center is reduced with increasing nonlinearity. Quite remarkably, for real multicycle seismic excitations AG at the valley edges may increase with soil nonlinearity. In contrast to the vertical component of an incident seismic motion, which is largely the result of P waves and is usually of too high frequency to pose a serious threat to structures, the valley-generated parasitic vertical component could be detrimental to structures: being a direct result of 2D wave reflections/refractions, it is well correlated and with essentially the same dominant periods as the horizontal component.

Seismic response of underground pipelines is investigat́ed theoretically considering dynamic soil-pipe interaction. A lumped mass model of the pipe is employed with the soil reactions derived from static and dynamic continuum theories. The soil is supposed to be homogeneous or composed of two different media separated by a vertical boundary. Axial and bending stresses in the pipe due to travelling waves are examined.
An extensive parametric study indicates that the axial stresses in the pipe are much higher than bending stresses. In a homogeneous medium, soil-pipe interaction reduces the stresses in the pipe compared to those calculated ignoring interaction. In a soil composed of two different media, the pipe stresses are highest close to the boundary and can exceed those predicted neglecting interaction.

An analysis procedure for seismic wave propagation effects on straight continuous buried pipelines is proposed. It shown that ground strain due to surface waves can be substantially larger than that due to body waves. An elastic model a buried pipeline surrounded by equivalent soil springs indicates that frictional slip between the pipeline and the surrounding soil springs is likely for high ground strains.
A method for estimating ground strain due to surface waves, based on data from the 1971 San Fernando earthquake, reviewed. An analysis procedure, which utilizes frictional forces near the soil-pipeline interface, is proposed for surfae wave effects on straight buried continuous pipelines. The proposed procedure is illustrated with an example.

In order to study the damage patterns of natural gas and water pipelines in the Ji-Ji earthquake, a GIS database and analysis procedures were established. Repair statistics was obtained from major natural gas companies and the Taiwan Water Supply Corporation (TWSC), and entered into the system. Then, repair rates (RR) were calculated. Previously, damage was analyzed without considering the corresponding pipeline material and diameters. In this study, new attempts were made to collect more data including those related to the composition of pipelines to provide a more detailed analysis of the relationship between earthquake forces and the resulting damage. Statistical analysis was also conducted to understand the correlation between RR and seismic parameters such as the peak ground acceleration, peak ground velocity, and spectrum intensity.

The paper identifies and analyzes the so-called ‘beam’ and ‘shell’ modes of buckling of buried pipelines. Such failures have occurred as a result of compressive loads induced to pipelines by large ground movements in seismically active areas. In the beam mode of buckling, the pipeline tears through the ground and lifts off in a characteristic Ω configuration. The shell mode of buckling is a more localized failure characteristic of shell type structures. The two types of instability are simulated numerically using appropriate nonlinear kinematics, inelastic material behaviour and approximate modelling of the soil-structure interaction mechanisms. Parametric sensitivity studies are presented. It is demonstrated that initial geometric imperfections can strongly influence the critical loads and strains of both types of instability. Conditions under which the two modes of buckling interact are also discussed.

This study defines the basis for the aseismic design of subsurface excavations and underground structures. It includes a definition of the seismic environment and earthquake hazard, and a review of the analytical and empirical tools that are available to the designer concerned with the performance of underground structures subjected to seismic loads. Particular attention is devoted to development of simplified models that appear to be applicable in many practical cases.RésuméCettee´tude de´finit les bases pour la conception ase´ismique d'excavations et de structures sous-terre. On inclut une de´finition de l'environnement se´ismique et du risque de tremblement de terre, ainsi qu'une revue des techniques analytiques et empiriques qui sonta`la disposition du concepteur pre´occupe´de la performance des structures sous terre et soumisesa`des actions se´ismiques. Une attention particulie`re est donne´e au de´veloppement de mode`les simplifie´s qui semblenteˆtre applicables dans la plupart du temps.

The response and stability of long, relatively thick-walled metal tubes under combined bending and external pressure were studied through combined experimental and numerical efforts. The experiments involved stainless steel 304 tubes with nominal diameter to thickness ratios of 34.7 and 24.5. Curvature-pressure interaction collapse envelopes were generated for two different loading paths involving bending followed by pressure and pressure followed by bending. The tube response, the critical collapse loads and the nature of the instabilities observed were found to depend on the loading path. A suitable formulation of the problem based on the principle of virtual work was used to numerically simulate the experiments. The J2 flow rule of plasticity was used to model the inelastic material behavior. The analysis successfully reproduced the limit load type of instabilities which govern the problem in the range of diameter to thickness ratios of interest.

An analytical model for determining the differential ground motion during an earthquake is developed. The ground motion is assumed to be a stationary random process, resulting from waves radiated from an underground source (fracture surface). The source motion is also modeled as a random process specified by a power spectral density. The spectral density of the ground motion is related to that of the source by a frequency transfer function. An analytical method for two-dimensional wave propagation is used to evaluate the displacements at the ground surface, from which the frequency transfer function is obtained through system identification. Power spectral densities of acceleration, crosscorrelation and spatial variation coefficients, as well as power spectral densities of differential acceleration obtained through the model are compared with data from an actual earthquake, the earthquake of January 29, 1981, recorded at Lotung, Taiwan. The comparison indicates that the results of the model are in good agreement with the earthquake data. Dynamic analyses of lifelines are also performed. The seismic input to the structures is considered to be either fully or partially correlated, and the results of the analytical stochastic ground motion model are used. The effect of the spatial variation of ground motions on the damage and reliability of horizontal systems is evaluated. National Science Foundation Grants INT 82-19528 and CEE 82-13729

Simulation of the response of the marina district Basin

- B Zhang
- A S Papageorgiou

Zhang B, Papageorgiou AS. Simulation of the response of the marina district Basin,
San Francisco, California, to the 1989 Loma Prieta earthquake. Bull Seismol Soc Am
1996;86:1382-400.

Northridge earthquake of

- J F Hall
- W T Holmes
- P Somers
- Eer Institute

Hall JF, Holmes WT, Somers P, Institute EER. Northridge earthquake of January 17,
1994: reconnaissance report. Earthquake Engineering Research Institute; 1996.

Response of buried pipelines subject to earthquake effects

- M J O'rourke
- X Liu

O'Rourke MJ, Liu X. Response of buried pipelines subject to earthquake effects.
1999.