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SLOPE FAILURE VERIFICATION OF BURIED STEEL PIPELINES

Charis J. Gantes1, George D. Bouckovalas2, Vlasis K. Koumousis3

ABSTRACT. A methodology for the evaluation of the effects of down-slope ground movements, induced by seismic activity, on buried pipelines made of steel, is presented. The basic assumptions, computational tools, numerical analysis options, pertinent code provisions and required checks are outlined. Representative results of the proposed methodology, as applied for the “Crude Oil Pipeline from Thessaloniki to Skopje”, are presented. INTRODUCTION A methodology for the evaluation of the effects of eventual down-slope ground movements, induced by seismic activity, on buried pipelines made of steel, is presented and applied for the design of the “Crude Oil Pipeline from Thessaloniki to Skopje”. Such ground movements induce straining of the pipeline in a different way than usual design limit states, and thus require special treatment, combining geological investigations, geotechnical evaluation to identify critical sites and compute direction and magnitude of anticipated movements, sophisticated numerical analysis to obtain pipeline strains, checks by means of appropriate failure criteria, and engineering judgment to propose suitable countermeasures. In the proposed approach, the pipeline is modelled with either beam or shell elements, and the soil with appropriate nonlinear springs in all directions, accounting for soil-pipeline interaction. Geometrically and material nonlinear analyses are carried out, accounting for large displacements, and adopting a nonlinear material law for the pipeline steel, and an elastic-perfectly plastic law for the soil. The suitability of beam elements with respect to shell elements is addressed. The selection of an appropriate pipeline length to be included in the model is investigated. The effects of the predominant direction of down-slope displacement with respect to the pipeline axis are discussed. Appropriate failure criteria are proposed in terms of allowable maximum strains. Finally, alternative countermeasures for critical sites, where the anticipated displacements exceed the allowable limits, are proposed and evaluated. 1 Associate Professor, School of Civil Engineering, National Technical University of Athens, Athens, Greece, e-mail: chgantes@central.ntua.gr 2 Professor, School of Civil Engineering, National Technical University of Athens, Athens, Greece, e-mail: gbouk@central.ntua.gr 3 Professor, School of Civil Engineering, National Technical University of Athens, Athens, Greece, e-mail: vkoum@central.ntua.gr

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PIPELINE DESIGN DATA The basic pipeline characteristics, which are required for the purposes of such a study, concern the pipeline geometry and cross-section, the operating internal pressure, as well as the constitutive law of the pipeline material. Cross-Section Characteristics Circular hollow cross-sections are used, denoted as NPS D, where NPS stands for Nominal Pipe Size and the number D denotes the outside diameter measured in inches. The wall thickness varies along the length of the pipeline, usually between a normal wall thickness, which is predominantly employed, and a heavy wall thickness, intended for use in areas where externally applied loads are extreme. At the locations of interest for the specific application presented in this paper, NPS 16 pipes with a wall thickness of 7.14 mm are used. Material Properties Pipes are usually made of steel with Young’s modulus equal to 210000 MPa and Poisson’s ratio equal to 0.30. The material behaviour is linear up to a stress level known as Specified Minimum Yield Strength (SMYS). The stress-strain law is usually approximated with a tri-linear curve, as shown in Fig. 1. The von Mises yield criterion, together with a kinematic hardening rule, is used to define yield. Pipe welds are either long-seam or spiral. For the specific application presented in this paper, pipes are made of API-5LX60 steel with SMYS equal to 413.685 MPa (58.82 ksi).

Figure 1. Typical pipeline steel stress-strain curve

Pressures and Temperatures The design pressures and temperatures follow the specifications issued by the manufacturer, according to the guidelines of pertinent codes. For the specific application presented in this paper, ANSI/ASME B31.4 is adopted, specifying design pressure of 10.2 MPa, maximum design temperature (above ground) equal to +38oC, and minimum design temperature (underground) equal to -10oC.

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Construction Techniques A general conformance to recognized codes of practice for construction, transportation, storing, placement, and backfilling of pipes is required. The nominal backfill cover is different for cross-country areas, rocky areas and under major roads. In all cases presented here a backfill cover of 0.90 m, intended for cross-country areas, is applied. FAILURE CRITERIA The code normally used for structural design of pipelines is ANSI/ASME B31.4 on Pipeline Transportation Systems for Liquid Hydrocarbons and Other Liquids. This code addresses essentially only straining of the pipeline due to pressure containment. For lifelines operating in extreme environment, such as areas of high seismic activity, post-elastic straining of the pipe material is likely and additional criteria are required [ASCE 1984, ASCE-ALA 2005]. Stresses and strains in buried pipelines may be classified as either load-controlled or displacement-controlled. In the present case of eventual down-slope ground movements caused by earthquake-induced slope failure, the loading is displacement-controlled, so that an upper strain limit has to be specified. During a seismic event the loading is exerted on a buried pipe by the displacement of the surrounding soil, and since the pipe is relatively flexible compared to the soil, the resulting action effects are such that it is more meaningful to specify failure in terms of strains than of stresses. Taking further into account that most pipelines are flexible relative to the surrounding soil, it is realized that they resist externally applied deformations mainly through axial (tensile or compressive) strains. Maximum allowable tensile strain The allowable tensile strain specified for buried pipelines by the European Seismic Code EC-8 (ENV 1998-3) is 5%, corresponding to an axial tensile stress, which is 25% higher than the SMYS of API-5LX60 steel. However, this limit is not acceptable for girth welds due to metallurgical alterations induced to the heat-affected zone of steel during the welding process. In general, the allowable tensile strain for butt (peripheral) welding can be conservatively taken as 0.5%, based on previous experience from similar projects in Greece and abroad. Pipe welds are either long-seam or spiral. With long-seam pipes, it may be possible to orient the seam so that it is not located at a position of high circumferential strain, thereby utilizing the tensile strain capacity of the plain pipe. When dealing with spirally welded pipes, however, the hoop strain always has a component perpendicular to the seam. Assuming a minimum value of 45o for the angle between the seam and the longitudinal axis of the pipe, the allowable tensile hoop strain for such pipes is modified by dividing it by 0.707, and becomes 0.5%/0.707=0.707%. In our case, long seam welding of the pipes is assumed; therefore, a total allowable strain of 0.5% is considered. Maximum allowable compressive strain Two modes of buckling failure are possible for a pipeline under extreme compressive actions. The pipeline may break free of the backfill cover and buckle upward as a beam in a global buckling mode, or it may buckle as a shell with local wrinkling of its wall in a local buckling mode. Wrinkling may be critical whenever the surrounding soil and the backfill cover provide sufficient confinement to prevent upward displacement. Thus, the strain limits, which are usually set by the industry, are stringent to prevent mainly local wrinkling. In general,

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resistance to the formation of elastic-plastic instability in a pipe is characterized by the SMYS of the pipe material, the shape of the stress-strain curve, and by the outside diameter (D) to thickness (t) ratio of the pipe. In simple terms, the first two factors are overlooked, and the limiting compressive strain for the formation of a buckle is given by

tD0035.084.0(%)e c* −= (1)

which equals 0.64% for an NPS 16 x 8.74 mm pipe, thus constituting a less strict criterion than the limiting tensile strain. Alternatively, based on the provisions of EC-8 (ENV 1998-3) for buried pipelines, the limiting compressive strain for the formation of buckles is defined as:

%5Dt40(%)e c,all <= (2)

For the pipeline dimensions relevant to the present case study, this expression gives an allowable compressive strain equal to 0.70%. Using the most unfavourable of these two values, the maximum allowable compressive strain has been considered equal to 0.64%. Load and Performance Factors It is common practice in pipeline design to set all load and material factors equal to 1.0. This is due to tight quality control on materials, strict limits on applied pressure enforced through pressure control devices, the displacement-controlled nature of ultimate limit states, and the less severe than average consequences of failure of cross-country pipelines, that are due to proper operational, monitoring, and maintenance procedures. DOWN-SLOPE GROUND DISPLACEMENTS Identification of Problem Sites The sites along the pipeline with potential slope stability problems are identified, based on data provided in the relevant geological and geotechnical reports. The basic information listed for each site includes its approximate extent, the natural ground water conditions, and the factors of safety computed from a static slope stability analysis (e.g. based on the Bishop method of slices) for dry as well as for wet soil conditions. For selected critical sites of the application presented here, this information is listed in Table 1. It is observed that all sites remain dry under natural hydro-geological conditions, with the ground water level met deeper than 10-15m from the ground surface. Thus, the event of partial or complete saturation of these slopes is rather extreme, as it may only be encountered during lasting periods of heavy rainfalls or at the wet period following snow melting. Furthermore, these slopes appear as sufficiently stable under static loads and dry conditions, with factors of safety higher than 2.03. Potential saturation has a critical effect on stability as it reduces the factors of safety drastically, to as low as 1.11. Hence, preventing complete saturation of the slopes is crucial, to avoid failure not only during earthquake activity, but also under normal (earthquake-quiet) conditions. Taking the acceptable factor of safety under static conditions as equal to 1.50 under dry conditions, and 1.20 under wet conditions, the application of appropriate measures (surface or deep drainage trenches, vegetation, etc.) is necessary for at least three sites, namely SK992, SK1171 and SK1200.

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Table 1: Description of sites with slope stability problems along the pipeline route Extent along the pipeline

route Static

factor of safety Site From To

Geological conditions

Natural ground water

conditions Dry Wet

992 991+030 992+050 As above, with a 2m cover of

debris and low plasticity, brownish silty clay

Dry 2.03 1.19

1013 1012+180 1013+000 4-7 m of upper pleistocene deposits resting on top of pliocene lake sediments

Dry 2.21 1.23

1171 1171+370 1173+00 Pliocene deposits of conglomerates, sands and silts Dry 2.11 1.18

1173 1173+000 1173+180 Pliocene deposits of conglomerates, sands and silts Dry 2.29 1.26

1200 1199a+000 1202+00 Talus, blocks of limestones and diabases within a silty matrix Dry 2.19 1.11

Calculation of Anticipated Displacements: Assumptions Methodology During earthquakes, static loads are increased due to seismic actions in the horizontal and the vertical directions, representing the inertia of the soil mass. Under the combined action of static and seismic loads, the slope may fail leading to down-slope ground displacements along the failure surface. For the geotechnical conditions of the slopes in Table 1, earthquake–induced slope instabilities are far less ominous, compared to a static failure, since the induced amount of displacement is generally limited. This is because failure, and the associated ground displacements, last for a very limited period of time (fractions of a second), only as long as the ground acceleration exceeds a critical acceleration ay, i.e. the horizontal acceleration that is required in order to reduce the pseudo-static factor of safety of the slope to 1.00. However, note that this may not be the case in the presence of saturated, cohesionless (e.g. sand and silt) soil layers, which liquefy due to earthquake shaking and lead to a post-shaking landslide. According to Newmark (1965), a reasonable upper bound to the down-slope ground displacements triggered by earthquakes, in absence of soil liquefaction, is given by the following relation:

y

max

y

2max

aa

aV

21δ = (3)

where amax and Vmax are the horizontal peak ground acceleration and velocity, respectively. The input data used for the computation of down-slope ground displacements are summarized in Tables 2 and 3 for two seismic events, the Design Probable (DPE) and the Design Maximum (DME) earthquakes, with 70 and 1000 years return period, respectively.

Table 2: Summary of input data for down-slope ground movement computations - DPE amax (g) Vmax (cm/sec) Dry conditions Wet conditions Site bedrock Aa ground bedrock Av ground ay (g) ay (g)

992 0.17 1.00 0.17 8.5 1.00 8.5 0.41 0.075 1013 0.17 1.60 0.26 8.4 1.65 13.8 0.27 0.06 1171 0.22 1.00 0.22 11.1 1.00 11.1 0.26 0.04 1173 0.22 1.00 0.22 11.1 1.00 11.1 0.29 0.065 1200 0.22 1.60 0.35 11.4 1.65 18.7 0.29 0.03

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Table 3: Summary of input data for down-slope ground movement computations – DME amax (g) Vmax (cm/sec) Dry conditions Wet conditions Site bedrock Aa ground bedrock Av ground ay (g) ay (g)

992 0.36 1.00 0.36 20.6 1.00 20.6 0.41 0.075 1013 0.35 1.60 0.56 21.1 1.65 34.8 0.27 0.06 1171 0.45 1.00 0.45 28.2 1.00 28.2 0.26 0.04 1173 0.45 1.00 0.45 28.2 1.00 28.2 0.29 0.065 1200 0.45 1.60 0.74 28.2 1.65 46.5 0.29 0.03

Peak Seismic Motion Parameters The peak seismic motion parameters for the different sites were computed from the corresponding values at the seismic bedrock of the pipeline route (Bouckovalas and Kavouklis, 2000) and the local geological conditions listed in Table 1. It was assumed that the peak seismic motion parameters varied, from ab

max and Vbmax at the seismic bedrock to

agmax=Aa·ab

max and Vgmax=Av·Vb

max at the ground surface (Aa, AV are soil amplification factors). To take into account that the potential failure surface extends to considerable depth within the soil cover (and may reach the underlying bedrock), down-slope ground movements were computed for the average of the bedrock and the ground surface motion parameters, i.e.

bmax

Vmax

bmax

amax V

2)A1(

V,a2

)A1(a

+=

+= (4)

Alternatively, the peak seismic motion parameters at ground surface could have been reduced to 2/3 or 1/2 (e.g. Kramer 1996). However, this approach is suitable rather for high and flexible embankments than for the natural slopes examined herein. The criteria set in the above mentioned report for soil effects on seismic ground motion parameters are as follows:

Table 4: Criteria for soil effects on seismic ground motion parameters

Bedrock Shallow Soil Deep Soil H<5m 5m<H<15m 15m<H<35m H>35m

Aa 1.00 1.60 1.25 1.00 Av 1.00 1.65 1.40 1.40

According to these criteria soil amplification of the seismic motion (Aa and Av > 1.00) was conservatively taken into account only for sites SK1013 and SK1200, where the ground surface is covered by recent soil deposits (pleistocene and talus formations) with a depth greater than about 5m. For the rest of the sites, it was assumed that As=Av=1.0. Critical Seismic Acceleration In brief, the slope stability analyses assume: (a) A downslope pointing horizontal acceleration ah and an upward pointing vertical acceleration av=0.5ah. Preliminary analyses have shown that this combination is less favourable as compared to the one with downward pointing vertical acceleration. (b) Failure surfaces that include the pipeline cross section (for slope gradients perpendicular to the pipeline axis) or major portions of its length (for slope gradients parallel to the pipeline axis). (c) Dry as well as fully saturated ground conditions. For each case of slope and groundwater conditions, the pseudo-static analyses were repeated for different values of ah and the results were presented as Factor of Safety (FS) versus horizontal acceleration diagram. The value of ay was consequently computed graphically for FS=1.0.

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Calculation of Anticipated Displacements: Results Computed down-slope ground movements for the DPE and the DME seismic events are summarized in Table 5, together with the possible extent of the affected length of pipeline axis and the direction of the ground movement relative to the pipeline axis, defined in terms of the directional angle ω (Fig. 2). It is observed that the largest ground displacements correspond to the DME seismic event combined with complete saturation of the slopes. In gross terms, displacements are reduced by an order of magnitude if the DPE is considered instead of the DME or if dry conditions are considered instead of wet.

Figure 2: Definition of directional angle ω

Table 5: Summary of computed down-slope ground displacements

Extent along the pipeline

route

Computed down-slope ground movement – DPE

(cm)

Computed down-slope ground

movement - DME (cm) Site

From To

Position of pipeline axis relative to the

maximum slope gradient (2) Dry Wet Dry Wet

992 991+030 992+050 Perpendicular (70-75o) 0 1 0 14

1013 1012+180 1013+000 Parallel (40 o) 0 4 5 96 1171 1171+370 1173+00 Parallel (30o) 0 9 3 114

1173 1173+000 1173+180 Perpendicular (90o) 0 3 2 43

1200 1199a+000 1202+00 Perpendicular (80-90o) 0 70 10 >150

The sites may be divided in two different groups, with reference to the direction of ground displacement relative to the pipeline axis: (a) The group of “perpendicular” displacements, where the direction of maximum slope gradient forms an angle ω>45ο with the pipeline axis (sites SK992, 1173 and 1200). In this case, the pipeline will primarily undergo lateral deflection of its axis line. (b) The group of “parallel” displacements, where the direction of maximum slope gradient forms an angle ω<45ο with the pipeline axis (sites SK1013 and 1171). In this case, the pipeline will primarily undergo tension at the upper part of the slope and compression at the lower part. Among the sites of the first group, SK1200 is clearly the most critical as it undergoes the largest down-slope displacements, under any seismic and groundwater conditions. Among the sites of the second group, both SK1013 and SK1172 undergo significant ground displacements. At both sites the pipeline axis is inclined relative to the direction of maximum

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slope gradient and consequently ground deformations will have two components: one longitudinal and one transverse. Due to the combined action of these components, phenomena of local instability may develop at the lower part of the pipeline well before the SMYS is reached. This event is more likely for site SK1013 where the directional angle ω, and consequently the percentage of transverse displacement, is larger. Therefore, numerical analyses have been carried out for sites SK1013 and 1200, taken as representative for “parallel” and “perpendicular” patterns of down-slope ground displacements. Nevertheless, due to length limitations, details are presented here only for the former site, which combines appreciable ground movements along as well as perpendicular to the pipeline axis.

STRESS ANALYSIS METHODOLOGY AND ASSUMPTIONS Pipeline Modeling The geometrically and material non-linear analysis is performed using an appropriate FEM code. Geometric non-linearity is treated by satisfying the equilibrium equations in the current deformed configuration. The inelastic behavior of the pipe material is considered by hybrid modeling, namely with 4-node isoparametric shell elements within the area of expected slope failure, in order to capture stress concentrations in a more accurate way, with 2-node isoparametric 3-D beam elements outside the area of expected slope failure, where a gradual reduction of stresses is expected, and with one rigid element at each interface of shell elements with a beam element, coupling the beam and the shell sub-models (shown schematically with radial lines in Fig. 3).

Figure 3: Coupling of the beam and shell part of the numerical model with a rigid element

Analyses can also be carried out with a pure 3-D beam model of the pipeline, in order to have a preliminary, still realistic, estimate of the pipeline response before advancing to the considerably more cumbersome hybrid modeling. In addition, the results of the beam model analysis are used in order to identify areas of higher stresses, which are then modeled with shell elements in the hybrid beam-shell model. Along the beam part of the pipeline, the 3-D beam elements must have sufficient number of control points along the perimeter of the pipe to account for the inelastic behavior. Stresses are computed at these points of all cross-sections, accounting for the contributions of axial forces and bending moments. The soil is modeled by 4 sets of inelastic springs in the axial and the two transverse directions (Fig. 4), with two different sets of vertical springs, one in the upwards and one in the downwards direction. The ground movement is modeled as an imposed displacement on the base nodes of all attached springs.

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Figure 4: Transverse soil springs in the beam part of the structural model (axial springs are

not shown for clarity purposes)

In the shell part of the pipeline, 16 elements are used along the periphery of each cross-section, while springs are attached in each of the X, Y, and Z directions at all nodes (Fig. 5). The properties of the transverse springs depend on the projected area of the cross-section in the corresponding direction.

X

Y

Z

Figure 5: Transverse soil springs (a) in a typical cross-section of the shell part of the structural

model (Y-Z plane), (b) 3-D view In the shell model, internal pressure is modeled as a uniformly distributed load on the internal face of all shell elements. Thus, a more accurate representation of the actual situation is achieved in comparison to a pure beam element model, where the cross-sectional behavior of the pipe under internal pressure can only be considered separately and consequently superimposed to the strains and stresses caused by ground movement. Equivalent Soil Springs In general, the pipeline is fully embedded into loose cohesionless backfill. Hence, it is assumed that the pipeline will deform entirely within this uniform material and consequently soil springs will be correlated to the properties of the backfill and not of the natural soil. The constitutive relations of the soil springs are considered bi-linear elastoplastic, although it turns out that, except from the vertical downward springs, the main parameter is the ultimate soil resistance, i.e. the soil springs behave essentially as “stick-slip” elements. The theory behind the computation of soil spring characteristics is briefly outlined in the following paragraphs. The presentation focuses upon cohesionless materials (sands) such as the backfill soil commonly used along pipeline routes. Axial Springs Axial spring restraint forces represent the skin friction on the cylindrical surface along the pipe. They are developed from similar theories as for the load transfer at axially loaded pile-soil interfaces. For sands and other cohesionless soils (e.g. gravel), they are obtained by integrating the shear stress along the area of contact between pipe and soil. Therefore, for a fully buried pipeline the ultimate axial resistance tu per unit length can be expressed as:

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δtan)K1(Hγ2Dπt ou +⋅⋅⋅

= (5)

where Ko is the coefficient of soil pressure at rest, H is the depth from the ground surface to the center of the pipeline, D is the external pipe diameter, γ is the effective unit weight of soil, and δ is the angle of friction between pipe and soil. An average value of δ equal to 2/3 of the backfill friction angle φ is used. The ultimate axial resistance is first attained at relative displacement xu of the order of 2.5 to 5.0 mm, for dense to loose sand, respectively [Singhal, 1980]. The value used for the present study is conservatively taken as the mean of this range, i.e. 38 mm. Transverse Horizontal Springs These springs simulate the resistance of the surrounding soils to any horizontal translation of the pipeline. Thus, the mechanisms of soil-pipeline interaction are similar to those of vertical anchor plates or footings moving horizontally relative to the surrounding soils, and thus mobilizing a passive type of earth pressure. For cohesionless soils, the relationship between the force per unit length of the pipe (p) and the horizontal displacement (y), has been expressed by a hyperbolic relationship of the form [Trautmann and O’Rourke,1983a]:

yBAyp⋅+

= (6)

where A=0.15yu/pu, B=0.85/pu, pu=γ·H·Nqh·D, Nqh is the horizontal bearing capacity factor [Hansen 1961], and yu=0.07 to 0.10(H+D/2) for loose sand, while yu=0.02 to 0.03(H+D/2) for dense sand. In the case of a bi-linear elastoplastic representation of the spring response fitted to Eq. (6) at p=0.5pu the previous values of yu must be reduced by a factor of 0.26. Taking further into account the mean value recommended for loose sands, the displacement at first yield finally becomes yu=0.022(H+D/2). Transverse Vertical Springs The resistance forces for the vertical springs are different for downward and upward movements, as the resistance applied from the relatively thin layer of soil above the pipe is significantly smaller. For the downward direction of motion, the pipeline is assumed to act as a cylindrically-shaped strip footing and the ultimate soil resistance qu is given by conventional bearing capacity theory. For cohesionless soils:

γ2

qu NDγ5.0DNHγq ⋅⋅⋅+⋅⋅⋅= (7) where Nq, Nγ are bearing capacity factors for horizontal strip footings, vertically loaded in the downward direction, given by Meyerhof (1955) as a function of φ. For fully buried pipelines and a bi-linear elastoplastic load-displacement relation, the displacement at first yield is zu,dn=0.10D÷0.15D), for dense to loose sands, respectively. In this study, the computations are carried out with the upper limit of that range, corresponding to loose sand backfill. For upward motions, based on tests performed with pipes that are buried in dry uniform sand, the relationship between the force q and the vertical upward displacement z, has been shown to vary according to the following hyperbolic relation [Trautmann and O’Rourke 1983b]:

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zBAzq⋅+

= (8)

where A=0.07zu/qu and B=0.93/qu. For cohesionless soils, the ultimate uplift resistance is expressed as [Trautmann and O’Rourke, 1983b]:

DNHγq qvu ⋅⋅⋅= (9) where the vertical uplift factor Nqv is a function of the depth to diameter ratio H/D and the angle φ. Based on field tests [Esquivel-Diaz, 1967, Trautman and O’Rourke 1983a], the value of uplift displacement at first yield is zu,up=(0.010÷0.015)H, for dense to loose sands, respectively. However, when a bi-linear elastoplastic expression is fitted to Eq. (8) at q=0.50qu, zu,up must be reduced by a factor of 0.13. Taking further into account the upper limit of the above range, corresponding to loose sand backfill, the uplift displacement at first yield used in this study becomes zu,up=0.002H. STRESS ANALYSIS AT SITE SK1013 Geomorphology Conditions Based on the available drawings, as well as the earthquake–induced ground displacements computed above it is concluded that: (a) In the case of extreme seismic activity (DME), landslide displacements for the specific site are of the order of 5 to 96 cm for dry and wet soil conditions, respectively. (b) Ground displacements will develop parallel to the maximum downslope gradient, i.e. at a directional angle ω=40o relative to the pipeline axis. (c) The pipeline length that is going to be affected by the landslide extends to an approximate length of 80m, as deduced from the relevant slope stability analyses. (d) Ground displacements are considered uniform, based on the common assumption that the soil mass will slide along the failure surface as a rigid block. Furthermore, displacements are taken as parallel to the sloping ground surface, acknowledging that the failure surface is relatively shallow. The pipeline verification in this region is performed with the aid of three different numerical models: a beam model, a hybrid beam-shell model without internal pressure and a hybrid beam-shell model with internal pressure. Beam Model A possible landslide in the area of bent SK 1013 is considered and its effects on strains and stresses along the pipeline are investigated. A total length of 517.5 m of the pipeline is modeled that accommodates the imposed displacements due to the landslide around the middle of the entire pipeline segment (Fig. 6 left). The axis of the pipeline is formed by a series of line segments and circular arcs, according to the recording plan and longitudinal section drawings of the pipeline. The pipeline is modeled using 3D beam elements and the surrounding soil using springs along the x-y-z directions. Nodes are spaced at 0.25 m along the pipeline. For the entire pipeline, 1562 nodes are used connecting 1561 beam elements. In addition, there are 6248 (4 x 1562) springs along the x, y, z upward and z downward directions. For the entire model, including the pipeline and the soil springs, 7805 elements are considered and 7806 nodes. The total number of active degrees of freedom for this model is 4686.

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Figure 6. Pipeline geometry and imposed translation on pertinent spring base nodes

The landslide movement is modeled as a uniform translation imposed to the base nodes of the spring elements extended along the down-slope part of the pipeline route, with a length of approximately 80m. The direction of the landslide movement, with respect to the x-z plane, coincides with the slope of the ground in the landslide area and has both a horizontal and a vertical component. The imposed translations are shown in Figure 6 (right) as vectors in red.

The stress analysis is performed imposing a total landslide translation of 140 cm in a number of steps following a Newton-Raphson iteration method. The value of 140 cm was selected following a number of trial analyses to identify the value of imposed translation that causes failure. The critical failure mode was found to be the development of axial tensile strain equal to 0.5%. In Figure 7 (left), the total translation of pipeline nodes in the landslide zone is presented. The red line corresponds to the undeformed and the blue line to the deformed pipeline configuration. In Figure 7 (right), the evolution of the total translation of the pipeline projected along the X global axis is presented for four characteristic time steps corresponding to 25%, 50%, 75% and 100% of the total imposed displacements. The effect of the soil-structure interaction, expressed mostly via the plastification of soil springs, results in reduced and smoothed pipeline translation values as compared to the imposed ground movement.

Figure 7. Total translation of the pipeline in the landslide zone

In Figure 8 the stresses of axial soil springs along the pipeline are shown. The constant stress regions near the landslide indicate full soil plastification, while the zero stress regions confirm the pipeline length considered in the numerical model is sufficient to be able to neglect boundary effects.

Figure 8. Stresses of axial soil springs along the pipeline

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In Figure 9, the evolution of the total strain (sum of axial normal strain and bending normal strain) at two characteristic points, 1 (left) and 2 (right), on the outer horizontal diameter and upper vertical one, respectively, is presented. The different curves correspond to 25%, 50%, 75%, and 92.5% of the total imposed translation. The peaks A, B, C correspond to geometric irregularities and changing curvature of the pipeline route near the top of the landslide, while the peaks D, E, F correspond to similar irregularities near its toe. Tensile strains reaching the 5‰ limit are observed at point 2 for imposed displacement equal to 0.925 x 1.40 m = 1.30 m.

Figure 9. Evolution of total strain at points 1 (left) and 2 (right)

Beam – Shell Hybrid Model In order to have a more accurate representation of pipeline strains and to account for the effects of internal pressure a beam-shell model is also used. A part of the pipeline in and around the landslide area, where strains and stresses obtained from the beam model analysis were found to be high, is modeled with shell elements for a length of 110 m. The remaining part of the pipeline is modeled with beam elements (Figure 10). In total, the number of elements is equal to 34862 and the number of nodes is equal to 34878. The total number of degrees of freedom of the model is 209268 and the active degrees of freedom are 52644.

Figure 10. Pipeline model with shell elements and part of the beam elements

Based on the results of the beam model analysis, and expecting that the more exact representation by shell elements in the critical region will activate increased redundancy, so that the allowable strain of 0.5% will be reached at larger imposed displacements, this analysis was carried out for imposed displacements of 1.80 m. In Figure 11, an overall view and a detail of the undeformed and deformed shapes of the hybrid model for imposed translation of 1.80 m are shown. No major differences in relation to the beam model are observed. In Figure 12, details of the major strains and stresses at the inner face of the shell, at the toe of the landslide, for imposed displacements of 1.80 m are presented. Zones in red color indicate areas where yielding has occurred. For the case with internal pressure 10.2 MPa the landslide movement is modeled in the same manner. No significant differences in the results are observed. The 0.5% strain is reached at approximately 1.44 m of imposed displacement.

A

C D

E

B

F

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Figure 11. Total pipeline translation and detail for imposed soil translation of 1.80 m

Figure 12. Major strains (left) and stresses (right) at the bottom of the landslide (1.80m)

CONCLUDING REMARKS The slope verification of buried steel pipelines examined herein is typical of a wide category of soil-structure interaction problems, where a multidisciplinary cooperation of experts is required, in geotechnical and structural engineering, as well as in numerical analysis methods. Similar problems include the verification of buried pipelines at active fault crossings and at areas where large ground movements are anticipated due to earthquake-induced liquefaction and lateral spreading. For the case analyzed in the paper, it is deduced that: (a) Wet soil conditions are far more critical than dry ones and should be always considered in

practice, even for cases of low water table, in order to take into account possible seasonal changes during periods of heavy rain falls or snow melting.

(b) The most likely mode of failure is yielding in tension, both at the head and at the toe of the slope. Nevertheless, different modes of failure should be expected for cases of curved pipeline segments and thinner wall sections where local instabilities (e.g. buckling or section ovalization) control the pipeline response.

(c) The beam and hybrid shell-beam models capture equally well the yielding mode of failure, with the former providing slightly more conservative estimates for the maximum strains. However, larger differences should be expected for the more complex modes of failure mentioned in (b) above, which cannot be predicted with the beam model.

(d) The allowable maximum downslope displacement is estimated as 144cm, i.e. in excess of the maximum anticipated slope displacements of 5cm and 96cm, computed for dry and wet soil conditions, respectively. Main factors that may reduce these safety margins in practice include the existence of field bends or the relative increase of the component of ground displacement which is perpendicular to the pipeline axis. For instance, numerical computations for site SK1200 (Tablew 2, 3 & 5), not shown here due to length limitations, show that the allowable displacement for the same pipeline running perpendicular to the maximum slope gradient is reduced to only 56cm.

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ACKNOWLEDGEMENTS Sincere appreciation is due to C&M Engineering Ltd. for providing the means, the necessary data and, most importantly, the opportunity to perform the study described above. The assistance in the numerical analyses of Dr. Christos Dimou, Dr. George Kouretzis and Dr. Minas Lemonis is also gratefully acknowledged. REFERENCES ASME/ANSI, B31.4-1992 Edition, “Pipeline Transportation Systems for liquid Hydrocarbons

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