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SOIL-PIPE-INTERACTION PHENOMENA ON SLOPES UNDER

ASYNCHRONOUS EARTHQUAKE EXCITATION

Athanasios A. MARKOU1, Amir M. KAYNIA2, Anastastios G. SEXTOS3, George D. MANOLIS4

ABSTRACT

The present work focuses on the response of pipelines traversing slopes under asynchronous

acceleration time histories induced by earthquakes. To this end, nonlinear generalized mechanical

models are developed and used in order to describe the soil-pipe interaction phenomena. More

specifically, two basic types of models are used: the first one comprises two elastoplastic generalized

spring elements connected in parallel with a trilinear elastic spring (labeled as sub-models 1 and 3),

while the second model comprises three elastoplastic elements, all connected in parallel (labeled as

sub-models 2 and 4). The purpose of the current study is twofold; (a) to introduce nonlinear

mechanical models that enable a smooth transition between the elastic and plastic phases while, at the

same time, control the damping in the soil-pipe interaction, and (b) to investigate the effect of the soil

strength and soil damping on the axial force that develops in pipelines on slopes. Results are presented

for the case of a real pipeline subjected to asynchronous accelerations along a submarine slope.

Keywords: soil-pipe interaction; mechanical models; offshore pipeline; nonlinear analysis; asynchronous

motion.

1. INTRODUCTION

Water, gas and oil pipelines have become important parts of a lifeline system. In the offshore sector,

for example, the recent decades have witnessed a marked development in submarine pipelines

associated with the production and distribution of oil and gas as a major energy source for the

economic development of numerous countries around the world. Earthquake is considered a major

threat to this lifeline in certain regions. The performance of pipelines under earthquake excitations has

been studied in the last three decades (ASCE 1984, ASCE 2001). The damage sustained by pipelines

subjected to earthquake excitation were attributed to permanent ground deformation in the direction

normal to the pipeline route, for example due to landslides, and high soil strains due to seismic wave

propagation along the pipeline (O'Rourke and Liu 1999).

Papadopoulos et al. (2017) studied the damages to a natural gas pipeline due to seismic wave

propagation. More specifically, the authors examined the effect of asynchronous excitation due to the

basin effect on the response of an underground pipeline, and they concluded that the stress distribution

along the pipeline is affected by the wave passage effect particularly in inhomogeneous soil media.

Kaynia et al. (2014) investigated the response of pipelines on submarine slopes under asynchronous

earthquake accelerations along the pipeline. Their study accounted for soil-pipe interaction (SPI) by

1Postdoctoral Researcher, Norwegian Geotechnical Institute, Oslo, Norway, athanasiosmarkou@gmail.com

2Technical Expert, Vibrations and Earthquake Engineering, Norwegian Geotechnical Institute, Oslo, Norway,

amir.m.kaynia@ngi.no

3Reader in Earthquake Engineering, Department of Civil Engineering, University of Bristol, Bristol, UK,

a.sextos@bristol.ac.uk

4Professor, Department of Civil Engineering, Aristotle University, Thessaloniki, Greece, gdm@civil.auth.gr

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means of soil springs, which traditionally are taken linear to the peak shear strength and strain-

softening post-peak strength. The current research aims at extending that study for the case of

nonlinear soil-pipe interaction by introducing nonlinear mechanical models that are capable of

capturing the smooth transition between elastic and plastic phases of nonlinear response (e.g. Markou

and Kaynia 2018; Markou and Manolis 2016a; 2016b) and are able to control soil damping within

acceptable limits as observed in cyclic soil tests. Finally, a model of a real offshore pipeline subjected

to asynchronous accelerations along a submarine slope (Kaynia et al 2014) is employed to investigate

the effect on the axial pipe force during soil-pipeline interaction as a function of soil strength and

damping.

2. NUMERICAL SIMULATION OF SOIL-PIPE INTERACTION

In this section, a computational model is developed for the response of a continuous pipeline lying on

or embedded in the ground while subjected to asynchronous ground motions along its length. The

analysis does not account for the material carried by the pipeline, gravity loads or thermomechanical

effects arising from the difference in temperature between the pipeline and the surrounding water. The

pipeline itself is modelled as a generalized beam element.

2.1 Computational model for pipeline

An idealization of a pipeline of arbitrary geometry lying on the ground and supported by lateral and

axial springs representing the SPI is shown in Figure 1 (Smith and Kaynia 2015). The pipeline is

excited under asynchronous earthquake motions in two directions on the X-Z plane. The actual

geometry of the pipeline for a real offshore pipeline is shown in Figure 2, along with the nodes used to

define its structure. Figure 3 shows an example of the asynchronous ground acceleration time histories

used in the present study at nodes 19 and 49 (see Figure 2). The horizontal and vertical motions along

the entire set of pipeline nodes were computed from a 2D FE dynamic nonlinear analysis of the soil

accounting for soil stratification and surface topography (Kaynia et al., 2014). It should be noted that

self-weight of the pipe is applied statically before any earthquake excitation, to take into consideration

initial soil conditions. The SPI phenomena are described by means of generalized nonlinear

mechanical models, which are discussed in the following section.

Figure 1. Soil-pipe interaction model under asynchronous earthquake excitation

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Figure 2. Longitudinal pipeline profile in X-Z plane.

Figure 3. Horizontal acceleration histories at nodes (a) 19 and (b) 49.

2.2 Nonlinear mechanical modeling of SPI

In 2017, Stubbs studied the SPI behavior of buried pipelines in shallow depths by implementing

laboratory experiments, see Figure 4 (Stubbs 2017, Crewe, 2018). As it is shown in Figure 5, the SPI

curves show a smooth transition from linear phase to the plastic one. Usually in most applications this

nonlinear transition is simulated by a linear function. However, in the present study, the form of the

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SPI curve is preserved. To this end, two different nonlinear mechanical models are developed and

used to account for SPI. The first generalized model, labeled as sub-models 1 and 3, is presented in

Figure 6. It consists of three elements connected in parallel, namely two elastoplastic elements

(elements 1 and 2) and a trilinear elastic spring (element 3). The second generalized model, denoted as

sub-models 2 and 4, comprises three elastoplastic elements connected in parallel, see Figure 7. Both

models are able to describe the smooth transition from the linear to plastic phase observed in the

aforementioned model tests. Additionally, model 2 is able to control the damping in the soil springs to

acceptable limits around 30% for large displacement amplitudes (e.g. Vucetic and Dobry 1991), while

model 1 provides a larger damping ratio, of the order of 60% for large displacement amplitudes. It

should be noted that the lateral soil springs in Figure 1 are assumed to obey a linear elastic constitutive

law.

a)

b)

Figure 4: Photographs of experimental setup, (a) during filling of a preliminary loose experiment (b) the load

transfer mechanism with load cell (photos taken by R. C. Stubbs, used with permission).

Figure 5. Force-horizontal displacement curve for loose sand at different depths, where D denotes the diameter

of the pipe (Stubbs 2017).

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Figure 6. Generalized mechanical models labeled 1 and 3 to account for SPI: (a) mechanical formulation with

the force-displacement loops for (b) sub-element 1, (c) sub-element 2 and (d) sub-element 3.

Figure 7. Generalized mechanical models labeled 2 and 4 to account for SPI: (a) mechanical formulation with

the force-displacement loops for (b) sub-element 1, (c) sub-element 2 and (d) sub-element 3.

The material parameters of the axial soil springs of sub-models 1 and 3 considered in the present study

are given in Table 1. It should be noted that these parameters are presented in values (force and

stiffness) per length and that sub-models 2 and 4 dissipate two times the amount of energy compared

to sub-models 1 and 3, respectively. In Table 2 the material parameters of the pipeline are

summarized.

The force per length against displacement amplitudes for sub-models 1-4 are presented in Figure 8. As

it was mentioned previously, the different energy dissipation ability of the models is clearly

demonstrated, while the same loading path is provided in all cases. Furthermore, the difference

between sub-models 1 and 3, shown in Figures 8(a) and (c), and sub-models 2 and 4, shown in Figures

8(b) and (d), is the reduction of the order of 50% of the damping ratio. The difference between sub-

models 3 and 4 and sub-models 1 and 2 is in their shear strength. More specifically, the shear strength

in sub-models 3 and 4 are half of those in sub-models 1 and 2.

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Table 1. Material parameters per unit length of the four models.

Sub-model 1

Sub-model 3

Q1(kN/m)

0.52

Q1(kN/m)

0.28

Q2(kN/m)

1.03

Q2(kN/m)

0.56

Q1s(kN/m)

1.55

Q1s(kN/m)

0.84

k01(kN/m2)

199.80

k01(kN/m2)

199.80

k02(kN/m2)

199.80

k02(kN/m2)

199.80

k01s(kN/m2)

166.50

k01s(kN/m2)

89.91

Table 2. Material parameters of the pipeline.

EI (kNm2)

EA (kN)

m (tn/m)

2.51 104

4.15 106

0.217

Figure 8. Force per length-displacement loops of (a) sub-model 1, (b) sub-model 2, (c) sub-model 3 and (d) sub-

model 4 for SPI.

In reference to the above, the differential equation of motion of the model can be described as follows

(Equation 1):

[M]{Ü(t)} + [F(t)] = -[M]{Üg} (1)

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where [M] is the mass matrix, {Ü(t)} is the acceleration array, {Üg} is the vector of the earthquake-

induced acceleration array and [F(t)] can be defined as follows (Equation 2):

[F(t)] = [K]{U(t)}+{FN(t)} (2)

where [K] is the stiffness matrix of the system, {U(t)} is the displacement array and {FN(t)} is the

array of the nonlinear forces. The above system was solved by using the Newmark constant

acceleration method (e.g. Chopra 2012).

3. NUMERICAL RESULTS

3.1 Maximum axial forces simulated by different SPI models

In this section, the results of maximum axial forces over the length of the pipeline are presented for the

four models. The envelope of the maximum axial force is presented for the case of tension, as well for

compression, along with the pipeline profile. More specifically, Figure 9(a) presents the axial forces

using sub-models 1 and 2. As expected, the largest forces occur at areas of largest changes in the

topography such as the escarpment (node 19 in Figure 2). The plots in Figure 9 show identical forces

indicating that for the case considered here, and possibly for similar cases, hysteretic damping in the

SPI springs has negligible effect on the pipe forces. This observation could imply that the response of

the pipeline on the slope is not dominated by the pipe dynamics. Figure 10 plots the axial forces using

sub-model 3, while Figure 11 displays the axial force for sub-model 4.

Figure 9. (a) Maximum axial force along the pipeline using models 1 and 2 and (b) longitudinal pipeline profile

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Figure 10. Maximum axial force along the pipeline using model 3.

Figure 11. Maximum axial force along the pipeline using model 4.

In all cases, the maximum values of the axial forces in terms of both tension and compression occurs

at the edge of the escarpment. In all numerical modeling scenarios, the tension force is larger than the

compression force apart from model 4, where the opposite is true.

3.2 Comparison of results for different SPI models

In this subsection, a comparison between the four models in terms of axial forces is presented. More

specifically, the results in Figure 12 display that the maximum tension and compression is provided by

the models with the highest strength (sub-models 1 and 2). On the other hand, the lowest value of the

maximum tension and compression is provided by the model with increased damping ratio and

reduced strength. The results show that the maximum earthquake-induced forces are reduced as the

shear strength of the soil is reduced. This behavior is expected as reduced soil strength can be viewed

as providing a kind of base isolation for the pipeline against earthquake motions along the slope.

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Finally, in Figure 13 the reference acceleration records are increased over 30% and the results are

compared for the case of sub-model 1. Despite the fact that the increase of the acceleration records is

of the order of 30%, the increase of the maximum tension and compression forces is not more than

20%. The results show that the relation between acceleration and axial force is not linearly

proportional, due to the nonlinear nature of the problem.

Figure 12. (a) Maximum axial force along the pipeline using models 1, 3, 4 and (b) longitudinal pipeline profile.

Figure 13. (a) Maximum axial force along the pipeline using model 1 under reference and increased over 30%

acceleration (b) longitudinal pipeline profile.

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4. CONCLUSIONS

A sensitivity analysis on the effect of the soil damping ratio and stiffness of the combined soil-pipeline

mechanical system on the maximum axial force that develops in a submarine pipeline under

seismically-induced ground motions is presented in here. To this end, two nonlinear generalized

models are introduced in order to provide smooth transition between the elastic and plastic phases of

response and in order to control the energy dissipation over a cycle of loading. The results indicated

that reduction in the soil stiffness and damping ratio of the order of 50% produced a significant

variation in the maximum axial force developed under asynchronous earthquake excitation. Both

tension and compression forces play a significant role in the design of the pipelines. To this end, the

parameters of the SPI system, namely soil strength and damping ratio, should be chosen carefully in

order to produce a successful design in terms of safety and performance.

5. ACKNOWLEDGMENTS

This work was supported by the Horizon 2020 MSCA-RISE-2015 project No. 691213 entitled

"Experimental Computational Hybrid Assessment of Natural Gas Pipelines Exposed to Seismic Risk

(EXCHANGE-RISK)". This support is gratefully acknowledged.

6. REFERENCES

ASCE (1984). Guidelines for the Seismic Design of Oil and Gas Pipeline Systems, Committee on Gas and

Liquid Fuel Lifelines, American Society of Civil Engineers Publication, Reston Virginia.

ASCE (2001). Guidelines for the Design of Buried Steel Pipe, American Lifelines Alliance, American Society of

Civil Engineers Publication, Reston Virginia.

Chopra AK (2012). Dynamics of Structures, Theory and Applications to Earthquake Engineering, 4th edition,

Prentice Hall, Boston.

Crewe, A., Sextos, A., Stubbs, R., Mylonakis, G. (2018). Experimental Identification of Stiffness and Ultimate

Resistance Of Buried Soil-Pipe Systems, 16th European Conference in Earthquake Engineering, Thessaloniki

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Kaynia AM, Dimmock P, Senders M (2014). Earthquake Response of Pipelines on Submarine Slopes. Offshore

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