Research Article
Determination of Seismic Load on Subsea Offshore Pipelines
Muravieva Ludmila Victorovna
Corresponding Author: Muravieva Ludmila Victorovna, Doctor of Engineering Science, Assistant of Yuri Gagarin State Technical University of Saratov, National Research Polytechnic University
Received: December 16, 2019; Accepted: January 06, 2020 Available Online: January 16, 2020
Citation: Victorovna ML. (2020) Determination of Seismic Load on Subsea Offshore Pipelines. J Agric Forest Meteorol Res, 3(6): 424-426.
Copyrights: ©2020 Victorovna ML. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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Buried pipeline to surrounding ground interaction is a vital factor that has an impact on the safe operation of the buried underground pipelines. Numerous earthquake research works describe above ground acceleration obtained in a single point which does not give full information about ground deformation. This article suggests using seismic loading calculation method for the buried offshore pipelines. The article contains formulas to evaluate the buried pipeline fatigue value.

Dynamic behaviors of underground pipe lines during earthquakes remain unknown, while the structures in weak ground have suffered damages from large earthquakes. From the seismic point of view, the problems lie in the fact that the dynamic behaviors’ of the structures have little relations to ground acceleration, but to ground deformation and in the fact that such structures have two dimensional extension along the surface of ground. As many investigations of the earthquake engineering treated ground acceleration such as the one at a point, they give little information’s for ground deformation or distribution of ground displacement along the surface. The article proposes a formula for determining the seismic load of a buried offshore pipeline.

The pipelines are generally recognized as a safe, economic and effective mean for gas and other commercial fluid transportation. Buried pipeline to surrounding ground interaction is a vital factor that has an impact on the safe operation of the buried underground pipelines. Buried pipeline behavior remains unknown during earthquakes. Pipeline needs to be buried in order to ensure its operational reliability and safety and minimize potential damages due to external and internal exposures.

This article is dedicated to seismic load calculation methods for the subsea offshore pipelines during earthquakes. Dynamic pipeline behavior is related to ground acceleration and ground deformation. It should be taken in to consideration that the pipelines are exposed to two-dimensional deformations along the ground surface. The earthquake research reports review the above ground acceleration obtained in a single point. Accelerograms provide incomplete information about the ground deformations and ground displacements along the earth surface. Among the proposed earthquake protection methods is increase pipe wall thickness, increase steel grade, protect pipes with textile covers.


Keywords: Subsea offshore pipeline, Seismic loading, Fatigue


Simulation model of the subsea buried pipeline is represented as a cylindrical beam rigidly fixed at the ends. Weight of water above the buried pipeline is considered as additionally added mass [1-4].

It is mentioned in the papers of the Japanese researchers, Sakurai and Takahashi [1] that bending stresses acting on the large diameter pipelines are comparable with the axial stresses. When ground surface moves according to the law Y=a0×sin (p(t-x/V)), bending strain of the pipeline can be determined by the following equation:

ε = r0 / v. A                                 (1)

where r0 is pipe radius, is observable seismic wave velocity, A is seismic acceleration.


Axial strain of the pipeline is prevailing [1]. Axial strain to bending strain ratio of the pipeline can be written as follows [1].

ε = - a. p / v cos (t – x / V)      (2)

where p is circular frequency of ground movement (equal to 2 π / T   );  a0  is  ground  surface  movement  amplitude; V  is


seismic wave velocity.


Let us express the earth surface acceleration:

A = - a0∙p2 sin (– V)                          (3)

where T is ground surface motion cycle.


Maximum pipelines train is expressed in the equation below:

ε =  a0 p / V a0 . p2 . A = 1 / 2 π T.A / V                    (4) 

The equation (4) is confirmed by the pipeline strain records represented in the research papers [1].

Earthquake causes relative axial displacement of the pipeline. Strain value can be calculated using the following equation:

AT4π2=u0 {1 + 1/ (p/ω0)2+ (V/ V)2 }= u0           (5)

where u0 is ultimate ground strength; Va is longitudinal wave velocity spreading in the pipeline (√(E/ρ)   

The pipeline is exposed to friction forces over its entire length during earthquake. Straight pipeline strains are equal to its relative displacement:

εu C0 . L / 4EA0 = C0 .vT / 4EA0                               (6)

where C0 is friction force acting per unit of pipe length.

Axial pipeline vibrations can be expressed via the following equation during movement within u<u0 range:

ρA0  (∂2 y / ∂) - EA0  (∂2 y)/(∂x2 ) + ky k∙a0  sin (t-x/v)                    (7)

The equation (7) can be solved as follows:

(x,t) = 1 / 1+ (ρ/ω0 ) 2 (V0/V) 2 - (ρ/ω0 )2 )∙ Y (x,t)      (8)

Natural pipeline frequencies depend on the density of liquid to be transported via the pipeline. Medium contained side the pipeline creates an additional weight on the pipeline system. It has a downward effect on the dynamic properties of the pipeline [5].

Stress level and allowable deformations of the pipeline walls are evaluated during subsea pipeline seismic strength analysis.

It is important to know natural frequencies of the structure to calculate is MIC loads and avoid a resonance effect.



Natural frequencies of the subsea gas pipeline fixed at both ends are calculated using the following equation:

ωn = √a12  λn2 + b2                                                        (12) 

where a = EF / m ; b = πDkx / m , k

linear proportionality factor between shear stresses ðœ , in the surrounding ground ðœ = k x (xt).



Inertia seismic load acting on the buried pipeline is calculated as follows:

S * ik = kA A. gm k η * ik β ε (ω k *). ðœ x                        (20)

where is a factor that considers possibility of a seismic event with in the design service life of the structure; g is gravitational acceleration (9.81 m/s2); N*ik = Xik


is mode factor; are natural frequency modes of the pipeline (beam functions); tx are shear stresses; А is design acceleration amplitude of the foundation expressed as fractions is calculated using table of the SP [6].

When we calculate inertia of seismic load, we should take into account a factor that is dependent on the damage which can be caused during earthquake; seismic wave directional angle towards the structure Cos( Ui , Ü âƒ—); a factor that takes into account damping properties of the structure [6].

Due to in sufficient information about their life and non-available country-wise classification of these is MIC data, seismic load on the buried pipelines shall be calculated more precisely using a spectral method as per the following procedure:

1.       Select the most loaded sections for subsequent strain-stress state analysis of the pipeline.

2.       Plot frequency response characteristics to calculate deformations in the selected locations ei(w) (taking into consideration damping properties of the ground), where w is excitation seismic frequency, w0 is natural frequency of the pipeline [7].

Frequency response characteristic is represented below:
|Φ(iω)|2=1/((ω0 (l)22 )2+(2(ξst+ ξgr⋅ ω0 (l)ω)2 )         

3.     Spectral strain density in i-th point is calculated as follows:

Sεi (ω) = εi2 (ω)SI (ω)                                                      (21) 


where is design spectral density of the spectral earthquake force I [4] (Annex 8).

 4.     Strain dispersion in i-th point,


Dεi = ∫0∞ Sεi  (ωdω                                                   (22)


5.     The required design strain is calculated as follows:

εip = √(Dεi                                     (23)


6.     Subsea pipeline dynamic response factor equals to:

βε (ωk) = ω0k2 √(Dε / D)     

Subsea pipeline service life is 50 years; however seismic events do not occur as scheduled. Operating modes and corrosion damages affect the service life of the pipeline.

Subsea pipeline cannot be seen by the observers. Variation of the transported fluid pressures and low cycle loading of the pipeline may initiate structural defects [8].

Seismic damage is non-local, it affects the whole structure. Taking in to account low-cycle loading, significant plastic strain observed in the circular welds of the pipelines, it is necessary to evaluate the fatigue cracking start in the pipeline during the seismic analysis of the subsea pipeline. Fatigue characteristics of the offshore subsea pipelines have not been studied. Structural life calculation method described in the article is based on the structural stress spectrum analysis.



Fatigue failures are associated with the stress cycle band:

δ= δn / = δ/ (Aσr-m ) = n (σr / (4m0exp [- (σr2 ⁄ (8m0)]δσr) / (Aσr-m) )                     (24)

where n is a number of stress cycles; misnegative slope of the stress-number curve S-N; sr is stress range (difference between maximum and minimum stress per cycle); А is stress-number fatigue factor of steel.


Fatigue failures for all stress cycle bands are expressed in the following way:

D = ∫0∞ (n(σr  ⁄ (4m0)) exp [-((σr2) ⁄ (8m0 ))] δσr)/(Aσr-m)                 (25)

where А is stress-number fatigue factor of steel.



The article describes seismic load calculation method for the subsea offshore pipelines, fatigue calculation ratios of the buried underground pipelines; a conclusion has been made to perform fatigue tests of the buried pipelines.

1.       Sakurai A, Takahashi T (1967) Dynamic stresses of underground pipe lines during earthquakes, Tokyo, Technical Laboratory 15.

2.       American Lifelines Alliance (ALA) (2001) Buried steel pipes (Guidelines for the design of buried steel pipe). Federal Emergency Management Agency (FEMA), American Society of Civil Engineers (ASCE) and Federal Emergency Management Agency (FEMA) 83.

3.       Muravieva LV (2015) Development of requirements for seismic resistance of steel offshore underwater pipelines with damages.

4.       Russian Maritime Register (2017) Rules for the classification and construction of subsea pipelines. Saint-Petersburg Russian maritime register, pp: 164.

5.       Napetvaridze SHG, Gekhman АS (1980) Seismic resistance of main pipelines and special structures of the oil and gas industry. Мoscow, Nauka Publication, p: 172.

6.       SR14.13330 (2014) Set of rules. Seismic Building Design Code, Moscow. Federal'noe agentstvo po tekhnicheskomu regulirovaniyu i metrologii, p: 88.

7.       SR 36.13330 (2012) Set of rules. Trunk pipelines, Moscow. Federal'noe agentstvo po tekhnicheskomu regulirovaniyu I metrologii, p: 130.

8.       Chopra AK (2001) Dynamics of structures, theory and applications to earthquake engineering. Berkley, Prentice-Hall Inc., p: 450.