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

INTRODUCTION

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 / v² . 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 = - a₀ . p / v cos p (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 p (t – x / V)                          (3)

where T is ground surface motion cycle.

AXIAL DISPLACEMENT OF THE PIPELINE

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:

AT² / 4π²=u₀ {1 + 1/ (p/ω₀)²+ (V_a / V)² }= u₀           (5)

where u₀ is ultimate ground strength; V_a 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:

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

The equation (7) can be solved as follows:

y (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 BURIED GAS PIPELINE

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

ω_n = √a₁²  λ_n² + b²                                                        (12) 

where a_T  = EF / m ; b²  = πD_H k_x / m , k_x 

linear proportionality factor between shear stresses 𝜏 _x , in the surrounding ground 𝜏 _x = k _x u (x, t).

MODEL OF INERTIA SEISMIC LOAD FOR BURIED PIPELINE

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

S * _ik = k_A A. gm _k η * _ik β _ε (ω _k *). 𝜏 _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 = X_ik

is mode factor; are natural frequency modes of the pipeline (beam functions); t_x are shear stresses; А is design acceleration amplitude of the foundation expressed as fractions is calculated using table of the SP [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 e_i(w) (taking into consideration damping properties of the ground), where w is excitation seismic frequency, w₀ is natural frequency of the pipeline [7].

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.