5. Main directions of development of pipeline strength standards

Taking into account parts 1–3, the perspective directions of calculation and experimental analysis of the strength of pipelines in the deterministic interpretation should include:

• Direct quantitative accounting of the degradation and aging in time of tube steels at various temperatures t and the number of cycles N, leading to a change in the basic design characteristics—the yield strength and strength :

$$\left| \sigma\_{\mathbf{y}}(\tau, t, \sigma, e, N), \sigma\_{\mathbf{u}}(\tau, t, \sigma, e, N) \right\rangle = \left| \sigma\_{\mathbf{y}}, \sigma\_{\mathbf{u}} \right\rangle \cdot F\_c \left\langle \tau, t, \sigma, e, N \right\rangle,\tag{6}$$

where and —kinetically varying yield and strength limits for a given time τ, temperature t, stress , and deformation e; —generalized functionals describing the change in the basic mechanical properties under the influence of temperature t, time τ, stress σ, cyclic N, and deformation e factors at all stages of the life cycle of the pipeline.

The functional Fсf g τ; t; σ;e; N with its parameters τ, t, σ, e, and N essentially reflects the processes of degradation and aging of pipeline steels in the process of sheet and pipe manufacturing, their transportation, construction, testing, and exploitation of pipelines.

Despite of a huge number of studies in factory laboratories; scientific institutes; design, construction, and operation organizations; and powerful industry research centers, in Russia and abroad, it has not yet been possible to obtain and justify this functional Fc with the appropriate statistical and probabilistic equations and parameters. The prerequisites for the formation of a system of initial equations for the functional Fc are presented in [4, 8, 11, 13, 14].

Currently, knowledge on the processes of aging and degradation in time τ of carbonaceous and low-alloy steels is reduced to the following basic provisions (Figure 5):


In all cases of aging (curves 1–4), the ratio of the yield strengths σ<sup>y</sup> to the tensile strengths σ<sup>и</sup> increases (due to a smaller change in the tensile strength σ<sup>и</sup> as compared to the yield point σy).

In the normative strength calculations [10], it is suggested not to take into account the areas of increase in the yield strength σyð Þ τ; t;е; σ; N due to aging, which goes to the margin of safety. In the refined basic and normative calculations of the strength of pipelines, one should take into account [4–9, 14–16]:

Figure 5. Scheme of aging processes of pipe steels.

• Mechanical properties (including limits and ) of structural pipe steels in the process of pipeline transportation, construction, and operation of pipelines are assumed to be

• Strength margins in Eq. (1) and margins and in Eqs. (2), (4), and (5) are accepted

• Degradation of pipes and pipelines is associated mainly with a decrease in wall thickness

• The crucial part in material consumption reduction is in the increase in nominal operating stresses , yield strength , and strength and reduction of margins and

The normative approach has an important development element in comparison with [2, 13] in it, the strength and durability evaluation is carried out not only by nominal stresses

but also by local deformations in the concentration zones created by structural, technological, and operational factors (welds, defects, corrosion). This makes the normative calculation of the strength of pipelines comply with both the modern deformation criteria [6, 7] and

Taking into account parts 1–3, the perspective directions of calculation and experimental

• Direct quantitative accounting of the degradation and aging in time of tube steels at various temperatures t and the number of cycles N, leading to a change in the basic design

where and —kinetically varying yield and strength limits for a given time τ, temperature t, stress , and deformation e; —generalized functionals describing the change in the basic mechanical properties under the influence of temperature t, time τ, stress σ, cyclic N, and deformation e factors at all stages of the life cycle

The functional Fсf g τ; t; σ;e; N with its parameters τ, t, σ, e, and N essentially reflects the processes of degradation and aging of pipeline steels in the process of sheet and pipe manufacturing, their transportation, construction, testing, and exploitation of pipelines.

Despite of a huge number of studies in factory laboratories; scientific institutes; design, construction, and operation organizations; and powerful industry research centers, in Russia and

ð6Þ

the norms in nuclear power engineering and rocket and space technology [9–11].

5. Main directions of development of pipeline strength standards

analysis of the strength of pipelines in the deterministic interpretation should include:

characteristics—the yield strength and strength :

unchanged.

90 Probabilistic Modeling in System Engineering

of the pipeline.

according to the Eq. (1).

unchanged for all stages of the life cycle .

due to corrosion (general and local) and erosion.


In accordance with the above, based on Eqs. (2)–(5), and taking into account Figures 2–5

$$m\_y = \frac{\sigma\_y(\tau, t, \sigma, e, N)}{\sigma\_{\text{max}}^s},\tag{7}$$

determining the nominal maximum operating stresses σ<sup>s</sup>

10–30%.

where σ<sup>s</sup>

Since σ<sup>s</sup>

max<sup>к</sup> > σ<sup>s</sup>

tration in the zone of cracks.

observations of the actual processes of metal loss while in the operation due to these mechanisms, the rate of corrosion and erosion reduction of the wall thickness dδ=dτ can be from 0.05– 0.1 to 0.3 mm/year. With wall thicknesses from 10 to 30 mm, the decrease of margins can reach

Thus, the aging of tubular steels and the degradation of pipes can, in the course of operation, with unfavorable combinations of all the abovementioned damaging factors lead to a substantial reduction in determined margins ny and n<sup>и</sup> and breach of strength as shown by Eqs. (1), (7), and (8). The number of such cases in real operation [3–5, 14] in the period of 1970–2015

A special place in the analysis of the pipeline strength is and will be occupied by the problems of their crack resistance and survivability, when formation and development of cracks of technological and operational origin are observed [3–6, 13–19]. In calculating the strength of pipelines with cracks of depth ℓ in thickness and length a over the surface, equations and criteria for linear and nonlinear fracture mechanics are used [3–7, 12, 13]. Then, the local stressstrain state at the crack tip is determined from the solution of the boundary value problem by

max<sup>к</sup> and deformations е<sup>s</sup>

<sup>K</sup>σ<sup>ℓ</sup> <sup>¼</sup> <sup>F</sup><sup>ℓ</sup>f g <sup>D</sup>; <sup>σ</sup>; <sup>ℓ</sup>; <sup>a</sup>; <sup>S</sup><sup>∗</sup> , (10)

� �=Fkf g <sup>D</sup>; <sup>δ</sup>; <sup>ℓ</sup>; <sup>S</sup>∗; <sup>a</sup> : (11)

<sup>n</sup>max—maximum rated stress in Eq. (1); and Kσ<sup>ℓ</sup>—effective coefficient of stress concen-

<sup>n</sup>max and Fkf g <sup>D</sup>; <sup>δ</sup>; <sup>ℓ</sup>; <sup>a</sup> <sup>≥</sup> 1, then safety margins from Eq. (7) for pipes with cracks

where <sup>F</sup><sup>ℓ</sup>f g <sup>D</sup>; <sup>σ</sup>; <sup>ℓ</sup>; <sup>a</sup>; <sup>S</sup><sup>∗</sup> —function of pipe geometry <sup>ð</sup>D, <sup>δ</sup>) and cracks (ℓ, <sup>а</sup>); and <sup>S</sup>∗—the structural parameter of the material, determined experimentally when testing samples with cracks.

In general, all the parameters of Eqs. (9)–(11) are deterministic, statistical, and probabilistic.

In calculating the strength of pipelines with defects, two basic estimated defect sizes are introduced: • ℓ<sup>о</sup> – Initial size (depth) of the defect, determined by the accepted methods of flaw detec-

maxк:

<sup>n</sup>max � Kσ<sup>ℓ</sup>, (9)

gradually decreased from 1.2–1.0 to 0.12–0.14 damages per 1000 km per year.

6. Analysis of resistance to the development of cracks

σs maxk;е s maxk � � <sup>¼</sup> <sup>σ</sup><sup>s</sup>

numerical methods with defining of stresses σ<sup>s</sup>

The value Kσ<sup>ℓ</sup> is determined on samples with cracks:

taking into account Eq. (9) will be further reduced (Figure 6):

<sup>ℓ</sup>;ð Þ n<sup>и</sup> <sup>ℓ</sup> n o <sup>¼</sup> ny; <sup>n</sup><sup>и</sup>

ny � �

tion (with their resolving power, sensitivity)

<sup>n</sup>max. As shown by laboratory tests and

http://dx.doi.org/10.5772/intechopen.75078

93

Probabilistic Analysis of Transportation Systems for Oil and Natural Gas

$$
\sigma\_y/n\_u = \sigma\_y(\tau, t, \sigma, e, N) / \sigma\_u(\tau, t, \sigma, e, N). \tag{8}
$$

Equations (7) and (8) mean that the safety margins ny and n<sup>и</sup> are dependent on the aging and degradation processes of the tubular steels, time-dependent τ, temperature t, the cyclicity N, and the stress-strain state σ – е. This circumstance, which was not explicitly reflected in domestic [1, 2] and foreign [11, 12] regulatory materials, is to be taken into account in promising developments of pipe strength standards.

In [2–5], an experimental analysis was made of the time-dependent change in the characteristics of the mechanical properties of tube steels, primarily the yield strength σ<sup>y</sup> and strength σ<sup>y</sup> from the tensile tests of samples cut from the pipes in the initial state and after prolonged use. The time <sup>τ</sup> was varied from <sup>τ</sup> ffi <sup>5</sup> � <sup>10</sup>�<sup>2</sup> to 3 � 105 <sup>h</sup>, operating temperature from �45 to +50�C, stress <sup>σ</sup> from 0.6 <sup>σ</sup><sup>y</sup> to 1.0 <sup>σ</sup>y, and deformation <sup>e</sup> from 0.8 � <sup>10</sup>�<sup>3</sup> to 3 � <sup>10</sup>�<sup>3</sup> .

The averaged data from these tests showed that the reduction of the yield strength <sup>σ</sup>yð Þ <sup>τ</sup>; <sup>t</sup>;е; <sup>σ</sup>; <sup>N</sup> during exploitation from the initial <sup>τ</sup><sup>0</sup> to the maximum of <sup>τ</sup> = 2, 3�105 h was 10– 15% of the yield strength σy: Meanwhile, the ratio of the yield strengths to the tensile strengths increased by 1.15–1.2. This means that the margin ny of the yield strength σ<sup>y</sup> can be reduced by 1.1–1.17 times, and the margin n<sup>и</sup> of the ultimate strength σ<sup>и</sup> by 1.20–1.25 times. This corresponds to the generalized statistical experimental data from Transneft, obtained during tests of laboratory samples from actually operated pipes.

However, it should be borne in mind that the bulk of pipeline damage is associated with the most severe damage of surface layers of pipes (due to corrosion, erosion, mechanical impacts). In the standard tensile testing of samples (with surface layers removed during their manufacture), this type of damage has little effect on the strength characteristics σ<sup>y</sup> and σи. For the experimental evaluation of the effect of surface damages, other tests are carried out. For example, cyclic bending tests of samples of full-scale gauge without surface treatment showed a reduction in the endurance limits at basic N = 10<sup>5</sup> –106 by 15–18% [16]. This should affect the abovementioned decrease in margins n<sup>т</sup> and n<sup>в</sup> (up to 10–15%).

For these margins ny and nи, the degradation of pipelines is significant due to a decrease in time τ because of corrosion and erosion of the wall thickness δ that is included in Eq. (1) for determining the nominal maximum operating stresses σ<sup>s</sup> <sup>n</sup>max. As shown by laboratory tests and observations of the actual processes of metal loss while in the operation due to these mechanisms, the rate of corrosion and erosion reduction of the wall thickness dδ=dτ can be from 0.05– 0.1 to 0.3 mm/year. With wall thicknesses from 10 to 30 mm, the decrease of margins can reach 10–30%.

Thus, the aging of tubular steels and the degradation of pipes can, in the course of operation, with unfavorable combinations of all the abovementioned damaging factors lead to a substantial reduction in determined margins ny and n<sup>и</sup> and breach of strength as shown by Eqs. (1), (7), and (8). The number of such cases in real operation [3–5, 14] in the period of 1970–2015 gradually decreased from 1.2–1.0 to 0.12–0.14 damages per 1000 km per year.
