6. Analysis of resistance to the development of cracks

• Continuous σ<sup>и</sup> under all types of aging and degradation and the change in values σ<sup>y</sup> and

• Effects of degradation of mechanical properties—decrease in relative yield point

• The decrease in plasticity (δ<sup>к</sup> from Figure 2), which accompanies aging and degradation,

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

ny <sup>¼</sup> <sup>σ</sup>yð Þ <sup>τ</sup>; <sup>t</sup>; <sup>σ</sup>;e; <sup>N</sup> σs nmax

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 promis-

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

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

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

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

+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>

, (7)

.

–106 by 15–18% [16]. This should affect the

ny=n<sup>и</sup> ¼ σyð Þ τ; t; σ;e; N =σиð Þ τ; t; σ;e; N : (8)

σ<sup>и</sup> in Eq. (6)

σ<sup>y</sup> ¼ σy=σи; σyð Þ τ; t;е; σ; N ≤ 1;

92 Probabilistic Modeling in System Engineering

as well as the fracture toughness

ing developments of pipe strength standards.

laboratory samples from actually operated pipes.

a reduction in the endurance limits at basic N = 10<sup>5</sup>

abovementioned decrease in margins n<sup>т</sup> and n<sup>в</sup> (up to 10–15%).

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 numerical methods with defining of stresses σ<sup>s</sup> max<sup>к</sup> and deformations е<sup>s</sup> maxк:

$$\left\{\sigma\_{\text{maxk}}^{s}, e\_{\text{maxk}}^{s}\right\} = \sigma\_{\text{maxk}}^{s} \cdot K\_{\text{off}} \tag{9}$$

where σ<sup>s</sup> <sup>n</sup>max—maximum rated stress in Eq. (1); and Kσ<sup>ℓ</sup>—effective coefficient of stress concentration in the zone of cracks.

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

$$K\_{\mathcal{CI}} = F\_{\mathcal{U}} \{ D, \sigma, \mathcal{U}, a, S\_\* \}, \tag{10}$$

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.

Since σ<sup>s</sup> max<sup>к</sup> > σ<sup>s</sup> <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 taking into account Eq. (9) will be further reduced (Figure 6):

$$\left\{ \left( n\_{\mathcal{Y}} \right)\_{\ell}, \left( n\_{\mathcal{U}} \right)\_{\ell} \right\} = \left\{ n\_{\mathcal{Y}}, n\_{\mathcal{U}} \right\} / \mathcal{F}\_{k} \{ D, \delta, \ell, \mathcal{S}\_{\*}, a \}. \tag{11}$$

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 detection (with their resolving power, sensitivity)

Figure 6. Influence of defects (such as cracks) on safety margins.

• ℓ<sup>к</sup> – The critical size (depth) of the defect at which the margin of safety ny (or nи) in Eq. (10) becomes less than 1

The calculations <sup>ℓ</sup><sup>к</sup> take an elliptical (ℓ=<sup>а</sup> <sup>≈</sup> <sup>1</sup>=3<sup>Þ</sup> or extended ð Þ <sup>ℓ</sup>=<sup>а</sup> ! <sup>∞</sup> fracture shape. Typically, the most dangerous ones are surface cracks, taking into account more intensive accumulation of corrosion, erosion, and mechanical damage in the surface layers.

The second and most common way of assessing the strength of pipelines is to estimate margins ny � � <sup>е</sup> and ð Þ n<sup>и</sup> <sup>е</sup> according to the equations and criteria of linear and nonlinear fracture mechanics [3, 7, 10, 16]. In this approach, the stress intensity factors are determined by the calculation for the given σ<sup>s</sup> <sup>n</sup>max in Eq. (1) and Fkf g <sup>D</sup>; <sup>δ</sup>; <sup>ℓ</sup>; <sup>a</sup> in Eq. (9):

$$K\_{l}^{s} = \sigma\_{\text{max}}^{s} \sqrt{\pi \ell} \cdot F\_{k} \{ D, \delta, \ell, a \} \tag{12}$$

When a sample or a pipe with a crack breaks up, a critical value of the stress intensity factor is reached at the crack tip in accordance with the linear fracture mechanics. Then, in calculating the crack, resistance (survivability) of pipes with cracks by analogy with Eq. (2) introduced a margin by the stress intensity factor:

$$m\_k = \frac{K\_{lc}}{K\_I^s}.\tag{13}$$

A generalized analysis of the strength, resource, reliability, survivability, and safety of complex technical systems of pipeline transport is made in one of the volumes [17] of the multivolume

Probabilistic Analysis of Transportation Systems for Oil and Natural Gas

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

95

Multiparameter pipelines with a wide range of service lives are functioning nowadays in Russia and in various countries across the world, according to parts 1 and 2 (Figure 7).

In further analysis of their initial and residual strength, durability, and crack resistance, both statistical data on service life τ and statistical data on changes in the mechanical properties of tubular steels σy, σи, KIc, as well as on developing defects ℓ, should be taken into account. This consideration can be performed on the basis of Eqs. (1)–(15) in both deterministic and statisti-

According to statistical data [20] on oil pipelines of Russia with a total length of more than 70,000 km (see Table 1), about 70% of them have a service life of more than 30 years. Their age

Statistical studies of mechanical properties (tensile strength σи) of 29 tube steels were carried out in 217 pipe sections manufactured at 14 plants. Upward bias from data on technical

Primary and repeated in-tube condition diagnostics on the length of more than 80,000 km of oil and gas pipelines revealed the presence of unacceptable corrosion and mechanical and erosive damage in 0.2–0.3% of pipes. This required repair and restoration works, as well as replacement of pipes or its sections. These works over the past 20 years have made it possible to reduce the

The generally recognized statistical characteristic of the technical condition and safety of pipelines with due regard of their period of operation is [1, 3–7, 17–20] the number of system failures

ð Þτ ) generated per time unit. The failure of a specific section of the pipeline is a very

frequency of accidents on pipelines from 0.14–0.16 to 0.09–0.10 per 1000 km per year.

conditions was revealed in 8.9% cases and downward bias 2.6%.

7. Statistical characteristics and probabilistic modeling of pipeline

series "Safety of Russia."

systems

cal forms.

(failures N<sup>o</sup>

structure is shown in Figure 7.

Figure 7. Statistics on the service life of pipelines.

By the values of K<sup>s</sup> <sup>I</sup> and KI<sup>с</sup> and Eqs. (9) and (13), the equation below can be obtained:

$$\left\{ \left( \mathfrak{n}\_{\mathcal{Y}} \right)\_{\mathcal{U}}, (\mathfrak{n}\_{\boldsymbol{u}})\_{\mathcal{U}} \right\} = \left\{ \mathfrak{n}\_{\mathcal{Y}}, \mathfrak{n}\_{\boldsymbol{u}} \right\} \cdot \frac{K\_{\mathcal{U}}}{\left\{ \sigma\_{\mathcal{Y}}, \sigma\_{\boldsymbol{u}} \right\} \sqrt{\pi \mathcal{E}} \cdot \mathcal{F}\_{\mathcal{k}}}.\tag{14}$$

The difference in margins according to Eqs. (11) and (14) should not be significant.

In the event of plastic deformations, instead of the stress intensity factors KI and KIc, the strain intensity factors should be used [4, 6, 8].

A generalized analysis of the strength, resource, reliability, survivability, and safety of complex technical systems of pipeline transport is made in one of the volumes [17] of the multivolume series "Safety of Russia."
