2. Basic design dependencies

In the second half of the twentieth century and the beginning of the twenty-first century in Russia and abroad, branched pipeline systems for hydrocarbons transportation, including the main and field oil and gas product pipelines have been constructed. At present, one of the world's largest pipeline systems operates in Russia (Table 1) with a total length of more than 500,000 km.

Design, construction, and operation of pipelines for many decades were based [1–5] mainly on the strength standards. These standards (in the form of state standards (GOST), industry standards (OST), building norms and rules (SNiP), guidelines (RD), technical regulations (TR), federal rules and regulations (FNiP), methodological recommendations (MR)) were based on:



Table 1. Types, purposes, and length of pipeline systems.

These figures indicate the exceptional importance of the integrated safety and security of the national oil, gas, and chemical complex, which constitute a significant part of the national and international safety problems. The scientific analysis of these problems, and the solution of fundamental, practical and economically significant tasks in the field of safety are becoming

In the second half of the twentieth century and the beginning of the twenty-first century, environmental and economic damage, accidents, and injuries at the facilities of the OGCC (including objects of the main pipeline systems (MPS)) became the subject of active interaction between state authorities, sectorial scientists, and design, technological, construction, and operating organizations. The leading roles in this interaction belong to the Security Council, Rostekhnadzor, the Russian Academy of Sciences, the research centers of the largest compa-

In the traditional and advanced safety developments for OGCC and MPS facilities, the priority will be under scientifically grounded combination of research, rationale, regulation, and expertise, as well as improvement of strength, durability, and safety of the technologies in the light

The solution of these problems mainly lies in deterministic, statistical, and probabilistic methods of modeling, calculations, tests, and justification of performance of OGCC and MPS

Therefore, the major focus is on the probabilistic, statistical, and deterministic analysis of

In the second half of the twentieth century and the beginning of the twenty-first century in Russia and abroad, branched pipeline systems for hydrocarbons transportation, including the main and field oil and gas product pipelines have been constructed. At present, one of the world's largest pipeline systems operates in Russia (Table 1) with a total length of more than

Design, construction, and operation of pipelines for many decades were based [1–5] mainly on the strength standards. These standards (in the form of state standards (GOST), industry standards (OST), building norms and rules (SNiP), guidelines (RD), technical regulations (TR), federal rules and regulations (FNiP), methodological recommendations (MR)) were

• Classical strength theories (I) maximum normal stresses (II) maximum deformations (III) maximum tangential stresses (IV) maximum forming energy

• Analysis of designed operational nominal stresses by methods of material resistance

more relevant as the scope and geography of OGCC expands in Russia.

nies (Transneft, Gazprom, Rosneft), and the leading universities in the country.

strength and durability of the main pipelines for oil and gas transportation.

facilities.

500,000 km.

based on:

2. Basic design dependencies

82 Probabilistic Modeling in System Engineering

and the theory of rods, plates, and shells

of the emerging spectrum of threats and risks in the context of diversifying economy.


Generally, the conditions of pipeline's strength, at present, can be described (Figure 1) [1–3] by the functional relation:

$$\begin{aligned} \sigma\_{n\max}^{s} &= F\_{\sigma} \left\{ p, N, M\_{u}, M\_{k}, \delta, D, E, R\_{u}, \mu \right\} \subseteq \left[ \sigma \right] = \frac{\sigma\_{on}}{n\_{\sigma}}, \\ \sigma\_{on} &\leq F\_{o} \left\{ \sigma\_{\max}, \mathcal{E}\_{\max}, \tau\_{\max}, V\_{\max} \right\} = F\_{\sigma} \left\{ \sigma\_{\tau}, \sigma\_{o}, \sigma\_{\text{y}} \right\} \end{aligned} \tag{1}$$

where —maximum designed stress for the most dangerous operating conditions (taking into account internal and external pressure р, axial forces N, bending , and torque in a critical section and a critical point); —critical (ultimate) stress, determined from the test

Figure 1. Scheme of operational loading of the pipeline.

data of standard specimens on strain (compression) at the stages of the beginning of fluidity (yield point ), reaching the ultimate strength (ultimate stress limit ) or the beginning of buckling (critical stress ); —longitudinal force along the x-axis; bending moments around the y- and z-axes; —torque around the x axis; margin of safety ( ); —pipeline wall thickness; D—diameter of the pipeline (external, internal, or mean); Е—modulus of longitudinal elasticity; —Poisson's ratio; and Rв—bend radius of the pipeline axis.

• In the ultimate stress zone: ultimate strength-ultimate resistance as the maximum engineering stress at the stage of uniformity loss of plastic deformations and neck forma-

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The calculated plastic (е<sup>p</sup> = 0.2%) and elastoplastic deformations (е = 0.5% and е = 1%) for modern tube steels are substantially smaller than the relative elongation in case of failure.

Introduction to calculation (1) stresses in the form of the above characteristics makes it possible to exclude the appearance of mechanical properties of three dangerous limit

• Beginning of fluidity and formation of plastic deformations ( , , , , ).

Since for the first two limiting states ≤ for tube steels hardening in the elastoplastic

When calculating pipeline's strength in limiting states in accordance with national standards and when the design resistances Ry (inadmissibility of plastic deformation development) and

where m—condition load effect factor; Kн—design safety factor; n—load safety factor; K1, K2—

ð2Þ

85

ð3Þ

Hence, in accordance with Eq. (1), the allowable stress must be minimal:

According to the third limiting state, there are two possible cases:

material resistance factor; and —factor for biaxial stress states.

In this connection, for tube steels .

• Failure after reaching the ultimate strength ( ).

This required the use of three safety margins :

• Critical stress under loss of stability .

range, then safety margins are ≤ .

R<sup>и</sup> (inadmissibility of destruction) are used, then

• Total loss of stability after reaching critical stresses.

tion under tension

• Yield strength .

• Tensile strength .

If then ≤ .

If then ≤ .

states:

All the calculated parameters of Eq. (1) can be considered in deterministic, statistical, and probabilistic formulation, taking into account the complication of operational conditions and the improvement of engineering methods of mathematical modeling, physical experimentation, and normative calculations.

The calculation of stresses as a function in Eq. (1) is the initial independent goal of solving boundary value problems—analysis of nominal stress-strain states under complex operational and exploitational loading regimes at all stages of the life cycle of pipes and pipelines.

In expression (1), based on the static tension diagram of a standard sample (Figure 2) in the conditional coordinates (without taking into account the reduction in the crosssectional area and increasing the sample length), as critical stress is used [3–5]

• In the yield zone: the yield strength as the ultimate resistance to elastic deformation—the limit of proportionality , the yield strength at the yield plateau, the conditional yield strength corresponding to the achievement of a given plastic deformation, for example, 0.2% ( ), or a specified elastoplastic deformation, for example, 0.5 ( ) or 1% ( 0)

Figure 2. Static tension diagram of a standard sample.

• In the ultimate stress zone: ultimate strength-ultimate resistance as the maximum engineering stress at the stage of uniformity loss of plastic deformations and neck formation under tension

The calculated plastic (е<sup>p</sup> = 0.2%) and elastoplastic deformations (е = 0.5% and е = 1%) for modern tube steels are substantially smaller than the relative elongation in case of failure. In this connection, for tube steels .

Introduction to calculation (1) stresses in the form of the above characteristics makes it possible to exclude the appearance of mechanical properties of three dangerous limit states:


This required the use of three safety margins :

• Yield strength .

data of standard specimens on strain (compression) at the stages of the beginning of fluidity (yield point ), reaching the ultimate strength (ultimate stress limit ) or the beginning of buckling (critical stress ); —longitudinal force along the x-axis; bending moments around the y- and z-axes; —torque around the x axis; margin of safety ( ); —pipeline wall thickness; D—diameter of the pipeline (external, internal, or mean); Е—modulus of longitudinal elasticity; —Poisson's ratio; and Rв—bend

All the calculated parameters of Eq. (1) can be considered in deterministic, statistical, and probabilistic formulation, taking into account the complication of operational conditions and the improvement of engineering methods of mathematical modeling, physical experimenta-

The calculation of stresses as a function in Eq. (1) is the initial independent goal of solving boundary value problems—analysis of nominal stress-strain states under complex operational and exploitational loading regimes at all stages of the life cycle of pipes and pipelines.

In expression (1), based on the static tension diagram of a standard sample (Figure 2) in the conditional coordinates (without taking into account the reduction in the cross-

• In the yield zone: the yield strength as the ultimate resistance to elastic deformation—the limit of proportionality , the yield strength at the yield plateau, the conditional yield strength corresponding to the achievement of a given plastic deformation, for example, 0.2%

( ), or a specified elastoplastic deformation, for example, 0.5 ( ) or 1% ( 0)

sectional area and increasing the sample length), as critical stress is used [3–5]

radius of the pipeline axis.

84 Probabilistic Modeling in System Engineering

tion, and normative calculations.

Figure 2. Static tension diagram of a standard sample.


Hence, in accordance with Eq. (1), the allowable stress must be minimal:

$$\begin{bmatrix} \sigma \end{bmatrix} = \min \left\{ \frac{\sigma\_y}{n\_y}, \frac{\sigma\_u, \sigma\_c}{n\_u, n\_c} \right\} \tag{2}$$

Since for the first two limiting states ≤ for tube steels hardening in the elastoplastic range, then safety margins are ≤ .

According to the third limiting state, there are two possible cases:

$$\text{If } \sigma\_c \le \sigma\_s \text{ then } n\_c \le n\_w.$$

$$\text{If } \sigma\_c \le \sigma\_\downarrow \text{ then } n\_c \le n\_\downarrow.$$

When calculating pipeline's strength in limiting states in accordance with national standards and when the design resistances Ry (inadmissibility of plastic deformation development) and R<sup>и</sup> (inadmissibility of destruction) are used, then

$$\mathbb{E}\left[\sigma\right] = \min\left\{ \frac{R\_y \cdot m\,\psi}{n \cdot K\_2 \cdot K\_\text{\tiny\!\cdot\text{K}\_\text{\tiny\text\textdegree}}}, \frac{R\_u \cdot m\,\psi}{n \cdot K\_1 \cdot K\_\text{\tiny\text\textdegree}} \right\} \tag{3}$$

where m—condition load effect factor; Kн—design safety factor; n—load safety factor; K1, K2 material resistance factor; and —factor for biaxial stress states.


Table 2. Calculated normative values of factors.

From Eqs. (2) and (3), it follows that margins and in the calculations for the allowed stresses are related to the factors m, K1, K2, and Kн, in Eq. (3) for calculations on the limiting states at and :

$$n\_\chi = \frac{K\_2 \cdot K\_u}{\varphi m}, \ n\_u = \frac{n \cdot K\_1 \cdot K\_u}{\varphi m} \tag{4}$$

and lesser p, D, , and were predominantly used. Under these conditions, when determining the thickness of the pipe wall , the margins and yield strength proved to be key

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87

The idea that increasing the pipe steels yield strength is crucial in those years led to the desire of metal scientists, technologists, and designers to reduce the material consumption of pipelines by increasing the yield strength by all available methods and means (alloying steels, thermomechanical processing of sheets and pipes while reducing margins ). The same approach was typical for the development of general engineering, energet-

In the process of accelerated development of pipeline systems, low-alloy steels, low-carbon low-alloy steels, and low-alloy thermo-hardened steels have been consistently used since

• Significant problems with increased damageability of objects such as pressure vessels and pipelines with high parameters of pressure P and temperature t in thermal

From the generalized statistical analysis of damage and destruction of various objects (including those working under increased pressure), it follows that engineering materials, design, and technological solutions associated with increase of and decrease of are insufficient to prevent large-scale emergency and sometimes catastrophic situations. It became clear that the existing engineering practice of calculation focused on the designation of independent margins and and the basic characteristics of strength and is entailed with the danger of a

factors, because they gave smaller permissible stresses under Eqs. (2) and (3).

This aspiration not supported by the necessary scientific justifications led to:

• Extended brittle fractures and loss of stability of the main pipelines

power engineering, bearing structures of civil and industrial buildings

ics, oil and gas chemistry, transport, and construction.

Figure 3. Basic determinate variations in design parameters of pipelines.

real and reliable operation of pipeline systems.

the 1960s.

. In essence, the safety margins and stability according to Eqs. (2)–(4) reflect the role of statistical and probabilistic uncertainties, inaccuracies, ignorance, and responsibility of pipeline systems.

Based on strength and stability calculations under Eq. (1) with addition of Eqs. (2) and (3) for the pipeline with given p, N, Mв, Mt, Rв, and D, the wall thickness is chosen to be greater than the minimum ratio of yield strength and strength to margins and with subsequent binding of stability with and .

Equation (2) defines the area of allowable stresses for deterministic normative calculations of pipeline strength (Figure 1).

The values of the factors in the calculations according to the norms [2] are given in Table 2.
