**4. The concept assessing for hazard of defects by risk criteria**

The above analysis shows that pipeline will invariably contain defects at some stage during its life. These defects will require a "fitness-for-purpose" assessment to determine whether or not to repair the pipeline. The full-scale tests of pipelines with defects and limit state functions method are used for such assessment. The limit state function method allows determining the limit size of defect upon reaching which the pipeline will fail. The limit state function L for pipe with defect can be write as:

$$\mathcal{L}\{P, \mathbf{Q}, \sigma\_f, \mathbf{D}, \mathbf{t}, l\} = l\_r(P, \mathbf{Q}, \sigma\_f, D, \mathbf{t}, l) - l\_i = \mathbf{0} \tag{1}$$

where *P* is operation pressure; *Q* is external loads; *σ<sup>f</sup>* is fracture stress; *D* is outside diameter of pipe; *t* is wall thickness of pipe; *lr* is allowable defect size; *li* is defect size in pipeline.

The defects sizes *li* are established during ILI. The allowable defects sizes *lr* are determined by calculation methods by the specified criteria for the strength and durability of structures, taking in to account the operating conditions and the character of the mechanisms of deformation and destruction [6–10]. It should be emphasized that in these methods the sizes of defects *li* and *lr* are assumed to be deterministic values.

In reality, the defects have inevitable random dispersion of sizes. For detected defects, these are caused by the random nature of the defects, as well as by statistical errors and the probabilistic nature of the operational characteristics (sensitivity and detectability) of non-destructive testing methods [16]. The dispersion of the calculate sizes of defects determined by statistical scattering loads, operating conditions and scattering of mechanical properties. A certain contribution to the possible dispersion of defect sizes is made by idealization of the shapes and schemes of defects. Taking this into account, instead of single-valued sizes in the calculations, it is necessary to use the probability densities distribution functions of defect sizes *f*(*li*) and *f*(*lr*).

Using the functions *f*(*li*) and *f*(*lr*) gives reason to believe that there are always nonzero probabilities *P* presence of defects with sizes *li* larger than *lr* (**Figure 1**):

**Figure 1.** *Probabilistic scheme of the defects hazard analysis.*

*Issues on Risk Analysis for Critical Infrastructure Protection*

$$P(l\_i > l\_r) = \bigcap\_{\substack{l \\ 0 \le l\_r}}^{\infty \text{ og}} f(l\_i) f(l\_r) dl\_r dl\_i \tag{2}$$

inter-field pipelines based on risk criteria. The basis of this method are requirements of standards [7, 9]. The risk is defined as the probability *Rf* negative consequences of pipeline accident, the scale of which is determined by the hazard class. The proposed hazard classes (risk matrix) for inter-field subsea pipelines are presented in **Table 1**. Quantitative economic and environmental damage assess-

The suitability of the pipeline for operation is determined by three-level assessment of the allowable size of defects by risk criteria (**Figure 2**). The first, basic level, determines the allowable defect sizes by the strength characteristics of metal for pipelines exposed to the main loads - internal overpressure and hydrostatic external pressure. The second, extended level, determines the allowable defect sizes by the strength characteristics for metal, taking into account the effect on pipelines of additional longitudinal and bending loads. The third, special level, determines the allowable sizes of cracks, crack-like defects and delamination by the characteristics

The calculations use information about: pipe sizes, location of the pipeline on the

The hazard of pipe defects depends on their shape and size. The sizes of defects are determined by their spatial coordinates *l* = {*lx*, *ly*, *lz*} (**Figure 3**). By shape the defects can be classified into volumetric and flat. For the volumetric defects the size *lx* ≥ *ly* ≥ *lz*, for the flat defects the size *lx* ≥ *ly*> > *lz*. The defect hazard calculations

*Dt* <sup>p</sup> , <sup>~</sup>*lz* <sup>¼</sup> *lz*

� � <sup>¼</sup> *<sup>σ</sup> <sup>f</sup>* � *<sup>σ</sup>eRF* <sup>~</sup>*lx*,~*lx*

Short-term local disturbance of the state of the ecological environment and/or insignificant material losses. Unscheduled pipeline shut-down and repair.

[*Rf*] 10�<sup>2</sup> 10�<sup>3</sup> 10�<sup>4</sup> 10�<sup>5</sup>

2*t D*

**Low Middle High Very high**

Neglected Uncritical Critical Catastrophic

Short-term damage to the environment and/or signifycant economic damage. Unscheduled pipeline shutdown and repair.

*RF* ~*lx*,~*lx*

*<sup>t</sup>* . These relative dimensions are used

� � � *<sup>P</sup>* <sup>¼</sup> <sup>0</sup> (7)

� � <sup>¼</sup> <sup>0</sup> (8)

Large-scale long-term environmental damage and large economic damage. Long shutdown and pipeline repair.

seabed, loads and impacts; the size, location and types of defects; mechanical

properties, industry standard requirements, and pipe specifications.

in this technique taking into account the classification of defects shape. The limit state function L for pipe volumetric defects may be write as:

> <sup>L</sup> *<sup>P</sup>*, *<sup>D</sup>*, *<sup>t</sup>*, *<sup>σ</sup> <sup>f</sup>* ,~*lx*,~*lx* � � <sup>¼</sup> *<sup>σ</sup> <sup>f</sup>*

<sup>L</sup> *<sup>P</sup>*, *<sup>D</sup>*, *<sup>t</sup>*, *<sup>σ</sup> <sup>f</sup>* ,~*lx*,~*lx*

ments are not considered here.

*Defects Assessment in Subsea Pipelines by Risk Criteria DOI: http://dx.doi.org/10.5772/intechopen.94851*

of crack resistance of the metal.

usually use relative defect sizes <sup>~</sup>*lx* <sup>¼</sup> *lx*ffiffiffiffi

Negligible environmen-tal and econo-mic impact. Pipeline repa-ir can be post-poned until the planned shutdown.

*Hazard classes of fracture for subsea inter-field pipeline.*

for hoop stress

**Hazard classes**

Failure classes

Level of loss

**Table 1.**

**155**

for equivalent stress

Exceeding the sizes *lr* leads to some losses *C* = *F*(*l*) due to the need to carry out repair operations or leakage and structural failure. Moreover, the larger the defect, the more significant losses can be. It should be emphasized that the losses are also random in magnitude, since it depends on the many technical and socio-economic factors.

Joint analysis of the probabilistic nature of defects, their hazard and possible losses leads to the concept of the admissibility of defects according to risk criteria [11, 18]. The essence of this concept is that the criterion condition for the admissibility of defects is represented in the form:

$$P(l\_i > l\_r) \times C(l) \le [R],\tag{3}$$

where [*R*] is the acceptable risk.

Assuming the defect size *li* as a fixed random variable from (3) we can obtain the following condition for the admissibility of a defect:

$$l\_i \le l\_{[R]} \tag{4}$$

where *l*[*R*] is the size defect at which the risk *R* is acceptable.

Due to the unresolved problem of assessment and statistical analysis of losses, currently, sufficiently substantiated proposals for determining the allowable risk have not been developed. As a rule, losses are categorized into some qualitative classes: negligible, acceptable, unacceptable, etc. [19, 20]. Each class of losses is associated with a certain acceptable level of its probabilities [*Rf*]. Taking this into account, instead of (3), one can go to a simpler form of assessing the admissibility of defects by risk criteria, which does not require a direct assessment of damages, namely:

$$P(l\_i > l\_r) = \int\_0^{l\_i} f(l\_r) dl\_r \le \left[ R\_f \right] \tag{5}$$

On this basis, similarly to (5), the following condition for the admissibility of defects can be written:

$$l\_i \le l\_{\left[ \mathcal{R}\_f \right]} \tag{6}$$

where *l*[*Rf*] is the size of the defect at which the probability of losses belongs to a given class.

Expressions (4) and (6), in fact, are a semi-probabilistic solution to problems (3) and (5), since they relate fixed random variables, one of which has a given probabilistic support.
