**3.1 Techniques of provision and enhancement of strength, in-service life and safety**

Taking into account a possibility of reaching in time of the ultimate limit states in the wide range of loading parameters, further it is required to define the following groups of situations occurring during SP functioning as presented in **Table 2**.

Each class of situations corresponds to diminution of safety level of the analyzed objects while diminution of safety level can be estimated on expressions (1)–(9) as per values of risks *R<sup>э</sup> <sup>i</sup>*ð Þ*t* of objects operation on a specified time interval of operation. Quantitative values of risks *R<sup>э</sup> <sup>i</sup>*ð Þ*t* are calculated as product of the probability of occurrence of each of the specified situation *i* - *Р<sup>э</sup> <sup>i</sup>*ð Þ*t* by economic losses values as per analyzed situation *U<sup>э</sup> <sup>i</sup>*ð Þ*t* . At the same time, the condition of safety provision takes the following form *nR* <sup>¼</sup> *Rc*ð Þ*<sup>t</sup> <sup>=</sup>R<sup>э</sup> <sup>t</sup>*ð Þ*t* where *Rc*ð Þ*t* is critical (inadmissible, unacceptable risk), *R<sup>э</sup> <sup>t</sup>*ð Þ*t* is designed risk for the moment of operation *t* for mode *i* and *nR* is the safety margin as per risks.

According to **Table 2**, the last three abovementioned groups of the situations (T5, T4, T3) occurring during objects functioning can be referred to a kind of the risks which are monotonously increasing up to critical values. Such risks, mainly, are caused by the controlled processes of damages and degradations of physicalmechanical properties of material relevant to its aging. The first two groups (T2, T1) correspond to the occurrence of the most dangerous situations with extreme impact parameters (earthquakes, tsunami, acts of terrorism and military actions). These cases require use of the most difficult calculations, tests, modeling, diagnostics, monitoring and protection. In this case, classic methods of a material consumption justification, constructability and efficiency are insufficient. In such statement, the approaches presented in clauses 2.9–2.12 have to be implemented.

#### **3.2 Risk-based inspections**

In case of use of foreign and domestic safety standards for risk analysis, the approaches given in [1, 2, 10, 11] can be rather efficient:

*KIe* <sup>¼</sup> *<sup>K</sup>pke*

eralized parameter depending on work-hardening index *m* and relative level of rated stresses; *m* is the work-hardening index for deformation curve; and *n* is the

*KI* ¼ *σ<sup>n</sup>*

value and designed parameters of mechanical properties

peak-to-peak range of deformations intensity factor *ΔK*ð Þ *<sup>N</sup>*

• cyclically hardening—*m(N)* increases with growth of *N*; and

• cyclically softening—*m(N)* decreases with growth of *N*. Then

<sup>¼</sup> <sup>1</sup> 2*πe*<sup>2</sup> *f*

*ΔK*ð Þ*<sup>k</sup> Ie* � �<sup>2</sup>

Expression (46) with regard to expressions (43), (44) is similar to known Paris-Erdogan equation when *С* and *mk* are material constants; however, in expression (46), the values *C* and *m* are variables and are calculated. Mechanical tests for identification of *KIe*, *KIec*, *dl=dN* within the frames of nonlinear destruction mechanics are more comprehensive than those in linear destruction mechanics when identified are values of *KIc* and *dl/dN*. In non-routine events, emergency and catastrophic situations in nonlinear setting of the problem analyzed are the following essential effects of redistribution of the local plastic deformations and creep deformations depending on *m*, *t*, *τ*, *N*, *F*, *Iσ*, *De* in case of probabilistic approach. Noted complexity is overcome within deformation destruction criteria at setting of the general problems of strength, in-service life, reliability, survivability, risks,

¼ *Ce ΔKI* � �*<sup>m</sup><sup>e</sup>*

*ΔK*ð Þ*<sup>k</sup> Ie ef* !<sup>2</sup>

cyclic properties of materials that can be as follows:

Expressions (41) and (44) make it possible to get conditions of local destruction—crack formation (41) and its development according to (43).

> *<sup>Δ</sup><sup>l</sup>* <sup>¼</sup> <sup>1</sup> 2*π*

If loading process is cyclic, the value Δ*l* is equivalent to crack increment in

*N* with a variable work-hardening index *m* = *m*(*N*). The value *m* = *m*(*N*) depends on

• cyclically stable—*m*(*N*) does not change depending on number of half-cycles

*<sup>σ</sup><sup>т</sup>* ; *<sup>σ</sup><sup>n</sup>* <sup>¼</sup> *<sup>σ</sup>n=σ*т; *<sup>σ</sup><sup>т</sup>* is the yield stress; *Pke* <sup>¼</sup> <sup>2</sup>�*n*ð Þ <sup>1</sup>�*<sup>m</sup>* ð Þ <sup>1</sup>�*σ<sup>n</sup>*

The value of stress intensity factor in terms of operation at stress *σ<sup>n</sup>* with regard

In presence of cracks and use of local criterion obtained is expression to plot the fracture diagram connecting increment of the crack length Δ*l* with the rated stress

> *KIe ef* !

*dN*, and the main parameter of loading appears to be the

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

where *KI* <sup>¼</sup> *KI*

*Probability, Combinatorics and Control*

t0 (4.14) equals to

where *ef* <sup>¼</sup> <sup>1</sup>

of *N*;

preplanned cycle *<sup>Δ</sup><sup>l</sup>* <sup>¼</sup> *dl*

*e*т ð Þ е*<sup>k</sup>* .

> *dl dN* <sup>¼</sup> <sup>1</sup> 2*π*

safety and SP equipment protection.

**106**

characteristic of structural material type *n* ≈ 0.5.

*<sup>I</sup>* , (43)

*<sup>π</sup><sup>l</sup>* � *F l* f g , *<sup>F</sup>*, *<sup>Q</sup>* <sup>p</sup> *:* (44)

*:* (45)

*Ie* in this very loading cycle

*:* (46)

<sup>1</sup>þ*<sup>m</sup>* is the gen-

**3.3 Monitoring and seismic protection of offshore platforms**

*Hybrid Modeling of Offshore Platforms' Stress-Deformed and Limit States…*

coefficient were experimentally developed [17, 18].

Sakhalin Island [1, 2, 17, 18].

*DOI: http://dx.doi.org/10.5772/intechopen.88894*

materials).

jack structure.

**Figure 20.**

**109**

*Bearing structure diagram.*

defined by bearing properties.

One essentially important question in the problem of protection of objects of offshore and land infrastructures is provision of SP seismic stability; this can be achieved with the help of developed scientific bases of design of self-lubricating, and self-adjusting sliding supports with reverse motion used as seismic-insulators for bridges, industrial and civil constructions. These works are also used for oil and gas offshore platforms on the continental shelf of the Russian Federation on the

It was proposed offshore structures protection against earthquakes to use the friction pendulum bearings (FPB) as the seismic-insulators [1, 12–14]. A calculation method for the service life of a FPB and the method of assessment of friction

The real possibility of pendulum sliding supports use as efficient mean for absorption of energy from external force appeared in the last 30–40 years thanks to development of new technologies (in particular in connection with development of

In the SP pendulum bearings used are pendulum characteristics, providing increase of the natural oscillations (vibrations) period of the isolated structure in a manner to avoid the maximal forces occurring at an earthquake. During an earthquake, the articulation slide block in the bearing moves (slides) along a stainless steel concave surface, forcing a support to move within small pendulum displacements. The schematic view of the bearing is presented in **Figure 20**. The plate with a spherical concave surface is mounted on the top as viewed from the deck; this is done to arrange convenient operation. At such location of a concave plate, the grease does not get on the slide face. The lower plate of the case is mounted on the

If forces occurring during an earthquake do not exceed the level of friction forces, then the structure supported by the bearing corresponds to the standard structure lying on the jack and has its own oscillation (vibration) period without insulator. As soon as the level of friction forces is exceeded, the structure starts oscillate with designed period; at that the dynamic response and damping are

The hemispherical design of the articulation slide block allows getting relatively uniform distribution of pressure under the slide block and this reduces the movement judder and prevents occurrence of high local pressure in the bearing.

space research works in the USSR and the USA) and to introduction of new tribotechnical materials (such as the antifriction self-lubricant weaved fibrous

**Figure 18.** *Basic diagram of implementation risk based inspections technique.*


In the approach (**Figure 19**) presented above by analogy with **Figure 4**, the classes and categories of criticality, consequences of damages from accidents and accidents can be assessed in a similar way to **Figure 4**.

The risks analysis technique is based on information about scenarios of dangerous situations and probabilities of their occurrence received a priory. It is possible for SP for which design and operation experiences are accumulated already. In engineering design performed according to clauses 2.9–2.12, the inspections frequency can be obtained upon calculations as per expressions (18)–(41).


**Figure 19.** *Criticality and risks matrix.*
