PSI - Issue 36

V. Zapukhlyak et al. / Procedia Structural Integrity 36 (2022) 378–385 V. Zapukhlyak, Yu. Melnychenko , І . Оkipnyi et al. / Structural Integrity Procedia 00 (2021) 000 – 000

383

6

      

      

  

    + −   total

 +  

    + −   total L

n

n

n

m

 3

 1

 2



L

k L

. і er і er k L L .

k L

−

( )

( P U

0)

P t



total

. і cor і cor .

. і ins і ins .

j

j

, (4)

1

1

1

i

i

i

=

=

=

1 5

j

=

DB

=

L

    + −   total L

  

   + − total L

n

n

 5

 4

total

k L

k L

. і soil і soil .

. і h і h .

1

1

i

i

=

=

where P ( t ) – possibility of the gas pipeline failure-free operation based on retrospective analysis; P j ( U j >0) – possibility of the gas pipeline failure-free operation under impacts and loading action on it; U j = R j - S j – difference in the pipeline load carrying capacity and its boundary state assessed on strength, resistance, stress-strain properties and crack resistance ( j =1…4; m =4); L заг – total length of the section under consideration; k cor.і , k er.і , k ins.і , k soil.і , k h.і – respectively, weight coefficients of corrosion and other defects, erosion defects, insulation defects, soil environment impact, depth of the gas pipeline burial; L cor.і , L er.і , L ins.і , L soil.і , L h.і – respectively, length of the gas pipeline section with a certain type of corrosion defects, erosion defects, insulation defects, soil environment, and also a certain depth of the gas pipeline burial which does not match the project one. The coefficients k cor.і , k er.і , k ins.і take into account the types of defects, their geometrical dimensions, and its influence on accidents or failures. The coefficient k soil.і is determined for the certain type of soil according to soil electrolyte impact rank

G =

,

(5)

k

. .max . .

el i soil

. і soil

G

el soil

where G гр.ел.і – soil electrolyte impact rank; G гр.ел. max – maximum value of the soil electrolyte impact rank among the soil types where the gas pipeline section under consideration is buried. The coefficient k h.і depends on the actual depth of the gas pipeline burial and it is determined as

h

,

(6)

1 = −

k

і av .

і h .

h

sp

where h av.і – average depth of the gas pipeline burial on і -section different from the specified (designed) one; h sp – specified (designed) depth of the gas pipeline burial. The probability of failure-free operation means that in the specified range of load t any failure of the GTS component won’t take place

 = N i 1

,

(7)

= − ( ) 1 1

(

)

P t

− i t t



N

where N – total number of objects of the GTS; t i – time period till the failure of each object of the GTS; η – Heaviside step function.

The pipe material load carrying capacity is determined by the tearing strength boundary and it is a random value with the well-known law of distribution. The durability of pipes is connected with their reliability P ( t ), i.e. with the probability of the fact, that during the time period T the maximum value of the function S ( t ) will never exceed the load carrying value R. According to the theory of a random function run off a random level, and also taking into account that the appearance of subsequent runs is an independent event which corresponds to the Poisson law, we have obtained the following function of reliability in the form