PSI - Issue 65

D.S. Ivanov et al. / Procedia Structural Integrity 65 (2024) 102–108 D.S. Ivanov, G.S. Ammosov, Z.G. Kornilova, A.A. Antonov / Structural Integrity Procedia 00 (2024) 000–000

106

5

4

64 D

(10)

I

The linear density of the pipeline is calculated using the formula

(11)

l D    

where ρ = 7800 kg/m 3 is steel density; D = 0,53 m ‒ pipeline diameter; δ = 0,013 m ‒ wall thickness. The solution to the problem according to the described algorithm is presented in Figure 2 and obtained with the following parameters: the number of nodes in the solution grid is 1000; the initial position of the pipeline is horizontal at a depth of 8 m; the initial soil responses are 45 kN/m at each node; the perturbance of the soil responses is 100 N/m; the coefficient in the gradient descent algorithm is 108. After approximately 10 thousand iterations, a function is obtained that is considered as a solution to the equation of the underground pipeline (4) and passes through the measured points. Figure 2 shows the position function of the underground pipeline on the section of the Tabaginskaya anabranch obtained by point planned-high-altitude measurements in April 2018. The left side of the Figure demonstrates the floodplain of the Lena River, the middle part is the coastal slope of the channel, and on the right is the anabranch bottom. The position of the pipeline is shown by a solid line; black circles are the measured position of the pipeline; the dashed line is the level of the daylight surface of the ground; the coordinates are taken from the reference point and measured in meters.

Fig. 2. Solution of the equation based on the data of the planned-high-altitude measurements: ‒‒‒‒ ‒ solution obtained by the described algorithm, ‒‒  ‒‒ ‒ measured position of the pipeline, ------ ‒ daylight surface of the soil.

Having obtained the pipeline position function, we calculate the second derivative inversely proportional to the bending radius. The stress in the pipeline is calculated using the formula by Iktin V.A. (2004) and A.M. Shammazov et al (2005):

2 2 ED d Z x dx 2 ( ) *

(12)

( ) x  

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