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Laboratory tests and analysis of CIPP epoxy resin internal liners used in pipelines – part II: comparative analysis with the use of the FEM and engineering algorithms

Tomasz Abel
Tomasz Abel
   | Sep 30, 2021
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Article Category: Original Study
Published Online: Sep 30, 2021
Page range: 307 - 322
Received: Nov 15, 2020
Accepted: Mar 16, 2021
DOI: https://doi.org/10.2478/sgem-2021-0007
Keywords
© 2021 Tomasz Abel, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

Three-point bending – test scheme.
Three-point bending – test scheme.

Figure 2

Computational models [11, 12].
Computational models [11, 12].

Figure 3

Imperfections of an existing conduit and liner: a) local deformation wv, b) ovalisation wGR,v, c) annular gap ws [6].
Imperfections of an existing conduit and liner: a) local deformation wv, b) ovalisation wGR,v, c) annular gap ws [6].

Figure 4

The value of critical pressure pcr for DN200.
The value of critical pressure pcr for DN200.

Figure 5

The value of critical pressure pcr for DN350.
The value of critical pressure pcr for DN350.

Figure 6

The value of critical pressure pcr for DN500.
The value of critical pressure pcr for DN500.

Figure 7

Static scheme (L=16h, see Fig. 1).
Static scheme (L=16h, see Fig. 1).

Figure 8

Example deflections for the force F1 (0.05%).
Example deflections for the force F1 (0.05%).

Figure 9

Example deflections for the force F2 (0.25%).
Example deflections for the force F2 (0.25%).

Comparison of results of numerical analyses and laboratory tests for a model of a liner with a diameter of 200mm and 7,50mm wall thickness.

No. h [mm] L [mm] Stage of deformation - 0,05% Stage of deformation - 0,25%
according to PN-EN ISO 178:2019-06 [9]
F1 [N] Lab. tests FEM difference F2[N] Lab. tests FEM difference
s1[mm] s2[mm]
1 7,60 121,60 8,70 0,95 0,82 15,53% 255,00 2,91 3,20 −9,21%
2 7,70 123,20 8,65 0,97 0,82 18,51% 253,50 2,87 3,18 −9,86%
3 7,50 120,00 8,55 0,90 0,81 11,19% 256,20 2,82 3,22 −12,41%
4 7,60 121,60 8,74 0,92 0,82 11,17% 251,50 2,75 3,16 −12,95%
5 7,70 123,20 8,61 1,03 0,81 26,75% 255,60 2,87 3,21 −10,60%
6 7,50 120,00 8,52 0,99 0,80 23,53% 253,80 3,04 3,18 −4,55%
Ave. 7,60 121,60 8,63 0,96 0,81 17,76% 254,27 2,87 3,19 −9,93%

Comparison of results of numerical analyses and laboratory tests for a model of a liner with a diameter of 200mm and 6,00mm wall thickness.

No. h [mm] L [mm] Stage of deformation - 0,05% Stage of deformation - 0,25%
according to PN-EN ISO 178:2019-06 [9]
F1 [N] Lab. tests FEM difference F2[N] Lab. tests FEM difference
s1[mm] s2[mm]
1 6,10 97,60 8,32 1,13 0,92 23,16% 242,1 2,92 3,10 −5,78%
2 6,20 99,20 8,12 1,09 0,90 21,40% 240,1 2,73 3,07 −11,36%
3 6,10 97,60 8,06 1,16 0,89 29,96% 238,1 3,02 3,05 −0,89%
4 6,00 96,00 8,16 1,15 0,90 27,67% 242,1 3,05 3,10 −1,73%
5 6,30 100,80 8,25 1,15 0,91 25,61% 240,5 2,85 3,08 −7,37%
6 6,10 97,60 8,41 1,03 0,93 11,02% 241,2 2,85 3,09 −7,87%
Ave. 6,13 98,13 8,22 1,12 0,91 23,07% 240,68 2,90 3,08 −5,84%

Percentage differences of results in each algorithm.

No. Diameter [mm] Calculation algorithm
Timo shenko's Glock's ASTM WRc RERAU DVWK-ATV
1 200 333,64% 347,14% 425,28% 291,81% 206,21% 100,00%
2 400,47% 331,02% 289,36% 350,26% 231,46%
3 456,26% 315,47% 212,63% 399,05% 245,70%
4 350 263,21% 340,42% 574,81% 230,21% 154,02%
5 306,53% 331,63% 430,29% 268,09% 175,18%
6 345,17% 322,74% 337,96% 301,88% 191,19%
7 500 261,29% 324,99% 518,01% 228,53% 140,09%
8 316,77% 313,00% 355,42% 277,05% 164,65%
9 349,33% 305,13% 289,15% 305,53% 176,56%

Comparison of results of numerical analyses and laboratory tests for a model of a liner with a diameter of 500mm and 14,00mm wall thickness.

No. h[mm] L [mm] Stage of deformation - 0,05% Stage of deformation - 0,25%
according to PN-EN ISO 178:2019-06 [9]
F1 [N] Lab. tests FEM difference F2[N] Lab. tests FEM difference
s1[mm] s2[mm]
1 14,00 224,00 9,50 2,09 1,10 90,06% 350,00 4,96 5,30 −6,46%
2 14,50 232,00 9,60 2,13 1,05 103,23% 351,00 4,67 5,32 −12,11%
3 14,10 225,60 9,56 1,90 1,11 71,45% 350,50 4,74 5,31 −10,60%
4 14,20 227,20 9,59 2,24 1,11 101,54% 349,80 4,83 5,30 −8,83%
5 14,60 233,60 9,49 2,12 1,10 92,87% 349,90 4,58 5,30 −13,52%
6 14,80 236,80 9,62 2,20 1,11 97,84% 349,20 4,46 5,29 −15,58%
Ave. 14,37 229,86 9,56 2,11 1,10 92,75% 350,07 4,71 5,30 −11,18%

Comparison of results of numerical analyses and laboratory tests for a model of a liner with a diameter of 200mm and 4,50mm wall thickness.

No. h [mm] L [mm] Stage of deformation - 0,05% Stage of deformation - 0,25%
according to PN-EN ISO 178:2019-06 [9]
F1 [N] Lab. tests FEM difference F2[N] Lab. tests FEM difference
s1[mm] s2[mm]
1 4,60 73,60 8,25 1,13 0,95 18,63% 230,20 −7,32%
2 4,70 75,20 8,41 1,38 0,97 42,37% 230,10 2,94 3,04 −3,21%
3 4,50 72,00 8,03 1,57 0,92 70,27% 227,50 3,26 3,00 8,64%
4 4,60 73,60 8,21 1,03 0,95 9,27% 227,10 2,63 3,00 −12,32%
5 4,70 75,20 8,38 1,19 0,96 23,83% 224,40 2,76 2,96 −6,95%
6 4,70 75,20 8,39 1,38 0,97 42,71% 222,10 2,76 2,93 −5,99%
Ave. 4,63 74,13 8,28 1,28 0,95 34,39% 226,90 2,86 3,00 −4,51%

Comparison of results of numerical analyses and laboratory tests for a model of a liner with a diameter of 500mm and 9,00mm wall thickness.

No. h [mm] L [mm] Stage of deformation - 0,05% Stage of deformation - 0,25%
according to PN-EN ISO 178:2019-06 [9]
Lab. Tests FEM difference Lab. Tests FEM difference
F1[N] s1[mm] F2[N] s2[mm]
1 9,00 144,00 8,85 1,34 1,22 10,16% 290,00 3,72 3,83 −2,75%
2 9,10 145,60 8,89 1,33 1,23 8,46% 295,60 3,61 3,90 −7,58%
3 9,20 147,20 8,91 1,35 1,23 10,10% 296,10 3,49 3,91 −10,66%
4 9,30 148,80 8,82 1,34 1,22 10,03% 267,10 3,23 3,53 −8,35%
5 9,00 144,00 8,89 1,38 1,23 12,80% 292,20 3,57 3,86 −7,46%
6 9,10 145,60 8,85 1,33 1,22 8,95% 293,50 3,53 3,88 −8,88%
Ave. 9,12 145,86 8,87 1,35 1,22 10,09% 289,08 3,53 3,82 −7,62%

Critical pressures according to the Timoshenko's and Glock's algorithms.

Timoshenko's formula Glock's formula
pcr=3*E*1R3 {p_{cr}} = {{3*E*1} \over {{R^3}}}  (1) pcr=E*(hD)2,2 {p_{cr}} = E*{\left({{h \over D}} \right)^{2,2}}  (2)
where:

E – Young's modulus of the liner's material [MPa]

I – moment of inertia of the system [m4]

R – nominal radius of the pipeline [mm]

h – liner's wall thickness [mm]

D – liner's diameter [mm]

Comparison of results of numerical analyses and laboratory tests for a model of a liner with a diameter of 350mm and 9,00mm wall thickness.

No. h [mm] L [mm] Stage of deformation - 0,05 % Stage of deformation - 0,25 %
according to PN-EN ISO 178:2019-06 [9]
F1 [N] Lab. Tests FEM difference F2[N] Lab. Tests FEM difference
s1[mm] s2[mm]
1 9,10 145,60 8,75 1,33 0,87 52,79% 260,00 3,27 3,49 −6,42%
2 9,20 147,20 8,76 1,13 0,87 29,39% 261,00 3,12 3,50 −11,00%
3 9,00 144,00 8,79 1,34 0,87 53,78% 262,50 3,34 3,52 −5,19%
4 9,30 148,80 8,86 1,34 0,88 51,86% 259,80 3,27 3,49 −6,23%
5 9,00 144,00 8,89 1,34 0,88 52,05% 259,50 3,34 3,48 −4,09%
6 9,10 145,60 8,85 1,37 0,88 55,37% 261,20 3,34 3,51 −4,68%
Ave. 9,12 145,86 8,82 1,31 0,88 49,23% 260,67 3,28 3,50 −6,27%

Comparison of results of numerical analyses and laboratory tests for a model of a liner with a diameter of 350mm and 7,50mm wall thickness.

No. h [mm] L [mm] Stage of deformation - 0,05% Stage of deformation - 0,25%
according to PN-EN ISO 178:2019-06 [9]
F1 [N] Lab. test FEM difference F2[N] Lab. tests FEM difference
s1[mm] s2[mm]
1 7,50 120,00 8,56 1,12 0,90 24,44% 246,00 3,10 3,10 0,13%
2 7,60 121,60 8,60 0,95 0,90 4,77% 247,60 2,94 3,12 −5,88%
3 7,70 123,20 8,59 1,18 0,90 31,14% 246,50 2,96 3,11 −4,68%
4 7,60 121,60 8,61 1,23 0,91 36,05% 248,20 3,06 3,13 −2,06%
5 7,50 120,00 8,62 1,15 0,91 27,11% 246,80 2,98 3,11 −4,31%
6 7,40 118,40 8,55 1,17 0,90 29,88% 248,90 3,18 3,14 1,33%
Ave. 7,55 120,80 8,59 1,13 0,90 25,56% 247,33 3,04 3,12 −2,57%

Comparison of results of numerical analyses and laboratory tests for a model of a liner with a diameter of 350mm and 6,00mm wall thickness.

No. h [mm] L [mm] Stage of deformation - 0,05% Stage of deformation - 0,25%
according to PN-EN ISO 178:2019-06 [9]
F1 [N] Lab. tests FEM difference F2[N] Lab. tests FEM difference
s1[mm] s2[mm]
1 6,10 97,60 8,31 1,03 0,92 12,22% 242,00 2,77 3,00 −7,67%
2 6,20 99,20 8,41 1,04 0,90 15,61% 243,20 2,85 3,01 −5,50%
3 6,00 96,00 8,36 1,02 0,93 10,64% 244,10 3,02 3,03 −0,17%
4 6,20 99,20 8,28 0,97 0,92 5,40% 242,10 2,73 3,00 −9,20%
5 6,30 100,80 8,36 1,00 0,93 8,00% 243,50 2,66 3,02 −11,96%
6 6,00 96,00 8,42 1,02 0,93 9,85% 241,50 2,87 2,99 −4,23%
Ave. 6,13 98,13 8,36 1,01 0,92 10,27% 242,73 2,81 3,01 −6,45%

Comparison of results of numerical analyses and laboratory tests for a model of a liner with a diameter of 500mm and 12,00mm wall thickness.

No. h [mm] L [mm] Stage of deformation - 0,05% Stage of deformation - 0,25%
according to PN-EN ISO 178:2019-06 [9]
F1 [N] Lab. tests FEM difference F2[N] Lab. tests FEM difference
s1[mm] s2[mm]
1 12,00 192,00 9,10 1,69 1,10 53,60% 320,00 4,15 4,50 −7,84%
2 12,20 195,20 9,32 1,76 1,13 56,46% 321,20 4,03 4,52 −10,80%
3 12,30 196,80 9,15 1,75 1,11 58,07% 325,20 4,10 4,57 −10,43%
4 12,10 193,60 9,12 1,73 1,10 56,60% 321,50 4,01 4,52 −11,27%
5 12,00 192,00 9,00 1,89 1,09 74,13% 325,60 4,40 4,58 −3,83%
6 12,40 198,40 8,95 1,68 1,08 55,72% 318,60 3,96 4,48 −11,53%
Ave. 12,17 194,66 9,11 1,75 1,10 59,06% 322,02 4,11 4,53 −9,27%

Results of calculation algorithm.

Sample no. Liner thickness h Diameter Radius Calculation algorithm
Timo- shenko's Glock's ASTM WRc RERAU ATV 143-2
[m] critical pressure pcr N/mm2
1 0,0045 0,200 0,100 0,57 0,59 0,73 0,50 0,35 0,17
2 0,0060 0,200 0,100 1,35 1,12 0,98 1,18 0,78 0,34
3 0,0075 0,200 0,100 2,64 1,82 1,23 2,31 1,42 0,58
4 0,0060 0,350 0,175 0,25 0,33 0,55 0,22 0,15 0,10
5 0,0075 0,350 0,175 0,49 0,53 0,69 0,43 0,28 0,16
6 0,0090 0,350 0,175 0,85 0,79 0,83 0,74 0,47 0,25
7 0,0090 0,500 0,250 0,29 0,36 0,58 0,26 0,16 0,11
8 0,0120 0,500 0,250 0,69 0,68 0,78 0,60 0,36 0,22
9 0,0140 0,500 0,250 1,10 0,96 0,91 0,96 0,55 0,31
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