Analysis and Evaluation on Residual Strength of Pipelines with Internal Corrosion Defects in Seasonal Frozen Soil Region
Abstract
:1. Introduction
2. Establishment of Three-Dimensional Pipeline-Soil Thermo-Mechanical Coupling Model
2.1. Pipeline-Soil Model Parameters
2.1.1. SOIL Material Parameters
2.1.2. Pipe Material Parameters
2.2. Establishment of the Pipeline-Soil Solid Model
2.3. Verification and Analysis of the Temperature Field
3. Mechanical Analysis of Inner Wall of Buried Non-Corroded Pipeline in Seasonal Frozen Soil Region
3.1. The Effect of Differential Frost Heave of Soils on the Deformation of Buried Pipelines
- According to the Vertical Displacement Curve as shown in Figure 9, the average vertical displacement of buried pipelines increases with decreasing temperature when at 90 D (October) to 240 D (March). The maximum vertical displacement occurred in the frost heave section of 180 D (January), which was 0.033 m. At this time, the vertical displacement deformation of the top, bottom and sides (9 o’clock direction) of the inner wall of the buried pipeline is shown in Figure 10, which reflects the deformation form of the buried pipeline under the differential frost heaving of the soil when the temperature is the lowest.
- The effect of subzero temperature from 120 D (November) to 210 D (February) on Mises equivalent stress is shown in Figure 11. When the temperature is lowest at 180 D (January), Mises equivalent stress is maximum. At this time, the Mises equivalent stress peak points, 241.6 MPa and 323.8 MPa, occur at the top (12 o’clock) of the inner wall of the pipeline approximately 1.5 m to the left of the junction of the soil transition section and the frost heave section and at the side (9 o’clock) of the inner wall of the pipeline approximately 2.5 m to the right of this junction.
- Due to the differential frost heaving of soil, the buried pipeline generates buckling deformation near the junction of the transition section and the frost heaving section. The offset along the pipeline length reaches the maximum in the buckling section, but it is much smaller than the vertical offset of the pipeline. In addition, due to the existence of circumferential extrusion force and axial friction force of soil on the pipeline, the offset along the length direction of the pipeline gradually decreases from the buckling section to both sides and finally tends to zero. As shown in Figure 8, the non-uniform tension between the cross-section M1 and cross-section M2 of the pipeline leads to the non-linear shear stress on the inner wall of the pipeline in the buckling section.
3.2. Effects of Different Internal Pressures on the Mechanical Properties of Buried Pipelines
4. Study on Residual Strength of Buried Pipelines with Single Internal Corrosion Defect in Seasonal Frozen Soil Region
4.1. Orthogonal Design Method
4.2. The Varying Regularity of Mises Equivalent Stress in the Corrosion Region of Buried Pipeline under Failure Pressure
4.3. One-Way Analysis of Extreme Variance for Orthogonal Design Method Result Data
- When the corrosion length was constant, the residual strength curve became steeper and steeper as the depth–thickness ratio of the corrosion defects in buried pipelines increased from 15% to 80%, as shown in Figure 16a; the relative decrease rate of residual strength of buried corrosion defect pipeline gradually increased, as shown in Table 5. In addition, the average residual strength of the pipeline changed from 24.840 MPa to 10.414 MPa, which was reduced by 14.426 MPa. The numerical fluctuation was about 2 times the corrosion length and 8 times the corrosion width, indicating that the corrosion depth was the main factor affecting the residual strength of the pipeline.
- When the corrosion depth was constant, the corrosion length increased from 100 mm to 600 mm, as shown in Figure 16b, the residual strength curve also becomes steeper and steeper. The residual strength of the buried pipeline with internal corrosion defects decreased gradually, and the average residual strength of the pipeline changed from 22.142 MPa to 15.632 MPa, which was reduced by 6.51 MPa. However, when the corrosion length increased from 600 mm to 900 mm, the relative reduction rate of residual strength decreased gradually, as shown in Table 6. At this time, the average residual strength of the pipeline changed from 15.632 MPa to 15.106 MPa, only reduced by 0.526 MPa. In conclusion, the corrosion length had a great effect on the residual strength of the pipeline. When the corrosion length exceeded 600 mm, the effect degree would gradually decrease.
- When the corrosion width increased from 50 mm to 600 mm, as shown in Figure 17, the failure pressure of the defective pipeline varied irregularly from high to low, but which showed a slight overall decreasing trend. It can be seen from Table 4 that the average residual strength of the pipeline decreased from 18.842 MPa to 17.022 MPa, only 1.82 MPa was reduced, and the influence of corrosion width on the residual strength of pipeline was limited. This meant that as the corrosion width increased the effect degree on the residual strength of the defective pipeline was less.
4.4. Fitting Formula of Residual Strength of Pipeline with Internal Corrosion Defects and Its Accuracy Verification
5. Conclusions
- The residual strength of pipelines with internal corrosion defects in permafrost regions can be evaluated safely and reliably by the orthogonal analysis method. The calculation is simple and convenient for engineering applications.
- The corrosion depth of the pipeline in the frozen soil area is the main factor affecting the residual strength of the pipeline; as the depth of corrosion defects increases, the residual strength decreases. The corrosion length is the second; but when the corrosion length reaches 600 mm, its effect on the residual strength of the pipeline is no longer significant. The corrosion width has the least effect on the residual strength.
- Based on the finite element numerical simulation data, a formula for calculating the residual strength of the pipeline with internal corrosion defects in seasonally frozen soil region was obtained by fitting. Compared with the existing corrosion evaluation specifications, the calculation results of the fitting formula obtained according to the stress concentration theory have small errors and uniform error distribution, which can better meet the prediction requirements of failure pressure of oil and gas pipelines with internal corrosion in seasonally frozen soil regions.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Temperature/°C | |||||||||
---|---|---|---|---|---|---|---|---|---|
−30 | −10 | −5 | −2 | −1 | −0.5 | 0 | 15 | 30 | |
Silty Clay (ω = 29.82%) | |||||||||
Thermal conductivity λ (W/m·℃) | 1.21 | 1.21 | 1.21 | 1.21 | 1.21 | 1.21 | 0.84 | 0.84 | 0.84 |
Specific heat C (J/kg·℃) | 1490 | 1490 | 1490 | 1490 | 1490 | 1490 | 1880 | 1880 | 1880 |
Soil expansion coefficient α (10−4) | 2.982 | 8.946 | 17.890 | 44.730 | 89.460 | 178.9 | 0 | 0 | 0 |
Fine Sand and Gravel (ω = 15%) | |||||||||
Thermal conductivity λ (W/m·℃) | 1.04 | 1.04 | 1.04 | 1.04 | 1.04 | 1.04 | 1.04 | 1.04 | 1.04 |
Specific heat C (J/kg·℃) | 2540 | 2540 | 2540 | 2540 | 2540 | 2540 | 3350 | 3350 | 3350 |
Soil expansion coefficient (10−4) | 1.500 | 4.500 | 9.000 | 22.500 | 45.00 | 90.00 | 0 | 0 | 0 |
Weathered Bedrock Residue (ω = 2.59%) | |||||||||
Thermal conductivity λ (W/m·℃) | 2.12 | 2.12 | 2.12 | 2.12 | 2.12 | 2.12 | 1.42 | 1.42 | 1.42 |
Specific heat C (J/kg·℃) | 1500 | 1500 | 1500 | 1500 | 1500 | 1500 | 1900 | 1900 | 1900 |
Soil expansion coefficient α (10−4) | 0.259 | 0.777 | 1.554 | 3.885 | 7.770 | 15.54 | 0 | 0 | 0 |
Temperature/°C | ||||||
---|---|---|---|---|---|---|
−20 | −10 | −5 | −2 | 0 | 20 | |
Silty Clay | ||||||
Density ρ (kg/m3) | 1920 | 1920 | 1920 | 1920 | 1920 | 1920 |
Poisson’s ratio ν | 0.32 | 0.32 | 0.32 | 0.32 | 0.35 | 0.35 |
Internal friction angle φ (°) | 26 | 26 | 26 | 26 | 24 | 24 |
Cohesion c (MPa) | 0.6 | 0.6 | 0.6 | 0.57 | 0.15 | 0.15 |
Elastic modulus E (MPa) | 200 | 100 | 50 | 23.4 | 6 | 6 |
Fine Sand and Gravel | ||||||
Density ρ (kg/m3) | 1834 | 1834 | 1834 | 1834 | 1834 | 1834 |
Poisson’s ratio ν | 0.15 | 0.15 | 0.15 | 0.15 | 0.2 | 0.2 |
Internal friction angle φ (°) | 20 | 20 | 20 | 20 | 18 | 18 |
Cohesion c (MPa) | 1.3 | 1.3 | 1.3 | 1.3 | 0.1 | 0.2 |
Elastic modulus E (MPa) | 500 | 300 | 100 | 70 | 3 | 3 |
Weathered bedrock residue | ||||||
Density ρ (kg/m3) | 2330 | 2330 | 2330 | 2330 | 2330 | 2330 |
Poisson’s ratio ν | 0.3 | 0.3 | 0.3 | 0.3 | 0.35 | 0.35 |
Internal friction angle φ (°) | 42 | 42 | 42 | 42 | 33.32 | 33.32 |
Cohesion c (MPa) | 25.2 | 25.2 | 25.2 | 25.2 | 12.6 | 12.6 |
Elastic modulus E (MPa) | 1400 | 1400 | 1400 | 1400 | 700 | 700 |
A Corrosion Depth | B Corrosion Length | C Corrosion Width | |
---|---|---|---|
1 | 1 (2.625) | 1 (100) | 1 (50) |
2 | 1 (2.625) | 2 (200) | 2 (100) |
3 | 1 (2.625) | 3 (300) | 3 (200) |
4 | 1 (2.625) | 4 (600) | 4 (300) |
5 | 1 (2.625) | 5 (900) | 5 (600) |
6 | 2 (4.375) | 1 (100) | 3 (200) |
7 | 2 (4.375) | 2 (200) | 4 (300) |
8 | 2 (4.375) | 3 (300) | 5 (600) |
9 | 2 (4.375) | 4 (600) | 1 (50) |
10 | 2 (4.375) | 5 (900) | 2 (100) |
11 | 3 (8.750) | 1 (100) | 5 (600) |
12 | 3 (8.750) | 2 (200) | 1 (50) |
13 | 3 (8.750) | 3 (300) | 2 (100) |
14 | 3 (8.750) | 4 (600) | 3 (200) |
15 | 3 (8.750) | 5 (900) | 4 (300) |
16 | 4 (13.125) | 1 (100) | 2 (100) |
17 | 4 (13.125) | 2 (200) | 3 (200) |
18 | 4 (13.125) | 3 (300) | 4 (300) |
19 | 4 (13.125) | 4 (600) | 5 (600) |
20 | 4 (13.125) | 5 (900) | 1 (50) |
21 | 5 (14.000) | 1 (100) | 4 (300) |
22 | 5 (14.000) | 2 (200) | 5 (600) |
23 | 5 (14.000) | 3 (300) | 1 (50) |
24 | 5 (14.000) | 4 (600) | 2 (100) |
25 | 5 (14.000) | 5 (900) | 3 (200) |
Results of the Simulation | Analysis of Results Data | ||||||
---|---|---|---|---|---|---|---|
Number | Residual Strength | Number | Residual Strength | A | B | C | |
Corrosion Depth | Corrosion Length | Corrosion Width | |||||
1 | 25.69 | 14 | 16.10 | T | 124.200 | 110.710 | 85.110 |
2 | 25.43 | 15 | 15.43 | 114.180 | 93.170 | 94.210 | |
3 | 25.09 | 16 | 20.93 | 92.320 | 87.110 | 86.820 | |
4 | 24.08 | 17 | 13.43 | 61.910 | 78.160 | 91.160 | |
5 | 23.91 | 18 | 11.22 | 52.070 | 75.530 | 87.380 | |
6 | 25.22 | 19 | 8.81 | ||||
7 | 23.31 | 20 | 7.52 | t | 24.840 | 22.142 | 17.022 |
8 | 22.19 | 21 | 17.12 | 22.836 | 18.634 | 18.842 | |
9 | 21.77 | 22 | 10.72 | 18.464 | 17.422 | 17.364 | |
10 | 21.69 | 23 | 9.85 | 12.382 | 15.632 | 18.232 | |
11 | 21.75 | 24 | 7.40 | 10.414 | 15.106 | 17.476 | |
12 | 20.28 | 25 | 6.98 | R | 14.426 | 7.036 | 1.820 |
13 | 18.76 |
Number | Relative Reduction Rate of Residual Strength of Pipeline | |||
---|---|---|---|---|
(1)(6)(11)(16)(21) | 1.8% | 15.3% | 18.5% | 33.4% |
(2)(7)(12)(17)(22) | 8.3% | 20.3% | 47.2% | 57.8% |
(3)(8)(13)(18)(23) | 11.6% | 25.2% | 55.3% | 60.7% |
(4)(9)(14)(19)(24) | 9.6% | 33.1% | 63.4% | 69.3% |
(5)(10)(15)(20)(25) | 9.3% | 35.5% | 68.5% | 70.8% |
Number | Relative Reduction Rate of Residual Strength of Pipeline | |||
---|---|---|---|---|
(1)(2)(3)(4)(5) | 1.0% | 2.3% | 6.3% | 6.9% |
(6)(7)(8)(9)(10) | 7.6% | 12.0% | 13.7% | 14.0% |
(11)(12)(13)(14)(15) | 6.8% | 13.7% | 26.0% | 29.1% |
(16)(17)(18)(19)(20) | 35.8% | 46.4% | 57.9% | 64.1% |
(21)(22)(23)(24)(25) | 37.4% | 42.5% | 56.8% | 59.2% |
Fitting Method | R2 | Sum of Squares | d-f | Mean Square | F | Sig | Durbin -Watson | Remark | |
---|---|---|---|---|---|---|---|---|---|
First-order polynomial model | Linear fitting | 0.897 | 909.916 | 3 | 303.305 | 60.697 | <0.0001 | 1.479 | |
Second-order polynomial model | Linear or non-linear fitting | 0.973 | 987.131 | 10 | 98.713 | 49.848 | <0.0001 | 2.331 | use |
Number | Corrosion Length (mm) | Corrosion Width (mm) | Corrosion Depth (mm) | DNV-RP-F101 | B31G | Blast Data | Fitting Formula |
---|---|---|---|---|---|---|---|
1 | 100 | 50 | 8.8 | 22.97 | 21.04 | 24.30 | 22.90 |
2 | 200 | 50 | 4.4 | 23.10 | 21.3 | 24.11 | 24.17 |
3 | 200 | 50 | 8.8 | 19.69 | 18.17 | 21.76 | 20.95 |
4 | 200 | 50 | 13.1 | 13.78 | 13.72 | 17.15 | 16.80 |
5 | 200 | 100 | 8.8 | 19.69 | 18.17 | 23.42 | 20.98 |
6 | 200 | 200 | 8.8 | 19.69 | 18.17 | 22.08 | 20.99 |
7 | 300 | 50 | 8.8 | 17.60 | 16.71 | 19.08 | 19.41 |
Maximum error | 3.727 | 5.250 | 2.436 | ||||
Minimum error | 1.010 | 2.370 | 0.058 | ||||
Residual sum of squares | 40.221 | 90.644 | 9.984 |
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Li, X.; Chen, G.; Liu, X.; Ji, J.; Han, L. Analysis and Evaluation on Residual Strength of Pipelines with Internal Corrosion Defects in Seasonal Frozen Soil Region. Appl. Sci. 2021, 11, 12141. https://doi.org/10.3390/app112412141
Li X, Chen G, Liu X, Ji J, Han L. Analysis and Evaluation on Residual Strength of Pipelines with Internal Corrosion Defects in Seasonal Frozen Soil Region. Applied Sciences. 2021; 11(24):12141. https://doi.org/10.3390/app112412141
Chicago/Turabian StyleLi, Xiaoli, Guitao Chen, Xiaoyan Liu, Jing Ji, and Lianfu Han. 2021. "Analysis and Evaluation on Residual Strength of Pipelines with Internal Corrosion Defects in Seasonal Frozen Soil Region" Applied Sciences 11, no. 24: 12141. https://doi.org/10.3390/app112412141
APA StyleLi, X., Chen, G., Liu, X., Ji, J., & Han, L. (2021). Analysis and Evaluation on Residual Strength of Pipelines with Internal Corrosion Defects in Seasonal Frozen Soil Region. Applied Sciences, 11(24), 12141. https://doi.org/10.3390/app112412141