Comparison of External Pressure Stability Calculation Methods for Reinforcing Rings of Buried Pressure Steel Pipes

Literature Overview

The paper by Lu Zhihang, Peng Yueyao, Wu Hegao, and Shi Changzheng (2020), published in Water Resources and Hydropower Engineering, compares three commonly used methods for calculating the external pressure stability of reinforcing rings on buried pressure steel pipes: the Amstutz method, the Jacobsen method, and the strength formula from the Chinese specification NB/T 35056-2015. The study is funded by the National Natural Science Foundation of China (Grant No. 51409194) and is conducted at the State Key Laboratory of Water Resources and Hydropower Engineering Science at Wuhan University. The research addresses a critical design issue in hydraulic engineering: the external pressure stability of reinforcing rings on buried steel pipes, which is essential for ensuring the structural integrity of penstocks and other pressure pipelines in hydropower projects.

Core Technical Findings

The comparison reveals significant differences between the three methods, particularly regarding the treatment of the gap value (the clearance between the reinforcing ring and the pipe wall). The Amstutz and Jacobsen formulas both show that the critical external pressure decreases with increasing gap value, which is physically reasonable because a larger gap reduces the effective contact and load transfer between the ring and the pipe. In contrast, the NB/T 35056-2015 strength formula does not account for the gap value, resulting in a critical external pressure that is independent of this parameter.

All three methods agree on the general trends: the critical external pressure increases with reinforcing ring height, pipe wall thickness, and steel yield strength, and decreases with increasing reinforcing ring spacing. However, the NB/T 35056-2015 formula consistently yields lower critical external pressures compared to the Amstutz and Jacobsen methods, making it notably conservative when the external water head is less than 130 m. The authors recommend adopting the Jacobsen method as one of the primary calculation methods in Chinese design specifications for buried pressure steel pipes.

Interpretation of Technical Points

The Amstutz method is based on the theory of elastic stability of thin-walled cylinders under external pressure, with modifications for the presence of reinforcing rings. The method assumes that the reinforcing rings act as discrete supports that reduce the effective buckling length of the pipe segment between rings. The Jacobsen method, developed for ship hull structures, provides a more refined approach that accounts for the interaction between the ring and the pipe shell, including the effect of the gap value on the effective stiffness.

The NB/T 35056-2015 strength formula is a simplified empirical formula that does not explicitly consider the gap value. This simplification is convenient for routine design calculations but may lead to overly conservative designs, especially for projects with large external water heads where the actual stability capacity is significantly higher than the predicted value. The conservatism of the NB/T formula below 130 m external water head suggests that it may be based on a different failure criterion or a more conservative safety philosophy than the Amstutz and Jacobsen methods.

Engineering Practice Considerations

For the design of buried pressure steel pipes with reinforcing rings, the following considerations are important:

• The gap value between the reinforcing ring and the pipe wall should be minimized to maximize the critical external pressure. In practice, this gap is typically controlled by the welding process and the fit-up procedure.
• The reinforcing ring height should be selected to provide adequate stability capacity while minimizing material usage. A height-to-thickness ratio of 3 to 5 is commonly used.
• The reinforcing ring spacing should be optimized based on the external pressure conditions and the stability requirements. Closer spacing increases stability but also increases fabrication and installation costs.
• The steel grade for reinforcing rings should be matched to the pipe material to ensure compatibility of thermal expansion and to avoid galvanic corrosion in aggressive environments.

The reinforcing rings are typically fabricated from steel plates conforming to GB/T 709 or GB/T 3274, with a steel grade of Q345 or Q355. The welding of reinforcing rings to the pipe wall is a critical process that requires careful control of heat input to avoid excessive distortion and residual stresses. The welds should be inspected by ultrasonic testing (UT) according to JB/T 4730 or ISO 17635, with acceptance criteria conforming to GB/T 3323 or ISO 5817. The fit-up gap between the ring and the pipe should be controlled to within 2 to 3 mm to ensure proper weld penetration and to minimize the effective gap value.

Study Insights and Implications

This comparative study provides valuable insights into the differences between various calculation methods for the external pressure stability of reinforcing rings. The recommendation to adopt the Jacobsen method as a primary calculation method in Chinese design specifications is well-supported by the comparative analysis. However, engineers should be aware that the choice of calculation method can significantly affect the design outcome, and that the NB/T 35056-2015 formula, while conservative, may still be appropriate for certain applications where simplicity and safety margin are prioritized over cost optimization. Future research should focus on developing more accurate methods that account for the complex interaction between the reinforcing rings, the pipe shell, and the surrounding soil, including the effect of soil stiffness on the external pressure distribution.