Comparison and Application of External Pressure Stability Calculation Methods for Buried Pressure Steel Pipe Stiffening Rings

Literature Overview

This paper by Lu Zhihang, Peng Yueyao, Wu Hega, and Shi Changzheng (2020, published in Water Resources and Hydropower Engineering, Vol. 51, No. 7, pp. 46–52) compares three commonly used calculation methods for the external pressure stability of stiffening rings on buried pressure steel pipes: the Amstutz method, the Jacobsen method, and the strength formula from the Chinese design code NB/T 35056–2015 (Design Code for Pressure Steel Pipes in Hydropower Stations). The study is funded by the National Natural Science Foundation of China (Grant No. 51409194).

Core Technical Content

The authors systematically compare the three methods by varying key parameters and analyzing the resulting critical external pressures. The comparison reveals significant differences in the treatment of gap effects, ring geometry, and material properties.

Comparative Analysis of Calculation Methods

Parameter	Amstutz Method	Jacobsen Method	NB/T 35056–2015 Code Formula
Gap effect consideration	Yes — critical pressure decreases with increasing gap	Yes — critical pressure decreases with increasing gap	No — independent of gap value
Ring height effect	Critical pressure increases with height	Critical pressure increases with height	Critical pressure increases with height
Wall thickness effect	Critical pressure increases with thickness	Critical pressure increases with thickness	Critical pressure increases with thickness
Yield strength effect	Critical pressure increases with yield strength	Critical pressure increases with yield strength	Critical pressure increases with yield strength
Ring spacing effect	Critical pressure decreases with spacing	Critical pressure decreases with spacing	Critical pressure decreases with spacing
Conservatism at H < 130 m	Baseline	Baseline	Significantly conservative
Recommended for code use	No	Yes (recommended)	Currently used but conservative

Gap Effect Analysis

The gap between the stiffening ring and the pipe wall is a critical parameter that reflects installation quality and fabrication tolerances. Both the Amstutz and Jacobsen methods account for this gap, recognizing that it reduces the effective composite action between the ring and the pipe wall. The code formula neglects this parameter, which leads to non-conservative results at small gaps and overly conservative results at larger gaps.

Interpretation of Technical Points

Theoretical Basis of Each Method

The Amstutz method is based on classical shell buckling theory, treating the pipe wall and stiffening ring as a composite cylindrical shell subjected to external hydrostatic pressure. The method incorporates the gap as a reduction factor in the effective stiffness of the composite section.

The Jacobsen method is a modification of the Amstutz approach that introduces empirical corrections for practical construction conditions. It provides a more nuanced treatment of the gap effect, accounting for the nonlinear relationship between gap size and stiffness reduction.

The NB/T 35056–2015 code formula is derived from simplified strength criteria that ensure the combined stress in the pipe wall and ring does not exceed the allowable stress. This approach is fundamentally different from a buckling-based analysis and does not capture the instability mechanism that governs external pressure failure.

Practical Implications of Method Selection

The choice of calculation method has direct consequences for design economy and safety:

Using the code formula at external heads below 130 m leads to significantly oversized stiffening rings, resulting in unnecessary material costs and construction complexity.
The Jacobsen method provides a more accurate prediction of critical external pressure, enabling optimized ring design that achieves the required safety factor with minimum material.
The gap parameter must be controlled during construction to ensure that the actual gap does not exceed the design value assumed in the stability calculation.

FMEA Analysis of External Pressure Stability

Applying Failure Mode and Effects Analysis (FMEA) to the external pressure stability of stiffening rings:

Failure Mode	Cause	Effect	Severity	Detection	Prevention
Ring buckling	Insufficient ring section	Pipe collapse	High	Hydrostatic test	Proper ring design using Jacobsen method
Gap development	Poor installation	Reduced composite action	Medium	Visual inspection	Construction quality control
Corrosion of ring	Environmental attack	Reduced section modulus	High	UT thickness measurement	Corrosion protection coating
Ring spacing error	Construction tolerance	Localized instability	Medium	Survey measurement	As-built verification
Weld defect at ring-pipe joint	Inadequate welding	Stress concentration	High	MT/PT inspection	Weld procedure qualification

Connection with Engineering Practice

The findings of this study have direct implications for the design and construction of buried pressure steel pipes in hydropower projects:

The Jacobsen method should be adopted as the primary calculation method for stiffening ring external pressure stability in Chinese design codes, replacing or supplementing the current conservative formula.
Construction quality control must include measurement of the gap between stiffening rings and the pipe wall, with acceptance criteria aligned with the design assumptions.
For external heads exceeding 130 m, the code formula becomes less conservative and may provide reasonable results, but the Jacobsen method should still be preferred for accuracy.
The stiffening ring design should consider the interaction between adjacent rings, as the ring spacing directly affects the effective buckling length of the pipe wall segment between rings.

Design Recommendations

Design Parameter	Recommendation	Rationale
Calculation method	Jacobsen method	Most accurate and less conservative
Gap control	≤ 2 mm (typical)	Ensures composite action
Ring height	Optimized per Jacobsen	Material efficiency
Ring spacing	Based on critical pressure	Prevents localized buckling
Corrosion protection	Full coverage coating	Long-term stability maintenance
Weld quality	100% UT inspection	Prevents defect-initiated buckling

Key Questions and Reflections

Several important considerations arise from this study:

The study compares methods based on critical external pressure, but the post-buckling behavior and ultimate collapse pressure are also important for safety assessment. The methods may differ significantly in their predictions of post-buckling capacity.
The gap parameter is highly sensitive to construction quality. In practice, gaps can develop over time due to settlement, thermal cycling, and corrosion. The long-term gap evolution should be considered in the design.
The study does not address the effect of ring misalignment or eccentricity, which can significantly reduce the effective stiffness of the composite section.
From a welding perspective, the ring-to-pipe weld is a critical connection that must transfer the full composite action load. Weld defects, particularly lack of fusion and porosity, can create initiation sites for buckling.

Study Insights and Implications

This paper provides a rigorous technical basis for the selection of calculation methods in the external pressure stability design of buried pressure steel pipe stiffening rings. The recommendation to adopt the Jacobsen method as the primary calculation approach is well-supported by the comparative analysis and has significant implications for design economy. The identification of the gap parameter as a critical variable that is neglected by the current code formula highlights the need for improved construction quality control and design-code alignment. The study also underscores the importance of method selection in engineering practice, where the choice between a conservative and an accurate approach can result in substantial cost differences without compromising safety. These insights should inform the revision of NB/T 35056 and related design standards to incorporate more sophisticated stability analysis methods.