Collapse of corroded pipes under external pressure considering corrosion asymmetry,non-uniformity,and initial ovality

Abstract

This paper presents an analytical investigation of elastic collapse of corroded pipes considering the corrosion asymmetry, non-uniformity and initial ovality and one novelty is that corrosion asymmetry effect is considered by introducing a misalignment parameter accounting for co-existing internal corrosion and external corrosion. Governing differential equations are derived including the effect of corrosion asymmetry, initial ovality and membrane extensibility. By perturbative techniques, the interaction between corrosion asymmetry and initial ovality is extensively discussed by explicitly calculating the critical initial ovality governing the mode shape changes during initial deformation and collapse deformation phase. One novelty is the introduction of mode shape $\infty$ and mode shape 8 characterized by the sign of sum of displacements of two points independent of rigid-body motion. The theoretical solution is agreeing well with the FEA results. Furthermore, for general non-uniform corrosion, unconditionally convergent power series solutions are formulated by Lyapunov artificial small parameter method. By using Holder’s inequality, an explicit estimation method of the needed truncation number is presented for good computation accuracy by a minimization process over Holder’s exponent thus enabling early truncation of the series properly in advance. An improved estimation method is proposed by coupling with Rayleigh quotient techniques and the domain interval partition approach is introduced to accelerate convergence by thoroughly discussing the special uniformly corroded case by mathematical arguments. As a novelty, this paper illustrates why this improvement might be not evident when corrosion is rather narrow theoretically. Finally by using Chebyshev polynomials and the mathematical algebraic ring structure (generated by polynomial and trigonometric functions) closed under addition, multiplication and integration operations, some calculations for rings with corrosion profile in a non-polynomial mode are presented. This paper is intending to enhance the understanding of the effect of corrosion defect on collapse of pipes under external pressure in offshore industry.

Keywords

Pipe external pressure collapse corrosion ovality perturbation power series

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