Discussion of “Modelling spatial variability in as-laid embedment for high pressure and high temperature (HPHT) pipeline design”

Abstract

The authors are thanked for their contribution regarding the spatial embedment variability of subsea pipelines (Westgate et al. 2016). The design of such pipelines against temperature-induced buckles is directly influenced by their embedment in the seafloor. The industry benefits from the presentation of observed installed embedments and the discussion of how such data can be used in design environments. The writer would like to draw the authors' attention to several points.Firstly, the expression shown in eq. (D1) (eq. (6) in the paper under discussion) is a simplification of the Hobbs solution for the infinite mode buckle capacity. The simplification obscures the dependency of the axial capacity on a characteristic, or effective, length of the pipeline buckle. The expression presented in the paper and the original Hobbs infinite mode expression follow in eqs. (D1) and (D2), respectively.In eq. (D2), E is the elastic modulus, I is the pipe moment of inertia, A is the pipe cross-sectional area, L is the lateral friction coefficient, w is the pipe weight, and L is the buckle length, which for this mode is found by a minimization procedure (Hobbs 1984) to have a critical value, L , ofEquation (D1) can be derived from eqs. (D2) and (D3) in two steps. Substituting (D3) in to (D2) yields, after some manipulation,Then using the thin-wall approximations for A and I in L , eq. (D1) is obtained, while noting in the authors' terminology L w = H brk . Equations (D1) and (D4) begin to diverge as the thin-wall pipe approximations lose accuracy.The physical reality is that there is a strict relation between the lateral soil resistance, the length of the structural buckle obtained in the solution (eq. (D4)), and the buckle capacity. Similar requirements develop if the lateral resistance is elastic, as for the beamon-elastic foundation problem described by Timoshenko and Gere (1961), or if elastic-plastic lateral resistance is simulated as is often the case for finite element solutions. The Hobbs infinite mode capacity assumes that a uniform lateral soil resistance to the buckle is fully mobilized over the entire length of the buckle. The illustrative conditions used in the paper under discussion render the use of eq. (D1) inappropriate unless H brk has a scale length longer than L . For the pipe A conditions in the paper, this dimension is approximately 35 m, depending on the choice of H brk . The Hobbs paper also includes buckle capacity solutions for several other modes involving isolated buckles in a long pipeline as opposed to the continuous sinusoidal shape for the infinite mode. Those other solutions, originally developed by Kerr (1978), all result in lower buckle capacities compared to the infinite mode, and all have longer buckle lengths (perhaps 60-100 m) than the infinite mode.The second point is then that, regardless of the buckle mode investigated, the averaging length for determining H brk should be greater than the associated critical length L , and therefore the reduction in buckle capacity described in the pape...