1. Introduction
With the gradual increase of marine oil and gas exploitation depth, high temperature, high pressure, corrosion effect, and ocean currents are all extreme conditions experienced by subsea pipelines, which then result in enormous economic losses and catastrophic and irreversible environmental pollution [
1]. Considering that the distance between deep-sea oil pipelines are usually large, which are generally over tens of kilometers, pipelines must provide excellent thermal insulation properties to prevent crude oil from wax deposition. Traditional single-layer insulation pipelines are becoming increasingly incapable of satisfy rigorous thermal insulation requirements. A pipe-in-pipe (PIP) structure consists of rigid outer pipe, inner pipe, and centralizer, which are connected using specialized joint nodes (bulkheads) at a certain distance [
2]. Thermal insulation materials (materials without structural strength, such as particles, foams, and aerogel) are added in the circumferential space formed between the inner and outer pipes. Considering that inner and outer pipes have different force transfer patterns, the PIP structure can be subdivided into compliant and non-compliant types [
3].
The global buckling of subsea pipelines belongs to the buckling strength of axial compression member problem; however, the pipe-soil interaction between the seabed and PIP structure and the internal interaction inside the PIP structure makes this a different problem [
4]. Similar to traditional pipelines, the PIP structure experiences the global buckling problem. However, the axial force computation of the PIP structure under the pressure effect is more complicated than that in a single-layer pipeline because the inner and outer pipes of the PIP structure work as a whole.
In the terms of theoretical studies, Liu [
5] studied the mechanical behavior of high-strength X80 pipeline when subjected to strike-slip fault displacements. Goplen and Fyrileiv [
6] indicated that the analysis and application of the PIP structure depend on taking it as a system rather than as two connected pipes. Sriskandarajah [
2] analyzed the force transfer mechanism of the outer pipe in the PIP structure and the probability of global buckling and provided an approximate expression of the effective axial force of the PIP structure. However, this expression neglects the influences of the collaborative working mechanism of inner and outer pipes and pipe-soil interaction. Zhao [
7] used finite element technology to analyze the global lateral buckling performances of compliant- and non-compliant-type PIP structures and considered the initial imperfections and nonlinear characteristics of the PIP structure in the calculation; however, the author did not provide a computational formula of corresponding buckling critical force of the PIP structure. Vaz and Patel [
8] established a differential control equation of global lateral buckling of the non-compliant type PIP structure based on a single-beam differential control equation. However, the study by Vaz and Patel neglects the two important factors in the theoretical framework of overall buckling, namely, frictional force and initial imperfections. Therefore, their analysis was only the first step in conducting a global buckling analysis of the PIP structure, and a large quantity of work remains to be improved.
Experimental studies have mainly concentrated on single-layer pipelines, and few studies have been reported on the buckling characteristics of the PIP structure. Allan [
9] investigated the global buckling behavior of elastic steel bars on rigid basis and verified the sensitivity of their buckling secondary to imperfections. Duan [
10] et al. used a small-size model and a mechanical loading mode to evaluate the global buckling of a PIP structure and obtained the axial force-displacement relationship and critical axial force during the buckling process. Maltby and Calladine [
11] evaluated the vertical buckling problems of buried pipelines. Their experimental results re-verified the sensitivity of global pipeline buckling secondary to imperfections, and no “combinational buckling patterns”, namely, simultaneous existence of vertical buckling and lateral buckling, were observed and described in the theoretical solutions. Taylor and Tran [
12] published a paper in 1996 in which they introduced their global buckling experimental device of the pipeline and observed that several imperfection patterns would reduce the vertical buckling critical temperature by 50%. Loen [
13] conducted an experimental study on the vertical buckling of buried and grooved pipelines and assessed the vertical buckling performances of buried pipelines under different soil conditions and different imperfection patterns. Karampour [
14] investigated the propagation buckling of subsea PIP structures under hydrostatic pressure and obtained new buckling modes in hyperbaric chamber tests of PIP structures. Alrsai [
15] studied the buckling mechanisms in PIP structures with thin and moderately thin carrier pipes with a diameter-to-thickness (
D0/t0) ratio in the range of 26–40, but the global buckling of the PIP structure was not mentioned.
Thus, previous studies have focused on theoretical studies, and the proposed computational formulas of buckling critical force of the PIP structure have not considered the influences of initial imperfections, pipe-soil interaction, and centralizers between the inner and outer pipes, for which they have certain limitations. Moreover, experimental studies have been scarcely reported in articles. Therefore, experiments were conducted with nine specimens with different initial wavelengths and amplitudes. Then, based on these experiments, the influence of the initial imperfections on the critical axial force, the critical temperature difference and critical displacement are discussed. In addition, a finite element model was established to simulate the experimental specimens. Based on a nonlinear finite element analysis, a parametric study was conducted to analyze the influence of several variables in the lateral buckling of the PIP structure, namely, the initial imperfections, the pipe-soil interaction, and the height and number of centralizers. The obtained results are presented and discussed. Finally, an analytical equation to compute the lateral buckling axial force is derived and verified based on the obtained experimental and numerical results. By comparing results with a practical project in South China Sea, the formula is shown to have high accuracy, which can provide a corresponding basis for steel pipeline design.