Table 1 Summary of the research methods for assessing or estimating the interaction behaviours between a buried pipeline and frost heave/thaw.

Nixon, et al.¹⁶

Soil: Elastic or nonlinear viscous continuum

Boundary: Nonlinear boundary

Pipeline: Completely passive component

The pipelines were regarded as completely passive components; The frost heave was separated from pipeline stress; The frost heave was treated as linear expansion

Selvadurai, et al.^19,20

Soil: Elastic, viscoplastic body

Pipeline: Flexible Beam

Frost heave: Water heat coupling

Characteristic: Separate consideration

Wu, et al.²¹ Wu, et al.²²

Soil: Elastoplastic body

Pipeline: Beam Unit

Frost heave: coefficient of linear expansion

Selvadurai and Shinde¹⁸

Soil: Elastic foundation

Pipeline: Beam element/solid element/shell element

Frost heave manifestation: experience determines the geometric shape and development of frost bubble growth

The manifestation of frost heave does not align with empirical observations

Kanie, et al.²³

Soil: Elastic foundation

Pipeline: Beam

Frost heave: Takashi empirical equation

Nixon²⁴

Frost heave: Separation ice model

Focus: Two dimensional frost heave prediction

Mainly aimed at predicting frost heave

Zheng, et al.²⁶,²⁷

Frost heave: Improvement of Takashi’s empirical equation

Focus: Two dimensional and three-dimensional frost heave prediction

Rajani and Morgenstern¹⁷

Soil: Elastoplastic foundation

Pipeline: Beam

Focus: Anti pull behavior of shallow buried pipelines

Non frozen soil

Liu²⁸

Soil: Elastic foundation

Pipeline: Thin walled structure

Focus: Mechanical behavior analysis of pipeline cross-section