Keywords: bifurcation, buckling, heatwave, limit point, non-linear, rail.

Extreme thermal events (heatwaves) are being recorded increasingly around the world, and a ramification of these events is an unprecedented number of reported cases of buckling of railways, since the heatwave induces compressive forces in the rails which in turn can lead to instability. Buckling of railways in plan, or lateral buckling, is localised and is akin to the buckling of shallow arches. The mechanics of the buckling phenomenon of railway tracks is relatively complex, and a number of approaches have been proposed in the scientific literature, based on limiting assumptions. Moreover, commercial finite element programs have been shown to be unsuitable for modelling the full range temperature-deflection response, because the algorithms for solving the geometric non-linear problem are not tractable to thermal loading. These formulations are deterministic, but the parameters that affect the buckling are stochastic, and so a realistic vulnerability assessment of railway buckling must consider the chance of buckling from a probabilistic basis. Using a fundamental model based on the non-linear response of shallow arches developed elsewhere by the author, this paper proposes an alternative deterministic formulation for railway instability caused by thermal straining, and it considers buckling in a lateral mode for which resistance is provided by the ballast, modelled as being plastic in shear. The deterministic formulation is tractable to Monte Carlo simulation, allowing for a rational probabilistic assessment of the vulnerability of buckling of railways and of the rationale for their adaptation.

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