Probabilistic analysis of crown settlement in high-speed railway tunnel constructed by sequential excavation method considering soil spatial variability

•(1) A new method of simulating soil spatial variability based on the UHPM is proposed.•(2) Ignoring soil spatial variability leads to small monitoring result.•(3) The influence of horizontal and vertical SOF on the crown settlement is studied. High-speed railways (HSRs) are extensively constructed in China, with the help of tunnels to cross through complex geological conditions. The sequential excavation method (SEM) is vastly adopted in the construction of loess tunnel. This study performs a probabilistic analysis of crown settlement, taking into account the spatial variability of the surrounding soil through Monte Carlo (MC) simulations. To illustrate the influence of horizontal and vertical scale fluctuations (SOFs) on crown settlement, an anisotropic random field of loess elastic modulus is simulated using the spectral representation method (SRM) and unified Hermite polynomial model (UHPM) for the random finite difference method (RFDM). The mean crown settlements obtained through stochastic analysis are consistently larger than the deterministic results in the 1st, 6th, and 9th construction steps. The maximum probabilities of stochastic crown settlement exceeding the deterministic results are 77.3% and 78.2% with varying horizontal and vertical SOFs, respectively. Amplification factors of 1.417 and 1.306 are necessary to ensure that the stochastic crown settlement of the HSR tunnel, constructed in spatially variable loess, satisfies a 5% and 10% exceeding probability. This study provides valuable guidance for the construction of HSR tunnels.