Buckling Instability of Monopiles in Liquefied Soil via Structural Reliability Assessment Framework

During devastating earthquakes, soil liquefaction has disastrous outcomes on bridge foundations, as mentioned in books and published research. To avoid foundation failure when the surrounding soil is fully liquefied, a bridge’s pile foundation design could be such that the bridge pier is directly resting on the top of a large-diameter monopile instead of the traditional multiple small-diameter piles. This paper discusses the gap of insufficient studies on large-diameter monopiles to support railway bridges subjected to buckling instability and the lack of simplified tools to quickly assess structural reliability. A framework could quickly assess the structural reliability by formulating a simplified reliability analysis. This study focused on pure buckling with shear deformation and reliability assessment to calculate a monopile’s failure probability in fully liquefied soils. In reliability assessment, with the critical pile length (Lcrit) and the unsupported pile length (Luns), the limit state function g(x) = [Lcrit − Luns] thus forms the basis for assessing the safety and reliability of a structure, indicating the state of success or failure. The Lcrit formulation is accomplished with a differential equation. Here, Luns assumes various depths of liquefied soil. The reliability index’s (β) formulation is achieved through the Hasofer–Lind concept and then double-checked through a normal or Gaussian distribution. A case study was conducted using a high-speed railway bridge model from a published research to demonstrate the application of the proposed methodology. To validate the minimum pile diameter for buckling instability when a fully liquefied soil’s thickness reaches the condition that Lcrit = Luns, this study applies the published research of Bhattacharya and Tokimatsu. The validation results show good agreement for 0.85–0.90 m monopile diameters. With a monopile diameter smaller than 0.85 m, the Lcrit = Luns limit was at lesser depths, while with a monopile diameter larger than 0.90 m, the Lcrit = Luns limit was at deeper depths. A load increase notably affected the large-diameter monopiles because the Lcrit movement required a longer range. In fully liquefied soil, buckling will likely happen in piles with a diameter between 0.50 m and 1.60 m because the calculated probability of failure (Pf) value is nearly one. Conversely, buckling instability will likely not happen in monopiles with a diameter of 1.80–2.20 m because the Pf value is zero. Hence, the outcome of this case study suggests that the reliable monopile minimum diameter is 1.80 m for supporting a high-speed railway bridge. Lastly, this paper analyzed the shear deformation effect on large-diameter monopiles, the result of which was 0.30% of Lcrit. Shear deformation makes minimal contributions to large-diameter monopile buckling.