Calculation method for composite modulus of flexible pile composite foundation for high-speed railway under post-work settlement source

The flexible pile composite foundation (FPCF) in deep soft soil regions often experiences post-work settlement, leading to rail irregularities in the high-speed railway (HSR). However, few studies have identified the characteristics of post-work settlement sources (PWSS) for FPCF. Hence, a calculation method for the composite modulus under the PWSS has yet to be established. Based on a full-scale field test of the FPCF for a high-speed railway (HSR), this study analysed the time-varying characteristics of the settlement and location of the PWSS. By analysing the properties of soft soil materials and the additional stress on FPCF, the formation mechanisms of PWSS were revealed. A 3D finite element model (FEM) of the FPCF-subgrade-ballastless track system was established, and the settlement curve was input at the location of the PWSS. The rationality of the numerical results was first verified through a scale-model experiment. Subsequently, based on the computational results of typical settlement transfer processes, it was found that settlement undergoes fast settlement, transitional following settlement, and following settlement during its transfer from the underlying layer to the rail. During the settlement transfer process, the reinforcement zone and embankment significantly reduced the settlement irregularities, which made the settlement of the ballastless track follow that of the subgrade bed. The pile compression modulus primarily regulated the rail amplitude, whereas the area replacement ratio primarily regulated the rail wavelength. Finally, based on the settlement transfer results, a method for determining the composite modulus was proposed, and a formula for calculating the composite modulus was derived. This formula contributes to a faster analysis of the influence of the PWSS of the FPCF on rail smoothness. •The settlement observation is performed in FPCF for HSR.•The PWSS of FPCF mainly generates slowly in the underlying layer.•Unevenness of settlement attenuates mainly in the reinforcement zone.•Establish composite modulus formula under PWSS.