Consolidation of the Saturated Composite Foundation With Periodic Reinforcing Piles by the FHFE Method

ABSTRACT The consolidation of the saturated composite foundation with periodic reinforcing piles (CFPP) under external loads is fundamental for the design of the composite foundation. To investigate the consolidation of the CFPP subjected to an arbitrary load accurately, the pseudo‐periodic property for the CFPP under a spatially harmonic load is introduced and proved in this study. Based on the pseudo‐periodic property of the CFPP, the Fourier harmonic finite element (FHFE) method for the CFPP is developed. To develop the method, the response of the CFPP to a spatially harmonic load is decomposed into a series of Fourier harmonics first. Then, by using the Biot's theory and virtual work principle, the FEM equations for each Fourier harmonic of the CFPP are established. By introducing the impendence matrix for the underlying half‐space bedrock, the coupled FEM equations for the Fourier harmonic of the CFPP and bedrock in the Laplace domain are developed. Solution of the coupled FEM equations for the Fourier harmonics in the Laplace domain and inversion of the Laplace transform yield the time‐spatial domain response of the CFPP to a spatially harmonic load. The total response of the CFPP to an arbitrary load can then be determined by synthesizing all the responses of the CFPP to the corresponding spatially harmonic components of the arbitrary load. With the proposed FHFE method for the CFPP, the influences of the permeability and shear modulus of the piles, spacing between the piles as well as load types are investigated.