Time-behavior of pile groups based on fractional derivative soil model

Based on the finite element method, the finite element equations for the vertically loaded pile groups are established by dividing the pile groups into a number of 2-node elements. To simulate the rheologic properties of saturated soft soils, the stress-strain relationship of the fractional Merchant model is derived by the Laplace transform. The elastic-viscoelastic correspondence principle is introduced to obtain the boundary element solutions for the fractional transversely isotropic viscoelastic saturated soft soils. In light of the displacement continuity of pile-soil interfaces, the governing equation for the interaction between the pile groups and the soils is derived by coupling the finite element equations for the pile groups and the boundary element ones for the soils. Later, the time behaviors of each state variable for the pile groups can be solved by introducing the displacement conditions of the pile cap. Based on the foregoing theory, numerical examples are griven to verify the rationality of the proposed method, and then the influences of fractional numbers on the time-dependent behaviors of the pile groups are discussed.