TIME-DEPENDENT ANALYSIS OF THE INTERACTION BETWEEN MULTILAYERED FRACTIONAL VISCOELASTIC SATURATED SOILS AND BEAMS

The study of the interaction between beams and saturated soils is of great significance in both mechanics and engineering fields. In this paper, the fractional Merchant model is adopted to solve the rheological consolidation of saturated soils, which can simulate the time-depending characteristics of the soils more accurately than the common integer order viscoelastic models. Based on the solution of consolidation for multilayered cross-anisotropic viscoelastic saturated soils, the finite element method (FEM) and the boundary element method (BEM) are coupled to investigate the interaction between beams and fractional viscoelastic saturated soils. The beam is discretized into a number of elements according to the Timoshenko beam theory, and then the global stiffness matrix equation of the beam is obtained. The precise integration solution of the viscoelastic soils is considered as the kernel function of the boundary integral, and the flexibility matrix equation of soils is established by the BEM. Finally, by coupling the FEM and the BEM, the solution of the interaction between multilayered fractional viscoelastic saturated soils and the Timoshenko beam is derived by introducing the displacement coordination condition and equilibrium condition for forces between them. The soil model adopted in this study is degenerated into the Kelvin model, and the results obtained are compared with those in the existing literature, which shows a good consistency. On this basis, the effects of the fractional order and stratification of soils on the interaction between beams and viscoelastic soils are discussed. Numerical results show that: the consolidation velocity of viscoelastic saturated soils with higher fractional order is obviously faster; for layered soils, the reinforcement of topsoil can effectively control the ground settlement and reduce the differential settlement. In practical engineering, the effects of rheology of saturated soils and soil stratification should be well considered to analyze the interaction between beams and soils more accurately.