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A rigorous mathematical formulation for the kinematic response of single piles embedded in multilayered soil subjected to vertically incident P-waves is proposed based on the modified Vlasov model. The governing equations and boundary conditions of the soil–pile system are obtained by using Hamilton's principle. The soil–pile interaction and the physical properties of the layered soils are taken into consideration in the proposed model. The accuracy of the proposed method is validated by the comparison of the proposed solution results with some existing solutions. A parametric study is conducted to investigate the effects of the soil inhomogeneity on the kinematic response of single piles. The results reveal that: as for the two-layered case, the thickness of the upper soft layer has a significant influence on the kinematic response of single piles; as for the three-layered case, the soil–pile interaction is very sensitive to the thickness and Young's modulus of the middle layer.
The significance of liquefaction related damage to pile foundations has been clearly demonstrated by the major earthquakes that have occurred during past years. Current project investigates seismic behaviour of a single pile in three-layered soil of Babol Citycenter site (located in Babol city, Mazandaran Province, Iran). The site soil consists of sandy and clayey soils modelled based on data collected from drilled boreholes. Numerical analysis performed using Flac2D finite difference program. Three different natural ground motion records are considered and influence of each earthquake on bending moment and horizontal displacement of the simulated pile is investigated. In addition, the effect of vertical surcharge on settlement of the pile during the earthquakes is investigated. Results illustrate that the maximum bending moments has been occurred on the interface of liquefiable and non-liquefiable soil layers.