Stiffness matrix method for analysis of torsionally loaded piles in multi-layered soil

A new, simple, and practical method to investigate the response of torsionally loaded piles on homogeneous or non-homogeneous multi-layered elastic soil is developed. The soil non-homogeneity is accounted for by assuming for each layer a shear modulus distribution that fits a quadratic function. The analysis of piles in multi-layered soil is carried out by subdividing the pile, at the soil-soil layer and soil-air interfaces, into multiple elements, and then using conventional matrix methods -such as those commonly implemented in structural analysis- to connect them. The governing differential equation (GDE) of an individual structural element is solved using the Differential Transformation Method (DTM). Next, the stiffness matrix is derived by applying compatibility conditions at the ends of the element. Piles partially or fully embedded in multiple layers and subjected to torsion can be analyzed in a simple manner with the proposed formulation -a tedious endeavor with other available solutions. Finally, explicit expressions for the coefficients of the matrix are provided. Four examples are presented to show the simplicity, accuracy, and capabilities of the proposed formulation.