Analysis of torsionally loaded non-uniform circular piles in multi-layered non-homogeneous elastic soils

Abstract

A new method for the torsional analysis of non-uniform circular piles partially or fully embedded in multi-layered elastic soils is developed. The mechanical response of non-uniform piles such as those with a linear variation in cross-section (i.e., tapered piles) or discontinuous variations (i.e., stepped piles), and reacting against a non-homogeneous elastic soil can be easily investigated with the proposed formulation. The non-homogeneity of the soil is incorporated by assuming a shear modulus distribution that fits a quadratic equation (i.e., G(z)=Go+sz+tz2). The governing differential equation (GDE) of a single non-uniform circular pile segment is derived and solved using the differential transformation method (DTM); then, the stiffness matrix of the segment is found by applying equilibrium and compatibility conditions at the ends of the element. The analysis of non-uniform piles in multi-layered soils is conducted by dividing the pile into multiple segments (i.e., each segment representing a change in soil properties or pile geometry) and then assembling them using classic matrix methods. The proposed matrix formulation is simple to implement, easy to incorporate into already available structural matrix analysis codes and provides accurate results when compared with more cumbersome analytical and numerical solutions. The simplicity, practicality and accuracy of the method is validated with five illustrative examples.