A Semi Analytical Model for Elastic Settlements of End-Bearing Piles in Inhomogeneous Soils

In this study, a novel approximate static solution is derived for the elastic settlements of end-bearing piles in vertically inhomogeneous soils. Following the seminal work of Nogami & Novak 1976 and previous work by some of the authors, the pile is modelled as a rod, and the soil as an approximate continuum of the Tajimi type. Soil inhomogeneity is introduced via a generalized power law variation of the soil shear modulus with depth. The eigenvalues and the associated soil modes are now obtained by solving a generalized eigenvalue problem that emerges from the use of appropriate shape functions in the solution, which satisfy the boundary conditions of the pile-soil system. Unlike existing models for homogeneous soil, the associated Fourier coefficients are now coupled and obtained as solutions to a set of simultaneous algebraic equations of equal rank to the number of modes considered. The solution is expressed in terms of generalized Fourier series and includes: (1) displacements and stress fields within the soil and along the pile-soil interface; (2) displacements and normal stresses along the pile length, and (3) static pile head stiffness. The results obtained from the proposed solution compare well against results from available methods in the literature.