ANALYTICAL MAPPED LAYER FOR AXISYMMETRIC PROBLEMS OF PILES IN STRATIFIED SOIL UNDERLAIN BY A BEDROCK

A novel semi-infinite layer to analyze axisymmetric problems of piles embedded in stratified soil with

an underlying bedrock is presented. This layer is unbounded in the radial direction and has a finite

thickness in the axial direction. It involves a mapping process to transform the cylindrical unbounded

domain to a local finite domain. Proper decay is introduced along the radial direction by using local

polynomials to interpolate displacements within the layer. Explicit expressions for stiffness

coefficients of the unbounded layer are derived. Hence, it is proved that the standard shape functions

of mapped infinite elements give divergent improper integrals for the stiffness of the unbounded

domain. This matter is fixed by developing new displacement functions based on continuity

properties for the first derivatives of displacements at infinity and Lagrange polynomials. Using these

functions, the stiffness matrix of the mapped layer is evaluated analytically. The accuracy of the

analytical mapped layer is verified by comparison with existing elastic solutions for piles embedded in

a single soil stratum. Then, useful results for axially loaded piles embedded in stratified soil with

underlying bedrock are presented.