A. S. Osman

Analytical Solution for the Consolidation around a Laterally Loaded Pile

This paper presents a closed-form analytical solution for the consolidation of soil around a laterally loaded pile, assuming the soil skeleton deforms elastically and under plane strain conditions. The problem is idealized as a circular rigid disk surrounded by a deformable soil zone. Drainage is assumed to occur at the boundary of the assumed zone of deformable soil around the pile. The response around the pile is obtained using an uncoupled consolidation analysis. The solution for the governing equation of excess pore water pressure is found by using the separation of variables technique. Expressions for the initial excess pore water pressure distribution are derived from the mean total stress changes given by the elastic solution. Curves showing decay of the excess pore water pressure with time, and also the variation of pile displacement, are plotted in nondimensional form. The parameters that affect the displacement prediction are illustrated and discussed. Comparison with three-dimensional analysis of a laterally loaded pile shows that the two-dimensional analysis can reasonably predict the consolidation process along the shaft of the pile.

Comparison between Coupled and Uncoupled Consolidation Analysis of a Rigid Sphere in a Porous Elastic Infinite Space

Linear consolidation analyses are usually treated either by means of Terzaghi-Rendulic uncoupled theory or Biots consolidation theory. In this note, the problem of consolidation displacements around an axially loaded sphere was considered. It is demonstrated that both the uncoupled analysis and the coupled analysis give the same governing equation for pore fluid pressure dissipation with time. A simplified procedure for deriving transient strain components is illustrated. A general solution for time-dependent displacements is obtained using uncoupled consolidation analysis. Close agreement is evident between the new approximate uncoupled analysis solution and the existing coupled analysis solution with a maximum error of less than 0.5%.

A semi-analytical solution for consolidation around a spherical cavity in an elasto-plastic medium and its potential application for tunneling

An analytical solution for consolidation around spherical cavity contraction is developed. This solution has the potential to evaluate consolidation around tunnel heads. The initial excess pore water pressure immediately after the creation of the cavity is estimated from the cavity expansion/contraction theory using a linear-elastic-perfectly-plastic soil model. Expressions for the decay of pore water pressure with time are obtained using elasticity. Curves showing the variation of pore water pressure with time are plotted in nondimensional form. Comparison with two-dimensional coupled stress-pore pressure finite element analysis shows that the proposed semi-analytical solution can successfully predict the poro-elasto-plastic behavior around spherical cavity.