Resumo : |
In this work, it was developed an exact solution for radial consolidation of cohesive soils by means of vertical drains, taking into account that the smeared soil mass near to drains is compressible and therefore undergoes consolidation. For this purpose, this research considers the consolidation equation proposed by Barron for vertical drains with free vertical strains. The solution was developed as a Fourier-Bessel series, that is, an infinite series based on Bessel eigenfunctions. These eigenfunctions were defined separately for non-smeared soils (far from the vertical drains) and for smeared soils, to which Barron's consolidation equation had distinct parameters (hydraulic conductivity and compression coefficient). The presented problem was then solved through analogy to heat and mass diffusion, as presented by Mikhailov and Özisik. Hence, fullfilment of both boundary conditions and continuity conditions between the two regions mentioned led to an eigenvalue problem, which was solved by the sign-count technique, as developed by Wittrick and Williams. For most of usual spacing values between either synthetic drains or granular columns, results were very similar to the results of Barron's solution, where smeared region did not undergo compression. In other words, the compressibility of the smeared region is not an important phenomenon in most practical cases, and the simpler solution developed by Barron leads to satisfactory results. Nevertheless, for practical cases of small spacing between sand drains, the presented solution (which is more exact) may produce a dissipation rate more than three times slower. In other words, this work showed that there are plausible situations in which Barron's solution lead to unsafe results. |