Analysis of Combined Vertical and Radial Consolidation of Soil under Time-Dependent Loading

Fine-grained compressible soils are usually associated with strength challenges in the course of carrying structures, roadways, embankments, and other civil engineering facilities. In addition, due to their low permeabilities, compressible soils take an awfully long duration to achieve optimal consolidation, with its attendant negative effects on the facilities supported by the soils. Engineering practitioners and researchers have established the efficacy of vertical drains for accelerating the consolidation process of such soils through the shortening of horizontal flow distances, thereby stabilizing them and improving their load-bearing capacities. Application of the pre-loading surcharge provides additional drive for rapid consolidation. The case of soils carrying time-dependent loading is quite topical because it reflects reality most appropriately. However, a rigorous analysis of soils undergoing vertical and radial consolidation with a constant or time-varying surcharge is conspicuously lacking in the literature because most authors of publications in this subject area have largely based their solution procedure on the assumed decoupling of the vertical and radial flows by treating their associated pore pressures as separate. This assumption, notwithstanding the simplification it introduces into the mathematics of the problem, is not supported by physics. Therefore, the theory presented herein aims at addressing that gap in the literature. Throughout this analysis, the coupled (vertical and radial) flow, driven by a common pore water pressure, is handled as a single process. Successive applications of the integral transformations of Laplace and finite Hankel have been used to obtain an explicit expression for the image of the pore water pressure as a function of the transformation parameters. This is followed by successive inversions of the integral transforms, leading to a closed-form solution in the sense of a generalized Fourier series. The classical definition of the average degree of consolidation is easily applied in this case, unlike other methods in the literature that rely on the principle of superposition, whose applicability in this circumstance remains questionable. The validity of the present analysis has been established through logical checks and comparison with previous results in the literature. This theory has been proven to be applicable to cases of constant as well as time-varying surcharges.

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