1-D consolidation of a single soil layer with depth-dependent stress by multi-stage loading

In geotechnical engineering, when the strength of soft soils is relatively low, a rapid loading rate can lead to ground failure. In this situation, a multi-stage loading scheme can be utilized to achieve higher soil strength by consolidating the soil layer to a certain degree before applying the next, larger load(s). Additionally, the total stress in the soil layer usually varies, and, in many cases, this variation is not uniform with depth, for example, when the loading is applied within a small area over a thick soil layer. In this study, a thorough, explicit analytical solution is presented for the consolidation of a single soil layer using a multi-stage loading with depth-dependent total stress. The particular case of a two-stage loading scheme is selected to investigate the consolidation behavior of a soil layer. Finally, the convergence of the analytical solution is assessed by comparing the calculated results using the various terms of the series to facilitate the use of the solution by engineers and to provide sufficient accuracy.