Simple Approach to Consolidation Due to Constant Rate Loading in Clays

Terzaghi’s one-dimensional consolidation theory is extended to constant rate of loading, where a simple expression relating average degree of consolidation and time factor is derived. This expression is used to assess Terzaghi’s approximation that the ramp load can be assumed as an instantaneous load, applied at $t_0\text{/}2$, where $t_0$ is the duration of loading. It is shown that this assumption overestimates the degree of consolidation by approximately 10%. Terzaghi’s approximation can be improved in two simple ways: (1) assume the load acts at $t_0\text{/}2$, estimate the degree of consolidation, and reduce it by 10% or (2) assume the load to act at $2t_0\text{/}5$ rather than $t_0\text{/}2$ in estimating the degree of consolidation, with no further adjustment. Nevertheless, the single $U\text{-}T$ expression developed herein maintains a level of simplicity comparable to Terzaghi’s approximation and is adequate for all practical purposes for computing the degree of consolidation during the loading, as well as beyond completion of loading. A numerical example is also given to illustrate the use of the proposed $U\text{-}T$ values for constant rate of loading.