Time Factor in Consolidation: Critical Review

The magnitude of consolidation settlement is often calculated using Terzaghi’s expression for average degree of consolidation ($U$) with respect to time. Developed during a time of limited computing capabilities, Terzaghi’s series solution to the one-dimensional consolidation equation was generalized using a dimensionless time factor ($T$), where a single $U\text{-}T$ curve is used to describe the consolidation behavior of both singly and doubly drained strata. As a result, any comparisons between one- and two-way drainage are indirect and confined to discrete values of time. By introducing a modified time factor $T^{*}$ in terms of layer thickness ($D$) instead of the maximum drainage path length ($H_{\text{dr}}$), it is now possible to observe the effect of drainage conditions over a continuous range of time for a variety of asymmetric initial excess pore pressure distributions. Although two separate $U\text{-}T$ plots are required (for singly and doubly drained cases), the time factor at specific times remains the same for both cases, enabling a direct visual comparison. The importance of a revised time factor is evident when observing the endpoint of consolidation, which occurs as $U$ approaches 100%. This occurs at $T^{*}\cong 0.5$ for two-way drainage and at $T^{*}\cong 2$ for one-way drainage, an observation not possible using the traditional expression for time factor.