Closed-form consolidation solutions for known loading functions

In engineering practice, loading varies with time. However, the classical one-dimensional theory of consolidation assumes the stress increase is instantaneously applied. Many approaches to the problem of time-dependent loading have been proposed over the years, from approximate methods to full developments of differential equations. The paper presents a simple method for finding a closed-form consolidation solution for time-dependent loading without the need for differential equations. Two sets of general equations were derived for both excess pore pressure and average degree of consolidation. Equations were solved for linear, parabolic, sinusoidal, and exponential load functions. Stepped and cyclic loads were also addressed and a numerical solution was developed to verify the obtained result. The method proved to be easy to apply and provides solutions with great simplicity. A case study of non-instantaneous loading on soft clay was also analyzed, and settlement prediction showed good results when compared to readings of the settlement plates.