A general simple method for calculating consolidation settlements of layered clayey soils with vertical drains under staged loadings

It is well known that the calculation of consolidation settlements of clayey soils shall consider creep compression in both "primary" consolidation and so-called secondary consolidation periods. Rigorous Hypothesis B method is a coupled method and can consider creep compression in the two periods. But this method needs to solve a set of nonlinear partial differential equations with a proper elastic viscoplastic (EVP) constitutive model so that this method is not easy to be used by engineers. Recently, Yin and his coworkers have proposed a simplified Hypothesis B method for single and two layers of soils. But this method cannot consider complicated loadings such as loading, unloading and reloading. This paper proposes and verifies a general simple method with a new logarithmic function for calculating consolidation settlements of viscous clayey soils without or with vertical drains under staged loadings such as loading, unloading and reloading. This new logarithmic function is suitable to cases of zero or very small initial effective stress. Equations of this simple method are derived for complicated loading conditions. This method is then used to calculate consolidation settlements of clayey soils in three typical cases: Case 1 is a single soil layer without vertical drains under loading only; Case 2 is a two-layered soil profile with vertical drains subjected to loading, unloading and reloading; and Case 3 is a real case of a test embankment on seabed of four soil layers installed with vertical drains under three stages of loading. Settlements of all three cases using the new general simple methods are compared with values calculated using rigorous fully coupled finite element method (FEM) with an elastic viscoplastic (EVP) constitutive model (Cases 1 and 2) and measured data for Case 3. It is found that the calculated settlements are in good agreement with values from FEM and/or measured data. It is concluded that the general simple method is suitable for calculating consolidation settlements of layered viscous clayey soils without or with vertical drains under complicated loading conditions with good accuracy and also easy to use by engineers using spreadsheet calculation.