Simplified approximate method for analysis of rocking systems accounting for soil inelasticity and foundation uplifting

• The paper develops a simplified approximate method to analyze rocking systems.
• The proposed method takes account of soil nonlinearity and foundation uplifting.
• A nonlinear rotational spring is employed, not requiring iterations.
• A simplified procedure to compute the dynamic settlement is outlined.
• The effectiveness of the method is verified through dynamic time history analyses.

A simplified approximate method to analyze the rocking response of SDOF systems lying on compliant soil is introduced, accounting for soil inelasticity and foundation uplifting. The soil–foundation system is replaced by a nonlinear rotational spring, accompanied by a linear rotational dashpot, and linear horizontal and vertical springs and dashpots. Considering a square footing on clay under undrained conditions, the necessary moment–rotation (M–θ) relations are computed through monotonic pushover finite element (FE) analyses, employing a thoroughly-validated constitutive model. Cyclic pushover analyses are performed to compute the damping–rotation (CR–θ) relations, necessary to calibrate the rotational dashpot, and the settlement–rotation (Δw–θ) relations, required to estimate the dynamic settlement. The effectiveness of the simplified method is verified through dynamic time history analyses, comparing its predictions with the results of 3D FE analyses. The simplified method is shown to capture the entire rotation time history θ(t) with adequate accuracy. The latter is used to compute the time history of dynamic settlement w(t), employing a simplified approximate procedure. The proposed simplified method should, by no means, be considered a substitute for more sophisticated analysis methods. However, despite its limitations, it may be utilized for (at least preliminary) design purposes.