Numerical modeling of rocking of shallow foundations subjected to slow cyclic loading with consideration of soil-structure interaction

Strong Vibration of buildings during seismic or wind loading may result in an uplift or partial separation of the foundation from the underneath soil. To date, various researches have indicated that Soil-Structure Interaction (SSI) has many favorable features including a probable increase in natural period of the soil-structure system and also a decrease in shear base demand in structures. Furthermore, Rocking is one of the most important factors in describing the rotational behavior of a structure built on a shallow foundation especially on a soft soil which can affect the dynamic behavior of the structure noticeably. To study the effects of rocking of shallow foundations subjected to slow cyclic loading with consideration of soil-structure interaction, a Finite Element Method (FEM) using ABAQUS software has been deployed to simulate the rocking motion of shallow foundations. For a more efficient simulation of the soil, both linear and non-linear elasto-plastic behavior of the soil has been taken into account in the analysis using the sub-routine coded in FORTRAN. The results notably show that allowing the foundation to rock may result in stiffness degradation of the soil-structure system and an increase in energy dissipation of soil-structure, especially in high rise structures. Additionally, results describe that deploying the linear elastic-perfect plastic approach may result in higher uplift of the foundation in comparison to that using a non-linear elasto-plastic approach, particularly in structures with lower heights.

💡 Research Summary

The paper investigates the rocking behavior of shallow foundations subjected to slow cyclic lateral loading, explicitly accounting for soil‑structure interaction (SSI). Using the finite‑element software ABAQUS, three building models (10, 20, and 30 stories, heights 30 m, 60 m, and 90 m) are coupled with a 20 m × 20 m rigid foundation and surrounding granular soil. Two constitutive representations for the soil are compared: (i) a linear elastic‑perfect‑plastic (E‑PP) model and (ii) a nonlinear elastic‑plastic (N‑EP) model that incorporates strain‑dependent shear modulus reduction and pressure‑dependent yielding, implemented through a custom FORTRAN sub‑routine based on Seed‑Idriss (1970) and Krämmer (1996) formulations. Rayleigh damping (α, β) is applied (8 % for soil, 5 % for the superstructure) to capture energy dissipation.

The loading protocol consists of three clusters of sinusoidal displacement histories, each containing three cycles with increasing amplitudes (0.25 m, 0.5 m, 0.75 m). During each cycle, rotation, moment, uplift, and settlement at the soil‑foundation interface are recorded, allowing construction of rotation‑moment hysteresis loops and evaluation of stiffness degradation and energy dissipation.

Key findings are:

1. Static Settlement – The linear model predicts settlements close to the Mayne‑Poulos (1999) analytical estimate (≈ 7–9 cm for the 10‑story case), whereas the nonlinear model yields substantially larger permanent settlements (≈ 57 cm for the same case) due to shear‑modulus degradation at high strains.

2. Stiffness Degradation – With increasing rotation, the contact area between foundation and soil reduces, causing a drop in rotational stiffness. The nonlinear model exhibits a 10‑15 % greater stiffness loss than the linear model, especially pronounced for the 30‑story building.

3. Energy Dissipation – Hysteresis loop areas are markedly larger for the nonlinear model, indicating 30‑40 % more input energy dissipated per cycle. Energy dissipation grows with both rotation amplitude and building height, confirming that rocking is an effective damping mechanism for high‑rise structures.

4. Uplift Behavior – The linear elastic‑perfect‑plastic model predicts higher uplift because the soil retains its stiffness up to the yield surface, whereas the nonlinear model yields earlier, reducing the uplift magnitude as the foundation re‑contacts the softened soil.

5. Contact Area and Mobilized Moment – The ratio of actual contact area to total foundation area (ζ) decreases with rotation. The nonlinear model can sustain higher mobilized moments at lower ζ values, suggesting improved overturning resistance compared with the linear model.

6. Experimental Validation – The numerical framework is validated against the S21 centrifuge test (Rosebrook & Kutter, 2015), which involved an aluminum shear‑wall structure on Nevada sand at 20 g. The rotation‑moment response from the nonlinear model matches the test data within 5 % error, confirming the adequacy of the custom soil sub‑routine.

The authors conclude that allowing controlled rocking of shallow foundations can beneficially increase the overall system period, reduce base shear demand, and provide substantial energy dissipation, particularly for slender high‑rise buildings. However, the nonlinear elastic‑plastic approach, while more realistic in capturing energy dissipation, also predicts significant permanent settlements that could be detrimental if not accounted for in design. Consequently, designers should consider a balanced strategy: exploit rocking for its damping advantages while rigorously evaluating permanent deformations and uplift, possibly employing a hybrid constitutive scheme that captures early yielding without excessive settlement.