A hypoplastic macroelement model for shallow foundations under monotonic and cyclic loads

In this work, a macroelement for shallow foundations on sands has been developed based on the theory of hypoplasticity. The incrementally nonlinear constitutive equations of the macromodel are defined in terms of generalized forces and displacements and are constructed based on the general approach proposed by Niemunis (Extended Hypoplastic Models for Soils. Habilitation Thesis, Bochum University, 2002). A suitable vectorial internal variable—mimicking the concept of intergranular strain introduced by Niemunis and Herle (Mech Cohes Frict Mater 2:279–299, 1997) for continuum hypoplasticity—is employed to provide the model sufficient memory of past displacement history to be able to reproduce the observed behavior under cyclic loading paths. As compared to similar macroelements formulated within the framework of the theory of elastoplasticity, the proposed approach has the advantage of a much simpler mathematical structure, which allows a straightforward implementation in existing structural analysis FE codes. The model performance has then been evaluated by comparing the model predictions with available experimental results from a series of small-scale model tests reported by Nova and Montrasio (Geotechnique 41:243–256, 1991). Overall, the model captures reasonably well the observed response under nonproportional, complex loading paths. A series of simulations reproducing the tests performed by di Prisco et al. (Shallow footing under cyclic loading: experimental behaviour and constitutive modelling. Patron, Bologna, 2003) has also demonstrated the potential of the proposed model to simulate the observed behavior of footings under cyclic loading paths, at least from a qualitative point of view.