Time evolution of stability of leaning towers

The paper deals with the time-history of tilting and final conditions - long term equilibrium or failure - of a tower (T) resting on deformable soils (S). The analysis is carried out on the base of a visco-elasto-plastic constitutive model, with a non associated flow rule, representing the mechanical response of the soil-foundation (F) geotechnical system, under loads whose intensity varies due to the time evolution of displacements of both F and T. The hardening function depends on the ratio between the current overturning moment on F and its ultimate value as well as on the ratio between the weight of the T-F system and the bearing capacity of the S-F system. The analysis reveals that the rotation of the T-F-S system may evolve according to two alternative possibilities. The first refers to an attenuating creep: in this case, the long term equilibrium condition of the system is analytically determined. The second possibility deals with creep rotations growing up towards the instability condition: the critical time, i.e. the time for tilting failure of the system, and the critical rotation are obtained. Simple computations show the role of the geometrical and mechanical parameters involved.