Time evolution of stability of leaning towers.

The paper deals with 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 one refers to an attenuating creep: in this case, the long term equilibrium condition of the system is analitically 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 put into evidence the role of the involved geometrical and mechanical parameters.