Effects of a counterweight on tilt evolution of leaning towers.

The effects of a counterweight applied on the foundation slab of a leaning tower resting on deformable soils are analysed. The analysis is carried out on the base of a visco-elasto-plastic constitutive model, representing the mechanical behaviour of the soil (S) - foundation (F) geotechnical system, under loads whose intensity varies according to the tilting of the tower. The concept of admissible counterweight is first developed. The immediate effects of an admissible counterweight, and above all the elastic tilt reduction of the tower, are then determined as a function of the geometry of the tower and of its foundation, of the characteristics - weight and eccentrity - of the counterweight as well as of the current yielding level of the S-F system. Time evolution of rotation of the foundation-tower system loaded by the counterweight is finally analysed. It is demonstrated that without further perturbations, the system generally evolves towards a long term equilibrium condition. On the contrary, expecially if the tower is subjected to perturbations, the progressively increasing rotation may lead the system towards an instability condition: the critical values of the rotation and of the time corresponding to this ultimate limit state are obtained. The analytical solutions of considered problems are expressed in closed form, making results easily applicable to practical cases.