Dimensional analysis of SDOF systems rocking on inelastic soil

Aiming to derive results of generalized applicability and provide a generalization framework for future research on the subject, this article performs a dimensional analysis of SDOF systems rocking on compliant soil, taking account of soil inelasticity, foundation uplifting, and P-?effects. The effectiveness of the proposed formulation, under static and dynamic conditions, is verified through numerical analyses of self-similar equivalent systems. Then, a parametric study is conducted to gain further insights on the key factors affecting the performance, with emphasis on metaplastic ductility and toppling rotation. It is shown that P-?effects may lead to a substantial reduction of (monotonic) moment capacity, especially in the case of slender and heavily loaded structures. Interestingly, this reduction in moment capacity is compensated (to some extent) by an overstrength that develops during cyclic loading. Asymmetric (near-field) seismic excitations tend to produce larger maximum and permanent rotation, compared to symmetric multi-cycle (far-field) excitations, which are critical in terms of settlement. The dimensionless toppling rotation ult /c (where c is the toppling rotation of the equivalent rigid block) is shown to be a function of the factor of safety against vertical loads FS v and the slenderness ratio h/B. In the case of lightly loaded systems (FS v ), soil plastification is limited and the metaplastic response approaches that of the equivalent rigid block: ult /c 1. The toppling rotation ult /c is shown to decrease with FS v : ult /c 0 for FS v 1. The role of the h/B becomes increasingly important when the response is governed by soil nonlinearity (FS v 1). Finally, an approximate simplified empirical equation is proposed, correlating ult /c with h/B and FS v.