Simplified and / or Analytical Methods
The comprehensive nature of the proposed research makes it difficult to develop a general simplified methodology for the complete problem. Nevertheless, some aspects of the problem or some individual sub-problems are amenable to analytical treatment.
The linear Winkler model has been a key physical approximation to the analysis of the idealized problem of rocking on a rigid or elastic base. Although this will by no means be the principal focus of the research, development of analytical solutions for such simplified problems will offer a valuable starting point for the subsequent more comprehensive analyses.
A simplified way to account for the effects of “plastic hinging” in the foundation is by development of a “macro–element”. Considered attached at the base of the footing, such an element can be nothing more than a nonlinear–inelastic rotational spring, the M–θ characteristics of which reflect : geometric (due to uplifting) and material (due to mobilisation of soil failure mechanisms) nonlinearities; degradation due to P–Δ effects ; and influence of cyclic loading.
Task 3.1. : Elastoplastic Winkler Models
Task 3.2. : Development of Macro–Elements