Risk estimation of rocking components subjected to ground motions
Keywords: stochastic analysis
Rocking
earthquake generation
non linear dynamics

The behaviour of a rocking object has fascinated the scientific community for many years. This is partly because its study is applicable to a wide variety of structural and non-structural elements, i.e., hospital equipment, industrial technology, bridge piers or art preservation. Rocking motion typically occurs in objects that are unrestrained at their base and are disturbed from their equilibrium position. However, despite the intuitive nature of rocking motion, it is in fact a highly complex dynamic problem in which sliding, uplifting, geometry, material non linearities and impacts also affect the behaviour.
Understanding of the mechanisms that may lead to failure of rocking bodies is of significant importance to quantifying and minimizing the associated risk. The most common model to describe the rocking problem is the Inverted Pendulum Model, IPM, proposed by Housner in 1963, which has been followed by multiple researchers. However, the IPM explicit makes the assumption that the contact forces are concentrated at the edges. While this concept is usually true for bodies which physical feet at their edges, it is not valid for bodies which have a flat base. Moreover, for reasons related to safety, characterizing the risk of these rocking elements subjected to ground motions is of increasing importance. Nonetheless, the mode of failure of these objects is mainly related to exceeding displacement or rotation limits. Consequently, several of the existing frameworks to estimate the risk may not be applicable. As a result, the survival of a rocking element during a ground motion is not a function of a single dominant frequency or the peak amplitude of the input. Hence, the risk of rocking elements requires the generation of realistic inputs to subject to the deterministic models.
This thesis develops a suitable dynamic model for relaxing the previous assumption of the IPM. Its effect is discussed numerically and experimentally showing that the associated uncertainty propagates to the conclusion of whether a rocking body would survive or fail when subjected to a ground excitation.
Additionally, a study of the rocking response of artifacts subjected to sound induced vibration is presented. The effect of these sound vibrations using different instruments is illustrated through the stability of artifacts. Conclusions are drawn regarding whether the case or the music source should be selected to protect the museum artifacts and which kind of music affects more the stability of these objects.
Finally, the earthquake generation problem is examined. The novel technique of implementing rejection methods with earthquakes generated from the Karhunen- Loève expansion as well as an estimation of seismological properties from the accelerogram are developed. This work will then focus on generating ground records compatible with seismological and design characteristics for the purpose of generating probability of failure curves for rocking bodies. Based on these results and to directly compare with design requirements, an innovate technique to produce the probability of failure for a lifespan is proposed. Examples comparing earthquake generation models illustrate the nowadays most optimal method for rocking bodies.