Dealing with uncertainty in Earthquake Engineering: a discussion on the application of the Theory of Open Dynamical Systems
Earthquakes, as a natural phenomenon and their consequences upon structures, have been addressed from deterministic, pseudo-empirical and primary statistical-probabilistic points of view. In the latter approach, 'primary' is meant to suggest that randomness has been artificially introduced into the variables of investigation. An alternative view has been advanced by a number ofresearchers that have classified earthquakes as chaotic from an ontological perspective. Their arguments are founded in the high degree of non-linearity of the equations ruling the corresponding seismic waves. However, the sensitivity of long time behavior of dynamic systems to variations in initial conditions, known as the Chaos Paradigm appears as a by-product of a deeper insight into natural phenomena known as Theory of Open Dynamical Systems ODS. An open system is currently defined as the relation between a part of nature, the main system which contains the observations we make, and its surrounding environment. ODS theory has been applied to different research subjects including physics, chemistry, and biology, for identifying and controlling undesired chaotic behavior in highly nonlinear dynamic systems. It is suggested that earthquakes and their interaction with structures constitute an example of an open system. Recognizing that in Earthquake Engineering the application of those concepts has not been previously investigated, in this paper a discussion related to the use of ODS concepts in that particular field is presented. Using the most basic case of a linear elastic single degree offreedom SDOF oscillator, differences in the prediction of the response of the system subjected to only one ground motion using a Newton classical approach and ODS concepts, which involve stochastic processes, are compared. Conclusions about the consequences of the application of ODS theory for re-understanding Earthquake Engineering are presented, and a general critique to primary probabilistic approaches for addressing the same problem is formulated.