The objectives of this project are (1) to extend the variability methods of seismic analysis to situations where the soil boundary swiftness matrix is associated with an unbounded region, and (2) to develop a set of nonlinear constitutive equations for the soil. This will make it possible to evaluate the effects of variation in the soil constitutive properties on the seismic ground motions and hence on the response of soil-(embedded) structure systems subjected to such ground motions. These results will be verified against Monte Carlo simulations. The algebraic complexities of the formulae depicting the higher-order statistical approximations will be handled in a digital computer by symbolic manipulation languages germane to artificial intelligence procedures. Automated sequential refinements of the final results of the statistical correlations will be explored. A major effort will be expended to develop a computer code which implements an appropriate stochastic equivalent linearization method within the framework of a finite element analysis to achieve this objective. Efforts will also be made to develop analytical outlines as to how the variability and nonlinear response analyses can be combined. This project will seek to fully extend the applicability of stochastic methods in earthquake engineering so that the inherent randomness and uncertainty existing in these problems can be rationally dealt with.
