9503766 Spanos This project conducts a research investigation featuring improved models which accurately describe the seismic response of equipment and of some other block-like structural systems. The approach undertaken in this study considers the impact of the block with the foundation as a continuous process of time. This impact model represents the influence of most of the important geometrical, mechanical, and material quantities such as material stiffness, block aspect ratio, value of the coefficient of friction, and the plastic behavior of the structure. Further, new numerical methods for analysis and design of multi-block systems based on versatile discrete element method will be developed. Stochastic analysis of block-like structures under earthquake excitations will also be carried out. Upon developing the theoretical and numerical aspects of the proposed methods, these models and the analyses will be applied to investigate the design problems of a variety of practical equipment and historical monuments structures. ***