| A substructure subtraction method for dynamic analysis of soil-structure interaction problems involving embedded structures, including pile foundations, is presented. The method is applicable to cases involving both direct and seismic loads. Also, a new sectional soil-pile finite element has been developed for dynamic analysis of pile foundations. The new element and the subtraction method have been used to model and analyze several dynamic problems accurately and efficiently.; The substructure subtraction method partitions a soil-structure system into three substructures. They are the free-field site, the excavated soil volume and the structure. As in the process of construction, the foundation of the structure replaces the excavated soil. Similarly, the method subtracts the mass and stiffness of the excavated soil volume from the system and adds in the corresponding properties of the structure. The advantage of this substructuring technique is that it eliminates the need for a separate scattering analysis. The subtraction method recognizes that soil-structure interaction occurs only at the common boundary of the substructures, that is, at the boundary of the foundation.; For soil-structure interaction problems, an impedance analysis involves determining the impedance matrix for the interaction degrees of freedom in the free-field-site substructure. The subtraction method uses the same procedure for impedance analysis as the flexible volume method. The latter is another substructure method which, unnecessarily, assumes that interaction occurs between the free-field site and the entire excavated soil volume. In general, the flexible volume method and the new subtraction method give identical results. However, the subtraction method is preferable because it involves fewer interaction degrees of freedom and thus requires less computational effort for the impedance analysis for cases involving embedded structures. The difference is significant when the foundations of structures are wide and deep, as is the case for large pile groups.; The subtraction method has been implemented into an existing computer program SASSI (System for Analysis of Soil-Structure Interaction) which operates in the frequency domain and thus assumes that all materials are linearly viscoelastic. Studies using the modified program investigate the accuracy and validity of the new method using several examples. The examples include embedded massless circular foundations, both rigid and flexible, and pile foundations. In some of the examples, advantage is taken of symmetry and anti-symmetry.; The proposed sectional soil-pile element consists of a soil part and a pile volume zone. In general, several soil-pile elements and a beam element are required to model a pile segment and the soil next to it. The beam element provides the mass and stiffness properties of the pile segment. The element can be used to model piles in a layered site. The sectional soil-pile element has been coded as part of the element library of SASSI. The validity of the element is investigated using several available solutions for the dynamic response of piles and pile groups.; The results of this study indicate that the substructure subtraction method provides accurate solutions to soil-structure interaction problems and requires fewer computing resources than the flexible volume method. The proposed sectional soil-pile element provides acceptable accuracy for dynamic problems involving pile foundations. |
