This paper presents a numerical study of soil-structure interaction (SSI) and structure-soil-structure interaction (SSSI) effects on response of twin buildings during earthquake excitations. The buildings are modeled as shear buildings and the soil is simulated by a discrete model representing a visco-elastic half-space subjected to earthquake acceleration. Equation of motion of twin buildings with different conditions, fixed based (FB), SSI and SSSI, are developed via an analytical procedure and solved numerically. Buildings responses are evaluated for aforementioned three conditions considering various soil types and compared together. One must say that soil causes change in distribution of responses throughout the buildings while ignoring soil interaction may lead to detrimental effects on buildings. Anyway, interaction between twin buildings with SSSI condition slightly mitigates soil unfavorable effects compare to one building with SSI condition. In addition, it is found that influence of soil is very significant for soft to stiff soils whereas negligible for hard soils.

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We study the minimizers of a functional on the set of partitions of a domain Ω ⊂ R n into N subsets W j of locally finite perimeter in Ω, whose main term is N j=1 ´Ω∩∂W j a(x)∂H n−1 (x). Here the positive bounded function a may for instance be related to the Landscape function of some Schrödinger operator. We prove the existence of minimizers through the equivalence with a weak formulation, and the local Ahlfors regularity and uniform rectifiability of the boundaries Ω ∩ ∂W j .