E0-190-2008_(8)Chapter_6(Substructure_Method)

# 8 without a void the displacement vector xsfq xssqt

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Unformatted text preview: without a void, the displacement vector {{XsFq} {XsSq}}T, and the stress vector {σ} on the F can be obtained. Appling the stress vector {σ} in the reverse direction on the interface F as shown in Fig.9: the displacement vector {{XσFq} {XσSq}}T are caused. The numerical condition of Fig.7: can be decomposed into that of Fig.8 and Fig.9: and sum of Fig.8 and Fig.9 satisfy the disappearance of the stress {σ} along the F. {XFq}={XSFq}+{XσFq} The displacement vectors {{XFq} {XSq}}T are the earthquake response of the soil with the void, (22) which can be expressed by the sum of {{XsFq} {XsSq}}T and {{XσFq} {XσSq}}T. In Eq.(22): (22) The first term in the right hand side corresponds to the earthquake response of the soil without a void, while the second to the response of the soil without the void due to the counter stress -{σ} on the interface F. Expressing the dynamic stiffness of the soil within the void by [KV] , which will be excavated as shown in Fig.10: Then, the equation of motion f...
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## This note was uploaded on 03/14/2014 for the course CE 5680 taught by Professor Drgrd during the Summer '14 term at Indian Institute of Technology, Chennai.

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