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Static and dynamic response of a semi-infinite porous material under a surface load

This paper studies a semi-infinite porous material containing randomly distributed spherical air voids subjected to a distributed surface load. A Green's function for a force in a semi-infinite solid with a fixed boundary condition is used to derive the elastic field. For one void embedded in a semi-infinite matrix material, using the equivalent inclusion method (EIM), the void has been replaced by the matrix but an eigenstrain is introduced to simulate the material mismatch. Through the stress equivalent condition, the eigenstrain is solved, and the elastic field can derived. The formulation is verified with the finite element simulation. When randomly distributed voids are considered, the self-consistent method has been used to evaluate the average strain in the porous material, so that the displacement of the loading head can be calculated. The formulation will be extended to dynamic loading condition too for compaction of soil or pavement materials. In addition, the proposed formulation of one-void in the semi-infinite domain can be extended to the case of multiple voids of different size and shape.

Author(s):

Gan Song    
Columbia University
United States

Huiming Yin    
Columbia University
United States