Geodesic
The effective model of porous block medium with slide contact on interfaces
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 30, Tome 275 (2001), pp. 140-164

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The medium under consideration consists of equal rectangle cells. The every cell contains four rectangle porous blocks with slide contact on interfaces between blocks. For this medium the effective model is established. This effective model is described by thirteen equations, is five-phase, and consists of four elastic phases and one fluid phase. In this model five waves propagate. The fronts of three waves are convex but two waves have concave fronts. The velocities of the waves along the axes are roots of equations which are derived in the paper. 
@article{ZNSL_2001_275_a11,
     author = {L. A. Molotkov},
     title = {The effective model of porous block medium with slide contact on interfaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {140--164},
     publisher = {mathdoc},
     volume = {275},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_275_a11/}
}
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L. A. Molotkov. The effective model of porous block medium with slide contact on interfaces. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 30, Tome 275 (2001), pp. 140-164. http://geodesic.mathdoc.fr/item/ZNSL_2001_275_a11/