Plastic and Viscous Flow Models

Computed earthquake-induced deformations in continental slope off Haifa, Israel, due to Haifa Earthquake scaled to 0.6 g. 

View from above a channelized density current (ink-dyed salt solution) that has entered a wide reservoir. (After Leeder, M.R., Sedimentology—Process and Product, Allen Unwin, London, 1982. Reprinted with permission of Taylor Francis Group.) 

This problem has been considered by Carslaw and Jaeger (1959) in the context of heat conduction and they developed the following solution  

Johnson (1970) analyzed subaerial debris flows by means of a steady-state Bingham model (plastic-viscous model with soil yield resistance, k, and linear viscosity, r ). In Johnson s model the shear stress (t ) resisting displacement is related to the velocity of movement (ra ) in the following expression  

For a slope that is uniform infinitely wide flow of thickness, H unit weight, 7 constant inclination, 5 a rigid plug of thickness Tfl can be determined as follows  

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