consol2 - 53:030 Class Notes; C.C. Swan, University of Iowa...

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Period #16: Soil Compressibility and Consolidation (II) A. Review and Motivation (1) Review: In most soils, changes in total volume are associated with reductions in void volume. The volume change of the soil grains is negligible. Changes in soil volume are produced by effective stresses. When loads are applied to soils, the increased compressive stresses can initially be taken up by the pore fluid. With time, though, the pore fluid pressure dissipates, and the increased compressive stresses are transferred to the soil skeleton. As this gradually occurs, the soil will compress. (2) Motivation: The important question that remains to be answered, is how long can this take? To better understand this, a common engineering consolidation model is presented here. 1 53:030 Class Notes; C.C. Swan, University of Iowa
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B. Rate of Consolidation in One-Dimension To begin, consider a very small element of soil being subjected to one- dimensional consolidation in the z-direction. Rate of fluid mass outflow = ρ w A { v z +[ (v z )/ z] z } Rate of fluid mass inflow = ρ w A v z Net rate of fluid mass outflow = outflow - inflow = ρ w A [ (v z )/ z] z = ρ w V (v z )/ z 2 53:030 Class Notes; C.C. Swan, University of Iowa x y z A = ( x)( y) V = ( x)( y)( z) = ( A)( z) v z +[ (v z )/ z] z = exit discharge velocity v z = entry discharge velocity Saturated Soil
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fluid mass conservation for this element: net rate of fluid mass outflow = net rate of internal fluid mass decrease ρ w V (v z )/ z = - {M w }/ t = - { ρ w e V s }/ t = - ρ w V s {e}/ t Aside: Note these assumptions: a) fluid is incompressible (i.e. ( ρ w )/ t = 0); and b) soil grains are also incompressible (i.e. ( V s )/ t = 0). ρ w V (v z )/ z = - ρ w V s {e}/ t, (v z )/ z = - ( V s / V ) {e}/ t (v z )/ z= - (1+e 0 ) -1 {e}/ t statement of fluid mass conservation. For
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This note was uploaded on 11/10/2010 for the course CIVIL 53:30 taught by Professor Swan during the Fall '09 term at University of Iowa.

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consol2 - 53:030 Class Notes; C.C. Swan, University of Iowa...

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