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45_CEG 4012 Notes Fall 2011 CEG 4012 Notes Fall 2011

45_CEG 4012 Notes Fall 2011 CEG 4012 Notes Fall 2011 - and...

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p29 Time Rate of Consolidation: Time ~ During the consolidation process: What %Pc will have occurred at a given time? p How much time is required for given %Pc to occur? One-Dimensional Consolidation: Theory presented by Karl Terzaghi in 1925 ENR. Assumptions: 1. The soil is fully saturated and homogenous. 2. The pore fluid and soil particles are both incompressible. 3. Fluid flow and volume change occur in only one direction. 4. Darcy's law is valid, Le. flowoc area, ~h, (1/L) (essentially the conservation of energy and momentum combined). o Consider the flow q through a small prism at a point (x,y,z) and conservation of mass:
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Unformatted text preview: and since qz = vzdA = vzdxdy ( dV) dV then dqz = _zdz dxdy = _zdxdydz dZ dZ if volume = V dV then dqz =-at if velocity = v then dv z = (~z dZ) q dx I I I • I I I )-------, , , , dz av dV and therefore _zdxdydz =- -(1 ) dZ dt recall Darcy's equation qz =-(k ~: dA) or, dividing by dA, v z =-(k ~:) where k is the permeability which is assumed to be constant and since (dh) = _1_(dU) where u is the excess pore pressure due to the applied load dZ 'Yw C3z k (au) then v =---z 'Yw az and substituting into (1) gives ~ a d : U dxdydz = aa V (2) 'Yw Z t...
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