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Unformatted text preview: Soil Mechanics CIVL2410 10. Consolidation 1 10. Analysis of Consolidation Contents 1. Introduction: the consolidation process ....................................................................................... 1 2. Derivation of the equation of consolidation for 1D conditions .................................................... 2 3. Boundary Conditions ................................................................................................................... 5 4. Initial Conditions .......................................................................................................................... 5 5. The Equation of Consolidation for a Homogeneous Soil ............................................................ 5 6. Analytic Solutions to the equations of consolidation ................................................................... 5 a) Twoway drainage...................................................................................................................5 b) Oneway drainage...................................................................................................................9 1. Introduction: the consolidation process From the response of soils under onedimensional conditions it is apparent that when the effective stress increases there will be a tendency for the soil to compress. However, when a load is applied to a saturated soil specimen this compression does not occur immediately. This behaviour is a consequence of the soil constituents, the skeletal material and pore water, being almost incompressible compared to the soil element; deformation can only take place by water being squeezed out of the voids. This can only occur at a finite rate and so initially when the soil is loaded it undergoes no volume change. Under one dimensional conditions this implies that there can be no vertical strain and thus no change in vertical effective stress. For 1D conditions we have ε ε σ σ zz v F I e e C e = = + = ′ ′ + ∆ 1 1 log( / ) (1) Hence if ε v = 0 then Δ e = 0 and s ’ F = s ’ I . When the load is first applied the total stress increases, but as shown above for 1D conditions there can be no instantaneous change in vertical effective stress, this implies that the pore pressure must increase by exactly the same amount as the total stress as: Δs’ = Δs  Δu (2) Subsequently there will be flow from regions of higher excess pore pressure to regions of lower excess pore pressure, the excess pore pressures will dissipate, the effective stress will change and the soil will deform (consolidate) with time. This is shown schematically in Figure 1. Figure 1: Variation of stress, pore pressure and settlement with time. Soil Mechanics CIVL2410 10. Consolidation 2 2. Derivation of the equation of consolidation for 1D conditions If we assume that the pore fluid and soil skeleton are incompressible, then: Volume decrease of the soil = Volume of pore fluid which flows out and thus Rate of volume decrease of soil...
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 Three '11
 DAirey
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