48_CEG 4012 Notes Fall 2011 CEG 4012 Notes Fall 2011

48_CEG 4012 Notes Fall 2011 CEG 4012 Notes Fall 2011 -...

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p32 o Symmetry in Time Factor Table: \-, Why do Cases 1a, 3 and 4 work for both double and single drainage, but Cases 1band 2 do not? The answer is symmetry. Think about what happens to the excess pore water pressure. If the initial excess pore pressure distribution is symmetrical about mid-height of a layer with thickness H, and the layer is doubly drained (top bottom): Pore fluid will move in the direction of least resistance, which for 1-0 consolidation is directly towards a drainage boundary. Pore fluid above mid-height of the layer will move upwards. Pore fluid below mid-height of the layer will move downwards. Therefore, the longest drainage path will be half the layer height = H/2. Also, since the pore fluid will not move across the "boundary" at mid-height, in behavior the mid-height level looks like an undrained boundary. Since the excess pore pressure distribution above and below mid-height is initially symmetrical and the conditions in each half are the same, the pore pressure distribution at any given time will remain symmetrical. Since the depth distribution of the effective stress change complements the excess pore pressure distribution
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Unformatted text preview: (i.e. Acr'z = -AU), it will also be symmetrical. Therefore, the average percent consolidation (U), and the corresponding time factor (T), at any given time will be the same above and below mid-height. The following initial pore pressure distributions are equivalent as shown: I Case 1a I Case 3 Case 4 J)o. ..{,lt I)''';'' ,.,,,. I-\--:. \. . rJ: 1. T = cyt = cyt (H/N)2 (h/2)2 O1i1i1J1;l;:Jm h----- = = = S",d,,,,:;e. . 10""-.1.;'.:1 ~k.,<-f.. Y<it ~'t-ktl"S{ <.<. ~ IS l"l.-ue /.-'. ... +tv-l-",t If! illl. tuoJ Jet./( "JlJ " ... /;JI 7 In summation: if the initial excess pore pressure distribution is symmetrical about the mid-height, then the behavior of a layer of height H with double drainage is identical to that of a layer with height = H/2 and single drainage. (This is why we defined the maximum drainage path = H/N.)...
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