degree of consolidation vs thickness 4

[pelelo]

Engineers,

I have been talking with a colleague about consolidation settlement for an specific clay (Normally consolidated and one way drainage). Such clay is 10 ft thick, will have 20 inches EOP settlement and will settle 4 inches in 6 months, he understands that the same clay layer having a thickness of 30 ft will settle the same 4 inches in 6 months (such as thickness does not affect the degree of consolidation).

Eventhough he did not show any numbers, I decided to run my own numbers and i got a different settlement time:

Original clay: U= 4/20 = 0.25 -> T = 0.049, from t = H2 x T / cv -> cv = (10)^2 x 0.049 / 4 months = 1.225 ft2 / months

Using cv for the 30 ft clay layer:

t = H2 x T / cv -> t = 30^2 x 0.049 / 1.225 ft2 / months = 36 months

Does my approach make sense?. My approach shows that for the same clay but with different thicknesses, the same settlement value (4 inches) will take longer to reach for the thickest layer.

anyone has any thoughts about this?

 

[oldestguy]

On this subject in my experience trying to predict settlement times only one case had the field measurements coincide roughly with the predictions. In the sampling sometimes sand seams are missed and one thinks his layers are thick but they are sometimes much less than info may say..

 

[pelelo]

Still, it doesn't make sense to me that the same clay but with different thicknesses is going to have the time of consolidation, for example to reach 40% consolidation.

Per the formula t = T x H2 / cv -> if thickness increases, time increases as well.

 

[geomane]

U = 4/20 = 0.2 not 0.25, so your Tv would change slightly.

If you want to calculate how long it would take for the 30ft thick clay layer to settle 4 inches, you need to know the total settlement (or EOP settlement) for that layer. If it has the same properties of the 10ft thick clay layer then it would settle more than 20 inches. Let’s assume it will settle 30 inches. Now if you want to calculate time rate to achieve 4 inches of settlement, U = 4/30 = 0.13 which gives you a different time factor (Tv). If you wanted to know how long it would take to achieve the same percent consolidation, say 40%, then your Tv would stay the same.

By looking at the formula, t = (H^2xTv)/cv, it is apparent that time is directly proportional to the thickness of the clay layer. If thickness (H) increases, time increases.

 

[pelelo]

Geomeane,

good catch.

I agree, thanks.

 

[HENRYZAU]

If the Cv is very low, and 6 months settlement is still within 60% (DOC<60%), similar settlement is expected at both sites. Otherwise 9m thick clay will settles more than 3m thick clay. Refer to Duncan's 1993 Terzaghi Lecture on limitations of conventional consolidation theory.

 

[Okiryu]

The total settlement will increase if the compressible layer increases but the time for the same first 4 inches of settlement to occur will be the same regardless the thickness of the compressible layer.

 

[pelelo]

Okiryu,

Thanks for your response. Would you able to prove your point based on the typical Time factor and H formulas given related to consolidation?. Per the typical formulas I used, I prove that the thicker the layer the longer it takes to reach 4 inches of settlement.

Thanks.

 

[Okiryu]

pelelo, I am based on the chart of pore pressure distribution thru depth and time factor (z/H vs. U%). Basically, that chart does not change even if the thickness of the layer changes. (I just recalled this was a question in the CA GE exam...)