Consolidation Settlement - Part 03

Rate of Consolidation 

Consolidation is the gradual dissipation of the excess pore water pressure, "delta U" from a clay layer. as a result of a load application "delta sigma" which induces the primary consolidation settlement. Many years or even decades may be required for the full dissipation of pore water pressure to occur, so geotechnical engineers need to evaluate the rate of consolidation settlement, in addition to the maximum consolidation settlement.

In order to estimate the degree of consolidation (rate) of a clay layer after a load application "delta sigma" the rate of excess pore water pressure dissipation needs to be determined. for one dimensional consolidation, Terzaghi derived the following deferential equation to estimate the rate of dissipation of "delta U" at some time "t" and depth "Z",


Cv is defined as the "Coefficient of Consolidation"

Coefficient of Consolidation

 


where,
Cv = Coefficient of Consolidation (units - m^2/year)
K = Soil compressibility
mv = Coefficient of volume compressibility
gamma w = Unit weight of water

Coefficient of Consolidation 

where,
Tv = time factor (no units)
Cv = Coefficient of Consolidation (units - m^2/year)
t = time after loading
H = the length of the longest drainage path (depend on boundary conditions)

Degree of Consolidation 

 

where,
Uz = degree of consolidation
Ui = initial pore water pressure
U = present pore water pressure

Average Degree of Consolidation 

where,
U = average degree of consolidation
St = settlement after t time
S infinity = final consolidation settlement

Relationship between average degree of consolidation and time factor

If,
U < 60%

U > 60%

Otherwise we can use this table and graph.

Example :
A soil layer is sandwiched between a sand layer and an impervious rock as shown in the figure. a soil fill of 2 m thick with a unit weight of 20 K N/m^3 was placed on the existing ground surface. assuming time taken for surcharging is very small and a constant pore pressure generation a cross the layer immediately after surcharging,
1) estimate the expected total consolidation settlement of the ground surface due to the application of the surcharge.
2) estimate the average degree of consolidation 6 months after the loading.
3) estimate the expected settlement of the ground surface after 6 months.




1) estimate the expected total consolidation settlement of the ground surface due to the application of the surcharge

for normally consolidated soil,

sigma v0' = (2 x 15) + 2 x (16 - 9.81) + 2 x ( 15 - 9.81 ) = 52.76 K Pa

Delta sigma = 2 x 20 = 40 K Pa

S = 4 / (1+0.8) x 0.42 x log {(52.76+40)/52.76} = 0228.7 mm

2)  estimate the average degree of consolidation 6 months after the loading

U = St / S infinity and Tv = Cv t / H^2

Tv = 4 x(6/12) / (4^2) = 0.125

using table Tv = 0.125 --------- U = 40% 

3)  estimate the expected settlement of the ground surface after 6 months

U = St / S infinity
0.4 = St / 0.2287
St = 91.5 mm