The groundwater table in the soil profile shown in Figure 11.21 is currently at the elevation labeled “initial.” A proposed dewatering project will cause it to drop to the elevation labeled “final.” Compute the resulting ultimate consolidation settlement.

A consolidation test performed on a sample from point A produced the following results:
$C_{c} /(1 +e_{0}) =0.14$

$C_{r} /(1 + e_{0} ) = 0.06$

$σ^{\prime }_{c}=3000 lb/ft^{2}$

Question

The groundwater table in the soil profile shown in Figure 11.21 is currently at the elevation labeled "initial." A proposed dewatering project will cause it to drop to the elevation labeled "final." Compute the resulting ultimate consolidation settlement.

A consolidation test performed on a sample from point A produced the following results:

[latex]C_{c} /(1 +e_{0}) =0.14 [/latex]

[latex]C_{r} /(1 + e_{0} ) = 0.06[/latex]

[latex]σ^{\prime }_{c}=3000 lb/ft^{2}[/latex]

Accepted Answer

At sample A

[latex]\sigma ^{\prime }_{z0}=\sum{\gamma H - u} =\left(121 lb/ft^{3}\right) \left(7.0 ft\right) +\left(125 lb/ft^{3}\right) \left(6.0 ft\right) +\left(127 lb/ft^{3}\right) \left(18.0 ft\right) +\left(110 lb/ft^{3}\right) \left(5.0 ft\right) - \left(62.4 lb/ft^{3}\right) \left(29.0 ft\right) =2623 lb/ft^{2}[/latex]

[latex]\sigma ^{\prime }_{z0}\approx \sigma ^{\prime }_{c}[/latex] ∴ normally consolidated

Layer	H (ft)	At midpoint of layer		[latex]\frac{C_{c}}{1 + e_{0}} [/latex]	Eqn.	[latex]\left(\delta _{c}\right) _{ult}[/latex] (in)
Layer	H (ft)	[latex]\sigma ^{\prime }_{z0} (lb/ft^{2})[/latex]	[latex]\sigma ^{\prime }_{zf} (lb/ft^{2})[/latex]	[latex]\frac{C_{c}}{1 + e_{0}} [/latex]	Eqn.	[latex]\left(\delta _{c}\right) _{ult}[/latex] (in)
1	7.0	423	423	0.011	11.23 [latex]\left(\delta _{c}\right) _{ult}=\sum{\frac{C_{c}}{1 + e_{0}} } H\log \left\lgroup\frac{\sigma ^{\prime }_{zf}}{\sigma ^{\prime }_{z0}} \right\rgroup [/latex]	0.0
2	6.0	1035	1210	0.011	11.23 [latex]\left(\delta _{c}\right) _{ult}=\sum{\frac{C_{c}}{1 + e_{0}} } H\log \left\lgroup\frac{\sigma ^{\prime }_{zf}}{\sigma ^{\prime }_{z0}} \right\rgroup [/latex]	0.1
3	9.0	1513	2126	0.009	11.23 [latex]\left(\delta _{c}\right) _{ult}=\sum{\frac{C_{c}}{1 + e_{0}} } H\log \left\lgroup\frac{\sigma ^{\prime }_{zf}}{\sigma ^{\prime }_{z0}} \right\rgroup [/latex]	0.1
4	9.0	2095	3233	0.009	11.23 [latex]\left(\delta _{c}\right) _{ult}=\sum{\frac{C_{c}}{1 + e_{0}} } H\log \left\lgroup\frac{\sigma ^{\prime }_{zf}}{\sigma ^{\prime }_{z0}} \right\rgroup [/latex]	0.2
5	7.0	2552	3837	0.14	11.23 [latex]\left(\delta _{c}\right) _{ult}=\sum{\frac{C_{c}}{1 + e_{0}} } H\log \left\lgroup\frac{\sigma ^{\prime }_{zf}}{\sigma ^{\prime }_{z0}} \right\rgroup [/latex]	2.1
6	8.0	2909	4194	0.14	11.23 [latex]\left(\delta _{c}\right) _{ult}=\sum{\frac{C_{c}}{1 + e_{0}} } H\log \left\lgroup\frac{\sigma ^{\prime }_{zf}}{\sigma ^{\prime }_{z0}} \right\rgroup [/latex]	2.1
[latex]\left(\delta _{c}\right) _{ult}=[/latex]						4.6

[latex]\left(\delta _{c}\right) _{ult}=[/latex] 4.6 in

Notice how most of the compression occurs in the normally consolidated clay, even though it remains below the groundwater table. The cause of settlement is an increase in effective stress, not drying, and the clay is most susceptible to this increase because it has the highest [latex]C_{c}/(1 + e_{0})[/latex].

Question 11.7: The groundwater table in the soil profile shown in Figure 11...

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