Fundamentals of Geotechnical Engineering (MindTap Course List)
Fundamentals of Geotechnical Engineering (MindTap Course List)
5th Edition
ISBN: 9781305635180
Author: Braja M. Das, Nagaratnam Sivakugan
Publisher: Cengage Learning
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Question
Chapter 9, Problem 9.19CTP
To determine

Plot the consolidation settlement versus time for the clay layer.

Expert Solution & Answer
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Explanation of Solution

Given information:

The thickness of the clay layer (H) is 6m.

The time (t) is 12months.

The final consolidation settlement (Sp) is 220mm.

The coefficient of consolidation of the clay (cv) is 3m2/year.

Calculation:

Consider the unit weight of water (γw) is 9.81kN/m3.

For the time (t) of 3months:

Calculate the maximum drainage path (Hdr) for two way drainage using the relation.

Hdr=H2

Substitute 6m for H.

Hdr=62=3m

Calculate the time factor (Tv) using the relation.

Tv=(cvtHdr2) (1)

Substitute 3m2/year for cv, 3months for t, and 3m for Hdr in Equation (1).

Tv=3m2/year×3months×1 year12months(3m)2=0.759=0.083

Refer Figure 9.33 “UTv relationships for ramp loading and instantaneous loading” in the Text Book.

Take the value of average degree of consolidation (U) as 21% for the value time factor (Tv) of 0.083.

Calculate the final consolidation settlement (Sp(f)) with 25% of the applied load using the relation.

Sp(f)=Percentageofloadapplied×Sp (2)

Substitute 25% for percentage of load applied and 220mm for Sp in Equation (2).

Sp(f)=25100×220=55mm

Calculate the consolidation settlement for 3months using the relation.

Consolidationsettlement=U×Sp(f) (3)

Substitute 21% for U and 55mm for Sp(f) in Equation (3).

Consolidationsettlement=21100×55=11.6mm

For the time (t) of 6months:

Calculate the time factor (Tv) as shown below.

Substitute 3.0m2/year for cv, 6months for t, and 3m for Hdr in Equation (1).

Tv=3m2/year×6months×1 year12months(3m)2=1.59=0.167

Refer Figure 9.33 “UTv relationships for ramp loading and instantaneous loading” in the Text Book.

Take the value of average degree of consolidation (U) as 31% for the value time factor (Tv) of 0.167.

Calculate the final consolidation settlement (Sp(f)) with 50% of the applied load as shown below.

Substitute 50% for percentage of load applied and 220mm for Sp in Equation (2).

Sp(f)=50100×220=110mm

Calculate the consolidation settlement for 6months using the relation.

Substitute 31% for U and 110mm for Sp in Equation (3).

Consolidationsettlement=31100×110=34.10mm

For the time (t) of 12months:

Calculate the time factor (Tv) as shown below.

Substitute 3.0m2/year for cv, 12months for t, and 3m for Hdr in Equation (1).

Tv=3m2/year×12months×1 year12months(3m)2=39=0.333

Refer Figure 9.33 “UTv relationships for ramp loading and instantaneous loading” in the Text Book.

Take the value of average degree of consolidation (U) as 43% for the value time factor (Tv) of 0.333.

Calculate the final consolidation settlement (Sp(f)) with 50% of the applied load as shown below.

Substitute 100% for percentage of load applied and 220mm for Sp in Equation (2).

Sp(f)=100100×220=220mm

Calculate the consolidation settlement for 12months using the relation.

Substitute 43% for U and 220mm for Sp in Equation (3).

Consolidationsettlement=43100×220=94.6mm

For the time (t) of 18months with t0 of 12months.

Calculate the time factor Tv using the relation.

Tv=cv(tt0)Hdr2 (4)

Substitute 3.0m2/year for cv, 18months for t,12months for t0,and 3m for Hdr in Equation (4).

Tv=3m2/year×(126)months×1 year12months(3m)2=1.59=0.167

Refer Table 9.5“ UTv Values for Non-Uniform Initial Pore Pressure Distributions” in the Text Book.

Take the value of Utt0 as 0.3377 for the value Tv of 0.167 for half-sine.

Calculate the average degree of consolidation (Ut) using the relation.

Ut=U0+(1U0)Utt0

Substitute 43% for U0 and 0.3377 for Utt0.

Ut=43100+(143100)×0.3377=0.43+0.1925=0.6225×100%=62.25%

Calculate the consolidation settlement for 18months using the relation.

Substitute 62.25% for U and 220mm for Sp in Equation (3).

Consolidationsettlement=62.25100×220=136.95mm

For the time (t) of 36months with t0 of 12months.

Calculate the time factor (Tv) as shown below.

Substitute 3.0m2/year for cv, 36months for t, 12months for t0, and 3m for Hdr in Equation (4).

Tv=3m2/year×(3612)months×1 year12months(3m)2=69=0.667

Refer Table 9.5 “ UTv Values for Non-Uniform Initial Pore Pressure Distributions” in the Text Book.

Take the value of Utt0 as 0.7725 for the value Tv of 0.600 for half-sine.

Take the value of Utt0 as 0.8222 for the value Tv of 0.700 for half-sine.

Calculate the value of Utt0 for the value Tv of 0.667 by interpolation as shown below.

0.7000.6670.7000.600=0.8222Utt00.82220.77250.33×0.0497=0.8222Utt00.0164=0.8222Utt0Utt0=0.806

Calculate the average degree of consolidation (Ut) using the relation.

Ut=U0+(1U0)Utt0

Substitute 43% for U0 and 0.806 for Utt0.

Ut=43100+(143100)0.806=0.43+0.4594=0.8894×100%=88.9%

Calculate the consolidation settlement for 36months using the relation.

Substitute 88.9% for U and 220mm for Sp in Equation (3).

Consolidationsettlement=88.9100×220=195.58mm

For the time (t) of 60months with t0 of 12months.

Calculate the time factor (Tv) as shown below.

Substitute 3.0m2/year for cv, 60months for t, 12months for t0, and 3m for Hdr in Equation (4).

Tv=3m2/year×(6012)months×1 year12months(3m)2=129.0=1.33

Refer Table 9.5 “ UTv Values for Non-Uniform Initial Pore Pressure Distributions” in the Text Book.

Take the value of Utt0 as 0.9152 for the value Tv of 1 for half-sine.

Take the value of Utt0 as 0.9753 for the value Tv of 1.5 for half-sine.

Calculate the value of Utt0 for the value Tv of 1.33 by interpolation as shown below.

1.51.331.51=0.9753Utt00.97530.91520.34×0.0601=0.9753Utt00.0204=0.9753Utt0Utt0=0.955

Calculate the average degree of consolidation (Ut) using the relation.

Ut=U0+(1U0)Utt0

Substitute 43% for U0 and 0.955for Utt0.

Ut=43100+(143100)0.955=0.43+0.5444=0.9744×100%=97.4%

Calculate the consolidation settlement for 60months using the relation.

Substitute 97.4% for U and 220mm for Sp in Equation (3).

Consolidationsettlement=97.4100×220=214.3mm

Show the values of time and consolidation settlement as in Table 1.

Time (months)Consolidation settlement (mm)
311.60
634.10
1294.60
18136.95
36195.58
60214.30

Table 1

Refer to Table 1.

Sketch the plot between consolidation settlement and time as in Figure 1.

Fundamentals of Geotechnical Engineering (MindTap Course List), Chapter 9, Problem 9.19CTP

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