EBK FUNDAMENTALS OF GEOTECHNICAL ENGINE
EBK FUNDAMENTALS OF GEOTECHNICAL ENGINE
5th Edition
ISBN: 8220101425829
Author: SIVAKUGAN
Publisher: CENGAGE L
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Chapter 11, Problem 11.6P

(a)

To determine

Find the expected primary consolidation settlement.

(a)

Expert Solution
Check Mark

Answer to Problem 11.6P

The expected primary consolidation settlement (Sp) is 245.2mm_.

Explanation of Solution

Given information:

The compression index Cc is 0.5.

The thickness of the clay layer (H) is 4 m.

The average permanent load on the clay layer Δσ(p) is 50kN/m2.

The average effective overburden pressure σo is 80kN/m2.

The initial void ratio e0 is 0.72.

Calculation:

Determine the maximum primary consolidation settlement caused by the structural load (Sp):

Sp=CcH1+e0logσo+Δσ(p)σo

Substitute 0.5 for Cc, 4 m for H, 0.72 for e0, 80kN/m2 for σo, and 50kN/m2 for Δσ(p).

Sp=0.5×41+0.72×log[80+5080]=0.2452m×1,000mm1m=245.2mm

Therefore, the expected primary consolidation settlement is 245.2mm_.

(b)

To determine

Find the pre-compression time.

(b)

Expert Solution
Check Mark

Answer to Problem 11.6P

The pre-compression time (t2) is 263days_.

Explanation of Solution

Given information:

The average permanent load on the clay layer Δσ(p) is 50kN/m2.

The average effective overburden pressure σo is 80kN/m2.

The surcharge load per unit area Δσ(f) is 60kN/m2.

The coefficient of consolidation cv is 2.5m2/yr.

The thickness of the clay layer (H) is 4 m.

Calculation:

Determine the ratio of (Δσ(p)/σo).

Substitute 50kN/m2 for Δσ(p) and 80kN/m2 for σo.

Δσ(p)σo=5080=0.625

Determine the value of (Δσ(f)/Δσ(p)).

Substitute 60kN/m2 for Δσ(f) and 50kN/m2 for Δσ(p).

Δσ(f)Δσ(p)=6050=1.2

Refer Figure 11.6, “Plot of U against Δσ(f)/Δσ(p) for various values of Δσ(p)/σo”, in the text book.

For Δσ(p)σo=0.625 and Δσ(f)Δσ(p)=1.2,

The degree of consolidation is U=57%

Refer Figure 11-8, “Plot of mid plane degree of consolidation against Tv” in the textbook.

For U=57%,

The time factor is Tv=0.45

Determine the pre-compression time t2 using the formula:

t2=TvHdr2cv

Here, Hdr is the maximum drainage path (H/2 for two-way drainage and H for one-way drainage, and t2 is the time duration of pre-compression.

Here, the drainage is two-way. Therefore, Hdr=H2.

Substitute 0.45 for Tv, (42)m for Hdr, and 2.5m2/yr for cv.

t2=0.45×(42)22.5m2yr=0.72yr×365days1yr=263days

Thus, the pre-compression time is 263days_.

(c)

To determine

Find the surcharge pressure that would eliminate the primary consolidation settlements beyond the preloading period.

(c)

Expert Solution
Check Mark

Answer to Problem 11.6P

The surcharge pressure that would eliminate the primary consolidation settlements beyond the preloading period is (Δσ(f)) is 196kNm2_.

Explanation of Solution

Given information:

The coefficient of consolidation cv is 2.5m2/yr.

The required time (t) is 6 months.

The thickness of the clay layer (H) is 4 m.

The average permanent load on the clay layer Δσ(p) is 50kN/m2.

The average effective overburden pressure σo is 80kN/m2.

Calculation:

Determine the time factor using the formula:

Tv=t2cvHdr2=t2cv(H2)2=4t2cvH2

Substitute 6 months for t2, 4 m for H, and 2.5m2/yr for cv.

Tv=4×6months×2.5m2yr(4m)2=4×(6months×1yr12months)×2.5m2yr(4m)2=0.31

Refer Figure 11-8, “Plot of mid plane degree of consolidation against Tv” in the textbook.

For Tv=0.31,

The value is U(z/Hdr=1)=0.423

Determine the value of (Δσ(p)/σo) ratio.

Substitute 50kN/m2 for Δσ(p) and 80kN/m2 for σo.

Δσ(p)σo=50kNm280kNm2=0.625

Determine the surcharge pressure using the formula:

U=log[1+Δσ(p)σo]log{1+Δσ(p)σo[1+Δσ(f)Δσ(p)]}

Substitute 0.625 for (Δσ(p)/σo), 0.41 for U, and 80kN/m2 Δσ(p).

log[1+0.63]log{1+0.63×[1+Δσ(f)Δσ(p)]}=0.4230.212log{1+0.63×[1+Δσ(f)Δσ(p)]}=0.423log{1+0.63×[1+Δσ(f)Δσ(p)]}=0.2120.423log{1+0.63×[1+Δσ(f)Δσ(p)]}=0.501

Simplify the Equation.

1+0.63×[1+Δσ(f)Δσ(p)]=100.5010.63×[1+Δσ(f)Δσ(p)]=3.173511+Δσ(f)Δσ(p)=2.17350.63Δσ(f)80kNm2=3.451

Δσ(f)=2.45×80kNm2Δσ(f)=196kNm2

Thus, the surcharge pressure that would eliminate the primary consolidation settlements beyond the preloading period is 196kNm2_.

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