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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Chapter 12, Problem 12.10P

(a)

To determine

Find the undrained cohesion of the clay using Bjerrum’s λ relationship.

(a)

Expert Solution
Check Mark

Answer to Problem 12.10P

The undrained cohesion of the clay using Bjerrum’s λ relationship is 18.9kN/m2_.

Explanation of Solution

Given information:

The height of the vane (h) is 127 mm.

The width of the vane (d) is 63.5 mm.

The torque (T) is 20Nm.

The liquid limit (LL) is 50.

The plastic limit (PL) is 18.

Calculation:

Find the ratio of height (h) to diameter (d):

Heighttodiameterratio=hd

Substitute 127 mm for h and 63.5 mm for d.

Heighttodiameterratio=12763.5=2

Find the value of K using the formula.

K=7πd36

Substitute 63.5 mm for d.

K=7π×(63.5mm×1m1,000mm)36=0.000938m3

Find undrained shear strength (cu(VST)) of vane shear test using the formula:

cu(VST)=TK

Substitute 20Nm for T and 0.000938m3 for K.

cu(VST)=200.000938=(21,322N/m21,000)kN/m2=21.3kN/m2

Find the plasticity index (PI) using the relation:

PI=LLPL

Substitute 50 for LL and 18 for PL.

PI=5018=32

Find the correction factor λ using the formula:

λ=1.70.54log(PI)

Substitute 32 for PI.

λ=1.70.54log(32)=0.887

Find the corrected undrained shear strength (cu(Corrected)) using the relation:

cu(Corrected)=cu(VST)×λ

Substitute 21.3kN/m2 for cu(VST) and 0.887 for λ.

cu(Corrected)=21.3×0.887=18.9kN/m2

Thus, the undrained cohesion of the clay by Bjerrum’s λ relationship is 18.9kN/m2_.

(b)

To determine

Find the undrained cohesion of the clay using Morris and Williams’ λ and PI relationship.

(b)

Expert Solution
Check Mark

Answer to Problem 12.10P

The undrained cohesion of the clay using Morris and Williams’ λ and PI relationship is 14.08kN/m2_.

Explanation of Solution

Refer to part (a);

The value of PI is 32.

Find the correction factor using the formula:

λ=1.18e0.08(PI)+0.57

Substitute 32 for PI.

λ=1.18e0.08(32)+0.57=0.661

Find the corrected undrained shear strength (cu(Corrected)) using the relation:

cu(Corrected)=cu(VST)×λ

Refer part (a), the undrained shear strength (cu(VST)) is 21.3kN/m2.

Substitute 21.3kN/m2 for cu(VST) and 0.661 for λ.

cu(Corrected)=21.3×0.661=14.08kN/m2

Thus, the undrained cohesion of the clay by Morris and Williams’ λ and PI relationship is 14.08kN/m2_.

(c)

To determine

Find the undrained cohesion of the clay using Morris and Williams’ λ and LL relationship.

(c)

Expert Solution
Check Mark

Answer to Problem 12.10P

The undrained cohesion of the clay using Morris and Williams’ λ and LL relationship is 39.5°_.

Explanation of Solution

Given information:

The liquid limit (LL) is 50.

Calculation:

Find the correction factor using the formula:

λ=7.01e0.08(LL)+0.57

Substitute 50 for LL.

λ=7.01e0.08(50)+0.57=0.698

Find the corrected undrained shear strength (cu(Corrected)) using the relation:

cu(Corrected)=cu(VST)×λ

Refer part (a), the undrained shear strength (cu(VST)) is 21.3kN/m2.

Substitute 21.3kN/m2 for cu(VST) and 0.698 for λ.

cu(Corrected)=21.3×0.698=14.88kN/m2

Thus, the undrained cohesion of the clay by Morris and Williams’ λ and LL relationship is 14.88kN/m2_.

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Students have asked these similar questions
Vane shear tests were conducted in the clay layer. The vane dimensions were 63.5 mm (D) x 127 mm (H). For the test at A, the torque required to cause failure was 0.051 Nm. For the clay, given: liquid limit = 46 and plastic limit = 21. (a) Estimate the undrained cohesion of the clay for use in the design by using Bjerrum's correction. A = 1.7 – 0.54 log[PI(%)] (b) Estimate the overconsolidation ratio of the clay. Use Eqations below. Cu(field) B- σο B = 22[PI(%)]-048 OCR %3| Dry sand y = 16.5 kN/m³ ·1.5 m Groundwater table Sand 1.5 m Ysat = 19 kN/m³ N60 5 :1.5 m • 8 Clay = 16.8 kN/m³ 1.5 m Ysat * A • 8 1.5 m • 9 1.5 m 10 Sand
Show solution. The answer must be  A. 36.87 B. 14
a. A vane shear test was conducted in a saturated clay. The height and diameter of the rectangular vane were 4 in. and 2 in., respectively. During the test, the maximum torque applied was 230 lb-in. Determine the undrained shear strength of the clay. b. The clay soil described in part (a) has a liquid limit of 58 and a plastic limit of 29. What would be the corrected undrained shear strength of the clay for design purposes? Use Bjerrum’s relationship for λ [Eq. (3.40a)].
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