Geotechnical Engineering Research Laboratory One University Avenue Lowell, Massachusetts 01854 Tel: (978) 934‐2621 e‐mail: [email protected] web site: http://faculty.uml.edu/ehajduk

Edward L. Hajduk, D.Eng, PE Lecturer PA105D Fax: (978) 934‐3052

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING

14.330 SOIL MECHANICS Exam #3: Shear Strength. Questions (2 Points Each - 20 Points Total): 1. Write the equation for the Mohr-Coulomb Failure Criteria for effective stresses in soils and detail the variables.

 f    tan    c Where: f = Shear Stress at Failure ' = Effective Normal Stress ' = Effective Friction Angle c' = Effective Cohesion 2. You have been given the results of a direct shear test on a well-graded sand (SW) sample. The Mohr-Coulomb effective stress failure criteria given to you from the test results are an effective friction angle of 33 degrees and an effective cohesion of 8.5 psi. Do you think these results are reasonable? Provide an explanation of your answer. ' = 33° is reasonable for sands. However, for sands c' ≈ 0. Therefore, a c' = 8.5 psi would not be reasonable. The soil may have been misclassified or the test was not run properly. 3. List the soil shear strength tests covered in class. Direct Shear Triaxial (CD, CU, UU) Unconfined Compression

14.330 2013 Exam 3 Solution

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Geotechnical Engineering Research Laboratory One University Avenue Lowell, Massachusetts 01854 Tel: (978) 934‐2621 e‐mail: [email protected] web site: http://faculty.uml.edu/ehajduk

Edward L. Hajduk, D.Eng, PE Lecturer PA105D Fax: (978) 934‐3052

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING

4. Write the equation for the Mohr-Coulomb Failure Criteria for total stresses in soils and detail the variables.

 f   tan   c Where: f = Shear Stress at Failure  = Normal Stress '= Friction Angle c = Cohesion 5. You are given three soil samples. Soil Sample 1 is a silty sand. Soil Sample 2 is a fat clay. Soil Sample 3 is a lean clay. You are told to conduct the following triaxial tests on the samples: a slow test on Sample 1, a rapid test on Sample 2, and a quick test on Sample 3. What triaxial tests are you conducting on each sample? Provide the common test names and 2 letter abbreviations. Soil Sample 1 – Slow Test = CD (Consolidated Drained) Soil Sample 2 – Rapid Test = CU (Consolidated Undrained) Soil Sample 3 – Quick Test = UU (Unconsolidated Undrained) 6. The direct shear test has been shown to be an effective test for determining the shear strength parameters (i.e. Mohr-Coulomb Failure Criteria) for coarse grained soils, especially sands. What is the major shortcoming of this test? The major shortcoming is the direct shear test forces the soil sample to fail along a fixed plane and not its preferred plane. 7. You have completed an unconfined compression test on a CL soil sample. The unconfined compression strength is 1120 psf. What is the undrained shear strength of this soil? Su = qu/2 = 1120 psf/2 = 560 psf. 8. Write the equation that relates unconfined compressive strength to undrained shear strength and detail the variables. Su = qu/2 Where: qu = Unconfined Compression Strength Su = Undrained Shear Strength

14.330 2013 Exam 3 Solution

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Geotechnical Engineering Research Laboratory One University Avenue Lowell, Massachusetts 01854 Tel: (978) 934‐2621 e‐mail: [email protected] web site: http://faculty.uml.edu/ehajduk

Edward L. Hajduk, D.Eng, PE Lecturer PA105D Fax: (978) 934‐3052

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING

9. Briefly describe soil sensitivity. variables.

Write any relevant equation(s) and detail the

Soil sensitivity is the ratio of undisturbed shear strength divided by disturbed shear strength.

Shear Stress

10. Identify the relative density of the sands in the direct shear test results shown on Page 4. What is the major cause of the shear strength difference between the two samples if you are told that they are from the same soil deposit?

Dense

Dilation is the difference!

Loose

Dense

Expansion Compression

Volume Change

Shear Displacement

14.330 2013 Exam 3 Solution

Shear Displacement

Loose

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Geotechnical Engineering Research Laboratory One University Avenue Lowell, Massachusetts 01854 Tel: (978) 934‐2621 e‐mail: [email protected] web site: http://faculty.uml.edu/ehajduk

Edward L. Hajduk, D.Eng, PE Lecturer PA105D Fax: (978) 934‐3052

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING

Problems: (1 – 25 points, 2 - 25 points, 3 – 15 points, 4 – 15 points, EC – 5 Points) NOTICE: You must detail your answers (i.e. show your work) for these four problems for full credit. You must follow assignment guidelines for these problems. PROBLEM #1 GIVEN: Soil from a local contractors sand pit is proposed for use as backfill behind a retaining wall for a local project. The project specifications require that the backfill material have a minimum peak soil friction angle of 33° at the required minimum compaction (i.e. 90% Standard Proctor). The results from the direct shear testing performed at the minimum required compaction by a local testing firm are presented in Table 1: Soil Description: Silty Sand (SM). Table 1. Direct Shear Results conducted at 90% MMD (ASTM D698). Shear Stress () (psf)

Confining Stress () (psf)

Peak

Residual

1

2000

1405

1405

2

2500

1695

1695

3

3500

2270

2270

Test

REQUIRED & SOLUTION: Based on the provided information, answer the following: What are the peak and residual Mohr-Coulomb Failure Criteria this material? Peak = Residual MC Failure Criteria. ' = 30°, c' = 250 psf (from Figure A). Does this material meet the project specifications regarding soil friction angle ()? No, since residual = 30° < 33° required by project specifications Do you think this soil was tested in a loose or dense state? Briefly explain your answer. Soil was tested in a loose state since peak = residual

14.330 2013 Exam 3 Solution

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Geotechnical Engineering Research Laboratory One University Avenue Lowell, Massachusetts 01854 Tel: (978) 934‐2621 e‐mail: [email protected] web site: http://faculty.uml.edu/ehajduk

Edward L. Hajduk, D.Eng, PE Lecturer PA105D Fax: (978) 934‐3052

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING

Shear Stress () (psf)

3000 Peak & Residual: ' = 30°, c' = 250 psf Best Fit Line

2500

' = 30°

2000 1500 1000 500

c' = 250 psf

0 0

500

1000

1500

2000

2500

3000

3500

Confining Stress (psf)

4000

Figure A. Shear Stress vs. Confining Stress Plot. PROBLEM #2 GIVEN: Soil from another local contractors sand pit is proposed for use as backfill behind a Mechanically Stabilized Earth (MSE) Wall for another local project. The project specifications require that the backfill material have a minimum residual soil friction angle of 34° at the required compaction (i.e. 95% Modified Proctor). Table 2 provides the results from the direct shear testing on this sample performed at the minimum required compaction by a local testing firm: Soil Description: Poorly Graded Sand (SP) Table 2. Direct Shear Results conducted at 95% MDD (ASTM D1557). Shear Stress () (psf)

Confining Stress () (psf)

Peak

Residual

1

2050

1600

1350

2

2500

2000

1700

3

3350

2650

2400

Test

14.330 2013 Exam 3 Solution

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Geotechnical Engineering Research Laboratory One University Avenue Lowell, Massachusetts 01854 Tel: (978) 934‐2621 e‐mail: [email protected] web site: http://faculty.uml.edu/ehajduk

Edward L. Hajduk, D.Eng, PE Lecturer PA105D Fax: (978) 934‐3052

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING

REQUIRED & SOLUTION: Based on the provided information, answer the following: What are the peak and residual Mohr-Coulomb Failure Criteria for this material? Peak MC Failure Criteria: p' = 38°, c' = 0 psf (from Figure B). Residual MC Failure Criteria: r' = 35°, c' = 0 psf (from Figure B). Does this material meet the project specifications regarding soil friction angle ()? Yes, since residual = 35° > 34° required by project specifications Do you think this soil was tested in a loose or dense state? Briefly explain your answer. Soil was tested in a dense state since peak > residual Peak: p' = 38°, c' = 0 psf

3000

Shear Stress () (psf)

Peak Best Fit Line Residual: r' = 35°, c' = 0 psf

2500

Residual Best Fit Line

2000 1500 1000 500

c' = 0 psf 0 (SP)

0

500

1000

1500

2000

2500

3000

Confining Stress (psf)

3500

4000

Figure B. Shear Stress vs. Confining Stress Plot.

14.330 2013 Exam 3 Solution

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Geotechnical Engineering Research Laboratory One University Avenue Lowell, Massachusetts 01854 Tel: (978) 934‐2621 e‐mail: [email protected] web site: http://faculty.uml.edu/ehajduk

Edward L. Hajduk, D.Eng, PE Lecturer PA105D Fax: (978) 934‐3052

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING

PROBLEM #3 GIVEN: The results from three (3) Consolidated Undrained triaxial tests conducted on samples from a normally consolidated CL soil deposit are presented in Table 3. Table 3. CU Results on normally consolidated CL sample.

Test

Minor Principal Stress at Failure ('3f) (psi)

Major Principal Stress at Failure ('1f) (psi)

Pore Pressure @ Failure (udf) (psi)

1

11

32

4

2

16.25

49.6

8.75

3

22.5

67.4

10

REQUIRED: Determine the Effective Stress Mohr-Coulomb Shear Strength Parameters (i.e. effective friction angle and effective cohesion) for this soil. SOLUTION: Effective Stress Mohr-Coulomb Envelope: '= 30°, c' = 0 psi. See Figure C.

Shear Stress () (psi)

40 Test 1 Test 2 Test 3

35 30

' = 30°

25 20 15 10 5 0

c' = 0 psi (NC Clay) 0

5

'3

'3

'3

'1f

'1f

'1f

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

Confining Stress (psi)

Figure C. Provided  vs.  Plot for Problem 3. 14.330 2013 Exam 3 Solution

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Geotechnical Engineering Research Laboratory One University Avenue Lowell, Massachusetts 01854 Tel: (978) 934‐2621 e‐mail: [email protected] web site: http://faculty.uml.edu/ehajduk

Edward L. Hajduk, D.Eng, PE Lecturer PA105D Fax: (978) 934‐3052

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING

PROBLEM #4 GIVEN & REQUIRED: Using the CU test data provided in Problem 3, determine the Total Stress MohrCoulomb Shear Strength Parameters (i.e. friction angle and cohesion) for this soil. SOLUTION: Total Stress Mohr-Coulomb Envelope: = 24°, c = 0 psi. See Figure C.

Shear Stress () (psi)

40 Test 1 Test 2 Test 3

35 30

' = 24°

25 20 15 10 5 0

c = 0 psi (NC Clay) 0

'3

5

'3

'3 '1f

'1f

'1f

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

Confining Stress (psi)

Figure D. Provided  vs.  Plot for Problem 4. EXTRA CREDIT (5 points): You are building a new embankment over cohesive soils. You need to determine the shear strength parameters to conduct slope stability and bearing capacity analyses at the end of construction (i.e. when the embankment is completed). What triaxial test(s) would you select to determine the shear strength parameters for these analyses? What would the shear strength parameter(s) be? UU – Unconsolidated Undrained (i.e. “Quick” Test). Gives you Undrained Shear Strength (Su).

14.330 2013 Exam 3 Solution

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