SOIL MECHANICS Exam #3: Shear Strength.

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 Where: f = Shear Stress at Failure ' = Effective Normal Stress ' = Effective Friction Angle c' = Effective Cohesion tan c 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 Page 1 of 8

4. Write the equation for the Mohr-Coulomb Failure Criteria for total stresses in soils and detail the variables. Where: f = Shear Stress at Failure = Normal Stress '= Friction Angle c = Cohesion f tan c 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? S u = q u /2 = 1120 psf/2 = 560 psf. 8. Write the equation that relates unconfined compressive strength to undrained shear strength and detail the variables. S u = q u /2 Where: q u = Unconfined Compression Strength S u = Undrained Shear Strength 14.330 2013 Exam 3 Solution Page 2 of 8

9. Briefly describe soil sensitivity. Write any relevant equation(s) and detail the variables. Soil sensitivity is the ratio of undisturbed shear strength divided by disturbed shear strength. 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? Shear Stress Dilation is the difference! Dense Loose Volume Change Expansion Compression Shear Displacement Dense Shear Displacement Loose 14.330 2013 Exam 3 Solution Page 3 of 8

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). Test Confining Stress ( ) (psf) Shear Stress ( ) (psf) Peak Residual 1 2000 1405 1405 2 2500 1695 1695 3 3500 2270 2270 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 Page 4 of 8

3000 Shear Stress ( ) (psf) 2500 2000 1500 1000 500 Peak & Residual: ' = 30, c' = 250 psf Best Fit Line ' = 30 c' = 250 psf 0 0 500 1000 1500 2000 2500 3000 3500 4000 Confining Stress (psf) 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). Test Confining Stress ( ) (psf) Shear Stress ( ) (psf) Peak Residual 1 2050 1600 1350 2 2500 2000 1700 3 3350 2650 2400 14.330 2013 Exam 3 Solution Page 5 of 8

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 Shear Stress ( ) (psf) 3000 2500 2000 1500 1000 500 Peak: p ' = 38, c' = 0 psf Peak Best Fit Line Residual: r ' = 35, c' = 0 psf Residual Best Fit Line c' = 0 psf (SP) 0 0 500 1000 1500 2000 2500 3000 3500 4000 Confining Stress (psf) Figure B. Shear Stress vs. Confining Stress Plot. 14.330 2013 Exam 3 Solution Page 6 of 8

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 ( u df ) (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 35 30 25 20 15 10 5 0 c' = 0 psi (NC Clay) Test 1 Test 2 Test 3 ' = 30 ' 3 ' 3 ' 3 ' 1f ' 1f ' 1f 0 5 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 Page 7 of 8

PROBLEM #4 GIVEN & REQUIRED: Using the CU test data provided in Problem 3, determine the Total Stress Mohr- Coulomb 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 35 30 25 20 15 10 5 0 c = 0 psi (NC Clay) Test 1 Test 2 Test 3 ' = 24 ' 3 ' 3 ' 3 ' 1f ' 1f ' 1f 0 5 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 (S u ). 14.330 2013 Exam 3 Solution Page 8 of 8