pcf REQUIRED: Determine the shear strength parameters for use in a preliminary shallow foundation design. SOLUTION:

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Basil Freeman
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1 SOIL MECHANICS Assignment #8: Shear Strength Solution. PROBLEM #1: GIVEN: A regional residential building contractor is planning on building a custom 4,100 ft² home on Martha s Vineyard, MA. The subsurface investigation for the house site shows that a poorly graded sand deposit exists from the existing ground surface to a depth of 25 ft. Density testing on the sand in-situ showed yielded an average moist unit weight of 120 pcf at an average moisture content of 10%. REQUIRED: Determine the shear strength parameters for use in a preliminary shallow foundation design. SOLUTION: 120 pcf pcf d 1 w SP. Use Figure 7 (NAVFAC DM 7.01, 1986) Figure 7. NAVFAC DM 7.01, Using Figure 7 of NAVFAC DM7.01: 31 ' 35. I d be conservative and use Assignment 8 Solution Page 1 of 9

2 PROBLEM #2: GIVEN: Soil from a local contractors soil pit is proposed for use as backfill behind a Mechanically Stabilized Earth (MSE) Wall for a local project. The project specifications require that the backfill material have a minimum residual soil friction angle of 35 at the required compaction (i.e. 98% D1557). The results from the direct shear testing performed at the minimum required compaction by a local testing firm are provided in a CSV file (14.330_2014_Assignment_8_P2.csv). From the provided information, answer the following: REQUIRED: Determine the peak and residual friction angles ( peak and residual ) for this soil. Determine if the soil meets the project specifications. Explain density (loose or dense) of the soil based on direct shear results. SOLUTION: Using data provided in Figure A (plotted from the provided data), determine the peak and residual shear strengths for the tests at the three (3) confining (i.e. normal) stresses. This summary is provided in Table A. Table A. Direct Shear Results (from Figure A). Test Confining Stress ( ) Shear Stress ( ) Peak Residual Plot of shear stress vs. normal stress to determine peak and residual is presented in Figure B. Assume no cohesion (i.e. c=0) since no soil classification is provided. A summary of the Mohr-Coulomb Failure Criteria from the direct shear testing is presented in Table B Assignment 8 Solution Page 2 of 9

Figure A. Direct Shear Results for Problem #2.

3 Figure A. Direct Shear Results for Problem # Assignment 8 Solution Page 3 of 9

4 Figure B. Shear Stress vs. Confining Stress for Direct Shear Results for Problem 2. Table B. Direct Shear Results Summary for Problem #2. State Friction Angle ( ) ( ) Cohesion (c) Peak Residual Since residual = 35.5 > 35 (Required residual by specification), this soil CAN be used for the project. This soil was tested in a dense state. That can be determined by volumetric behavior of the soil during the direct shear test and from the fact that peak > residual Assignment 8 Solution Page 4 of 9

5 PROBLEM #3: GIVEN: During the subsurface exploration at a new roadway embankment, soil samples were collected from a CL soil layer. The results of the CD triaxial testing for this soil are presented in Table 1. Table 1. CD Triaxial Testing Results for CL soil layer samples. Test Minor Principal Stress at Failure ( ' 3f ) Major Principal Stress at Failure ( ' 1f ) REQUIRED: Determine the effective and total Mohr-Coulomb Failure Criteria for this soil. SOLUTION: The effective Mohr circles are presented in Figure C. Using Figure C, the Mohr- Coulomb Failure Criteria were determined for the effective stresses case. Friction angles and cohesion for the effective stress envelope are summarized in Table C. Table C. CU Triaxial Test Results Summary for CL soil. State Friction Angle ( ) Cohesion Effective ( and c ) 30 2 Note that since no determination of the soils overconsolidation was provided, fit the best fit line in Figure C to the tangent of all the Mohr circles. Since c' > 0, the soil is overconsolidated Assignment 8 Solution Page 5 of 9

6 Figure C. CD Test Results for Problem 3 (Effective Stresses). PROBLEM #4: GIVEN: You have been asked to evaluate metal slag from a steel plant for use as backfill for a project you are assigned. The project specifications require that the backfill material have a minimum residual friction angle of 30 at the required compaction (i.e. 98% D1557). The results from the direct shear testing performed at the minimum required compaction by a local testing firm are provided in a CSV file (14.330_2014_Assignment_8_P4.csv). From the provided information, answer the following: REQUIRED: Determine the peak and residual friction angles ( peak and residual ) for this soil. Determine if the soil meets the project specifications. Explain density (loose or dense) of the soil based on direct shear results. SOLUTION: Using data provided in Figure D (plotted from the provided data), determine the peak and residual shear strengths for the tests at the three (3) confining (i.e. normal) stresses. This summary is provided in Table D Assignment 8 Solution Page 6 of 9

7 Figure D. Direct Shear Results for Problem # Assignment 8 Solution Page 7 of 9

8 Table D. Direct Shear Results (from Figure D). Test Confining Stress ( ) Shear Stress ( ) Peak Residual Plot of shear stress vs. normal stress to determine peak and residual is presented in Figure B. Assume cohesion (if applicable) since no soil classification is provided. Note cohesion cannot be negative! A summary of the Mohr-Coulomb Failure Criteria from the direct shear testing is presented in Table E. Figure E. Shear Stress vs. Confining Stress for Direct Shear Results for Problem 2. Table B. Direct Shear Results Summary for Problem # Assignment 8 Solution Page 8 of 9

9 State Friction Angle ( ) ( ) Cohesion (c) Peak Residual Since residual = 20.2 < 30 (Required residual by specification), this material CANNOT be used for the project. This soil was tested in a dense state. That can be determined by volumetric behavior of the soil during the direct shear test and from the fact that peak > residual Assignment 8 Solution Page 9 of 9

SOIL MECHANICS Assignment #7: Shear Strength Solution.

14.330 SOIL MECHANICS Assignment #7: Shear Strength Solution. PROBLEM #1: GIVEN: Direct Shear test results from a SP soil shown in Figure A (from 14.330_2012_Assignment_#8_P1.csv on the course website).