GeotechnicalEngineeringResearchLaboratory EdwardL.Hajduk,D.Eng,PEOneUniversityAvenue LecturerLowell,Massachusetts01854 PA105DTel:(978)934‐2621 Fax:(978)934‐3052e‐mail: Edward_Hajduk@uml.eduwebsite:http://faculty.uml.edu/ehajduk

DEPARTMENTOFCIVILANDENVIRONMENTALENGINEERING

14.330 2013 Assignment 5 Solution Page 1 of 10

14.330 SOIL MECHANICS Assignment #5: Stresses in a Soil Mass.

PROBLEM #1 (20 Points): GIVEN: You are a staff engineer for a local geotechnical engineering firm. As part of the geotechnical exploration for a project, several subsurface tests have been conducted. You are given the results of one traditional soil boring with Standard Penetration Testing (SPT). The results of this boring, labeled as B-2, are presented on page 3 of this assignment. Based on testing of collected soil samples, the encountered soils have the unit weights listed in Table 1. Table 1. Summary of Soil Unit Weights from Boring B-2.

UCSC Symbol (pcf) sat (pcf)

SP (Upper) 107 111

ML 102 106

CH 108 114

SM 111 114

SP (Lower) 114 120

CL 117 121

NOTE: Assume the asphalt and base course layers are removed and replaced with material identical to that underneath them. REQUIRED: Determine the total, pore pressure, and effective stresses in the soils from the ground surface to the bottom of the borehole (i.e. a depth of 75 ft). Provide a plot of these stresses with depth. SOLUTION: ’ = – u (Effective Stress = Total Stress – Pore Pressure) = * Soil Height = w * Height of Water See Figure A for solution. Note values rounded to nearest 5 psf.

GeotechnicalEngineeringResearchLaboratory EdwardL.Hajduk,D.Eng,PEOneUniversityAvenue LecturerLowell,Massachusetts01854 PA105DTel:(978)934‐2621 Fax:(978)934‐3052e‐mail: Edward_Hajduk@uml.eduwebsite:http://faculty.uml.edu/ehajduk

DEPARTMENTOFCIVILANDENVIRONMENTALENGINEERING

14.330 2013 Assignment 5 Solution Page 2 of 10

Figure A. Total Stress, Pore Pressure, and Effective Stress with Depth (Static

Conditions). PROBLEM #2 (10 Points): GIVEN: You have just learned that a hydraulic gradient of 0.07 upwards exists at your project site. REQUIRED: Using this information, recalculate the effective stresses from the ground surface to the bottom of the borehole (i.e. a depth of 75 ft). Plot these effective stresses with depth. Briefly explain the effect of the upward water seepage on the effective stress compared to the static conditions.

14.330 2013 Assignment 5 Solution Page 3 of 10

SOLUTION: Upward flow causes an increase in porewater pressure by izw, where i = hydraulic gradient (0.07), z = depth below water table, w = unit weight of water. Therefore, 'flow = 'static - izw (increase in pore pressure = decrease in effective stress) See Figure B for solution.

Figure B. Total Stress, Pore Pressure, and Effective Stress with Depth (Upward Flow). PROBLEM #3 (10 Points): GIVEN: You have just learned that a hydraulic gradient of 0.07 downwards exists at your project site.

14.330 2013 Assignment 5 Solution Page 4 of 10

REQUIRED: Using this information, recalculate the effective stresses from the ground surface to the bottom of the borehole (i.e. a depth of 75 ft). Plot these effective stresses with depth. Briefly explain the effect of the downward water seepage on the effective stress compared to the static conditions. SOLUTION: Downward flow causes a decrease in porewater pressure by izw, where i = hydraulic gradient (0.07), z = depth below water table, w = unit weight of water. Therefore, 'flow = 'static + izw (increase in pore pressure = decrease in effective stress). See Figure C for solution.

Figure C. Total Stress, Pore Pressure, and Effective Stress with Depth (Downward

Flow).

14.330 2013 Assignment 5 Solution Page 5 of 10

PROBLEM #4 (50 Points): GIVEN: Figure 1 presents the general cross-section of two planned footings at your project site.

Figure 1. Planned Shallow Foundation Dimensions.

The project structural engineer has given you design loads of 100 kips for the columns and 6 kips per linear foot for the wall loads. Refer to Boring B-2 on page 3 for the soil profile at both footing locations. REQUIRED: From the provided information, determine the following:

The change in vertical effective stresses under the center of the footings using Boussinesq, Westergaard, and 2V:1H methods in 0.5B increments to a depth of 5 times the footing width.

The change in vertical stress distributions under the horizontal footing centerlines at depths of B and 2B to a distance of 4.5B away from the footing centerline.

Provide a brief commentary on the differences between the methods for both footings.

SOLUTION: Determine applied footing stress q: Column Footing qcolumn = P/A = 100 kips/(25ft2) = 4 ksf. qcolumn = 4 ksf. Strip (i.e. Wall) Footing qstrip = P/A = [(6 kips/ft)(1 ft Unit Length)/[(2ft)(1ft Unit Length)] qstrip = 3 ksf. Change in Vertical Total Stresses: Change in total vertical stress with depth from Boussinesq and Westergaard methods determined from Pressure with Depth Charts provided in class and attached to the end of this solution. 2V:1H Approximation based on the following formula: = Q/[(B+z)(L+z)] (Equation A), where: Q = Foundation Load, B = Foundation Width, L = Foundation Length (unit length of 1 used for strip), and Z = depth below footing.

WALL FTG COLUMN FTG

4 ft 4 ft

EXISTING GND SURFACE

5 ft x 5 ft

2 ft

14.330 2013 Assignment 5 Solution Page 6 of 10

See Tables B and C for calculations for the column and strip footings, respectively and Figure D for graphical representations. Table B. Summary Calculations for Column Footing.

Depth (B) Depth (ft) Bouss. (q)1

Bouss. (psf)

West. (q)2

West. (psf)

2V:1H (psf)3

0.0 0.0 1 4000 1 4000 4000

0.5 2.5 0.68 2720 0.5 2000 1780

1.0 5.0 0.37 1480 0.22 880 1000

1.5 7.5 0.2 800 0.13 520 640

2.0 10.0 0.11 440 0.074 295 445

2.5 12.5 0.077 310 0.049 195 325

3.0 15.0 0.047 190 0.035 140 250

3.5 17.5 0.04 160 0.026 105 200

4.0 20.0 0.033 130 0.019 75 160

4.5 22.5 0.025 100 0.017 70 130

5.0 25.0 0.019 75 0.014 55 110 NOTES:

1. From Boussinesq Pressure Distribution with Depth Chart. 2. From Westergaard Pressure Distribution with Depth Chart. 3. From Equation A.

Table C. Summary Calculations for Strip Footing.

Depth (B) Depth (ft) Bouss.

(q)1 Bouss.

(psf) West. (q)2 West. (psf)

2V:1H (psf)3

0.0 0.0 1 3000 1 3000 3000

0.5 1.0 0.78 2340 0.59 1770 750

1.0 2.0 0.55 1650 0.4 1200 400

1.5 3.0 0.4 1200 0.28 840 250

2.0 4.0 0.31 930 0.22 660 170

2.5 5.0 0.26 780 0.17 510 125

3.0 6.0 0.22 660 0.15 450 95

3.5 7.0 0.18 540 0.135 405 75

4.0 8.0 0.16 480 0.12 360 60

4.5 9.0 0.144 430 0.099 295 50

5.0 10.0 0.132 395 0.09 270 40 NOTES:

1. From Boussinesq Pressure Distribution with Depth Chart. 2. From Westergaard Pressure Distribution with Depth Chart. 3. From Equation A.

14.330 2013 Assignment 5 Solution Page 7 of 10

Figure D. with Depth.

14.330 2013 Assignment 5 Solution Page 8 of 10

Stresses at Planes B and 2B under Footing – Square Footing Change in Total Vertical Stress () can be determined using the Boussinesq or Westergaard charts provided in the lecture notes. Using the Boussinesq charts for the square footing, changes with stress away from the footing were calculated and are shown in Table D. Note that after distance of ~3B at a depth of 1B and a distance of ~4B at a depth of 2B, the change in vertical effective stress is negligible. Figure E provides this data in graphical form. Table D. Summary Calculations at Planes below Footing of 1B and 2B for Column Footing (using Boussinesq Charts).

B x (ft) /q @ z=B @ z=B (psf)

/q @ z=2B

@ z=2B (psf)

-4.5 -22.5 0.000 0 0.000 0

-4 -20 0.000 0 0.000 0

-3.5 -17.5 0.000 0 0.003 10

-3 -15 0.001 5 0.006 25

-2.5 -12.5 0.004 15 0.010 40

-2 -10 0.008 30 0.020 80

-1.5 -7.5 0.021 85 0.040 160

-1 -5 0.081 325 0.067 270

-0.5 -2.5 0.230 920 0.090 360

0 0 0.360 1440 0.110 440

0.5 2.5 0.230 920 0.090 360

1 5 0.081 325 0.067 270

1.5 7.5 0.021 85 0.040 160

2 10 0.008 30 0.020 80

2.5 12.5 0.004 15 0.010 40

3 15 0.001 5 0.006 25

3.5 17.5 0.000 0 0.003 10

4 20 0.000 0 0.000 0

4.5 22.5 0.000 0 0.000 0

14.330 2013 Assignment 5 Solution Page 9 of 10

Figure E. under Footing - Column Footing.

PROBLEM #5 (10 Points): GIVEN: At the same project site, the project plans call for adding 5 ft of SP-SM fill over the entire site. This fill has a saturated unit weight of 115 pcf and a moist unit weight of 110 pcf after compaction to 98% of D698. A surface parking lot will eventually be placed on top of the fill. REQUIRED: Calculate and plot the total stresses, pore pressure, and effective stresses to the end of Boring B-2. Use the information provided in Problem #1 for your calculations. SOLUTION: Assume the five (5) feet of fill acts as a new soil layer. This is a valid assumption, since no dimensions of the site were given.

14.330 2013 Assignment 5 Solution Page 10 of 10

Therefore, the increase in total stresses () is equal to the moist unit weight of the SP-SM fill multiplied by the fill height (i.e. = (SP-SM)(fill height) = (110 pcf)(5ft) = 550 psf). Since there is no change in pore water pressure (u = 0) due to the added fill, the change in total stresses equals the change in effective stresses (i.e. = '). Therefore, add = (5ft)(1150 pcf) = 550 psf to total and effective stresses calculated with depth in Problem #2. Solution is plotted in Figure F.

Figure F. Total Stress, Pore Pressure, and Effective Stress with Depth (Static

Conditions with 5 ft of additional Fill).