Homework Assignment No 6 Geotech

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Texas Tech University *

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3321

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Mechanical Engineering

Date

Apr 3, 2024

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CE 3321 HW#5 1 of 3 CE 3321 H OMEWORK A SSIGNMENT N O . 6 (Deadline 11:59 pm, Tuesday, November 21 st , 2023; Total 45 points) 1. The normal stress (  ) acting in soil at a certain depth below the ground surface is 120 kPa. The cohesion ( c ) and friction angle (  ) of the soil are 10 kPa and 31°, respectively. Compute the shear strength (  f ) of the soil under the given normal stress using the Mohr-Coulomb failure criterion. [4 points] 2. A series of direct shear tests has been performed on sand samples. All tests were performed on 3.00-in-diameter, 1.25-in tall cylindrical specimens. The results of these tests are summarized in the following table: Test No. Normal load (lb) Shear load at failure (lb) 1 100 84 2 200 159 3 400 319 Assuming the shear area remains constant during the test, determine the cohesion and friction angle using the test results. [6 points] 3. A series of triaxial compression tests has been performed on three identical 2.50- in-diameter samples of clay. All of the samples had an initial height of 6.00 inches. The test results were as follows. Test No Conditions at Failure Cell Pressure (psi) Deviator Stress (psi) 1 5.3 8.0 2 10.5 11.4 3 20.0 17.0 (a) Plot the Mohr’s circles at failure (use a compass), (b) draw Mohr-Coulomb failure envelop, and (c) determine cohesion c and friction angle  of the clay . [7 points] 4. A series of consolidated-undrained (CU) triaxial compression tests with pore water pressure measurements was performed on three identical samples of clay. The cell pressure, deviator stress at failure and porewater pressure at failure obtained for each test specimen are shown in the table below.

CE 3321 HW#5 2 of 3 Test No Conditions at Failure Cell Pressure (psi) Deviator Stress (psi) Pore Pressure (psi) 1 20 36.2 1.5 2 35 61.8 2.5 3 55 96.3 4.0 (a) Plot the Mohr’s circles at failure (use a compass) for effective stresses. (b) Then, determine effective stress strength parameters, c ' (in lb/ft 2 ) and  ' . [8 points] 5. The figure below shows a cut that will be made as a part of a new roadway construction project. The slope of the existing ground is 3H (Horizontal):1V (Vertical). The height of the cut is 24 ft and the slope of the cut is 1H:2V. It is known that the soil mass has bedding planes dipping in the direction of the cut (See figure). The total stress strength parameters corresponding to bedding plane (at the interface) are: c = 0.5 ksf and  = 20  . Soil unit weight = 120 lb/ft 3 . Groundwater table was not encountered (a) Determine the weight of the soil mass in kips/ft. [3 Points] (b) The required factor of safety (FS) for this construction project is 1.5. Calculate the factor of safety and check whether the minimum FS requirement has been satisfied. [5 Points] 2V 1H 1V 3H 24ft 48ft Original ground surface Bedding Plane

CE 3321 HW#5 3 of 3 6. (a) Using the ordinary method of slices, perform an effective stress analysis to compute the factor of safety for the failure surface shown in the figure below. In order to calculate porewater pressure acting at base of each slice, use the following pressure heads as representative values for each slice: [8 Points] Slice No. No.1 No.2 No.3 No.4 No.5 Pressure head (ft) 13 20 18 7 0 Notes: This problem is almost identical to we solved during class. Prepare a table similar to the one shown on Page 623 of the textbook. (b) Assume an earthquake occurs and the sand stratum liquefies and loses all its strength (i.e. c  = 0 and   = 0 during earthquake). Compute a new factor of safety for the same failure surface shown above. According to this analysis, will the slope survive the earthquake? [4 Points] Notes: Recalculations of weights of each slice are not necessary. Also, note that you do not need to recalculate resistance components associated with the strength of clayey silt. Although the sand stratum loses all its strength, the strength parameters of the clayey silt remain unchanged. 30 ft a = -11 a = 6 a = 20 a = 31 a = 50

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