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INDIAN INSTITUTE OF TECHNOLOGY MADRAS, CHENNAI Department of Civil Engineering CE 3350 Geotechnical Engineering

Tutorial # 1: Shear Strength of Soils and Site Investigation Note: Make suitable assumptions wherever necessary.

1. The following results were obtained when a loose silty sand (in dry condition) was tested in shear box test.

Normal stress (kN/m2 125 ) 235 345 Maximum shearing stress (kN/m2 90 ) 160 237

Determine: (a) The shear strength parameters of soil and (b) The magnitude of principal stresses and orientation of principal plane for the first test. Comment on the likely volume changes during shear.

2. The CU tests carried out on saturated normally consolidated clay showed that cu = 0 and φu = 150. If the pore pressure coefficient A at failure was 0.92, what are the values of c′ and φ′ for the soil?

3. An in situ vane shear test was conducted in clay soil at the bottom of borehole. A torque of 153 Nm was required to shear the soil. What was the undrained strength of clay? The vane was 100 mm in diameter and 150 mm long.

4. For a direct shear test on a dry sand, the following are given: • Specimen size: 75 mm × 75 mm × 30 mm (height) • Normal stress: 200 kN/m2 • Shear stress at failure: 175 kN/m2 (a) Determine the angle of friction, φ′ (b) For a normal stress of 150 kN/m2, what shear force is required to cause failure in the specimen?

5. The following are the results of four drained, direct shear tests on a normally consolidated clay. Given: • Size of specimen = 60 mm × 60 mm • Height of specimen = 30 mm.

Draw a graph for the shear stress at failure against the normal stress, and determine the drained angle of friction from the graph.

6. For a normally consolidated clay, φ′ = 24°. In a drained triaxial test, the specimen failed at a deviator stress of 175 kN/m2. What was the chamber confining pressure σ3′?

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12. (a) For a Shelby tube, given: outside diameter = 76.2 mm and inside diameter = 73 mm.

What is the area ratio of the tube? (b) Following is the variation of the field standard penetration number (N60) in a sand

deposit:

The groundwater table is located at a depth of 6 m. Given: the dry unit weight of sand from 0 to a depth of 6 m is 18 kN/m3 and the saturated unit weight of sand for depth 6 to 12 m is 20.2 kN/m3. Using the relationship of Skempton, calculate the corrected penetration numbers.