Stress Paths
Stress Point ½ 1 3 ) ½ 1 3 ) 3 1
q Stress Point ½ 1 3 ) ½ 1 3 ) p 1 3 1 3 p , q 2 2
3 1f
p Stress Path q
q Stress Path K h v p 1 tan q 1 K h K tan 1 tan p 1 K v
q Failure Envelope K hf f vf p 1 K hf 3f f K tan f 1 K vf 1f f
Not tangent!
Direct Shear Test
Example • A direct shear test is run on a medium dense sandy silt with n = 65 kPa. At failure the shear stress is 41 kPa. • Draw the Mohr circles for the initial and failure conditions and determine: – The principal stresses at failure – The orientation of the failure plane – The orientation of the plane of maximum normal stress at failure – The orientation of the plane of maximum shear stress at failure
80 60 Shear stress, (kPa) 40 20 0 20 40 60 80 100 120 140 Normal stress, (kPa)
Triaxial Shear Test
3 1f
Example • A conventional triaxial compression (CTC) test is run on a loose sand with a friction angle of 20. The cell pressure is 30 psi. Determine the following: – The orientation of the failure plane – The stresses acting on the failure plane at failure – The axial stress at failure – The stress path corresponding to this test
ff ff 1f
q CTC or AC 45° p cell
q RTC LE or 45° p cell
q cell p 45° CTE or LC
q cell p 45° RTE AE or
q RTC CTC or AC LE or p vo CTE or LC RTE AE or
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