Stress Paths Stress Point 1 3 ) 1 3 ) - PDF document

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