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

Stress Paths

  1 3 ½13) ½13) Stress Point 

q p ½1 3) ½1  3) Stress Point

1 3 1 3

p , q 2 2        

3 1f 

 

q p Stress Path

q p Stress Path



h v

K   

h v

1 tan q 1 K K tan 1 tan p 1 K              

q p Failure Envelope



hf f vf

K   

hf 3f f f vf 1f f

1 K K tan 1 K           

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 40 20

Shear stress,  (kPa)

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

 1f   ff ff 

CTC cell q 45° p

• r AC

RTC cell q 45° p LE or

CTE cell q 45° p

• r LC

RTE cell q 45° p AE or

vo q RTE p RTC CTE CTC or AC

• r LC

LE or AE or