Stress Paths

13

½13)

½13)

Stress Point

q

p

½1 3)

½1 3)

Stress Point

1 3 1 3p , q2 2

3 1f

q

p

Stress Path

q

p

Stress Path

h vK

h

v

1 tan q 1 KK tan1 tan p 1 K

q

p

Failure Envelope

hf f vfK

hf 3f ff

vf 1f f

1 KK tan1 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

0

Shea

r str

ess,

(k

Pa)

20 40 60 80 100 120 140Normal 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

or AC

RTC

cell

q

45°p

LE or

CTE

cell

q

45°p

or LC

RTE

cell

q

45°p

AE or

vo

q

RTE

p

RTC

CTE

CTC or AC

or LC

LE or

AE or