Geomechanics 1: Week 6
Soil Shear Strength
Question time!
Shear box problem-sand
Problem: In a direct shear test a shear displacement of 4mm corresponds with the peak
shear load of T = 80N. If an applied vertical load of N = 100N is acting on a shear box of
60mm x 60mm, what is the peak angle of friction for the sample?
Solution:
How to find stresses on an inclined plane?
, Equation for Mohr circle of stresses
2 2
æ s + sy ö æ sx - sy ö
çç s a - x ÷÷ = çç ÷÷ cos 2 2a..............(1)
è 2 ø è 2 ø
2
æ sx - sy ö
ta2 = çç ÷÷ sin 2 2a.....................................( 2)
è 2 ø
------------------------------
2 2
æ sx + sy ö æ s - sy ö
(1 + 2) Þ çç s a - ÷÷ + ta2 = çç x ÷÷ .....(3)
è 2 ø è 2 ø
(X - A )2 + (Y - B) 2 = R 2 ..............(4)
Mohr-Coulomb strength envelope
(combing Mohr circle with Coulomb failure envelope)
- Coulomb strength envelope becomes tangent with Mohr circle at failure
- Maximum obliquity of tf/sf (at B) on the failure plane
- Also max ratio of (s1/s3)f at failure
- At failure, tf<tmax (note max shear stress is radius of circle which occurs at normal
stress corresponding to A)
- Physical orientation of the plane can be seen
Soil Shear Strength
Question time!
Shear box problem-sand
Problem: In a direct shear test a shear displacement of 4mm corresponds with the peak
shear load of T = 80N. If an applied vertical load of N = 100N is acting on a shear box of
60mm x 60mm, what is the peak angle of friction for the sample?
Solution:
How to find stresses on an inclined plane?
, Equation for Mohr circle of stresses
2 2
æ s + sy ö æ sx - sy ö
çç s a - x ÷÷ = çç ÷÷ cos 2 2a..............(1)
è 2 ø è 2 ø
2
æ sx - sy ö
ta2 = çç ÷÷ sin 2 2a.....................................( 2)
è 2 ø
------------------------------
2 2
æ sx + sy ö æ s - sy ö
(1 + 2) Þ çç s a - ÷÷ + ta2 = çç x ÷÷ .....(3)
è 2 ø è 2 ø
(X - A )2 + (Y - B) 2 = R 2 ..............(4)
Mohr-Coulomb strength envelope
(combing Mohr circle with Coulomb failure envelope)
- Coulomb strength envelope becomes tangent with Mohr circle at failure
- Maximum obliquity of tf/sf (at B) on the failure plane
- Also max ratio of (s1/s3)f at failure
- At failure, tf<tmax (note max shear stress is radius of circle which occurs at normal
stress corresponding to A)
- Physical orientation of the plane can be seen
