# Soil Mechanics - Shear Stress in a Soil Sample

## Homework Statement

Two consolidated and drained (CO) triaxial compression tests (tests A and 8)
were conducted on dense dry sand at the same void ratio. Test A had a cell
pressure of 150 kPa, while in test B the cell pressure was 600 kPa (u=OkPa).
These stresses were held constant throughout the test. At failure, they had
maximum principal stress differences of 600 and 2550 kPa, respectively. You

a) Plot the Mohr circles for both tests at initial conditions and at failure.
b) Determine shear strength of this soil.
c) Determine the shear stress on the failure plane at failure for both tests?
d) Determine the orientation of the failure plane in each specimen (use
equations or graphical solution).
e) Determine the orientation of the major principal plane at failure.
f) Determine the orientation of the plane of maximum shear stress at failure
g) If these soil samples were tested in direct simple shear, would the soil
exhibit compression or dilation?

## The Attempt at a Solution IMG_0971[/url[/B]
] by Ryan Stewart, on Flickr

<< Fixed up image by Mentors >> B. Determine the Shear Strength of the Soil

τ = (Ơ1 - Ơ3)/2 Sin(2θ)
=(2550)/2 * Sin (66.4 *2)
=935.5 KPa

C. Determine the shear stress

Sample B

θ = 45 + ∅/2
=45 + 42.8/2
θ=66.4

Cos∅ = Ơn/r
Ơn = Cos∅ x r
= Cos (180-2θ) x 1875
= 1273.95 KPA

τ = c + Ơn tan (2θ)
= 0 + 1273.95 x tan (2 x 66.4)
= 1375.7 KPA

This is as far as I've gotten just wanted to make sure I was on the correct path before continuing.

Thanks for any help!

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