Question

A cylindrical soil sample was subjected to axial principal stresses, and radial principal stresses, . The soil could not support additional stresses when = 300 kPa and =100 kPa.

(a) Determine the soil's friction angle, .

(b) Find the angle of the failure plane at failure within the soil sample, .

(c) What is the normal stress on the failure plane at failure, ? (in kPa)

(d) What is the shear stress on the failure plane at failure, ? (in kPa)

(e) What is the maximum shear stress experienced within the soil sample, ? (in kPa)

Answer #1

A soil element is subjected to a minor principle stress of 50
kPa on a plane rotated 20 °counterclockwise from vertical. If the
deviator stress is 120 kPa and the shear strength parameters are a
friction angle of 30° and a cohesion of 5 kPa, determine the
magnitude of the stresses on the failure plane and the orientation
of this plane with respect to the major principle stress plane.

A soil sample was taken from the field and tested in the lab in
drained triaxial conditions. If the soil failed at a major
principle stress σ1 ’ = 130 kPa, and a minor principle stress σ3 ’
= 55 kPa:
a) What is the effective stress friction angle of the soil?
b) What was the shear stress at failure?
c) What was the normal stress at failure? Please using the Mohr
circle to illustrate your answer.

A geotechnical engineer is evaluating the stability of a silty
sand slope as shown (next page).
This evaluation is considering the potential for a shear failure
at an infinitesimal point (soil
element) on the trial shear surface.
At this particular point, the soil is found to be subjected to a
major principal stress of +450
kN/m2 and a minor principal stress of +50 kN/m2.
(A) Using the Pole Method, find the intensity of the normal and
shear stresses acting on...

Derive an expression for the strain energy stored in a material
when subjected to three principal stresses.
A material is subjected to a system of three mutually perpendicular
stresses as follows: f tensile, 2f tensile and f
compressive. If this material failed in simple tension at a stress
of 180 MN/m2, determine the value offif the criterion
of failure is:
(a) maximum principal stress;
(b) maximum shear stress;
(c) maximum strain energy.
Take Poisson’s ratio v = 0.3.

A direct shear test was run a cylindrical sample of sands using
a vertical force of 160N. The sample had a diameter of 51mm.
Determine: a) If the maximum horizontal force was
1065N, what was the peak friction angle? b) If
this material is tested using a triaxial apparatus, what will be
the major principle stress σ1 ’ at failure, under the minor
principle stress of σ3 ’ = 120 kPa?

The soil strength properties of a saturated soil specimen are
known as: CUU = 35 kPa, ϕUU = 0֯;
Ccu = 12 kPa, ϕcu = 12֯; C’ = 3
kPa, ϕ’ = 28֯. The shear stress on the potential failure
plane is _________kPa when the maximum principal stress is 400 kPa,
the minimum principal stress is 250 kPa and the pore water pressure
is 160 kPa. (Hint: σ 1 ′ = σ 3 ′ K P + 2 c ′...

A cylindrical storage tank contains liquefied propane
under a pressure of 1.5 MPa (gage pressure P=1.5 MPa) and is
subjected to an axial force F=60 kN. Knowing that the tank has an
inner diameter of 320 mm and a wall thickness of 3 mm, find the
principal stresses and determine the maximum shear stress.

A machine element is subjected to the following bi-axial state
of stress:
σx=80 MPa σy=20 MPa;
τxy=40 MPa.
If the shear strength of the material is 100 MPa, and the yield
strength is 300 MPa, determine the factor of safety using
(a)Tresca’s Maximum-Shear-Stress Theory and
(b) von Mises’ Distortion Energy Theory.

A drained triaxial test is conducted on a soil with friction
angle of 25° and zero cohesion, using a chamber pressure sc=300 kPa
and a back pressure (this is the term used to denote the initial
value of the pore pressure, u0) equal to 200 kPa. The shear stage
of the test is performed DRAINED by increasing the axial stress s1,
while concurrently decreasing the chamber pressure s3 so that their
sum remains constant (s1+s3 = constant). Draw the effective...

Three samples of the same depleted reservoir formation were
analyzed using conventional tri-axial cell and the results of axial
and radial stresses at the point of failure are reported below:
Sample
Sample Radial
Stress
(MPa)
Axial Stress (MPa)
1
0.358
8
2
1.052
10
3
1.692
12
(a) Using graphical representation of Mohr circles determine the
value of cohesion and internal friction angle of this formation.
You must draw the circles and failure criteria into exact scale and
read the...

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