Reference no: EM133206435 , Length: Word count: 3 Pages

Question 1: Use a Mohr circle to find σN and τ on a plane at 25°, when σ1 = 200 MPa and σ3 = 50 MPa.  Please note the angle of the plane is measured anti-clockwise from the σ1 direction.  After working with the graph, calculate σN and τ to check your answers.

Question 2: In a point in the subsurface, the rock is experiencing the following stress field σ1 = 120 MPa, σ2 = 90 MPa, and σ3 = 85 MPa.

a. Plot the Mohr Circles for this stress field

b. Determine the mean normal stress (σmean)

c. The mean normal stress is also the lithostatic stress. Assuming that the density of the rock column above this point is 2.8 g/cm3, calculate the depth at which these stress conditions occur.

d. Determine the deviatoric stresses for the three principal stress axes.

e. Interpret the deviatoric stresses on the point.

f. What is the differential stress?

Question 3: Construct a Mohr diagram to represent a state of stress in which the principal stresses are determined to be: σ1 = 40 MPa, σ2 = 22 MPa, and σ3 = 18 MPa. And answer the following questions:

a. Draw a model of a fault, where σ3 is the vertical component of principal stress.  Determine the normal and shear stresses on a fault dipping at 40° to the east.

b. Draw a model of a fault, where σ3 is the vertical component of principal stress.  Determine the normal and shear stresses on a fault dipping at 40° to the west.

c. Why should we care about the sign of τ?

d. Double-check your estimates of σN and τ in parts a and b, by calculating them using our standard equations for σN and τ.

e. Calculate the mean stress

f. Calculate the deviatoric stress for each of the three principal stresses - interpret the deviatoric stresses based on their signs!

g. The rock along the fault is saturated and exerts a pore pressure of 15 MPa.  Draw a second Mohr diagram to show the influence of the pore pressure.  Determine the σN and τ for both situations a and b with the new complication of pore pressure.