Mini-lecture 11.4 - Mohr-Coulomb criterion I, part of the topic Brittle deformation and faulting in the Geodynamics course at the University of Helsinki. Lecture slides: matskut.helsinki.fi/handle/12...
In real life, the difference between the principle stresses is 90 degrees as they are tangential to each other, but on mohr circle they are 180 degrees apart, so to get real representation of them we need to multiply real life angle by 2 or divide circle angle by 2
Thanks for the video it was helpful. I have a question: The cohesion is the ability for the rock to hold itself together, how about the joint? (in joints the particles are not held together anymore) what is the definition of cohesion in the shear strength of joints? Is it apparent cohesion?
Good question. Assuming there has been nothing that has precipitated within a joint or fracture that might fill in the space and bind the two sides together, the cohesion should be zero. The shear strength may still be nonzero, depending on the frictional contact between the two sides and the pressure holding them together, but the cohesion could be zero.
Geotechnical question how can you solve it? laboratory experiments determined the frictional properties of a sandstone as m = 0.67 and C = 20 MPa. Use the Mohr diagram to determine the strength (differential stress) of this sandstone at a depth of 2 km in MPa, assuming that the mean stress at this depth is 50 MPa.
This sounds like a homework problem, so I won't solve this completely for you, but perhaps I can give you a few hints. For me, the key to a problem like this lies in trigonometry. First, you know that mu, the coefficient of friction, is the slope of the line on the Mohr diagram. This is also equal to the tangent of the friction angle (mu = tan(phi)). The line on the Mohr diagram crosses the y-axis at the value of the cohesion. The mean stress is equal to the average value of the principal stresses, and is at the center of the Mohr circle. Thus, the center of the circle should be at sigma_n = 50 MPa in your case. What you need to do is find the differential stress, which is the radius of the Mohr circle. You can find its length using trigonometry. If you look at the Mohr circle plot, there is a triangle formed by the sloped line (the failure criterion), the normal stress axis, and the radius of the circle extending from its center to point A in the diagram. You need to know two things. First, you need the length of the side of the triangle running along the x-axis, and second, the length of the radius (differential stress). To find the length of the side of the triangle running along the x-axis, you will need the friction angle, cohesion and mean stress. From there it should be fairly easy to find the radius of the circle. Good luck!
