STRESS (part II)

1.	For problem 3 of problem set 2, determine the depth at which we would find a pressure of 1 kbar (i.e., 1000 bar).  Be very careful with units.  

2.	If the stress state at a point is defined by 1 = 500 MPa (E-W direction), 2 = 300 MPa (N-S direction), and 3 = 100 MPa (vertical direction), what is the traction vector on a 1 square meter area surface dipping 45° toward the NE?  To answer this question, you first will need to determine the stress tensor and the direction cosines to the surface.  

Extra credit:  Specify the traction vector in terms of its magnitude and unit vector (trend and plunge).  

3.	Use Mohr’s circle for stress to determine the magnitudes and orientations of the (horizontal) principal stresses if we know that a vertical N-striking plane has n = 500 MPa and s = 100 MPa, and another vertical plane has n = 300 MPa and s = -100 MPa.  Draw a sketch map showing your results.  Also determine the mean stress, differential stress, maximum and minimum principal deviatoric stresses.  

4.	Suppose the Coulomb failure criterion for a block of granite is defined by a cohesive strength of 100 MPa and an angle of internal friction of 35°.  During an experiment, shear failure occurs when the normal stress is 100 MPa on the rupture surface (ignore the effects of fluid pressure).  Determine the shear stress on the fracture at failure, the principal stress magnitudes at the time of failure, and the orientation of the fracture relative to 1.  

5.	For the problem above, write the (2D) stress tensor for the state of stress when failure occurred (assume that the fracture developed perpendicular to one of the coordinate axes of our reference frame).