Vocabulary Terms

You should be able to define the following terms.
 

Force	Stress Gradient	Newton	Stress
Stress Tensor	Differential Stress	Load	Normal Stress
Stress Ellipse & Ellipsoid	Triaxial Stress	Hydrostatic Stress	Mass
Principal Stress Directions	Fundamental Stress Equations	Uniaxial Stress	Lithostatic Stress
Mohr Stress Diagram	Shear Stress	Stress Field	Weight
Dynamic Analysis	Theta	Mean Stress	Deviatoric Stress

Concepts

You should be able to give short answers to the following questions:

1) What are the goals of Dynamic Analysis?

2) What is the difference between mass and weight?

3) What are the units of : a) mass, b) weight, ) c) load, and d) force?

4) Determine the mass of a cube of rock (v = 1 m³) with a density of 2700 kg/m³

5) What are the types of Forces? What is the difference between Body Forces and Contact Forces? Give examples.

6) Define "Load". What is "Gravitational Loading", "Thermal Loading", and "Displacement Loading"?

7) The vertical stress s_z acting on a point within the Earth is 40 MPa. The density of the overlying rock is 2700 kg/m³. Gravity is 9.8 ms^-2. How far is the point below the Earth's surface?

8) Identify the components of the Mohr Circle for Finite Stress. Plot a Mohr Circle for Finite Stress. Read pertinent data off of a Mohr Circle for Finite Stress (e.g., Mean Stress, Differential Stress, Deviatoric Stress, s₁, s₃, s_n, s_s, etc.).

9) How does the magnitudes of the normal (s_n) and the shear stress  (s_s) vary as a function of orientation of the plane of interest to the maximum principal stress? Consider the strain ellipse as a visual representation of this relationship, and the Mohr circle for strain as a graphical representation of this relationship.

10) The vertical stress s_z  acting on a point within the Earth is 30 MPa, the horizontal stress s_x   is 50 MPa. What is the magnitude and orientation of the stress acting on a plane dipping 25^o to the east? Use the fundamental stress equations, or a Mohr Cirlce diagram, and Pythagoream's theory to solve this one.

11.) Two rocks were deformed, both by faulting,  under the stress conditions given below. In each case the normal stress s_n acting on the fault was 40 MPa. What are the orientaions of the fault planes relative to s₁ in each case, and what is the shear stress s_s  acting on each fault plane?
Rock A  s₁= 60 MPa and s₃= 10 MPa. Rock B  s₁= 60 MPa and s₃= 30 MPa.

12.)  The Texas Gulf Coast is an area of concave upward normal faults. The vertical stress and dip of the fault planes vary with depth (see the table below). The horizontal stress is 100 MPa and is uniform throughout the area. Determine s_n acting on the fault plane at 5 km depth. Determine which fault plane has the greatest shear stress s_s.