In the case of normal faults, the rock mass is pushed down in a vertical direction, thus the pushing force ( "'greatest "'principal stress ) equals the weight of the rock mass itself.
42.
In the case of thrusting, the rock mass'escapes'in the direction of the least principal stress, namely upward, lifting the rock mass up, thus the overburden equals the "'least "'principal stress.
43.
In the case of thrusting, the rock mass'escapes'in the direction of the least principal stress, namely upward, lifting the rock mass up, thus the overburden equals the "'least "'principal stress.
44.
Using the double angle approach we measure the angles " BOC and " BOE in the Mohr Circle ( Figure 8 ) to find double the angle the major principal stress and the minor principal stress make with plane B in the physical space.
45.
Using the double angle approach we measure the angles " BOC and " BOE in the Mohr Circle ( Figure 8 ) to find double the angle the major principal stress and the minor principal stress make with plane B in the physical space.
46.
As the faces slide in opposite directions, tension is created at the tip, and a mode I fracture is created in the direction of the " ? h-max ", which is the direction of maximum principal stress.
47.
It is assumed that the brittle material has no tensile strength . ( In case of reinforced concrete this assumption is necessary because the concrete has small shrinkage cracks . ) Therefore, the principal stresses of the brittle material need to be compression.
48.
To determine the equation of the stress ellipsoid we consider the coordinate axes x _ 1, x _ 2, x _ 3 \, \ ! taken in the directions of the principal axes, i . e ., in a principal stress space.
49.
Secondly, a \ D * a works, were a is a standard rotation matrix about an axis, i . e . for the 1-3 plane ( if sigma1 was the highest principal stress and sigma3 was the lowest ), it would be:
50.
Other examples of sets of tensor invariants are the set of principal stresses ( \ sigma _ 1, \ sigma _ 2, \ sigma _ 3 ) or the set of mechanics invariants ( I _ 1, J _ 2, J _ 3 ).
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