Question

The maximum and minimum principal stresses in a zone of active normal faulting are 28 MPa and 8 MPa, respectively. The fault plane strikes N30°E and dips 60° towards SE. Considering Anderson's theory of faulting, the normal stress on the fault plane is _______MPa. (In integer)

Answer 1

Correct Answer: 13

To determine the normal stress on the fault plane using Anderson's theory of faulting, we start by examining the principal stresses and fault plane orientation. Given are maximum (σ1 = 28 MPa) and minimum (σ3 = 8 MPa) principal stresses, with the fault plane striking N30°E and dipping 60° towards SE. According to Anderson's theory, the normal stress (σn) on a fault plane is calculated using the formula: 
σn = (σ1 + σ3)/2 + (σ1 - σ3)/2 * cos(2θ),
where θ is the angle between the maximum principal stress direction and the normal to the fault plane. Given the fault dips 60°, the angle θ relative to the horizontal stress (σ1, striking N30°E) is 30°. Substituting the values:
σn = (28 + 8)/2 + (28 - 8)/2 * cos(120°).
This simplifies to:
σn = 18 + 10 * cos(120°).
Since cos(120°) = -0.5,
σn = 18 - 5 = 13 MPa.
Therefore, the normal stress on the fault plane is 13 MPa