Question

In a zone of active normal faulting, the maximum and minimum in situ principal stresses (compressive in nature) are 30 MPa (\( \sigma_1 \)) and 10 MPa (\( \sigma_3 \)), respectively. The fault plane striking N-S has a dip amount of 60° towards E. Considering Anderson theory of faulting and using the given information, the calculated normal stress on the fault plane is \(\underline{\hspace{1cm}}\) MPa. (in integer)

Hint:

To calculate the normal stress on a fault plane in active faulting, apply Anderson's theory using the principal stresses and the dip angle of the fault.

Answer 1

Correct Answer: 15

Using Anderson's theory of faulting, the normal stress on the fault plane \( \sigma_n \) is calculated using the formula: \[ \sigma_n = \frac{\sigma_1 + \sigma_3}{2} + \frac{\sigma_1 - \sigma_3}{2} \cos(2\theta), \] where \( \theta = 60^\circ \). Substituting the given values: \[ \sigma_n = \frac{30 + 10}{2} + \frac{30 - 10}{2} \cos(2 \times 60^\circ) = 20 + 10 \times \cos(120^\circ) = 20 + 10 \times (-0.5) = 15. \] Thus, the normal stress on the fault plane is \( \boxed{15} \) MPa.