 Solution

Interpret the vertical, apparently unoffset fractures as opening geological joints. Their normals are east–west, so the least principal stress ${\sigma }_3$ must be east–west and sufficiently tensile in effective stress. The other two principal stresses lie within the vertical north–south geological joint plane; their ordering cannot be recovered from this fracture orientation alone.

One example, with compression positive and coordinates east, north, up, isHere ${\sigma }_1$ is vertical, ${\sigma }_2$ north–south, and ${\sigma }_3=-3\mathrm{MPa}$ east–west. The geological joint opens east–west when its tensile strength is $3\mathrm{MPa}$. An isotropic pore pressure can make the east–west effective stress tensile even while the total normal stress remains compressive. Draw opening arrows pointing away from the vertical fracture, rather than sliding arrows along it.