Question: Given the stresses relative to compass coordinates (x=east, y=north, z =up), xx = 14.9, yy = 21.0, zz = 29.0, yx = 8.4, xz =

Given the stresses relative to compass coordinates (x=east, y=north, z =up), σxx = 14.9, σyy = 21.0, σzz = 29.0, τyx = −8.4, τxz = 0, τyz = 0 in MPa with compression positive, find the principal stresses σ1, σ2, σ3 (magnitude and orientation). Show with a suitable sketch. Then consider an unlined shaft that will be 4 × 8 m in section, choose the best opening shape (ellipse, ovaloidal, or rectangle) and best orientation from the rock mechanics perspective, assuming the given stress state is critical to the design sketch.

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