= Solution
Choose coordinates $(x,y,z)=(\mathrm{east},\mathrm{north},\mathrm{up})$ and use compression-positive <effective stress>. One possible tensor, in MPa, is
$$
\boxed{\boldsymbol\sigma'=\begin{pmatrix}10&0&0\\0&15&0\\0&0&20.3961\end{pmatrix}.}
$$
Its ordered <principal stresses> are vertical $\sigma_1'$, north–south $\sigma_2'$ and east–west $\sigma_3'$. On the $55^\circ$ east-dipping plane,
$$
\sigma_n'=\sigma_1'\cos^255^\circ+\sigma_3'\sin^255^\circ,
\qquad
|\tau|=(\sigma_1'-\sigma_3')\sin55^\circ\cos55^\circ,
$$
so $|\tau|/\sigma_n'=0.36397$, as required by the conditional friction estimate. The scale is illustrative: no absolute <stress> magnitude is supplied. A corresponding total <stress tensor> is $\boldsymbol\sigma^c=\boldsymbol\sigma'+P_f\mathbf I$ for any specified <isotropic> <pore fluid pressure> $P_f$.
Back to article page
