A note on notation

In this thesis I will attempt to stick to the following stress notation conventions. In the first sections $\sigma_{ij}$ signifies any general stress tensor but once the concept of effective stress has been introduced $\sigma_{ij}$ is the effective stress and $S_{ij}$ the applied stress. All stresses are considered positive when compressive. The term hydrostatic stress is often used for the situation $\sigma_{1}$ = $\sigma_{2}$ = $\sigma_{3}$. This becomes a little confusing when pore pressures and boreholes are present and I will reserve hydrostatic for the stress (or pressure) exerted by the weight of a unit area column of the fluid in question. Vectors are in bold, ${n}$, tensors and matrices bold underlined, $\underline{A}$.

  

$\underline{\sigma}$, 

$\underline{D}$, 

$\underline{T}$  General, deviatoric and reduced stress tensor


$\sigma_{xx}$, 
$\sigma_{yy}$, 
$\sigma_{zz}$, 		 Normal stress components in a Cartesian 


$\sigma_{11}$, 
$\sigma_{22}$, 
$\sigma_{33}$ 		 coordinate system 


$\sigma_{rr}$, 
$\sigma_{\theta\theta}$, 
$\sigma_{zz}$, 		 Normal stress components in a                                    cylindrical coordinate system 


$\sigma_{xy}$, 
$\sigma_{xz}$, 
$\sigma_{yz}$, 		 Shear stress components in a Cartesian 


$\sigma_{12}$, 
$\sigma_{13}$, 
$\sigma_{23}$ 		  coordinate system 


$\sigma_{r\theta}$, 
$\sigma_{rz}$, 
$\sigma_{\theta z}$, 		 Shear stress components in a                                     cylindrical coordinate system 


$\sigma_{1}$, 
$\sigma_{2}$, 
$\sigma_{3}$		 Magnitudes of the principal stresses 



${\ensuremath{\sigma_{1}}}$, 

${\ensuremath{\sigma_{2}}}$, 

${\ensuremath{\sigma_{3}}}$ 		 Principal stress vectors 



${\hat{\ensuremath{\sigma_{1}}}}$, 

${\hat{\ensuremath{\sigma_{2}}}}$, 

${\hat{\ensuremath{\sigma_{3}}}}$ 		Orthonormal basis vectors in the principal stress directions 


$\sigma_{1N}$, 
$\sigma_{1E}$, 
$\sigma_{1d}$ 		  Components of 

${\hat{\ensuremath{\sigma_{1}}}}$ in theNorth, East, down coord. sys. 


${n}$ 		 Vector normal to a plane, unit length 


${t}$ 		 Traction vector on a plane 

$\sigma_n$, 

${\sigma_n}$ 		 Normal stress magnitude and vector, on a plane 

$\tau$, 
${\tau}$ 		 Shear stress magnitude and vector, in a plane 


$\sigma_{H}$, $\sigma_h$, $\sigma_V$ Maximum and minimum horizontal stress andvertical stress 

$P$, $P_0$, $P_b$ General fluid pressure, pore pressure, borehole                         fluid pressure