Shear mode

For the shear mode a Coulomb friction envelope is used. The yield function has the form

$\displaystyle f_2($$\displaystyle \mbox{\boldmath$\sigma$}$$\displaystyle ,\kappa_2) = \vert\tau\vert+\sigma\tan\phi(\kappa_2)-c(\kappa_2)$ (59)

According to [17] the variations of friction angle $ \phi$ and cohesion $ c$ are assumed as
$\displaystyle c$ $\displaystyle =$ $\displaystyle c_0\exp\left(-\mbox{$\displaystyle\frac{c_0}{G^{II}_f}$}\kappa_2\right)$ (60)
$\displaystyle \tan\phi$ $\displaystyle =$ $\displaystyle \tan\phi_0+(\tan\phi_r-\tan\phi_0)\left(\mbox{$\displaystyle\frac{c_0-c}{c_0}$}\right)$ (61)

where $ c_0$ is initial cohesion of joint, $ \phi_0$ initial friction angle, $ \phi_r$ residual friction angle, and $ G^{II}_f$ fracture energy in mode II failure. A non-associated plastic potential $ g_2$ is considered as

$\displaystyle g_2=\vert\tau\vert+\sigma\tan\Phi-c$ (62)

Figure: Shear behavior of proposed model for different confinement levels in MPa ( $ c_0=0.8\ \rm{MPa},\ \tan\phi_0=1.0,\ \tan\phi_r=0.75,{\rm and}\ G_f^{II}=0.05\ {N/mm}$)

Borek Patzak