2. Ratings#
2.1. Generalities#
The deformations are positive in extension and the stresses are positive for tensile states.
Notion |
Description |
\({I}_{1}\text{=}\text{tr}(\sigma )\) |
First constraint invariant |
\(s\text{=}\sigma \text{-}\frac{\text{tr}(\sigma )}{3}I\) |
Constraint deviator |
\({s}_{\text{II}}\text{=}\sqrt{s\text{.}s}\) |
Second invariant of the deviatory stress tensor |
\(e\text{=}\varepsilon -\frac{\text{tr}(\varepsilon )}{3}I\) |
Deformation deviator |
\({\varepsilon }_{\nu }\text{=}\text{tr}(\varepsilon )\) |
Trace of deformations: volume deformation |
\({\varepsilon }^{p}\) |
Plastic deformation tensor |
\({\varepsilon }_{{}_{\nu }}^{p}\text{=}\text{tr}({\varepsilon }^{p})\) |
Variation in plastic volume |
\(\delta {\gamma }^{p}\text{=}\sqrt{\frac{2}{3}d{e}^{p}:d{e}^{p}}\) |
Cumulative plastic shear deformation |
\({\mathrm{\sigma }}_{1}\) |
Major main constraint |
\({\mathrm{\sigma }}_{3}\) |
Minor primary constraint (\({\mathrm{\sigma }}_{1}<{\mathrm{\sigma }}_{2}<{\mathrm{\sigma }}_{3}\)) |
\(H\) |
Hooke matrix |
\(\mu\) |
Lamé coefficient |
2.2. Model parameters#
Notion |
Description |
\(\mathrm{\gamma }\) |
Work hardening parameter (defined in paragraph 3.2.3) |
\(S\) |
Represents the state of damage and fracturing of the rock |
\(m\) |
Model smoothing parameter |
\({\mathrm{\sigma }}_{c}\) |
Strength of healthy rock without any damage |
\({\mathrm{\gamma }}^{\text{rup}}\) |
Work hardening parameter corresponding to material breakage |
\({\mathrm{\gamma }}^{\text{res}}\) |
Work hardening parameter corresponding to the start of residual resistance |
\(({\mathrm{S\sigma }}_{c}^{2}{)}^{\text{rup}}\) |
Product value \(S{\sigma }_{c}^{2}\) at breakpoint reached in \({\mathrm{\gamma }}^{\text{rup}}\) |
\(({\mathrm{S\sigma }}_{c}^{2}{)}^{\text{end}}\) |
Product value \(S{\sigma }_{c}^{2}\) at damage initiation \((\mathrm{\gamma }=0)\) |
\(({\mathrm{m\sigma }}_{c}{)}^{\text{rup}}\) |
Product value \(m{\sigma }_{c}\) at breakpoint reached in \({\mathrm{\gamma }}^{\text{rup}}\) |
\(({\mathrm{m\sigma }}_{c}{)}^{\text{end}}\) |
Product value \(m{\sigma }_{c}\) at damage initiation \((\mathrm{\gamma }=0)\) |
\(E\) |
Young’s module |
\(\mathrm{\nu }\) |
Poisson’s ratio |
\(\mathrm{\beta }\) |
Characterize residual resistance |
\({\phi }^{\text{end}}\) |
Friction angle at damage initiation \((\mathrm{\gamma }=0)\): optional parameter taken to be zero by default |
\({\phi }^{\text{rup}}\) |
Friction angle at break reached in \({\mathrm{\gamma }}^{\text{rup}}\) |
\({\phi }^{\text{res}}\) |
Friction angle at residual resistance reached in \({\mathrm{\gamma }}^{\text{res}}\) |
\(\mathrm{\alpha }\) |
Model parameter characterizing the post-fracture behavior of the material |