Table 1 Five elastic determination equations of transversely isotropic slate.
The joint dip angle β(°) | Calculating equations |
|---|---|
\(\beta = {0}^\circ\) | \(\frac{{\Delta \varepsilon_{x} }}{{\Delta \sigma_{r} }} = - \frac{{v_{2} }}{{E_{{2}} }}\) (10) |
\(\frac{{\Delta \varepsilon_{y} }}{{\Delta \sigma_{z} }} = - \frac{{v_{2} }}{{E_{{2}} }}\) (11) | |
\(\frac{{\Delta \varepsilon_{r} }}{{\Delta \sigma_{r} }} = \frac{1}{{E_{{2}} }}\) (12) | |
\(\beta = {90}^\circ\) | \(\frac{{\Delta \varepsilon_{x} }}{{\Delta \sigma_{r} }} = - \frac{{v_{{1}} }}{{E_{{1}} }}\) (13) |
\(\frac{{\Delta \varepsilon_{y} }}{{\Delta \sigma_{r} }} = - \frac{{v_{2} }}{{E_{{2}} }}\) (14) | |
\(\frac{{\Delta \varepsilon_{r} }}{{\Delta \sigma_{r} }} = \frac{1}{{E_{{1}} }}\) (15) | |
\(\beta = {45}^\circ\) | \(\frac{{\Delta \varepsilon_{x} }}{{\Delta \sigma_{r} }} = - \frac{{1}}{{2}}\left( {\frac{{v_{{1}} }}{{E_{{1}} }} + \frac{{v_{{2}} }}{{E_{{2}} }}} \right)\) (16) |
\(\frac{{\Delta \varepsilon_{y} }}{{\Delta \sigma_{r} }} = \frac{{1}}{4}\left( {\frac{1}{{E_{1} }} + \frac{1}{{E_{2} }} - \frac{1}{{G_{2} }}} \right) - \frac{{v_{2} }}{{{2}E_{2} }}\) (17) | |
\(\frac{{\Delta \varepsilon_{r} }}{{\Delta \sigma_{r} }} = \frac{{1}}{4}\left( {\frac{{1}}{{E_{2} }} + \frac{{1}}{{E_{1} }} + \frac{1}{{G_{2} }} - \frac{{2v_{2} }}{{E_{2} }}} \right)\) (18) |
