Table 1 Summary of flat rock pillar formulae.

Hedley³³

\({S_{p0}}=0.578{\sigma _c}\frac{{{w^{0.5}}}}{{{h^{0.75}}}}\)

power law

σ_c = 230 MPa

Kimmelmann³⁴

\({S_{p0}}=0.691{\sigma _c}\frac{{{w^{0.46}}}}{{{h^{0.66}}}}\)

power law

σ_c = 94 MPa

Krauland³⁵

\({S_{p0}}=0.354{\sigma _c}\left( {0.778+0.222\frac{w}{h}} \right)\)

linear

σ_c = 100 MPa

\({S_{p0}}=0.420{\sigma _c}\frac{w}{h}\)

power law

-

Potvin³⁶

Sjöberg³⁷

\({S_{p0}}=0.308{\sigma _c}\left( {0.778+0.222\frac{w}{h}} \right)\)

linear

σ_c = 240 MPa

Lunder et al³⁸

\({S_{p0}}=0.44{\sigma _c}\left( {0.68+0.52\kappa } \right)\)

Where\(\left\{ \begin{gathered} \kappa =\tan \left( {{{\cos }^{ - 1}}\frac{{1 - {C_{pav}}}}{{1+{C_{pav}}}}} \right) \hfill \\ {C_{pav}}=0.46{\left[ {\log \left( {\frac{w}{h}+0.75} \right)} \right]^{\frac{{1.4}}{{(w/h)}}}} \hfill \\ \end{gathered} \right.\)

confinement

-

Esterhuizen et al³²

\({S_{p0}}=0.65{\sigma _c} \cdot LDF \cdot \frac{{{w^{0.30}}}}{{{h^{0.59}}}}\)

power law

LDF represents the coefficient of discontinuity, and its value ranges from 0 to 1.