Table 3 Empirical equations derived in this study.

From: Brittle-ductile transition stress of different rock types and its relationship with uniaxial compressive strength and Hoek–Brown material constant (mi)

Equation

Rock type

Coefficient of determination (%)

\({\upsigma }_{\mathrm{TR}}=0.058{\mathrm{UCS}}^{1.578}\)

Igneous rocks

89

\({\upsigma }_{\mathrm{TR}}=1.361{\mathrm{UCS}}^{0.947}\)

Sedimentary rocks

72

\({\upsigma }_{\mathrm{TR}}=0.491{\mathrm{UCS}}^{1.140}\)

Metamorphic rocks

68

\({\upsigma }_{\mathrm{TR}}=3.911{\mathrm{mi}}^{1.5992}\)

Igneous rocks

83

\({\upsigma }_{\mathrm{TR}}=17.218{\mathrm{mi}}^{0.868}\)

Sedimentary rocks

51

\({\upsigma }_{\mathrm{TR}}=17.413{\mathrm{mi}}^{0.677}\)

Metamorphic rocks

18