Characterization of Rock Joint Roughness from the Classified and Weighted Uphill Projection Parameters

Acknowledgments

Notation

A₀

maximum possible contact area in the shear direction (dimensionless);

C

3D roughness parameter (dimensionless);

L

joint length (mm);

L_Eqv

equivalent length of a rock joint along the shear direction (mm);

L_max

maximum projection length of a rock joint along the shear direction (mm);

$\overline{L}$

average joint length (mm);

JCS

joint wall compressive strength (MPa);

JRC

joint roughness coefficient (dimensionless);

JRC_Er

average estimation error of JRC (dimensionless);

JRC_Es

estimated JRC by the fitting formulae (dimensionless);

JRC_Ex

experimentally back-calculated JRC by Barton's JRC–JCS criterion (dimensionless);

S

projection area of a rock joint (mm²);

S_i

projection area of each uphill segment of a joint profile along the shear direction (mm²);

$S_{\mathrm{up}},S_{\mathrm{up}}^{\mathrm{2nd}},S_{\mathrm{up}}^{\text{1st}}$

simplifications of ((S_i × 100)/L²), ((S_i(0.5) × 100)/L²), and ((S_i(5.0) × 100)/L²), respectively (dimensionless);

V_i

covered volume of each uphill segment of a joint surface along the shear direction (mm³);

$V_{\mathrm{up}},V_{\mathrm{up}}^{\mathrm{2nd}},V_{\mathrm{up}}^{\text{1st}}$

simplifications of ((V_i × 1,000)/SL), ((V_i(0.5) × 1,000)/SL), and ((V_i(5.0) × 1,000)/SL), respectively (dimensionless);

$\sqrt{V^{*}/\mathrm{SL}}$

translational overlapping volume parameter (dimensionless);

$V_{\mathrm{sum}}^{*}/V_{\mathrm{Total}}$

“hourglass parameter” (dimensionless);

${\theta }_{max}^{*}$

maximum apparent gradient of asperity along the shear direction (°);

σ_n

effective normal stress applied on a rock joint (MPa); and

τ_peak

peak shear strength of a rock joint (MPa).

References