Rock Mechanics Worked Examples

Estimate total vertical stress below 100 m of rock with unit weight 24 kN/m³ over 100 m at 27 kN/m³. Assume a level, laterally extensive profile.

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A prescribed joint has total normal stress 12 MPa, water pressure 3 MPa, effective cohesion 5 MPa and effective friction angle 30°. Compare its modeled shear strength with the dry value.

Two comparable direct-shear tests on a joint fail at effective normal/shear stresses (8, 7) and (15, 11) MPa. Fit a straight line over this tested range.

Total principal stresses are 80 and 20 MPa; uniform joint pressure is 10 MPa with unit effective-stress coefficient. The plane normal lies in the major–minor principal section and makes 30° with the major principal stress direction. Find the effective circle and stresses on that plane.

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For an isotropic Mohr–Coulomb material with $c'=5\ \mathrm{MPa}$ and $\phi'=30^\circ$, find major effective stress at failure when minor effective stress is 10 MPa.

A prescribed total state has equal principal stresses of 20 MPa. Compare uniform joint pressure of 5 MPa with 25 MPa.

A plane has effective normal stress 6 MPa, driving shear 4 MPa, $c'=1.5\ \mathrm{MPa}$ and $\phi'=25^\circ$. Compare its ratio with a hypothetical project requirement of 1.30. No additional pore pressure is to be subtracted.

Use prescribed Hoek–Brown constants $\sigma_{ci}=100\ \mathrm{MPa}$, $m_b=1$, $s=0.01$ and $a=0.5$. Find major effective stress at failure for minor effective stress 10 MPa, and the rock-mass unconfined strength.

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A 1.00 m run recovers sound pieces of 20, 8, 12, 7, 25 and 28 cm separated by natural breaks. Count pieces longer than 10 cm. Find total recovery and RQD.

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An RMR89 assessment supplies ratings of 7 for strength, 13 for RQD, 10 for spacing, 20 for condition and 10 for groundwater. The applicable orientation adjustment is $-10$. Compute basic and adjusted ratings.

Use $RQD=75$, $J_n=9$, $J_r=1.5$, $J_a=2$, $J_w=0.66$ and $SRF=1$. Excavation span is 10 m and the supplied ESR is 1.3. Then consider $J_w=0.33$ and $SRF=2$, holding other inputs fixed.

Two headings have different records: A shows sudden energetic ejection from highly stressed massive rock; B shows progressive closure over weeks in weak ground, without evidence of mineral swelling. What should their assessments distinguish?