Highway Rock Cut: Kinematic Admissibility and Permanent Support of a Wedge Failure
A 2.4 km section of a new dual carriageway requires an 8 m high rock cut through interbedded sandstone and shale. The cut face is oriented 060/85. Bedding strikes consistently at 072/38 and carries 5–20 mm clay-filled seams with slickensides. Two joint sets are mapped: J1 150/75 and J2 315/80. During excavation a 30 m³ wedge detached from the face at chainage 12+300, injuring no one but closing one lane for two days. A 25 mm crack has opened behind the crest, and seepage is visible along the bedding at the toe. The design friction angle for the bedding seams is 27° with zero effective cohesion assumed. The road will carry 40,000 vehicles per day, and the client wants a permanent solution with a 50-year design life, not a temporary catch fence. Construction is paused pending geotechnical review.
1. Carry out a kinematic assessment. Is planar sliding on bedding admissible, and is the observed wedge kinematically possible? Show the checks.
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Planar sliding requires the discontinuity to daylight in the face and to dip more steeply than its friction angle, with its dip direction close to the face dip direction.
Bedding dips at 072/38; the face dips at 060/85. The angular difference in dip direction is 12°, well within the usual 20° tolerance, and the face is steep enough to daylight the plane. The bedding dip of 38° exceeds the design friction angle of 27°, giving a driving-resistance imbalance of about 11°. Planar sliding is therefore kinematically and frictionally admissible.
For the wedge, J1 is 150/75 and J2 is 315/80. Taking normals to the two planes and computing their cross product gives an intersection line plunging about 30° toward roughly 051°. That is within about 9° of the face dip direction and plunges steeper than 27°, so the wedge can daylight and slide. The observed 30 m³ failure is consistent with this geometry, probably releasing on the clay-filled bedding as the basal plane.
Conclusion: both planar and wedge modes are admissible. The 25 mm crest crack indicates that the failure surface extends behind the crest, so the current catch fence is not a permanent solution. The design must be based on a wedge with a basal bedding plane, not on a simple face-stability chart.
2. Design a permanent support system for the 8 m cut, with reasoning on bolt length, capacity, orientation and drainage.
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The wedge weighs about 30 m³ × 25 kN/m³ = 750 kN. Stability requires bolts anchored into stable rock behind the wedge, not merely into the moving block.
Proposed support:
- Pattern bolts on a 2 m × 2 m grid: 4.5 m long, 25 t working capacity, tensioned to about 70% of capacity. Bolt length must exceed the wedge depth plus the anchorage bond length; in a 8 m cut with a 030–040° basal plane, 4.5 m gives anchorage beyond the release surface.
- Bolt orientation should be perpendicular to the bedding where possible, plunging about 10–15° downward, so the bolt tension has a component normal to the basal plane rather than parallel to it.
- 100 mm steel-fibre-reinforced shotcrete with welded mesh over the face, plus 150 mm at the crest, to retain small blocks between bolts.
- Toe buttress of mass concrete or rockfill at the seepage zone, because the clay seams will soften; this also protects against undercutting during future maintenance.
- Horizontal drains: 50 mm holes at 5 m spacing, 10–15° upward, extending 15 m into the slope to lower the water table behind the face. Seepage along the bedding is the main trigger, so drainage is a structural measure, not an extra.
Check the basal plane for sliding with the bolts: even if only half the bolts are effective, 10 × 25 t × 9.81 ≈ 2.4 MN resisting, against a 750 kN wedge, giving a comfortable factor. Verify by limit-equilibrium wedge analysis and install two load cells for confirmation.
3. What construction-stage controls and monitoring would you impose before allowing excavation to resume?
Read the worked answer
Excavation should not simply resume with the support design issued. The slope must first be stabilised and instrumented.
Controls:
- Remove loose material and install the toe buttress before further benching.
- Excavate in 2 m lifts, installing bolts and shotcrete before the next lift; leave no unsupported face overnight.
- Prohibit blasting within 20 m of the instrumented section; use mechanical ripping or controlled blasting with vibration limits of 25 mm/s at the crest.
- Divert surface water, seal the crest crack with flexible grout, and install the horizontal drains before the wet season.
Monitoring:
- Optical prisms at 10 m intervals along the crest, read weekly during construction and monthly for the first year;
- crackmeters across the 25 mm crack and any new cracks;
- piezometers in two boreholes behind the face to confirm drainage response;
- bolt load cells on 5% of bolts.
Trigger levels: movement of 5 mm/week or 15 mm cumulative, or crack opening of 3 mm, requires stopping work and reassessment. Any turbid seepage at the toe indicates seam erosion and requires immediate drainage improvement. The performance criterion should be a stable crest and no new movement over two consecutive wet seasons.