Slope Stability for a Road Cut in Weathered Clay
A new 8 m high road cut is to be made in a stiff, overconsolidated clay with a unit weight of 19 kN/m3, effective cohesion c' = 15 kPa, effective friction angle phi' = 22 degrees, and a groundwater table at 6 m depth. The proposed slope angle is 45 degrees. A thin, continuous, smooth bedding plane dips out of the slope at 18 degrees and has a residual friction angle of 14 degrees with zero cohesion. The slope is 200 m long and is to be built with a 1 m wide berm at mid-height. A nearby existing road runs 15 m from the crest. The client wants a factor of safety of at least 1.5 for the design life of 50 years, and the site is in a moderate seismic zone with a peak ground acceleration of 0.15 g.
1. Assess the slope against both circular and planar failure and state which controls.
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Planar sliding on the bedding plane is the critical mechanism because the bedding dips out of the slope at 18 degrees, which is less than the slope angle of 45 degrees and less than the friction angle of the intact clay but close to the residual 14 degrees. For a planar slide with zero cohesion on the plane, the factor of safety is FS = tan(phi_residual)/tan(dip) = tan(14)/tan(18) = 0.249/0.325 = 0.77. That is below 1.0 - the slope would slide on the bedding plane as soon as it is excavated. Even with the full friction angle of 22 degrees, FS = tan(22)/tan(18) = 0.404/0.325 = 1.24, still below 1.5. So the bedding plane controls and the design is unacceptable as proposed. For circular failure, a quick estimate using Taylor's stability chart for phi' = 22 degrees and a 45 degree slope gives a stability number around 0.10-0.12, so FS = c'/(N x gamma x H) with the chart's N - a rough check gives FS around 1.3-1.6, but the planar slide governs because it is kinematically admissible and has zero cohesion. The berm does not help a planar slide that daylights below it.
2. Propose a design change and check it, including the seismic case.
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Options: (1) Flatten the slope to less than the bedding dip - impossible for an 8 m cut without a very long slope; (2) install a shear key or toe buttress; (3) use soil nails or ground anchors through the bedding plane; (4) drain and add a toe berm. The most reliable is a row of ground anchors or soil nails crossing the bedding plane, designed to provide the missing shear resistance. Required: FS = 1.5, so the resisting force must be 1.5 times the driving force. Driving force per metre of slope length = W sin(18), where W is the weight of the wedge above the plane. For an 8 m high slope at 45 degrees, the wedge length along the plane is about 8/sin(45) = 11.3 m, and the wedge weight per metre is roughly 0.5 x 19 x 8^2 x (1/tan(18) - 1/tan(45)) - this needs a proper wedge calculation, but the key point is that the anchors must supply the difference between the required and available resistance. A typical design would use 4-6 m long nails at 1.5 m spacing, grouted into the stable zone behind the plane, with a facing of shotcrete and drainage. For seismic, add a pseudo-static force kh x W with kh = 0.15/2 = 0.075 (or 0.15 depending on the code), which increases the driving force by about 7.5% and must be included in the anchor design. Also install horizontal drains to lower the water table, since the current 6 m depth reduces effective stress on the plane.
3. What monitoring and construction controls would you specify?
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During construction: excavate in short lengths (e.g., 10 m) and install nails immediately, not leaving an unsupported face overnight. Verify the bedding plane location and orientation by mapping each excavation face; if it is steeper or smoother than assumed, stop and redesign. Install inclinometers and piezometers through the slope before excavation, and read them weekly during construction and monthly for the first year. Set trigger levels: 5 mm of cumulative displacement or 1 mm/week triggers a review; 10 mm triggers stopping work. Install a surface survey network on the crest and the existing road. Check that the existing road 15 m from the crest is outside the failure surface - for a planar slide daylamping at the toe, the crest tension crack may extend back several metres, so the road may be at risk; a stability check including the road surcharge is needed. Specify drainage: a cut-off drain at the crest, a toe drain, and horizontal drains. Finally, require an as-built review and a 50-year inspection and maintenance plan, since anchors and drains degrade.