7.3 Bearing Capacity and Slope Stability

Soil Strength Problems Behind Water Projects

The WRE Soil Mechanics scope includes bearing capacity and slope stability because water structures are built on and in soil. A pump station, valve vault, tank, clarifier, basin embankment, channel bank, or wall footing can be controlled by the ground beneath it. You do not need to be a geotechnical specialist, but you must recognize the failure mode and use the correct stress basis.

Bearing Capacity Basics

Bearing capacity is the soil support limit under a footing or mat. The ultimate bearing capacity qult is the pressure at shear failure; the allowable bearing pressure qall is usually qult divided by a factor of safety, typically 2.5 to 3, unless a geotechnical report gives a serviceability-based allowable directly.

The general Terzaghi strip-footing form is qult = c Nc + q Nq + 0.5 gamma B Ngamma, with three resistance sources: cohesion (c Nc), surcharge at footing level (q Nq), and soil weight below the footing (0.5 gamma B Ngamma). The bearing factors Nc, Nq, and Ngamma depend only on the friction angle phi. The exam often supplies the factors or a simplified qult, so prioritize correct setup and gross/net interpretation.

• Gross pressure is the full applied pressure at foundation level, including the structure plus backfill over the footing.
• Net pressure subtracts the pressure of soil removed by excavation (the prior overburden at that depth). Net allowable = net ultimate / FS.

Groundwater matters: if the water table rises into the bearing zone, use the buoyant unit weight in the soil-weight term, which reduces qult. For WRE footings near basins, streams, or wet wells, never assume dry soil unless stated.

Slope Stability Basics

Slope stability compares resisting shear strength to driving forces, expressed as a factor of safety FS = resisting / driving. FS greater than 1 means resistance exceeds demand under the assumed model, but design criteria commonly require FS of 1.3 to 1.5 for long-term static conditions and higher under seismic loads. WRE slopes include levee embankments, pond banks, channel side slopes, lagoon berms, and temporary cuts.

Driving force rises with added fill, traffic, stockpiles, or stored water. Resistance falls with seepage, high pore pressure, weak clay seams, poor compaction, toe undercutting at a channel, or vegetation loss. Rapid drawdown is the signature WRE case: an outside pool drops faster than the embankment can drain, so the slope loses its external water support while internal pore pressures remain high, cutting effective stress and resistance.

Calculation and Judgment Workflow

1. Identify the structure or slope and the likely failure surface.
2. Decide short-term undrained, long-term drained, or a stated simplified model.
3. Use effective stress when pore pressure affects drained strength.
4. Convert ultimate to allowable with the specified FS.
5. Compare service load to qall, or compute the slope FS.
6. Re-check whether groundwater, surcharge, toe erosion, or drawdown changes the answer.

Worked Example: Bearing with a High Water Table

A 6 ft square footing bears 4 ft deep in sand, phi = 32 degrees, gamma = 120 pcf. Take Nq = 23 and Ngamma = 30 (supplied). With the water table well below the footing, the soil-weight term uses gamma = 120 pcf. If instead the water table rises to the footing base, that term uses gamma_b = 120 - 62.4 = 57.6 pcf, roughly halving the 0.5 gamma B Ngamma contribution.

• Surcharge term: q Nq = (4 x 120) x 23 = 11,040 psf.
• Soil-weight term, dry: 0.5 x 120 x 6 x 30 = 10,800 psf.
• Soil-weight term, submerged: 0.5 x 57.6 x 6 x 30 = 5,184 psf.

The submerged case drops qult by about 5,600 psf, near a 25 percent reduction here. For WRE footings near wet wells, basins, and streams this is a routine, decisive effect.

Slope Stability Quick Reference

For a simple infinite slope in cohesionless soil with seepage parallel to the slope, FS = (gamma_b / gamma_sat) x (tan phi / tan beta), where beta is the slope angle. Dry or no-seepage cohesionless slope reduces to FS = tan phi / tan beta. These show why a slope stable when dry can drop below 1.0 once seepage develops.

Typical minimum design FS values are about 1.5 for long-term static, 1.3 for end-of-construction or rapid drawdown, and 1.0 to 1.1 for pseudo-static seismic, though exam problems will state the criterion.

WRE Exam Traps

A bearing answer can be arithmetically right yet wrong if a net service pressure is compared to a gross allowable, or if a rising water table was ignored in the soil-weight term. A slope answer fails if it treats a dry cut as still stable once seepage begins. When the prompt mentions cracks, seepage exits, soft clay, recent filling, or channel toe erosion, the correct choice usually addresses the geotechnical mechanism, not a hydraulic tweak.