Structural Engineering & Statics
where the load goes
Concept

Pore pressure — where it appears

The pressure of the water in a soil's pores, which pushes the grains apart and takes part of the load off their contacts. Friction depends on the stress between grains, so a rise in pore pressure lowers a soil's shear strength without any change in the load on it.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

Every one of these soils failed that slope. For a 10 m slope at 35° in soil of 19 kN/m³ with a pore pressure ratio of 0.25, over a firm stratum 5 m below its toe, which has slipped: the pairs of effective cohesion and friction angle that put its critical circle at a factor of safety of exactly one, by Bishop's method. At no friction the cohesion is 32.1 kPa; at 20° it is 12.4; at 40°, 2.0; and the line reaches no cohesion at 48.1°, where a skin of soil slides parallel to the face. Labelled, the depth of each pair's slip below the original ground: 13.6 m at 0°, 8.8 m at 5°, 7.4 m at 10°, 5.2 m at 20°, 3.6 m at 30°, 2.3 m at 40°.

A failed slope gives a line, not a soil

A slope that has slipped is the one full-scale strength test geotechnics ever gets, and the standard way to read it is to set its factor of safety to one and solve for the soil. One equation cannot give two strengths. What it gives is a line of cohesions and friction angles, every one of which fails the slope exactly, and the repair designed on one point of that line can be worth a factor of 1.07 or of 1.51. The slip itself says which point: each soil on the line fails along a different surface, and the depth of the scar is the second equation.

equilibrium · Slope stability Each slip is a shear test at one normal stress. The soil's strength, τ = 8 + σ′·tan 24° (line), and the mean effective normal stress and shear stress along the critical slip of each of five slopes that fail in it: 55° and 3.8 m high, 8 kPa; 45° and 5.2 m high, 13 kPa; 35° and 8.2 m high, 23 kPa; 28° and 14.1 m high, 42 kPa; 22° and 41.5 m high, 109 kPa. Every slip is one point on the line. Two slips fix the line as two shear-box tests do, and fix it well only if their normal stresses are far apart: the steep, short slopes test the soil where cohesion is most of its strength, the flat, tall ones where friction is.

Two slips are a shear test

One failed slope gives a line of soils, every one of which fits the failure. Two failed slopes give two lines, and where they cross is a soil that fits both. Whether the crossing means anything depends on how differently the two slopes loaded the ground: two slips at one angle cross only at zero cohesion, two at nearby angles cross anywhere in a twenty-degree band, and a flat, tall slope beside a steep, short one pins the soil to within two degrees — because each slip is a shear test at one normal stress, and a strength line needs two tests far apart.

equilibrium · Slope stability How long the pumps must run is set by how fast the water comes back. The floors that must be cast before the pumps stop under a 20 × 30 m basement dug 6 m below a water table at the surface, its 0.9 m slab and walls weighing 18.7 MN against 35.3 MN of uplift when the water is back, so that the weight stays ahead of the water at every instant, against the water's recovery time on a logarithmic scale, for a floor every 5, 7 and 10 days. If the water returns at once, five floors — the building has to be nearly heavy enough on its own. With a floor every 5 days: 3 at a 3-day recovery, 2 at 7, 0 at 14; a floor every 7 days: 4 at a 3-day recovery, 3 at 7, 1 at 14; a floor every 10 days: 4 at a 3-day recovery, 3 at 7, 2 at 14. Dashed, the closed form for weight added continuously at a floor a week, which runs about one floor below the steps: a floor arrives at the end of its cycle, not through it.

The water that comes back while the floors go up

A basement below the water table is built dry, inside an excavation kept pumped, and the building that will one day hold it down is not there yet. When the pumps stop, the water comes back over days and the frame goes up a floor a week, and the basement is safe only if the weight stays ahead of the water at every instant. How long the pumps must run is not set by how heavy the building is. It is set by one ratio — how much weight the frame adds while the ground refills — and for a basement that needs five floors on it to hold itself down, a seven-day recovery asks for three and a fourteen-day one for one.

equilibrium · Uplift

Named alongside it

The objects these essays reach for when they reach for this one.

Back analysisBishop methodCohesionEffective stressFactor of safetyFriction angleSlope stabilityConstruction sequenceHydrostatic pressurePartial factorTension pileUplift

All concepts