At the beach, walk on the wet sand just above the waves and it is firm enough to run on. Stand still on it and bounce a little, and a shine of water creeps up around your feet and the ground goes soft. Dry sand a metre higher is loose and slow. Sand under water is different again. It is the same grains every time; what changed is where the water is, and how fast you shook it.
That is the whole problem of geotechnical engineering. Steel is made in a mill to a specification. Concrete is mixed to a recipe. Soil is whatever the last glacier, river or volcano left, it differs from one corner of a site to the next, and every building, bridge and dam in the world finally rests on it.
Sometimes the ground says so loudly. The Tower of Pisa began to sink while it was still being built, in 1178, because its shallow foundation, about three metres deep, sat in weak subsoil. Work stopped for most of a century, partly through war, and that pause let the soil settle and gain strength, which is a large part of why the tower is still standing. It is the most famous lesson in this subject, and we will come back to it.
Who takes it: civil engineers, usually in the third year, as a first course in soil mechanics followed by a second in foundation engineering; geological, mining and environmental engineers take it too. Programmes that follow the ASCE Civil Engineering Body of Knowledge treat geotechnical engineering as one of the core areas of the degree.
What it is for: working out how much weight soil can carry, how far it will sink, and when a slope or a bank will move.
Comes after: Mechanics of Materials (34/11) and Fluid Mechanics (34/15).
Leads to: Structural Design: Concrete & Steel (34/65), whose footings and piles rest on this; Hydraulics & Water Resources (34/67), for dams and seepage; and Construction Management (34/70), where excavations and temporary works live.
What this piece will and won't give you: you won't be able to design a foundation after this, and no engineer would trust a number from a toy. You will see why wet soil is weaker than dry, why clay sinks for decades, and why an earthquake can turn a street into soup.
Easier first reads on the same ground: Statics: Why Things Stand Still (34/10), Mechanics of Materials (34/11) and Everyday Physics: The Answers Hiding in Plain Sight (Physics 5). All soil values below are illustrative round numbers, not design values.
A lump of soil is three things at once: solid grains, water, and air. The grains touch at their corners and the gaps between them, the voids, are filled with water, air or both. Engineers start every problem by counting the three. Take a soil with a void ratio of 0.7 (voids are 70% of the volume of the solids). Four-tenths of its volume is empty space. Fill the voids with water and it weighs about 19.3 kN per cubic metre instead of 15.3 when dry, a quarter more.
Read it as: the weight of the grains plus the weight of the water, divided by the total volume. Here e is the void ratio, S the fraction of voids holding water, Gs about 2.65 for quartz grains, and γw = 9.81 kN/m³ for water.
Change how loosely the grains are packed and how much of the gap is filled with water.
The key discovery of the subject, by Karl Terzaghi in the 1920s, is what the water does under load. Put weight on soil and two things can carry it: the grain-to-grain contacts and the pressure of the water in the voids. Only the contacts give friction, and friction is what soil strength is. Terzaghi's principle says that soil behaves according to the part carried by the grains, the effective stress:
Read it as: effective stress is the total stress minus the water pressure. At 10 m depth with the water table at 2 m, the total stress is about 196 kPa and the water pressure 78 kPa, so the grains carry only 118 kPa. Raise the water table and the grains carry less. Push water upward through sand fast enough and the effective stress falls to zero, the sand floats, and a cofferdam floor boils. This is "quicksand", and it needs flow, not a special kind of sand.
Move the point deeper, raise the water table, or push water upward through the soil.
How fast water moves is its own measurement. Darcy's law says the velocity is the permeability times the hydraulic gradient, and permeability differs by many orders of magnitude between clean gravel and clay. That one fact, how slowly water leaves, is what the next idea is about.
Squeeze a wet sponge and the water leaves at once. Squeeze a sponge whose holes are a thousand times smaller and it takes a long time. A clay layer under a new load behaves like the second sponge. At first the water takes the extra load, because it cannot escape. As it seeps out, the load moves to the grains, which pack closer, and the ground settles. That slow transfer is consolidation.
Terzaghi gave it two equations. The amount of final settlement depends on how compressible the clay is and how much the load is. The time it takes depends on how far the water has to travel:
Read it as: time grows with the square of the drainage path. Twice the distance means four times the wait. A 10 m clay layer that can drain only upward needs Tv = 0.848 for 90% of its settlement; with cv = 2 m²/yr that is 42 years. If sand lets it drain both up and down, the path is 5 m and the wait is 10.6 years.
Pick the load, the clay, and whether water can leave from one side or both. Drag the time.
This is Pisa. Construction stopped around 1178 and resumed in 1233 and 1272, and the long pauses let the soil under it consolidate. The tilt reached 5.5 degrees by 1990, and the tower was closed on 7 January 1990. Remedial work from 1993 to 2001 used about 870 tonnes of lead counterweights and removed soil from beneath the high side, about 70 tonnes in all. The tilt came down to 3.97 degrees, by about 45 cm at the top, back to where it had been in 1838. The tower reopened on 15 December 2001. Notice that engineers did not strengthen the tower; they fixed the ground, and they did it by taking soil away.
Pile dry sand and it stops at a steady angle, the angle of repose, whatever the size of the pile. That angle is a picture of friction between grains. Soil shear strength follows the same law as a block on a ramp (34/10), with one change: the squeeze that counts is the effective stress.
Read it as: strength is a little cohesion plus the effective squeeze times a friction factor. Sand has no cohesion to speak of, so for a thin layer sliding on a slope the factor of safety is simply tan φ′ ÷ tan β. A dry sand slope with φ′ = 32° stands at any angle under 32°. At 25° the factor of safety is 1.34. Now let rain fill the layer. The water pressure cancels part of the squeeze, and the factor of safety drops to 0.65. The slope that stood now slides, though no one touched it.
Raise the angle until it fails. Then fill the soil with water and see how far the safe angle falls.
A footing spreads a column's weight over a patch of soil. Load it more and more and, in the end, the soil under it shears along a bowl-shaped surface and the footing plunges. The pressure at that point is the ultimate bearing capacity. The bearing-capacity equation for a long strip footing, in Terzaghi's form, has three terms, one for each way the soil helps:
Read it as: cohesion, plus the weight of the soil beside the footing (the deeper you bury it, the more it helps), plus the weight of the soil under the footing (a wider footing mobilises more of it). The N values depend only on the friction angle (here the classical Prandtl–Reissner values, and Vesic's for Nγ). Engineers then divide by a safety factor, commonly 3, and check that the actual pressure is below it. A footing 2 m wide, 1 m deep in loose sand (φ = 30°) has an ultimate capacity near 690 kPa. Flood the site, and it falls to about 290.
If the good ground is deep, no spread footing will do. Engineers drive or drill piles through the weak layer so that they carry the load by friction along their sides, by bearing at their tips on something firm, or both.
Pick the ground, the footing, and the load per metre of footing length. Then flood the site.
Loose, water-filled sand wants to pack tighter when shaken. If the water cannot leave in time, it takes the load instead, the water pressure climbs, and the effective stress falls. Strength is effective stress times friction, so strength falls with it. When the pressure of the water has risen to equal the squeeze the grains were under, the effective stress is zero and the sand has no strength: this is liquefaction. It happens in loose sandy and silty ground below the water table; clay and dense gravel mostly resist.
The Christchurch earthquake of 22 February 2011 was a magnitude 6.2 earthquake, centred about 6.7 km south-east of the city centre, and 185 people died. Liquefaction caused extensive damage to homes in the eastern suburbs, covering streets and gardens with silt and sand; the figures for how much silt was removed vary between sources (several hundred thousand tonnes). Some of the worst-hit areas were designated a residential red zone, judged not feasible to rebuild. The lesson for engineers is that a site can be perfectly strong on a calm day and have almost no strength for thirty seconds.
Slide from calm ground to full liquefaction in sand at 5 m depth (water table at 1 m).
On 19 September 1985 a magnitude 8.0 earthquake struck off the Pacific coast of Michoacán, more than 350 km from Mexico City. By the time the waves reached the city they were far weaker than at the coast, yet the damage was terrible: 412 buildings collapsed in the city and thousands more were seriously damaged. Estimates of the dead range widely, from about 5,000 to far more, with about 10,000 the figure most often given. The cause was the ground. Much of the city sits on the dried bed of Lake Texcoco, soft, water-saturated volcanic clay 7 to 37 m deep, and a soft layer on stiff rock acts like a tuning fork.
Read it as: the layer's natural period is four times its thickness divided by the speed of shear waves in it. For 37 m of clay with Vs = 74 m/s that is 2 s. The lakebed's own period is commonly put at about 2 to 2.5 s, which matched the natural period of buildings of 6 to 15 storeys, and those suffered most. Resonance (Vibrations, 34/17) did the rest. A simple rule gives a building a period of about 0.1 s per storey, shorter than the ground's, but a cracked and yielding building gets more flexible, and its period stretches towards the ground's.
Press the lakebed button, then try buildings of different heights. Slide the damage control to see a cracked building drift into resonance.
Soil is grains, water and air, and the part the grains carry, the effective stress, is what gives it strength. Change the water and you change the ground: rain weakens a slope, a flood weakens a footing, an earthquake can take a sand's strength away for half a minute, and a soft layer can amplify the shaking above it. Clay is slow, so what you build today is still settling in forty years.
Try this: next time you walk across wet sand, stamp and watch the water rise around your foot. That is effective stress changing under your feet. Then notice how the shoreline slope relates to the angle the sand will stand at.
Sources. The three-phase relations, Terzaghi's effective stress principle, one-dimensional consolidation, the infinite-slope model, the strip-footing bearing capacity equation and the quarter-wavelength resonance of a soil layer are standard textbook geotechnics (see the books above). Every number in the interactives was computed in node: the void-ratio example (e = 0.7: 19.3 and 15.3 kN/m³), effective stress at 10 m (196 − 78.5 = 117.5 kPa), the consolidation example (sc = 716 mm; t90 = 42.4 yr one-way, 10.6 yr two-way; U checked against Tv = 0.197 and 0.848), the slope example (tan 32° ÷ tan 25° = 1.34 dry, 0.65 wet), bearing capacity (Nq = 18.40, Nc = 30.14 and Vesic's Nγ = 22.40 at 30°; qult about 694 kPa dry and 293 kPa flooded) and the soil period (4 × 37 ÷ 74 = 2.0 s). All soil properties, the 5%-damped building and the 0.1 s-per-storey rule are illustrative simplifications. Facts about Pisa (construction dates, 5.5 and 3.97 degrees, 1990 and 2001, 870 tonnes of lead, 70 tonnes of soil), Christchurch (22 February 2011, Mw 6.2, 6.7 km, 185 deaths, red zone) and Mexico City (19 September 1985, Mw 8.0, over 350 km, 412 collapsed, 7–37 m of lakebed clay, 6–15 storeys) are taken from the Wikipedia articles on those events; the death-toll range for Mexico City varies widely by source.
Go deeper. Das, Budhu, Terzaghi–Peck–Mesri and Petroski are standard titles; check the current edition with your bookshop. The NPTEL course listing was confirmed on the NPTEL site.