The basement that leaks before it floats

The water that comes back while the floors go up followed a basement through the weeks between the pumps stopping and the building being heavy enough to hold it down. In that race the water came back to the level it started at and stayed there. That essay ended on the case it had left out: a basement whose water table does not stay where it was designed, because the abstraction that kept it down has stopped, or a neighbour has stopped pumping, or the ground has simply been recharging for decades under a city that no longer draws on it. The rise is slow — centimetres a year — and it is a load that arrives over the building’s life rather than its construction.

Everyone’s first question about such a basement is whether it will float, and for a finished building it almost never will. The second question is the one that matters: what a rising water table does to the base slab, which was never designed against the building’s weight at all.

The same box, under a finished building #

The basement is the one a basement is a boat drew: 20 × 30 m in plan, with a slab 0.9 m thick and walls 0.4 m thick. It is dug 9 m, into ground whose water table stood 3 m below the surface when the basement was designed, so the slab has a 6 m head under it. The building is complete: eight storeys above, each adding 8 kN/m², a total weight of 60,000 kN against an uplift of 35,300. Under EN 1997-1’s check for uplift, which credits nine tenths of the weight, the building uses 0.65 of what holds it down.

Now let the water rise. Each metre adds 5,900 kN of uplift, a sixth of what was there. Three metres take it to the surface — it can rise no further without flooding the street — and at that point the building uses 0.98 of its weight. The building does not float within any rise the ground allows. That is the comfortable answer, and it is the answer to the wrong question.

What the slab carries #

The flotation check weighs the whole building. The base slab is held down by its columns and walls and spans between them under the uplift on its underside, and the only weight it has to set against that uplift is its own: 0.9 m of concrete, 21.6 kN/m², against 58.9 kN/m² of water. What it carries in bending is the difference, 37.3 kN/m² upward.

The slab is computed as a Kirchhoff plate, clamped along its walls and held at its six columns, under that net pressure. The figure is a flat slab’s moments drawn upside down. Between the columns the slab bows upward and its top face is in tension, 97 kN·m per metre midway between two columns along a column line and about half that in the middle strip between the lines. At the columns the bottom face is in tension, 207 kN·m per metre averaged over the strip of slab half a bay wide that design reads there, and more at the column itself. Along the walls, which clamp the slab’s edge, the bottom face is in tension too. The reinforcement goes where a floor’s would go, with top and bottom exchanged — and the punching check at the columns is a flat slab’s, with the column pushing down through a slab the water pushes up.

Every one of those moments is proportional to the net pressure, and the net pressure is the difference between two numbers that do not move together. The water’s share grows with the head; the concrete’s does not. A metre of rise adds 9.8 kN/m² to the 37.3 the slab carries: 26 per cent a metre, against the 17 per cent a metre the same rise adds to the building’s uplift. At the ultimate limit state, where the water’s pressure is multiplied by 1.35 and the slab’s weight, which helps, by 1.0, the slab’s design load grows by 23 per cent a metre. Either way, the slab is spending its margin faster than the building is.

Two ways of keeping water out #

A basement slab under a head of water is rarely sized by its strength. It is sized by its cracks, because a crack is a path for water, and a basement that is to be dry — a car park, a plant room, anything with people or equipment in it — is designed against them. There are two ways of reading that requirement, and they disagree about which cracks matter.

The older reading, the one British practice for water-retaining concrete followed for decades in BS 8007, limits the surface width of every crack: 0.2 mm, flexural cracks included, on the reasoning that a crack of that width seals itself under a steady head as calcium carbonate is deposited in it. By that reading the slab here is designed by the width of its bending cracks. With 25 mm bars, the steel a 0.2 mm limit needs at the design head is between two and three times what the slab’s strength needs: 1,970 mm² per metre against 890 in the bottom face at the columns, and 1,260 against 420 in the top face between them.

EN 1992-3 reads it differently. It limits by width only the cracks that pass through the whole thickness of the slab — the ones a slab’s early shrinkage and the restraint of its walls and piles leave, which carry water straight through. Their limit depends on the head over the slab’s thickness: 0.2 mm for a ratio of five or less, falling to 0.05 mm at thirty-five. For a flexural crack it asks something else: that a compression zone at least 50 mm deep, or a fifth of the slab’s thickness, remain uncracked, so that no water can find a way through.

The check that runs out first #

Take the first reading, and suppose the designer gave the slab a quarter more steel than the 0.2 mm limit needed — 25 mm bars at about 200 mm in the bottom face and 310 in the top. At the design head its cracks are 0.140 mm. The three checks then run against the rise at three different rates, and only one of them is used up. Flotation creeps toward one and does not reach it. The slab’s bending starts at about a third and ends at three fifths. The crack width starts at 0.70 of the limit and passes it at a rise of 1.65 m.

The crack check runs out first because it reads the slab’s net load at service, which grows by 26 per cent a metre, without the partial factor on the water that dilutes the growth at the ultimate limit state, and because it was the check the steel was chosen by, so it began with the least room. Once the cracks are fully formed, their width grows in proportion to the steel’s stress, and the steel’s stress in proportion to the net load: the same steel gives a wider crack as surely here as anywhere, and what has changed is the load rather than the steel.

The two faces run out almost together, because each was given steel in proportion to its own moment: 0.136 mm between the columns and 0.140 at them at the design head. They are not equally placed, though. The bottom face is the face against the water, and a bending crack in it at a column fills under the full head and pushes water toward the compression zone from below. A crack in the top face between the columns opens on the dry side, and water reaches it only by crossing the slab some other way first — through a joint, a through-crack, or the compression zone of a crack in the bottom face nearby. The first damp patches are therefore expected over the columns, and their position is a measurement of where the bottom face’s moment is largest.

So the first sign that a rising water table has outgrown a finished basement is not a building lifting. It is a wet slab — damp patches over the column heads where the bottom face’s cracks have opened, or along the column lines midway between columns where the top face’s have, appearing decades after the basement was handed over dry.

The limit that tightens #

The second reading moves the problem rather than removing it. A flexural crack’s compression zone, in a cracked section that is still elastic, has a depth set by the steel ratio and the modular ratio and not by the moment: 142 mm at the columns and 116 between them for this slab, against the 50 mm required, and the same at every rise. By EN 1992-3’s test, the slab’s bending cracks never become leaks, however high the water goes.

But its through-cracks are judged against a limit that the rise makes tighter. The limit depends on the head over the thickness because the time a crack takes to seal itself depends on how hard the water is pushing through it, and a higher head flushes away the deposit that would close it. Under 6 m of water the 0.9 m slab’s through-cracks may be 0.192 mm wide; under 7 m, 0.186; under 9 m, 0.175. A slab whose restraint cracks were controlled to the limit for the head it was designed for has through-cracks a tenth too wide once the water reaches the ground, and those are the cracks that were sealed when the slab was young. Either way the water reads it, the rise spends the slab’s watertightness and not its strength.

How much rise a margin buys #

The relation between steel and tolerated rise is nearly a straight line: every tenth more steel than the crack limit needed buys about two thirds of a metre of rise, until about 1.45 times the steel, which tolerates the whole 3 m to the ground. Neither of the other two checks appears in that figure, because neither is reached. The basement’s response to a rising water table is decided by a serviceability check that its designer chose the steel for, and the margin on it is the only margin that matters.

At a few centimetres a year, a metre and a half of rise is half a century: the building’s design life, more or less. Read that way, the extra steel is not a factor of safety on the slab’s strength but a schedule. It is the number of years before the slab starts to let water in, if the water keeps rising at the rate the boreholes show, and it can be bought at the design stage for the price of closer bar spacing and at no other stage for any price short of a new slab.

The heavier slab, the faster it goes #

The obvious remedy for an uplift problem is weight, and a basement is a boat showed what a thicker slab buys against flotation. Against the slab’s own bending it buys the opposite of what intuition expects. A slab whose weight cancels most of the water under it carries a small difference, and a metre of rise is a large share of a small number. The 2 m slab under a 6 m head carries only 11 kN/m² of net uplift, and a metre more water nearly doubles it.

That is not an argument against thick slabs. The thick slab carries a small net load and has a great deal of depth to carry it with, so its stresses are low, and the rise that doubles its load may still leave it well inside its limits. But it means that the margin a heavy slab was designed with is spent at a rate set by the difference between its weight and its water. A weight has to be known before it can be relied on, and here that is doubly true: the slab’s own weight is the larger part of what holds the slab down against its load, and any error in it is an error in a number that the rise is chipping away.

Flotation and the slab, in a few lines #

The building: 600 m² × 6 m × 9.81 = 35,300 kN of uplift at the design head; 0.9 × 60,000 = 54,000 kN credited weight; 0.65. Three metres more: 52,900 against 54,000, 0.98.

The slab’s net load: 58.9 − 0.9 × 24 = 37.3 kN/m², and a metre more water is 9.81, or 26 per cent of it. The building’s: 9.81 against 58.9, a sixth.

The slab’s moment: a flat slab’s total static moment across a bay is the pressure times the bay’s width times the square of its span over eight. For a 7.5 m span and a 6.67 m bay width under 37.3 kN/m² that is 1,750 kN·m across the bay. Split between support and span in a flat slab’s usual proportions, and the column strip given three quarters of the support share over half the bay’s width, it is about 260 kN·m per metre at the column face and 110 midway between columns — the same order as the plate’s 207 and 97, both lower in the plate because the walls’ clamping takes some of the moment that a flat slab’s interior bay would share between its columns and its span.

The compression zone: a 0.9 m slab with 2,470 mm² per metre at an effective depth of 838 mm has a steel ratio of 0.0029; with a modular ratio of 5.9, the cracked section’s neutral axis is at 0.17 of the effective depth, 142 mm, whatever the moment.

Where the plate stops #

The slab is elastic and uncracked in its stiffness. A cracked slab is softer where it is most cracked, and redistributes moment away from the column strips toward the middle strips; the crack widths at the columns would be a little less and those between them a little more.

The columns and walls do not move. A slab held down by columns that are themselves held down by the building above is supported by something that can rise a little as the uplift grows; if it does, the moment at the columns falls and the moment between them grows. A basement on tension piles, as in the piles that would lift the ground, is the extreme of that.

The crack width is EN 1992-1-1’s, for fully formed cracks under a steady load. A water table that rises over decades is as steady as a load gets, and long-term values are used throughout. But the expression estimates a characteristic width, and it leaves out the axial tension a slab restrained by its walls carries from shrinkage, which adds to every bending crack’s width and is what turns some of them into through-cracks.

Where the water really comes in #

They cannot show the slab’s joints, its waterproofing membrane, or the drainage layer some basements carry beneath them, any of which may decide where the water comes in long before a crack does. They cannot show the through-cracks of early age, which are set by the restraint of the slab’s walls and piles rather than by its load and which no figure here computes. And they cannot show the rate of rise, which is a measurement in a borehole rather than a property of the structure, and which turns the rise tolerated into a number of years only when someone has measured it.

Still open: the basement that is pumped to keep it dry #

A basement whose slab has started to leak is often given back its design head by a pump: a sump, drains under the slab, and a pump that lowers the water beneath it. That is permanent drainage — the arrangement the first basement essay found usually refused, because a pump’s life is a fraction of a building’s — arriving as a repair rather than a design. Whether a slab relieved by drainage it was not designed for is then safe only while the pump runs, and what happens to its cracks, its bending and the building’s flotation in the hours after the pump stops, is the question that ends this race the way the previous one began.