And here is a natural example, reminding us that nature seldom expends enough energy to make things impregnable. So what are the virtual "criteria" by which natural things come to be as they are? This tree was acting as a cantilever against the wind. The roots on the upwind side experienced bending and shear, and they eventually failed.
Even if you build soundly, your structure may founder through circumstances. This house was built on land that later subsided because of mine workings below. It has been dismantled and rebuilt in the Black Country museum.
Every bridge has to rest on the ground in at least one place. The supports have to be placed so as not to move unacceptably, which means that the stresses must be reduced to values that can be supported by the ground. On hard, strong rock, the supports can be narrow, but in weaker ground, a wider foundation may be necessary.
These three pictures show a piece of foam plastic which has been strained by pushing objects against it, to represent a pillar resting on the ground. The strains are revealed by the square graticule that was drawn with a fibre pen. From the distortions we can deduce the following facts -
The strains are concentrated near the point of application.
The strains are spread over a large area.
There is tension, as revealed by the curved upper edge, which is
longer than the original straight edge.
There is shear, as revealed by the angles which are no longer
And of course there is compression.
The final configurations are those which minimise the total strain energy.
This picture tries to give a rough idea of the way that pressure diffuses through the ground under a heavy weight. A more exact picture could be made by drawing contours of equal stress. The ground has to able to withstand the stresses at all points without giving way, either quickly or by creep. In any volume where this is not the case, the ground must be replaced by a structural material which is designed to take the load and spread it into the ground at a supportable magnitude. This type of diagram cannot be exact, because the behaviour of the ground is dependent on its type. Even something as simple as the contact pressure under a pier is not constant across the section, and the behaviours with clay and sand are actually opposite.
If you tread on wet sand on a beach, you can often see the sand around your foot apparently drying out, because the grains have been disturbed, allowing more water into the gaps. The size of this area reveals the spread of forces around an object on the ground. Sand is, of course, not a good material on which to build, though damp sand can be used by children of all ages to build surprisingly large and complicated structures.
One way to work out the size of an excavation is to dig out a weight of soil equal to the weight of the structure that is to be supported. This is an empirical rule.
The "leaning tower of Pisa" is a well-known example of the difficulty of soil engineering.
Problems with soil include -
Differing types of soil
Variation of properties within a site
Variation of properties with time -
Variation of water content
Effect of flash flooding
Effects of earthquakes
Melting and freezing of included water.
Click here for a web-site dealing with earth structures and related matters. It also includes numerous links to web-sites about engineering and science.
Some of the problems that be encountered in building foundations are -
Depth of poor ground above firm rock
Depth of water above ground, which itself may be poor
Speed of water flow
Tidal variation in depth of water.
The flow of water past an obstacle can generate scouring, especially when the flow is fast and turbulent. The lifting and carrying ability of water increases as a high power of the speed. If the scouring reaches low enough, foundations can be threatened. In fact, even the normal flow of river water past bridge piers can generate scouring which can bring down a bridge. The presence of the piers changes the flow, producing acceleration and turbulence. The lifting and carrying power of a fluid increase as a high power of the speed. The ancient Romans knew about this, and took precautions. Foundations need to penetrate to secure ground, and a pavement around piers can help to protect the bed. You can often see the results of scouring around a post or a boulder on a sandy beach, after the tide has gone out. The next diagrams, which are sections at right angles to the flow, show the general effect.
Furthermore, because of turbulence, the pressure on the bridge fluctuates with a wide frequency spectrum; people on a bridge that is nearly submerged report feeling strong vibrations.
These pictures show some bridges which are equipped with concrete or stone platforms to eliminate scouring. They all span the river Wye, which has carried away many spans in the past.
The first picture, taken in mid summer at a time of very low water in the river Wye, shows the very large depression that has been scoured out of the shingle. The piers will have been founded further down on good ground. The notice is for the benefit of people who wish to swim or paddle in the water, which is in any case dangerous because of swirling currents.
This picture shows the preparation of the foundations of a small building. Steel reinforcing bars have been connected together to form structures which will resist tensile forces if the ground moves under the load from the building. Pure concrete would crack very easily, as it cannot resist much tension. The reinforced beam acts as a bridge over ground that is giving way.
Queenhill Bridge crosses the river Severn in a region where the alluvium is very deep. Parts of the bridge are as far below ground as the superstructure is above it. The foundations had to go deep in order to find good ground.
For arch bridges, foundations are of particular concern, because of the outward thrust, which can be much greater than the weight of the arch.
Here is a picture of Telford's bridge over the river Severn at Over, near Gloucester. After the centring was removed, the crown sank about ten inches, or 25 cm, but the bridge was used continuously and safely from 1829 to 1974. It was then replaced by a wider bridge which could take greater volumes of traffic. The ground in the area is alluvial, and not suitable for building, and for this reason, Gloucester, like Worcester, is built almost entirely on the east side of the river. Telford had wanted to use his standard 150 foot cast iron arch, which would have been lighter and cheaper, but some important people in Gloucester objected to the use of cast iron. If non-technical considerations are allowed to over-ride technical ones, there may be a price. That is not to say that the appearance of structures is unimportant - of course it is - local people have to see them and live with them.
We can calculate how much ground movement will produce a given drop if we assume that the structure is rigid apart from a central hinge. The diagram below shows how this works.
The rate of change of the rise R as a function of the span S is given by the equation -
dR / dS = - S / 2R.
So for very flat arches, the sag can be large for a small change in span. Furthermore, the flatter the arch, the greater the outward thrust. This is discussed in the page about arches.
For example, if the span is 30 metres, and the rise is 3 metres, and the span increases by 5 cm, the sag will be 5 X 30 / 2 X 3 in cm, which is 25 cm, or 10 inches.
The thrusts on the ground add up to more than the weight of the arch, because it they are composed of vertical parts, which take the weight, and horizontal parts, which keep the arch from spreading.
Whatever the type of ground, we might ask what happens to the thrust as it enters the ground. It does something like this -
The pressure decreases as we look further from the springing of the arch. The purpose of abutments is to take the pressure until it has decreased to the point where the ground can be relied upon. The next picture hints at this.
Because the ground is not moving under the compressive forces (after everything has settled down), we know that some opposing forces must exist. The ground under the arch is in tension, but the stresses are very weak, because the forces are diffused through a large volume.
The opposite situation arises with a suspension bridge: the cables have to be anchored to prevent them pulling out of the ground. Here at Clifton, the wrought iron chains go into sloping tunnels in the ground, where they are securely anchored. Where the ground is unsuitable for anchoring cables, massive anchorages have to be built; these rely on sheer weight to hold the cables. The Humber bridge has an anchorage of this type. Inside the anchorages of a suspension bridge, the cables are usually fanned out to hundreds of individual fixtures.
The beautiful tower of Cirencester church has buttresses which go right down into the ground in the west wall. Because of difficulties with the ground, threatening the tower, this wall had to be taken down on the south side in order to add the buttresses. The NW and SW corners of the tower are also well buttressed. Should you climb the helical stairway to the top to see the splendid view of the town and country, you can be quite sure that the tower will stay upright.
There is actually something peculiar about these buttresses - they are straight. If you look at the page about the funicular you will see that the buttresses should logically curve towards the ground. In the case of Cirencester we can imagine that the builders wanted to anchor the buttresses as far from the tower as possible, in the hope of finding better ground.
Perhaps appearance entered into the design, since a window was required, and curving the buttress around the window would have looked rather strange. On the other hand, the builders might not have understood the flow of the forces at all, as everything seems to have been done empirically in the middle ages. In the first picture, we see that the buttress actually reaches the ground perilously near the corner of the building, but in fact there probably isn't much thrust left in it by that point: it has probably gone into the lower part of the wall.
These pictures are of St Bartholomew's Church, Chosen Hill, Gloucestershire, dating from 1175. The church was built at the north-east corner of the flat top of the hill, with a superb view over the Severn valley. A big disadvantage of the site was that the congregation had to walk up a steep hill from the village, except for those who could afford a horse, or even a horse and carriage.
Another disadvantage, which only revealed itself in the long term, is that the ground is largely of clay, on which the builders piled earth from the bottom of the hill. The problem was made worse by trees and shrubs drying out the soil. The ground under the east end of the church is moving slowly towards the edge of the hill, producing a distinct camber. This is reflected in the roof line of the church in the pictures above. It can also be seen in the broken line of masonry courses in the picture at left.
No masonry building can be expected to survive such treatment without damage, and in the pictures below we can see cracks in the north and south sides of the church at the east end, which is moving imperceptibly. Look also for a deformed window, displaced headstones and tombs, and metal crosses holding rods that go through the building. You can even see transform faults, albeit minute compared with those that are prevalent in the ocean floor around the areas of spreading like the mid-Atlantic ridge.
A possible solution to such a problem is to build a concrete raft for the foundation.
Instead of attempting great rigidity, we can take the opposite approach. This wooden framed building is not triangulated, and it can therefore change its shape. Any resulting cracks in the brickwork cannot propagate past the next baulk of timber. For a good description of the benefits of flexible construction read about Nansen's great explorations to find out about his flexible sledges and his field repairs under extreme conditions.
What is the essence of the problem of building on ground? Let us try to look at all the possibilities.
A A space station. If it is never going to re-enter the atmosphere, it does not have to withstand the stresses caused by weight. Parts of it have to withstand the pressure of the internal air. Other parts have to withstand the forces induced by docking. A collision caused by a badly executed docking will probably be dangerous, if not catastrophic. The individual parts have to withstand the forces induced during the acceleration phases of the launch - the acceleration itself, and the buffeting caused by sitting on a rocket which is producing noise. NASA's lunar lander of the late 20th century was reminiscent of an arthropod. Not many earthbound structures are built like that.
B Objects in air - balloons, airships, parachutes, aeroplanes. These all have distinctive structural features, which include the need to land on the ground. All of them have to create their own foundation in the form of lift or buoyancy.
C Objects in water - boats, ships, submarines, floating docks, floating harbours. The sea is the ultimate in soft ground, and we tend to think of ships as rather rigid objects. But if their strength, including fatigue strength, is not up to the job, they can break in two. Looking at a Viking ship, we realise that great rigidity is not always the object of the game. From the example of a ship, we see that a building on soft ground could be built on a strong and rigid raft, such as a reinforced concrete slab. You could even imagine a boat shaped foundation that might ride through the soil liquefaction that earthquakes can cause in poor ground. It would expensive. For Nansen's great Arctic journey, his ship, Fram, was designed to ride up when the sea froze, to avoid being crushed by the ice. It worked.
D Objects under water - submarines, submersibles. These are related as much to airships as they are to ships - look at the shape of a fast submarine. Exploratory submersibles are often more ungainly in appearance, rather like some helicopters. The great advantage of the submarine over the ship is that it does not have generally have to contend with massive waves. The disadvantage is the need to withstand great pressure, about one extra atmosphere equivalent, for every 10 metres of depth.
The point is that the combination of support and structure should possess combinations of strength and rigidity - or flexibility if you prefer - that will withstand all reasonably frequent events at a reasonable cost. And whether you go for flexibility or stiffness, the ability to absorb energy is what counts. Glass is pretty stiff, but not many glass boats exist. Yet a combination of glass fibres with an epoxy resin matrix provides a wonderfully strong composite material.
We have distinguished clearly between solid, liquid and gas, but in fact this distinction can in some cases be maintained over only short periods, because of the phenomenon of creep. Although the ice-cap of Greenland rises from the edges, as Nansen found, the thickness increases much more quickly than the slope would indicate. The weight of the ice has depressed the centre of Greenland, pressing the crustal rock into the supporting mantle below. The system is moving towards obedience to Archimedes' Principle. Should the ice melt, Greenland would slowly rise. This process has happened in Northern Europe since the retreat of the last ice sheets.
Mountains, too, can cause the crust to sink into the mantle. Great ranges like the Andes and the Himalayas do just this. And as they are slowly eroded, the mantle will slowly push up their roots to compensate. This is Archimedes' principle on a gigantic scale.
Technical Terms to look up
Active earth pressure, alluvium, aquifer, caisson, cofferdam, compaction, compensated foundation, grout, passive earth pressure, pile, raft, Rankine's theory, rockfill, sheet piling.