On Pile Caps

Different ways of tackling the same problem

The soil beneath some buildings is of insufficient stiffness to support the weight of heavy buildings. The solution is to carry their weight on piles, which extend deep underground. In some cases the piles are embedded in rock and are known as end bearing. In other cases rock is located far below the ground surface and therefore piles rely on generating friction with the ground. 

When more than one pile is require to carry a column’s load it is necessary to construct a bridge between them on which the column may sit. This concrete bridge is known as a pile cap. Pile caps are therefore important structures that lie unseen and unnoticed below ground level.

Since they are unseen pile caps are simple functional structures without a care for visual taste or aesthetic consideration. They are amongst the simplest structures an engineer can design.....or so you might think.

The real world turns out to be more complicated than that, because nobody is entirely sure how pile caps work. This is a surprising fact, even for some engineers, who assume their well worn methods of design represent absolute truth.

This should not be a surprise, because most will know that there are two standard methods of design; the so-called ‘strut and tie method’ and the ‘beam theory method’. It is curious that some see no significance in the fact that two methods exist. Fewer still seem to realise that we are not limited to two; there are in fact many more ways of considering the problem. 

When you appreciate this you can see different ways of analysing all sorts of problems. It liberates your mind from the sort of engineering that cannot see past the prescriptive methods set down in text books and codes of practise. It gives the engineer licence to explore other load-paths and freedom to innovate. That said, let’s not get ahead of ourselves.

Perhaps one of the simplest structures conceivable is a column supported on two piles with a two-pile cap distributing the load evenly. We know the cap distributes the load; the question is how?

Let’s look at ‘beam theory’ first. Using this approach we assume the cap is a large beam made of reinforced concrete, which behaves much like the joists in a house. As the beam is loaded it begins to bend i.e. it takes up the form of a curve. When it does so the top surface necessarily becomes shorter and the bottom surface becomes longer. Self-evidently the surface that is becoming shorter is being squashed and is therefore in compression and the surface that is being stretched must therefore be in tension.

Every engineer knows that concrete is strong in compression, but weak in tension. In fact concrete will begin to crack when the tensile forces are still quite small. For this reason concrete is reinforced with steel bars, which are strong and resilient in tension. Bars are placed into the zones where tension exists. In this case at the bottom of the pile cap.

Now let’s look at the alternative ‘strut and tie’ model. Using this approach the engineer assumes the existence of an imaginary triangle with it peak touching the top surface of the cap, just below the column, and its base stretched over the piles below.

It is not difficult to imagine fifty percent of the  column’s load traveling down each leg of the triangle by means of compression. These are the eponymous struts. One might be tempted to assume that since the load travels by compression there is no need of reinforcement, however we must pay close attention to the angle between the two struts. Since they are not vertically aligned our imaginary triangle struts must have a horizontal component to the force which they carry. This horizontal force wishes to push the two legs apart, much like the force that causes a house of cards to spread and fall.

To prevent our imaginary triangle from spreading there must be a tie, which is conveniently provided by the bottom chord of the triangle. Again, since concrete cannot resist tension, steel reinforcing bars are inserted into the bottom of the concrete. Curiously, the quantity of steel that this approach requires is different to that derived by beam theory.

Now that we have examined the two ‘normal methods’ we can of course try some other methods. Instead of an imaginary triangle, why not assume an imaginary arch with a reinforced tie at the base?

Another approach would be to turn the ‘strut and tie’ model upside down and assume an inverted triangle. This is an interesting, if slightly convoluted, concept, which would be tricky to build, but is perfectly tenable. In this example tension bars would extend from the top corners of the pile cap down to the middle of the bottom surface. The legs of the triangle would be loaded in tension and would therefor pull the top surface together forcing it into compression.

The reason this approach is more convoluted is because the peak of the imaginary triangle does not sit directly below the column and its base does not sit directly above the piles. To complete the load-path it is therefore necessary to imagine a strut in the middle of the triangle that transfers load from the column down to the peak of the triangle. Two more struts are requires, one at either side of the base to transfer load into the piles.

Of course, if we can invert the ‘strut and tie’ we can also invert the ‘arch model’. For similar reasons this is also a tricky arrangement to build, but perfectly viable.

We now have four methods by which we could potentially transfer load from a single column into two piles. There are many more. For example, instead of a ‘strut and tie’ we could consider an imaginary truss. When we do so it is not difficult to imagine the many and varied ways in which the internal chords of the truss might be arranged.

So which method is the ‘real’ load path by which the pile cap actually transfers load. The truth is it doesn’t actually matter. So long as the engineer has designed at least one way in which it could work the structure will stand. The contractor who has to build it may not see it that way, but for the purposes of this exercise that does not matter. The point is that for even the simplest of structures many possible load-paths exist and that is an interesting conclusion.

Perhaps more interesting still is what happens when we consider a single column and a single pile. Surely that has to be straightforward, right? I’ll answer that question next time.