On Pile Caps [again]

The single pile cap

At the conclusion of my prior post ‘On Pile Caps’ I posed the question; would a single column supported by a single pile result in a straightforward pile cap design? It has to, right? The load-path is so obviously simple. Load passes from the column directly into the cap and from there directly into the pile. It’s surely a clear example of load transfer by direct bearing? There isn’t any bridging to be done.

We are only one paragraph into this post so patently there’s something else going on. The question is what? To answer that question we need to take a step back and start thinking about the mechanics of materials in a more nuanced way.

We are going to do this by putting concrete aside for moment and considering some other materials that make it easier to visualise what might be going on.

When a bar or rod is loaded in tension it will start to stretch in the direction of the load. The amount it stretches is proportional to the material’s stiffness. What is perhaps less obvious is that while the rod stretches it is also experiencing a lateral contraction perpendicular to the action of the load.

You can actually see this happen if you stretch an elastic band, however in stiffer materials the phenomenon is harder to detect without instrumentation.

We can also reverse this process. If we take a short rod [to ensure it does not buckle] and apply a compressive load it will start to squash in the direction of the load. As before the amount it squashes is proportional to the materials stiffness. Since we are reversing the load’s direction we can reasonably expect the rod to experience a lateral expansion perpendicular to the direction of the applied load.

This phenomenon can also be seen visually if, for example, you were to squash a bathroom sponge.

In engineering terminology the amount a material shortens or lengthens is known as strain. The ratio of lateral strain to axial strain is known as Poisson’s ratio after the French Mathematician and Physicist Simeon Poisson.

Now, since lateral strain results from the application of a vertical strain [tensile or compressive] we can logically deduce that there must also be a lateral force, which is proportional to the applied vertical load. The relationship between vertical and lateral load is of course Poisson’s ratio. Posssion’s ratio for concrete is approximately 0.2, which means that the magnitude of lateral load is roughly 20% of the vertical load.

If we now return to our pile cap we can deduce that there is in fact a limit to the bearing pressure that may be applied to the pile cap by the column. As the applied vertical load increases the lateral load will also increase causing the sides of the cap to push apart. This is of course a tensile action, which we know concrete does not like. It follows that the point is quickly reached where the sides of the pile cap will literally burst apart. To prevent this from happening containment reinforcement is required to resist the tensile forces.

Having established the effect of Poisson’s ratio we are still not quite done.

One of the practicalities of pile design, particularly friction piles, [see prior post] is that their circumference has to be large or there will be insufficient friction to prevent it from sinking into the ground. This means that the pile diameter is likely to be much bigger than the column diameter. 

The implication is that load must spread from beneath the column into the pile. If the difference in diameter is sufficiently large then a ‘strut and tie’ arrangement is set up in the pile cap, which is akin to that described in my prior post about two-pile caps.

It turns out that passing load through a single pile cap has a more complicated load-path than you might think, because the effect of Posison’s ratio and load spreading must both considered.