Stress Increase in Soils

We have looked at bearing capacity of the soil in the previous section but checking only that is not enough. We must also make sure that, even if the soil can bear the pressure, it will not settle too much.  Before calculating settlement amount in soil however, we must first know the stresses in soil.

We have already seen total and effective stresses that exist in natural soil a few sections before in this book. But when we introduce new loads to the soil such as by building structures on it, the stresses increase beyond those existing natural levels. This new stress increase will cause a certain settlement in the soil.

In other words, we must know how much stress at what depth and what horizontal location increased in soil below as a result of new loads that we introduce. There are various methods to estimate stress increase in soils.

Mathematical solutions exist for estimating stresses increase in soil, based on point loading, strip (linear) loading and area loading, which go beyond an introduction level text. The purpose though, is always the same: Given a certain new loading, find the stress increase in soil at a certain depth, and horizontal distance relative to the loading.

Stress in soil due to point load

To illustrate the point, we will only present area loading, which means, uniformly loading of soil from a square or circular footing.

The most straightforward of them, called 2:1 method, is shown below:

Stress distribution below footing – 2:1 method

In this method, the stress below a footing gets distributed gradually over a larger area which widens as 2 vertical to 1 horizontal distance below the footing. This means, the vertical stress on the soil decreases with increasing depth.  

There are other more complex methods, developed by researchers. One of the most commonly known methods, developed by Boussinesq in 1883, mathematically estimates the stresses at a certain depth and horizontal location. For these estimates to be valid, he assumed that the soil medium is perfectly elastic (no permanent deformations upon stress removal), homogeneous and isotropic (transmits stress equally in all directions). Although we will not present the equations here, the graphical representation of those equations looks similar to the figure below. Note that this graph is drawn just to present the concept to show that as we go on a further curve, the percentage of q reduces dramatically, and it not specifically given here the shape of loading:

Soil strength 20

Typical stress bulb below footing

The curves represent the percentage of stress q that is imposed on the soil by the footing. For example at the imaginary line where the foundation touches soil, that line  would be a straight line and its value would be 100% of q. Then as soon as we start to go deeper, the percentage would decrease and the lines start to be more and more curved. So each curve represents the equal stress points given as a percentage of q. In other words, if you just traveled on one curve, there would always be same stress increase due to foundation stress q.

As can be seen in the figure above, the equal vertical stress curves resemble bulbs, that is why they are called stress bulbs (they are also called pressure isobars). Also you can see that as soon as we get further away from a foundation horizontally, the effect of that load reduces dramatically and reduces to zero after a very short distance. For each shape of foundation and type of loading such as point or linear or area loading, different stress bulbs exist.

There are also charts that engineers use, such as influence charts, and other graphs, based on extensive research, to make this process simple and estimate stresses in soil. (Actually in our age, it is mostly left to software, but that is also based on theory). After finding stresses in soil, the settlement amounts can be estimated as we will look into below… 

In the next post of this series, we will discuss “Elastic Settlement”

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