# Angle of Internal Friction

Think of this post as a direct continuation of the previous two posts of this series, shear strength of soil and lateral earth pressure. Now let’s present another very important characteristic of soil, the angle of internal friction, which we briefly mentioned already before in those sections.

Let’s consider a block resting on a surface, where there is its weight and the table has friction.

In the figure above, when we try to push this block, we must apply a certain horizontal force, shown here as T. If we apply less than that, we can not push it. Again, let’s think about the ratio of horizontal to vertical as we just showed.

This angle Ø, is called, “Angle of Internal Friction”.

And if we applied the concept for soil loading it looks like this:

So, this is the angle where the soil fails, when stresses are applied in all directions. Here σ2 would be perpendicular to the page you are looking at and equal to σ3, thus, it is usually not shown. This is also how we test the strength of soils in the lab, in triaxial test, which we will talk about shortly.

Rearranging the equation above, we reach to the famous equation in geotechnical engineering, which relates shear stress to normal stress as:

And if we put it in graph form, it will look like:

The larger this angle of internal friction, the stronger the soil. It determines how large friction a soil can generate inside. The more friction is generates, the more it can resist loads from above, and the less it converts that vertical stress to horizontal stress. In other words, angle of internal friction is the ability to withstand shear stress. Remember the example in previous section. We said we can not walk on water, because it’s angle of internal friction is zero. We had left it at that. Now we can say why. The angle of internal friction of water is zero, because, water has no resistance to shearing. But soil has resistance to shearing. That is why, when we step on soil, we can walk on it. Unlike water, soil doesn’t convert all of the vertical stress to horizontal stress without resistance, because it has shear resistance / strength. It resists, as in K value we saw in previous section, and only some of it is converted to horizontal stress. So again, shear resistance is the key, to a soil’s strength.

Both clay or sandy soils have internal friction angle – especially sands. It characterizes their strength. For preliminary calculations, a value of 30 degrees may be assumed for angle of internal friction of sand, before any further data can be obtained. For clays, in undrained conditions, (when the water did not have enough time to escape under loading) the friction angle is approximately 0 as long as clay remains saturated. In drained conditions however, (when water had enough time to escape after loading) the friction angle for clays at failure (in the critical state) is somewhere between 20 and 30 degrees, which is considerably less than sands, but still provides an amount of resistance.

In the next post of this series, we will discuss “Direct Shear Test”