When we want to test the shear strength of soil vs. how much we press on it vertically, we can use a mechanism like below, which is called direct shear test. It is the most basic shear test method for soil. In it’s simplest from it can be shown as:
Direct shear test is a very simple but common test. In this test, as you can see, the failure plane is fixed as horizontal. So we can not draw a Mohr’s circle here, because as you have seen before in our previous post for Mohr’s Circle, that circle represented different failure planes. (That post is under structural section but it makes no difference, principles for drawing Mohr’s circle are the same. Therefore, not controlling failure plane is the major limitation of direct shear test.
And then, for various values of N and T, we can obtain a simple graph as follows:
This angle here, is the angle of internal friction of this sand, depending on its initial density. This graph is for dense sand. The reason we drew two lines here is because, for the same force N, the force T to shear the sample varies between beginning and final stages, after large amount of sliding. For dense sand, at first, we spend a lot of effort, to start pushing, and that is why, the Ø in the beginning is Øpeak but in later stages, pushing is easier, once it starts to move. That angle then is called Øresidual or Øultimate. This is similar to trying to push a heavy block on the floor. At first you spend more effort, but once it starts moving, then you can continue pushing with less effort.
This means for example, when you analyze a soil slope stability problem, if you see that the soil was dense but it deformed greatly, you must use the residual, lower value of Ø. If you use the initial higher value, your design will not be safe. If however no deformation or very little deformation has occurred, it is okay to use the higher angle value, which results in more strength value for soil.
And in this graph above, you see how differently dense and loose sands behave when we continue to push them in shear. The graph for dense sand describes just the same thing with previous figure. First we need a lot of effort, shear stress, and then after a peak is reached, we need less stress to deform it more. Loose sands however, need low stress to deform them at first, but then, ultimately, they reach to same stress level with dense sands. On the graph at the bottom, we can see that dense sands volume keeps increasing, and loose sands volume keeps decreasing, until they reach to critical state. The critical state, which we will see later in a little more detail, is the ultimate state of soil, a region where the soil’s own characteristic properties come into equation, irrelevant of how much dense or compact they were in the beginning. For example, critical void ratio, as seen in the figure, is a material property. In other words, it is a defining characteristic of that material, as it does not depend on density of material anymore. In other words, it is a characteristic of material. Critical state soil mechanics is a relatively newer subject in comparison to decades old of established soil mechanics theory but very useful. We will describe of briefly in the coming sections.
If the initial density of soil is more, this graph would be steeper, which means a higher Ø, which means a stronger soil. There is one exceptional case however. When the sand is extremely dense, under very high confining pressures, the sand particles are actually crushed on to each other, under heavy stresses. When this happens, the particles are now less angular and more round, which decreases the overall amount of friction, and consequently, Ø. This may be the case, for instance, at the bottom of a high earth embankment dam. The vertical stress from above is so high, and the confining horizontal pressure is so high, that the particles can be crushed, and the Ø at the bottom of the dam may be lower than the Ø at the upper parts of the dam. This difference can amount to considerable difference in calculations, as Ø affects all foundation calculations.
In the next post of this series, we will discuss “Triaxial Test”